Philippe Herbaux
email: philippe.herbaux@univ-lille2.fr

Cyril Masselot
email: cyril.masselot@univ-fcomte.fr

"Territorial Intelligence and Governance"

Keywords:

As with European experiments, in various regions in France, territorial intelligence projects have been initiated since 2003. (see the regions of Lower Normandy, Lorraine, Réunion Island, the Aquitaine region, etc.).The objective of these is to gather and exploit information which is not confined to particular sectors and the collective processing of which can contribute to durable development. Apart from institutions, civil society and the inhabitants of the territory, it is observed that companies and in particular small and medium sized enterprises are natural partners who show interest in such initiatives. Both the different economic chains and the participating organizations thus derive considerable benefit in terms of the anticipation of threats and in the reaffirmation of the territory as a common resource worth defending. Above and beyond the information processing systems operating within these organizations or economic chains, the articulation of internal actions to generate informational capital in terms of local territorial intelligence, produces a leverage effect with visibility of European or even worldwide visibility (Herbaux, 2007) 52 . Nonetheless these experiments lead to widely differing results, of which the progressive abandonment of the project by the companies involved is one of the most commonly observed.

To support a theoretical contribution as a thread for this communication, we report on the results of a Delphi type survey completed in 2006 and covering 53 companies in the Nord-Pas de Calais region involved in a process of territorial intelligence since 2003. This revealed that 43 companies out of the 53 concerned had not followed through on their internal information sharing project and contented themselves, by default, with the results by economic sector derived from public regional surveillance.

510

Beyond this apparent disengagement from the process initiated, we may be curious about this apparent discretion of a group of actors concerning local government. This work nonetheless did generate a consensus around certain observations among the actors questioned, particularly as regards an initiative for which they did not deny the final utility but for which the requirements necessitated a significant modification to their internal culture. After the initial conventional responses: «security of patrimonial data, new choices in investment of time, lack of means, different priorities, etc.», repeated and differentiated questioning of those concerned revealed that the progressive abandonment of these practices and commitments bore a relationship with a number of human factors of relational and cognitive nature, thus depriving the project of its founding principles. This observation echoed that of the implication suggested by Girardot en 2005 53 on the theme of multi-level governance. Although the financial aspect is a factor in the long term survival of regular investments of man-hours, this criterion appeared progressively more marginal to the general project among the actors surveyed, as against several positions cited as prerequisites. Based on a synthesis of the results of the study, we propose five key success factors to promote within organizations to promote the logic of information sharing. To this effect, our proposal for a model named in French «CADIE» (Communication, Appui, Durée, Implication, Ecoute -or, in English, Communication, Support, Duration, Attentiveness) suggests several attitudes to which organizations must adhere to develop long-term integration in a territorial intelligence network.

The limitations of our proposal arise from the small size of the sample at our disposal and the regional limits of our data gathering. This experimentation, duplicated in various European regions would benefit from a multi-cultural gloss and thus would provide the template for a preliminary European approach to the logic of territorial intelligence.

Keywords:CADIE, territorial intelligence, sustainable territorial development, SME, mutualisation.

INTRODUCTION

The setting-up of a logic of information mutualisation and treatment within an organisation is a long and perilous exercise. This undertaking is one of the pillars of an anticipative vision on risks and breaches within countries and organisations.

Here are the results of a survey linked with the economic aspect of an experimental regional territorial intelligence plan within a political territory (the Nord-Pas de Calais region in France). This enquiry questions the permanence of practices of information treatment enforced as part of the regional plan. Among other things, it highlights the difficulties SMEs have to keep mutualised information systems animated. In short, it offers a few preliminary postures to be developed in order to make an action of collecting and treating information within SMEs inside a territorial intelligence logic last.

TERRITORIAL INTELLIGENCE

Intelligence?

If intelligence is considered an individual attribute in most cases, its collective aspectwhich can express itself within a territory -is often disregarded. Each inhabitant's implicit adherence to common resources, as a political space, encourages him or her to participate in its preservation. In the case of territory, intelligence -from Latin inter (between) and ligare (to link with), becomes a collective posture of management of knowledge whose aim is to preserve -if not to develop -existing resources.

This aim seems to be the thread and the very reason for territorial intelligence logics. One of the aspects of this posture is naturally linked to the anticipation of risks and breaches capable of reaching the existing capital, especially in its relationship to employmentemployment being a major preoccupation in the eyes of the resident (Herbaux, 2006).

Yet, this conclusion must not submit territorial intelligence to the 'all economic', which would be a bit simplistic; if employment, by and large economy, is one of the keys to multiple awareness a systemic vision is required here. It was developed by Girardot (2004), among others, in his multi-level governance concept. To back up this statement, it is to be noted that the treatment of information in economics -and especially so within competitiveness poles -undergoes a structure pressure, that of its participants' cultural heterogeneity. Strategic cursors do not lie at the same level; regional or almost Europeans for some, and de facto worldwide in the case of international firms' branches.

Hence the necessity for a preliminary conclusion: Within these organisations, the spreading of information oscillates between the landmarks of local polarisation of worldwide diffusion.

A double movement

Local polarisation

The initiated movement of cognitive concentration within the territorial intelligence collective logics is now being amplified in France through the existence of competitiveness 512 poles 54 . Nevertheless and according to Musso (2005), one should differentiate between the aspect of knowledge management dealing with cognitive capacities and knowledge management dealing with the field of applied knowledge, which generates a capacity for apprenticeship. In this last instance, the tacit (individual capitalisation) turns into explicit (formalisation of knowledge) and allows what we call 'individual unformulated' (Herbaux, ibid) to become shared knowledge. This is what network adherence implicitly benefits.

The territory or country is where informal communication per se and combined with unspoken things gives a rhythm to exchanges between humans. Somehow, this equates a capitalisation of culture in the best possible scenarii by placing itself within the development project. At a local level, rites, heroes, symbols and values which make up its genesis, create the stage for signs and postures (Bourdieu's habitus, 1994), thus establishing some grammar for communication which founds the local group's identity. Therefore, the combination of scientific, experiment, empiric and industrial inputs turn the local into a place of generation of rare resources (Bertacchini, 2005).

Worldwide diffusion

Indigenous traditional undertakings, a few spin-offs and quite often branches of worldwide firms which like to immerse their research and development services blossom on this concentrated knowledge soil. The outcome of that research then feeds a worldwide spreading of processes into established networks, in a logic of globalisation.

It can be then considered that local resources (or the management of knowledge) is perceived and these majors' branches take part in it before they spread them throughout the world in order to conquer new markets. This conclusion is linked with what Polanyi (1983) observed: 'the expression of the tacit is linked with geographical proximity; its scattering is tied to the progressive codification of unformulated knowledge which progressively turns it into explicit knowledge 55 '.

Elaboration of local construction

A paradox lies in the fact that the building up of explicit knowledge within a territory may eventually be used by those whose power allows them to access worldwide network diffusion. Concretely and among other things, the existing nuances of culture between big and small businesses translate into a relationship which is different from information systems.

The majors established their network on the basis of an interactive system where information lies at the heart of strategic survival. Thus, the capacity a decision centre takes 54 Initiated in France as soon as 2004, competitiveness poles make a few of Porter's statements -from his June 1998 publication, The Competitive Advantage of Nations -theirs. In short, This is about taking the global strategy for a territory so as to enforce a common strategy of economic development into account.. The latter aims at gaining a critical mass in order to bring some high added value technology to markets with a serious potential for development. 55 Therefore, tacit knowledge is more difficult to manage and to exploit. Its explicit knowledge valuability then is transferable and explainable through a code, i.e. a scientific or technical language. 513 to react live conditions its access and its duration on new high added value markets. There, the mutualisation of information through a substantial use of ICT (Information and Communication Technology) is of a structural nature.

The local SME, sometimes involved in a competitiveness pole, more seldom has expertise in this culture of mutualisation and if technical tools do exist, practices are not in accordance with expected uses. Obstacles seem to be of a more cultural nature (power and information) rather than technological.'Language and writing are two distinct sign systems: the second one's sole reason for being is to represent the first one', de Saussure said. Wouldn't the difficulty to overcome the 'coffee machine' transmission phase be linked with lived deals? And for some structures: limited to SME confinement?

THE DELPHI SURVEY

Expérimental scheme

Since 2001, the research-action endeavour led on the regional environment Nord-Pas de Calais was part of a survey on the treatment of information at a territorial level. The aim was to back up enforcement on territorial intelligence scheme and question its efficiency.

Backing up a regional programme funded accordingly to State guidelines had allowed this research-action in a programme which had made many actors from institutional, economic and academic background sectors involved 56 . Within this regional plan, 53 companies were thus helped in their enforcing an integrated information system and this is the object of the survey dealt with here.

Interest

When having to express themselves publicly on a personal position, some individuals taking part in a workshop do not always give their genuine opinion. Pressure coming from the group and from the expressed or tacit majority creates self-censorship limiting some participants to silent agreement. Therefore, it is important to address what Neumann 57 named a spiral of silent, i.e. the growing pressure individuals within a group undergo to preserve their opinions whereas feeling they are a minority.

The choice of investigation method must allow all opinions to spring while minimising active and implicit pressures. Anonymity is part of this expression. In a context of SMEs involved in a quality survey, it is important that each actor has a good understanding of the project, of the analysis mechanism and of the aims sought by the initiator. This is an essential factor for the success of a quality survey. Among the few existing quality survey techniques (individual interview, experience investigation, projective case study etc.), the Delphi method appeared to be the most compatible with the sought goal: use the 56 534 companies were made aware, 134 individuals representing institutions 400 or so students. Training for 104 SME actors and 80 consultants. Initiation and follow-up for 53 companies and 162 executives and managers. 57 Elisabeth-Noelle Neumann, sociologist and professor emeritus from the University of Mainz. 514 experience feedback from a population initiated to territorial and economic intelligence processes.

Initially, the Delphi method was elaborated by RAND Corporation as soon as 1969 and it is a process of group decision following a classical thesis, antithesis and synthesis structure. It is led via successive -and if possible anonymous -questions asked by a group of actors, in most cases experts in the specific field. Used among other things in the field of human sciences, it allows to find better consensus answers to a controversy complex topic or offers a debated alternative to the issue studied. A final meeting physically gathering participants validates a collective opinion on each topic tackled.

Methodology

The classical Delphi methodology was adapted to the context. Some aspects were adapted or rehandled.

The survey led during the last three months of 2005 benefited from three Master 1 students' implication. It was about a group of companies who had taken part in the 2001-2005 experimental regional plan. Out of the 53 companies involved in this regional action, only 47 (their spoke-persons) did effectively take part in this survey. The typology of these structures, designated as employing between 2 and 200 people, was established in sectors of metal undertaking, biochemistry, printing, services, food industry and manufacture.

In order to escape group pressure, and thanks to an individual number, each actor anonymously and electronically 58 replied to the conclusion proposed by collective thoughts. The use of electronic work group may be perceived as a 'facilitator' for that type of survey. Yet, it does not prevent physical gatherings between all the experts when discussing its synthesis.

Progressive agreements reshape the answers which are then processed with each occurrence 59 . Extreme views are mentioned during general debates until a consensus is possibly come to. Nonetheless, the latter is not always reached and it must end up on two detailed positions.

The three survey themes were put to participants in the form of a questionnaire made up of 18 propositions, i.e. six for each theme.

Procedure: following an individual phone interview during which the participant agrees to be part of the survey, a message of explanation is sent by e-mail bearing the campus and survey address. Answers are continuously recorded under an electronic Adobe file. Data are filed automatically then put into a chart on Excel.

Graphic results after each occurrence (Delphi1, 2,3...) are then sent to each participant and simultaneously capitalised on the campus. Thus, experts can appreciate the evolution of 58 Questionnaire electronically treated as Adobe Reader file 59 Repetitive process represents between 2 and 4 minutes for each occurrence and allows each expert to refine his or her opinion as exchanges go by. 515 agreements and disagreements on the discussed issues progressively thanks to the synthesis graphic changes and thanks to the capitalised footprints of respective opinions.

THE CSDIL SYSTEM

Introduction

In the context of this summary, the reader is spared the whole survey process for the benefit of a synthesis on the three aspects of questions.

The analysis of exchanges and their being put into perspective allowed to suggest a few recommendations -gathered together under the acronym 'CSDIL' (CADIE in French) -to the operators involved in the territorial intelligence logics. This acronym, CSDIL, sums up the five aspects of recommendations born from the analysis the group of experts consulted came up with, namely:

-Communication -Support -Duration -Implications -Listening
It does not pretend to be an unchangeable rule but it expresses the return of experience of a group of actors having taken part in a regional experimental territorial intelligence scheme. For each item, a few conclusions and suggestions agreed to by experts, executives or officials from partner SMEs were presented.

Communication

a) The communication plan for territorial intelligence grounds must insert itself in time; without being continuous it still must provide support for key phases of the operation.

b) Institutional communication tends to swallow the part of actors or reduce them to a mere witness function.

c) The managing of the communication budget is most often secured by the project manager; partners too ought to be associated to it. -endogenous support by a qualified and competent consultant.

Support

516

-exogenous support by a benchmarking of practices within a company club that gathers monthly.

Duration

The enforcement of an information treatment system must comply with existing information systems within the administrative Region as well as the State. This action bearing a systemic feature cannot be subjected to precipitation.

a) The lay-out of a territorial intelligence scheme over 7 or 8 years allows noncontinuous interventions, be they technical or of a financial support nature. Globally, this does not increase the cost.

b) The preparation of a territorial intelligence plan often depends on State and regional services. An agency effect 60 occurs in that the initiator and the beneficiary naturally have different visions of the future programme (e.g.: set over time for involved organisation and short-term aims for the project management).

Implications

Experts recognised the existence of considerable dynamics for enforcement between SMEs and the whole of partners within experimentation. But this tie needs to be fuelled, animated and valued throughout time on the basis of a few pre-requisites: a) Check prior aware adherence of SMEs wishing to get involved in a regional territorial intelligence scheme; b) Choose consulting cabinets genuinely specialised in association with younger cabinets; c) Make information transfers between institutions (customs, police, county authorities, tax administration etc.) and SMEs more fluid.

listening

a) Collective elaboration of the regional territorial intelligence (institution, company, civilians) b) Acknowledging a company's facts in a momentary interruption of its participation (choice of human resources affectation with regards to emergency). c) Gradual and personalised access (assimilation time for various practices, according to organisations). 60 Agency effect: unbalance caused by the knowledge one of the parties may have of the future development of a convention.

CONCLUSION

If public investment generated short-term results in terms of territorial intelligence in the SME sector, it globally did not resist the ordeal of time in order to go from an initiation phase to a development one.

The operational taking over, inherent to the weight and burdens of State initiatives and Regional ones, must be established in the first stages of a regional territorial intelligence scheme. It thus avoids a gap in the help provided for actors and organisations involved, and therefore acts towards a capitalisation of processes and results.

Throughout exchanges, the word 'culture' was regularly used: 'this is not our culture', 'this is about a radical change in culture', 'you cannot achieve a revolution in culture every day'.

In such cases, how could SMEs be better associated with a logic of territorial governance without them thinking they might loose their 'soul' in it? The issue is not of a technical or a technological nature but rather of an anthropological one. Time is the most demanding factor within a SME' one participant said.

The management of time is the main critical factor yet to be tamed for the enforcement of a regional territorial intelligence plan. Item B6: Pensez-vous que la mise en oeuvre d'un système intégré de traitement de l'information pour une Pme/Pmi, demande une discrétion qui n'est pas obtenue dans le cas d'une adhésion à un programme régional?

C) Volet Information et pouvoir

Item C1: Concevez-vous que la mise en oeuvre d'un système de traitement de l'information dans une entreprise renforce le pouvoir du dirigeant?

Item C2: Pensez-vous que l'organisation du système d'information dans l'entreprise le rend plus accessible à la malveillance?

Item C3: Etes-vous sensible au fait que l'apprentissage puis la pratique de mutualisation de l'information peut agir sur le climat social de l'entreprise?

Item C4: Considérez-vous que le décideur doit bénéficier seul des ultimes informations stratégiques?

Item C5: Constatez-vous que la compréhension du projet de l'entreprise par les partenaires d'un plan régional d'intelligence territorial est bien souvent limitée?

Item C6: Etes-vous de ceux qui avancent que mettre en oeuvre un système mutualisé de traitement de l'information au sein de l'entreprise, c'est offrir des clés de décision au tiers.

a)

  Institutional financial support to organisations participating should last several years. b) There can be two types of technical support:

Fig 1 .

 1 Fig 3. Synthesis of Delphi 5

  Item B1: Considérez-vous que le financement public est déterminant pour l'engagement de la Pme/Pmi dans un processus d'intelligence territoriale? Item B2: Jugez-vous les financements subsidiaires accordés aux Pme/Pmi engagées dans le processus d'intelligence territoriale insuffisants? tardifs? trop contraignants par les rapports et données à établir? Item B3: Avez-vous le sentiment, et ce dans le cadre d'un programme régional, que les administrations et institutions partenaires sont très accessibles à vos requêtes? Item B4: Vous constatez que le soutien public est fixé pour une durée continue; concevez-vous qu'il puisse être séquencé sur plusieurs années? 521 Item B5: Jugez vous que les structures bénévoles de conseil (ressources humaines, information, communication etc.) sont peu ou pas représentées dans le plan régional d'intelligence territoriale?

	Annexe 2. Questionnaire
		ENQUETE -questionnaire-
	Les trois volets d'affirmations inductives comportent 18 items. Les réponses se ventilent
	en six options: a) entièrement d'accord b) plutôt d'accord c) indécis d) plutôt peu d'accord
	EXPERTS/ QUESTIONS e) pas d'accord f) opinion non exprimée. Les participants sont invités à renvoyer le 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47
	QA1 QA2 questionnaire électronique à nouveau coché après chaque échange collectif. Les synthèses
	QA3 QA4 graphiques paraissent aussitôt sur le groupe de travail électronique Claroline © ; elles
	QA5 QA6 traduisent l'évolution des positions du groupe.
	QB1
	QB2
	QB3 QB4 A) Volet partenariat et durée
	QB5 QB6 QC1 Item A1: A votre avis, le partenariat est-il nécessaire à la réalisation de votre projet
	QC2 QC3	intégré de système de collecte et de traitement de l'information?
	QC4 QC5 QC6 Item A2: Pensez vous qu'une durée d'accompagnement technique de 6 mois est suffisant
		pour la mise en oeuvre d'un dispositif de traitement de l'information dans une
		Pme/Pmi?
	réponses/ questions Item A3: Jugez vous que l'accompagnement ne tient pas assez compte des variations 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47
	QA1 QC6	brutales du plan de charge de l'entreprise engagée (commande urgente, rupture
	QC3 QC1	de stock etc.)
	QB5
	QA2 QC2 Item A4: Êtes vous d'accord avec cette remarque: «la multitude de partenaires engagée
	QA6 QB2	dans l'opération expérimentale d'intelligence territoriale en rend
	QB4 QC4	progressivement la finalité floue»?
	QA5
	QB1 QB3 Item A5: Pensez-vous que le système partenarial devrait s'inscrire pour chaque enjeu
	QA3 QA4	(recueil, traitement, formation etc.) de façon articulée et pour une période plutôt
	QC5 QB6	pluri-annuelle?
	Item A6: Avez-vous l'impression que la lisibilité des missions pour chaque partenaire est
		claire pour chaque entreprise (institutions, prestataires choisis par appel d'offre,
	réponses/ questions	1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 financeurs etc.)
	QB6
	QB2 QB5 b) Volet soutien public
	QC3
	QB4
	QB1
	QA4
	QC1
	QB3
	QA1
	QA6
	QA3
	QA2
	QC4
	QA5
	QC5
	QC2
	QC6
		520

Girardot J. J., «intelligence territoriale et participation» 5° colloque TIC et territoire, Besançon 2006.


P Bonifacio

E Caffau

H.-G Ludwig

Cu i resonance lines in turn-off stars of NGC 6752 and NGC 6397. ⋆ Effects of granulation from CO5BOLD models

Keywords: Hydrodynamics -Line, formation -Stars, abundances -Galaxy, globular clusters -NGC 6397, NGC 6752

Context.

Copper is an element whose interesting evolution with metallicity is not fully understood. Observations of copper abundances rely on a very limited number of lines, the strongest are the Cu i lines of Mult. 1 at 324.7 nm and 327.3 nm which can be measured even at extremely low metallicities. Aims. We investigate the quality of these lines as abundance indicators. Methods. We measure these lines in two turn-off (TO) stars in the Globular Cluster NGC 6752 and two TO stars in the Globular Cluster NGC 6397 and derive abundances with 3D hydrodynamical model atmospheres computed with the CO5BOLD code. These abundances are compared to the Cu abundances measured in giant stars of the same clusters, using the lines of Mult. 2 at 510.5 nm and 578.2 nm. Results. The abundances derived from the lines of Mult. 1 in TO stars differ from the abundances of giants of the same clusters. This is true both using CO5BOLD models and using traditional 1D model atmospheres. The LTE 3D corrections for TO stars are large, while they are small for giant stars. Conclusions. The Cu i resonance lines of Mult. 1 are not reliable abundance indicators. It is likely that departures from LTE should be taken into account to properly describe these lines, although it is not clear if these alone can account for the observations. An investigation of these departures is indeed encouraged for both dwarfs and giants. Our recommendation to those interested in the study of the evolution of copper abundances is to rely on the measurements in giants, based on the lines of Mult. 2. We caution, however, that NLTE studies may imply a revision in all the Cu abundances, both in dwarfs and giants.

Introduction

There is no wide consensus on the nucleosynthetic origin of copper, and the complex picture drawn by the observations has no straightforward interpretation. Multiple channels can contribute to the production of this element. According to Bisterzo et al. (2004) there are five such channels: explosive nucleosynthesis, either in Type II supernovae (SNII) or in Type Ia supernovae (SNIa), slow neutron capture (s-process), either weak (i.e. taking place in massive stars in conditions of hydrostatic equilibrium during He and C burning) or main (i.e. occurring in the inter-shell region of low-mass asymptotic giant branch stars) and the weak sr-process. The latter occurs in massive stars in the C-burning shell when neutron densities reach very high values, intermediate between typical s-process neutron densities (10 9 -10 11 cm -3 ; Despain 1980) and r-process neutron densities (10 20 -10 30 cm -3 ; Kratz et al. 2007). The contribution of the s-process, both weak and main, to the solar system Cu abundance is estimated by Travaglio et al. (2004a) to be 27%. Explosive nucleosynthesis in SNII can account for 5% to 10%

Send offprint requests to: Piercarlo.Bonifacio@obspm.fr ⋆ Based on observations made with the ESO Very Large Telescope at Paranal Observatory, Chile (Programmes 71.D-0155, 75.D-0807, 76.B-0133) ⋆⋆ Gliese Fellow of the solar system Cu (Bisterzo et al. 2004). The contribution of SNIa is probably less well known, however, as pointed out by McWilliam & Smecker-Hane (2005), the available SNIa yields of Cu are rather low (Travaglio et al. 2004b;Thielemann et al. 1986). Bisterzo et al. (2004) claim that the bulk of cosmic Cu has indeed been produced by the weak sr-process.

Observations of copper abundances in Galactic stars show a decrease in the Cu/Fe ratio at low metallicities. This was first suggested by Cohen (1980), on the basis of the measurements in giant stars of several Globular Clusters of different metallicities (Cohen 1978(Cohen , 1979(Cohen , 1980)). It was not until the comprehensive study of Sneden et al. (1991) that this trend was clearly defined in a robust way, resting on measurements in a large sample of stars. Recent studies of field (Mishenina et al. 2002;Bihain et al. 2004) and Globular Cluster stars [START_REF] Shetrone | [END_REF](Shetrone et al. , 2003;;Simmerer et al. 2003;Yong et al. 2005) have confirmed this trend (see Fig. 1 of Bisterzo et al. 2004). Somewhat at odds with these general results are the observations of the Globular Cluster ω Cen (Cunha et al. 2002;Pancino et al. 2002). Even though this cluster shows a sizeable spread in metal abundances (-2.20 ≤ [Fe/H] ≤ -0.70, [START_REF] Johnson | [END_REF], the Cu/Fe abundance ratio is nearly constant, with no discernible trend.

Observations in Local Group galaxies [START_REF] Shetrone | [END_REF](Shetrone et al. , 2003) ) show that metal-poor populations display low Cu/Fe ratios, similar to what is observed in Galactic stars of compara-Fig. 1. Cu i 324.7 nm line in the programme stars. The spectra are displaced vertically by 0.4 units, with respect to each other, for display purposes. ble metallicity. However, McWilliam & Smecker-Hane (2005) noted that the metal-rich population of the Sgr dSph displays considerably lower Cu/Fe ratios than Galactic stars of comparable metallicity. This result is confirmed by the measurements of Sbordone et al. (2007), who also include stars of the Globular Cluster Terzan 7, associated to the Sgr dSph.

The majority of the Cu measurements are based on the Cu i lines of Mult. 2 1 , sometimes one line of Mult. 7 is used. The exceptions are the measurements of Bihain et al. (2004) and Cohen et al. (2008), who use the resonance lines of Mult. 1 and Prochaska et al. (2000) who, to our knowledge, are the only ones who have made use of the strongest line of Mult. 6 in the near infrared. While for stars of metallicity above -1.0 one may have a choice of several lines to use, when going to metal-poor stars, for instance below -1.5, the only usable Cu abundance indicators are the two strongest lines of Cu i Mult. 2 in giant stars and the resonance lines of Mult. 1 in both dwarfs and giants. The advantage of the lines of Mult. 1 is that they are very strong, at high metallicity they are strongly saturated and therefore not ideal for abundance work, but, they remain measurable down to an extremely low metallicity. Bihain et al. (2004) have been able

1 we refer to the multiplet designation of Moore (1945) Fig. 2. Cu i 327.3 nm line in the programme stars. The spectra are displaced vertically by 0.4 units, with respect to each other, for display purposes.

to measure the 327.3 nm line in the extremely metal-poor dwarf G64-12 ([Fe/H]∼ -3). Observationally the main disadvantage of Mult. 1 is that it lies in the UV, fairly near to the atmospheric cut-off. A very efficient UV spectrograph, like UVES and a large telescope, like VLT, may circumvent this problem. There are many spectra suitable for the measurement of the Cu i lines of Mult. 1 in stars of different metallicities in the ESO archive2 . The main purpose of our investigation is to assess the quality of the Cu i lines of Mult. 1 as abundance indicators. Our strategy is to compare for the first time Cu abundances in main sequence and giants of the same cluster, because Cu is not expected to be easily destroyed or created. This test will indicate the reliability of our modelling. Globular Clusters NGC 6397 and NGC 6752 span an interesting range in metallicity -2.0 to -1.5, which is relevant for a large fraction of the observations in field stars.

Observations and equivalent width measurements

The spectra analysed here are the same as in Pasquini et al. (2004) and Pasquini et al. (2007) and described in the above pa- pers. They were obtained with the UVES spectrograph [START_REF] Dekker | Proc. SPIE[END_REF] at the ESO VLT-Kueyen 8.2m telescope. We here use the blue arm spectra, which are centred at 346 nm. Both clusters were observed with a 1 ′′ slit and a 2 × 2 on-chip binning, which yields a resolution of about 40 000. The reduced spectra were downloaded from the ESO archive, thanks to the improved strategies for optimal extraction [START_REF] Ballester | Proc. SPIE[END_REF]), the S/N ratios are greatly improved compared to what was previously available. The equivalent widths (EWs) of the two Cu i lines of Mult. 1 were measured with the IRAF task splot and are provided in the on-line Table 6.

In addition to the four cluster stars we analyse the field star HD 218502 as a reference. Its atmospheric parameters are close to those of the cluster stars. For this star we work with the data used by Pasquini et al. (2004) as well as with the data observed in 2005, in the course of ESO programme 76.B-0133 (see Smiljanic et al. 2008). For this star we used six spectra: two with 1. ′′ 0 and 2 × 2 binning, two with 1. ′′ 0 and 1 × 1 binning, two with 1. ′′ 2 and 1 × 1 binning. Each pair of spectra was coadded, the equivalent widths were measured on the coadded spectrum and then the three equivalent widths were averaged. The spectra of all the five stars analysed here are shown in Fig. 1 and2.

One of the goals of the present analysis is to compare the Cu abundances in the TO stars with those measured in giant stars of the same cluster. For NGC 6752 we can rely on the recent analysis by Yong et al. (2005), who analysed 38 giants in this cluster, making use of high-resolution high-S/N ratio UVES spectra. The atomic data used by Yong et al. (2005) are the same as those here used. The analysis is based on 1D ATLAS models and LTE spectrum synthesis. That the ATLAS models employed by Yong et al. (2005) use the approximate overshooting option in ATLAS, while those we use do not, brings about only minor differences. Thus the measurements of Yong et al. (2005) are directly comparable to our own. The measurements of Yong et al. (2005) are, however, based only on the strongest line of Mult. 2. Because we aim to compare the abundance derived from the lines of Mult. 1 and Mult. 2 we retrieved UVES reduced spectra of one of the stars of Yong et al. (2005) from the ESO archive: Cl* NGC 6752 YGN 30. We used three spectra of 1800 s obtained with the dichroic # 1, the blue arm spectrum was centred at 346 nm and the red arm spectrum at 580 nm. The slit was set at 1. ′′ 0 in the blue arm and 0. ′′ 7 in the red arm; the CCD binning was 1 × 1 for both arms. The corresponding resolution is ∼ 45 000 for the blue arm and ∼ 60 000 in the red arm.

For the cluster NGC 6397, though, we were unable to find any recent analysis that included the measurement of Cu. In fact the only measurement of Cu in this cluster which we could find is due to Gratton (1982). In order to make the Gratton (1982) measurements directly comparable to our own we used the published EWs of the Cu i lines of Mult. 2 and derive the abundances with our models, spectrum synthesis codes, and atomic data.

Cu abundances

Atomic data

To determine the Cu abundances for the TO stars we used the Cu i resonance lines of Mult. 1 at 324.7 nm and 327.3 nm. The log g f values were taken from Bielski (1975) and the hyperfine structure and isotopic shifts for the 63 Cu and 65 Cu isotopes from [START_REF] Kurucz | [END_REF]. We used the same sources for the two lines of Mult. 2 at 510.5 nm and 587.2 nm that we used for the giant stars. The line list used for the computations is given on-line in Table 5. The line at 327.3 nm is free from blends in metal-poor TO stars and the continuum is usually easily determined. The stronger 324.7 nm line, though, lies in a more complex spectral region. The only truly blending feature is a weak OH line (324.7615 nm), but, the line is on the red wing of a complex blend, mainly of iron lines, of which several have poor log g f values. The continuum is more difficult to determine for this line, given the larger line crowding in this region. We experimented with different choices for the Van der Waals broadening of the lines, the ABO theory (Anstee & O'Mara 1995;[START_REF] Barklem | [END_REF]Barklem et al. 1998a,b) and the WIDTH approximation (Kurucz 1993a[START_REF] Kurucz | [END_REF][START_REF] Castelli | [END_REF], see also Ryan 1998). For the transitions under consideration the WIDTH approximation and the ABO theory yield almost identical values.

Atmospheric parameters

The adopted atmospheric parameters for our programme stars are given in Table 1 and were taken from Pasquini et al. (2004) and Pasquini et al. (2007). For the giant star Cl* NGC 6752 YGN 30 we adopted the atmospheric parameters of Yong et al. (2005). For the two giants in NGC 6397 we adopted the atmospheric parameters of Gratton (1982). For the reader's convenience the atmospheric parameters of the giant stars are provided here online in Table 7.

Model atmospheres and spectrum synthesis.

For each star we computed a 1D model atmosphere using version 9 of the ATLAS code (Kurucz 1993a[START_REF] Kurucz | [END_REF] under Linux (Sbordone et al. 2004;Sbordone 2005). We used the opacity distribution functions described by [START_REF] Castelli | IAU Symposium[END_REF] and microturbulent velocity 1 km s -1 , the mixing-length parameter, α MLT , was set to 1.25, and the overshooting switched off. This model atmosphere was used as input to the SYNTHE code (Kurucz 1993b[START_REF] Kurucz | [END_REF], with different Cu abundances, to compute a curve-of-growth for each line. The Cu abundances were derived by interpolating in these curves of growth. The corresponding abundances are given in the second column of Table 2, the σ is the variance of the abundances of the two lines. The abundances for the individual lines can be found on-line in Table 6.

The use of three dimensional hydrodynamical simulations to describe stellar atmospheres (hereafter 3D models) has led to the important notion that the outer layers present steeper temperature gradients than predicted by traditional 1D static model atmospheres (Asplund et al. 1999;Asplund 2005;[START_REF] González Hernández | [END_REF] and that this effect is considerably more pronounced for metal-poor stars. In addition to the different mean temperature profile, the 3D models differ from traditional 1D models because they account for the horizontal temperature fluctuations. Both effects may or may not be important, depending on the line formation properties of the transition under con-

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 A(Cu) -2.4 -2.2 -2.0 -1.8 -1.6 -1.4
Log(EW/λ) Fig. 3. Curves of growth (COG) for the Cu i 327.3 nm transition. The dotted line to the left is the COG for the 3D model d3t63g40m20n01, the three solid lines to the right are those for the corresponding 1D LHD model for three values of the microturbulent velocity: 0.5, 1.0 and 1.5 km s -1 , bottom to top. The dashed line is the 3D COG shifted arbitrarily by +0.58 dex along the x-axis. This highlights that the shape of the 3D COG differs from that of the corresponding 1D COGs and therefore the 3D correction depends on the EW of the transition. sideration. In order to investigate these effects for the Cu i lines we used several 3D models computed with the code CO 5 BOLD (Freytag et al. 2002(Freytag et al. , 2003;;Wedemeyer et al. 2004). The characteristics of the 3D models employed in this study are given in Table 3. The line formation computations for the 3D models were performed with the Linfor3D code3 . For each 3D model we used also two reference 1D models: the 3D and the 1D LHD , which we define below.

The 3D models are computed on-the-fly by Linfor3D by averaging the 3D model over surfaces of equal Rosseland optical depth and time. The 3D model has, by construction, the mean temperature structure of the CO 5 BOLD model, therefore the difference in abundance A(3D)-A( 3D ), allows us to single out the effects caused by temperature fluctuations (see Caffau & Ludwig 2007).

The 1D LHD model is a 1D, plane parallel, LTE, static, model atmosphere and employs the same micro-physics and opacity as the CO 5 BOLD models; it is computed with the LHD code. These models are our models of choice to define the "3D correction" as A(3D) -A(1D LHD ), where A is the abundance of any given element. More details on the LHD models may be found in Caffau & Ludwig (2007) and Caffau et al. (2010).

In any given Linfor3D run we made computations also for the 3D model and for a 1D LHD model, with the same T eff , log g, and metallicity as the 3D model.

The computation of a 3D model is still very time consuming, even on modern computers (several months), it would be impractical to compute a specific 3D model for any set of our atmospheric parameters. Our strategy is therefore the following: we perform an abundance analysis with ATLAS model atmospheres computed for the desired set of atmospheric parameters; we use a grid of 3D models with atmospheric parameters that bracket the desired ones and compute the relevant 3D corrections by linear or bi-linear interpolation in the grid, as appropri- The line formation computations were performed using SYNTHE for the ATLAS models and Linfor3D for all other models. As a consistency check we used Linfor3D with an ATLAS model as input and verified that the line profiles and EWs are consistent with the results derived from SYNTHE+ATLAS. The difference between the two line formation codes amounts to a few hundredths of dex in terms of abundance, a quantity that is irrelevant with respect to the size of the 3D corrections under consideration.

For three out of the six TO stars under study, the Cu i lines are strong (EW> 4.0 pm), therefore they are surely in the saturation regime. Their 3D correction depends on the adopted microturbulence in the adopted reference 1D atmosphere. To take this into account, different 1D LHD curves of growth were computed with microturbulent velocities of 0.5, 1.0 and 1.5 km s -1 , to allow us interpolation to any desired value of ξ. For weaker lines the microturbulent velocity does not play a fundamental rule, so that the 3D correction is mostly insensitive on the choice of this parameter. We find that the 3D curve of growth is not a simple translation of a 1D curve of growth, but has a distinct shape. An example to illustrate the effect is shown in Fig. 3. An immediate consequence is that for all lines we considered, the 3D correction depends on the EW, even for the weaker lines. We note that the dependence of the 3D correction on the microturbulence implies that the abundance obtained by applying the correction to an abundance derived from a 1D model depends on the adopted microturbulence. One of the reasons to prefer the use of 3D models is to avoid the use of this parameter. The correct way to treat this is, not to use the 3D correction, but to derive the abundance by an interpolation in a set of 3D curves of growth, or to use suitable fitting functions, as done for lithium by [START_REF] Sbordone | A&A in press[END_REF]. But this requires the use of a larger set of 3D models, which bracket the effective temperatures of the studied stars. For the purpose of the present exploratory investigation we believe the approach of using 3D corrections is adequate, especially because the conclusion of the study is that 3D-LTE abundances are unreliable. Finally we point out that it may be that current 3D models do not correctly capture turbulence at small scales (Steffen et al. 2009). If this were indeed the case all abundances derived from saturated lines are doubtful, whether they are de- We therefore computed the 3D correction for each of the measured EWs for each of the relevant 3D models. In general the 3D correction will also depend on the treatment of convection in the 1D reference model, hence on the adopted α MLT . The lines under consideration do not form in the deepest layers, which are the most affected by the choice of α MLT , thus they are insensitive to it. All 1D LHD models employed have α MLT = 1.0. The computed A(3D) -A(1D LHD ) corrections, as well as the A(3D) -A( 3D ) corrections are given on-line in Table 8. The 3D abundances provided in Table 2 are obtained by applying to the 1D abundances the 3D corrections in Table 6, which were obtained by interpolating the corrections in Table 8.

The six stars under study have very similar effective temperatures. All are within roughly 100 K of the effective temperatures of the 3D models listed in Table 3 (T eff ∼ 6300 K). Therefore it is not necessary to include more 3D models and perform an interpolation in T eff . The metallicities and gravities of the models in Table 3 bracket the metallicities and gravities in Table 1. We used a bi-linear interpolation in metallicity and gravity for the two stars of NGC 6752 and for HD 218502. The three stars of NGC 6397, though have a metallicity of almost -2.0, therefore a linear interpolation in surface gravity was sufficient.

The computation of 3D models for typical giant stars is much more time consuming than for F-type and cooler dwarfs. The radiative relaxation time in the surface layers of warm giants becomes significantly shorter than the dynamical time scale, which makes it computationally expensive to properly capture the time evolution of the system. At present we have only two fully relaxed models of metal-poor giants. The parameters are given in Table 3 and the metallicities are -1.0 and -2.0. The surface gravity is larger than that of the majority of the giant stars analysed in either cluster. Only the faintest stars analysed by Yong et al. (2005) have parameters T eff and log g close to those of our giant models. In spite of this we believe that we can use the 3D corrections derived from this model, as a first order approximation as representative of the corrections in giant stars of both clusters. This is possible because the 3D corrections are rather small, especially when compared to those of dwarf stars. This is partly because giant 3D models do not show a pronounced over-cooling, compared to 1D models, as dwarfs display. This conclusion is also based on the examination of several snapshots of not fully relaxed giants of different atmospheric parameters, which we are in the process of computing. The 3D correction for the giant models is -0.1 dex for both the examined Cu i lines of Mult. 2 for the model of metallicity -2.0 and 0.0 dex (actually +0.01) for the model of metallicity -1.0. We apply a correction

Results

HD 218502

The analysis of the reference star HD 218502 shows that the abundances derived from the two Cu i resonance lines (Table 6) agree well, both with 1D and 3D models. This gives us confidence in the reliability of the atomic data used. It also suggests that with good quality data, the EWs of both lines can be satisfactorily measured in spite of the complexity of the spectral region, especially for the 324.7 nm line. Our 1D abundance (A(Cu)= 1.52 ± 0.09) agrees, within errors with what reported by Bihain et al. (2004, A(Cu)= 1.70 ±0.17). We note a small difference in the effective temperature adopted in the two analyses (about 100 K) and a difference in the data: our UVES spectra are of considerably higher quality than the CASPEC spectra used by Bihain et al. (2004), who measured only the 327.3 nm line. This agreement is expected because the atomic data are the same in the two analyses and the 1D model atmospheres used are similar, the main difference being the overshooting. This check suggests that we may reasonably assume that our Cu abundances should be consistent with those of Bihain et al. (2004), which are based on the UV resonance lines. An inspection of Fig. 6 of Bihain et al. (2004) suggests that these measurements substantially agree with those of Mishenina et al. (2002), which are essentially based on the measurements of the lines of Mult. 2. Yet one should take into account the large error bars that derive from the relatively poor S/N ratio that is achievable in the UV range.

The 3D correction for the lines of Mult.1 is large and the 3D abundance in this star is well below all the measurements in giant stars of similar metallicity. An application of 3D corrections to all measurements of Bihain et al. (2004) would probably break the agreement with the measurements of Mishenina et al. (2002). We have inspected the available red spectra of HD 218502, to see if any of the lines of Mult. 2 could be detected, but this was not the case.

TO stars in NGC 6752 and NGC 6397

For the cluster stars there is also a good consistency between the abundances derived from the two resonance lines for any given line, in spite of the much lower S/N ratios in the cluster stars. This suggests that there is no major inconsistency in the EW measurements.

The weighted mean 4 of the abundances of the clusters, reported in Table 4, displays an error in the mean that is reasonably small. We believe that the mean abundances for the two clusters obtained from the dwarf stars are indeed representative of the Cu i abundance derived from the lines of Mult. 1. Considering that each spectrum of a TO star in these clusters amounts to about 10 hours of integration with UVES, it is unlikely that in the near future better data or data for a larger number of stars will be available, although it would clearly be desirable.

Star Cl* NGC 6752 YGN 30

In this star, like in the other giant stars observed by Yong et al. (2005), both the lines of Mult. 1 and of Mult. 2 are measurable, which provides for a consistency check. We did not measure the line at 324.7 nm since the region is extremely crowded in these cool giants, but the line at 327.3 nm is clean and unblended. For Mult. 2 we only measured the 510.5 nm line, since the other line is not present in the spectrum, because it falls in the gap between 4 The error on the weighted mean has been taken to be the largest between

1 σ 2 i -1 and 1 σ 2 i -1 × 1 (n-1) (x i -<x>) 2 σ 2 i
, where x i are the data points σ i are the associated errors, x is the mean value and n is the number of data point (see e.g., Agekan 1972, pages 144-150).

the two CCDs. The two lines (324.7 nm and 510.5 nm ) provide inconsistent results, the line of Mult. 1 provides an abundance that is 0.54 dex higher than that of the line of Mult. 2 (see online Table 6). The abundance we derive from the line of Mult. 2 substantiallly agrees with the measure of Yong et al. (2005), our abundance is 0.13 dex smaller. Of this difference 0.05 dex are because we use ATLAS models without overshooting, while Yong et al. (2005) use models with overshooting, the remaining difference should be attributed to a difference in the measured EW and possibly to the different spectrum synthesis codes used (MOOG by Yong et al. 2005 and SYNTHE by us). The 3D corrections for both lines of Mult. 1 and Mult. 2 are small and agree to within a few hundredths of dex. The abundance from the two lines cannot be brought into agreement by using 3D models.

Giant stars in NGC 6397

The error in the mean of the two giants is 0.18 dex, which is essentially identical to the estimate of Gratton (1982) of 0.2 dex on the copper abundance. Even making use of 1D models the abundance of the giant stars is considerably higher than in the dwarf stars.

Effects of atmospheric parameters

We intend to quantify the effect of changing atmospheric parameters on the derived abundances. The abundances derived from the Cu i resonance lines are fairly sensitive, for a neutral species, to the adopted surface gravity. For dwarf stars a change of ±0.25 dex in log g induces a change of ∓0.1 dex in abundance. For the giant stars they are only slightly less sensitive, ∓0.06 dex. On the other hand for giant stars the dependence on gravity of the abundances derived from the lines of Mult. 2 is very weak ∓0.01 dex.

An inspection of on-line Table 8 allows us to estimate the effect of surface gravity on the 3D corrections for the lines of Mult. 1. By increasing the gravity by 0.5 dex, the 3D correction increases by 0.1 to 0.2 dex, depending on how saturated the line is. Since the 3D correction is negative, this means that it decreases in absolute value. The opposite trends with surface gravity on the 1D abundance and 3D correction imply that the two effects tend to cancel and the overall sensitivity of the 3D abundance on surface gravity is small.

The dependence of abundances on effective temperatures for the lines of Mult. 1 is similar for dwarfs and giants, and is about ±0.2 dex for a change of ±100 K in effective temperature. To evaluate the dependence of the 3D corrections on the effective temperature we used four models, extracted from the CIFIST grid (Ludwig et al. 2009). All four models have effective temperature around 5900 K, their metallicities are -1.0 and -2.0 and their log g 4.0 and 4.5. The result is that for a decrease of 300 K the 3D correction increases by 0.2 dex. Again the variation of the 3D correction goes in the opposite direction with respect to the variation in the 1D abundance. Combining the results we conclude that a decrease of 300 K in effective temperature results in a decrease by 0.4 dex in copper abundance (3D).

For the giants stars we also estimated the variation of the abundances derived from the lines of Mult. 2, which amounts to about ±0.1 dex for a variation of ±100 K in effective temperature.

Hydrodynamical models and spectrum synthesis.

Clearly the large 3D corrections derived for the Cu i resonance lines are driven by the fact that in the outer layers the hydrodynamical models are considerably cooler than the corresponding 1D models, the so-called "overcooling". This shifts the ionisation equilibrium towards neutral copper, and as a consequence the line contribution function shows a strong peak in these layers, contrary to the 1D model (se Fig. 4). From a physical point of view this is expected, simply because the hydrodynamical model is observed to transport flux through convection even in layers where the corresponding 1D model is formally stable against convection (overshooting). One should however ask to which extent the computed overcooling depends on the assumptions made. Bonifacio (2010) pointed out the difference in the overcooling for metal-poor giants computed with CO 5 BOLD and that computed by Collet et al. (2007). Behara et al. (2009) pointed out that for extremely metal-poor dwarfs the overcooling is considerably less in CO 5 BOLD models computed with 12 opacity bins than in models computed with 6 opacity bins, like the ones used here.

For the time being we have relatively few CO 5 BOLD models computed with 12 opacity bins, among which we have one with parameters identical to one used in the present investigation: T eff = 6300, log g= 4.0 and metallicity = -2.0. In Fig. 6 we show the mean temperature structures of the two models. Obviously the difference is smaller than what is displayed by the models 1 dex more metal-poor shown by Behara et al. (2009). The qualitative conclusion is confirmed by comparison of the curves of growth. In Fig. 7 the curve of growth for the 327.3 nm line used in the present investigation is compared to the one computed from the corresponding 12 bin model. As can be appreciated from the plot, for a given equivalent width the 12 bin model will yield a Cu abundance that is higher by approximately 0.1 dex, thus correspondingly decreasing the 3D correction.

Another matter of concern is that the current version of Linfor3D treats scattering as true absorption. That is to say, although scattering processes such as Rayleigh scattering off hydrogen atoms are taken into account as opacity sources, in the solution of the transfer equation the source function is set equal to the local Planck function, without a term depending on the mean radiation intensity (S ν = B ν ). To which extent can this approximation affect our computations, especially in the near ultraviolet, where scattering processes are a non-negligible source of opacity ? We assessed this by using 1D models and 1D spectrum synthesis. We used a slightly modified version of the SPECTRV code in the SYNTHE suite so that scattering is treated as true absorption when the card SCATTERING OFF is set in the input model (see e.g. [START_REF] Castelli | Kurucz's models, Kurucz's fluxes and the ATLAS code. Models and fluxes available at OAT[END_REF]). We computed line profiles both with SCATTERING ON and SCATTERING OFF for the model at T eff = 6296 K log g= 4.0 and metallicity -2.0 (rlevant to HD 218502) and for the model T eff = 4943 log g= 2.42 and metallicity -1.5 (relevant to Cl* NGC 6752 YGN 30). It turns out that in both cases the difference is irrelevant to our analysis (0.6% in the continuum and 0.03% in the residual intensity for the dwarf model and 14% in the continuum and 2% in the residual intensity). The effect of treating scattering as true absorption is very similar on the continuum and in the lines, thus implying a small effect on the residual intensity and equivalent width.

Recently [START_REF] Hayek | A&A in press[END_REF] have introduced a proper treatment of scattering in their magneto-hydrodynamical simulation code, BIFROST. For the Sun and solar-type stars they do not find a significant impact of continuum scattering on the temperature structure. We thus believe that although the impact of a proper treatment of scattering needs to be investigated in metal-poor dwarfs, it seems unlikely that the results presented here will be seriously challenged by this.

Discussion

If we consider the abundances in Table 4 at face value we are led to the inescapable conclusion that the Cu abundances in dwarfs and giants do not agree. Even though the abundances are almost compatible, within errors, at least in the 1D case, this systematic difference should not be overlooked. The behaviour is different between the two clusters: in NGC 6752 the dwarfs provide a higher abundance than the giants, while in the case of NGC 6397, they provide a lower value than the giants; this both using 1D and 3D models. For NGC 6752 the difference in 1D abundances is of one order of magnitude (1 dex), but this is reduced to only 0.3 dex if we look at the 3D abundances, which are almost compatible with the errors. The situation is reversed in NGC 6397, in 1D the abundances of dwarfs is only 0.15 dex lower than that in giants, while in 3D, the diferece is 0.9 dex. This behaviour may be understood in terms of the different line formation properties in dwarfs and giants and how they change with different Cu abundance. In Fig. 4 we show, as an example, the contribution functions of the EW at disc-centre for one of our models for a dwarf star, for two different Cu abundances. In the top panel A(Cu)=0.2 and the line is on the linear part of the curve of growth, in the bottom panel, A(Cu)=1.7 and the line is saturated. In both cases the 3D contribution function is very different from the 1D one and is peaked in the outer layers of the atmosphere. The formation of the lines of Mult. 2 in the atmospheres of giants is instead much less affected by 3D effects, as depicted in Fig. 5. The contribution functions of the lines of Mult. 1 in the giant model are morphologically similar to what is shown in Fig. 5, confirming the weak overcooling present in this model. While the above arguments explain the behaviour of the 3D corrections, they have no bearing in the abundance difference that we find between dwarfs and giants.

In these situations one has always to consider two possible alternatives: i) the difference is true and has an astrophysical origin; ii) the difference arises from shortcomings in the analysis. In our opinion hypothesis i) must be discarded. It seems extremely far fetched to devise a physical mechanism by which Cu should be overabundant in dwarf stars, like in NGC 6752, while the reverse is true in NGC 6397. Where giants have a higher Cu abundance, one could imagine to explain such a scenario either by invoking diffusion in TO stars, or Cu production in giant stars, or perhaps even a combination of both. However, an examination of Table 4 shows that the differences that need explanation are far too large to be created by diffusion, and the Cu production would also have to be highly efficient. In addition note that the Cu abundances in the large sample of Yong et al. (2005) are extremely uniform, which speaks against Cu production.

Thus we are left with the conclusion that the abundance determinations in either dwarfs or giants, or both, are wrong. Let us start by examining the 3D abundances in dwarf stars. Contribution functions like those shown in Fig. 4 must give rise to concerns about the LTE approximation used in our computations. The outer and less dense layers of the atmosphere, which contribute mostly to the line EW, are those in which the photon mean free path is longest and deviations from LTE may be expected. The situation is even more extreme in a 3D atmosphere where photons from a hot up-draft may transfer horizontally and overionise a neighbouring cool down-draft. A morphologically similar situation is indeed observed for the Li i doublet in metalpoor stars (Asplund et al. 2003;[START_REF] Cayrel | [END_REF]. In LTE the contribution function displays a double peak, with a substantial contribution from outer cool layers, in NLTE this peak is entirely suppressed by overionisation. The nearly exact cancellation between 3D and NLTE correction that takes place for the Li i doublet, and results in 3D-NLTE abundances in very close agreement with 1D-LTE abundances, should not be taken as a general rule. Nevertheless we believe that the Cu i lines of Mult. 1 cannot be described by 3D-LTE computations, but NLTE effects should be properly accounted for.

This leads to the question of how reliable the LTE approximation is for the 1D computations. That even in 1D the abundances in dwarfs and giants differ by a factor of the order of 2, surely prompts to see if for NLTE computations the two sets of abundances may be brought into agreement. Bihain et al. (2004) tried to fit the Cu i lines of Mult. 1 in the solar spectrum, but were unable to reproduce the core of the lines. This was attributed mainly to the presence of a chromosphere that influences the cores of strong lines. Deviations from LTE, however, could be another, possibly concomitant, cause for the failure to reproduce the line core in LTE. For Pop II dwarf stars chromospheric effects should not be strong, in view of their old age, even if chromospheres were present.

Let us finally consider the Cu abundances in giant stars. Our limited computations suggest that they should not suffer large 3D effects. The test we conducted for the giant star in NGC 6752 suggests that the LTE synthesis does not allow us to reproduce satisfactorily the lines of Mult. 1 and of Mult. 2 with the same Cu abundance. Indeed the discrepancy is quite large (0.5 dex); significant deviations from LTE for either or both sets of lines could be responsible for this. Which should be further investigated in order to produce reliable Cu abundances. The evolution of copper with metallicity, essentially based on the measurements of Mult. 2 in giant stars, shows a rather sharp drop in [Cu/Fe] around [Fe/H]=-1.5. This means that it takes place around A(Cu)=2.0. In the curve of growth for the 510.5 nm line of Mult. 2 for our giant model, this is roughly the abundance for which the line begins to enter in the saturation regime. If the Cu i lines of Mult. 2 suffer deviations from LTE it is likely that these depend on the line strength and may show a rather sharp change just when the line enters a saturation regime. This behaviour is observed, for instance, for the sodium D lines (see Fig. 6 of [START_REF] Andrievsky | [END_REF]). These considerations render NLTE computations for Cu very desirable.

Unfortunately, to our knowledge, up to now no such computations have been published, nor does a Cu model atom exist.

Among the possible causes for the discrepancy in abundances between giants and dwarfs one may also consider errors in the atmospheric parameters. One may conclude that this cannot be the case by noticing the discrepancy between the Cu abundance derived from Mult. 1 and Mult. 2 in star Cl* NGC 6752 YGN 30, for which lines of both multiplets are measured. Given that the response of both multiplets to a change in effective temperature is similar, the conflicting results cannot be resolved by changing the effective temperature. Of course the discrepancy between the two multiplets can be resolved in 1D by invoking a higher microtrubulence, but it would be necessary to raise it by 1 km s -1 . This increase would then cause a strong trend between iron abundances and equivalent widths. Furthermore this would not allow us to solve the discrepancy in the 3D analysis. Indeed while the 3D correction for Mult. 2 would not change sig-nificantly with this increase in microturbulence, those of Mult. 1 would increase by about 0.4 dex, thus breaking the agreement between the two multiplets forced in 1D. Formally one can certainly find a value of the microturbulence that forces the 1D abundance plus 3D correction of the two mutliplets to be equal, while leaving a discrepancy in the 1D abundances. This however would again cause an abundance spread among lines of other elements (e.g. iron) and can hardly be invoked as a solution of the problem. Although at the moment we do not have enough 3D models for giant stars to perform a full 3D analysis, as done by [START_REF] Sbordone | A&A in press[END_REF] for lithium, we believe that our results indicate that this analysis will provide discrepant abundances from the two multiplets.

Let us further consider if changes in the atmospheric parameters of giant or dwarf stars in either cluster may allow us to reconcile their copper abundances. As discussed in Sect. 5 a decrease in effective temperature of 300 K in dwarf stars implies a decrease by about 0.4 dex. Therefore for the dwarf stars in NGC 6752 a decrease in effective temperature by about 225 K while keeping the temperature of giants constant, would reconcile the copper abundances of the to sets of stars. While not implausible, this change would certainly cause a mismatch in the abundances of other elements between giants and dwarfs, most notably iron, which would become less abundant in dwarfs than in giants. While one could argue that atmospheric phenomena such as diffusion may alter abundances of dwarf stars, it seems then contrived to invoke a different behaviour between copper and iron. But let us now turn to the other cluster, NGC 6397. Here the situation is reversed, the dwarfs display a lower abundance than giants. However here one would need to invoke an increase in effective temperatures of the dwarf stars by over 500 K, placing them at T eff around 6700 K and the cluster turn-off at about 6900 K. While these exceedingly high temperatures may be appealing (one would immediately solve the cosmological lithium problem!) they appear impossible to reconcile with the colours of the cluster and theoretical isochrones.

Although the precise value of the atmospheric parameters assigned to the stars certainly plays a role in the difference in copper abundances between dwarfs and giants in the two clusters, we may dismiss the hypothesis that it may be cancelled by a suitable choice of parameters.

Conclusions

Our study of the Cu i lines of Mult. 1 in the TO stars of the globular clusters NGC 6397 and NGC 6752 allow us to draw several conclusions:

1. the Cu abundance derived from the Cu i lines of Mult. 1 in dwarf stars differs from that derived in giants from the Cu i lines of Mult. 2 in the same clusters; 2. the Cu i lines of Mult. 1 in dwarf stars show large 3D corrections when computed in LTE; 3. the Cu i lines of Mult. 2 in giant stars show small 3D corrections when computed in LTE; 4. the contribution functions of the Cu i lines of Mult. 1 in dwarf stars suggest that these cannot be reliably computed under the LTE approximation; 5. for the only star for which we have measured both the lines of Mult. 1 and of Mult. 2 we find that the derived abundances disagree by 0.5 dex, both using 1D and 3D models.

From the above we conclude that the Cu i lines of Mult. 1 are not reliable indicators of copper abundances. A full 3D-NLTE treatment of these lines should be used. When treated in 1D these lines yield abundances which, in the studied cases, differ from the abundances in giants by 0.2 to 1 dex, but the difference can be in either direction (lower or higher abundance in dwarfs). That the dwarf/giant discrepancy is in opposite directions for two clusters that differ by only 0.5 dex in metallicities also suggests that NLTE alone might not be able to reconcile the abundances in the two groups of stars. Whether the combination of 3D and NLTE effects may achieve this is an open issue, although it seems to be doubtful. Clearly a new investigation of Cu abundances in giants of NGC 6397 would be highly welcome, to place this discussion on firmer grounds.

Investigation of departures from LTE both in dwarfs and giants is needed to place the copper abundances on a firm footing. Without knowledge of these departures we recommend that the abundances measured in giants from lines of Mult. 2 should be preferred for the studies of chemical evolution. The main motivation for this recommendation is that the 3D effects for the Cu i lines used in giants are rather small.

Fig. 4 .Fig. 5 .

 45 Fig. 4. Contribution functions of the EW at disc-centre, defined in a way that their integral over log τ λ gives the EW (Magain 1986), for the Cu i 324.7 nm line and the model d3t63g40mm20n01 for two different values of Cu abundance. In the upper panel A(Cu)=0.2, in the lower panel A(Cu)=1.7. The solid lines refer to the 3D model, the dashed lines to the corresponding 1D LHD model.

Fig. 6 .

 6 Fig.6. Comparison between the temperature structures of two models with T eff = 6300, log g= 4.0 and metallicity -2.0, computed with 6 and 12 opacity difference. The difference is not as large as it is at lower metallicities (see Fig.1ofBehara et al. 2009).

Fig. 7 .

 7 Fig. 7. Comparison between the curves of growth for the 327.3 nm line computed for the two models shown in Fig. 6. Solid symbols correspond to the 6 bin model and open symbols to the 12 bin model.

Table 1 .

 1 Atmospheric parameters of the programme stars.

	Star	T eff	log g [Fe/H]	ξ
		K	[cgs]	dex	km s -1
	Cl* NGC 6752 GVS 4428	6226 4.28	-1.52	0.70
	Cl* NGC 6752 GVS 200613 6226 4.28	-1.56	0.70
	Cl* NGC 6397 ALA 1406	6345 4.10	-2.05	1.32
	Cl* NGC 6397 ALA 228	6274 4.10	-2.05	1.32
	Cl* NGC 6397 ALA 2111	6207 4.10	-2.01	1.32
	HD 218502	6296 4.13	-1.85	1.00

Table 2 .

 2 Copper abundances for the programme stars.

	Star	A(Cu)	σ	A(Cu)	σ
		1D		3D
	Cl* NGC 6752 GVS 4428	3.23	0.08	2.56	0.16
	Cl* NGC 6752 GVS 200613	3.01	0.05	2.23	0.07
	Cl* NGC 6397 ALA 1406	1.33	0.03	0.74	0.05
	Cl* NGC 6397 ALA 228	1.30	0.03	0.73	0.05
	Cl* NGC 6397 ALA 2111	1.19	0.02	0.60	0.02
	HD 218502	1.52	0.09	0.95	0.04

Table 4 .

 4 Mean copper abundances for the two clusters.

	Star	A(Cu)	σ	A(Cu)	σ
		1D		3D
	NGC 6752 dwarfs	3.04	0.07	2.28	0.12
	NGC 6752 giants	2.03	0.05	1.98	0.05
	NGC 6397 dwarfs	1.25	0.05	0.63	0.04
	NGC 6397 giants	1.40	0.17	1.30	0.17

ate; the 3D abundance is obtained by applying the interpolated 3D correction to the 1D abundance.

Table 3 .

 3 CO 5 BOLD models employed in the study.

	Model	T eff	log g [M/H] N t	time	t c	Resolution	Box Size
		K				s	s		Mm 3
	d3t50g25mm10n01 4990	2.5	-1.0	20 475990 1411.9 160 × 160 × 200 573.2 × 573.2 × 245.4
	d3t50g25mm20n01 5020	2.5	-2.0	20 403990 1388.3 160 × 160 × 200 584.0 × 584.0 × 245.4
	d3t63g40mm10n01 6260	4.0	-1.0	20	43800	12.2	140 × 140 × 150	26.0 × 26.0 × 12.8
	d3t63g40mm20n01 6280	4.0	-2.0	16	27600	49.0	140 × 140 × 150	26.1 × 26.1 × 12.8
	d3t63g45mm10n01 6240	4.5	-1.0	20	24960	16.0	140 × 140 × 150	7.0 × 7.0 × 4.0
	d3t63g45mm20n01 6320	4.5	-2.0	19	9120	15.9	140 × 140 × 150	7.0 × 7.0 × 4.0
	rived applying a 3D correction or directly derived from the 3D
	curves of growth.

Table 5 .

 5 Atomic data for the Cu i lines used.

	Isotope	λ	log g f	χ
		nm		eV
	65 Cu	324.7510 -0.868 0.000
	63 Cu	324.7512 -0.868 0.000
	65 Cu	324.7512 -0.868 0.000
	63 Cu	324.7513 -0.868 0.000
	65 Cu	324.7513 -1.266 0.000
	63 Cu	324.7514 -1.266 0.000
	63 Cu	324.7551 -0.421 0.000
	65 Cu	324.7552 -0.421 0.000
	63 Cu	324.7553 -0.868 0.000
	63 Cu	324.7554 -1.567 0.000
	65 Cu	324.7554 -0.868 0.000
	65 Cu	324.7555 -1.567 0.000
	63 Cu	327.3927 -0.864 0.000
	63 Cu	327.3930 -1.563 0.000
	63 Cu	327.3969 -0.864 0.000
	63 Cu	327.3972 -0.864 0.000
	65 Cu	327.3925 -0.864 0.000
	65 Cu	327.3929 -1.563 0.000
	65 Cu	327.3970 -0.864 0.000
	65 Cu	327.3973 -0.864 0.000
	65 Cu	510.5503 -3.720 1.389
	63 Cu	510.5505 -3.720 1.389
	65 Cu	510.5506 -2.766 1.389
	63 Cu	510.5509 -2.766 1.389
	65 Cu	510.5509 -2.720 1.389
	65 Cu	510.5510 -3.896 1.389
	63 Cu	510.5511 -2.720 1.389
	63 Cu	510.5512 -3.896 1.389
	65 Cu	510.5515 -2.653 1.389
	63 Cu	510.5517 -2.653 1.389
	65 Cu	510.5519 -2.398 1.389
	63 Cu	510.5520 -2.398 1.389
	65 Cu	510.5530 -2.750 1.389
	63 Cu	510.5531 -2.750 1.389
	63 Cu	510.5536 -2.148 1.389
	65 Cu	510.5536 -2.148 1.389
	63 Cu	510.5558 -1.942 1.389
	65 Cu	510.5560 -1.942 1.389
	65 Cu	578.2053 -2.924 1.642
	65 Cu	578.2062 -3.225 1.642
	63 Cu	578.2066 -3.225 1.642
	65 Cu	578.2074 -2.526 1.642
	63 Cu	578.2078 -2.526 1.642
	65 Cu	578.2105 -2.526 1.642
	63 Cu	578.2106 -2.526 1.642
	63 Cu	578.2117 -2.526 1.642
	65 Cu	578.2117 -2.526 1.642
	65 Cu	578.2173 -2.079 1.642

Table 7 .

 7 Atmospheric parameters for the giant stars in NGC 6752(Yong et al. 2005) and NGC 6397(Gratton 1982).

	Star	T eff	log g [Fe/H]	ξ
		K	[cgs]	dex	km s -1
	Cl* NGC 6752 YGN 30 4943 2.42	-1.62	1.27
	NGC 6397 211	4210 0.80	-2.0	3.0
	NGC 6397 603	4400 1.50	-2.0	2.6

Table 6 .

 6 Copper abundances from the individual lines.

	Star	Type	Line	EW	A(Cu) 1D 3D-1D LHD
		G/D	nm	pm	dex	dex
	Cl* NGC 6752 GVS 4428	D	324.7 12.66	3.29	-0.62
	Cl* NGC 6752 GVS 4428		327.3 11.31	3.17	-0.73
	Cl* NGC 6752 GVS 200613	D	324.7 11.33	3.04	-0.76
	Cl* NGC 6752 GVS 200613		327.3 10.44	2.97	-0.79
	Cl* NGC 6752 YGN 30	G	327.3 16.81	2.43	-0.05
	Cl* NGC 6752 YGN 30		510.5	2.32	1.89	-0.05
	Cl* NGC 6397 ALA 1406	D	324.7	5.35	1.36	-0.58
	Cl* NGC 6397 ALA 1406		327.3	3.44	1.31	-0.59
	Cl* NGC 6397 ALA 228	D	324.7	5.34	1.28	-0.58
	Cl* NGC 6397 ALA 228		327.3	3.94	1.32	-0.57
	Cl* NGC 6397 ALA 2111	D	324.7	5.18	1.17	-0.58
	Cl* NGC 6397 ALA 2111		327.3	3.64	1.20	-0.58
	NGC 6397 211	G	510.5	4.25	1.14	-0.1
	NGC 6397 211		578.2	2.20	1.46	-0.1
	NGC 6397 603	G	510.5	3.61	1.34	-0.1
	NGC 6397 603		578.2	1.62	1.69	-0.1
	HD 218502	D	324.7	6.57	1.58	-0.60
	HD 218502		327.3	4.62	1.45	-0.53

Table 8 .

 8 3D corrections. = 0.5 ξ = 1.0 ξ = 1.5 ξ = 0.5 ξ = 1.0 ξ = 1.5 Cu i 324.7 nm d3t63g40m10n01 113.3 -0.623 -0.415 -0.107 -0.573 -0.392 -0.115 d3t63g40m10n01 126.6 -0.485 -0.333 -0.067 -0.418 -0.284 -0.052 d3t63g40m10n01 6.57 -0.382 -0.276 -0.197 -0.365 -0.256 -0.175

	model	EW(pm)	3D-3D	3D-1D LHD
	ξ d3t63g45m10n01 113.3 -0.411 -0.237	0.021 -0.405 -0.262 -0.041
	d3t63g45m10n01	126.6 -0.322 -0.192	0.030 -0.298 -0.190 -0.005
	d3t63g45m10n01	6.57 -0.325 -0.232 -0.162 -0.362 -0.267 -0.194
	d3t63g40m20n01	113.3 -0.929 -0.652 -0.323 -1.228 -0.995 -0.701
	d3t63g40m20n01	126.6 -0.790 -0.517 -0.173 -1.061 -0.828 -0.524
	d3t63g40m20n01	6.57 -0.565 -0.468 -0.400 -0.768 -0.649 -0.560
	d3t63g40m20n01	5.34 -0.525 -0.464 -0.420 -0.676 -0.607 -0.555
	d3t63g40m20n01	4.40 -0.505 -0.462 -0.430 -0.635 -0.589 -0.553
	d3t63g45m20n01	113.3 -0.599 -0.368 -0.058 -1.012 -0.845 -0.619
	d3t63g45m20n01	126.6 -0.545 -0.333 -0.032 -0.924 -0.763 -0.534
	d3t63g45m20n01	6.57 -0.350 -0.252 -0.187 -0.778 -0.677 -0.599
	d3t63g45m20n01	5.34 -0.322 -0.259 -0.216 -0.710 -0.649 -0.602
	d3t63g45m20n01	4.40 -0.303 -0.258 -0.226 -0.674 -0.632 -0.599
			Cu i 327.3 nm
	d3t63g40m10n01	113.1 -0.677 -0.423 -0.116 -0.654 -0.421 -0.132
	d3t63g40m10n01	104.4 -0.699 -0.443 -0.158 -0.687 -0.451 -0.173
	d3t63g40m10n01	4.62 -0.306 -0.256 -0.219 -0.281 -0.231 -0.194
	d3t63g45m10n01	113.1 -0.446 -0.243	0.016 -0.459 -0.287 -0.057
	d3t63g45m10n01	104.4 -0.476 -0.264 -0.024 -0.507 -0.326 -0.098
	d3t63g45m10n01	4.62 -0.289 -0.243 -0.209 -0.314 -0.268 -0.233
	d3t63g40m20n01	113.1 -0.831 -0.558 -0.241 -1.139 -0.928 -0.648
	d3t63g40m20n01	104.4 -0.867 -0.589 -0.326 -1.202 -0.984 -0.704
	d3t63g40m20n01	4.62 -0.492 -0.444 -0.409 -0.625 -0.573 -0.534
	d3t63g40m20n01	3.94 -0.496 -0.458 -0.431 -0.619 -0.580 -0.550
	d3t63g40m20n01	2.60 -0.575 -0.553 -0.537 -0.686 -0.665 -0.648
	d3t63g45m20n01	113.1 -0.621 -0.381 -0.080 -0.965 -0.821 -0.619
	d3t63g45m20n01	104.4 -0.599 -0.340 -0.087 -1.000 -0.850 -0.655
	d3t63g45m20n01	4.62 -0.300 -0.250 -0.215 -0.673 -0.626 -0.591
	d3t63g45m20n01	3.94 -0.291 -0.251 -0.224 -0.656 -0.620 -0.592
	d3t63g45m20n01	2.60 -0.274 -0.251 -0.235 -0.630 -0.610 -0.594

http://archive.eso.org

http://www.aip.de/∼mst/Linfor3D/linfor 3D manual.pdf

Acknowledgements. We are grateful to L. Pasquini for many useful comments on an early version of this paper. The authors P.B., E.C., H.-G.L. acknowledge financial support from EU contract MEXT-CT-2004-014265 (CIFIST). We acknowledge use of the supercomputing centre CINECA, which has granted us time to compute part of the hydrodynamical models used in this investigation, through the INAF-CINECA agreement 2006, 2007.