Sebastien Guillot

Matthew Kerr

Paul S Ray

Slavko Bogdanov

Scott Ransom

Julia S Deneva

Zaven Arzoumanian

Peter Bult

Deepto Chakrabarty

Keith C Gendreau

Wynn C G Ho

Gaurava K Jaisawal

Christian Malacaria

M Coleman Miller

Tod E Strohmayer

Michael T Wolff

Kent S Wood

Natalie A Webb

Lucas Guillemot

Ismael Cognard

Gilles Theureau

Typeset using L A T E X default style in AASTeX62 NICER X-RAY OBSERVATIONS OF SEVEN NEARBY ROTATION-POWERED MILLISECOND PULSARS

Keywords: pulsars: general -pulsars: individual (PSR J0614-3329, PSR J0636+5129, PSR J0751+1807, PSR J1012+5307, PSR J1552+5437, PSR J1744-

NICER observed several rotation-powered millisecond pulsars to search for or confirm the presence of X-ray pulsations. When broad and sine-like, these pulsations may indicate thermal emission from hot polar caps at the magnetic poles on the neutron star surface. We report confident detections (≥ 4.7σ after background filtering) of X-ray pulsations for five of the seven pulsars in our target sample: PSR J0614-3329, PSR J0636+5129, PSR J0751+1807, PSR J1012+5307, and PSR J2241-5236, while PSR J1552+5437 and PSR J1744-1134 remain undetected. Of those, only PSR J0751+1807 and PSR J1012+5307 had pulsations previously detected at the 1.7σ and almost 3σ confidence levels, respectively, in XMM-Newton data. All detected sources exhibit broad sine-like pulses, which are indicative of surface thermal radiation. As such, these MSPs are promising targets for future Xray observations aimed at constraining the neutron star mass-radius relation and the dense matter equation of state using detailed pulse profile modeling. Furthermore, we find that three of the detected millisecond pulsars exhibit a significant phase offset between their X-ray and radio pulses.

INTRODUCTION

Millisecond pulsars (MSP) are old neutron stars (with characteristic ages τ ∼ 10 9 yr) named so based on their millisecond range rotation periods (P 25 ms), the fastest known having P 1.4 ms (Hessels et al. 2006). In contrast, the bulk of the pulsar population is observed with spin periods in the ∼0.1-10 s range. As they age, these pulsars evolve beyond the so-called "pulsar death line" (Sturrock 1971;Hibschman & Arons 2001) where they stop emitting in the radio band. Old pulsars spinning at millisecond periods must have experienced a "recycling" process of spin-up. Pulsar recycling occurs via the transfer of angular momentum due to the accretion of matter from a binary companion onto the neutron star (NS), during the low-mass X-ray binary phase (Bisnovatyi-Kogan & Komberg 1974;Alpar et al. 1982;Radhakrishnan & Srinivasan 1982). Once this recycling process ends, the magnetic field re-establishes the MSP magnetosphere, enabling the re-activation of the pulsed radio emission. Overall, MSPs are characterized by their large ages, exceptional rotational stability, and low magnetic fields (B ∼ 10 8-9 G).

While strong evidence exists that low-mass X-ray binaries are the progenitors of MSPs (Wijnands & van der Klis 1998;Papitto et al. 2013), not all MSPs are found in binary systems. This may be because the orbital modulations of a MSP have not yet been discovered (possibly due to faintness, or long orbital periods, e.g., Bassa et al. 2016;Kaplan et al. 2016), or because the NS is truly isolated. Possible explanations invoke the ablation of the companion (as in black-widow and redback systems, Chen et al. 2013) or the disruption of the binary system (via stellar encounters in dense environments). It has also been suggested that some isolated MSPs might have been formed by the direct collapse of a massive white dwarf (Freire & Tauris 2014).

X-ray pulsations in MSPs were first discovered in ROSAT observations of PSR J0437-4715 [START_REF] Becker | [END_REF]. These apparently thermal pulsations were ascribed to heating of the surface due to internal friction, or due to polar cap heating caused by magnetospheric return currents along open NS magnetic field lines (Harding & Muslimov 2001, 2002). Since this discovery, the X-ray emission from a handful of MSPs (mostly in globular clusters) has been identified as due to hot ∼ 10 6 K thermal (blackbody-like) emission from an area much smaller than the entire NS surface (e.g., Zavlin 2006;Bogdanov et al. 2006Bogdanov et al. , 2011;;Forestell et al. 2014;Lee et al. 2018). These small and hot polar caps at or close to the NS surface generate broad sine-like modulations with large pulsed fraction (∼30-70%) as the NS rotates. It was realized early on that the X-ray pulse profiles of MSPs could provide probes of the physical properties of NSs (compactness, or mass-to-radius ratio, Pavlov & Zavlin 1997) when modeled with a realistic NS atmosphere (Zavlin et al. 1996). This seminal work prompted detailed studies of the modeling of X-ray pulsations of MSPs (e.g., Bogdanov et al. 2007Bogdanov et al. , 2008;;Bogdanov & Grindlay 2009).

Measuring the compactness-and, in the best circumstances, the radius-of a NS is a crucial tool to determine the still-unknown equation of state (EOS) of dense nuclear matter. Obtaining constraints on the NS radius from the modeling of MSP pulse profiles provides a powerful method to discriminate between the numerous theoretical models describing dense nuclear matter (for a recent review, see Lattimer & Prakash 2016). Modeling MSP pulse profiles is a very promising technique that complements alternative methods making use of other classes of thermally emitting NSs (e.g., Heinke et al. 2006Heinke et al. , 2014;;Webb & Barret 2007;Guillot et al. 2013;Guillot 2016;Özel et al. 2010, 2016;Bogdanov et al. 2016;Steiner et al. 2010;Miller 2013Miller , 2016;;Steiner et al. 2013Steiner et al. , 2018;;Baillot d'Etivaux et al. 2019), and methods exploiting the gravitational wave signals from NS-NS mergers as demonstrated with the GW 170817 event (e.g., Abbott et al. 2017Abbott et al. , 2018;;De et al. 2018).

The Neutron star Interior Composition Explorer (NICER; Gendreau & Arzoumanian 2017) was designed to fully exploit the pulse profile modeling technique which requires data with high signal-to-noise ratios (S/N), the main scientific goal of the NICER mission being to constrain the radii of NSs from observations of a handful of MSPs. An additional science goal of the mission is to study the X-ray flux modulations of pulsars and discover new sources of Xray pulsations [START_REF] Ray | & NICER Working Group on Pulsation Searches and Multiwavelength Coordination[END_REF]. This includes searching for X-ray pulsations from NSs that would be suitable for pulse profile modeling with NICER or with future missions (e.g., STROBE-X, Ray et al. 2019a;eXTP, Watts et al. 2019; or the Athena X-ray Observatory, Nandra et al. 2013). Prior to the launch of NICER, only four thermally-dominated MSPs were known to exhibit highly significant X-ray pulsations: PSR J0437-4715 [START_REF] Becker | [END_REF]Zavlin et al. 2002;Bogdanov 2013), PSR J0030+0451 [START_REF] Becker | Neutron Stars, Pulsars, and Supernova Remnants[END_REF]Bogdanov et al. 2008), PSR J2124-3358 [START_REF] Becker | [END_REF]Zavlin 2006;Bogdanov et al. 2008) and PSR J1024-0719 (Zavlin 2006). A few other MSPs showed tentative or marginal detections: PSR J0751+1807 at 1.7σ and PSR J1012+5307 at almost 3σ (Webb et al. 2004b); and PSR J1614-2230, at the 4σ level (Pancrazi et al. 2012).

Most radio MSPs hosted in globular clusters are found to be positionally coincident with soft, thermal X-ray sources (e.g., Bogdanov et al. 2006Bogdanov et al. , 2011;;Forestell et al. 2014), whose spectra suggests that their emission also arises from the heated magnetic polar caps of the NS. A long Chandra HRC observation of 47 Tuc yielded 4σ pulsation detections for three MSPs hosted by this cluster (Cameron et al. 2007). Some MSPs with non-thermal emission also exhibit pulsations in the X-ray band, although they tend to be characterized by short-duty-cycle pulse profiles with hard nonthermal spectra (e.g., PSR B1821-24 in the globular cluster M28, PSR B1937+21, Gotthelf & Bogdanov 2017;Deneva et al. 2019), likely caused by magnetospheric emission. Others, such as PSR J0218+4232, have a hard non-thermal spectrum with moderately broad X-ray profiles Webb et al. 2004a;Deneva et al. 2019.

Aside from the thermally-emitting MSPs mentioned above, those in globular clusters, and the non-thermal emitters, a number of relatively nearby MSPs show apparently thermal X-ray emission, but were not previously observed in a mode permitting searches for pulsations and/or with sufficient exposures. These include PSR J0023+0923 (a blackwidow with a very soft X-ray spectrum; Gentile et al. 2014), PSR J0034-0534 (Zavlin 2006), PSR B1257+12 (the pulsar with planets; Pavlov et al. 2007), PSR J1400-1431 (a very nearby but very X-ray faint MSP; Swiggum et al. 2017), and PSR J1909-3744 (Kargaltsev et al. 2012;Webb et al. 2019). A complete list of X-ray emitting MSPs in the Galactic field has been compiled by Lee et al. (2018).

No systematic study exists on the offsets between the radio and X-ray pulses of rotation-powered MSPs, in part because of the challenging aspects of properly aligning the pulse profiles. For those MSPs with thermal emission, originating from the footprints of the magnetic field at the NS surface, one naturally expects the X-ray and radio profiles to be aligned. This is indeed observed for a handful of MSPs: PSR J0437-4715 (Bogdanov 2013), PSR J0030+0451 (Bilous et al. 2019), or PSR J1231-1411 (Ray et al. 2019b). However, some exceptions include PSR J1614-2230 (Pancrazi et al. 2012) or PSR J2124-3358 [START_REF] Becker | [END_REF], although for the later, the 1σ uncertainty is 1 ms, i.e., ∼20% of the total spin period. For non-thermal MSPs, for which the emission originates in the magnetosphere, some have been observed with near perfect alignment (PSR B1821-24 or PSR B1937+21, Deneva et al. 2019), possibly suggesting a similar location for the origin of the radio and X-ray emission. Others, however, show a significant offset, such as PSR J0218+4232, in which the broad double-peaked radio pulse lies halfway between the two moderately broad X-ray pulses (Deneva et al. 2019).

A selection of nearby MSPs in the field of the Galaxy with known thermal emission, but no prior firm detection of X-ray pulsations, have been targeted by NICER to detect or confirm the presence of polar-cap emission causing pulsations. Here we report on the results from these observations and the discovery of pulsations in some of them. Section 2 briefly presents the targets and some of their basic properties. Section 3 describes the observations performed, the data reduction and search method. The results are presented in Section 4 and are followed by a brief discussion on the properties of the detected pulsations and conclusions in Section 5.

TARGETS

For this investigation, we considered MSPs that had no previous securely identified X-ray pulsations. This included targets with only marginal detections of pulsations. The basic properties of these MSPs are summarized in Table 1, and we provide below an overview of some of their characteristics and details about prior X-ray observations. Other MSPs with known pulsations and observed by NICER for EoS determination purposes are presented in Bogdanov et al. (2019).

PSR J0614-3329

The 3.1 ms spin period of PSR J0614-3329 was discovered by the Robert C. Byrd Green Bank Telescope (GBT) from a source detected in γ-rays with the Fermi Large Area Telescope (LAT; Ransom et al. 2011) but with no known counterpart at any other wavelength. With a period derivative of Ṗ ≈ 1.75×10 -20 s s -1 , this pulsar's surface dipolar magnetic field is B ≈ 2.38×10 8 G (Ransom et al. 2011). The orbital period of 53.6 d was also measured from radio timing. The companion star, tentatively a helium white dwarf, was identified from its optical colors in g, r, and i band Gemini observations, despite the pulsar's proximity to a background galaxy (∼ 10 , Testa et al. 2015). Finally, X-ray data obtained with the Neil Gehrels Swift Observatory indicated a likely thermal X-ray spectrum with a blackbody temperature kT BB = 0.23 ± 0.05 keV (Ransom et al. 2011).

PSR J0636+5129

The Green Bank Northern Celestial Cap (GBNCC) survey for pulsars discovered this 2.87 ms pulsar in a 95.6 minute binary orbit (Stovall et al. 2014). Based on its orbital properties, the system was initially classified as a black widow binary, although some features typically seen in black widow pulsars are lacking (e.g., eclipses and dispersion measure variations; Stovall et al. 2014). The binary companion was recently discovered as a magnitude r ≈ 24 low-mass (M < 0.02 M ) companion star. As no radial velocity information was available, no constraints on the pulsar mass were obtained (Draghis & Romani 2018). XMM-Newton data of PSR J0636+5129 showed a thermal spectrum, with kT BB = 0.18±0.03 keV. Although a purely non-thermal model could not be formally excluded, the resulting power-law photon index was unusually soft, Γ = 5 +5 -1 , indicating a likely thermal spectrum (Spiewak et al. 2016).

PSR J0751+1807

PSR J0751+1807, a MSP with P = 3.48 ms, was discovered by the Arecibo Observatory in a search targeting unidentified EGRET sources (Lundgren et al. 1995). The MSP is in a 6 hr binary system with a helium white dwarf companion. Initial mass measurements via radio timing detection of orbital decay and Shapiro delay resulted in a NS mass of 2.1 ± 0.2 M (Nice et al. 2005). However, more recent radio timing observations found a significantly different NS mass of 1.64 ± 0.15 M and a companion mass of 0.16 ± 0.01 M (Desvignes et al. 2016). The reported parallax distance of this MSP is D = 1.07 +0.24 -0.17 kpc. Finally, its spin down Ṗ ≈ 0.8×10 -20 s s -1 implies a surface dipole magnetic field strength of B ≈ 1.7×10 8 G. In the X-ray waveband, the XMM spectrum is well described by a power law with photon index Γ = 1.6 ± 0.2 (Webb et al. 2004b), but not by a single blackbody, which suggests the possibility of a non-thermally emitting MSP. These data also showed a hint of pulsations at the 1.7σ confidence level.

PSR J1012+5307

PSR J1012+5307 was discovered with the Lovell radio telescope at Jodrell Bank Observatory [START_REF] Nicastro | [END_REF]. This 5.26 ms pulsar is in an orbit with a low-mass helium white dwarf (van Kerkwijk et al. 1996). While some orbital parameters (e.g., P orb ≈ 0.6 d) were measured in the discovery observation, they have since then been refined (Fonseca et al. 2016). Using the radial velocity curve of the companion, as well as the companion mass (determined via optical spectroscopy), Callanan et al. (1998) estimated the pulsar mass to be 1.64 ± 0.22 M , and a more recent estimate resulted in 1.83 ± 0.11 M (Antoniadis et al. 2016). Having an independent mass measurement makes this pulsar a potentially interesting NICER target for radius measurements. The X-ray spectrum of PSR J1012+5307, obtained with XMM-Newton, is consistent with both absorbed power law (Γ ∼ 1.8) and absorbed blackbody models (Webb et al. 2004b). If the emission is thermal, the blackbody temperature, kT BB = 0.26 ± 0.04 keV, is consistent with that of other similar MSPs. Webb et al. (2004b) also reported a 3σ detection of X-ray pulsations at the spin frequency of the pulsar. The distance to this pulsar has recently been updated by identifying the optical counterpart in the GAIA-DR2 catalog, resulting in a distance measurement of 907 ± 131 pc when combining the GAIA parallax with various other measurements (Mingarelli et al. 2018).

PSR J1552+5437

PSR J1552+5437 was recently discovered in the radio band with the Low-Frequency Array (LOFAR, van Haarlem et al. 2013) in an unassociated Fermi -LAT γ-ray source. This P = 2.43 ms pulsar was the first MSP to be discovered at low radio frequencies (115-150 MHz, Pleunis et al. 2017), and its timing solution was used to confirm the presence of pulsations at the same spin period in the original Fermi LAT source 3FGL J1553.1+5437. No X-ray counterpart was detected in a short 2.9 ks observation with the Neil Gehrels Swift Observatory. No optical counterpart is known for this pulsar.

PSR J1744-1134

Discovered in the Parkes 436 MHz survey of the southern sky (Manchester et al. 1996), this nearby P = 4.08 ms pulsar is now routinely observed for pulsar timing array purposes (e.g., Reardon et al. 2016;[START_REF] Arzoumanian | [END_REF]). The X-ray counterpart of PSR J1744-1134 was discovered in ROSAT data [START_REF] Becker | [END_REF]. It has since then been observed by Chandra, with the X-ray spectrum likely indicating thermal emission with black-body temperature of kT BB ∼ 0.3 keV (Marelli et al. 2011). No optical counterpart has been found despite deep searches, setting an upper limit of V < 26.3 (Sutaria et al. 2003).

PSR J2241-5236

PSR J2241-5236 is another pulsar discovered among Fermi LAT unidentified γ-ray sources (Keith et al. 2011). It has a spin period of 2.19 ms. It is classified as a black-widow pulsar with intra-binary shock, in a 3.5 hr orbit with a M > 0.012 M companion, at a dispersion measure distance of 0.960 kpc (Yao et al. 2017). A Chandra observation of PSR J2241-5236 identified a soft X-ray source with a spectrum described by two black bodies with temperatures of kT BB ∼ 0.07 keV and ∼ 0.26 keV (Keith et al. 2011).

Other thermally-emitting MSPs

The following other MSPs were also observed with NICER, but their results are not reported in the present paper:

• PSR J1231-1411, a 3.68 ms pulsar, was discovered in a search campaign of unassociated Fermi -LAT sources with the GBT (Ransom et al. 2011). With a 0.2-12 keV flux of 1.9×10 -13 erg cm -2 s -1 , it is the third brightest thermally-emitting MSP and thus a target well suited for NS compactness measurement with NICER. The pulsar is in a 1.86-d orbit with a low-mass white dwarf (Ransom et al. 2011), possibly associated with a magnitude g = 25.4 optical counterpart (Testa et al. 2015). X-ray pulsations from PSR J1231-1411 were detected, but are reported in detail elsewhere (Ray et al. 2019b;Bogdanov et al. 2019).

• PSR J1614-2230 was discovered in a Parkes radio search targeting unidentified EGRET sources (Hessels et al. 2005;Crawford et al. 2006). It is a MSP with P = 3.15 ms bound to a massive white dwarf companion in a P b = 8.7 d orbit. The pulsar is particularly important for the NICER mission because it is one of the most massive NSs known (Miller 2016), with M = 1.908 ± 0.016 M [START_REF] Arzoumanian | [END_REF]). X-ray pulsations from this pulsar were detected with NICER, but are reported in full detail elsewhere (Arzoumanian et al. 2019, in prep.), confirming a ∼ 4σ detection in XMM data (Pancrazi et al. 2012).

• PSR J0740+6620 is another GBNCC-discovered pulsar, in a 4.77 d orbit with a white-dwarf companion (Stovall et al. 2014;[START_REF] Lynch | [END_REF]Beronya et al. 2019). An intense timing campaign with the GBT permitted detection of a Shapiro-delay signal, resulting in a pulsar mass 2.14 +0.10 -0.09 M (Cromartie et al. 2019). Although with somewhat large uncertainties, the high NS mass puts this pulsar on a par with PSR J1614-2230 for dense matter EOS constraints (Miller et al. 2019). The NICER observations of this pulsar are also reported in Arzoumanian et al. (2019, in prep.). Note-These ObsIDs include all observations acquired from the beginning of the mission (2017 July) through 2019 March 23. The exposure time columns report, from left to right, the total duration of data collection ("Raw"), the exposure time after the standard filtering described in Section 3 ("Std. Filt."), and the final exposure time resulting from the GTI-sorting optimization ("Opt. Filt."). For J1552+5437 and J1744-1134, no optimized exposure time is given since no detection is claimed (see Section 4).

OBSERVATIONS AND DATA REDUCTION

3.1. NICER X-ray Timing Instrument, data filtering and pulse phase assignments

We observed the seven MSPs listed in Section 2 using NICER. Table 2 presents these data, giving the ObsIDs used, the total exposure accumulated, and the total exposure available after filtering. We processed all the data available until 2019 March 23 with HEASOFT v6.23 and the NICER specific package NICERDAS v3. We filtered the raw data with the standard criteria:

• pointing offset is < 0.015 • from the source,
• pointing > 20 • from the Earth limb (> 30 • in the case of a bright Earth),

• excluding South Atlantic Anomaly passages,

• selecting events in the 0.25-12 keV energy range.

Additional filtering was necessary to ensure minimal contamination from non-astrophysical background. First, we excluded detectors with DET ID 14, 34, and 54-these are known to be more sensitive to optical loading than others, complicating analyses for soft sources such as our MSPs. Then, we used a filtering criterion based on the rate of "overshoots" (representing large deposition of energy within a detector, and defined by the housekeeping parameter FPM OVERONLY COUNT) and on the magnetic cutoff rigidity (COR SAX, in GeV/c). An empirical relation was found to minimize periods of high background, even at low cutoff rigidities, in order to maximize the exposure. For each pulsar, we excluded observed time intervals with the conditions1 : FPM OVERONLY COUNT > (1.52 × COR SAX -0.633 ) and FPM OVERONLY COUNT > 1.0 Some pulsars required slightly different filtering options. For example, a portion of the exposure for PSR J1552+5437 was acquired with a pointing offset > 0.015 • , and therefore this condition was relaxed to include pointing offset < 0.1 • . When necessary, these additional criteria are described for each pulsar in Section 4.

Finally, the pulse phase of each photon was computed using the pulsar timing analysis software PINT (task photonphase), given the ephemeris for the pulsar of interest (see Appendix B). Note that photonphase computes the transformation from the Terrestrial Time (TT) standard used for time tagging of NICER events to Barycentric Dynamical Time (TDB) using the NICER orbit files (provided as one of the standard products for each ObsID) and the pulsar astrometric parameters (position, proper motion, and parallax) provided in the epheremides-only the Solar System Ephemeris has to be specified (DE421 or DE436). The H-test is then employed to quantify the presence of pulsations (de Jager et al. 1989; de Jager & Büsching 2010), either in the full band, or in the soft X-ray band (0.25-2.0 keV), setting a 3σ single-trial limit to claim the detection of pulsations. We report the detections and non-detections of pulsations in Section 4. Despite our stringent filtering described above, the background, variable throughout the ObsIDs, may still contaminate significantly the pulse profiles of the detected pulsars. We describe in the next section a method of GTI selection to minimize background contamination and provide cleaner pulse profiles.

Good time interval (GTI) sorting method

Because each NICER exposure occurs under different observing conditions (pointing with respect to the Sun, Earth, or Moon, location of the ISS, space weather, etc.), the amount of non-astrophysical background can vary greatly between ObsIDs, and even within single ObsIDs. Faint sources, such as the MSPs studied in this paper, are most affected by background: GTIs with low background improve the S/N, while those with high background dilute the pulsations and decrease the S/N. To minimize the background contamination and maximize the S/N, we therefore only consider the GTIs with low background. This is done by splitting the GTIs into small segments of at least 10 s (to have a good estimate on the background count rate) and at most 100 s. These GTIs are then ordered by their corresponding total count rate, which we use as a proxy for the background rate since the MSP contribution to the total rate is of the order of a few percent and is constant. We employ the H-test to quantify the significance of the pulsations. We do so cumulatively on the sorted GTIs (from the lowest to the highest count rate). This is illustrated in Figure 1 for PSR J0614-3329, which shows the cumulative H-test significance as a function of GTIs with increasing background count rates. The H-test significance first increases as low-background GTIs are added and then stabilizes or decreases when higher background GTIs are being included. This methods permits finding the optimal cut (indicated by the vertical line in Figure 1) that maximizes the H-test significance by excluding GTIs with the highest background rates.

To further increase the pulse profiles S/N, i.e., reducing the background contributions, additional improvement can be achieved by optimizing the selected energy range. In some GTIs, optical loading may cause a sharp increase of the count rate below ∼ 0.4 keV. Excluding part or all of the 0.25-0.4 keV energy range may therefore further increase the detection significance of the pulsations. Similarly, since the thermal spectra of MSPs are expected to drop rapidly above ∼1.5 or 2 keV, an optimization of the high-energy cut-off can minimize the background contribution to the pulse profiles. Here, we perform a grid search for the low-and high-energy cut-offs (with ranges 0.25-1.0 keV and 0.9-3.0 keV, respectively) and the resulting optimal energy ranges are reported in Table 3.

Nançay Radio Telescope pulsar timing data

Timing solutions for all pulsars, except PSR J1552+5437 and PSR J2241-5236, have been constructed by analyzing pulsar observations made with the Nançay Ultimate Pulsar Processing Instrument (NUPPI) in operation at the Nançay Radio Telescope (NRT) since August 2011. In these observations, 512 MHz of frequency bandwidth are recorded in the form of 128 channels of 4 MHz each, which are coherently de-dispersed in real time and phase-folded at the expected topocentric periods of the observed pulsars (see Guillemot et al. 2016, for additional details on pulsar timing observations with the NUPPI backend). We considered timing observations made at 1.4 GHz, which represent the bulk of pulsar observations with NRT. For each pulsar, we used all of the available NUPPI data through 2019 June. Data reduction steps were performed using the Psrchive software library (Hotan et al. 2004). We cleaned the data of radio frequency interference and calibrated the observations in polarization using the SingleAxis method. High-S/N profiles were built by summing up the 10 best detections of each pulsar, and times of arrival (TOAs) were extracted by cross-correlating the observations with smoothed versions of the summed profiles. For each NUPPI observation, we formed one TOA per 128 MHz of bandwidth. The TOAs at multiple frequencies enabled us to track potential variations of the dispersion measure (DM). We used the TOA datasets and the Tempo2 pulsar timing package [START_REF] Hobbs | [END_REF]) to build timing solutions for each pulsar, fitting for their astrometric, rotational, and DM parameters, as well as orbital parameters for those pulsars in binary systems. The timing solutions, presented in Appendix B, obtained with this procedure describe the TOAs appropriately. We note that these timing solutions are sufficient for the purpose of calculating the phases of X-ray photons, as done in the present paper, over the span of NICER's data collection, but they might not be the most optimal solution for long-term timing of these pulsars.

Parkes pulsar timing data

Timing solutions for PSR J2241-5236 made use of data collected with the Parkes radio telescope, primarily for the Parkes Pulsar Timing Array (project P456). The observing strategy is described in Reardon et al. (2016), and the data reduction by Kerr et al. (2018), but we summarize them here. Observations of 64 min duration are performed with approximately a three-week cadence in three radio frequency bands, typically centered on 732 MHz, 1369 MHz, and 3100 MHz. Down-converted voltages are digitized, converted to spectra via a polyphase filterbank, and autocorrelated to form Stokes parameters. These multi-channel time series are folded at the known pulsar spin periods into pulse profiles and integrated for 64 s before output for archiving. Observations of a pulsed noise diode enable gain and b H-test significance after optimization of the GTI and energy band (see Section 5 for a short discussion of the number of trials). c Pulsed count rates are provided in the optimal energy range provided for each pulsar.

Note-The results for PSR J1231-1411, PSR J0740+6620, and PSR J1614-2230 are reported elsewhere (Ray et al. 2019b andArzoumanian et al. 2019, in prep.).

polarization calibration. Data are reduced using Psrchive and TOAs extracted using an analytic profile. As described above, timing solutions are prepared with Tempo2. To enable absolute alignment of the radio and X-ray profiles, we selected a single high-S/N TOA to serve as the reference epoch (the TZRMJD parameter; see Section 5.2). The timing solution makes use of radio data collected between 2010 Feb 9 and 2018 Apr 22, requiring extrapolation to fold NICER data acquired outside of this epoch. We verified the timing solution on ad hoc data acquired through 2018 Nov 10 and observed no substantial deviations of these pulse arrival times from the predicted phase.

RESULTS

The results of the pulsation searches are presented in Table 3, which contains the single-trial detection significance, the H-test significance after GTI optimization, and the optimal energy range for each observed MSP. The optimization of the energy range permitted finding the low-energy cut, which depends on how much optical-loading noise is present, as well as the high-energy cut, which depends primarily on the brightness of the MSP (and its spectral shape, i.e., surface temperature). Five out of the seven pulsars show pulsations in the soft X-ray band, with a single-trial significance (before GTI optimization) > 4.3σ, except for PSR J1012+5307 (at 3σ). With the GTI optimization described above, the H-test significance for the detected pulsars are all > 4.7σ. The two non-detected pulsar have single-trial H-test significance of 1.5σ and 2.5σ for PSR J1552+5437 and PSR J1744-1134, respectively.

PSR J0614-3329

For this pulsar, a simple phase-folding of the events with a recent ephemeris (Table 5) in the full NICER energy range resulted in a significant 7.5σ single-trial detection of the pulsations, and 11σ when selecting events in the soft (0.25-2.0 keV) band. Optimization of the GTIs (see Section 3.2) improved the significance to 11.4σ. A grid search in energy concluded that the 0.33-1.43 keV energy range is optimal, resulting in a 14σ significance, for a total exposure time of 181 ks. The pulse profile is shown in Figure 2, together with the NRT pulse profile at 1.4 Ghz from the data used to generate the timing solution.

PSR J0636+5129

The standard filtering described in Section 3 leaves 400 ks of exposure for PSR J0636+5129. After folding all events in the 0.25-12.0 keV with an ephemeris from NRT observations (Table 6), the H-test significance of 2.5σ is not sufficient for a confident claim of detection. However, restricting the energy range to the soft 0.25-2.0 keV band Figure 2. NICER pulse profiles (black, 16 bins per phase) for the five pulsars with detected pulsations (obtained in their respective optimal energy ranges, see Table 3), together with their radio pulse profile at 1.4 GHz (red) from the Nançay or Parkes radio telescopes. The ephemerides used for folding are presented in Tables 5 through 11, respectively. Two rotational cycles are shown for clarity.

brings the detection significance to 4.3σ, and shows a broad single pulse. Further improvement is obtained with our GTI optimization, which results in 5.5σ H-test significance for a total of 347 ks of good exposure. The pulse profile, obtained in the 0.27-0.91 keV optimal energy range, is shown in Figure 2.

PSR J0751+1807

Observations of PSR J0751+1807 were performed with an offset pointing, in an effort to minimize contamination from nearby sources. Using archival XMM data and sources in the 3XMM-DR8 catalog (Rosen et al. 2016), we determined the exact position to maximize the S/N for the pulsar-see Appendix A for the results of the pointing offset determination, and see Bogdanov et al. (2019) for a description of the method.

In the case of PSR J0751+1807, the initial single-trial H-test significance after standard filtering and folding (see ephemeris in Table 7) is 4.1σ in the full 0.25-12.0 keV range. This detection increases when using only events in the 0.25-2.0 keV soft band, where thermal emission would be the strongest. There, we obtain a detection significance of 6.5σ. Finally, as done above for the other pulsars, the GTI optimization further improves the H-test significance: 7.5σ (0.25-2.0 keV), and 8.5σ when the optimal energy range of 0.32-1.82 keV is used. The pulse profile, resulting from 424 ks of selected GTIs is shown in Figure 2. Our confident detection confirms the marginal 1.7σ detection claimed from early XMM data of this pulsar (Webb et al. 2004b).

PSR J1012+5307

A 590 ks exposure of PSR J1012+5307 was obtained with NICER, after standard filtering. However, after event folding with the ephemeris of Table 8, the X-ray pulsations remain undetected in the full 0.25-12 keV band (∼ 2σ), and marginally detected (3σ) when using soft-band photons only. A fraction of the exposure, early in the mission, was obtained at low Sun angles, close to the instrument's 45 • limit. Our GTI optimization helps to minimize the impact of exposures with high optical-loading background, such as those at low Sun angles. Applying this optimization improves the H-test significance to 3.7σ in the 0.25-2.0 keV band, and 4.67σ when also optimizing the energy range-we find that 0.31-1.94 keV is optimal. A total of 548 ks of exposure, out of the 590 ks available, is selected to generate the optimal pulse profile for PSR J1012+5307 (Figure 2). Although the detection of the pulsations in the NICER data is somewhat marginal, our observations confirm the 3σ detection in XMM-Newton data (Webb et al. 2004b). While the apparent X-ray/radio peak separation, ∼ 0.3 phase, is consistent between the XMM and NICER data sets, the double peak structure of the XMM data (Figure 9 of Webb et al. 2004b) is not evident in the NICER data.

PSR J1552+5437

NICER observed this pulsar for a total of 72 ks after standard filtering. Unfortunately, a record-keeping error resulted in the use of incorrect pointing coordinates, offset ∼ 2. 4 from the pulsar's reported position (Pleunis et al. 2017). Therefore, the standard angular distance filtering criterion (excluding > 0. 9) had to be relaxed during the processing; the other standard filtering criteria (Section 3) were retained, resulting in 69 ks of good exposure, but with reduced sensitivity to the off-axis source. After folding with the ephemeris of Table 9, the single-trial detection significance is ∼ 1.5σ whether we choose the full energy range or the soft band only. Applying the GTI optimization increases the significance to 3σ and 2.8σ for these two cases, respectively; however, only small fractions of the total exposure (6 ks and 28 ks, respectively) are retained by the optimization. Optimizing both sorted GTIs and the energy range also leads to an unrealistically small selection of GTIs (resulting in only 140 events out of ∼67000).

Overall, we conclude that no pulsations were firmly detected from this pulsar. Assuming the detection is real, however, the pulsations would correspond to a pulsed count rate of 0.008±0.004 c/s (consistent with a non-detection of pulsations), equivalent to a Swift-XRT rate of 0.0004 c/s. One would therefore expect 1.2 counts in a 2.9 ks Swift-XRT exposure, which is consistent with the Swift non-detection. Longer NICER observations, with the correct pointing, are warranted to confirm or refute the possible presence of X-ray pulsations from this pulsar, or alternatively, longer X-ray imaging observations are required to determine the actual existence of X-ray emission from this pulsar2 .

PSR J1744-1134

A total of 71 ks of exposure are available for this pulsar after standard filtering. The ephemeris from the Nançay Radio Telescope (Table 10) allows us to calculate the pulse phase of each photon. However, whether we choose the full Note-The pulsed X-ray fluxes and luminosities reported are unabsorbed. The luminosities are calculated with the distances reported in Table 1. The Ė values reported have been corrected for the Shklovskii effect [START_REF] Shklovskii | [END_REF].

energy band or the 0.25-2.0 keV range, or we attempt to optimize it, the detection significances remain 2.3σ, 2.5σ, and 2.7σ, respectively. Optimization of the GTIs to exclude those with high background also results in low-significance detections of pulsations and unrealistically small selections of GTIs (< few ksec). We therefore conclude that no pulsations are seen from PSR J1744-1134. Past observations of this pulsar, obtained with Chandra, do not have the timing resolution necessary to confirm or refute our conclusions.

PSR J2241-5236

The phase-folding of event times from PSR J2241-5236 leads to pulsations detected with a single-trial significance of 4.5σ when considering the full NICER band, and 4.9σ when using 0.25-2.0 keV photons. GTI optimization permits excluding periods of high background and increases the significance to 6.3σ (0.25-2.0 keV). Finally, the grid search described above to find the optimal energy range yields 0.41-1.14 keV, i.e., excluding the range where the optical loading is the strongest, and resulting in pulsations with a significance at the 7.4σ confidence level. Using these 100 ks of optimally selected GTIs, we provide the pulse profile for PSR J2241-5236, along with the Parkes Radio Telescope pulse profile, in Figure 2. 4.8. PSR J0740+6620, PSR J1231-1411, and PSR J1614-2230 The detection of X-ray pulsations from J1231-1411 has been reported in Ray et al. (2019b) and Bogdanov et al. (2019), while PSR J1614-2230 is the subject of another article in preparation (Arzoumanian et al. 2019, in prep.), confirming the detection reported in Pancrazi et al. (2012). The NICER observations of PSR J0740+6620 are also presented in Arzoumanian et al. (2019, in prep.).

DISCUSSION AND CONCLUSION

Thermal luminosity vs spin-down luminosity

From the pulsed count rates listed in Table 3, deduced from the pulse profile after GTI and energy range optimizations, we estimated with WebPIMMS3 the pulsed X-ray unabsorbed flux and luminosity (with distances from Table 1) for the MSPs with detected pulsations. To do so, we used the blackbody temperatures published in the literature (see Section 2, or assuming kT BB = 0.1 keV for PSR J0751+1807). We also assumed the value of hydrogen column density n H obtained from neutral H maps using the HEASARC n H tool4 (with the most recent maps from HI4PI Collaboration et al. 2016). These pulsed luminosities are listed in Table 4 together with spin-down luminosity Ė (corrected for the Shklovskii effect). We find efficiencies L X / Ė in the range 10 -5 -10 -3 , similar to those of other MSPs (e.g., Figures 9 and 10 in Lee et al. 2018), but the values that we report in Table 4 should be viewed as lower limits since they were derived from the pulsed flux only.

Radio-X-ray phase separation

Producing properly phase-aligned radio and X-ray pulse profiles can be challenging. For most radio pulsar timing studies an overall absolute phase error is irrelevant, but for alignment with other wavebands, correct absolute timing is critical, so we provide some detail here. In this work, the phase 0.0 is defined by the radio template used to extract the radio TOAs. The NRT templates are aligned such that the peak of the main pulse is the fiducial point. Pulsar timing codes (TEMPO, Tempo2, and PINT) produce a fictitious TOA that has zero residual to the model (with its time, observing site, and frequency defined by the TZRMJD, TZRSITE, and TZRFRQ parameters). The PINT photonphase task or the Tempo2 photons plugin will assign pulse phases to the X-ray photons using this reference. Possible sources of error include: [START_REF][END_REF] uncertainty in extrapolating from the radio arrival time to infinite frequency because of dispersion measure uncertainty; (2) uncalibrated cable or pipeline delays in data taking systems; (3) inconsistent application of observatory clock corrections (e.g., confusion over whether TZRMJD is in observatory clock time or UTC); ( 4) using different ephemerides or positions when barycentering the two datasets, etc.

The phase alignments shown in Figure 2 are made with the timing models presented in this paper (Tables 567891011). To provide a cross check for potential errors in the alignment procedure, we reproduced Figure 2 for PSR J0636+5129 and PSR J1012+5307 using timing models from NANOGrav [START_REF] Arzoumanian | [END_REF], which are from the Green Bank Telescope, instead of NRT. We obtained very similar profiles and peak separations, giving us confidence that the alignments presented in Figure 2 are correct; in particular, that the clock corrections from NRT are properly taken into account by the PINT photonphase task.

We use the Fourier decompositions presented in Figure 3 to determine the phase of the X-ray pulses and therefore the phase offset ∆φ with the radio peak:

• PSR J0614-3329: Both X-ray and radio main peak are broad and essentially aligned (∆φ ∼ 0.07). Furthermore, the secondary radio peaks appear to be somewhat aligned with the secondary X-ray pulse (see Figure 2).

• PSR J0636+5129: The seemingly broad and asymmetric X-ray profile (fast rise and slower decay) of this pulsar leads the radio pulse by ∆φ ∼ 0.3-0.4.

• PSR J0751+1807: The main radio pulse lags the X-ray peak by ∆φ ∼ 0.1. However, a "precursor" radio pulse precedes the main radio pulse by ∼0.1 in phase, and is therefore aligned with the X-ray pulse.

• PSR J1012+5307: This pulsar also displays a large offset, with the X-ray pulse leading the main radio pulse by ∆φ ∼ 0.3, while the secondary radio pulses fall in the trough of the X-ray profile.

• PSR J2241-5236: The X-ray pulse is broad, with a duty cycle of more than 60%, and a peak that lags the narrow radio pulse (duty cycle of a few percent at most) by ∆φ ∼ 0.2.

The ∆φ offsets in the range 0.2-0.3 for three out of the five MSPs in our sample are in contrast with other MSPs studied with NICER. As listed in Section 1, three of the four pulsars presented in Bogdanov et al. (2019) all have near perfect alignment between the X-ray and radio pulses (PSR J0437-4715, PSR J0030+0451, and PSR J1231-1411)), while others have misaligned X-ray and radio pulses, such as PSR J1614-2230. The large ∆φ ∼ 0.2 -0.3 phase offsets between the radio and X-ray measured in this work may put into question the surface heating patterns and the centered dipolar nature of these MSP magnetic fields. For example, the location of the hot regions, separated by ∼ 65 • (Riley et al. 2019), at the surface of PSR J0030+0451 suggest a magnetic field that significantly deviates from a simple centered dipolar field (Bilous et al. 2019), even though the X-ray and radio pulses are aligned. Additionally, the observed radio profiles could find their origin in the outer edge (i.e., non-axial) parts of the beam, instead of the core of the beam emission (Lyne & Manchester 1988;Kramer et al. 1999), therefore resulting in an offset with the X-ray pulses coming from the footprints of the magnetic field at the NS surface. Overall, the relationship between the X-ray and radio pulsations of thermally-emitting MSPs therefore ought to be studied in more detail, and a more systematic study of radio and X-ray profiles could help constrain the complexity of the magnetic fields in these sources. The phase alignment of the radio and X-ray pulses with the γ-ray pulsations may also be informative, although the latter originates from emission further out in the magnetosphere and does not necessarily align with the radio or X-ray profiles.

Harmonics in the pulse profiles

For the five pulsars with detected pulsations, we apply a Fourier decomposition technique to search for the presence of harmonics in the broad, sine-like profiles. We find that PSR J0614-3329 is the only one that requires two harmonics (using a single harmonic leaves structured residuals and gives χ 2 ν > 2). For the other four pulsars, a single sine function is sufficient to describe the pulse profile (i.e., χ 2 ν ≈ 1 and white residuals). Figure 3 shows the harmonic fits and residuals for the five pulsars.

The detection of higher harmonics may provide evidence for the various effects that distort the pulses from a simple sinusoid (See below) and/or for the presence of a second visible polar cap (i.e., a secondary pulse, as clearly seen in the case of PSR J0030+0451, Bogdanov & Grindlay 2009). At spin frequencies up to ∼ 300 Hz, atmosphere beaming (since MSP surface emission is not isotropic), as well as self-occultation of the polar caps by the star, make the pulse profile deviate from a sinusoidal shape. Above 300 Hz, other effects, such as Doppler boosting and aberration, add more power to the harmonic content (Miller & Lamb 2015).

The two harmonics in PSR J0614-3329 can be readily interpreted as due to the presence of a secondary pulse, about half a phase from the dominant pulse (see Figures 2 and3). This likely originates from a second polar cap, similar to that observed in PSR J1231-1411 and PSR J0030+0451 (Bogdanov et al. 2019). For the other four pulsars of the present study, the single harmonic detected may simply be ascribed to the low S/N of the data sets. For comparison, the key NICER targets used for pulse profile modeling (PSR J0437-4715, PSR J0030+0451, PSR J1231-1411, and PSR J2124-3358) show up to four harmonics in their pulse profiles (Bogdanov et al. 2019), with high S/N provided by deep (∼1-2 Ms) exposures. Observations with exposures of 1-5 Ms for the five pulsars reported here will likely reveal their full harmonic content and is required to perform pulse profile modeling analyses to extract mass and radius constraints.

Conclusion and perspectives

We present a systematic search for X-ray pulsations using NICER timing observations of a set of seven nearby rotation-powered MSPs. X-ray pulsations are securely detected from five of the targets. Specifically, the single-trial significance is > 4.3σ for all MSPs except for PSR J1012+5307 (3σ). This significance is improved (≥ 4.7σ in all cases) when optimizing the selection of GTIs to favor low background count rates (see Section 3.2). Although the number of trials involved with the GTI sorting method is not straightforward to quantify exactly, it is much less than the number of GTIs for a given MSP data set. Indeed, since they are sorted by increasing total rate, they are highly correlated, making the trial factor for our GTI sorting method on the order of a few.

Because of the low count rates for the MSPs in the present paper (see Table 3), a proper spectral analysis was unfortunately not possible. Using a NICER background model (Ray et al. 2019b;Bogdanov et al. 2019), we estimate that 5-10% of the total detected counts in the soft X-ray band (0.5-2.0 keV) originate from the observed pulsars. Given the uncertainties involved with modeling the background5 , we refrain from providing spectral parameters for these faint pulsars. Imaging instruments sensitive in the soft X-ray band, such as XMM-Newton, eROSITA [START_REF] Predehl | Society of Photo-Optical Instrumentation Engineers[END_REF], or the future Athena X-ray Observatory (Nandra et al. 2013) are better suited for such spectral analyses.

The results of this paper nonetheless enlarge the sample of radio MSPs detected as pulsed X-ray sources-in particular, those with thermal emission. All five MSPs detected have broad pulsed profiles, fitted with one or two harmonics (see Section 5.3). Published studies of these MSPs showed that they also have X-ray spectra consistent with thermal emission6 (simple or double black body, see Section 2 for the details). The broad pulses and the spectral shapes lead us to tentatively conclude that we observe thermal X-ray pulsations from these five MSPs. We note that more detailed spectral analyses, with high S/N, is necessary to confirm with certainty the spectral nature of these pulsations. Indeed, PSR J0218+4232 displays a pair of rather broad X-ray pulses (∼ 0.25 phase), connected by a "bridge" joining them (Deneva et al. 2019). However, its X-ray spectrum is hard and purely non-thermal (with a power-law photon index Γ ≈ 1.1), making the detection of pulsations possible up to ∼ 10 keV in the NICER data (Webb et al. 2004a;Rowan et al. 2019, submitted to ApJ). To confirm the thermal nature of the MSPs studied here would require observations with spectro-imaging X-ray instruments.

Figure 1 .

 1 Figure 1. Evolution of the pulsation detection significance (units of σ) as a function of the GTIs sorted by total count rate, equivalent to the cumulative exposure time (totaling 181 ks), for PSR J0614-3329. The dashed vertical line indicates the optimal GTI cut that maximizes the detection significance. In other words, adding GTIs to the left of this line increases the detection of pulsations, while adding high-background GTIs, to the right of the line, decreases the detection significance.

Figure 3 .

 3 Figure 3. Fourier decomposition of the NICER pulse profiles of the five MSPs with detected pulsations, with 64 phase bins. Only PSR J0614-3329 required more than one harmonic. In each panel, the dashed lines are the harmonic components, and the red solid line is the sum of the components. The bottom plot of each panel shows the residuals. Only one rotational cycle is shown.

Figure 4 .

 4 Figure 4. (left) XMM-Newton EPIC MOS image of PSR J0751+1807 and nearby sources. The teal '×' shows the position of the optimal NICER pointing that maximizes the S/N from the pulsar, i.e., minimizes the contamination from all other sources (blue circles) within 6 . The dashed yellow circle shows the size of the NICER 6. 2 half-power diameter point spread function.(right) Map of the S/N of PSR J0751+1807 as a function of NICER pointing. The green star shows the pulsar position, and the red circle shows the calculated optimal pointing position that maximizes the S/N. The optimal pointing is 1 from the pulsar position and permits a gain in S/N of a few percent.

Table 1 .

 1 Selection of nearby MSPs targeted by NICER

	Pulsar	P	Ṗ	P orb	D	M	Timing
		(ms) (×10 -21 )	(d)	(pc)	(M )	Solution
	PSR J0614-3329 3.10	17.5	53.6	∼2690	unknown	NRT
	PSR J0636+5129 2.87	3.38	0.066	203 +27 -21	unknown	NRT
	PSR J0740+6620 2.88	12.2	4.77	400 +200 -100	2.17 +0.11 -0.10	(1)
	PSR J0751+1807 3.48	7.79	0.25	1070 +240 -170	1.64±0.15	NRT
	PSR J1012+5307 5.26	17.1	0.6	907±131	1.83±0.11	NRT
	PSR J1231-1411 3.68	22.8	1.86	∼420	unknown	(2)
	PSR J1552+5437 2.43	2.80	...	∼2600	• • •	Fermi/LOFAR
	PSR J1614-2230 3.15	9.624	8.7	670 +50 -40	1.908±0.016	(1)
	PSR J1744-1134 4.08	8.935	...	440 +20 -20	• • •	NRT
	PSR J2241-5236 2.19	6.64	0.15	∼960	unknown	Parkes
	1 NICER observations presented in Arzoumanian et al. (2019, in prep.)
	2 NICER observations presented in Ray et al. (2019b).
	Note-Distances with quoted uncertainties are based on measurements of parallax from radio
	timing. For the rest, a dispersion measure (DM)-based distance estimate is given (Yao et al.
	2017). The Ṗ value reported are not corrected for the Shklovskii effect. "NRT" stands for
	the Nançay Radio Telescope.

Table 2 .

 2 NICER observations of selected millisecond pulsars

	Targeted	ObsID	Raw	Std. Filt.	Opt. Filt.
	Pulsar	range	Exp. (ks) Total Exp. (ks) Total Exp. (ks)
	PSR J0614-3329 0030050101 -0030050110	82
		1030050101 -1030050158	151	188	181
		2030050101 -2030050103	29
	PSR J0636+5129 1030070101 -1030070197 2030070101 -2030070107	403 40	399	347
	PSR J0751+1807 1060030101 -1060030217 2060030201 -2060030211	462 51	443	424
	PSR J1012+5307 0070040101 -0070040113	45
		1070040101 -1070040215	570	590	548
		2070040201 -2070040212	54
	PSR J1552+5437 1033180102 -1033180116	75	72	• • •
	PSR J1744-1134 0030160101 -0030160109	16
		1030160101 -1030160125	62	71	• • •
		2030160101 -2030160106	5
	PSR J2241-5236 1031010101 -1031010182 2031010101	254 3	113	100

Table 3 .

 3 Results of the pulsation searches

	Pulsar	single-trial H-test GTI opt. H-test Energy range	Pulsed
		significance a	significance b	(keV)	count rate c (s -1 )
	PSR J0614-3329 11.0σ	14.0σ	0.33-1.43	0.027±0.002
	PSR J0636+5129	4.3σ	5.5σ	0.27-0.91	0.008±0.001
	PSR J0751+1807	6.5σ	8.5σ	0.32-1.82	0.014±0.001
	PSR J1012+5307	3.0σ	4.7σ	0.31-1.94	0.007±0.001
	PSR J1552+5437	1.5σ		No detection
	PSR J1744-1134	2.5σ		No detection
	PSR J2241-5236	6.3σ	7.4σ	0.41-1.14	0.020±0.002
	a Single-trial H-test significance in the 0.25-2.0 keV energy range.

Table 4 .

 4 Pulsed thermal luminosities, spin-down luminosities and efficiencies

	Pulsar	n H	kT BB	(a)	F pulsed 0.2-10.0 keV	L pulsed 0.2-10.0 keV	Ė	L X /	Ė
		(10 20 cm -2 ) ( keV) ( erg cm -2 s -1 )	( erg s -1 )	( erg s -1 ) (10 -4 )
	PSR J0614-3329	3.0	0.23	3.5×10 -14	3.0×10 31	2.4×10 34	13.0
	PSR J0636+5129	9.5	0.18	2.1×10 -14	1.0×10 29	5.6×10 33	0.2
	PSR J0751+1807	6.2	0.10	3.2×10 -14	4.4×10 30	5.7×10 33	7.7
	PSR J1012+5307	0.8	0.26	7.8×10 -15	7.7×10 29	2.7×10 33	2.9
	PSR J2241-5236	1.1	0.26	3.2×10 -14	3.5×10 30	2.5×10 34	1.4
	(a) We assumed a 0.1 keV blackbody for PSR J0751+1807, and the values presented in Section 2
	for the others.

Table 8 .

 8 Ephemeris of PSR J1012+5307 used in this work and obtained from observations with the Nançay Radio Telescope. Digits in parentheses represent the 1σ uncertainty on the last quoted digit of a parameter value.

	Parameter	Value

Table 10 .

 10 Ephemeris of PSR J1744-1134 used in this work and obtained from observations with the Nançay Radio Telescope. Digits in parentheses represent the 1σ uncertainty on the last quoted digit of a parameter value.

The filtering criteria on FPM OVERONLY COUNT are adopted into the standard NICERDAS pipeline as of version 6.0 (https://heasarc.gsfc. nasa.gov/docs/nicer/nicer analysis.html).

NICER-XTI is a non-imaging instrument, and the detection of a faint pulsar can be confirmed with certainty from the detection of its pulsations.

Available at https://heasarc.gsfc.nasa.gov/cgi-bin/Tools/w3pimms/w3pimms.pl

Available at https://heasarc.gsfc.nasa.gov/cgi-bin/Tools/w3nh/w3nh.pl; Although these values are integrated along the line of sight through the Galaxy, all five pulsars are > 18 • above the Galactic Plane and these n H values should be reasonable estimates.

NICER is a non-imaging instrument and the background is modeled based on observations of blank-sky exposures, as well as housekeeping and space-weather parameters.

[START_REF] Ephemeris | J0636+5129 Right Ascension[END_REF] In all five cases, the spectral analyses, reported in the literature, were performed on rather low S/N data from Swift-XRT, XMM, or Chandra, with less than a few hundred of counts.

fellow. This work was supported in part by NASA through the NICER mission and the Astrophysics Explorers Program. This research has made use of data and software provided by the High Energy Astrophysics Science Archive Research Center (HEASARC), which is a service of the Astrophysics Science Division at NASA/GSFC and the High Energy Astrophysics Division of the Smithsonian Astrophysical Observatory. We acknowledge extensive use of NASA's Astrophysics Data System (ADS) Bibliographic Services and the ArXiv. The Nançay Radio Observatory is operated by the Paris Observatory, associated with the French Centre National de la Recherche Scientifique (CNRS). The National Radio Astronomy Observatory is a facility of the National Science Foundation operated under cooperative agreement by Associated Universities, Inc. S.M.R is a CIFAR Fellow and is supported by the NSF Physics Frontiers Center award 1430284. We acknowledge financial support from the Programme National de Cosmologie et Galaxies (PNCG), Programme National Hautes Energies (PNHE), and Programme National Gravitation, Références, Astronomie, Métrologie (PNGRAM) of CNRS/INSU, France. This work benefited from the support of the Entretiens sur les Pulsars funded by Programme National High Energies (PNHE) of CNRS/INSU with INP and IN2P3, co-funded by CEA and CNES. Facilities: NICER, Nançay Radio Telescope, Parkes Radio Telescope Software: astropy (Astropy Collaboration et al. 2018, https://ascl.net/1304.002), PINT (Luo et al. 2019, https:// ascl.net/1902.007), TEMPO2 (Hobbs & Edwards 2012, https://ascl.net/1210.015), HEAsoft (Nasa High Energy Astrophysics Science Archive Research Center (Heasarc) 2014, https://ascl.net/1408.004), NICERsoft, (https://github.com/paulray/ NICERsoft)

The detection of pulsations, if they are indeed of thermal origin, seems to confirm that for the majority of MSPs the main source of their X-ray emission comes from their heated polar caps. The findings of this Letter also make these MSPs promising targets for follow-up X-ray observations with NICER and/or with future proposed telescopes such as STROBE-X (Ray et al. 2019a) or eXTP (Watts et al. 2019), to enable constraints on the NS massradius relation and the dense matter EOS via the pulse profile modeling technique. The binary MSPs with independent mass measurements from radio timing, PSR J0751+1807 and PSR J1012+5307, are of particular interest in this sense since they can offer more stringent constraints on the NS radius. PSR J0614-3329, the brightest of the five MSPs studied here, is also a promising target.

Following the discoveries of X-ray pulsations from five MSPs, NICER continues to observe these targets to better characterize their X-ray pulse profiles. These MSPs will require a few Ms of exposure per pulsar with NICER Ḟurthermore, NICER will also target newly discovered MSPs such as those discovered by the Arecibo PALFA survey (Parent et al. 2019).

The authors are grateful to the referee for their insightful suggestions that contributed to improving this paper. S.G. acknowledges the support of the French Centre National d' Études Spatiales (CNES). C. M. is a NASA Postdoctoral APPENDIX A. POINTING OPTIMIZATION FOR PSR J0751+1807 Figure 4 in this appendix presents the results of the pointing optimization for PSR J0751+1807, as described in (Bogdanov et al. 2019).

B. MILLISECOND PULSAR EPHEMERIDES

In the following tables (5)[START_REF] Ephemeris | J0636+5129 Right Ascension[END_REF][START_REF] Ephemeris | J0751+1807 Right Ascension[END_REF](8)(9)(10)[START_REF] Ephemeris | 36.21305(1[END_REF], we present the ephemerides from the NRT, the Parkes Radio Telescope, and LOFAR used to calculated the phases of X-ray events detected by NICER. We stress that these ephemerides were obtained for the sole purpose of phase-folding X-ray events, and should not be used as long-term timing solutions for these pulsars.


Ons Jallouli
email: ons.jallouli@univ-nantes.fr

Safwan El
email: safwan.elassad@univ-nantes.fr

Maryline Chetto
email: maryline.chetto@univ-nantes.fr

Robust Chaos-based Stream-Cipher for Secure Public Communication Channels

In this paper, we propose a novel stream cipher based on a chaotic system. In order to get the cipher text, the plain text is simply XORed with the key-stream generated by a strong pseudo chaotic number generator (PCNG). Then, all the security of the system is based on the used PCNG. The structure of the proposed PCNG includes two chaotic maps which are weakly coupled by a predefined matrix and integrates a swap function. The PCNG passes all statistical NIST's randomness tests. Also, analysis and experimental results show that the proposed stream cipher has a large key space, a high key sensitivity, and can resist against chosen-plaintext attack and chosen-ciphertext attack. Indeed, for each new execution of the system using the same secret key, the generated keysteram is different due to the IV-setup function. The computing performance of the proposed system is comparable to the main algorithms of eStream such as Rabbit and HC-128.

I. INTRODUCTION

Nowadays, due to the widespread transmission over various communication networks, data security is gaining more importance and has been a subject of intense research. Obviously, designing efficient image encryption schemes has become a focal research topic. During the last years, and due to the interesting features of chaos in cryptography, a large number of chaos-based image encryption schemes has been proposed. Some of them have proved to be vulnerable to certain types of attacks [START_REF] Wong | A fast image encryption scheme based on chaotic standard map[END_REF][2] [START_REF] Tang | Image encryption using chaotic coupled map lattices with time-varying delays[END_REF]. Recently, some published works on chaosbased block ciphers are very efficient in terms of security and computing time [START_REF] Zhang | An image encryption scheme using reverse 2-dimensional chaotic map and dependent diffusion[END_REF] [START_REF] Zhang | Chaotic image encryption based on circular substitution box and key stream buffer[END_REF][6] [START_REF] Farajallah | Fast and secure chaosbased cryptosystem for images[END_REF]. Also, some interesting works on lightweight stream ciphers are recently published [START_REF] Manifavas | A survey of lightweight stream ciphers for embedded systems[END_REF] [START_REF] Vidal | A fast and light stream cipher for smartphones[END_REF] [10] [START_REF] Garasym | High-speed encryption method based on switched chaotic model with changeable parameters[END_REF]. Stream ciphers are potential candidates for data encryption, along with block ciphers. Stream ciphers are a class of symmetric cryptography. They are inherently suitable for time-critical applications, with little computational resources, where the speed of encryption and decryption is a concern. The main characteristic of a stream cipher is its speed on different platforms, and also chip area, power consumption for hardware implementations. A stream cipher is a symmetric cryptosystem. It means that, in order to encrypt / decrypt the message, emitter and receiver must share the same key. A common way to build a stream cipher is to use a pseudorandom number generator (or keystream generator) and xoring this keystream with the plain-text / cipher text. Several stream ciphers have been proposed in the literature. e.g., A5/1 [START_REF] Barkan | Instant ciphertext-only cryptanalysis of gsm encrypted communication[END_REF], RC4 [START_REF] Klein | Attacks on the rc4 stream cipher[END_REF], SEAL [START_REF] Rogaway | A software-optimized encryption algorithm[END_REF], SNOW [START_REF] Ekdahl | Snow-a new stream cipher[END_REF]. Most of the proposed stream ciphers have proved to be very weak and insecure [START_REF] Kelsey | Cryptanalytic attacks on pseudorandom number generators[END_REF].

The eStream project was held in February 2004 [START_REF] Robshaw | The estream project[END_REF] by the European Network of Excellence for Cryptology (ECRYPT), in order to encourage cooperation between researchers in security. Its main goal is to give rise to a standarisation of secure and efficient stream ciphers. 34 stream cipher candidates were submitted as a response to the call by eStream and only few proposals are chosen at the end of the project: HC-128, Rabbit, Salsa20/12 and SOSEMANUK as softwareoriented ciphers, and Grain v1, MICKEY 2.0 and Trivium in the hardware category. It had been noted that the finalist stream ciphers were proven to be secure against attacks. However, new cryptanalysis works mention some security flaws for some of these ciphers [START_REF] Manifavas | A survey of lightweight stream ciphers for embedded systems[END_REF].

In this paper, a robust chaos-based stream cipher is proposed. It based on a strong Pseudo Chaotic Number Generator (PCNG) to generate the key stream. To provide high robustness, the PCNG integrates two chaotic maps : Piece-Wise Linear Chaotic Map (PWLCM) and Skewtent map. Its structure includes a coupling and swap functions. The proposed structure passes all NIST's randomness tests justifying the good statistical properties of the key stream. In addition, security analysis and experimental results show that our stream cipher has a high security level, resistant to various typical attacks. Also, the proposed chaos-based stream cipher has good computing performance.

The paper is organized as follows: In section II, we describe the structure of the proposed PCNG and we give the NIST 's result. The performance of the proposed chaos-based stream cipher in terms of security analysis and time consuming are given in section III. Finally, in section IV, we conclude the paper.

II. PROPOSED PSEUDO CHAOTIC NUMBER GENERATOR

In this section, first, we describe in details the structure of the proposed PCNG used in our stream cipher. The PCNG is the central element of any stream cipher. Second, we present the experimental results of the NIST statistical test that were carried out on the key-strem generated by the proposed PCNG in order to quantify its statistical cryptographic properties.

A. Architecture of the pseudo chaotic generator

The proposed structure is presented in Fig. [START_REF] Wong | A fast image encryption scheme based on chaotic standard map[END_REF]. It consists of three main function blocks: Key-setup, Internal State and Output function. It takes a secret key "K" and 64 bits initial vector "IV" as input, and as output, it generates a pseudochaotic samples, each quantified on N=32 bits.

The structure uses two chaotic maps: PWLCM and Skew Tent maps, and includes a coupling and swap chaotic techniques.

Xp(0) = Xp ⊕ IV p Xs(0) = Xs ⊕ IV s (1)
Where IV p = lsb(IV ) and

IV s = L cir [lsb(IV ), 3].
⊕ denotes the XOR operator, lsb(IV ) is the 32 least significant bits of IV and L cir [S, q] performs the q-bits left circular shift on the binary sequence S.

Notice that, the secret key K of the system is formed by:

• the initial conditions Xp and Xs of the chaotic maps Pwlcm and Skewtent, ranging from 1 to 2 N -1, • the control parameters Pp and Ps of Pwlcm and Skewtent maps, in the range [1, 2 N -1 -1] and [1, 2 N -1] respectively, • the parameters of the coupling technique, ε ij , ranging from 1 to 2 k with k ≤ 5 and i, j ∈ {1, 2}. These initial conditions, parameters and initial vector are chosen randomly from Lunix generator: "/dev/urandom".

Internal state: The samples Xp(n) and Xs(n) are produced by using a coupling and swap chaotic techniques. The equation of the system is governed by:

Xp(n) Xs(n) = (2 N -ε 11 ) ε 12 ε 21 (2 N -ε 22 ) × F p[Xs(n -1)] F s[Xp(n -1)
] .

(2) Where F p[Xp(n -1)] and F s[Xs(n -1)] are the discrete functions of the chaotic maps Pwlcm and Skew Tent maps respectively [START_REF] Jallouli | A novel chaotic generator based on weakly-coupled discrete skewtent maps[END_REF].

Output function: The output samples X(n) are calculated throughout the produced samples Xp(n) and Xs(n) as follows:

X(n) = Xp(n) ⊕ Xs(n). (3)

B. NIST statistical test

We highlight the robustness of the proposed chaotic generator through the NIST (National Institute of Standards and Technology) statistical test that is carried out in order to quantify the good randomness of the produced sequences (keystreams). The NIST designed a battery of 15 statistical tests based on mathematical theory to test randomness of binary sequences produced by pseudo-random number generators [START_REF] Elaine | Recommendation for random number generation using deterministic random bit generators[END_REF], [START_REF] Rukhin | A statistical test suite for random and pseudorandom number generators for cryptographic applications[END_REF]. We generated 100 different binary sequences each one with a different secret key and containing 31250 samples (size of each sequence is n=10 6 bits), with a level of significance α = 0.01 ). We present the obtained results of NIST for a generated sequence X in Table I. As we can see, the sequence X has successfully passed all NIST tests, since the computed P -value of each test is > 0.01. Therefore we conclude that the output sequence of our PRNG is enough random, and it resists against statistical attacks. In this section, we study the performance in terms of security and computing time of our proposed chaos based stream-cipher. We use as plaintext the color image of "Lena" image (256 × 256 × 3) shown in Fig. (2a). Fig. (2c) shows the encrypted image of Lena. It can be seen from this result that visually there are no relationship between the original image and its encrypted one.

A. Key space, chosen plaintext and chosen ciphertext attacks

A good stream-cipher algorithm should resist all kinds of known attacks such as exhaustive attack, chosen plaintext and chosen ciphertext attacks. Basically, it should be sensitive to the secret key, and the key space should be large enough to resist brute-force attacks. For the proposed crypto-system, the size of the secret key is given by:

|K| = (|Xp| + |Xs|) + (|P p| + |P s|) + 4 × |ε ij | = 147 bits (4)
where |Xp| = |Xs| = |P s| = 32 bits ; |P p| = 31 bits and |ε ij | is equal to 5 bits. Therefore the secret key size is large enough to prevent the exhaustive searching. Thus, the brute-force attack on the key is computationally unfeasible. Also, the proposed system can resist against chosen plaintext and chosen ciphertext attacks. Indeed, due to the IV-Setup function, encrypting the same plaintext several times using a same secret key, gives ciphertexts totally different from each other.

B. Key sensitivity

An efficient crypto-system must be very sensitive to the secret key; a small change in the secret key causes a greatly significant change in the output. We evaluate the key sensitivity by using the Hamming Distance D Hamming test.

We calculate the average Hamming Distance D Hamming (using 100 secret keys), between two sequences X and Y , ciphered with only one change in the least significant bit of the parameter P p. The Hamming distance D Hamming (X, Y ) is given by the following equation :

D Hamming (X, Y ) = 1 N b × N b K=1 (X[K] ⊕ Y [K]) (5)
With N b is the number of bits in a sequence. The obtained result of Hamming distance is equal to 0.499995 (close to the optimal value of 50%). This means that the secret key is very sensitive.

Two others quantitative measures are usually used, the number of pixels change rate (NPCR) and the unified average changing intensity (UACI), in order to test the key sensitivity attacks. NPCR is designed to evaluate the changed pixel numbers in cipher image, while only one bit changes in the key. The optimal value of NPCR is almost 99.61 %. UACI refers to the average values of difference in intensity between two cipher images. The optimal value of UACI is almost 33.46 %. The parameters NPCR and UACI are defined as bellow :

N P CR = 1 L × C × P × P p=1 L i=1 C j=1 D[i, j, p] × 100% (6) D[i, j, p] = 0, if C 1 [i, j, p] = C 2 [i, j, p] 1, if C 1 [i, j, p] = C 2 [i, j, p] (7)
U ACI = 1 L × C × P × 255 × P p=1 L i=1 C j=1 |C 1 -C 2 | × 100% (8)
We have found that the NPCR is 99.608 % and the UACI is 33.47 %, showing thereby that the encryption scheme is very sensitive with respect to little change in the secret Key. We ensure this uniformity by applying the chi-square test given by:

χ 2 exp = K-1 i=0 (O i -E i ) 2 E i . ( 9
)
Where K is the number of levels (here 256), O i are the observed occurrence frequencies of each color level (0-255) in the histogram of the ciphered image, and E i is the expected occurrence frequency of the uniform distribution, given here by E i = (L × C × P )/256 [START_REF] Assad | A new chaos-based image encryption system[END_REF]. We give in Table II, the results of Chi-square test of three ciphered images (Baboon, Peppers, and Lena) having the size of (256×256×3), with a significant level of 0.05. We observe that for the three images, χ 2 exp < χ 2 th (255, 0.05). Therefore, the distribution of the histograms is uniform.

Fig. 1 :

 1 Fig. 1: Structure of the proposed PCNG. Key-setup: Its role is to calculate the initial values Xp(0) and Xs(0) of the chaotic maps Pwlcm and Skewtent respectively from Xp and Xs of the secret key K and from the initial vector IV . The initial values Xp(0) and Xs(0) are calculated as follows: Xp(0) = Xp ⊕ IV p Xs(0) = Xs ⊕ IV s(1)

CFig. 2 :

 2 Fig. 2: Lena image, encrypted Lena and their histograms.(a) Lena image, (b) histogram of Lena Image, (c) Encrypted Lena image, (d) histogram of encrypted Lena Image.

TABLE I :

 I P-values and Proportion results of NIST.

	Test	P -value Proportion
	Frequency test	0.249	98
	Block-frequency test	0.063	99
	Cumulative-sums test	0.862	98
	Runs test	0.456	100
	Longest-run test	0.720	100
	Rank test	0.924	100
	FFT test	0.596	98
	Nonperiodic-templates	0.540	98.784
	Overlapping-templates	0.817	98
	Universal	0.720	98
	Approximty entropie	0.972	98
	Random-excursions	0.325	98.674
	Random-excursions-variant	0.273	98.401
	Serial test	0.720	99.5
	Linear-complexity	0.475	100
	III. SECURITY ANALYSIS AND SIMULATION RESULTS OF
	THE PROPOSED STREAM CIPHER

TABLE II :

 II Theoretical and experimental values for the Chi-Square test.

		Baboon	Peppers	Lena
	χ 2 th χ 2 exp	293 253.5	293 259.1	293 251.2

ACKNOWLEDGMENT

The authors would like to thank the European program: Erasmus Mundus scholarship E-GOV-TN.

D. Computing performance

We have analyzed the speed of the proposed algorithm on an Intel Core i5 @ 2.60 GHz with 15.6 GB Running on Ubuntu 14.04 Trusty Linux, using a C compiler. In this implementation, we do not parallelize processes and operations. We applied the proposed algorithm to the Lena image of size (256×256×3). We evaluated the computing performance as follows: for 100 different keys, we executed our algorithm and then, we calculated the average encryption time in (Micro second), the average encryption throughput (ET) in (MByte) and the number of cycles per byte (NCpB).

ET =

Image size(M Byte) Encryption time(s)

Table III presents the speed performance of the proposed algorithm. In Table IV we compare the speed performance in term of needed cycles to encrypt one byte (NCpB) of our proposed algorithm with two algorithms of the eStream project, namely Rabbit and HC-128 stream ciphers [START_REF] Robshaw | The estream project[END_REF]. We note that the proposed stream cipher has good computing performance while having a very high level of security.

IV. CONCLUSION

In this paper, we proposed a novel stream cipher based on a strong pseudo chaotic number generator (PCNG), which contains two chaotic maps weakly coupled by a predefined matrix and integrates a swap function. Through the security analysis and the obtained experimental results, we find that our algorithm is very secure and its computing performance is comparable with those of project eStream. All these features prove that our chaos-based stream cipher is very suitable for encrypting data before their transmission over public transmission channels.


Ons Jallouli
email: ons.jallouli@univ-nantes.fr

Mohammed Abutaha
email: mohammad.abu-taha@univ-nantes.fr

Safwan El Assad
email: safwan.elassad@univ-nantes.fr

Maryline Chetto
email: maryline.chetto@univ-nantes.fr

Audrey Queudet
email: audrey.queudet@univ-nantes.fr

Olivier Deforges
email: olivier.deforges@insa-rennes.fr

Comparative Study of two Pseudo Chaotic Number Generators for Securing the IoT

The extremely rapid development of the Internet of Things brings growing attention to the information security issue. Realization of cryptographically strong pseudo random number generators (PRNGs), is crucial in securing sensitive data. They play an important role in cryptography and in network security applications. In this paper, we realize a comparative study of two pseudo chaotic number generators (PCNGs). The First pseudo chaotic number generator (PCNG1) is based on two nonlinear recursive filters of order one using a Skew Tent map (STmap) and a Piece-Wise Linear Chaotic map (PWLCmap) as non linear functions. The second pseudo chaotic number generator (PCNG2) consists of four coupled chaotic maps, namely: PWLCmaps, STmap, Logistic map by means a binary diffusion matrix [D]. A comparative analysis of the performance in terms of computation time (Generation time, Bit rate and Number of needed cycles to generate one byte) and security of the two PCNGs is carried out.

I. INTRODUCTION

The conversion from closed enterprise IT networks to public networks (Internet) is increasing continuously and justly raising questions about security. With the huge and rapid revolution of the Internet, we are increasingly interconnected on intelligent devices, and a lot of various digital data, such as text, image, video, or audio, travel from one destination to another via the network channel. Some of these data might be sensitive and confidential, therefore they need to be secured. The need to develop methods to secure these transactions has become a challenge for many researchers. Randomness in data processing is a key factor for security. Then, the generation of pseudo-random numbers is a very important topic which continue to encourage the researchers since many decades. Indeed, a pseudo-random number generator (PRNG) is defined as an algorithm enabling to generate a sequence of numbers with high properties of randomness. The design of a PRNG depends on applications to which it is dedicated. For data protection, Pseudo Chaotic Number Generators (PCNGs) are the central element of any strongly secure chaos-based block and stream ciphers [START_REF] Assad | A new chaos-based image encryption system[END_REF] [2] [3] [4] [START_REF] Masuda | Cryptosystems with discretized chaotic maps[END_REF]. For that, many PCNGs have been proposed in the literature for stream ciphers [START_REF] Assad | Chaos based information hiding and security[END_REF] [7] [START_REF] Lian | A chaotic stream cipher and the usage in video protection[END_REF].

In this paper, we realized and presented a comparative study of two PCNGs for stream ciphers. The first PCNG is based on non-linear recursive filter. The second PCNG uses a coupling technique based on a binary diffusion matrix. Both PCNGs integrates a chaotic switching technique.

The paper is organized as follows: In section II, we describe the structures of the two proposed PCNGs. The performance of both PCNGs in terms of time consuming and security analysis is given in section III. Finally, in section IV, we conclude the paper.

II. PROPOSED PSEUDO CHAOTIC NUMBER GENERATORS: PCNGS

In this section, we describe in details the structure of the two proposed PCNGs. The first PCNG uses two chaotic maps with a delayed feedback loop and a chaotic multiplexing technique. The second PCNG is based on four different chaotic maps coupled by a binary diffusion matrix and uses a chaotic switching technique.

All the initial conditions, parameters and initial vector for the two PCNGs are chosen randomly from Lunix generator "/dev/urandom".

A. Architecture of the pseudo chaotic number generators

The architecture of the PCNG1 is presented in Figure 1.

It consists of two nonlinear recursive filters of order one. The first recursive filter contains a discrete Skew Tent map (STmap) and the second recursive filter contains a discrete Piecewise Linear Chaotic map (PWLCmap). The outputs of these recursive filters are given respectively by:

X s = ST map{F 1[n -1], P 1} ⊕ Q1 (1)
with

F 1[n -1] = mod[U s + X s(0) + (K1 s × X1 s), 2 N ] (2)
And the equation of the recursive cell containing the PWLC map is defined by:

X p = P W LCmap{F 2[n -1], P 2} ⊕ Q2 (3)
output function produces the output sequence X(n), by using a chaotic switching technique.

The equation of the system is given by:

⎡ ⎢ ⎢ ⎣ Xp1(n) Xs(n) Xp2(n) Xl(n) ⎤ ⎥ ⎥ ⎦ = D ⎡ ⎢ ⎢ ⎣ F p[Xp1(n -1)] F s[Xs(n -1)] F p[Xp2(n -1)] F l[Xl(n -1)] ⎤ ⎥ ⎥ ⎦ . ( 7
)
where D is the binary diffusion matrix:

D = ⎡ ⎢ ⎢ ⎣ 1 1 1 0 1 1 0 1 1 0 1 1 0 1 1 1 ⎤ ⎥ ⎥ ⎦ . ( 8
)
And is the operator defined as we can see in the following equation :

⎡ ⎢ ⎢ ⎣ Xp1(n) Xs(n) Xp2(n) Xl(n) ⎤ ⎥ ⎥ ⎦ = ⎡ ⎢ ⎢ ⎣ F p[Xp1(n -1)] ⊕ F s[Xs(n -1)] ⊕ F p[Xp2(n -1)] F p[Xp1(n -1)] ⊕ F s[Xs(n -1)] ⊕ F l[Xl(n -1)] F p[Xp1(n -1)] ⊕ F p[Xp2(n -1)] ⊕ F l[Xl(n -1)] F s[Xs(n -1)] ⊕ F p[Xp2(n -1)] ⊕ F l[Xl(n -1)] ⎤ ⎥ ⎥ ⎦ . ( 9
)
The obtained samples of the sequence X(n) are controlled by the chaotic switching technique, using the obtained sample Xl(n) and two threshold T h1 and T h2, as defined as follows:

X(n) = ⎧ ⎨ ⎩ Xp1(n), if 0 < Xl(n) < T h1 Xs(n), if T h1 ≤ Xl(n) < T h2 Xp2(n), otherwise (10)
Where T h1 = 0.8 × 2 N and T h2 = 0.9 × 2 N .

III. EXPERIMENTAL RESULTS

In this section, we give the obtained performance of the two PCNGs in terms of computing time and robustness against known and statistical attacks.

A. Computing Performance of PCNGs

The experiment is made using a two 32-bit multicore Intel Core(TM) i5 processors running at 2.60 GHz with 16 G of main memory. This hardware platform was used on top of an Ubuntu 14.04 Trusty Linux distribution, and the programming is done in code C. We provide below, for different sizes of data bytes, the average generation time in micro second GT(μs), the average bit rate en Mega bit par second BR(Mbit/s), and the average of the needed number of cycles to generate one byte, NCpB(Cycles/B). The average is calculated by using 100 different secret keys. The results obtained in tables I, II, III, show that the PCNG2 has better computing performance than PCNG1. Besides, these computing performance are better than some known pseudo-random number generators of the literature: Jallouli et al. [START_REF] Jallouli | A novel chaotic generator based on weakly-coupled discrete skewtent maps[END_REF], Franc ¸ois et al. [START_REF] Franc ¸ois | A new image encryption scheme based on a chaotic function[END_REF], QUANTIS [START_REF] Hartmann | Practical guide to computer simulations[END_REF] and Blum Blum Shub [START_REF] Blum | A simple unpredictable pseudo random number generator[END_REF].

B. Security analysis and statistical attacks

We report below first the security analysis in terms of key size, keystream attack and key sensitivity attack. Then, we give the obtained results of several statistical tests that were carried out in order to quantify the good statistical properties of the proposed PCNGs.

1) Key size, Keystream attack and Key Sensitivity of the PC-NGs :

The key size |K1| and |K2| of the PCNG1 and PCNG2 respectively consists of all initial conditions and parameters of the proposed system and they are large enough to resist the brute force attack. Indeed, |K1| = 4 × 32 + 23 + 21 + 32 + 31 + 32 + 32 = 299 bits, and |K2| = 4 × 32 + 32 + 2 × 31 = 222 bits.

Also, as for each new execution the produced keystream is totally different from each others, due to the IVg value, so, the system can resist against keystream attack. Besides, the key

HD(S 1 , S 2 ) = 1 Nb × Nb K=1 (S 1 (K) ⊕ S 2 (K)) (11)
Where Nb is the number of bits in a sequence.

The obtained average value of Hamming distance is equal to 0.499999 and 0.499887 for PCNG1 and PCNG2 repetitively. These values are close to the optimal value of 50%, which indicate the high sensitivity on the secret key.

2) Mapping and Histogram:

The Mapping (X(n + 1) = f (X(n))) reflects the dynamic behavior of the system. As we can see in Figure 3a, the resulting mapping of a given produced sequence by the PCNG1 seems to be random in comparison with a mapping (a signature) of a given known map. Similar visual result is obtained for the PCNG2. A good PCNG must produce sequences that have uniform distribution in the whole phase space. Visually, the obtained histogram in Figure 3b for a given generated sequence is uniform.

To confirm this result we applied the Chi-Square and we obtained 991.962210 and 1030.832 as an experimental value for PCNG1 and PCNG2, which is smaller than the theoretical value 1073.642651, then the histogram is uniform for the two PCNGs. Also, the uniformity of the sequence generated by the PCNG1 is better than one produced by PCNG2. Indeed, more the experimental value of Chi-Square is smaller than the theoretical one, better is the uniformity of the generated sequence.

3) Auto and Cross-correlation: Another good property of a PCNG is that, the generated sequences must be uncorrelated. Thus, the cross-correlation of two sequences x and y (generated with slightly different keys) must be close to zero. The correlation coefficient ρ xy of the two sequences x and y is given by:

ρ xy = Ns i=1 (x i -x)(y i -ȳ) [ Ns i=1 (x i -x) 2 ] 1/2 × [ Ns i=1 (y i -ȳ) 2 ] 1/2 . ( 12

4) NIST Test:

NIST test is one of the most standards for investigating the randomness of binary data [START_REF] Elaine | Recommendation for random number generation using deterministic random bit generators[END_REF]. This test is a statistical package that consists of 188 tests and sub-tests that, were proposed by NIST in order to assess the randomness of an arbitrarily long binary sequences. Figure 4 give the results for sequences X1 and X2 generated by PCNG1 and PCNG2 respectively.

We observe that, sequence X2 does not pass only one sub-test. In contrast, sequence X1 has successfully passed all the NIST tests. Therefore, the proposed chaotic generator PCNGs are robust against statistical attacks and the security performance of the first PCNG1 is better than the second one.

IV. CONCLUSION

In this paper, we realized a comparative study of the performance in terms of computation time and security of two proposed PCNGs. The analysis study and the obtained results of the two PCNGs show that the two proposed PCNGs have strong cryptographic properties. Security performance of the first proposed PCNG is better than the second one but it is slightly slower. Also, these PCNGs are faster than some proposed generators of the literature and will be used for a secure chaotic stream cipher in development.

Fig. 1 :Fig. 2 :

 12 Fig. 1: Structure of the first proposed PCNG1

Fig. 3 :

 3 Fig. 3: Statistical tests results

Fig. 4 :

 4 Fig. 4: Statistical tests results

x i and ȳ = 1

 1 NsNs i=1 y i are the mean values of x and y respectively. The obtained correlation coefficients are 0.0021 and 0.0030 for PCNG1 and PCNG2; they are close to zero.

TABLE I :

 I Generation Time of PCNG1 and PCNG2

	Data Bytes PCNG1 GT(μs)	PCNG2 GT(μs)
	64	6	2
	128	8	4
	256	11	8
	512	19	13
	1024	32	23
	2048	57	46
	4096	109	52
	16384	332	196
	32768	520	338
	65536	712	654
	125000	1282	1179
	196608	1830	1600
	393216	2902	2801
	786432	5502	4237
	3145728	21723	16727
	12582912	85009	66666

TABLE II :

 II Bit Rate of PCNG1 and PCNG2

	Data Bytes PCNG1 BR(Mbit/s)	PCNG2 BR(Mbit/s)
	64	85.33	171.81
	128	128	212.44
	256	186.18	255.36
	512	215.58	306.12
	1024	256	348.44
	2048	287.44	349.11
	4096	300.62	621.07
	16384	394.8	666.35
	32768	504.12	774.13
	65536	736.36	801.61
	125000	780.03	804.68
	196608	859.49	982.54
	393216	1083.99	1122.67
	786432	1143.49	1484.75
	3145728	1158.49	1504.48
	12582912	1184.15	1509.95

TABLE III :

 III Number of cycles per byte of PCNG1 and PCNG2

	Data Bytes	PCNG1 NCpB(Cycles/B)	PCNG2 NCpB(Cycles/B)
	64	232.5	121.06
	128	155	97.91
	256	106.5	81.45
	512	92	67.95
	1024	77.5	59.69
	2048	69	59.58
	4096	66	33.49
	16384	50.2	31.21
	32768	39.3	26.87
	65536	26.9	25.95
	125000	25.4	25.85
	196608	23.1	21.17
	393216	18.3	18.53
	786432	17.3	14.01
	3145728	17.1	13.83
	12582912	16.8	13.78

ACKNOWLEDGMENT

The authors would like to thank the European program: Erasmus Mundus scholarship E-GOV-TN, and the European Celtic-Plus project 4KREPROSYS -4K ultra HD TV wireless REmote PROduction SYStems, 2015.