Free Access
Issue
A&A
Volume 587, March 2016
Article Number A109
Number of page(s) 12
Section Astrophysical processes
DOI https://doi.org/10.1051/0004-6361/201527847
Published online 26 February 2016

© ESO, 2016

1. Introduction

More than 160 pulsars have now been detected as pulsed sources of GeV γ-ray emission by the Large Area Telescope (LAT), the main instrument on NASA’s Fermi Gamma-Ray Space Telescope1. Millisecond pulsars (MSPs), neutron stars with very short rotational periods (P ≲ 30 ms) that have been spun up by accretion from a binary companion (Alpar et al. 1982; Bhattacharya & van den Heuvel 1991; Tauris & van den Heuvel 2006) currently represent over 40% of this total. In addition to those already detected as pulsed sources of γ rays, two dozen more MSPs were discovered in targeted radio searches at the locations of unassociated Fermi-LAT sources with pulsar-like properties, and will likely be confirmed as the sources of the high-energy emission, once accurate timing models that are valid over months to years are available for them. A recent systematic study of the temporal and spectral emission properties of pulsars in γ rays is presented in the Second Fermi-LAT Pulsar Catalog (hereafter 2PC; Abdo et al. 2013), and Johnson et al. (2014) carried out a systematic modeling analysis of MSP radio and γ-ray light curves in the context of a selection of geometric emission models.

As the Fermi mission continues, the accumulation of γ-ray data by the LAT enables us to detect pulsations from fainter and fainter pulsars. This is especially true with the advent of the Pass 8 data, which is based on much improved LAT event reconstruction algorithms (Atwood et al. 2013), increasing the sensitivity of the LAT to γ-ray pulsations. As is shown in, for example, 2PC, the γ-ray luminosity of pulsars Lγhd2, where h is the γ-ray energy flux and d is the distance, scales with the so-called spin-down luminosity Ė = 4π2I/P3, where I denotes the neutron star moment of inertia (generally, and here, assumed to be 1045 g cm2, corresponding to canonical mass and radius values of 1.4 M and 10 km respectively), P is the rotational period and is the spin-down rate. Increased sensitivity to γ-ray pulsations thus enables us to probe greater distances as well as smaller Ė values, i.e., less and less energetic pulsars. Observing low Ė objects in γ rays allows us to constrain the deathline for γ-ray emission, which we define as the spin-down luminosity limit under which pulsars can no longer produce detectable high-energy radiation. Prior to this work, the empirical deathline was Ėdeath ~ 3 × 1033 erg s-1 (see 2PC). This deathline is a key unknown for models of high-energy emission from pulsars.

The present study focuses on MSPs which, among several other differences, are more widely distributed in Galactic latitudes than normal, non-recycled pulsars. Because of the bright γ-ray diffuse background at low Galactic latitudes, faint normal pulsars are more difficult to observe than faint MSPs. The sample of low Ė objects is thus likely more complete among γ-ray MSPs than normal γ-ray pulsars. Additionally, as the sample of γ-ray pulsars grows, the MSP pulse profile and luminosity distributions appear increasingly to differ from those of the normal pulsars, warranting that the two populations be studied separately.

One difficulty in probing the high-energy emission deathline for MSPs is that low Ė MSPs tend to have very small spin-down rates, typically of the order of ~ 10-21 s/s (we omit these units when quoting spin-down rates in the remainder of the text). Such low spin-down rates can be strongly affected by kinematic effects causing the apparent (measured) values, obs, to differ substantially from the intrinsic spin-down rates, int. In turn, this can lead to spin-down luminosity values that are bad estimates of the true energy budget that can be converted into γ-ray emission. The intrinsic spin-down rate can be expressed as (1)In the above expression, Gal is the difference between the line of sight acceleration of the pulsar and the Solar System in the gravitational potential of the Galaxy (see for example 2PC for further details), and Shk denotes the kinematic Shklovskii correction caused by the pulsar’s transverse proper motion (Shklovskii 1970), calculated as (2)where μ denotes the transverse proper motion of the pulsar. We note that for pulsars undergoing line of sight acceleration in an external gravitational field, as is for instance commonly observed for pulsars in globular clusters, the spin-down rate is shifted by alP/c, where al is the acceleration along the line of sight. From the above expressions it is clear that accurate spin-down rate, proper motion, and distance estimates are important for properly characterizing our γ-ray MSPs, and especially those near the γ-ray emission deathline that are most sensitive to inaccuracies in corrections. We note that varying moment of inertia (I) values could also play a role in the Lγ versus Ė relationship. In future analyses it may be worthwhile to account for the influence of the moment of inertia on this relationship.

Table 1

Main properties of the MSPs in this study.

The present article reports on the analysis of radio pulsar timing data taken at the Nançay Radio Telescope (NRT) for a selection of γ-ray MSPs with no or incomplete proper motion information. We obtained solid proper motion parameters for the selected pulsars, and new distance estimates from timing parallaxes for a few of them. With the new proper motion and distance data we then derived new spin-down luminosity Ė estimates and reassessed the question of the high-energy emission deathline. We also searched the data recorded by the LAT for pulsations using pulsar timing information from the NRT, and discovered pulsed GeV emission from four MSPs: PSRs J0740+6620, J09311902, J14553330, and J17302304. In Sect. 2, we present the list of pulsars selected for the radio timing analysis with NRT data, and present the results of this analysis. The analysis of LAT γ-ray data for PSRs J0740+6620, J09311902, J14553330, and J17302304 is reported in Sect. 3. The latter sections are followed by a discussion of the detectability of energetic MSPs in γ rays, the deathline for γ-ray emission from MSPs and the relationship between Lγ and Ė. Section 5 summarizes our results.

2. Radio timing analysis

2.1. Pulsar selection

The list of MSPs considered in the study was built by selecting those with significant γ-ray pulsations detected with the Fermi-LAT, and that are also regularly observed at the NRT. We further selected MSPs with no or incomplete transverse proper motion (μ) information in version 1.51 of the Australian Telescope National Facility (ATNF) pulsar database2 (Manchester et al. 2005), i.e., with either the “PMRA” or the “PMDEC” parameter missing, or with the “PMTOT” parameter available but both “PMRA” and “PMDEC” missing. Pulsars with complete proper motion information available were therefore rejected.

A few pulsars of interest were added manually to the list obtained after the selection described above. PSRs J06102100, J10240719 and J12311411 are cases of objects with large Shklovskii corrections causing very low or negative Ė values, indicating possible issues with their proper motion and distance estimates (see discussions in 2PC; Espinoza et al. 2013; Guillemot & Tauris 2014). These three pulsars were added to our list of targets, with the hope of shedding light on the causes of the likely overestimated Shklovskii corrections. Although the MSP discovered at Nançay in a Fermi-LAT unassociated source PSR J2043+1711 has a published proper motion measurement (Guillemot et al. 2012), the much increased radio timing data span since the latter publication was likely to provide improved constraints on μ. Finally, the four new γ-ray MSP detections PSRs J0740+6620, J09311902, J14553330, and J17302304 were included in the study, to obtain pulsar timing parameters enabling precise phase-folding of the LAT data (see Sect. 3).

Table 1 lists the 19 MSPs retained for our study and some of their properties. Nine distances come from timing parallax measurements, of which seven come from this work, described in the next section. The remaining distances come from the electron column density along the line of sight to the pulsar (the dispersion measure, DM) and the NE2001 Galactic free electron model (Cordes & Lazio 2002). The DM distance uncertainties were estimated by varying the DM by ±20% as in 2PC. For each line of sight, we examined the NE2001 electron density versus distance. The density is highly structured for most of these pulsars, with unphysical steps, dips, and spikes, especially for the first few kpc: see Fig. 4 of Hou et al. (2014) for examples. The DM value is small (<25 pc cm-3) for half of these MSPs, making the estimated distance particularly sensitive to the local density model, with uncertainties perhaps larger than those tabulated.

2.2. Methodology

The radio pulsar timing analysis was carried out by analyzing data recorded with the Berkeley-Orléans-Nançay (BON) and the NUPPI (a version of the Green Bank Ultimate Pulsar Processing Instrument3 designed for the NRT) instruments in operation at the NRT, a meridian telescope equivalent to a 94 m dish located near Orléans, France. The BON backend was the main pulsar timing instrument at Nançay after it started operating in late 2004. BON observes primarily at 1.4 GHz, with a frequency bandwidth of 64 MHz before July 2008 and then 128 MHz. Data recorded with this instrument are coherently dedispersed within 4 MHz channels, ensuring good timing resolution. In August 2011, BON was replaced as the principal instrument for pulsar observations by NUPPI, a new backend giving access to a much increased frequency bandwidth of 512 MHz, also coherently dedispersed. NUPPI pulsar observations are primarily carried out at 1.4 GHz. The BON backend is still active and is used in parallel to NUPPI, with a central frequency for BON observations moved up to 1.6 GHz while NUPPI observations remain centered at 1.4 GHz. Because the frequency band recorded by the BON backend after August 2011 overlaps with the one covered by NUPPI, we excluded from our datasets BON observations made simultaneously with NUPPI observations, to avoid duplication of astrophysical information. As a result, and since no 1.4 GHz BON data were available for PSR J0740+6620, only NUPPI data were analyzed for this pulsar.

The subsequent data reduction was done using the PSRCHIVE analysis software library (Hotan et al. 2004). We cleaned the data for the selected MSPs of radio frequency interference (RFI) using a median smoothed automatic channel zapping algorithm as implemented in PSRCHIVE, and polarization-calibrated the data with the SingleAxis method of the software package. For each pulsar and observation system (BON 1.4 GHz and NUPPI 1.4 GHz), we combined up to 10 observations with the highest signal-to-noise ratios (S/N) to produce high-S/N integrated profiles. These profiles were smoothed to produce template profiles, and times of arrival (TOAs) were then extracted by cross-correlating the template profiles with the observations. The TOA extraction was carried out using the “Fourier phase gradient algorithm” that uses the property that two functions shifted in the time domain have Fourier transforms that differ by a linear phase gradient (a detailed description of the method can be found in Taylor 1992), except for the pulsars with generally low S/N profiles PSRs J00340534 and J2043+1711, for which the “Fourier domain with Markov chain Monte Carlo algorithm” gave more realistic TOA uncertainties. The TOA data were analyzed with the Tempo2 pulsar timing software (Hobbs et al. 2006). A detailed description of pulsar timing equations and techniques can be found in, e.g., Lorimer & Kramer (2012). We used the DE421 Solar system ephemeris (Folkner et al. 2009) for the conversion of the TOAs to Barycentric Coordinate Time (TCB).

In a first iteration of the timing analysis, the BON observations were split into two frequency channels of 32 MHz before July 2008 and of 64 MHz after that date, and the NUPPI observations were split into four frequency channels of 128 MHz each. The multi-frequency TOA datasets created with this procedure allowed us to track potential time variations of the integrated column density of free electrons along the line of sight, the DM. Using Tempo2 and the TOA datasets, we obtained new timing solutions for each pulsar by fitting for their astrometric parameters (equatorial coordinates and proper motion components), rotational parameters (rotational frequency and first time derivative), and binary parameters when applicable. We also fitted for the DM value and for its first time derivative (“DM1” parameter in Tempo2), excluding the latter parameter from the model if not significant. We fitted a systematic time offset (“JUMP” parameter) between the BON and the NUPPI TOA datasets, in order to accommodate differences in the observing systems and in the template profiles. The timing solutions obtained after this first iteration were then used to phase-fold the observation files, and new integrated profiles and template profiles were created with the updated observation files.

In the second iteration of the analysis, we concatenated the frequency information from the 1.4 GHz BON and NUPPI data to produce one TOA per observation, representing the entire frequency bandwidth available. The DM parameters were frozen at the values obtained from the previous step, and the timing analysis was repeated. To clean the TOA residual data of any remaining outliers degrading the timing analysis, we rejected residuals ri verifying |ri − med(r)| >, where med(r) denotes the median value of the residuals, σ is the median absolute deviation (MAD; see for example Huber 1981), and setting K to 3 which approximates a cut at two standard deviations for a Gaussian distribution.

In the case of PSR J09311902, the Nançay timing dataset was complemented by adding Westerbork Synthesis Radio Telescope (WSRT) TOAs generated from the PuMa-II backend (Karuppusamy et al. 2008). Observations for this pulsar were done on a monthly basis at two frequencies using the 1380 MHz receiver with a bandwidth of 160 MHz and the 350 MHz receiver with a bandwidth of 80 MHz. All data were coherently dedispersed using dspsr and folded using the PSRCHIVE software in a similar way as the Nançay data. To generate TOAs, synthetic templates were generated based on high S/N additions of all available observations at each frequency. The extended timing baseline and the quality of the WSRT TOAs improved the measurement of the astrometric parameters.

Table 2 summarizes the properties of the TOAs selected at this stage of the analysis. The main results from the timing analysis with Tempo2 are summarized in Sect. 2.3.

Table 2

Properties of the radio timing data analyzed in this study.

2.3. Results

The post-fit timing residual root-mean-square (rms, given by the “TRES” parameter in Tempo2) values for each MSP considered in this study are given in Table 2, along with a summary of the main properties of the NRT TOAs. Reduced χ2 values for the MSPs in the table range from 1.0 to 2.5, indicating that the timing solutions describe the TOAs adequately. For all pulsars, the timing precision and time interval considered enabled us to measure the proper motions. In a few cases we could also detect an annual parallax in the TOA residuals. For a pulsar at a distance d and with an ecliptic latitude of β, the parallax effect introduces a sinusoidal variation in the TOA residuals with an amplitude of l2cos2(β) /(2cd), where l is the Earth-Sun distance, and c is the speed of light. The effect is subtle: at d = 1 kpc and for β = 0 the amplitude is only 1.2 μs; so it was only measurable for a subset of the MSPs with low residual rms values.

The proper motion and parallax measurements are listed in Table 3 along with the associated 1σ uncertainties from Tempo2. Also given in the table are the previously reported values when available, for comparison. For the MSPs with no parallax measurement we determined 2σ upper limits; these limits are also reported in the table. Our PM and PX values are consistent with the latest results from the EPTA collaboration (Desvignes et al. 2016) who combined data recorded with the BON backend, analyzed with different methods, and from other radio telescopes. Our measurements are also compatible with those published by the NANOGrav and PPTA collaborations (Matthews et al. 2016; Reardon et al. 2016).

We explored how the Lutz-Kelker effect (Lutz & Kelker 1973) changes the inferred pulsar distances, using the code provided by Verbiest et al. (2012), for the six pulsars for which we measured a timing parallax. For four of the pulsars, the ATNF database lists values of the flux density at 1400 MHz, which we provided to the code. The distance is decreased for all six pulsars. For four of the pulsars the corrected distance is within 15% of PX-1, with no consequences for our conclusions. For PSRs J2017+0603 and J2214+3000 the distances decrease to 0.4 and 0.2 kpc, respectively, i.e., about 40% of the uncorrected values. Even this rather significant change does not qualitatively change our conclusions (e.g., for the γ-ray luminosity and efficiency values; see the paragraphs for these two pulsars below). We neglect the Lutz-Kelker effect in the rest of this paper.

The new proper motion parameters as well as the distances derived from the parallax measurements were used to calculate the Shklovskii corrections to . The distances of pulsars with no detection of the parallax signature were determined using the NE2001 model of Galactic free electron density (Cordes & Lazio 2002). The spin-down rate values corrected for the Shklovskii effect and for the acceleration in the Galactic potential are given in Table 1. In the following we present the salient results stemming from the timing analysis, and the new spin-down rate estimates. The cases of PSRs J06102100 and J10240719 are discussed in separate Sects. 2.4 and 2.5.

Table 3

Proper motion and parallax measurements for the pulsars considered in this study.

  • PSR J00340534: nearly nine years of NRT data yield a total transverse proper motion of μ = (12.6 ± 1.4) mas yr-1, significantly smaller than the value of (31 ± 9) mas yr-1 determined by Hobbs et al. (2005) and thus reducing the Shklovskii correction appreciably: our estimate of int is about 70% larger than the value of ~2.9 × 10-21 reported in 2PC, assuming the same NE2001 distance of (0.54 ± 0.11) kpc. The pulsar’s efficiency of conversion of spin-down power into γ radiation, η = Lγ/Ėint, decreases slightly from about 3% to 2%.

  • PSR J0340+4130: the modest proper motion determined for this pulsar of (3.85 ± 0.33) mas yr-1 introduces a small Shklovskii correction to the observed spin-down rate value at the NE2001 distance of (1.73 ± 0.30) kpc. A γ-ray luminosity of about 7.3 × 1033 erg s-1 was determined in 2PC for this pulsar. The slightly reduced Ėint value compared to that quoted in 2PC makes the γ-ray efficiency η to be ~110%. PSR J0340+4130 is likely closer than the NE2001 distance of 1.73 kpc, which would reduce Lγ significantly and also diminish the Shklovskii correction. No significant timing parallax is detected for this pulsar with the present NRT dataset.

  • PSR J06143329: this pulsar is listed in 2PC as having an implausible γ-ray efficiency value of about 215%, at the NE2001 distance of (1.9 ± 0.4) kpc. Interestingly, we measure a very modest transverse proper motion of μ = (2.00 ± 0.11) mas yr-1 for this MSP, leading to a negligible Shklovskii correction. No parallax measurement was possible with the Nançay timing data. Yet, the pulsar may lie at as little as a quarter of the NE2001 distance, given its high γ-ray efficiency.

  • PSR J0740+6620: this pulsar, named PSR J0741+66 in Stovall et al. (2014) and PSR J0742+66 in the ATNF pulsar database, is found to be at right ascension αJ2000 = 07h40m45.798(5)s and declination δJ2000 = + 66°20′33.65(2)′′. We propose that this object should be referred to as PSR J0740+6620, and use this name in the rest of the article. For this pulsar we find a high μ value of (32.6 ± 4.1) mas yr-1 that, at the NE2001 distance of (0.68 ± 0.10) kpc, makes our estimate of the intrinsic spin-down rate smaller than the observed one by almost 50%. The corrected Ėint value above 1034 erg s-1 and the small distance make J0740+6620 a good candidate for the detection of γ-ray pulsations, and the pulsar is actually found to coincide with the 3FGL source J0740.8+6621. The detection of γ-ray pulsations from this pulsar is presented in Sect. 3.

  • PSR J0751+1807: our estimates for the total proper motion and parallax of this pulsar differ appreciably from those reported in Nice et al. (2005), putting J0751+1807 at a greater distance of (1.51 ± 0.35) kpc. At this distance and for the transverse proper motion we measure, the Shklovskii correction to is about a third of the apparent spin-down rate. The spin-down power is thus significantly smaller than that inferred from the apparent spin properties. Using the new distance and Ėint estimates, and the γ-ray energy flux for PSR J0751+1807 reported in 2PC, we find a rather large efficiency of about 70%, suggesting that the actual pulsar distance may be at the small end of the uncertainty range.

  • PSR J09311902: this pulsar was discovered with the Green Bank Telescope as part of the 350 MHz drift-scan survey. Its discovery and a full description of its timing properties will be presented in Lynch et al. (in prep.). For this MSP, the combined Nançay and WSRT timing dataset allowed us to measure a modest proper motion of μ = (4.6 ± 1.2) mas yr-1. Even at the relatively large NE2001 distance of (1.88 ± 0.51) kpc, the observed spin-down rate is found to be very weakly affected by the Shklovskii effect. Weak γ-ray pulsations are detected for this pulsar (see Sect. 3). Its high γ-ray efficiency of about 200% (with large uncertainties) suggests a smaller distance than the NE2001-predicted value. We note that η< 100% would imply d< 1.4 kpc, whereas a typical η ~ 10% would be obtained for a much smaller distance of about 0.4 kpc.

  • PSR J12311411: at face value, the previously-published μ value of (104 ± 22) mas yr-1 and the NE2001 distance of (0.44 ± 0.05) kpc cause the Shklovskii-corrected int and Ėint terms to be negative, which is unrealistic for a rotation-powered, non-accreting MSP. Our analysis yields no parallax measurement for this pulsar, but a significantly reduced μ value of (62.34 ± 0.26) mas yr-1 leading to Ėint ~ 6 × 1033 erg s-1, a typical value for a γ-ray MSP, and η ~ 40 % which is also acceptable.

  • PSR J14553330: the Nançay timing data available for this pulsar enable us to measure the proper motion components with good accuracy, leading to μ = (8.11 ± 0.05) mas yr-1, lower than the previously reported (25 ± 12) mas yr-1 from Toscano et al. (1999). Additionally, we determined a parallax of (0.99 ± 0.22) mas, placing J14553330 at a distance of (1.01 ± 0.22) kpc, and thus further away than the (0.53 ± 0.07) kpc predicted by the NE2001 model. In Sect. 3 we show that J14553330 exhibits faint yet significant γ-ray pulsations.

  • PSR J16142230: our best-fit value for the transverse proper motion is consistent with earlier measurements. The detection of a significant parallax of π = (1.30 ± 0.09) mas enables the calculation of a revised distance to this pulsar, of d = (0.77 ± 0.05) kpc, lower than the NE2001 distance of (1.27 ± 0.20) kpc. A γ-ray efficiency of about 40% is obtained when using the new distance and Ėint estimates, slightly higher than the ~33% reported in 2PC, but not atypical.

  • PSR J17302304: the NE2001 model places this pulsar at a distance of (0.53 ± 0.05) kpc. We measure a parallax placing this pulsar a little farther away, at d = (0.84 ± 0.19) kpc. Using this distance value and our measurement of the transverse proper motion, we get a relatively well constrained Ėint value of (8.4 ± 2.2) × 1032 erg s-1. This Ėint value is lower than those of all known γ-ray MSPs, with the possible exceptions of PSRs J06102100 and J10240719, for which Ėint is essentially unconstrained (see Sects. 2.4 and 2.5). Yet, pulsation searches in the LAT data for this MSP reveal significant γ pulses (see Sect. 3). PSR J17302304 may thus be the γ-ray pulsar with the lowest spin-down power value known at present.

  • PSR J1741+1351: the best-fit proper motion of (11.62 ± 0.13) mas yr-1 is in good agreement with the value reported by Espinoza et al. (2013) of (11.71 ± 0.01) mas yr-1. On the other hand, we do not detect the parallax signature reported in the latter article, but our 2σ lower limit remains compatible with it. For this pulsar we therefore assume their parallax distance of (1.08 ± 0.05) kpc. For this distance and our proper motion measurement, we find a typical γ-ray efficiency of 4% for this pulsar.

  • PSR J18112405: the detection of this pulsar in GeV γ rays with the Fermi-LAT was reported recently by Ng et al. (2014). Nançay timing measurements enable us to measure a value for the transverse proper motion of μ = (9.2 ± 5.1) mas yr-1, only weakly affecting the spin-down rate and spin-down power, assuming a distance for the pulsar of (1.8 ± 0.5) kpc, based on the NE2001 model. The γ-ray efficiency remains typical for this pulsar, at about 20%, in accordance with the value published in Ng et al. (2014). Interestingly, the 2σ upper limit on the parallax determined from the NRT TOAs constrains the distance of PSR J18112405 to be greater than 2.5 kpc, and thus larger than the NE2001 distance of 1.8 kpc. A greater distance would imply an increased γ-ray luminosity, and in turn, an increased efficiency.

  • PSR J18233021A: unlike the other MSPs in our sample, this pulsar has a that is a few orders of magnitude higher than those of other MSPs, and that is mostly unaffected by the Shklovskii correction. It is also the only MSP in the sample to be in a globular cluster, NGC 6624. The apparent spin-down rate is likely affected by line of sight acceleration in the cluster. Nevertheless, as was first noted by Freire et al. (2011), the pulsar’s large γ-ray luminosity indicates that it is a very energetic MSP and that most of its apparent spin-down rate is therefore intrinsic. Our proper motion measurement for PSR J18233021A is compatible within uncertainties with the value found by Kharchenko et al. (2013) for NGC 6624, of ~9.85 kpc, suggesting that the MSP is bound to the cluster.

  • PSR J2017+0603: the transverse proper motion derived for this pulsar is small: μ = (2.35 ± 0.08) mas yr-1. The timing analysis also reveals a parallax signature, leading to a distance estimate for this pulsar of (0.9 ± 0.4) kpc, i.e., less than the (1.57 ± 0.16) kpc predicted by NE2001. The smaller distance and new Ėint estimate bring the γ-ray efficiency reported in 2PC from 75% to 25%, which is closer to the average η value for the MSP population (Johnson et al. 2013).

  • PSR J2043+1711: for this MSP discovered at Nançay at the location of a Fermi-LAT source (Guillemot et al. 2012), the proper motion components are consistent with those reported previously and are more accurately determined: the transverse proper motion is now found to be μ = (12.8 ± 0.4) mas yr-1, compared to (13 ± 2) mas yr-1 previously. We are currently insensitive to the timing parallax effect, so that our best estimate of this pulsar’s distance remains the NE2001 prediction, of (1.76 ± 0.32) kpc. The 2PC luminosity leads to a γ-ray efficiency of about 100%, suggesting a smaller distance for this pulsar.

  • PSR J2214+3000: the analysis of the Nançay timing data enables us to measure a parallax, placing the pulsar at d = (0.60 ± 0.31) kpc, closer than the value predicted by NE2001 based on its dispersion measure, of (1.54 ± 0.19) kpc. We also find the transverse proper motion of this pulsar to be μ = (20.96 ± 0.11) mas yr-1. With the new distance and revised spin-down power value, the γ-ray efficiency reported in 2PC of about 50% decreases to a very typical ~10%.

  • PSR J2302+4442: the timing analysis of this MSP yields a small proper motion of μ = (5.85 ± 0.12) mas yr-1, such that the Shklovskii correction assuming the NE2001 distance of (1.19 ± 0.23) kpc very weakly affects and Ė. Using the γ-ray luminosity published in 2PC of Lγ ~ 6.2 × 1033 erg s-1, we find that the efficiency η remains very high, at about 170%. PSR J2302+4442 might thus well be at a closer distance than the (1.19 ± 0.23) kpc from NE2001.

2.4. PSR J06102100

The γ-ray pulsations from this pulsar were first reported by Espinoza et al. (2013) and its high-energy emission properties were reassessed in 2PC. Both studies came to the conclusion that, at the NE2001 distance of ~3.54 kpc, the very low intrinsic spin-down power value is well below the empirical deathline for γ-ray emission and the inferred γ-ray efficiency is unrealistically large. Based on infrared observations in the direction of PSR J06102100 showing pronounced nebulosity around the pulsar, Espinoza et al. (2013) proposed that unmodeled line of sight material could explain the apparently overestimated NE2001 distance.

From the analysis of the Nançay timing data, we determined a transverse proper motion of (19.10 ± 0.08) mas yr-1 that is slightly greater than the (13 ± 3) mas yr-1 reported by Burgay et al. (2006), and the (18.2 ± 0.2) mas yr-1 reported in Espinoza et al. (2013) and assumed in 2PC. We did not measure any significant timing parallax effect that would provide us with a revised distance estimate. Consequently, with the same distance value as used in previous γ-ray studies of this MSP and a slightly larger transverse proper motion, the issues of the very low Ėint and high η values persist, with Ėint ~ 8 × 1031 erg s-1 and η> 200.

thumbnail Fig. 1

Spin-down power Ė and γ-ray efficiency η as a function of the distance, for PSR J06102100. ĖShk denotes the Shklovskii correction to Ė, ĖGal is the contribution from the line of sight acceleration in the Galactic potential, and Ėint is the spin-down power obtained after correction for these effects. The blue curve represents the γ-ray efficiency, η (the y-axis scale is in percent), and the gray-shaded area shows the region excluded by the condition η> 0. Finally, the red dashed line shows the NE2001-predicted distance for PSR J06102100 of 3.54 kpc, and the green-shaded region represents the zone excluded by the 2σ lower limit on the distance from our timing analysis, of 0.77 kpc.

Open with DEXTER

Figure 1 plots the Ė and η values for PSR J06102100 as a function of the distance, assuming a proper motion of 19.10 mas yr-1 and the 3FGL energy flux of 1.15 × 10-11 erg cm-2 s-1. Also shown in the figure are the distance range excluded by the condition Ėint> 0 (or equivalently η> 0) which is ensured for d< 3.57 kpc, and the range excluded by our determination of a 2σ lower limit on the distance, of 0.77 kpc. One can immediately see that the NE2001 distance is very close to the value at which Ėint = 0, hence the very low spin-down power and high efficiency. At the 2σ lower limit on the distance the efficiency is already high, with η ~ 12%, and it reaches 100% at d ~ 1.78 kpc.

Assuming that the observed spin-down rate is not affected by line of sight acceleration caused for instance by the presence of an unknown body attracting PSR J06102100, we can infer that the distance to the pulsar likely lies between 0.8 and 1.8 kpc and that the pulsar’s intrinsic spin-down power is in the range from 4 × 1033 to 7 × 1033 erg s-1, i.e., well above the deathline for MSP γ-ray emission. In the absence of a better distance estimate for PSR J06102100, we consider that the intrinsic spin-down power of this MSP is currently unknown and that it cannot be used for probing the γ-ray emission deathline.

2.5. PSR J10240719

The signature of the transverse proper motion in the Nançay data is strong for this isolated pulsar, and the timing yields a very significant μ = (59.67 ± 0.04) mas yr-1, in accordance with the previously-reported measurement of Verbiest et al. (2009), and among the highest values measured to date for any MSP. For this total proper motion, accounting for the Galactic acceleration and Shklovskii correction to leads to a negative (hence, implausible) intrinsic spin-down rate, for any distance d greater than ~0.4 kpc. As was noted by, for example, Espinoza et al. (2013) and in 2PC, using the NE2001 distance of 0.39 kpc leads to a very small intrinsic Ėint well below 1033 erg s-1, while for the parallax distance of 0.53 kpc reported by Hotan et al. (2006), it becomes negative. As can be seen from Table 3, we find a parallax distance for PSR J10240719 of (1.13 ± 0.18) kpc that is even larger than the value obtained by Hotan et al. (2006), and for which the Shklovskii correction actually exceeds the apparent spin-down rate itself, thus giving a negative corrected value. In Espinoza et al. (2013) and 2PC, the issue of the negative γ-ray efficiency η = Lγ/Ė was alleviated by using the NE2001 distance. Nevertheless, our parallax measurement brings additional indication that the actual distance is likely greater than 0.4 kpc, and that another explanation than an overestimated distance needs to be found to mitigate the negative spin-down rate issue.

As was already noted by Verbiest et al. (2009), the timing of PSR J10240719 reveals evidence for low-frequency, long-term noise in the residuals, the so-called “red noise”. Our analysis confirms this trend: fitting for a second period derivative, , yields a significant value of (7.0 ± 0.6) × 10-32 s-1. Pure magnetic dipole braking with an index such that n = 3 would lead to s-1, i.e., several orders of magnitude smaller than the value we measure, and with the opposite sign. Therefore, the origin of this term in the timing residuals of PSR J10240719 is likely extrinsic.

A natural explanation for the negative Shklovskii-corrected spin-down rate and the presence of a significant second period derivative in the Nançay timing data could be that PSR J10240719 undergoes acceleration along the line of sight, caused by the existence of a second body in the vicinity of the pulsar. Joshi & Rasio (1997) presented a method for determining the mass of the putative companion and the orbital parameters, in the cases where only a small fraction of the orbit is covered. With this method, the full determination of the orbital parameters and the mass requires the measurement of the first five derivatives of the period. With the present data for J10240719, only P, , and can be significantly detected. Subsequent period derivatives may become measurable with an increased timing dataset.

Nonetheless, deep VLT observations of the field of PSR J10240719 conducted by Sutaria et al. (2003) revealed the presence of two stars near the position of the pulsar. One possibility could therefore be that PSR J10240719 is associated with one of the two nearby stars, in a wide orbit causing the MSP to undergo acceleration along our line of sight. Follow-up observations by Bassa et al. (in prep.) may confirm the association of the pulsar with either the bright or the faint optical source, or deny this scenario.

We conclude that the intrinsic spin-down rate (int) of this MSP is not accurately known at present, and that consequently the pulsar should not be used as a probe of the deathline for γ-ray emission from MSPs.

Table 4

Properties of PSRs J0740+6620, J09311902, J14553330, and J17302304 in GeV γ rays.

3. Gamma-ray analysis

We characterized the γ-ray emission from PSRs J0740+6620, J09311902, J14553330, and J17302304 by analyzing data from the Large Area Telescope (LAT), the electron-positron pair conversion telescope on the Fermi satellite launched in June 2008 (Atwood et al. 2009). We selected LAT data from the much improved Pass 8 reconstruction algorithms (Atwood et al. 2013). The event list was restricted to those recorded between 2008 August 4 and 2015 July 1, with energies between 0.1 and 300 GeV, and with zenith angles smaller than 90° to limit the contamination of the datasets from the Earth’s limb. The analysis was carried out with the Fermi Science Tools4 (STs) v10-01-01. The data were phase-folded using the ephemerides obtained from the analysis described in Sect. 2, with the Fermi plug-in for Tempo2 (Ray et al. 2011).

For each of the four MSPs we created individual γ-ray datasets by selecting photons found within 15° of the pulsars. In parallel, we constructed spectral models for these regions of interest (ROIs) by selecting 3FGL sources within 20° of the MSPs, and by including models representing the Galactic diffuse emission and the isotropic diffuse and residual instrumental background emission, using the gll_iem_v06.fits and iso_P8R2_SOURCE_V6_v06.txt files produced by the Fermi-LAT collaboration. Of the four MSPs considered in this high-energy analysis, PSRs J0740+6620 and J09311902 have counterparts in the 3FGL catalog, named 3FGL J0740.8+6621 and J0930.91904, respectively. We shifted the positions of these two sources in our models to the radio timing positions found for the MSPs. For PSRs J14553330 and J17302304 we added new sources, also placed at the best-fit coordinates from the timing analysis.

The spectral parameters of sources more than 5° away from the pulsars were fixed at the values determined in the 3FGL analysis, except for sources with Test Statistic (TS) values higher than 1000, which were fixed at the 3FGL results if more than 10° away. Spectral parameters of other sources were left free in the fits. The contributions from the four MSPs were modeled as a function of energy E as exponentially cutoff power laws of the form N0(E/ 1 GeV)− Γexp(E/Ec), where N0 represents a normalization factor, Γ is the power law index and Ec is the exponential cutoff energy. The Fermi ST gtlike was used in conjunction with the MINUIT optimizer to determine the spectral parameters of the sources in the models, by means of a maximum likelihood analysis. To increase the signal-to-noise ratios of the pulsars, we restricted the datasets to pulse phase ranges determined from the inspection of the γ-ray pulse profiles, described below.

The results of the spectral analysis for PSRs J0740+6620, J09311902, J14553330, and J17302304 are presented in Table 4. All four MSPs are detected as significant sources of γ-ray emission, as can be noted from the TS values. The γ-ray emission of two of the four pulsars is very weak, which prevented us from measuring the Γ parameter in these cases. To derive meaningful constraints on the other parameters, the spectral index of PSR J09311902 was fixed at the value of 1.85 ± 0.16 found in 3FGL. For PSR J14553330 we fixed the Γ parameter to 1.3, the average value of MSP spectral indices tabulated in 2PC. Also given in Table 4 are the γ-ray luminosities above 0.1 GeV, Lγ = 4πhd2 (this assumes a beaming correction factor, fΩ, defined in, e.g., 2PC, of 1), and the conversion efficiencies η = Lγ/Ėint. The efficiency values for PSRs J0740+6620 and J14553330 are fairly typical for γ-ray MSPs. For PSRs J09311902 and J17302304 the large efficiency uncertainties stem mainly from the distance uncertainties, and the efficiencies are consistent with being below 100%. We also tried fitting the pulsar spectra with simple power laws of the form N0(E/ 1 GeV)− Γ, and found that the exponentially cutoff power-law shapes are preferred in all four cases, with 1 to 4σ significance.

thumbnail Fig. 2

Integrated Fermi-LAT γ-ray and Nançay radio profiles for the MSPs J0740+6620, J09311902, J14553330 and J17302304. Two full radio profiles are shown. For PSR J0740+6620 we display the LAT events recorded after MJD 55 800. Radio light curves all correspond to 1.4 GHz Nançay profiles recorded with the NUPPI backend, with 2048 bins per rotation except for PSR J09311902 for which the number of bins was reduced to 256 to improve the signal-to-noise ratio of the profile. The 30-bin γ-ray light curves were constructed by selecting Fermi-LAT photons found within 5° of the pulsars and with energies above 0.1 GeV. The photons were then weighted by the probability that they were emitted by the pulsars, as calculated based on spectral likelihood results.

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The best spectral models for the regions around the MSPs were used to compute probabilities that the photons in the ROIs were emitted by the pulsars, using the ST gtsrcprob. Having assigned weights and pulse phases to each photon in our datasets, we produced weighted γ-ray profiles; these profiles are shown in Fig. 2. We find weighted H-test TS significances (Kerr 2011) above 5σ for all four objects, indicating significant γ-ray detections and bringing the number of MSPs detected as pulsed γ-ray sources to 71. For PSR J0740+6620 our timing solution is found to determine accurate pulse phases after MJD 55 800; we therefore selected events recorded during this time interval. Figure 2 also shows integrated 1.4 GHz radio profiles, with the correct relative radio/γ-ray alignment. In all cases the first γ-ray peak lags the main radio component, a fairly standard feature in radio and γ-ray pulsars.

4. Discussion

With the Fermi-LAT detections of PSRs J0740+6620, J09311902, J14553330 and J17302304, 71 MSPs have now been observed to emit GeV γ-ray pulsations. Nearly half of the total number of known γ-ray pulsars are MSPs, and about a third of all Galactic disk MSPs (i.e., MSPs outside of globular clusters) are seen in γ rays. Figure 3a is an update of the spin-down power Ė normalized by d2 versus P plot for Galactic disk MSPs with measured spin-down rates, previously shown in Guillemot & Tauris (2014), but with a larger MSP sample and with the new γ-ray detections. The two known γ-ray MSPs in globular clusters PSRs J18233021A and J18242452A are included in the plot. On the other hand, the γ-ray pulsars J06102100 and J10240719 are not plotted, having implausible Shklovskii-corrected spin-down powers (see Table 1), as argued in Sects. 2.4 and 2.5.

One striking feature of the MSP population, as can be seen from Fig. 3a, is that a large majority of the energetic and nearby ones are seen in γ rays. Above Ė/d2 = 5 × 1033 erg s-1 kpc-2, 75% of Galactic disk MSPs with known spin-down rates have been detected by the Fermi-LAT. High Ė/d2 MSPs that are undetected in γ rays could be further away than currently estimated, they could be less energetic (in particular if their proper motions and thus their Shklovskii-corrected spin-down rates are unknown), or they could be seen under unfavorable viewing angles as argued by Guillemot & Tauris (2014). At present, the least energetic γ-ray MSP known is PSR J17302304, with Ėint = (8.4 ± 2.2) × 1032 erg s-1. The latter value thus represents the current empirical deathline for γ-ray emission from MSPs, and future LAT observations of MSPs will tell if lower-Ė MSPs can produce detectable γ-ray emission.

thumbnail Fig. 3

Left: spin-down power Ė divided by the square of the distance d as a function of the period P, for MSPs in the Galactic disk. PSRs J18233021A and J18242452A, two MSPs in globular clusters but detected in γ rays, are included in the plot. Green stars represent γ-ray MSPs, undetected ones are shown as red circles. Guillemot & Tauris (2014) explain non-detections of energetic and distant MSPs in γ rays as due to unfavorable viewing angles. All Ė values are corrected for the effect of the acceleration in the Galactic potential. Filled symbols indicate pulsars for which we could correct for the kinematic Shklovskii effect. The right-hand panel shows the cumulative fraction of MSPs detected in γ rays, with decreasing Ė/d2 as indicated by the green arrow. Right: spin-down power values for the MSPs with Ė/d2 ≥ 1.5 × 1032 erg s-1 kpc-2. Half of the MSPs in this sample are seen with the Fermi-LAT. The green histogram shows the γ-detected MSPs, the empty histogram corresponds to the total number of MSPs in each Ė decade. The dashed line shows the fraction of γ-detected MSPs per Ė decade.

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thumbnail Fig. 4

Luminosity Lγ = 4πhd2 above 0.1 GeV as a function of the spin-down power (Ė) for the sample of MSPs considered in this work (red triangles), and other MSPs with Shklovskii-corrected Ė values (blue diamonds). Vertical error bars in gray represent the uncertainties due to the distance, while colored error bars represent the uncertainties on the γ-ray energy flux, h. The dashed line represents Lγ = Ė, and the dash-dotted line indicates the heuristic luminosity . Empty symbols represent pulsars with distance values estimated via the dispersion measure and the NE2001 model of Cordes & Lazio (2002), filled symbols are pulsars whose distances were determined with other methods, such as the measurement of the timing parallax.

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Figure 3b shows a histogram of Ėint values for MSPs with Ėint/d2 ≥ 1.5 × 1032 erg s-1 kpc-2, being the limit above which 50% of the MSPs shown in Fig. 3a are seen with the LAT. To a first approximation, the MSPs in this sample can be considered detectable. One possible improvement would consist of accounting for the background γ-ray emission present at the locations of these MSPs, and comparing these background levels to the maximum γ-ray fluxes one could expect from the MSPs. Nevertheless, we find that the majority of these MSPs are located at high Galactic latitudes and therefore generally lie in regions of weak background γ-ray emission. The plot confirms the idea that the γ-ray detectability of an MSP depends crucially on its spin-down power. In this sample, the ratio of γ-detected MSPs increases with Ė, and in particular 100% of the MSPs with Ė ≥ 1035 erg s-1 are seen by the LAT.

Figure 4 confirms that MSPs are detectable in γ rays only when Ė>Ėdeath ~ 1033 erg s-1. Our discovery of γ-ray pulsations from PSR J17302304 suggests that the minimum Ėdeath value could be less than that. Models describing particle acceleration and γ-ray emission in the magnetosphere of pulsars must therefore be able to explain high-energy emission from such low Ė pulsars. In addition, with this reduced empirical deathline we expect the Milky Way to host more γ-ray-emitting MSPs than previously thought. Population synthesis analyses aiming to predict the contribution from unresolved MSPs to the diffuse γ-ray emission in the Milky Way and their possible contribution to the Galactic Center excess (see for example Calore et al. 2014) will need to account for this increased number of γ-ray MSPs in the Galaxy. We note that all of the MSPs with LγĖ in Fig. 4 have distances estimated via their DM values and the NE2001 model, while MSPs with distances determined with other methods generally have efficiencies well below 100%. Given the large DM distance uncertainties discussed in Sect. 2.1, the γ-ray luminosities greater than Ė in Fig. 4 do not necessarily indicate that Ė is underestimated. The moment of inertia g cm2 (where M and R are the neutron star mass and radius) that we use is compatible with the range of most observed neutron star masses, 1 <M< 2 M, combined with the currently acceptable range of predicted neutron star radii, 9 <R< 15 km.

One key ingredient in several of these population studies is the relationship between the γ-ray luminosity of MSPs and the spin-down power. Knowing how Lγ scales with Ė, one can in principle predict the emitted flux and, after populating the Galaxy with MSPs, estimate their contribution to the diffuse emission. Precise proper motion and distance measurements such as those described in Sect. 2.3 help refine this relationship. Quite striking in Fig. 4 is that for ĖĖdeath, the luminosity is mostly uncorrelated with Ė. For instance, for Ė values between 1033 and 1034 erg s-1, calculated Lγ values are found to vary by two orders of magnitude. The apparent lack of a clear correlation contrasts with what is seen for young pulsars with higher spin-down power, which follow the rough trend suggested in Fig. 4 for Ė ≳ 5 × 1034 erg s-1. The relation comes from simple arguments (Arons 1996) that only partially describe the accelerating region.

The luminosity values shown in Fig. 4 were calculated as Lγ = 4πhd2, i.e., assuming a geometrical correction factor, fΩ, of 1. The spread in the luminosity distribution could thus be partly explained by our line of sight sampling the γ-ray beam’s neutron star latitude profile more or less favorably. However, Johnson et al. (2014) found little variation in the fΩ factors obtained for a sample of γ-ray MSPs and under different emission models, their fΩ values being typically close to unity. Varying geometrical correction factors thus likely play a limited role in the large Lγ spread. The spin-down power may also be affected by magnetospheric parameters, such as the magnetic inclination, α, or the current flows. Spitkovsky (2006) and Pétri (2012) considered pulsars with force-free magnetospheres and found the following expression for the spin-down power: Ėff ≃ 3 / 2Ėvac(1 + sin2α) where Ėvac = 4π2I/P3 is the vacuum spin-down power typically used for estimating Ė. Similar to the correction to Lγ due to the fΩ term, this correction to Ė can only partially mitigate the spread.

How brightly an MSP emits in γ rays, and how much of its total energy budget it converts into high-energy emission, surely depends on the shape and extent of the zone where electron cascades occur, and on the electric potential that can be sustained across the zone. The latter is mitigated by the plasma currents flowing through and around the zone. Continued modeling efforts to reproduce observations such as in Fig. 4, and especially to allow predictions of the γ-ray luminosity for arbitrary P, , and α values would permit improved estimates of the MSP contribution to the diffuse background.

5. Summary

We have presented the analysis of several years of Nançay and Westerbork radio timing data for a selection of γ-ray MSPs, which enabled us to determine their proper motions, and measure timing parallaxes for four of them. These parameters were used to improve our estimates of their spin-down power values by correcting for the Shlovskii effect, and of their γ-ray luminosities. We have also presented the analysis of more than six years of Pass 8 Fermi-LAT γ-ray data, leading to the discovery of high-energy pulsations for four MSPs: PSRs J0740+6620, J09311902, J14553330, and J17302304. The latter object is now the least energetic γ-ray pulsar known, setting the empirical deathline for γ-ray emission from MSPs to Ėdeath ~ 8 × 1032 erg s-1. PSRs J06102100 and J10240719, whose Ė values are likely unknown, could be even less energetic objects.

By considering the population of known Galactic disk MSPs, we have confirmed that those seen to emit γ rays by the Fermi-LAT are the energetic and nearby ones. In the sample of MSPs with Ė/d2 values above 5 × 1033 erg s-1 kpc-2, 75% are observed to emit pulsed γ-ray emission. Nevertheless, selecting γ-ray MSPs with Shklovskii-corrected Ė values, we have shown that above Ėdeath the spin-down power and the γ-ray luminosity appear mostly uncorrelated, in spite of the improved Ė and Lγ estimates. Varying moments of inertia, emission geometries and more realistic prescriptions for the energy budget that MSPs can convert into γ-ray emission could mitigate the lack of apparent correlation. Continued analyses of Pass 8 LAT data may also reveal γ-ray pulsations from even less energetic MSPs, constraining the γ-ray emission deathline and the spin-down-power versus luminosity relationship further.


Acknowledgments

We thank Cees Bassa for helpful discussions and constructive suggestions. The Fermi-LAT Collaboration acknowledges generous ongoing support from a number of agencies and institutes that have supported both the development and the operation of the LAT as well as scientific data analysis. These include the National Aeronautics and Space Administration and the Department of Energy in the United States, the Commissariat à l’Energie Atomique and the Centre National de la Recherche Scientifique/Institut National de Physique Nucléaire et de Physique des Particules in France, the Agenzia Spaziale Italiana and the Istituto Nazionale di Fisica Nucleare in Italy, the Ministry of Education, Culture, Sports, Science and Technology (MEXT), High Energy Accelerator Research Organization (KEK) and Japan Aerospace Exploration Agency (JAXA) in Japan, and the K. A. Wallenberg Foundation, the Swedish Research Council and the Swedish National Space Board in Sweden. Additional support for science analysis during the operations phase is gratefully acknowledged from the Istituto Nazionale di Astrofisica in Italy and the Centre National d’Études Spatiales in France. The Nançay Radio Observatory is operated by the Paris Observatory, associated with the French Centre National de la Recherche Scientifique (CNRS). The Westerbork Synthesis Radio Telescope is operated by the Netherlands Institute for Radio Astronomy (ASTRON) with support from The Netherlands Foundation for Scientific Research (NWO).

References

All Tables

Table 1

Main properties of the MSPs in this study.

Table 2

Properties of the radio timing data analyzed in this study.

Table 3

Proper motion and parallax measurements for the pulsars considered in this study.

Table 4

Properties of PSRs J0740+6620, J09311902, J14553330, and J17302304 in GeV γ rays.

All Figures

thumbnail Fig. 1

Spin-down power Ė and γ-ray efficiency η as a function of the distance, for PSR J06102100. ĖShk denotes the Shklovskii correction to Ė, ĖGal is the contribution from the line of sight acceleration in the Galactic potential, and Ėint is the spin-down power obtained after correction for these effects. The blue curve represents the γ-ray efficiency, η (the y-axis scale is in percent), and the gray-shaded area shows the region excluded by the condition η> 0. Finally, the red dashed line shows the NE2001-predicted distance for PSR J06102100 of 3.54 kpc, and the green-shaded region represents the zone excluded by the 2σ lower limit on the distance from our timing analysis, of 0.77 kpc.

Open with DEXTER
In the text
thumbnail Fig. 2

Integrated Fermi-LAT γ-ray and Nançay radio profiles for the MSPs J0740+6620, J09311902, J14553330 and J17302304. Two full radio profiles are shown. For PSR J0740+6620 we display the LAT events recorded after MJD 55 800. Radio light curves all correspond to 1.4 GHz Nançay profiles recorded with the NUPPI backend, with 2048 bins per rotation except for PSR J09311902 for which the number of bins was reduced to 256 to improve the signal-to-noise ratio of the profile. The 30-bin γ-ray light curves were constructed by selecting Fermi-LAT photons found within 5° of the pulsars and with energies above 0.1 GeV. The photons were then weighted by the probability that they were emitted by the pulsars, as calculated based on spectral likelihood results.

Open with DEXTER
In the text
thumbnail Fig. 3

Left: spin-down power Ė divided by the square of the distance d as a function of the period P, for MSPs in the Galactic disk. PSRs J18233021A and J18242452A, two MSPs in globular clusters but detected in γ rays, are included in the plot. Green stars represent γ-ray MSPs, undetected ones are shown as red circles. Guillemot & Tauris (2014) explain non-detections of energetic and distant MSPs in γ rays as due to unfavorable viewing angles. All Ė values are corrected for the effect of the acceleration in the Galactic potential. Filled symbols indicate pulsars for which we could correct for the kinematic Shklovskii effect. The right-hand panel shows the cumulative fraction of MSPs detected in γ rays, with decreasing Ė/d2 as indicated by the green arrow. Right: spin-down power values for the MSPs with Ė/d2 ≥ 1.5 × 1032 erg s-1 kpc-2. Half of the MSPs in this sample are seen with the Fermi-LAT. The green histogram shows the γ-detected MSPs, the empty histogram corresponds to the total number of MSPs in each Ė decade. The dashed line shows the fraction of γ-detected MSPs per Ė decade.

Open with DEXTER
In the text
thumbnail Fig. 4

Luminosity Lγ = 4πhd2 above 0.1 GeV as a function of the spin-down power (Ė) for the sample of MSPs considered in this work (red triangles), and other MSPs with Shklovskii-corrected Ė values (blue diamonds). Vertical error bars in gray represent the uncertainties due to the distance, while colored error bars represent the uncertainties on the γ-ray energy flux, h. The dashed line represents Lγ = Ė, and the dash-dotted line indicates the heuristic luminosity . Empty symbols represent pulsars with distance values estimated via the dispersion measure and the NE2001 model of Cordes & Lazio (2002), filled symbols are pulsars whose distances were determined with other methods, such as the measurement of the timing parallax.

Open with DEXTER
In the text

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