L Blin

S Dolev

M Potop-Butucaru

S Rovedakis

Construction auto-stabilisante d'un arbre couvrant de poids minimum †

Keywords: Algorithme distribué, Auto-stabilisation, Construction d'arbre couvrant de poids minimum

L'arbre couvrant de poids minimum offre une solution de routage ayant le double avantage de donner une structure de communication simple et économique. Dans ce papier, nous présentons un nouvel algorithme auto-stabilisant pour la construction d'un arbre couvrant de poids minimum dans un système distribué et asynchrone. Notre solution améliore l'existant en permettant d'atteindre un meilleur compromis entre le temps de convergence, O(n 2 ), et la complexité en mémoire nécessaire sur chaque noeud du réseau, O(log 2 n). Le temps de convergence est amélioré d'un facteur multiplicatif Θ(n) au prix d'un facteur multiplicatif de O(log n) sur la mémoire. La clé de voûte de ce travail est l'utilisation d'une méthode de nommage auto-stabilisante permettant d'identifier pour toute paire de noeuds le plus proche ancêtre commun dans l'arbre.

Introduction

Since its introduction in a centralized context, the minimum spanning tree (or MST) problem gained a benchmark status in distributed computing thanks to the seminal work of Gallager, Humblet and Spira [START_REF] Gallager | A distributed algorithm for minimum-weight spanning trees[END_REF].

The emergence of large scale and dynamic systems, often subject to transient faults, revives the study of scalable and self-stabilizing algorithms. A scalable algorithm does not rely on any global parameter of the system (e.g. upper bound on the number of nodes or the diameter). Self-stabilization introduced first by Dijkstra in [START_REF] Edsger | Self-stabilizing systems in spite of distributed control[END_REF] deals with the ability of a system to recover from catastrophic situation (i.e., the global state may be arbitrarily far from a legal state) without external (e.g., human) intervention in finite time.

Although there already exists self-stabilizing solutions for the MST construction, none of them considered the extension of the Gallager, Humblet and Spira algorithm (GHS) to self-stabilizing settings. Interestingly, this algorithm unifies the best properties for designing large scale MSTs : it is fast and totally decentralized and it does not rely on any global parameter of the system. Our work proposes an extension of this algorithm to self-stabilizing settings. Our extension uses only logarithmic memory and preserves all the good characteristics of the original solution in terms of convergence time and scalability. [START_REF] Sandeep | Self-stabilizing multicast protocols for ad hoc networks[END_REF] the first self-stabilizing algorithm for the MST problem. This MST construction is based on the computation of all shortest paths (for a certain cost function) between all pairs of nodes. The time complexity announced by the authors, O(n) stays only in the particular synchronous settings considered by the authors, in asynchronous setting the complexity is Ω(n 2 ) rounds. A different approach was proposed by Higham and Liang [START_REF] Higham | Self-stabilizing minimum spanning tree construction on message-passing networks[END_REF]. The algorithm checks every edge whether it eventually belongs to the MST or not. The memory used by each node is O(log n) bits, but the information exchanged between neighboring nodes is of size O(n log n) bits, thus only slightly improving that of [START_REF] Sandeep | Self-stabilizing multicast protocols for ad hoc networks[END_REF]. Its computation is expensive in large scale systems. The time complexity of this approach is O(mD) rounds where m and D are the number of edges and the diameter of the network respectively, i.e., O(n 3 ) rounds in the worst case. The main drawback of these solutions is its lack of scalability since each node has to know and maintain global parameter of the system (network size, diameter, ...). In [START_REF] Blin | A new selfstabilizing minimum spanning tree construction with loop-free property[END_REF] we proposed a self-stabilizing loop-free algorithm for the MST problem. The proposed solution improves on the memory space usage since each participant needs only O(log n) bits while preserving the same time complexity as the algorithm in [START_REF] Higham | Self-stabilizing minimum spanning tree construction on message-passing networks[END_REF].

Related Works. Gupta and Srimani presented in

Contributions.

Our contribution published also in [START_REF] Blin | Fast self-stabilizing minimum spanning tree construction -using compact nearest common ancestor labeling scheme[END_REF] is therefore twofold. We propose for the first time in self-stabilizing settings a O(log 2 n) bits scheme for computing the nearest common ancestor. Furthermore, based on this scheme, we describe a new self-stabilizing algorithm for the MST problem. An exhaustive state of art is proposed in Table 1. Our algorithm does not make any assumption on the network size (including upper bounds) or the existence of an a priori known root. Moreover, to our knowledge our solution has the best existing space/time compromise over the existing self-stabilizing MST solutions. The convergence time is O(n 2 ) asynchronous rounds and the memory space per node is O(log 2 n) bits.

Model and notations

We consider an undirected weighted connected network G = (V, E, w) where V is the set of nodes, E is the set of edges and w : E → N is a positive cost function. We note n the number of nodes in the network (i.e., |V | = n). Nodes represent processors and edges represent bidirectional communication links. Each node v has a unique identifier noted Id v . The processors asynchronously execute their programs consisting of a set of local variables and a finite set of rules.

In the sequel we consider the system can start in any configuration. That is, the local state of a node (the value of the local variables of the node and the state of its program counter) can be corrupted. We don't make any assumption on the bound of corrupted nodes. In the worst case all the nodes in the system may start in a corrupted configuration. In order to tackle these faults we use self-stabilization techniques [START_REF] Dolev | Self-Stabilization[END_REF].

Our self-stabilizing solution to MST problem

The central notion in the GHS approach [START_REF] Gallager | A distributed algorithm for minimum-weight spanning trees[END_REF] is the notion of fragment. A fragment is a partial spanning tree of the graph, i.e., a fragment is a tree which spans a subset of nodes. An outgoing edge of a fragment F is an edge with a unique endpoint in F. The minimum-weight outgoing edge of a fragment F is the outgoing edge of F with minimum weight, denoted in the following as ME F . In the GHS construction, initially each node is a fragment. For each fragment F, the GHS algorithm identifies the ME F and merges the two fragments endpoints of ME F . The merging process is recursively repeated until a single fragment remains, which is a MST.

Our solution combines both the blue and red rules [START_REF] Daniel | A data structure for dynamic trees[END_REF]. The blue rule application needs that each node identifies its own fragment. The red rule requires that nodes identify the fundamental cycle corresponding to every adjacent non-tree-edge. In both cases, we use a self-stabilizing labeling scheme (see Section 3.1) which provides at each node a distinct informative label such that the nearest common ancestor of two nodes can be identified based only on the labels of these nodes. Thus, the advantage of this labeling is twofold. First the labeling helps nodes to identify their fragments. Second, given any non-tree edge e = (u, v), the path in the tree going from u to the nearest common ancestor of u and v, then from there to v, and finally back to u by traversing e, constitute the fundamental cycle C e .

Construction auto-stabilisante d'un arbre couvrant de poids minimum

Self-stabilizing Nearest Common Ancestor Labeling scheme

Our labeling scheme uses the notions of heavy and light edges introduced in [START_REF] Harel | Fast algorithms for finding nearest common ancestors[END_REF]. In a tree, a heavy edge is an edge between a node u and its largest subtree. The other edges between u and its other children are tagged as light edges. We extend this edge designation to the nodes, a node v is called heavy node if the edge with its parent is a heavy edge, otherwise v is called light node. Moreover, the root of a tree is a heavy node. The idea of the scheme is as follows. A tree is recursively divided into disjoint paths : the heavy paths and the light paths which contain only heavy and light edges respectively.

To label the nodes in a tree T , the size of each subtree is needed to identify heavy edges at each level of T . To this end, each node v maintains a variable named size v which is a pair of integers : (i) a local estimation of the size of the subtree rooted at v, and (ii) the identifier of v's child in the largest subtree. These information are used by v to identify the heavy edge leading to a child. The computation of size v is processed in a bottom-up fashion. A leaf node v has no child, therefore size v = (1, ⊥). Moreover, each node v in T maintains a pointer towards its parent stored in variable p v .

Based on the heavy and light nodes in a tree T (using locally variable size v ), each node v can compute its label in a top-down fashion. The label of a node v stored in variable ℓ v is a list of pair of integers. Each pair of the list contains : (i) the identifier of a node, and (ii) the distance to the root of the heavy path. The root v of a fragment has a label equal to (Id v , 0), respectively the identifier of v and the distance to itself, otherwise it corrects its label. When a node u is tagged by its parent as a heavy node (i.e., size p v [1] = Id u ), then u takes the label of its parent but it increases by one the distance of the last pair of the parent label. For example, if the label of u's parent is (3, 1)(2, 0) then u's label is equal to (3, 1)(2, 1). When a node u is tagged by its parent v as a light node (i.e., size p v [1] = Id u ), then u becomes the root of a heavy path and it takes the label of its parent to which it adds a pair of integers composed of its identifier and a zero distance. For example, if the label of u's parent is (3, 1)(2, 0) and u's identifier is 14 then u's label is equal to (3, 1)(2, 0)(14, 0). A heavy or light node with a locally incorrect label can correct its label using the one of its parent in the tree.

The labels given by this scheme to the nodes of a tree can be ordered following a lexicographic order. Given two nodes u, v in a tree T , the label of the nearest common ancestor of u and v is obtained by taking the smallest (following the lexicographic order) common part (considering node identifiers) between ℓ u and ℓ v . For example, if the label of u (resp. v) is (3, 2)(13, 0) (resp. (3, 1)(2, 1)) then the common part is (3, 2) and (3, 1) which gives (3, 1) for the nearest common ancestor label for u and v.

Self-stabilizing algorithm for the minimum spanning tree problem

In this section we describe our self-stabilizing algorithm for constructing the minimum spanning tree. our algorithm executes two phases : the first phase corrects the existing structure (Tree, cycle) and the second phase merges the fragments. Our algorithm uses the GHS approach to merge the fragments using minimum outgoing edges to construct a spanning tree, and deletes the edge of maximum weight in each fundamental cycle to recover from invalid configurations. In both cases, it uses the labeling algorithm to identify fragments and fundamental cycles. In the following, merging operations have a higher priority than the recovering operations. That is, the system recovers from an invalid configuration iff no merging operation is possible.

The minimum weighted edge. According to the labeling scheme described in Section 3.1, given a (correct) fragment F any node v ∈ F is able to locally detect among its neighbors the ones which belong to F by comparing the labels. To this end, v computes the nearest common ancestor with its neighbors. If v has no common ancestor with a neighbor u (i.e., the labels are totally distinct) then u belongs to a fragment different than v's fragment, otherwise u and v are in the same fragment.

Each fragment computes its minimum outgoing edge in a bottom-up fashion. To this end, each node sends to its parent the outgoing edge of minimum weight among its adjacent edges and edges sent by children. To store the information related to an outgoing edge e = (x, y), each node v maintains a variable mwe v which is a pair of values : (i) the weight of edge e, and (ii) the label of the common ancestor of x and y. When the root of the fragment has computed its outgoing edge e of minimum weight (i.e., the minimum outgoing edge of the fragment), then it can start a merging operation (described in Paragraph "Fragments merging").

The edge e belongs to a MST and can be used to perform a merging between the two adjacent fragments.

When a node v in fragment F has no adjacent outgoing edge or outgoing edge sent by a child, then v sends to its parent information concerning internal edges of F (edges not in F whose extremity nodes are in F). These edges are sent in a bottom-up fashion in F following fundamental cycles. These information are used to repair the fragment if necessary (described in Paragraph "MST correction").

Fragments merging. When the minimum outgoing edge e = (u, v) of a fragment F v is computed by the root r of F v , then a merging operation is started by r. To this end, the parent pointers are reversed on the path between r and v in F v (i.e., following the nodes x in F v such that mwe x = mwe r ). During this reorientation the labels are locked. That is, each node x on the path between r and v (including r and excluding v) changes its label to : ℓ x := (⊥, ⊥). When v becomes the root of the fragment F v it can merge with the fragment F u . Note that, the node among u and v with the smallest identifier becomes the root of the new fragment F given by the merging of F u and F v . After the addition of the outgoing edge e, the labeling process is re-started in F. The merging phase is repeated until a single fragment is obtained (i.e., there is no outgoing edges of a fragment).

MST correction. The system can start in any arbitrary configuration, so we must be able to detect incorrect fragments (i.e., with an edge part of no MST). Therefore, a node v with an incoherent parent (which is not in its neighborhood) or present in a cycle (its label is contained or is inferior to its parent label) becomes the root of a fragment by setting its parent pointer to void and its label to (Id v , 0).

Consider a part of a fragment with no outgoing edge. In this case, each node v piggy back up information concerning internal edges (stored in variable mwe v ). The edges are sent following an order on the label of the nearest common ancestor associated to edges (the ancestor nearest to the root of fragment first). The information concerning an internal edge e is sent following the fundamental cycle of e and its transmission is stopped at the nearest common ancestor associated to e. If the parent x of a node v has the same information with v about an internal edge e and the weight of the edge w(v, x) > w(e) then the edge (v, x) is removed from the tree, since (v, x) can be the edge of maximum weight in the fundamental cycle C e .

Theorem 1 Starting from any arbitrary configuration our algorithm eventually constructs a minimum spanning tree in at most O(n 2 ) rounds using O(log 2 n) bits of memory per node.

R éf érences

  † La version longue de ce papier a été publié à la conférence DISC 2010 et est supporté par le projet ANR SHAMAN.

		a priori knowledge	space complexity	convergence
				time
	[GS03]	network size and	O(n log n)	Ω(n 2 )
		the nodes in the network
	[HL01]	upper bound on diameter	O(log n)	O(n 3 )
			+messages of size O(n log n)
	[BPBRT09]	none	O(log n)	O(n 3 )
	This paper and [BDPBR10]	none	O(log 2 n)	O(n 2 )
	TAB. 1: Distributed Self-Stabilizing algorithms for the MST problem


R Loginov
email: raisa.loginov@hus.fi

T Karlsson

K Höckerstedt

D Ablashi

Lautenschlager

I Lautenschlager

Quantitative HHV-6B antigenemia test for the monitoring of transplant patients

Human herpesvirus-6 (HHV-6) infection, mostly caused by variant B, is common after transplantation. Here, we report a new modified method using an HHV-6B glycoprotein IgG antibody, OHV-3, and attempt to quantify the HHV-6 antigenemia after liver transplantation. Twentyfour liver transplant recipients were frequently monitored by the HHV-6 antigenemia test, which detects the HHV-6B virion protein in peripheral blood mononuclear cells (PBMC). HHV-6B antigens were now retrospectively demonstrated using a glycoprotein OHV-3 IgG antibody in the immunoperoxidase staining from the same specimens and quantified as positive cells/10,000 PBMC. The results were confirmed and quantified by DNA hybridization in situ. Altogether, 206 blood specimens were analyzed. During the first six months, HHV-6 antigenemia was

detected in 17/24 (71%) recipients by using the HHV-6B virion antibody. In total, 37% (77/206) of specimens were positive with the virion antibody and 39% (78/201) by the OHV-3 antibody. The peak number of OHV-3-positive cells in the PBMC varied from 5 to 750/10,000 (mean 140/ 10,000). The OHV-3 antibody was useful to quantify the HHV-6B antigenemia. The findings of the HHV-6B quantitative antigenemia using the OHV-3 antibody correlated well with the previous qualitative HHV-6 antigenemia assay, and can be used as an alternative quantitative method in the monitoring of HHV-6 in transplant patients.

Human herpesvirus-6 (HHV-6) is a ubiquitous virus which is widespread throughout the world [START_REF] De Bolle | Update on human herpesvirus 6 biology, clinical features, and therapy[END_REF]. Two major subgroups of HHV-6 have been identified, variants A and B, of which variant B is the most common. Like other herpesviruses, HHV-6 can remain in a latent or persistent state in the host after primary infection and can reactivate under immunosuppression. HHV-6 has been recognized as a potentially significant pathogen in both solid organ and stem cell transplant recipients [START_REF] Ljungman | Human herpesvirus-6 infection in solid organ and stem cell transplant recipients[END_REF][START_REF] Zerr | Human herpesvirus 6: a clinical update[END_REF][START_REF] Massih | Human herpesvirus 6 infections after liver transplantation[END_REF]. HHV-6 infections, mostly caused by variant B, occur in the early posttransplant period, usually within the first four weeks after transplantation. In liver transplantation, HHV-6 reactivations are mostly asymptomatic, but clinical symptoms such as encephalitis, hepatitis, or graft dysfunction have been described [START_REF] Ljungman | Human herpesvirus-6 infection in solid organ and stem cell transplant recipients[END_REF][START_REF] Zerr | Human herpesvirus 6: a clinical update[END_REF][START_REF] Massih | Human herpesvirus 6 infections after liver transplantation[END_REF]. The most sensitive techniques for the detection of HHV-6 infection are polymerase chain reaction (PCR)-based methods [START_REF] Massih | Human herpesvirus 6 infections after liver transplantation[END_REF]; both qualitative and quantitative methods have been described. However, by PCR methods, it is not always possible to differentiate between latent and active viral infections. On the other hand, there is a recognized phenomenon of HHV-6 integration into host cell DNA [START_REF] Ward | Human herpesvirus 6 chromosomal integration in immunocompetent patients results in high levels of viral DNA in blood, sera, and hair follicles[END_REF], and such integration is characterized by a high viral load in the blood using quantitative PCR methods. The detection of cellular HHV-6 DNA by in situ hybridization in peripheral blood mononuclear cells (PBMC) of liver transplant patients [START_REF] Loginov | HHV-6 DNA in peripheral blood mononuclear cells after liver transplantation[END_REF] has shown a good correlation with the HHV-6 antigenemia test and may be used in the monitoring of those patients. The HHV-6 antigenemia test, which detects the viral antigens in PBMC by monoclonal antibodies and immunoperoxidase staining, has been used to demonstrate an active HHV-6 infection in transplant patients [START_REF] Lautenschlager | Human herpesvirus-6 antigenemia after liver transplantation[END_REF][START_REF] Volin | Human herpesvirus 6 antigenaemia in allogeneic stem cell transplant recipients: impact on clinical course and association with other beta-herpesviruses[END_REF]. The HHV-6 antigenemia test was demonstrated to correlate with quantitative PCR [START_REF] Härmä | HHV-6-DNAemia related to CMV-DNAemia after liver transplantation[END_REF], but the method itself is rather qualitative than quantitative. The HHV-6 antigenemia assay indicates the presence of an active infection and also enables to differentiate between HHV-6A and HHV-6B infections [START_REF] Lautenschlager | Human herpesvirus-6 antigenemia after liver transplantation[END_REF]. The purpose of this retrospective study is to improve the HHV-6 antigenemia test so that it will be possible to quantify the positive cells.

Twenty-four consecutive adult transplant recipients, who underwent liver transplantation during the year 2006, were frequently monitored for HHV-6 infection up to six months post-transplantation. A total of 206 blood specimens were analyzed (mean 8.5 samples/patient, range 5-13). For the HHV-6 antigenemia test, PBMC were isolated by Ficoll-Paque density gradient centrifugation and cytocentrifuged onto microscope slides. In parallel, slides were acetonefixed and stored at -70°C for later examination. HHV-6 infections were originally diagnosed by the HHV-6 antigenemia test in PBMC using indirect immunoperoxidase staining with a monoclonal antibody against HHV-6B (MAB8535, Chemicon, Inc., Temecula, CA), a 101-kDa virion protein as described earlier [START_REF] Lautenschlager | Human herpesvirus-6 antigenemia after liver transplantation[END_REF]. Retrospectively, the quantitative detection of HHV-6 antigenemia was performed from the same specimens using the HHV-6Bspecific OHV-3 IgG antibody (obtained from the HHV-6 Foundation Reagents Repository), which detects 98-kDa and 92-kDa glycoproteins of HHV-6 [START_REF] Okuno | Analysis of a glycoprotein of human herpesvirus 6 (HHV-6) using monoclonal antibodies[END_REF]. The number of OHV-3-positive cells was counted per 10,000 PBMC. In the event of discrepancies between the results, the specimens were further analyzed by using a third monoclonal antibody (Ref-11-242, Argene Biosoft, Varilhes, France), which detects both HHV-6 variants A and B. HHV-6 DNA was also retrospectively analyzed from 104 available PBMC specimens from 16 patients by in situ hybridization using a biotinylated oligoprobe mixture (Qiagen, Cologne, Germany) detecting both HHV-6A and B variants [START_REF] Loginov | HHV-6 DNA in peripheral blood mononuclear cells after liver transplantation[END_REF]. The HHV-6 in situ hybridization findings were quantified as DNA-positive cells/10,000 PBMC and correlated to the antigenemia results.

HHV-6 antigenemia was detected in 17/24 (71%) recipients within the first six months after liver transplantation using the HHV-6B virion antibody (MAB8535, Fig. 1a). The HHV-6 antigenemia appeared during the first three weeks after transplantation in all cases. All patients, except for one with a weak positivity (patient number 22), also demonstrated HHV-6 antigen by the OHV-3 antibody, and these findings were quantified as positive cells/10,000 PBMC (Table 1). The positive staining by the OHV-3 antibody was clear, and was seen in the cytoplasma only (Fig. 1b). Altogether, 37% (77/206) of specimens were positive with the MAB8535 antibody and 39% (78/201) of specimens with the OHV-3 antibody. The peak number of OHV-3-positive cells varied from 5 to 750/10,000 PBMC, and the mean was 140/10,000 PBMC.

One recipient (patient number 18) was HHV-6 antigenemia-negative by both antibodies (MAB8535 and OHV-3) during the follow-up. Six patients had discrepancies between the results and the specimens of these patients were then further analyzed using a third antibody detecting both HHV-6A and HHV-6B variants. These six patients were all negative by MAB8535 during the followup, but positive by both OHV-3 antibody and the one detecting both HHV-6A and B. This finding suggests that, when the OHV-3 antibody is directed against other viral proteins, it could pick up an antigen which is not detectable by the virion protein antibody. However, double infection could not be excluded in these patients.

HHV-6 DNA in situ hybridization was performed to confirm the antigenemia findings. Concurrent HHV-6 DNA was detected in 14/15 patients who were antigen-positive by either or both of the two HHV-6 antibodies, MAB8535 and OHV-3 (Table 1). The positive reaction of the in situ hybridization was seen as a spotted, dark nuclear staining (Fig. 1c). One patient who showed faint staining by MAB8535 antibody (patient number 22), was negative by OHV-3 antibody and had no HHV-6-DNA. The number of HHV-6 DNA-positive cells was counted per 10,000 PBMC. The number of HHV-6 DNA-positive cells varied from 8 to 2,920/10,000 PBMC (mean 559). The HHV-6 DNA findings correlated well with the antigenemia findings. Two patients (numbers 1 and 5), who had discrepancies between the results of the two used antibodies, both showed HHV-6 DNA in their mononuclear cells.

In 7/17 patients, HHV-6 antigens were also demonstrated in the liver biopsies associated with graft dysfunction. In five cases, intragraft HHV-6 was found together with mild to moderate acute rejection, and the patients were treated with high doses of steroids. The other two patients with HHV-6-positive biopsy and graft dysfunction recovered without any treatment. The mean peak number of OHV-3positive cells (133/10,000) in patients with hepatic infection did not differ to those without (140/10,000). Four patients developed cytomegalovirus (CMV) infection during the follow-up and they were treated with intravenous ganciclovir. However, antiviral treatment was started on all of these patients after the peak of the HHV-6 episode was already over. In other patients, HHV-6 antigenemia lasted usually for some weeks without any specific symptoms and subsided slowly without treatment.

An active HHV-6 infection can be diagnosed from the peripheral blood specimens of liver transplant patients by detection of the virus-specific antigens in mononuclear cells [START_REF] Lautenschlager | Human herpesvirus-6 antigenemia after liver transplantation[END_REF]. The method has been shown to correlate with wholeblood quantitative PCR [START_REF] Härmä | HHV-6-DNAemia related to CMV-DNAemia after liver transplantation[END_REF]. However, the previous HHV-6 antigenemia test is rather qualitative than quantitative, because no obvious changes can be seen in the number of antigen-positive cells but instead in the intensity of staining in the PBMC. In this study, we used the HHV-6B OHV-3 monoclonal antibody and quantified the number of positive PBMC during the follow-up of the first six months after adult liver transplantation. The intensity of the positive signal by OHV-3 was clear-cut and the number of positive cells was easy to quantify. The OHV-3 monoclonal antibody made it possible to quantify the HHV-6 load from the PBMC of transplant patients, but the peak values of OHV-3-positive cells varied widely. The same kind of variation was also seen in the HHV-6 DNA in situ assay, where we quantified HHV-6 DNA-positive mononuclear cells after liver transplantation [START_REF] Loginov | HHV-6 DNA in peripheral blood mononuclear cells after liver transplantation[END_REF]. The HHV-6B-specific OHV-3 antibody results correlated quite well with the HHV-6 (MAB8535) antigenemia findings in most cases. However, there was discordance between the results in some cases, especially in the case of faint staining. The OHV-3 antibody seemed to be more sensitive in detecting HHV-6B antigenemia. When the antigenemia results were compared to those of HHV-6 DNA in situ hybridization, specimens positive by either one or both of the HHV-6 antibodies MAB8535 and OHV-3, good correlation was found.

Six patients had a discrepancy in the results of the two HHV-6B antibodies used. The specimens of these six patients were further analyzed and four patients demonstrated clear positive findings by a third antibody detecting both A and B variants. Thus, those patients had either double infection or the two antibodies used may react with different epitopes of the viral antigen. Two patients (numbers 1 and 5) who had discrepancies between the results of the HHV-6 antibodies were found to be positive by in situ hybridization.

The quantitative HHV-6 antigenemia assay provides an alternative possibility to quantify HHV-6 infection. This method might be useful in the differentiation between a latent and an active infection. In the case of HHV-6 integration, where quantitative PCR methods show high copy numbers in the blood, the demonstration of HHV-6 proteins could be more diagnostic. On the other hand, due to the retrospective nature of the present study, no plasma or serum material was available from our patients to perform PCR.

In liver transplant patients, most HHV-6 reactivations are asymptomatic. In our patients, no other specific symptoms but graft dysfunction was associated with HHV-6 anti- The OHV-3-positive cells and HHV-6 DNA in situ-positive cells were counted per 10,000 PBMC *HHV-6 antigenemia and HHV-6 DNA in situ hybridizations after liver transplantation of six patients with different findings withMAB8535, OHV-3, and HHV-6A + B variant specific antibodies genemia. However, in most cases of intrahepatic HHV-6, graft dysfunction was obviously due to rejection and only in two cases due to HHV-6. Four patients developed symptomatic CMV infections after the peak of HHV-6 antigenemia. However, correlation between HHV-6 viral load by the quantitative method and the clinical symptoms was difficult because of CMV or concurrent rejections.

In conclusion, the findings of the HHV-6B quantitative antigenemia demonstrated by the OHV-3 antibody correlated well with the previous qualitative HHV-6 antigenemia assay. The glycoprotein antibody OHV-3 made it possible to quantify the number of positive cells better than the previous virion protein antibody, and this monoclonal antibody appeared to be similar in sensitivity in detecting HHV-6 infection. The quantitative HHV-6 antigenemia assay may be used as an alternative test in the monitoring of the viral load of transplant recipients and other patients with suspected HHV-6 infection. However, further investigation of the clinical significance of the HHV-6 antigenemia peaks is necessary.

Fig. 1

 1 Fig. 1 HHV-6-positive lymphocytes demonstrated by immunoperoxidase staining using (a) the HHV-6B virion antibody (MAB8535) and (b) the glycoprotein antibody OHV-3. Note the intense cytoplasmic staining by the glycoprotein antibody OHV-3. (c) HHV-6 DNApositive cells (arrows) demonstrated by in situ hybridization (original magnification ×1,000)

Table 1

 1 The follow-up of HHV-6 antigenemia and DNA in situ hybridizations of 24 recipients after liver transplantation

	Specimens	MAB8535	OHV-3	ISH	Specimens	MAB8535	OHV-3	ISH	Specimens	MAB8535	OHV-3	ISH
	Patient 2				Patient 11				Patient 17
	1	pos	200	nd	1	neg	0	nd	1	pos	80	60
	2	pos	50	200	2	+/-	0	nd	2	neg	0	neg
	3	pos	30	nd	3	neg	20	nd	3	neg	0	neg
	4	pos	30	nd	4	neg	nd	nd	4	neg	0	neg
	5	pos	30	nd	5	neg	0	nd	5	neg	0	neg
	6	pos	10	nd	6	neg	0	nd	6	neg	0	neg
	7	+ / -	5	640	7	neg	nd	nd	7	neg	0	neg
	8	+ / -	20	35	8	neg	20	nd	Patient 18
	9	+ / -	0	75	9	neg	0	nd	1	neg	0	neg
	10	+/-	5	72	Patient 12				1	neg	0	neg
	11	pos	nd	nd	1	+/-	10	1,170	2	neg	0	neg
	12	pos	100	70	2	neg	0	neg	3	neg	0	neg
	13	pos	0	nd	3	neg	0	neg	4	neg	0	neg
	Patient 3				4	+/-	40	880	5	neg	0	neg
	1	pos	20	nd	5	neg	20	350	6	neg	0	neg
	2	pos	50	nd	6	neg	0	neg	7	neg	0	neg
	3	+ / -	50	nd	7	neg	0	neg	8	neg	0	neg
	4	+ / -	15	1,100	8	neg	0	neg	9	neg	0	neg
	5	neg	5	nd	9	neg	60	330	10	neg	0	neg
	6	neg	100	nd	Patient 13				11	neg	0	neg
	7	neg	20	nd	1	+/-	5	nd	Patient 20
	8	neg	5	nd	2	+/-	0	n d	1	p o s	5	5 5
	9	neg	0	neg	3	+/-	0	nd	2	pos	0	600
	10	neg	0	neg	4	+/-	50	nd	3	pos	10	170
	11	neg	0	neg	5	+/-	0	nd	4	neg	0	neg
	12	neg	0	neg	6	neg	10	880	5	neg	0	neg
	Patient 4				7	neg	0	nd	6	neg	5	nd
	1	neg	0	nd	8	neg	30	nd	7	pos	50	850
	2	pos	40	2,000	9	+/-	120	480	8	+/-	50	40
	3	neg	0	neg	Patient 14				9	+/-	10	40
	4	neg	0	neg	1	+/-	0	n d	1 0	+ / -	0	neg
	5	neg	0	neg	2	pos	0	nd	11	neg	0	neg
	6	neg	0	neg	3	pos	0	nd	Patient 21
	7	neg	0	neg	4	+/-	5	nd	1	pos	130	110
	8	neg	0	neg	5	+/-	0	n d	2	+ / -	0	neg
	Patient 6				6	neg	0	nd	3	neg	0	neg
	1	neg	0	nd	7	neg	0	nd	4	neg	0	neg
	2	+ / -	20	nd	Patient 15				5	neg	0	neg
	3	+ / -	10	nd	1	pos	200	nd	6	neg	0	neg
	4	pos	5	nd	2	pos	50	nd	7	neg	0	neg
	5	pos	5	nd	3	pos	5	nd	8	neg	0	neg
	6	+ / -	0	nd	4	pos	5	nd	Patient 22
	7	neg	0	nd	5	+/-	nd	nd	1	+/-	0	neg
	8	neg	0	nd	6	pos	nd	nd	2	+/-	0	n d
	9	+ / -	0	n d	7	+ / -	0	nd	3	neg	0	neg
	Patient 9				8	+/-	0	nd	4	neg	0	neg
	1	+ / -	380	2,920	9	+/-	0	nd	5	neg	0	neg
	2	neg	260	1,630	Patient 16				6	neg	0	neg

Acknowledgments We want to acknowledge the support of the HHV-6 Foundation for providing the OHV-3 MAB, the hybridoma, which was donated by Prof. K. Yamanishi. The OHV-3 monoclonal antibody is available, free of charge, to other transplantation investigators for research purposes from the HHV-6 Foundation Reagents Repository.

This study was supported by grants from the Sigrid Jusélius Foundation (to K. Höckerstedt and I. Lautenschlager) and the Helsinki University Hospital Research Funds (to I. Lautenschlager).

The authors thank Marjatta Palovaara for the technical assistance and Stephen Venn and Courtney Devin for correcting the English text.


M Punturo

M Abernathy

F Acernese

B Allen

N Andersson

K Arun

F Barone

B Barr

M Barsuglia

M Beker

N Beveridge

S Birindelli

S Bose

L Bosi

S Braccini

C Bradaschia

T Bulik

E Calloni

G Cella

E Chassande-Mottin

S Chelkowski

A Chincarini

J Clark

E Coccia

C Colacino

J Colas

A Cumming

L Cunningham

E Cuoco

S Danilishin

K Danzmann

G De Luca

R De Salvo

T Dent

R Derosa

Di Fiore

A Di Virgilio

M Doets

V Fafone

P Falferi

R Flaminio

J Franc

F Frasconi

A Freise

P Fulda

J Gair

G Gemme

A Gennai

A Giazotto

K Glampedakis

M Granata

H Grote

G Guidi

G Hammond

M Hannam

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S Husa

S Huttner

G Jones

F Khalili

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K Kokkotas

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M Lorenzini

E Majorana

I Mandel

V Mandic

I Martin

C Michel

Y Minenkov

N Morgado

S Mosca

B Mours

M Üller-Ebhardt

P Murray

R Nawrodt

J Nelson

R Oshaughnessy

C D Ott

C Palomba

A Paoli

G Parguez

A Pasqualetti

R Passaquieti

D Passuello

L Pinard

R Poggiani

P Popolizio

M Prato

P Puppo

D Rabeling

P Rapagnani

J Read

T Regimbau

H Rehbein

S Reid

L Rezzolla

F Ricci

F Richard

A Rocchi

S Rowan

A R Üdiger

B Sassolas

B Sathyaprakash

R Schnabel

C Schwarz

P Seidel

A Sintes

K Somiya

F Speirits

K Strain

S Strigin

P Sutton

S Tarabrin

J Van Den Brand

C Van Leewen

M Van Veggel

C Van Den Broeck

A Vecchio

J Veitch

F Vetrano

A Vicere

S Vyatchanin

B Willke

G Woan

P Wolfango

K Yamamoto

Third Generation of Gravitational Wave Observatories and their Science Reach

Keywords: numbers: 04, 80, Nn

Large gravitational wave interferometric detectors, like Virgo and LIGO, demonstrated the capability to reach their design sensitivity, but to transform these machines into an effective observational instrument for gravitational wave astronomy a large improvement in sensitivity is required. Advanced detectors in the near future and third generation observatories in more than one decade will open the possibility to perform gravitational wave astronomical observations from the Earth. An overview of the possible science reaches and the technological progress needed to realise a third generation observatory are discussed in this paper. The status of the project Einstein Telescope (ET), a design study of a third generation gravitational wave observatory, will be reported.

Introduction

The first generation of interferometric gravitational wave (GW) detectors (GEO600 [1], LIGO [2], TAMA [3], Virgo [4]) approximately reached their design sensitivities and thus demonstrated the effectiveness of the working principle. The major detectors currently operative are a enhanced versions of the first generation (Virgo+ and E-LIGO), with larger laser power and some technological improvements.

Advanced detectors (like "Advanced LIGO" [START_REF] Harry | Advanced LIGO reference design[END_REF] and "Advanced Virgo" [START_REF] Flaminio | Advanced Virgo Baseline Design[END_REF]) will show a sensitivity improved roughly by a factor of ten with respect to the initial interferometers. They are based on technologies currently available, sometimes tested in reduced scale prototypes, but still to be implemented in full scale. According to the current models of GW sources, sensitivity of the advanced interferometers is expected to guarantee the detection of the signals generated by astro-physical sources within months to a year at most. For example, at the nominal sensitivity of the advanced detectors, the expected detection rate of the GW signal generated by a binary system of coalescing neutron stars is about a few tens per year [START_REF] Cbc Group | Rate predictions for LIGO-Virgo Compact Binary Coalescence events[END_REF][START_REF]Advanced Virgo Preliminary Design[END_REF]. But apart from extremely rare events, the expected signal-to-noise ratio (SNR) of these detections obtained with the advanced detectors is too low for precise astronomical studies of the GW sources and for complementing optical and X-ray observations in the study of fundamental systems and processes in the Universe.

These considerations led the GW community to start investigating a new (third) generation of detectors. With a considerably improved sensitivity these new machines will open the era of routine GW astronomy. Since the first detection of a GW signal is expected to occur in the advanced interferometers, it is especially the understanding and enhancement of the observational aspects that the planning of the third generation must focus on.

To realize a third generation GW observatory with a significantly enhanced sensitivity (let us consider a target of a factor of ten improvement in sensitivity with respect to the advanced detectors in a wide frequency range), several limitations of the technologies adopted in the advanced interferometers must be overcome and new solutions must be developed to reduce the fundamental and technical noises that will limit the next generation machines.

In this paper. for lack of space availability, we will focus on a small subset of the possible scientific goals of a third generation GW observatory and give a short overview of the technological challenges introduced by this new generation of machines and under evaluation within the framework of the Einstein Telescope (ET) design study [START_REF]The Einstein Telescope design study (FP7-Capacities, Grant Agreement 211743[END_REF].

Science reaches

Fig. 1 shows the typical expected sensitivity of an advanced gravitational wave detector. A gravitational wave observatory with a sensitivity a factor ten better (see Fig. 2) [START_REF] Hild | Pushing towards the ET sensitivity using conventional technology[END_REF] will open a new avenue for understanding physics of the extreme phenomena in the Universe [START_REF] Amaro-Seoane | Einstein Telescope Design Study: Vision Document[END_REF] (for a recent review see reference [START_REF] Sathyaprakash | [END_REF]):

Astrophysics: Measure in great detail the physical parameters of compact stars [i.e., neutron stars (NS) and black holes (BH)] in a binary system [13,14], constrain the equation-of-state of NS and solve the enigma of gamma ray bursts (GRB) [15,[START_REF] Amaro-Seoane | Einstein Telescope Design Study: Vision Document[END_REF]. General Relativity: Test general relativity by comparing observations of massive binary star systems with numerical relativity (NR) predictions and constrain alternative theories of gravity (such as the Brans-Dicke theory) through the observation of NS-BH coalescences [START_REF] Amaro-Seoane | Einstein Telescope Design Study: Vision Document[END_REF]. Cosmology: Measure cosmological parameters from standard sirens of gravity [16,17] and probe the primordial Universe through the measurement of the GW stochastic background [START_REF] Amaro-Seoane | Einstein Telescope Design Study: Vision Document[END_REF].

Astroparticle physics: Measure or constrain the neutrino and graviton masses through the detection of the GW emitted in a supernova [18].

In what follows we will describe a few selected topics; a more detailed description can be found in the ET science vision document [START_REF] Amaro-Seoane | Einstein Telescope Design Study: Vision Document[END_REF].

Binary systems

Binary neutron stars (NS-NS) could be seen up to a distance of 400 Mpc in advanced detectors. The expected rate of mergers within that distance gives an event rate of about 40 per year [START_REF] Cbc Group | Rate predictions for LIGO-Virgo Compact Binary Coalescence events[END_REF] with guaranteed detections. The low signal-to-noise ratio (SNR) of such events might not permit detailed measurement of the physical properties of the sources but advanced detectors could begin to impact cosmography by independently measuring the Hubble constant to a few percent [START_REF] Nissanke | Exploring short gamma-ray bursts as gravitational-wave standard sirens[END_REF]. This is because binary neutron stars are self-calibrating standard sirens, allowing a direct measurement of their A possible sensitivity (tick curve) of an underground, long suspension, cryogenic, signal and power recycled single third generation gravitational wave observatory (see Table 1 in [START_REF] Hild | Pushing towards the ET sensitivity using conventional technology[END_REF]) compared to a typical sensitivity curve of an advanced detector (dashed curve). It is worth to underline that the evaluation of the possible noise level of a third generation GW observatory is an ongoing activity, still far to be concluded within the ET design study. For this reasons the curves are updated regularly and labeled with progressive letters to be distinguished. In the tick curve (socalled ET-B), corresponding to a single wide-band detector, the suspension thermal noise contribution is missing.

luminosity distance and sky location from a knowledge of the gravitational-wave amplitude in a network of three or more detectors. The total mass, mass ratio and other intrinsic parameters of the binary can all be measured, by matched filtering the data with templates that have been computed to a very high accuracy [START_REF] Blanchet | [END_REF]21,22,23] using approximation methods to solve Einstein's equations. This would be a milestone for cosmology, especially since there is currently a gap in the measurement of the expansion rate of the Universe at around 300 Mpc (see e.g. Ref. [24], especially their Fig. 1 where one can see that measurements are sparse in the red-shift range 0.1 < z < 0.4). The expected distance up to which the inspiral phase of compact binaries could be detected is shown in fig. 3 (left panel) which reveals that binary neutron stars can be observed from a red-shift of z ∼ 2. One should expect to detect millions of binary neutron star mergers per year within the distance reach of ET. Red-shift could be measured to a small fraction (say, 1 in 1,000) of these events, for instance by identifying them in coincidence with gamma-ray bursts. The measured values of red-shift and luminosity distance can be fitted to a cosmological model to infer cosmological parameters. Expected errors in the estimation of the cosmological parameters shown in Table 1 [17] are comparable to those from other cosmology missions such as the Joint Dark Energy Mission.

The distance reach of ET shown in figure 3 is computed using signals in the socalled restricted post-Newtonian (PN) approximation. This is an approximation in which one retains the amplitude of the waveform to the lowest-order in PN expansion neglecting higher order corrections. At the lowest-order the signal contains only the second harmonic of the orbital frequency while the higher-order corrections contain other harmonics. The effects of sub-dominant harmonics are not completely understood yet but we already know that they could facilitate observation of heavier binaries as well as greatly improve the accuracy with which the source parameters can be measured [13,14,25]. Accurate measurement of the parameters will allow the determination of the mass function of neutron stars and black holes, the maximum mass of a neutron star and its equation-of-state and provide a comprehensive history of the formation and evolution of compact binaries. Such studies will give answers to other astrophysical questions such as the history of star formation, the birth of intermediate-mass black holes and their growth [START_REF] Gair | Exploring intermediate and massive black-hole binaries with the Einstein Telescope[END_REF][START_REF] Gair | Probing seed black holes using future gravitational-wave detectors[END_REF], etc.

Observation of the merger of binary black holes can open a new era for fundamental physics. Moments before the coalescence, the component black holes in a binary experience ultra strong gravitational fields created by each other. Recent advances in analytical [START_REF] Buonanno | [END_REF]29,30,31,32,33,34] and numerical relativity [35,36,37,38,39,40,41] has made it possible to predict the characteristics of the signal emitted in the process of merger. Comparison of the predicted signal amplitudes and fluxes with the observation will enable tests of general relativity that can never be carried out by any other means. It should be possible to check if the spacetime geometry of the merged object is that of a black hole or some other exotic object, if black holes are enclosed in a horizon, etc.

Isolated Neutron Stars

Neutron stars (NS) are one possible end state of massive stars that result in a gravitational collapse followed by supernova of Type II, Type Ib or Type Ic. Our knowledge of neutron stars comes mainly from the observation of the radio and Xray emissions of hundreds of pulsars currently known. The composition of a NS and the cause of its pulsation in radio are still under debate. It is believed that the NS crust consists of ordinary matter (chiefly iron) ordered in an atomic lattice embedded in a sea of free electrons. The outer core could consist of a mixture of nuclei, free protons, neutrons and electrons. The inner core of the star could be a superfluid of neutrons. According to some models, the core could consist of strange quarks (see [42] for a review).

The main mechanism for the emission of GW by a NS is due to the quadrupolar moment generated by its ellipticity . In this case the GW emission occurs at twice the rotational frequency of the NS. The amount of ellipticity that a NS could support is related to the equation-of-state of the ultra-dense nuclear matter of the star. According to the current models the crust of the star could support 10 -6 -10 -7 , whereas the solid core could sustain up to 10 -3 . A higher ellipticity could indicate a solid quark star. Fig. 4, upper panel, shows the minimum ellipticity in known pulsars that would be detectable in "ET-B" (see figure 2 [START_REF] Hild | Pushing towards the ET sensitivity using conventional technology[END_REF]). The lower panel shows the detection range, for different ellipticities, for a blind search (i.e. unknown sky position and frequency). The possibility of detecting continuous GW emission of NS having ellipticity below 10 -6 -10 -7 will place interesting constrains on the supra-nuclear equation-of-state.

Just as helioseismology helped determine the internal structure of the Sun, asteroseismology -the study stellar oscillations -could help constrain the equationof-state of a NS. Glitches in pulsars are believed to be the result of stellar quakes that could excite quasi-normal mode oscillations of the star, emitting gravitational waves with characteristic frequencies and damping times [43]. By observing the frequency and damping times of the quasi-normal modes it should be possible to measure the mass and radius of a neutron star with an accuracy of 10% or better [44], which would constrain the equation-of-state of the star and hence its composition.

Table 1. Errors in the determination of the cosmological parameters through the detection of 5192 realizations of a catalogue containing 1000 BNS merger events, of known red-shift [17]. The fractional 1-σ width of the distributions σ Ω Λ /Ω Λ , σ Ω M /Ω M and σ w /|w| are shown, accounting for the weak lensing errors in the left column and considering it corrected in the right column. The meaning of these parameters is described in [17] and briefly hereafter: Ω M and Ω Λ are the (dimensionless) energy densities of the Dark Matter and Dark Energy, respectively; w is the Dark Energy equation of state parameter (w = 1 corresponds to a cosmological constant).

Free parameters

σ

Ω Λ /Ω Λ σ Ω M /Ω M σ w /|w| 3

Supernova explosion and Neutrino mass measurement

A supernova (SNe) caused by the collapse of a massive star's iron core to a NS is the most energetic event in the Universe, releasing ∼ 10 53 erg of gravitational energy. Most of this energy (∼ 99%) is emitted in neutrinos, but a very small fraction, depending on the asymmetry of the collapse, could be emitted in GW. The precise mechanism of the collapse and the ensuing supernova is still unknown and, hence, the amount of energy emitted in GW is under debate, but recent evaluations (see [45] for a review) limit it to 10 -7 -10 -8 solar masses. The possibility of coincident measurement of neutrinos, electro-magnetic waves and gravitational waves could put a very strong constraint on the core collapse supernova mechanism. The limited amount of energy emitted in GW (consequently, the reduced distance reach) and the low SNe rate in the Milky Way and Local Group (less than 1 event per 2 decades [46]) make the detection of the GW emitted by SNe rather improbable in initial and advanced detectors. Einstein Telescope might be sensitive to supernovae at a few Mpc, with an expected event rate of ∼ 0.5 yr -1 [47]. If, as expected, at the time of the implementation of the ET observatory, megaton-class neutrino detectors are operational and have a range similar to ET, it will be possible to provide coincident observations with an acceptable event rate. The (almost) simultaneous detection of GW and neutrinos could result in an independent measurement of the neutrino mass. In fact, the time delay between the two detections can be expressed as ∆t = ∆t SN + ∆t p + ∆t d , where ∆t SN is the emission time difference, ∆t p is the propagation time and ∆t d is the time difference due to the different location of the detectors. If ∆t SN is known through the model (or if it is lower than 1 ms), it is possible to measure the neutrino mass with an accuracy better than 1 eV [18].

Limits of the second generation detectors and technological challenges for the third generation

The typical sensitivity of an advanced or second generation interferometric gravitational wave detector is shown in Fig. 1. If we consider only the fundamental noises, the sensitivity of these apparatuses will be dominated

• at very low frequency (below 4-5 Hz) by the seismic noise and the gravity gradient noise (see Sect.

Seismic noise

Ground based interferometric GW detectors are and will be limited, in the very low frequency range, by the natural and anthropomorphic vibration of the soil where the instrument is realised. Seismic noise acts on the suspended test masses in two ways:

• through the suspension chain, shaking each stage according to its transfer function

• coupling the mass vibration in the soil layers, perturbed by the seismic waves, directly with the test-mass displacement, via the mutual attraction force expressed by Newton's universal law of gravitation (so-called Gravity Gradient noise or Newtonian noise).

Seismic noise filtering.

In a GW detector the seismic vibrations must be sufficiently filtered by the suspension chain before it reaches the test masses. Currently the filtering system is realised through a chain of harmonic oscillators that filter the seismic vibration horizontally (inverted and "normal" pendulums) and vertically (blades). Virgo currently implemented the most sophisticated of such passive filtering systems and it shows the best sensitivity below 40 Hz. The so-called Virgo Super-Attenuator pushes the residual seismic noise below the thermal noise of a first generation detector like Virgo starting from about 4 Hz [48].

Recent evaluations [49], supported by direct measurements in the Virgo detector, demonstrated the full validity of the passive filtering design also considering the stringent requirements of a second generation GW detector like Advanced Virgo, where the suspension thermal noise is reduced by an order of magnitude. Passive filtering is not the only way attempted to fight the seismic noise in a GW detector; in the advanced LIGO design, an active philosophy [50] has been implemented: in a chain of three sub-systems the displacement and the accelerations caused by the seismic noise are read through position and acceleration sensors and are actively and hierarchically suppressed through hydraulic and electro-magnetic actuators.

In a third generation GW detector, there are additional requirements that make the achievement of the sensitivity targets very challenging; in fact, the first requirement is the improvement of the noise level in relation to the advanced detectors roughly by a factor of ten in the whole detection frequency band, but the second and more difficult requirement is to access the frequency region between 1 and 10 Hz, excluded in the advanced detectors. The achievement of both these targets is too challenging to be requested from an improved seismic filtering system and alternative (or better additive) solutions must be found. It is well known that underground sites are seismically quieter (i.e. see [START_REF] Bialowons | Measurement of ground motion in various sites[END_REF]) and the possibility to realise an underground GW detector has been analysed and selected by the LCGT [START_REF] Uchiyama | [END_REF] (Large Scale Cryogenic GW Telescope) collaboration in Japan. The comparison between the seismic noise in the TAMA [53] site (Tokyo) and in the LISM [54] site (Kamioka mine, the prime candidate as an LCGT site) shows a reduction in the low-frequency region, by going underground, by a factor of 100 in terms of acceleration and by two to three orders of magnitude in displacement spectral amplitude. A corresponding and even larger noise reduction has been reached in the output of the LISM interferometer, due to the fact that going underground several other "technical" noises, induced by external disturbances like wind, scattered light or temperature fluctuations, are suppressed by the quietness of the site.

Hence, an underground site can offer the possibility to achieve the desired sensitivity improvement with respect to an advanced detector in the same frequency band. A preliminary investigation [49] on the compliance of the Virgo Super-Attenuator with the requirements of a third generation detector has shown a satisfactory behavior above 4 Hz, whereas to access the 1 -3 Hz frequency range major technical upgrades of the suspension system must be realised.

Gravity Gradient Noise.

In the GW interferometers, the suspended test masses are subject to the random gravitational forces generated by seismic noise and by moving massive bodies [55,56,57]. Obviously the importance of this disturbance depends on the seismic noise level and on the contribution of the other low-frequency noise sources to the noise budget; it is evident that the seismic filtering chain doesn't play any role for this noise source, since the gravitational force is a direct interaction between the suspended mirrors and the neighboring masses. In the first generation of GW detectors the gravity gradient noise does not play any role and in the advanced detectors (due to the improvement of the sensitivity at low frequencies) it starts approaching the overall noise level, but remaining negligible above 10 Hz (see Fig. 1).

In the third generation of GW detectors, the more stringent requirements in terms of sensitivity at low frequency enhance the importance of this noise source. The reduction of the seismic noise, due to the possibility to realise the observatory in an underground site, opens new questions about the validity of the current noise modeling. Recent evaluations [START_REF] Cella | Low Frequency Limit, Talk at the Fujihara Seminar[END_REF][START_REF] Cella | Gravity Gradient Noise: estimates & reduction strategies[END_REF] have shown the importance, in the noise modeling, of the surface seismic waves, the irrelevance of the experimental cavity shape and the attenuation, going deeply underground ( 100 m), of the gravity gradient noise, at least above 1 -2 Hz. If that very low frequency range needs to be accessed to fulfil the science requirements of a third generation observatory, a major effort must be performed to complement the seismic attenuation with the subtraction of the residual gravity gradient noise through the signals extracted from a network of sensors located around the detector [START_REF] Cella | Low Frequency Limit, Talk at the Fujihara Seminar[END_REF].

Thermal noise

By thermal noise we indicate all those processes that modulate the optical path of the light in the interferometer coupling it to the Brownian fluctuation or to the stochastic fluctuation of the temperature field in the optical components. It is common to distinguish between the suspension thermal noise, affecting the position of the test masses (considered a rigid body) through the fluctuations of the suspension wires or fibres, and the mirror thermal noise, which is the overlap of all the fluctuation and dissipation processes occurring in the test masses and in the high reflectivity coatings.

Suspension thermal noise.

To model and understand the thermal noise in the interferometers (in thermal equilibrium) two fundamental instruments are used: the equi-partition theorem, which relates the temperature of a system to its average energies, and the Fluctuation-Dissipation Theorem (FDT) [START_REF] Callen | [END_REF], which relates the power spectrum of the fluctuations of a system (in thermal equilibrium) to its dissipation processes, described by the mechanical impedance. The equi-partition theorem tells how much thermal energy is present in a thermo-dynamical system, whereas the FDT describes how that energy is distributed in frequency. The strategies to reduce the thermal noise impact in the second generation GW detectors are essentially an evolution of what has been applied in the initial machines and are essentially based on the reduction of the dissipation in the suspension system, in order to concentrate all the fluctuation energy into the normal modes of the system, resulting in a low noise level off-resonance.

Already in the initial detectors particular attention has been devoted to the reduction of the dissipation in the suspension by selecting the right material for the suspension wires [61,62,63,64], by optimizing the clamping [65] and the mirrorto-wire contact [66] design. Thanks to the pioneering work of the Glasgow group in the GEO600 collaboration [START_REF] Robertson | Proc. of the Third E. Amaldi Conference AIP[END_REF][START_REF] Cagnoli | [END_REF], the second generation of GW detectors will adopt the so-called monolithic [69] suspensions (already operative in GEO600 since 2001), fully realized in fused silica, which simultaneously reduces the clamping losses and minimizes the losses in the suspension fibres, because of the low mechanical dissipation of fused silica [70].

In addition to the minimization of the mechanical losses through the selection of the best materials and geometries, another means for reducing the suspension thermal noise must be used in the third generation of GW detectors: the temperature. According to the equi-partition theorem, the temperature is directly proportional to the energy stored in each degree of freedom of the suspended system allowing to reduce the fluctuation amplitude by lowering the temperature. Furthermore, at low temperature, some materials show a suppression of the dissipation mechanisms.

Hence, cryogenics is one of the most appealing technologies to reduce the thermal noise of the optics suspension in a third generation GW detector. The first problem to be solved in a cryo-interferometer is how to cool down the test masses without introducing additional vibrations that spoil the very low frequency performances. New technologies are now available, for example based on cryo-cooling systems [71] that are actively damped to reduce the seismic vibration and that promise an easier achievement of low temperatures with less impact on the low frequency performance of the interferometer than previous cryo-coolers. A special design of the suspension system is needed to cool down the test mass without introducing additional vibration. Progress in channeling the heat transmission through a second, parallel seismic filtering system has been made in the ILIAS [START_REF] Caparrelli | Report ILIAS-JR3-C1 activity[END_REF] project.

Even more important is the right choice of the material for the realisation of the last stage of the suspension system. The fused silica suspension, developed for the second generation GW detectors, cannot be used in cryogenics because of its poor thermal conductivity and because of a well known dissipation peak of that amorphous material at low temperature. In order to be a good candidate for a cryogenic suspension, the material must exhibit a high thermal conductivity at the operation temperature chosen, to permit an efficient heat extraction (which is crucial, because of the relatively high heating power deposited in the test masses by the high light power stored in the interferometer cavities), a low mechanical dissipation angle (to reduce the Brownian thermal noise), a low thermal expansion coefficient (to minimise the thermo-elastic noise), and a good breaking strength (to safely support the test masses). Currently there are two candidate materials for this role: Sapphire and Silicon. Sapphire has been selected to realise the suspension fibres of LCGT [START_REF] Uchiyama | [END_REF] both for its dissipation [START_REF] Uchiyama | [END_REF] and for its thermal conductivity properties [74]; Silicon, on the other hand, has been preliminary studied within the ILIAS project and it has been found suitable to realise both suspension fibres [75] and ribbons [76]. However, it is matter of fact that currently only sapphire has been used to realize a full cryogenic suspension and the usage of Silicon still needs a successful R & D activity.

Mirror thermal noise.

The major limitation of the sensitivity of the second generation of GW detectors in the 40-200 Hz range will be the thermal noise related to the high reflectivity dielectric coating applied to the main cavities mirrors. While the mirror substrate material chosen (synthetic fused silica) shows low mechanical dissipation, the high refraction component in the dielectric coating (Tantalumpentoxide Ta 2 O 5 ) shows high mechanical losses that dominate the dissipation of the test mass [77,78].

Third generation GW detectors could benefit of all the R & D activities currently performed to reduce the mirror coatings thermal noise contribution in the advanced GW detectors (include Titanium dopants in the Tantalum layers [79], optimization of the amount of high dissipation material in the coating [START_REF] Agresti | Optimized multilayer dielectric mirror coatings for gravitational wave interferometers[END_REF][START_REF] Villar | Measurement of Thermal Noise in Multilayer Coatings with Optimized Layer Thickness[END_REF]); but, unfortunately, we cannot expect a further reduction of the dissipation if a cryogenic-interferometer is realized (and tantala-silica based coatings are used). In fact, measurements performed to characterize the coatings for the LCGT detectors have shown that the mechanical dissipation in a multi-layer Tantalum-pentoxide coating is rather independent of the temperature [START_REF] Yamamoto | [END_REF] and more recent measurements [82] have even shown a low temperature dissipation peak in a single-layer of Ta 2 O 5 doped with TiO 2 .

Furthermore, because of the broad dissipation peak shown by fused silica at low temperature, in the cryo-interferometers it is impossible to choose the low mechanical loss, low optical absorption substrates developed for the advanced detectors. Hence, as a result from the suspension development (see Sect. 3.2.1), currently the best material candidate to realize the test masses are Sapphire (selected in LCGT) and crystalline Silicon, showing a very low mechanical dissipation angle (about 3-4×10 -9 ) at low temperature. Sapphire is transparent to the standard wavelength adopted in the GW detectors (1064 nm). It shows relatively small thermal lensing [START_REF] Tomaru | [END_REF] due to its large thermal conductivity at low temperature (2330 W• m -1 K -1 at 10 K), but its optical absorption is high (about 90 ppm/cm [85]), constraining the interferometer design and limiting the future light power increase in the main Fabry-Perot cavities. Silicon shows a similar thermal conductivity (1200 W• m -1 K -1 at 12.5 K), but it is transparent only at a longer wavelength (λ 1500 nm), where it shows an incredibly low absorption (about 3 × 10 -8 cm -1 at 1445 nm [86]), which requires to reconsider all optical and electro-optical component choices in the interferometer.

To solve the coating problem, either a new high refraction index material with a low dissipation at cryogenic temperature, suitable to realize the needed high reflectivity coating, is found or a completely different solution must be developed. For example, a promising R & D activity is addressed to produce high reflectivity mirrors with just one dissipative layer of dielectric coating material on the substrate [87] or even without any additional layer, realizing the so-called resonant waveguide grating [88] by nano-structuring the surface of the Silicon substrate. Other promising R & D activities, here not discussed because of the lack of space availability, are addressed to realize the high finesse Fabry-Perot cavities, needed in the future GW detectors, minimizing the dissipating coating layers (replacing the end mirror of the long Fabry-Perot cavity with an additional anti-resonant cavity, the so-called Khalili cavity [89]), or eliminating them (using the total internal reflection phenomenon through the Brewster's angle reflectors [90] or using the corner reflectors [91]).

The coupling of the mirror surface vibration, induced by the various thermal noise sources, with the GW detector sensitivity is affected by the beam size in the Fabry-Perot cavities (larger is better). Because of the finite size of the substrates, the requirements in terms of diffraction losses and in terms of optical stability of the Fabry-Perot cavities, the beam size cannot grow infinitely and some other technique must be investigated. The potential in terms of thermal noise reduction of Fabry-Perot cavities with resonant beams with a flatter radial distribution of the light intensity [START_REF] Agresti | Flat Beam Profile to Depress Thermal Noise[END_REF] is well known; some attention has been drawn towards the possibility of using Laguerre-Gauss modes of orders higher than (0, 0) resonating in the Fabry-Perot cavities [START_REF] Mours | [END_REF]94]. According to the most recent results [START_REF] Franc | Effect of Laguerre Gauss modes on thermal noise, talk at the ET-WP3-meeting[END_REF], in the case of a cryogenic interferometer (10 K) adopting a Silicon mirror with a diameter of 62 cm and a thickness of 30 cm, resonating a (3, 3) Laguerre-Gauss mode with a beam waist radius of 7.2 cm it is possible to suppress the cumulative mirror thermal noise by a factor 1.71 with respect to a Gaussian beam with a waist size if 11.9 cm (beam sizes selected to give diffraction losses of 1 ppm). These numbers show that it is important to push the development of such techniques for minimizing the thermal noise contributions to the overall noise budget.

Quantum Noise

The origin of Quantum Noise

Quantum Noise in interferometric gravitationalwave detectors arises from the quantization of the electro-magnetic field. All first generation (initial) and second generation (advanced) interferometric gravitationalwave detectors are based on the Michelson principle. In all of them the operating point is chosen such that all field components symmetrically present (in amplitude and phase) in both interferometer arms (like the laser carrier light), returning from both arms, constructively interfere towards the input (symmetric) port and destructively interfere towards the output (asymmetric) port. Asymmetric field components, like a GW introduces them, show up at the asymmetric, the output port. Due to phase relations (resulting from energy conservation) at the beam splitter [START_REF] Zeilinger | General properties of lossless beam splitters in interferometry[END_REF], fields entering the interferometer from the output port get split into the two interferometer arms with a phase shift of ±π, w.r.t. the light entering from the symmetric port, and cause asymmetric field components in the interferometer arms, which, returning to the asymmetric port, cannot be distinguished from a GW signal. Hence it is mostly fluctuating fields entering the output port that we have to worry about. According to Quantum Mechanics the lowest energy state of the quantized electromagnetic field (also called zero-point field or vacuum state) still has energy fluctuations of ω/2 per mode of the field, distributed over both quadratures, amplitude and phase. The level of fluctuations can be traded between the quadratures as only the product is limited by Heisenberg's uncertainty principle. These fluctuations can enter the interferometer through the output port, asymmetrically add to the light field in the interferometer arms and cause noise inside the interferometer and in the output field: the Quantum Noise. A comprehensive description of the Quantum Noise and means to fight it can be found in [START_REF] Corbitt | Quantum Noise and Radiation pressure Effects in High Power optical Interferometers[END_REF] and references cited within. The resulting strain noise spectral density for a simple Michelson interferometer is given by:

S h = ( 1 κ + κ) h 2 SQL 2 (1)
with κ = 4I 0 ω 0 c 2 MΩ 2 and h SQL = 4 MΩ 2 L 2
where ω 0 is the angular frequency of the laser light, Ω the gravitational wave signal frequency, L the arm length, c the speed of light, M the mirror masses, and I 0 the laser power. The Quantum Noise usually shows up in two forms: shot noise and radiation pressure noise. Shot noise is the intensity Quantum Noise on the photo detector. Radiation pressure noise results from the impulse transfer of the photons upon reflection from a test mass. The (differential) quantum fluctuations in the power of the beams impinging on the mirrors leads to real mirror displacements having the same effect as a gravitational wave. In Eq. 1 the 1/κ term represents the shot noise at the readout while the κ term stands for the radiation pressure effect. The optimal sensitivity that can be reached for a given frequency by trading shot noise versus radiation pressure by chosing the best light power is called the Standard Quantum Limit (SQL).

The interferometric measurement of gravitational waves relies on the conversion of a differential length change of the interferometer arms into an power change of the light at the output of the interferometer. Phase noise of the vacuum fluctuations which can enter the interferometer through the output port, gets converted into intensity fluctuations of the light returning to the output port, which is then measured by the photo-detector. Without the vacuum fluctuations from the output port the signal from the interferometer would show only negligible shot noise on the output beam. While the amount of the vacuum fluctuations entering the interferometer through the output port is constant, the amount of carrier light in the interferometer arms can be changed. This results in a shot noise level on the photo-detector that is proportional to the amplitude of the light leaving the interferometer output. The gravitational-wave signal on the other hand is proportional to the light power inside the interferometer, which translates into a proportionality of the light power on the photo-detector, as long as no other power dependent processes introduce additional noise. Hence the SNR scales with the square-root of the light power in the interferometer.

Increasing the Light Power

So one solution for improving the sensitivity (for frequencies where shot noise dominates) is to increase the light power inside the interferometer arms. High power in the interferometer arms is achieved by three different means:

• High power lasers • Power Recycling • Arm Cavities
High power lasers The most obvious way to increase the light power inside the interferometer is to use a powerful laser. All first and second generation interferometric GW detectors use lasers with a wavelength of 1064 nm. During the construction and operation of the first generation the available laser power increased from about 10-20 W in the first generation to 200 W available for the second generation. According to current plans solid state 1 kW lasers will be available for the third generation. The use of high laser power gives rise to thermal problems with the light absorbed in auxiliary optics like modulators, Faraday rotators or polarizers. The absorbed light will lead to a local temperature increase which through the temperature dependence of the refractive index will lead to thermal lensing. This in turn can lead to reduced quality of mode matching to the optical resonators. Especially the main optics in the interferometer arms will show strong thermal lensing effects as they are exposed to light power levels in the MW range in future detector generations. Although the absorption levels of fused silica have been cut down in the past to a level of 0.25 ppm/cm for bulk absorption and to the sub-ppm level for coating absorption, thermal lensing will still pose a problem and elaborated thermal compensation systems are needed to compensate the effect [START_REF] Vinet | On Special Optical Modes and Thermal Issues in Advanced Gravitational Wave Interferometric Detectors[END_REF].

The need to achieve low absorption combined with good mechanical performance at low temperatures (see chapter 3.2.2) will require to select a new material for the test masses. The physical properties of Silicon make it a good candidate. High power fibre lasers are currently being developed but have not yet reached the performance level of solid state lasers. A current overview of available laser sources and prospects for the third generation of interferometric gravitationalwave detectors is given in [START_REF] Mavalvala | General Relativity and Gravitation[END_REF].

Power Recycling The carrier light as well as all common fluctuations returning from the interferometer arms constructively interfere towards the input port where they can be reflected with a mirror located in the input, called Power Recycling mirror. The interferometer together with this mirror then forms an optical resonator where the light power can resonantly be enhanced. This technique is called Power Recycling [100] and essentially has the same effect as directly increasing the laser power injected into the interferometer. All detectors of the first and second generation use and will use power recycling. With a laser power of about 200 W the second generation will reach power levels inside the arm cavities of around 800 kW. The third generation is aiming at a light power in the interferometer arms in the few Megawatt range. With the promising prospect of 1 kW high-power-lasers available for the third generation there will be no need to increase the Power Recycling factor beyond what is foreseen in the second generation.

Arm Cavities Placing Fabry-Perot cavities in the interferometer arms resonantly enhances the light in the individual arms and with it the signals created by the GW. The amount of power enhancement is limited by the fact that the linewidth of the optical resonator decreases with increasing build-up until relevant parts of the frequency spectrum fall outside of the resonance of the cavity and the GW signals do no longer get simultaneously enhanced with the carrier light. The low transmission of the input mirror then causes a reduction of signal amplitude for high frequencies signals at the output port, i.e. a reduced sensitivity. The possible power enhancement in the interferometer arms is hence a compromise between a low relative shot noise level and bandwidth.

Approximate numbers for power requirements for the 1st to the third generation are given in the upper part of table 2.

Signal Recycling

The second generation of interferometric gravitational-wave detectors (in this sense treating GEO600 as a second generation instrument) uses an additional technique to lower the relative shot noise: Signal Recycling [101]. The signals being generated by the GW (with a phase difference of π) in the interferometer arms constructively interfere towards the output port. If these signals are sent back towards the interferometer with a recycling mirror they get reflected back to the output port by the interferometer, similar to the laser power being reflected back to the input port. Together with the interferometer this mirror forms an optical resonator, the Signal Recycling cavity. By microscopic adjustment of the position of the Signal Recycling mirror the resonance of this cavity can be tuned to any desired frequency. Depending on this tuning the bandwidth of the interferometer can either be narrowed (called Signal Recycling in the case where the carrier frequency is close to a resonance) or widened (called Resonant Sideband Extraction in the anti resonant ). The tuning changes the resonance conditions of the fields in the signal recycling cavity and with it the phase relation between the signal sidebands and the carrier at the output port and inside the interferometer arms. Signal Recycling enhances the GW Signal being generated inside the optical cavity but does not enhance the fluctuations entering the cavity from the output port.

Beside the optical resonance, detuned Signal Recycling produces another optomechanical resonance, typically at lower frequencies (see Fig. 1), which gives an improvement in sensitivity and, through the correlations that it introduces between amplitude and phase fluctuations, even allows to beat the Standard Quantum Limit [104,105]. Already in the advanced detectors this additional optomechanical resonance lets the Quantum Noise fall below the Standard Quantum Limit, as can be seen in Fig. 1.

Squeezing

As indicated above the fluctuations in the different quadratures of the field entering the output port can be traded against each other, still fulfilling the requirements of Heisenberg's uncertainty relation. If such a squeezed state, where the phase noise is lowered at the cost of the amplitude noise, is injected into the output port, the shot noise of the light registered by the photo-detector will be lowered. Squeezed light sources at 1064 nm were tested in many tabletop experiments and at the suspended 40m-prototype at the California Institute of Technology [106,107,108]. Only recently squeezed shot-noise in the audio detection band of gravitational wave detectors was demonstrated [109, 110], a detector compatible control scheme developed [111] and the strongest squeezing effect ever observed [112,113]. At the same time as the shot noise is reduced the radiation pressure contribution will increase. By appropriately rotating the phase angle of the squeezing as a function of frequency, which can be achieved by sending the squeezed state through filter-cavities [114,[START_REF] Corbitt | Optical Cavities as amplitude filter of squeezed fields[END_REF]103], the shot noise (at high frequencies) and the radiation pressure noise (at low frequencies) can be simultaneously reduced. In case of using squeezing together with a detuned interferometer (i.e. not tuned to zero frequency, which means that the laser carrier frequency is not resonant in the Signal Recycling cavity), the rotation of the squeezing ellipse with respect to the light coming from the interferometer (due to the dispersion of the Signal Recycling cavity) causes an increased amount of Quantum Noise outside of the Signal Recycling resonance due to the anti-squeezed quadrature of the injected squeezing [105]. Instead of filtering the squeezed state similar to fighting the radiation pressure noise, as mentioned above, this effect can be avoided by using twin Signal Recycling [117]. In addition twin Signal Recycling resonantly enhances both signal sidebands, at positive and negative frequencies.

Squeezing is already being implemented in the current generation of interferometric gravitational-wave detectors in the case of GEO-HF, the upgrade of GEO600 [115], aiming at a squeezing level of 6 dB over the entire frequency range of interest. 6 dB effective squeezing at the photo-detector lowers the shot noise by a factor of two corresponding to a light power increase of a factor of 4. An overall gain from squeezing of about 10 dB, i.e. a factor of 3 in noise amplitude spectral density, for the third generation presently seems realistic. Squeezed light injection may also be tested at one of the LIGO interferometers within the next years.

Radiation Pressure Noise

Whereas increasing the power in the interferometer lowers the relative readout noise, i.e. the shot noise, it increases the radiation pressure noise. The impulse transfer of the photons onto the mirrors upon reflection causes a force acting onto the mirrors, the radiation pressure p = 2I/c, where I is the light power and c the speed of light. The amplitude fluctuations on the light this way get converted into mirror motion causing the so called radiation pressure noise. The mechanical susceptibility of a free mass (or a pendulum mass well above its resonance frequency) to a force is (MΩ) -2 , were M is the mass of the test mirror and Ω the Fourier frequency of interest. Radiation pressure therefore is more important at low frequencies, which also shows in equation 1. The worsening of the Quantum Noise at frequencies below about 20 Hz shown in Fig. 1 is due to this effect.

Increasing the mirror mass decreases the mechanical susceptibility and hence cuts down the effect of radiation pressure on test mass movement. Consequently the mirror mass will increase from the first to the second generation as indicated in Table 2.

Reducing the differential amplitude fluctuations in the interferometer arms by using squeezed states replacing the vacuum fluctuations entering the output port can further lower the radiation pressure effect.

Parametric instabilities

The high laser power, stored in the main Fabry-Perot cavities, could bring another crucial problem: the parametric instabilities [118]. In this phenomenon, the optical modes of the Fabry-Perot cavities couple with the acoustic models of the mirrors spoiling the cavity's performance, up-to the unlock of the cavity. There are studies evaluating the effect on the advanced interferometers [119,120] and on LCGT [121].

The relevance of the parametric instabilities issue strongly depends on the selected design options and it ha been computed [START_REF] Yamamoto | Parametric instability of a cavity of Einstein Telescope[END_REF] that the number of the instable modes of the ET cavity is a few hundreds times larger than that of the LCGT cavity (where the problem is negligible) and it is probable that a methods to suppress the parametric instabilities is necessary (i.e. introducing a localized mechanical dissipation in the mirror's substrate, by applying a dissipative coating on the barrel surface), but a dedicated R & D activity is needed.

Scenarios for the 3rd generation GW observatories

In this section we will describe a possible evolution scenario that should lead us to the third generation of GW detectors. We will describe the most probable options based on currently known technologies. For this reason we will neglect (although they may be scientifically interesting) some new technical options or some new solutions such as atom-interferometers [START_REF] Dimopoulos | Gravitational Wave Detection with Atom Interferometry[END_REF].

Single detector or multi-detector observatory

As described in the previous section, to realise a third generation GW detector, the technologies currently operative in the initial and planned for the advanced detectors must be stressed and new solutions must be adopted. Although the R & D advances may lead to a completely different result, a third generation GW detector could be based on the following technologies • long arms, probably about 10 km long, to enhance the sensitivity to the dimensionless space-time strain h; • underground site, to suppress the seismic and gravity gradient noises;

• long seismic filtering chains, to push the low frequency limit toward 1 Hz;

• cryogenic test masses, to suppress suspension and mirror thermal noises;

• large and flat beams, to suppress thermal noise and mitigate the mirror thermal lensing; • high power laser (about 1 kW), high finesse Fabry-Perot cavities, high power recycling factor, signal recycling and squeezed light state injection, to suppress the quantum (shot) noise; • heavy test masses and filtered squeezed state injection, to suppress radiation pressure noise.

A first evaluation of the potential of a similar detector has been performed [START_REF] Hild | Pushing towards the ET sensitivity using conventional technology[END_REF] within the ET project, considering only conventional technologies. Targeting for a wideband detector, the sensitivity (named ET-B) of an underground, long suspension, cryogenic, signal and power recycled single Fabry-Perot enhanced Michelson detector has been evaluated (see Table 1 in [START_REF] Hild | Pushing towards the ET sensitivity using conventional technology[END_REF]) and the resulting sensitivity is plotted in Fig. 2. In this evaluation, the cross-compatibility between the different technologies has been neglected, but the technological difficulties are evident. For example, the need of high power in the Fabry-Perot cavities (about 3 MW) conflicts with the requirement of a cryogenic suspension optimized for thermal noise, because of the opposite geometrical constraints given by the optimization of heat removal and the optimization of the geometrical dilution factor. Therefore the option to realise a wideband third generation observatory, combining two (or more) detectors, specialised on different frequency bands, has been evaluated in [START_REF] Hild | [END_REF]. Here the output of a low-frequency-specialised detector is combined with the output of a high-frequency machine. The former one could be a cryogenic interferometer at an underground site, with long suspensions, but moderate optical power, whereas the high frequency interferometer could essentially be a long arm advanced detector, implementing squeezed light states, a very high power laser and large test masses. This so-called Xylophone philosophy [125,126] decouples the technological requirements of a high power interferometer from the requirements of a cryogenic detector; obviously, the capability to tune the sensitivities of the two (or more) detectors constituting the observatory permit to better fit the sensitivity of such an observatory to the wanted sources, but it is worth to stress the fact that the main objective of the Xylophone strategy is to avoid the technical difficulties that could make the sensitivity "ET-B" of Fig. 2 an impossible target for a single wide-range interferometer implementation.

A possible realization of such as Xylophone strategy, evaluated in [START_REF] Hild | [END_REF] for the ET design study, is plotted in Fig. 5.

Detector Geometry

All the currently active GW detectors are L-shaped, with orthogonal arms; although this geometry maximises the sensitivity of the single detector with respect to the arm length, other geometries are possible. In particular, triangular-shaped detectors have been proposed in the past [START_REF] Winkler | Plans for a large gravitational wave antenna in Germany MPQ Report 101[END_REF][START_REF] Maischberger | Vorschlag zum Bau eines großen Laser-Interferometers zur Messung von Gravitationswellen MPQ Report[END_REF] and also the LISA geometry is triangular. A detailed analysis of the benefits and drawbacks of a triangular-shaped third generation GW observatory is described in [129] and here we report only the conclusions.

Co-located interferometers could be extremely useful to extract additional information from the GW observation; for example, two L-shaped detectors, forming a 45 • angle, could fully resolve the two polarisation amplitudes of the incoming wave. Three co-located interferometers, rotated by an arbitrary angle, through the virtual interferometry [130] technique, could do the same, supplying additional benefits like null-stream channels and redundancy. Obviously in an underground site, the realisation of a similar cluster of orthogonal L-shaped detectors is practically impossible, due to the huge cost of the infrastructures (several tunnels to accommodate the arms, several caverns to realise the central and end stations). If the angle between the two arms of each detector is reduced to 60 • , three detectors can be accommodated in a triangular-shaped underground site, minimizing the total length of tunnels, probably the number of caverns and recovering a sensitivity equivalent to two sets of orthogonal L-shaped double detectors, rotated by 45 • (see Fig. B1

of [129]).

For these reasons and because of the relevant role that the cost of the infrastructures will play in a third generation GW underground observatory, the selection of the geometry will probably be driven by the selection of the site and not vice versa: if a site that can accommodate a triangular observatory is found, the triple co-located interferometers will be the best choice, otherwise the two sets of orthogonal L-shaped double detectors will be more appealing.

Network of detectors

So far we assumed that a single site facility forms the third generation observatory. Depending on the astrophysical goals, the directionality of a detector could be of crucial importance, playing a role even larger than the sensitivity. This can be the case if a GW source needs to be spotted in a multitude of electro-magnetic sources.

Currently a network of at least three well separated detectors is needed to reconstruct the direction in the sky of a coalescing binary star system, the most promising GW source. In Sec. 2.1 it has been anticipated that, thanks to the improved sensitivity, a third generation GW observatory could gain a lot in directionality, using the additional information embedded in the full-PN approximation. In principle, two detectors at the same site could fully resolve the GW source. In practice, because of the limited accuracy, it may be advantageous to have two or more detection facilities spaced as widely as possible. Although only one third-generation project is being studied now, there is hope that other projects, e.g. a LIGO successor, will follow, resulting in a worldwide network of third generation detectors forming one big observatory. Using two distant detectors, the five parameters needed to reconstruct the source direction can be extracted from the four amplitudes from two sites and the single time delay.

For the detection of the stochastic GW background multiple co-located detectors would be best suited. The distance should be big enough to rule out common environmental noise sources but close enough that stochastic background noise still shows up coherently in the detectors.

Timelines

The evolution to the third generation of GW detectors has been, is and will be a long path. Currently the main effort is made in Europe and only the European scenario will be depicted. After a series of preliminary activities supported by the European Commission within the Framework Programme 6 (FP6), a conceptual design study is currently funded under FP7: the Einstein Telescope design study [START_REF]The Einstein Telescope design study (FP7-Capacities, Grant Agreement 211743[END_REF]. This proposal was approved and funded for three years, starting from May 2008. The major goal of the ET project is to deliver a conceptual design for such a facility, investigating the technological feasibility, the science targets, the site requirements and prepare a costing draft for the infrastructure.

Although the efforts and the attention of the worldwide GW scientific community are currently focused on the realisation of the advanced detectors (Advanced LIGO, Advanced Virgo and LCGT), the activities devoted to the third generation must continue with increasing speed. In Fig. 6 the expected evolution of the GW detectors in the World is shown. The last line of the table shows the long path still in front of the European project ET. After the current conceptual design study phase, a preparatory phase is expected to be necessary to define the technological details, and the legal and organizational issues. The start of construction (2018-2019) is expected to occur after the first detection of GWs, which is reckoned to happen within at most one year after the advanced detectors will have reached their nominal sensitivity. The construction and commissioning of a third generation GW detector cannot be much shorter than what has been needed for bringing the first generation of interferometers into operation and hence a period of about 6-7 years of intense activity is deemed neccessary before collecting the first science data with the Einstein Telescope ET.

Figure 1 .

 1 Figure 1. Typical sensitivity of a 2nd generation GW detector shown here for advanced Virgo with 125W of injected power. The sensitivity is dominated at very low frequency by the seismic noise, at low and intermediate frequencies by the suspension and mirror thermal noises and radiation pressure noise and at high frequencies by the shot noise.

Figure 2 .

 2 Figure 2.A possible sensitivity (tick curve) of an underground, long suspension, cryogenic, signal and power recycled single third generation gravitational wave observatory (see Table1in[START_REF] Hild | Pushing towards the ET sensitivity using conventional technology[END_REF]) compared to a typical sensitivity curve of an advanced detector (dashed curve). It is worth to underline that the evaluation of the possible noise level of a third generation GW observatory is an ongoing activity, still far to be concluded within the ET design study. For this reasons the curves are updated regularly and labeled with progressive letters to be distinguished. In the tick curve (socalled ET-B), corresponding to a single wide-band detector, the suspension thermal noise contribution is missing.

Figure 3 .

 3 Figure 3. Left: The distance reach of ET-B (at an SNR=10) for inspiral signals as a function of the intrinsic (red solid line) and observed (blue dashed line) total mass. Right: SNR for binaries at a distance of 3 Gpc as a function of the component masses.

Figure 4 .

 4 Figure 4. Upper panel: Smallest ellipticity of known pulsars detectable in ET (ET-B sensitivity) [11]. Lower panel: The detection range for a blind search of NS in ET (ET-B sensitivity) [11].

  3.1), • in the 4-50 Hz range by the thermal noise (see Sect. 3.2.1) of the optics suspension system and by the quantum noise, related to the radiation pressure (see Sect. 3.3.5) exerted on the suspended mirror by the photons in the main Fabry-Perot cavities, • in the 40-300 Hz range by the thermal noise of the suspended mirrors (mainly the coating contribution, see Sect. 3.2.2) • and at higher frequencies by the shot noise component of the quantum noise (see Sect. 3.3.2).

Figure 5 .

 5 Figure 5. Sensitivity of a third generation GW observatory implemented by two frequency-specialised (LF & HF) detectors (Xylophone topology[START_REF] Hild | [END_REF], curve socalled "ET-C"), with respect to a single wide frequency range interferometer ET implementation

Figure 6 .

 6 Figure 6. Roadmap for the evolution of some of the GW detectors in the World. In the last line the expected evolution of the third generation observatory ET (Einstein Telescope) is shown. After the current conceptual design phase (DS), and before the construction, a preparatory construction phase (PCP) is expected, where the detailed technical, legal and organization aspects of the project will be defined.In the evolution timeline of the Virgo and LIGO detectors are shown the (current) Virgo+ and E-LIGO phases, corresponding to a limited upgrade of the initial interferometers, with input laser power increased by about a factor 2 -3 and other technical improvements preparatory of the "advanced" phase. The time evolution of the Japanese interferometers (TAMA, LCGT, DECIGO) and of the other projects like ACIGA in Australia are not plotted.

Table 2 .

 2 Typical light powers and mirror masses for different generations of GW interferometers

	Detector generation	1st	2nd	3rd
	Laser power	10 W	200 W	1 kW
	Light power @ beam splitter 200 W 2 kW	20 kW
	Light power inside ifo arms 15kW 800 kW 3MW
	Mirror mass	10 kg	40 kg	200 kg
	case

Acknowledgments

This work has been performed with the support of the European Commission under the Framework Programme 7 (FP7) "Capacities", project Einstein Telescope (ET) design study (Grant Agreement 211743), http://www.et-gw.eu/