NICER X-Ray Observations of Seven Nearby Rotation-powered Millisecond Pulsars

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 $\dot{P}\approx 1.75\times \,{10}^{-20}\,\,{\rm{s}}\,{{\rm{s}}}^{-1}$, this pulsar's surface dipolar magnetic field is B ≈ 2.38 $\times \,{10}^{8}$ G (Ransom et al. 2011). The orbital period of 53.6 days 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).

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 nonthermal model could not be formally excluded, the resulting power-law photon index was unusually soft, Γ = 5${}_{-1}^{+5}$, indicating a likely thermal spectrum (Spiewak et al. 2016).

PSR J0751+1807, an MSP with P = 3.48 ms, was discovered by the Arecibo Observatory in a search targeting unidentified Energetic Gamma Ray Experiment Telescope (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 an 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${}_{-0.17}^{+0.24}$ kpc. Finally, its spin down $\dot{P}$ ≈ 0.8 $\times \,{10}^{-20}$ s $\,{{\rm{s}}}^{-1}$ implies a surface dipole magnetic field strength of B ≈ 1.7 $\times \,{10}^{8}$ 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 nonthermally emitting MSP. These data also showed a hint of pulsations at the 1.7σ confidence level.

PSR J1012+5307 was discovered with the Lovell radio telescope at Jodrell Bank Observatory (Nicastro et al. 1995). 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 day) were measured in the discovery observation, they have since 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-data release 2 (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 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.

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; Arzoumanian et al. 2018). The X-ray counterpart of PSR J1744−1134 was discovered in ROSAT data (Becker & Trümper 1999). It has since been observed by Chandra, with the X-ray spectrum likely indicating thermal emission with blackbody 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 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 blackbodies with temperatures of kT_BB ∼ 0.07 keV and ∼0.26 keV (Keith et al. 2011).

The following other MSPs were also observed with NICER, but their results are not reported in this Letter.

• 1.  
  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 $\times \,{10}^{-13}$ erg cm⁻² $\,{{\rm{s}}}^{-1}$, 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 days 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 (Bogdanov et al. 2019; Ray et al. 2019b).
• 2.  
  PSR J1614−2230 was discovered in a Parkes radio search targeting unidentified EGRET sources (Hessels et al. 2005; Crawford et al. 2006). It is an MSP with P = 3.15 ms bound to a massive white-dwarf companion in a P_b = 8.7 days 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_⊙ (Arzoumanian et al. 2018). X-ray pulsations from this pulsar were detected with NICER, but are reported in full detail elsewhere (Z. Arzoumanian et al. 2019, in preparation), confirming a ∼4σ detection in XMM data (Pancrazi et al. 2012).
• 3.  
  PSR J0740+6620 is another GBNCC-discovered pulsar, in a 4.77 days orbit with a white-dwarf companion (Stovall et al. 2014; Lynch et al. 2018; 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${}_{-0.09}^{+0.10}$ 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 Z. Arzoumanian et al. (2019, in preparation).

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:

• 1.  
  pointing offset is <0015 from the source,
• 2.  
  pointing >20° from the Earth limb (>30° in the case of a bright Earth),
• 3.  
  excluding South Atlantic Anomaly passages,
• 4.  
  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 conditions²⁰ :

$$\begin{eqnarray*}\begin{array}{rcl}{\mathtt{FPM}}\_{\mathtt{OVERONLY}}\_{\mathtt{COUNT}} & \gt & (1.52\times {\mathtt{COR}}\_{{\mathtt{SAX}}}^{-0.633})\\ \mathrm{and}\ {\mathtt{FPM}}\_{\mathtt{OVERONLY}}\_{\mathtt{COUNT}} & \gt & 1.0.\end{array}\end{eqnarray*}$$

Some pulsars required slightly different filtering options. For example, a portion of the exposure for PSR J1552+5437 was acquired with a pointing offset >0015, and therefore this condition was relaxed to include pointing offset <01. 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 good time interval (GTI) selection to minimize background contamination and provide cleaner pulse profiles.

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 Letter, 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 as 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, because the thermal spectra of MSPs are expected to drop rapidly above ∼1.5 or 2 keV, an optimization of the high-energy cutoff can minimize the background contribution to the pulse profiles. Here, we perform a grid search for the low- and high-energy cutoffs (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.

Zoom In Zoom Out Reset image size

Table 4.  Pulsed Thermal Luminosities, Spin-down Luminosities, and Efficiencies

Pulsar	nH	kTBBa	${F}_{0.2-10.0\,\mathrm{keV}}^{\mathrm{pulsed}}$	${L}_{0.2-10.0\,\mathrm{keV}}^{\mathrm{pulsed}}$	$\dot{E}$	${L}_{X}/\dot{E}$
	(${10}^{20}$ cm−2)	(keV)	( erg cm−2 $\,{{\rm{s}}}^{-1}$)	( erg $\,{{\rm{s}}}^{-1}$)	( erg $\,{{\rm{s}}}^{-1}$)	(${10}^{-4}$)
PSR J0614−3329	3.0	0.23	3.5 $\times \,{10}^{-14}$	3.0 $\times \,{10}^{31}$	2.4 $\times \,{10}^{34}$	13.0
PSR J0636+5129	9.5	0.18	2.1 $\times \,{10}^{-14}$	1.0 $\times \,{10}^{29}$	5.6 $\times \,{10}^{33}$	0.2
PSR J0751+1807	6.2	0.10	3.2 $\times \,{10}^{-14}$	4.4 $\times \,{10}^{30}$	5.7 $\times \,{10}^{33}$	7.7
PSR J1012+5307	0.8	0.26	7.8 $\times \,{10}^{-15}$	7.7 $\times \,{10}^{29}$	2.7 $\times \,{10}^{33}$	2.9
PSR J2241−5236	1.1	0.26	3.2 $\times \,{10}^{-14}$	3.5 $\times \,{10}^{30}$	2.5 $\times \,{10}^{34}$	1.4

Notes. The pulsed X-ray fluxes and luminosities reported are unabsorbed. The luminosities are calculated with the distances reported in Table 1. The $\dot{E}$ values reported have been corrected for the Shklovskii effect (Shklovskii 1970).

^aWe assumed a 0.1 keV blackbody for PSR J0751+1807, and the values presented in Section 2 for the others.

Download table as:  ASCIITypeset image

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 NRT since 2011 August. 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 data sets and the TEMPO2 pulsar timing package (Hobbs et al. 2006) 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 this Letter, over the span of NICER's data collection, but they might not be the most optimal solution for long-term timing of these pulsars.

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 minutes duration are performed with approximately a three-week cadence in three radio frequency bands, typically centered on 732, 1369, 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 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 February 9 and 2018 April 22, requiring extrapolation to fold NICER data acquired outside of this epoch. We verified the timing solution on ad hoc data acquired through 2018 November 10 and observed no substantial deviations of these pulse arrival times from the predicted phase.

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.

Zoom In Zoom Out Reset image size

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 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.

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).

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.

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 ∼24 from the pulsar's reported position (Pleunis et al. 2017). Therefore, the standard angular distance filtering criterion (excluding >09) 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 ∼67,000).

Overall, we conclude that no pulsations were firmly detected from this pulsar. Assuming that the detection is real, however, the pulsations would correspond to a pulsed count rate of 0.008 ± 0.004 c s⁻¹ (consistent with a non-detection of pulsations), which is equivalent to a Swift-X-Ray Telescope (XRT) rate of 0.0004 c s⁻¹. 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 pulsar.²¹

A total of 71 ks of exposure are available for this pulsar after standard filtering. The ephemeris from the NRT (Table 10) allows us to calculate the pulse phase of each photon. However, whether we choose the full 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 ks). 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.

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.

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 (Z. Arzoumanian et al. 2019, in preparation), confirming the detection reported in Pancrazi et al. (2012). The NICER observations of PSR J0740+6620 are also presented in Z. Arzoumanian et al. (2019, in preparation).

From the pulsed count rates listed in Table 3, deduced from the pulse profile after GTI and energy range optimizations, we estimated with WebPIMMS²² 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 tool²³ (with the most recent maps from HI4PI Collaboration et al. 2016). These pulsed luminosities are listed in Table 4 together with spin-down luminosity $\dot{E}$ (corrected for the Shklovskii effect). We find efficiencies ${L}_{X}/\dot{E}$ in the range ${10}^{-5}$–${10}^{-3}$, which are 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 as they were derived from the pulsed flux only.

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: (1) 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 data sets, etc.

The phase alignments shown in Figure 2 are made with the timing models presented in this Letter (Tables 5–11). 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 (Arzoumanian et al. 2018), which are from the GBT, 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 Δϕ with the radio peak.

• 1.  
  PSR J0614−3329: Both X-ray and radio main peak are broad and essentially aligned (Δϕ ∼ 0.07). Furthermore, the secondary radio peaks appear to be somewhat aligned with the secondary X-ray pulse (see Figure 2).
• 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 Δϕ ∼ 0.3–0.4.
• 3.  
  PSR J0751+1807: The main radio pulse lags the X-ray peak by Δϕ ∼ 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.
• 4.  
  PSR J1012+5307: This pulsar also displays a large offset, with the X-ray pulse leading the main radio pulse by Δϕ ∼ 0.3, while the secondary radio pulses fall in the trough of the X-ray profile.
• 5.  
  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 Δϕ ∼ 0.2.

Zoom In Zoom Out Reset image size

The Δϕ 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 Δϕ ∼ 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.

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 ${\chi }_{\nu }^{2}$ > 2). For the other four pulsars, a single sine function is sufficient to describe the pulse profile (i.e., ${\chi }_{\nu }^{2}$ ≈ 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 (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 and 3). 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), thanks to the 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.

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, because 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 this Letter (see Table 3), a proper spectral analysis was unfortunately not possible. Using a NICER background model (Bogdanov et al. 2019; Ray et al. 2019b), 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 background,²⁴ we refrain from providing spectral parameters for these faint pulsars. Imaging instruments sensitive in the soft X-ray band, such as XMM-Newton, eROSITA (Predehl et al. 2014), or the future Athena X-ray Observatory (Nandra et al. 2013), are better suited for such spectral analyses.

The results of this Letter 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 emission²⁵ (simple or double blackbody; see Section 2 for 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 nonthermal (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; D. M. Rowan et al. 2019, in preparation). To confirm the thermal nature of the MSPs studied here would require observations with spectro-imaging X-ray instruments.

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 polarcaps. 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 mass–radius 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 as 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. Furthermore, NICER will also target newly discovered MSPs such as those discovered by the Arecibo PALFA survey (Parent et al. 2019).