A Comprehensive Library of X-Ray Pulsars in the Small Magellanic Cloud: Time Evolution of Their Luminosities and Spin Periods

XMM-Newton was launched in 1999 December by the European Space Agency. It carries three identical grazing incidence X-ray telescopes, whose point-spread function (PSF) is sufficient to spatially separate most of the individual bright X-ray sources of the SMC. Up until 2014 (the cutoff for this project), 116 XMM-Newton observations of the SMC were available in the archive, as listed in Table 1.

XMM-Newton has the largest effective area of any X-ray satellite at energies below 2 keV, a record it will retain until the Neutron Star Interior Composition ExploreR (NICER) launches; it also has a 30 cm optical/UV telescope (the Optical Monitor; Mason et al. 2001) allowing simultaneous X-ray and optical/UV coverage. XMM-Newton's X-ray telescopes each feed one of the European Photon Imaging Cameras (EPIC; Strüder et al. 2001; Turner et al. 2001), which comprise the PN, and Metal Oxide Semi-conductor (MOS1, MOS2) instruments covering the energy range 0.1–15 keV with moderate spectral resolution.

From the XMM-Newton archive we acquired the EPIC PN data (which have a higher time resolution than the MOS data) for all publicly available SMC observations obtained from 2000 to 2014. In Figure 1 the number of observations in which the different known SMC pulsars appeared in the field of view (FOV) and the number of positive detections of them by the PN camera are shown in green and red, respectively. The spin periods of these SMC pulsars range from 0.72 to 4693 s. Here, positive detections means photon counts and flux are recorded in the XMM-Newton Science Archive (XSA).⁶ The X-ray source detections are above the processing likelihood of 6.⁷ In this histogram, we can see how many times each source was caught in quiescence (corresponding to non-detections), and we can identify the sources that are appear to be permanent (at least in the context of our 15 year study baseline) rather than transient emitters.

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In our data analysis pipeline, we begin with the SXP catalog of Coe & Kirk (2015), which contains pulse periods and celestial coordinates of each known pulsar, determined from the existing body of publications that includes X-ray and optical counterpart identifications. Most of the SXP pulsars have positions known to sub-arcsecond accuracy. We take the XMM-Newton source catalog obtained from the XSA and search for EPIC detections (both MOS and PN) in a positional search radius for each known pulsar. The initial search uses a search radius of 15'' about the known SXP coordinates. Every XSA catalog point-source within this radius is evaluated based on its positional offset and uncertainty, requiring the relative offset to be smaller than $3({\sigma }_{c}\lt 3)$ for a positive identification with the SXP object, where ${\sigma }_{c}$ is the combined uncertainty computed via Equation (1),

$$\begin{eqnarray}&&{\sigma }_{c}\equiv \displaystyle \frac{{r}_{\mathrm{off}}}{\sqrt{{r}_{\mathrm{xmm}}^{2}+{r}_{\mathrm{sys}}^{2}+{r}_{\mathrm{psr}}^{2}}},\end{eqnarray} \tag{ 1 }$$

and where r_off is the offset between the known position and the detected point-source position, r_xmm is the XMM-Newton Science Archive (XSA) Right Ascension and Declination (RADEC) combined error (determined while fitting the detection), r_sys is the XSA systematic error of the XMM-Newton fields, and r_psr is the uncertainty of the known position of the pulsar.

Our data reduction of these sources included the standard procedures of the XMM-Newton Science Analysis Software (SAS, version 14.0.0) from the XMM-Newton Science Operations Center (SOC). We retained the standard XMM-Newton event grades (patterns 0–4 for the PN camera), as these have the best energy calibration. The PN data were analyzed using the commands evselect and epiclccorr in SAS. For the EPIC detectors (Strüder et al. 2001; Turner et al. 2001), the data for the point-like sources were extracted from circular regions of radius 20''. Background levels were estimated and subtracted using annular regions defined by inner and outer radii of 30'' and 60'' centered on each source.

Source fluxes were directly obtained from the XSA using the known pulsar coordinates. If a source was not detected but it was in the FOV, then we recorded the upper limit to the flux that was calculated from the "Flux Limits from Images from XMM-Newton" (FLIX)⁸ server.

It was necessary to extract XMM-Newton light curves from scratch at the native timing resolution of the detectors (0.0734 s for PN) because the XSA pipeline versions are generated using a binning scheme that precludes high-resolution timing analysis. We also extracted and archived the event list (Time, Energy) for each individual source. This product is the starting point for performing a range of advanced event-based analyses, e.g., FFT (Israel & Stella 1996), quantiles (Hong et al. 2005), energy-dependent pulse profiles, and 2D phase-energy-intensity histograms (Schönherr et al. 2014; Hong et al. 2016).

The times of arrival of the photon events were shifted from the local satellite frame to the barycenter of the solar system using the task barycen in the SAS software. Additional improvements using the cleaned event file and the "gti" (good time interval) task tabgtigen were also made in order to exclude the times when the background was very high. The rate threshold of the "gti" fits file applied to the event file was set at 0.6 counts s⁻¹. A pulsation search was performed following the procedure described in Section 2.4.1 to search for periodicities in the broad, soft (0.2–2 keV), and hard (2–12 keV) energy bands.

The Chanda X-ray Observatory was launched in 1999 July, carrying the High Resolution Mirror Assembly (HRMA), the highest angular resolution X-ray optics ever flown in space. The HRMA focuses X-ray light on either the Advanced CCD Imaging Spectrometer (ACIS) or the High Resolution Camera (HRC). For this project we used ACIS data, which provide sub-arcsecond source positions, photon energies, and event timing to 3.2 s resolution in standard operation.

The known X-ray pulsars in the SMC (Coe & Kirk 2015) were searched for in the first 15 years of Chandra observations obtained from the Chandra Data Archive. We applied the latest Chandra calibration files to each image, and we reduced the data with the Chandra Interactive Analysis of Observations software package (CIAO, version 4.5; Fruscione et al. 2006). We created X-ray images within the 0.3–7.0 keV energy band in which Chandra is best calibrated and most sensitive. First, the image files were obtained by executing fluximage on the reprocessed event files. We then used mkpsfmap to generate a corresponding image whose amplitude is the PSF size in terms of the region that encloses 95% of the counts at 1.5 keV. The task evalpos was used to look up the PSF size at each source position in this image, and dmmakereg was used for generating the appropriate sized circular source extraction and annular background extraction regions.

After verifying the accuracy of the Chandra astrometry for the fields of interest, we placed our extraction regions at the coordinates of each pulsar to extract the source and background events. Finally, source fluxes and light curves were extracted with the CIAO tools srcflux and dmextract, respectively. The tool srcflux was used with a power-law spectral model with photon index 1.5 and an absorption column $5\times {10}^{21}$ cm⁻², representative of the line-of-sight to the SMC.

srcflux was also used to determine whether the pulsar was detected, in which case a flux measurement is reported, or not, in which case an upper limit is reported instead. The source flux was extracted within the region that encloses 95% of the counts at 1.5 keV. This region was determined for each detection separately using the PSF map. The srcflux derived net photon counts ≥1 at 90% (1.65σ) confidence level were recorded as detections. If the net counts are 0, then the upper limit is reported. For srcflux positive detections, a source event file, light curve, and pulse-height spectrum were extracted and saved in the library along with the appropriate response files. Light curves were extracted at 3.2 s resolution, set by the read-mode most commonly encountered in the archival data set. A pulsation search was performed following the procedure described in Section 2.4.1.

The number of times each source was in a Chandra FOV and the number of times each source was detected by Chandra are shown in Figure 2. As in the analogous Figure 1 for the XMM-Newton data, this plot serves to illustrate the frequency of each source being caught in quiescence (non-detections) and allows us to identify the "permanent" rather than transient emitters.

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The Rossi X-ray Timing Explorer (RXTE) launched in 1995 December carrying the Proportional Counter Array (PCA), All-Sky Monitor (ASM), and High Energy X-ray Timing Experiment. The PCA consisted of 4 Xenon-filled Proportional Counter Units (PCUs) and provided individual event timing at μs resolution and moderate energy resolution over the range 2–60 keV. Starting in 1997 the SMC was observed approximately weekly with the PCA for some 16 years, accumulating ∼1000 observations (Table 1) before RXTE was deactivated in 2012 January. Data in Good Xenon mode were extracted in the 3–10 keV energy range (maximizing S/N) using the FTOOLS suite. In our subsequent analysis, we used the output of the IDL pipeline products (PUlsar Monitoring Algorithm or PUMA) up to year 2012 (Galache et al. 2008). To summarize the data reduction: the data were first cleaned using standard FTOOLS scripts,⁹ then the FTOOL maketime was used to generate the GTI files. We extract the light curves with 0.01 s binning¹⁰ and we applied background subtraction and barycentric correction. Finally, the count rates were normalized to account for the varying number of active Proportional Counter Units. Further details can be found in Galache (2006), Galache et al. (2008), Townsend et al. (2011, 2013), and Klus et al. (2013).

The number of RXTE observations with collimator response >0.2 of each known SMC pulsar is shown in Figure 3. RXTE PCA was not an imaging detector, and this figure shows only the number of observations for which the coordinates of each pulsar were in the 2° full width at zero intensity (FWZI) FOV.

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2.4.1. Pulsar Detection

Following the approach established in prior works based on the Lomb-Scargle (LS) periodogram (Laycock et al. 2005, 2010; Galache et al. 2008), we searched for pulsations in the light curves of each pulsar from each satellite detection. The significance, s, of each periodicity was calculated from the number M of independent frequencies and the LS power P_X according to Press et al. (1992):

$$\begin{eqnarray}&&s=[1-M\exp (-{P}_{X})]\cdot 100 \% .\end{eqnarray} \tag{ 2 }$$

The error in spin period was calculated from the standard deviation of the frequency (Horne & Baliunas 1986):

$$\begin{eqnarray}&&\delta \omega =\displaystyle \frac{3\pi {\sigma }_{N}}{2{{TA}}_{s}\sqrt{N}},\end{eqnarray} \tag{ 3 }$$

where ${\sigma }_{N}^{2}$ is the variance of the light curve, N is the number of data points, T is the total length of the data, and A_s is the amplitude of the signal.

Each periodogram was automatically scanned to look for the expected fundamental and harmonics of the pulsar. For the imaging instruments the specific pulsar is known, so the search is very targeted. For RXTE the periods of all known pulsars in the FOV of the PCA collimator are searched, and we used the fundamental harmonics of [0.8–1.2] × P with the s ≥ 99% and all the collimator responses in the later analysis. Confidence levels are assigned following the prescription of Press et al. (1992) computed for a search over a 10% tolerance range on the expected period. We treat significance ≥99% as a valid detection and do not adjust the threshold to account for the number of observations. This ensures a uniform criterion that does not change if the definition of the sample were to change. When a detection was made we obtained the spin period, then folded the light curve and obtained the pulsation amplitude and the pulsed fraction (PF). The pulsed fractions of the light curves were calculated by integrating over the pulse profile according to the prescription of Bildsten et al. (1997). Here,

$$\begin{eqnarray}&&\mathrm{PF}=\displaystyle \frac{\tfrac{{\displaystyle \sum }_{j}^{{n}_{\mathrm{bin}}}({f}_{j,\mathrm{mean}}-{f}_{\min })}{{n}_{\mathrm{bin}}}}{\tfrac{{\displaystyle \sum }_{i}^{N}{f}_{i}}{N}},\end{eqnarray} \tag{ 4 }$$

where n_bin is the number of bins for each folded light curve, ${f}_{j,\mathrm{mean}}$ is the mean photon count rate in each bin, f_min is the minimum of ${f}_{j,\mathrm{mean}}$, and f_i is the photon count rate of the un-binned light curves.

Note that for RXTE we did not compute pulsed fractions since the PCA is a non-imaging detector and multiple sources are always in the FOV, so the un-pulsed component cannot be reliably measured.

2.4.2. Cross-calibration

In order to combine the data for the three satellites together it is necessary to account for differences in sensitivity and energy range. In principle, the response functions of each instrument are well characterized and good cross-calibration for flux, and luminosity is possible for the imaging instruments. Since RXTE is not an imaging instrument, and has very different properties, we took an empirical approach to scale the pulse amplitudes. For the purposes of plotting our results in this paper we performed a cross-calibration to normalize the luminosities and pulse amplitudes (count rates) to be on the same scale as the XMM-Newton PN. In the case of Chandra, this was accomplished using the tool PIMMS¹¹ (Portable, Interactive, Multi-Mission Simulator) to convert the count rate from the ACIS-I detector (with no grating) into XMM-Newton PN count rate (with no grating and medium filter). The input energy range was 0.3–7 keV and the output energy range was 0.2–12 keV. We used power-law models with absorption $5\times {10}^{21}$ cm⁻² (calculated using NASA's HEASARC tool¹² for the SMC sightline) and photon index of 1.5. With a 1 count s⁻¹Chandra detection, the predicted XMM-Newton count rate is about 4 counts s⁻¹. Thus, the pulsation amplitudes from Chandra were scaled by a factor of 4.

For the RXTE data we do not directly measure absolute flux due to the likelihood of source confusion. Many observations feature two or more pulsars active simultaneously (commonly 1–3, but in one case 7). Instead we followed an empirical approach to estimate total flux from pulse amplitude (which we measure directly): we used PIMMS to calculate the absorbed fluxes from the measured pulse amplitudes, assuming a fixed pulsed fraction. We set both the input and the output energy range of the PCA detector to 3–10 keV. From the PIMMS power-law model described above, the predicted flux for 1 count PCU⁻¹ s⁻¹ was ${ \mathcal F }=({9.23}_{+0.10}^{-0.12})\times {10}^{-12}\,\mathrm{erg}\,{\mathrm{cm}}^{-2}\,{{\rm{s}}}^{-1}$. A proxy for the X-ray luminosity was then calculated according to

$$\begin{eqnarray}{L}_{X} & = & \displaystyle \frac{A\,{ \mathcal F }}{{PF}}\,4\pi {r}^{2}\\ & = & (1.06\times {10}^{37}\,\mathrm{erg}\,{{\rm{s}}}^{-1})A,\end{eqnarray} \tag{ 5 }$$

where A is the pulsation amplitude in the unit of counts s⁻¹, PF is the (unknown) pulsed fraction that can vary between 0.1 and 0.5 (Coe et al. 2015), and r = 62 kpc is the distance to the SMC. In the last step of Equation (5), we chose to set PF = 0.4 so that our X-ray luminosities are comparable with the corresponding values obtained by Klus et al. (2013), who used average count rates (over many observations) instead of individual A values to calculate fluxes.

Figure 4 shows the X-ray luminosities from all observations we mentioned and from all three telescopes. The observations cover the range ${L}_{X}={10}^{31.2}\mbox{--}{10}^{38}$ erg s⁻¹. Filled and unfilled symbols indicate that pulsations were detected or not detected, respectively. We see that RXTE has provided the majority of the detections, since it has observed the most frequently (approximately every week for 15 years). The additional value of Chandra and XMM-Newton is clear in two ways. First, these imaging instruments are able to distinguish pulsed emission from un-pulsed. Second, they are in the form of many detections at lower luminosity, which increases the dynamic range. This is an important attribute because the transition between different accretion modes likely occurs below the typical sensitivity of RXTE. Figure 4 provides valuable information on the disappearance of pulsation. And in this context, we have recently performed an analysis of the propellor transition on this ensemble of pulsars (Christodoulou et al. 2016). Minor differences between Christodoulou et al. (2016) and our Figure 4 are due to inclusion of XMM-MOS data in the former work and slightly different S/N screening criteria.

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In terms of detecting pulsations, a useful empirical result on the sensitivities of XMM-Newton, Chandra, and RXTE to pulsars as a function of count rate was obtained by analyzing the library. By constructing histograms of source counts for all positive pulsation detections (s ≥ 99%), the distributions of pulsation amplitude and number of events per detection can both be examined.

Figure 5 shows the number of observations with pulsations detected by XMM-Newton at s ≥ 99%. The abscissa shows the actual EPIC PN photon counts that yielded the pulsation detections in the histogram. The ordinate of the blue histogram is the number of sources from the observations with pulsations detected in each bin (in intervals of 100 counts). The distribution indicates a threshold of about 200 counts below which our ability to detect pulsations becomes rapidly diminished. The distribution of detected pulsations peaks at around 300 counts for XMM-Newton and represents the completeness limit of the survey. Observations should therefore be designed to obtain 200+ counts when searching for periodicities. The decline toward lower net counts is due to the expected decline in ability to resolve pulsations in fainter sources and shorter observations, while the decline toward higher net counts reflects the underlying distribution of pulsar luminosity. The red histogram is the cumulative number of observations with pulsations detected as a function of photon counts. In total, there are ∼70 XMM-Newton observations with pulsations detected in the SMC.

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Figures 6–8 show similar distributions for pulse amplitude for all three satellites (expressed in net count rate). They are the histograms of all known pulsars detected with s ≥ 99% by XMM-Newton, Chandra, and RXTE, respectively. The abscissae are equally binned in logarithmic count rate. It is apparent that a turnover occurs just above ${\mathrm{log}}_{10}\,A\simeq -1.2$ or 0.06 count s⁻¹ for both ACIS and PN, and for the RXTE amplitude histogram a similar turnover occurs at ${\mathrm{log}}_{10}\,A\simeq -1.7$ or 0.02 count s⁻¹. To compute the completeness fraction of the XMM-Newton, Chandra, and RXTE surveys, the underlying pulsar L_X and PF distributions would need to be obtained first. We hope that modeling efforts will be motivated by statistical results such as these.

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Useful results can be inferred by transforming the empirical turnover points of Figures 6–8 into completeness limits in terms of flux or pulsar luminosity. Assuming the same PIMMS energy ranges and power-law model described in Section 2.4, the turnover points measured in Figures 6–8 yield completeness limits of flux ${C}_{\mathrm{XM}}=5.2\times {10}^{-13}\,\mathrm{erg}\,{\mathrm{cm}}^{-2}\,{{\rm{s}}}^{-1}$, ${C}_{\mathrm{Ch}}=1.0\,\times {10}^{-12}\,\mathrm{erg}\,{\mathrm{cm}}^{-2}\,{{\rm{s}}}^{-1}$, and ${C}_{\mathrm{RX}}=2.5\times {10}^{-12}\,\mathrm{erg}\,{\mathrm{cm}}^{-2}\,{{\rm{s}}}^{-1}$, corresponding to luminosity values of $7.6\times {10}^{35}$ erg s⁻¹, $1.6\times {10}^{36}$ erg s⁻¹, and $7\times {10}^{36}$ erg s⁻¹, for XMM-Newton, Chandra, and RXTE, respectively.

In the combined pipeline, the standard data products for each pulsar include the pulse period, luminosity, pulsed fraction, pulse amplitude, and the spin period detection significance. The time evolution of these quantities yields the period derivative $\dot{P}$, the accretion torque, the orbital period, and the duty cycle of each source. Time-series plots of these quantities are provided as multi-panel figures for all pulsars in the sample, and the underlying data are provided in machine-readable form. These time series can be read as a history of the on/off status and outburst state of each pulsar as a function of time. Such information is useful for comparison with other time-domain databases extending over the same time period, for example, the OGLE and MACHO optical monitoring facilities. The plots are also intended as a useful resource for researchers interested in selecting their own sub-samples for further analysis or modeling.

As an example, the results for the HMXB pulsars SXP348 and SXP1323 are illustrated in Figures 9(a) and (b), respectively. Each plot has five panels, with the data from each satellite plotted with a different color and symbol.

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View figure set (58 panels)

Tarball of figure set images

The first (top) panel is the time series of L_X in units of erg s⁻¹ following the cross-calibration scheme described in Section 2.4.2. These are in fact the same points that appear in Figure 4. L_X values are plotted for all positive point-source detections (whether pulsed or not) from Chandra and XMM-Newton and for RXTE pulsed detections.

The second panel reports the pulsed fraction for Chandra and XMM-Newton detections with pulsations at s ≥ 99% with solid symbols. Detections at s < 99% are open symbols.

The third panel shows pulse amplitude in units of count rate, where the Chandra and XMM-Newton rates are in units of PN count ${{\rm{s}}}^{-1}$ after scaling as described in Section 2.4.2, and RXTE rate is in units of count ${\mathrm{PCU}}^{-1}\,{{\rm{s}}}^{-1}$. We have followed the practice of earlier works (e.g., Galache et al. 2008) by plotting RXTE values even in cases of no pulsation detection; these open points are intended to represent upper limits.

The fourth panel shows the spin period (P), with values plotted only for cases of detection at s ≥ 99%. A linear fit is also displayed in order to highlight the long-term trend in period derivative. In the example of SXP348 (Figure 9(a)), two epochs of spin up are seen, each lasting about 500 days, between which the pulsar returns to its long-term average value. In our second example, SXP1323 (Figure 9(b)), there is an overall long-term spin-up trend, with other apparently organized variations superimposed. This analysis was performed for all the pulsars with sufficient data to do so, and the slopes of these linear fits, their uncertainty, and the standard deviation of the points around the fit are collected together in Table 3. Here, standard deviation implies how much the period of the pulsar varies on long timescales: a low standard deviation indicates that the data points tend to be close to the best-fitting line of the set, while a high standard deviation indicates that the data points are spread out over a wider range of values around the best-fitting line.

Table 3.  Long-term Average Spin Period Trends ($\dot{P}$)

Pulsar	$\dot{P}$	${\sigma }_{s}$		Class	# of
	(s day−1)	(s)			points
SXP2.37	−1.2e–05 ± 8e–06	0.010	−1.50	U	19
SXP2.76	3.0e–05 ± 0e–06	0.000	≫1.5	D	2
SXP4.78	−2e–06 ± 1e–06	0.004	−2.00	U	11
SXP5.05	−6e–06 ± 1.2e–05	0.021	−0.50	C	5
SXP6.85	−1e–06 ± 2e–06	0.011	−0.50	C	52
SXP7.78	6e–06 ± 1e–06	−0.50	6.00	D	28
SXP7.92	1.9e–04 ± 1.1e–04	0.171	1.72	D	6
SXP8.02	−1.30e–05 ± 8e–06	0.024	−1.63	U	4
SXP8.88	3e–06 ± 1e–06	0.011	3.00	D	43
SXP11.5	1.4e–05 ± 1.6e–05	0.040	0.875	C	10
SXP11.9	−1.2e–05 ± 4e–06	0.025	−3.00	U	3
SXP15.3	−2e–06 ± 5e–06	0.015	−0.40	C	16
SXP16.6	2e–06 ± 3e–06	0.015	0.67	C	14
SXP18.3	3e–06 ± 4e–06	0.025	0.75	C	75
SXP46.6	−4.8e–05 ± 1.6e–05	0.229	−3.00	U	79
SXP51.0	5.3e–05 ± 1.7e–05	0.155	3.12	D	38
SXP59.0	−4.4e–05 ± 1e–05	0.110	−4.40	U	93
SXP65.8	1.0e–04 ± 8.4e–05	0.029	1.19	C	5
SXP74.7	7.7e–05 ± 1.3e–04	0.966	0.57	C	21
SXP82.4	5.3e–05 ± 8.2e–05	0.283	0.65	C	19
SXP91.1	−1.144e–03 ± 7.3e–05	1.140	−15.67	U	60
SXP95.2	2.2e–04 ± 1.4e–04	0.234	1.56	D	8
SXP101	−1.6e–04 ± 3.4e–04	0.860	−0.48	C	6
SXP138	4.6e–04 ± 2.6e–04	0.577	1.75	D	6
SXP140	−1.1e–04 ± 5.0e–04	0.837	−0.21	C	7
SXP144	7.4e–04 ± 1.2e–04	0.950	6.24	D	51
SXP152	−1.06e–04 ± 7.2e–05	0.338	−1.47	C	21
SXP169	−6.3e–04 ± 1.4e–04	1.010	−4.52	U	35
SXP172	−3.03e–04 ± 7.0e–05	0.642	−4.33	U	47
SXP175	2.5e–04 ± 2.5e–04	0.639	1.01	C	8
SXP202A	−2.9e–04 ± 2.7e–04	1.236	−1.06	C	14
SXP214	−8.9e–05 ± 2.0e–04	1.135	−0.45	C	18
SXP264	1.4e–04 ± 6.9e–04	1.564	0.20	C	8
SXP280	1.0e–03 ± 7.9e–04	1.168	1.27	C	6
SXP292	2.7e–04 ± 3.4e–04	0.868	0.81	C	10
SXP293	−5.0e–05 ± 1.7e–04	0.774	−0.29	C	13
SXP304	2.9e–04 ± 8.7e–04	1.621	0.33	C	11
SXP323	−1.51e–03 ± 2.8e–04	1.829	−5.44	U	27
SXP327	−3.0e–04 ± 2.6e–04	0.449	−1.18	C	7
SXP342	1.48e–03 ± 9.1e–04	5.294	1.63	D	24
SXP348	−2.5e–04 ± 7.6e–04	3.531	−0.33	C	25
SXP455	−1.3e–03 ± 9.5e–04	4.244	−1.35	C	20
SXP504	9e–06 ± 3.8e–04	3.713	0.02	C	37
SXP523	−1.8e–03 ± 2.1e–03	5.313	−0.87	C	9
SXP565	2.3e–04 ± 1.1e–03	4.497	0.20	C	14
SXP645	1.5e–04 ± 6.4e–04	3.220	0.24	C	16
SXP701	3.0e–03 ± 1.0e–03	7.288	2.93	D	31
SXP726	2.0e–04 ± 6.2e–03	10.022	0.03	C	9
SXP756	−4.1e–03 ± 1.6e–03	10.226	−2.48	U	27
SXP893	−6.8e–04 ± 1.2e–03	9.591	−0.59	C	42
SXP967	−6.3e–04 ± 1.50e–03	5.452	−0.43	C	11
SXP1062	7.1e–03 ± 2.2e–03	2.889	3.23	D	15
SXP1323	−6.5e–03 ± 2.8e–03	19.014	−2.32	U	50
SXP0.72	⋯	⋯	⋯	⋯	1
SXP2.16	⋯	⋯	⋯	⋯	1
SXP9.13	⋯	⋯	⋯	⋯	1
SXP153	⋯	⋯	⋯	⋯	1
SXP4693	⋯	⋯	⋯	⋯	1

Note. Period derivative $\dot{P}$ and its error are determined from a linear fit to the time series of P measurements. σ_s is the standard deviation indicating how much the period of the pulsar varies on long timescales around the linear fit. is the ratio of $\dot{P}$ to its own error as described in Section 3.3. Classification is based on the sign and value of : U: $\epsilon \leqslant -1.5$ (long-term spin up), D: $\epsilon \geqslant +1.5$ (long-term spin down), C: $-1.5\lt \epsilon \lt +1.5$ (consistent with no long-term variation). In the last column, # of points is the number of detected pulsations used in the linear fit.

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The fifth (bottom) panel reports the significance of the highest power-spectrum peak in the search range for that pulsar (see Section 2.4.1). Pulsation searches were only performed for light curves with greater than 50 counts in the case of XMM-Newton and Chandra. The solid symbols denote s ≥ 99% and in turn dictate how the points in other panels are plotted.

As expected for accreting pulsars in binary systems, all the pulsars in our library show variations in their pulse periods. These variations stem from periodic Doppler shifting of the frequency due to orbital motion and from the exerted accretion torques. The first type of periodic variation may reveal the orbital period of the binary (see, for example, Townsend et al. 2013), whereas the second type of secular variation gives us a window into the physics of angular momentum transfer and dynamical evolution in binary systems (Davidson & Ostriker 1973; Ghosh & Lamb 1979). The two types of variations can be seen in some of the multi-panel figures included as supporting material. The orbital modulation in some sources is not very clear, e.g., SXP348 in Figure 9(a), due to the few spin period data points. Schmidtke & Cowley (2006) found weak evidence for an orbital period of 93.9 days for SXP348 in OGLE-II data. However, Schmidtke et al. (2013) reported from re-analysis of the same data (plus OGLE-III and -IV data in which it was not found), that the period was an artifact. Coe & Kirk (2015) simply quoted its orbital period as 93.9 days. From MJD 51000 until MJD 52000 is about 10 orbital cycles (with an orbital period of 94 days). During MJD 51000–52000, it only shows spin down and up once. SXP1323 (Figure 9(b)) has no secure orbital period known according to Coe & Kirk (2015). Here, we carry out a linear regression of the spin periods of 53 pulsars for which we have enough data in order to search for secular drifts on timescales much longer than the orbital periods.

We have investigated the entire spin period history of each pulsar in our library by calculating the best-fit slope to the measured spin periods and its corresponding errors, as described in Section 3.2. The best-fit slopes, i.e., the measured $\dot{P}$ values, are listed in Table 3 and they are also included in the multi-panel history plots such as the figure set of Figures 9(a) and (b). At the  = 1.5 level or better, we find that 12 pulsars spin up and 11 pulsars spin down, while 30 pulsars appear to have $\dot{P}\approx 0$. The "C" in Table 3 does not mean that the 30 pulsars do not go through spin-up and/or spin-down episodes, but that no net changes of significance are observed over the ∼15 year duration of the survey. Some sources could well have undergone spin period changes that have averaged out over the survey period. In our data set, five pulsars only have one single detection with s ≥ 99% pulsations found as shown in Table 3. The remaining seven pulsars do not have significant pulsations detected at all.

The cumulative outcome of this analysis is illustrated in Figure 10, in which we plot the known orbital periods P_orb versus the known spin periods P (Coe & Kirk 2015) with additional color-coded information about the sign of $\dot{P}$. Green and red symbols indicate that the pulsars spin up ($\dot{P}\lt 0$) or down ($\dot{P}\gt 0$), respectively (e.g., SXP1323; Figure 9(b)). On the other hand, blue symbols indicate pulsars have no $\dot{P}$ value due to lack of observations or lack of pulsations detected in our survery. Unfilled symbols at the bottom of Figure 10 show the pulsars for which P_orb is unknown; currently, 43 SMC pulsars in our library do have measured orbital periods.

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The relation between the orbital and spin periods of 43 pulsars in Figure 10 can be reasonably matched by a power law. The best-fit power law to the data is described by the equation

$$\begin{eqnarray}&&{P}_{\mathrm{orb}}=12.066{\left(\displaystyle \frac{P}{1{\rm{s}}}\right)}^{0.425}\,\,\mathrm{days}.\end{eqnarray} \tag{ 6 }$$

This equation shows that the longer the orbital period the wider the binary orbit; hence, lower mass transfer with lower specific angular momentum occurs, and ultimately the pulsar rotation ends up being slower. Figure 10 is effectively our updated version of the well-known Corbet (1984) diagram for the SMC. Overall, the HMXB spin period distribution has been shown to be bimodal by Knigge et al. (2011). Those authors suggested that there are two underlying populations resulting from the two distinct types supernovae—electron capture and iron-core-collpase—that produce neutron stars.

We will incrementally release this library to the public, from which one can download all of the light curves, periodograms, point-source event lists, spectra (within the soft, hard, and broad energy bands) of each known pulsar in the SMC and LMC. For this paper, release 1.0 provides the long-term observable parameters (i.e., count rate, luminosity, spin period, pulsation amplitude, pulsed fraction) of the known pulsars in the SMC with the combination of all three satellite detections. The library is provided in catalog form and as a series of multi-panel figures (58 in total).