TIMING OF FIVE PALFA-DISCOVERED MILLISECOND PULSARS

The MSPs described here were discovered in the inner-Galaxy region of the PALFA survey between 2010 September and 2012 September. During this time, the PALFA survey used the Mock spectrometers²⁵ to record data from the 7-beam ALFA receiver centered at 1375 MHz with 322.617 MHz of bandwidth across 960 channels and a sample time of 65.476 $\mu {\rm{s}}$. PALFA uses 268 s integrations per pointing in the inner-Galaxy. Additional details can be found in Lazarus et al. (2015).

The PALFA survey uses three pipelines to search for radio pulsars: (1) a full-resolution²⁶  PRESTO-based pipeline (Lazarus et al. 2015), (2) the Einstein@Home pulsar search pipeline (Allen et al. 2013), and (3) a PRESTO-based reduced-time-resolution "Quicklook" pipeline (Stovall 2013). The five MSPs presented here were all discovered using pipeline (1) on the Guillimin supercomputer operated for Compute Canada by McGill University, so it is the only pipeline we describe in some detail.

Prior to searching the data for pulsars, pipeline (1) performs radio frequency interference (RFI) excision which consists of multiple components. The first removes known RFI that is specific to electronics at the Arecibo Observatory. Then narrow-band RFI is identified in both the time- and frequency-domain using PRESTO's rfifind routine. The narrow-band RFI is masked out of subsequent processing. Next, broadband signals are identified by analyzing the DM = 0 $\mathrm{pc}\ {\mathrm{cm}}^{-3}$ timeseries. Bad time intervals are identified as samples whose values are more than six times larger than the local standard deviation. Such samples are replaced with the local median bandpass. At this stage, the data are de-dispersed into trial dispersion measures (DMs) ranging from 0 to ∼10,000 $\mathrm{pc}\ {\mathrm{cm}}^{-3}$. The DM steps were chosen to balance the contributions to pulse broadening from the sample duration, the despersive smearing within a single frequency channel, the dispersive smearing within a frequency sub-band, and the dispersive smearing due to the finite DM step size. We used the DDplan.py tool from PRESTO to determine the step sizes versus trial DM. The minimum step size was chosen by allowing smearing up to 0.1 ms. The resulting maximum DM smearing is about 0.1 ms at DMs of a few tens of $\mathrm{pc}\ \ {\mathrm{cm}}^{-3}$, increases to 1 ms for DMs of a few hundred $\mathrm{pc}\ \ {\mathrm{cm}}^{-3}$, and reaches 10 ms for DMs of about 10,000 $\mathrm{pc}\ \ {\mathrm{cm}}^{-3}$. After de-dispersion, two additional RFI excision steps are performed. The first is to remove "red" noise from each de-dispersed time-series using PRESTO's rednoise routine which performs a median removal using logarithmically increasing block sizes in the frequency domain. The second is to remove from the power spectrum, Fourier bins of RFI identified in lists of identified RFI that are generated dynamically from the combined ALFA beams and for each beam individually from the entire observing session, which typically consist of about 30 pointings. Each de-dispersed timeseries is searched for periodic signals using common Fourier search techniques and for individual pulses in the time domain using the PRESTO software package (Ransom et al. 2002). The periodic signal search has two components: the first is a zero-acceleration search and the second searches for signals with constant accelerations up to $\sim 1650\ {\rm{m}}\ {{\rm{s}}}^{-2}$ (Lazarus et al. 2015). The best candidates (roughly 100 per search pointing) are folded into diagnostic plots for further evaluation. Due to the large number of candidates that are generated by this pipeline, we have investigated multiple ways of sorting through them. One method uses machine learning algorithms to sort through the candidates using image pattern recognition (Zhu et al. 2014). PSR J1938+2012 was identified using this image pattern recognition technique, while the other four MSPs were identified by sorting on various heuristic ratings (see Table 4 of Lazarus et al. 2015).

After discovery, follow-up observations of each of the five new MSPs were conducted in order to determine rotational, astrometric, and binary parameters where applicable. This is done by accounting for every rotation of the pulsar over the entire data span by observing at appropriate spacings in time such that the number of pulses between observations is unambiguous. Once we obtained phase-connected solutions spanning more than one month, we observed each pulsar on a roughly monthly basis. PSRs J1906+0055, J1933+1726, J1938+2012, and J1957+2516 were timed using the 305 m William G. Gordon Telescope at the Arecibo Observatory while PSR J1914+0659 was timed using the 76 m Lovell Telescope at the Jodrell Bank Observatory.

From 2011 September 9 to 2013 September 20, observations of PSRs J1906+0055 and J1957+2516 at the Arecibo Observatory were performed using the ALFA receiver with the Mock spectrometers. These observations were typically conducted as test pulsars for the PALFA survey and were therefore recorded in the same mode as search observations described in Lazarus et al. (2015) and had integration times of between 268 and 600 s.

After 2012 February 18, follow-up observations of PSRs J1906+0055, J1933+1726, J1938+2012, and J1957+2516 were conducted using the L-wide receiver with the Puerto Rican Ultimate Pulsar Processing Instrument (PUPPI), which is a clone of the Green Bank Ultimate Pulsar Processing Instrument (GUPPI).²⁷ Initial observations consisted of incoherent search mode observations with 800 MHz of bandwidth that was split into 2048 channels with a sample time of 40.96 $\mu s$. These data were then folded using the fold_psrfits routine from the psrfits_utils software package.²⁸ Later observations were performed using PUPPI in coherent fold mode with the same 800 MHz of bandwidth split into 512 frequency channels and were written to disk every 10 s. RFI was excised from both incoherent and coherent PUPPI files using a median-zapping algorithm included in the PSRCHIVE ⁵ software package (van Straten et al. 2012).

Follow-up timing observations of PSR J1914+0659 at Jodrell Bank were done using a dual polarization cryogenic receiver with a center frequency of 1525 MHz and bandwidth of 350 MHz. Data were processed by a digital filter bank producing 700 frequency channels of 500 kHz bandwidth. The output of each channel was folded at the nominal topocentric period of the pulsar and the resultant profiles written to disk every 10 s. RFI was removed using a median-zapping algorithm and the data were then incoherently de-dispersed at the pulsar's DM and folded profiles were produced for total integration times of typically 40 minutes.

In order to construct the initial timing solutions for the four binary pulsars, we performed a fit of the observed periods from early observations to orbital Doppler shifts for circular orbits. For each of the five pulsars, we constructed pulse templates by summing together data from multiple observations and fitting Gaussian components to the summed profiles. Examples of summed profiles for each of the pulsars presented here were previously included in Lazarus et al. (2015). For each observation, we generated pulse times-of-arrival (TOAs) using pat from the PSRCHIVE software package to cross-correlate the pulsar's template profile with the data in the Fourier domain (Taylor 1992). The observations from Arecibo were split into 2–4 frequency sub-bands depending on the pulsar's brightness, and each sub-band was used to generate a TOA allowing us to fit for the DM. The TOAs were then fitted to a model for each pulsar to get the final timing solutions using TEMPO ³⁰ For all timing solutions, we used the DE421 solar system ephemeris and the BIPM clock timescale. The final timing solutions are given in Table 1 and the timing residuals are shown in Figure 1.

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Table 1.  Timing Solutions and Derived Parameters for Five PALFA-discovered MSPs

Parameter	PSR J1906+0055	PSR J1914+0659	PSR J1933+1726	PSR J1938+2012	PSR J1957+2516
Timing Parameters
R.A. (J2000)	19:06:48.68051(4)	19:14:17.647(2)	19:33:22.9828(3)	19:38:40.0803(1)	19:57:34.6115(3)
Decl. (J2000)	00:55:07.886(1)	07:01:11.00(7)	17:26:49.606(9)	20:12:50.827(3)	25:16:02.076(3)
Pulsar Period (s)	0.0027895524236884(2)	0.01851182255144(3)	0.02150723378644(1)	0.0026341351275486(6)	0.003961655342404(1)
Period Derivative (s s−1)	3.32(1) × 10−21	3.1(3) × 10−20	4.9(1) × 10−20	7.5(6) × 10−22	2.744(9) × 10−20
Dispersion Measure (pc cm−3)	126.8317(9)	225.3(2)	156.90(3)	236.909(5)	44.137(3)
Reference Epoch (MJD)	56408.0	56351.0	56466.0	56511.0	56408.0
Span of Timing Data (MJD)	55814–57001	55873–57101	56186–56746	56186–56834	55814–57001
Number of TOAs	187	61	45	96	151
rms Residual (μs)	7.84	245.61	33.95	20.19	19.15
EFAC (JB/Mock/PI/PC)a	–/1.0/1.0/1.4	1.0/1.1/–/–	–/–/1.1/–	–/–/1.1/–	–/1.5/2.0/2.1
1400 MHz Mean Flux Density (mJy)	0.1	⋯	0.04	⋯	0.02
Binary Parameters
Orbital Period (days)	0.6096071304(3)	⋯	5.15393626(2)	16.2558195(1)	0.2381447210(7)
Orb. Per. Derivative (s s−1)	⋯	⋯	⋯	⋯	12(2) × 10−12
Projected Semimajor Axis (lt-s)	0.6250279(9)	⋯	13.67353(1)	8.317778(4)	0.283349(6)
Epoch of Ascending Node (MJD)	56407.5586451(1)	⋯	56466.1820553(6)	56514.938959(1)	56407.8681189(6)
ECCsin(OM)	−1.0(3) × 10−6	⋯	−1.8(1) × 10−5	9.9(8) × 10−6	2(3) × 10−5
ECCcos(OM)	1(2) × 10−6	⋯	6.5(1) × 10−5	−3.2(9) × 10−6	2(2) × 10−5
Mass Function (${M}_{\odot }$)	0.0007055	⋯	0.1033	0.002338	0.0004307
Min. Companion Mass (${M}_{\odot }$)	0.12	⋯	0.79	0.18	0.099
Med. Companion Mass (${M}_{\odot }$)	0.14	⋯	0.96	0.21	0.12
Derived Parameters
Galactic Longitude (°)	35.51	41.79	53.18	56.2	62.77
Galactic Latitude (°)	−3.0	−1.85	−1.02	−0.76	−1.97
Eccentricity	1.4 × 10−6	⋯	6.7 × 10−5	9.4 × 10−6	2.8 × 10−6
DM Derived Distanceb (kpc)	3.3	6.1	5.5	7.7	3.1
Surface Mag. Field Strength (G)	$0.97\times {10}^{8}$	$7.7\times {10}^{8}$	$10.4\times {10}^{8}$	$0.45\times {10}^{8}$	$3.3\times {10}^{8}$
Spindown Luminosity (erg s−1)	$60.4\times {10}^{32}$	$1.96\times {10}^{32}$	$1.95\times {10}^{32}$	$16.2\times {10}^{32}$	$174.0\times {10}^{32}$
Characteristic Age (Gyr)	13.3	9.34	6.92	55.6	2.29

Note. Numbers in parentheses represent 1σ uncertainties in the last digits as determined by TEMPO, scaled such that the reduced ${\chi }^{2}=1$. All timing solutions use the DE421 Solar System Ephemeris and the UTC(BIPM) time system. Derived quantities assume an R = 10 km neutron star with $I={10}^{45}\ \mathrm{gm}\,{\mathrm{cm}}^{2}$. Minimum companion masses were calculated assuming a $1.4\ {M}_{\odot }$ pulsar. The EFAC values correspond to subsets of TOAs from observations from Jodrell Bank (JB), Mock spectrometers, and the ALFA receiver (Mock), PUPPI with L-wide in incoherent search mode (PI), and PUPPI with L-wide in coherent search mode (PC). The DM derived distances were calculated using the NE2001 model of Galactic free electron density, and have typical errors of $\sim 20 \%$ (Cordes & Lazio 2002).

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All of the binary pulsars presented here are in highly circular orbits (eccentricity <10⁻⁴). Since there is a strong correlation between the longitude of periastron (ω) and the epoch of periastron passage (T₀) in low-eccentricity binaries, we used the ELL1 binary model in TEMPO (see the appendix of Lange et al. 2001). The ELL1 model removes this correlation by using the parameterization ${\epsilon }_{1}=e\ \sin \ \omega$, ${\epsilon }_{1}=e\ \cos \ \omega$, and ${T}_{\mathrm{asc}}={T}_{0}-\omega {P}_{b}/2\pi$ where e is the eccentricity and P_b is the orbital period. This parameterization is superior for cases where xe² (x is the projected semimajor axis) is much smaller than the error in the TOAs, as is the case for all binary pulsars presented here. The timing residuals as a function of orbital period are presented in Figure 2.

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The procedure described in Section 2.3 is known to often result in the underestimation of TOA errors. Therefore, the TOA uncertainties for each recording instrument mode were multiplied by a scaling factor to produce a fit with ${\chi }^{2}$ equal to 1 for that subset of residuals. This results in more conservative estimates for the timing parameter uncertainties. The scaling factors (EFACs) used for each pulsar are given in Table 1.

For the PUPPI observations taken in coherent mode we also obtained observations of a noise diode, which are suitable for use in polarization calibration. Such observations were made for PSRs J1906+0055, J1933+1726, and J1957+2516. We used observations of the bright quasar B1442+10 made by the NANOGrav Collaboration (NANOGrav Collaboration et al. 2015) for flux calibration. The calibration of polarization and flux were performed using the pac tool from the PSRCHIVE analysis package using the SingleAxis model. We searched for rotation measures in the range −2,000 to 2,000 $\mathrm{rad}\ {{\rm{m}}}^{-2}$, but did not detect substantial polarization for any of these three MSPs. The mean flux densities are included in Table 1.

PSR J1906+0055 is a 2.8 ms pulsar with a DM of 127 $\mathrm{pc}\ {\mathrm{cm}}^{-3}$. It is in a highly circular, 14.6 hr orbit with a companion having a minimum mass of 0.12 M_⊙ (assuming a pulsar mass of 1.4 M_⊙) and a median mass of 0.14 M_⊙ (assuming a pulsar mass of 1.4 M_⊙). Therefore, the companion is likely a He white dwarf. The DM-derived distance for J1906+0055 from the NE2001 model (Cordes & Lazio 2002) for the Galactic electron density is 3.3 kpc. PSR J1906+0055's 14.6 hr orbit makes it a potential candidate for detection of orbital decay and for constraining dipolar gravitational radiation (Freire et al. 2012).

PSR J1914+0659 is an isolated, partially recycled pulsar with a spin period of 18.5 ms and a DM of 225 $\mathrm{pc}\ {\mathrm{cm}}^{-3}$. Its DM-derived distance is 6.1 kpc. Based on the spin period and period derivative, it is likely the result of a disrupted double neutron star system (Lorimer et al. 2004).

PSR J1933+1726 is a partially recycled pulsar with a spin period of 22 ms and a DM of 157 $\mathrm{pc}\ {\mathrm{cm}}^{-3}$ in a highly circular, 5 day orbit with a fairly high-mass companion. The companion's minimum mass is 0.8 M_⊙. This companion mass combined with the low orbital eccentricity indicates the companion is likely to be a CO white dwarf (Camilo et al. 2001). The DM-derived distance for this system is 5.5 kpc. The relatively high companion mass makes this system a candidate for a future Shapiro delay measurement if it has a favorable orbital inclination angle.

PSR J1938+2012 is a 2.6 ms pulsar with a DM of 237 $\mathrm{pc}\ {\mathrm{cm}}^{-3}$ and is in a highly circular, 16 day orbit. The companion's minimum mass is 0.2 M_⊙ and is therefore likely a He white dwarf. Its DM is among the highest known for rapidly rotating MSPs (P $\leqslant \,5$ ms; see Figure 3) The DM-derived distance for this system is 7.7 kpc.

PSR J1957+2516 is a 4.0 ms pulsar with a DM of 44 $\mathrm{pc}\ {\mathrm{cm}}^{-3}$ that is in a highly circular, 6.8 hr orbit. The eccentricity of the system is unconstrained by the timing solution presented here, but has an upper limit of 4 × 10⁻⁵. We have plotted the orbital phase of non-detections of PSR J1957+2516 during observations of 600 s or longer in Figure 2 as black Xs. These non-detections are consistent with eclipsing as they occur near the orbital phase of 0.25 which corresponds to superior conjunction. However, we cannot rule out that these non-detections are not due to scintillation, since the pulsar has a fairly low DM. There have also been detections of the pulsar during portions of the orbit where it appears to have been eclipsed at other times (see Figure 2). However, we note that the detections that occured near an orbital phase of 0.25 are from the top of the band only (i.e., the pulsar was not detected below about 1.4 GHz in that session). In addition to the possible eclipses, we also detected an orbital period derivative of 12 × 10⁻¹², making this a likely redback or black widow system. PSR J1957+2516's companion mass is $\approx 0.1$ M_⊙ and is consistent with this being a redback system. However, as shown in Figure 4, it lies between the black widow and redback populations in the orbital period versus minimum companion mass diagram.

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For all of the binary pulsars presented here, we examined archival optical and infrared data³¹ for possible counterparts at the locations given in Table 1. Only PSR J1957+2516 was found to have a potential counterpart. We identified a potential near-infrared counterpart to PSR J1957+2516 from the Two Micron All-Sky Survey (2MASS; Skrutskie et al. 2006). 2MASS J19573440+2516014 lies $2\buildrel{\prime\prime}\over{.} 5$ away from the pulsar. This is considerably larger than the typical 2MASS astrometric uncertainty of $\sim 0\buildrel{\prime\prime}\over{.} 1$, but it led us to further examine the field. On visually inspecting the 2MASS image the source appeared extended in the east-west direction by $\sim 5^{\prime\prime}$, overlapping with the position of PSR J1957+2516. Therefore we obtained further near-infrared imaging with the WIYN High Resolution Infrared Camera (WHIRC; Meixner et al. 2010) on the WIYN 3.5 m telescope in order to resolve the extended source. Our data consist of $14\times 30\,{\rm{s}}$ exposures with the J filter and $11\times 30\,{\rm{s}}$ exposures with the K_s filter on the night of 2014 May 10. The data were reduced according to standard procedures and calibrated relative to 2MASS. We very clearly show (Figure 5) that the single 2MASS source is actually a blend of three sources: two relatively bright stars and one fainter star. The position of the pulsar is between one of the brighter stars and the fainter star but inconsistent with all of them given the uncertainties (the WHIRC astrometry is accurate to $\pm 0\buildrel{\prime\prime}\over{.} 1$). Further investigation to subtract the brighter stars and look for a source coincident with the pulsar is ongoing.

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None of the five MSPs presented here are positionally coincident with γ-ray sources from the Fermi Large Area Telescope (LAT) 4-Year Point Source Catalog (3FGL; see Acero et al. 2015). This is not surprising given the relatively small spin-down rates and much larger distances of these MSPs compared to the current sample of γ-ray detected MSPs (Abdo et al. 2013), as well as the strong diffuse γ-ray background in the Galactic plane. The only exception is PSR J1957+2516, which is relatively nearby (D = 3.1 kpc) and has a moderately high spin-down rate ($\dot{E}=1.74\times {10}^{34}$ erg s⁻¹). To look for high-energy emission from this MSP, we retrieved all Pass8 Fermi LAT data within 8° of the radio timing position of PSR J1957+2516 spanning from the start of the mission through 2016 March 16. The data products were first filtered with the Fermi Science Tools v10r0p5 using the event selection criteria recommended by the Fermi Science Support Center.³² Using the counts, exposure, source maps, and live-time cube generated from these data as well as a spatial/spectral source model taken from the 3FGL catalog, we carried out a binned likelihood analysis to test for the presence of a γ-ray source at the pulsar position. We further include a new source at the pulsar position modeled with an exponentially cut-off power-law, as appropriate for a pulsar. The best-fit model from the binned likelihood analysis results in a negative value for the test significance for a source at the pulsar position. This is an indication that the addition of a γ-ray source coincident with PSR J1957+2516 is not warranted by the data, which in turn, suggests that this MSP does not produce γ-ray emission that is detectable above the background level. We also folded the Fermi photons for each of the five MSPs using the Fermi plugin for tempo2 ³³ and the pulsar ephemerides presented here. For the fold we selected events $\leqslant 0\buildrel{\circ}\over{.} 8$ from the MSP position and used events with energies ranging from 0.1 to 10 GeV, however there was no evidence of pulsations for any of the five MSPs. We note that in the case of the likely redback PSR J1957+2516, the orbital period derivative may have varied over the timespan of the Fermi data. Therefore, detection of pulsations in Fermi data for this pulsar may still be possible with a more extensive pulsation search with varying orbital period derivative.