Chandra and HST Studies of Six Millisecond Pulsars in the Globular Cluster M13
MMNRAS , 1–9 (2020) Preprint 21 January 2021 Compiled using MNRAS L A TEX style file v3.0
Chandra and HST Studies of Six Millisecond Pulsars in theGlobular Cluster M13
Jiaqi Zhao, ★ Yue Zhao, Craig O. Heinke Department of Physics, University of Alberta, CCIS 4-183, Edmonton, AB T6G 2E1, Canada
Accepted XXX. Received YYY; in original form ZZZ
ABSTRACT
We analyse 55 ks of
Chandra
X-ray observations of the Galactic globular cluster M13. Usingthe latest radio timing positions of six known millisecond pulsars (MSPs) in M13 from Wang etal. (2020), we detect confident X-ray counterparts to five of the six MSPs at X-ray luminositiesof 𝐿 𝑋 (0.3-8 keV) ∼ × − erg s − , including the newly discovered PSR J1641 + + 𝐿 𝑋 < . × erg s − . We analyse X-ray spectra of all six MSPs, which arewell-described by either a single blackbody or a single power-law model. We also incorporateoptical/UV imaging observations from the Hubble Space Telescope (HST) and find opticalcounterparts to PSR J1641 + + + + Key words: stars: neutron – pulsars: general – globular clusters: individual: NGC 6205 –X-rays: stars
Radio millisecond pulsars (MSPs), also known as rotation-poweredMSPs, are fast-spinning pulsars (spin periods 𝑃 (cid:46)
30 ms) with lowspin-down rates ( (cid:164) 𝑃 ∼ − − − ), implying large characteris-tic ages 𝜏 ≡ 𝑃 /( (cid:164) 𝑃 ) (cid:38) 𝐵 𝑝 ∝ ( 𝑃 (cid:164) 𝑃 ) / ∼ − G. Low-mass X-ray binaries(LMXBs) are conventionally considered the progenitors of MSPs,where a neutron star (NS) is spun up by accreting material fromits companion star until it has a rotational period of a few millisec-onds (Alpar et al. 1982; Bhattacharya & van den Heuvel 1991). Thehigh stellar densities of globular clusters (GCs) create numerousLMXBs, which then produce MSPs, and hence GCs provide idealplaces to observe them in large numbers (Camilo & Rasio 2005).To date, the total number of pulsars found in 30 GCs is 157, andmore than 90% of them are MSPs .MSPs are mostly found in binary systems, which is consistentwith the evolution of MSPs via LMXBs. The so-called “spider”MSP binaries represent a distinct group of MSP binary systemswith low-mass nondegenerate companion stars. Specifically, spiderbinaries are classified into two groups based on the companion ★ E-mail: [email protected] For an up-to-date catalog of pulsars in GCs, see masses: black widows with companion masses 𝑀 𝑐 ∼ .
02 M (cid:12) , andredbacks with companion masses 𝑀 𝑐 ∼ . (cid:12) (Roberts 2011).Alternatively, MSPs may be coupled with compact objects, suchas helium-core white dwarfs (WDs), which are the most commoncompanions to MSPs in GCs (e.g. Camilo & Rasio 2005). MSPscoupled with another neutron star or even a detected radio pulsarhave been discovered in a few systems, like PSR J0737 − 𝐿 𝑋 ∼ − erg s − . For a few relatively youngand energetic MSPs, like PSR B1821 −
24, the X-ray luminositiescan reach up to ∼ erg s − (e.g. Bogdanov et al. 2011a). The X-rays produced by MSPs can be characterized based on their spectralproperties, namely thermal (blackbody-like spectra) or non-thermal(power-law spectra) emission (Becker & Trümper 1999; Bogdanov2018). Thermal X-ray emission is believed to be generated fromthe hot surface of the NS, specifically from the hot spots near themagnetic polar caps, heated by the return flow of relativistic par-ticles from the pulsar magnetosphere (e.g. Harding & Muslimov2002). Non-thermal X-ray emission can be further categorized intotwo sub-groups, i.e. pulsed and non-pulsed non-thermal emission.Pulsed non-thermal X-rays are observed with narrow X-ray pulsa-tions, implying highly beamed X-ray radiation, which is most likelyproduced in the pulsar magnetosphere (Verbunt et al. 1996; Saitoet al. 1997; Takahashi et al. 2001). Therefore, only very energetic © a r X i v : . [ a s t r o - ph . H E ] J a n Zhao, Zhao & Heinke
Table 1.
Chandra
Observations of M13Telescope/ Date of Observation ExposureInstrument Observation ID Time (ks)
Chandra /ACIS-S 2006 Mar 09 7290 27.9
Chandra /ACIS-S 2006 Mar 11 5436 26.8
MSPs with relatively strong spin-down luminosities could emit suchX-ray radiation (e.g. Possenti et al. 2002). Non-pulsed non-thermalX-ray emission is commonly detected from spider pulsar systems,where the relativistic pulsar wind may collide with the material fromits companion star, creating an intra-binary shock and emitting non-pulsed, non-thermal X-rays (e.g. Arons & Tavani 1993; Stapperset al. 2003; Bogdanov et al. 2005; Gentile et al. 2014; Roberts et al.2015).The globular cluster M13 (NGC 6205) is located in theconstellation of Hercules, with a low foreground reddening of 𝐸 ( 𝐵 − 𝑉 ) = .
02 (Harris 1996, 2010 edition). The distance is slightlyuncertain, with a range of reported values (mostly isochrone fittingto the colour-magnitude diagram, but also using RR Lyrae variablesand the tip of the red giant branch) from 7.1 ± . ± . ± . + + + ∼ .
019 M (cid:12) (Wang et al. 2020). The nature ofthe companions for PSRs J1641 + + + Chandra observations. We also in-vestigate the optical counterparts to those MSPs in binary systems,based on observations from the
Hubble Space Telescope ( HST ).This work is organized as follows. In section 2, we describe the ob-servations and data reduction procedures. In section 3, we presentthe X-ray spectral fitting results for the six MSPs, and the searchfor counterparts to the MSPs in optical/UV bands. We discuss theX-ray spectral properties and the nature of the companion stars insection 4. Finally, we draw conclusions in section 5.
The X-ray data used in this work consists of two
Chandra X-rayObservatory observations of M13 in 2006, with a total exposuretime of 54.69 kiloseconds (see Table 1). For both observations, thecore of M13 was positioned on the back-illuminated ACIS-S3 chipand configured in FAINT mode. The data reduction and analysis were performed using ciao (version 4.12, CALDB 4.9.1, Fruscione et al. 2006). We first re-processed the data with the chandra_repro script to generate newlevel 2 event files of the observations, applying the newest calibra-tion updates and bad pixel files. We filtered the data to the energyrange 0.5 − Chandra data.We created a co-added image of M13 by merging the eventfiles from the two observations using reproject_obs script. InFigure 1, the positions of the six MSPs are marked by blue circleswith 1 (cid:48)(cid:48) radii, centered on the precise radio pulsar timing positions(Wang et al. 2020). Other brighter X-ray sources are also visiblein this image, including a quiescent low-mass X-ray binary (Shawet al. 2018) and cataclysmic variables (e.g. Servillat et al. 2011). Weformally detected the X-ray counterparts to most of the MSPs byapplying the ciao tool wavdetect , a Mexican-Hat Wavelet sourcedetection tool (Freeman et al. 2002). We specified the wavelet scales(a list of radii in pixels) of 1.0, 1.4, and 2.0, and a significancethreshold for source detection of 10 − (false sources per pixel).Consequently, five X-ray counterparts were detected, all but MSPA, with positions consistent with the radio positions.To analyse the X-ray spectra of the MSPs, we extracted theemission from the circular regions with a radius of 1 (cid:48)(cid:48) centered onthe radio positions in energy band 0.5 − specextract script. The extraction process wasperformed separately for each observation, and then we used the combine_spectra script to co-add the spectra correspondinglyfor each pulsar to obtain the combined spectra for spectral analysis.The background was taken from source-free annular regions aroundthe MSPs. We use imaging data taken by the Wide Field Camera 3 (WFC3; GO-12605) and Advanced Camera for Surveys (ACS; GO-10775) onboard the
HST . GO-12605 (PI: Piotto) contains exposures in two UVfilters, F275W (UV ) and F336W (U ), along with an exposurein F438W (B ); while GO-10775 (PI: Sarajedini) is comprisedof exposures in V (F606W) and I (F814W). For all filters,we retrieved the FLC data products from the Mikulsky Archive forSpace Telescope (MAST) ; these are images that have been pipe-lined, flat-fielded, and have charge transfer efficiency trails removed.Detailed information on these observations is summarised in Table2. To search for faint potential counterparts to the MSPs, weuse the drizzlepac software (version 3.1.6) to generate combined HST images. FLC files in each filter are first re-aligned by the
TweakReg tool to a reference image (chosen to be the longestFLC exposure) and then combined using the
AstroDrizzle tool.
AstroDrizzle corrects for geometric distortion, flags cosmic raysand small-scale detector defects, and combines images with user-defined re-sampling. We use 𝑝𝑖𝑥 𝑓 𝑟𝑎𝑐 = . Chandra Interactive Analysis of Observations, available at https://cxc.harvard.edu/ciao/ https://archive.stsci.edu/hst/search.php MNRAS , 1–9 (2020) illisecond pulsars of M13 ED C AED C AED C A
BBB
FFF
F B
Figure 1.
Left: merged 0.5 − (cid:48)(cid:48) radii and letters). Thecenter of M13 is marked with a red cross. The smaller red circle shows the 0 . (cid:48)
62 core radius of M13, while the larger one shows the 1 . (cid:48)
69 half-light radiusof M13 (Harris 1996, 2010 edition). The green boxes surrounding the MSPs are detailed in the right figure. Right: the 28 (cid:48)(cid:48) × (cid:48)(cid:48) core region of M13 whichincludes MSPs A, C, D, and E (the largest green box in the left figure). MSPs B and F are inset at source-free places with the same scale. The X-ray emissionfrom all MSPs but A are clearly visible. North is up, and east is to the left. Brighter X-ray sources visible in the left image include cataclysmic variables and aquiescent X-ray binary (see Servillat et al. 2011; Shaw et al. 2018). the original pixel scales (0 . (cid:48)(cid:48) /pixel for WFC3, 0 . (cid:48)(cid:48) /pixel forACS).Starting from December 2019, MAST released updated abso-lute astrometry information for ACS and WFC3 data. Most FLCdata products are now aligned to the Gaia DR2 catalogue, reduc-ing the astrometric uncertainties to ∼
10 mas . The observed M13fields contain stars included in Gaia DR2, so we use the defaultWCS information to set our absolute astrometry. We performed all spectral fits using ciao’s modeling and fittingapplication, Sherpa . X-ray emission from MSP A was only detectedin the latter observation (Obs ID: 5436) with just two photons. Wecannot determine whether the two photons originated from MSP A,or are just background emission. However, we fitted the spectrumof MSP A, and set the obtained fits as the upper limits, finding 𝐿 𝑋 < . × erg s − . The other five MSPs in M13 (MSPsB, C, D, E, and F) show faint and relatively soft X-ray emission(Figure 2), with X-ray luminosities ∼ × − erg s − . We https://archive.stsci.edu/contents/newsletters/may-2020/new-absolute-astrometry-for-some-hst-data-products Available at https://cxc.cfa.harvard.edu/sherpa/ adopted the WSTAT statistic , a Poisson log-likelihood functionincluding a Poisson background, within Sherpa to fit X-ray spectrawith few photons. In addition, we grouped the data to include atleast one photon in each bin due to the limited number of photons(Humphrey et al. 2009). For all six detected MSPs, we fitted thespectra by fixing the hydrogen column density ( 𝑁 H ) to the cluster.We estimated 𝑁 H from the known reddening (Harris 1996, 2010edition) and an appropriate conversion factor (Bahramian et al.2015) and obtained a value of 1 . × cm − , given that interstellarextinction 𝐸 ( 𝐵 − 𝑉 ) generally gives the best predictions of 𝑁 H (Heet al. 2013).We considered spectral models of the X-ray emission fromMSPs (Bogdanov et al. 2006) involving a blackbody (BB), a power-law (PL), and combinations of these. For the BB model, we usedthe xsbbodyrad model in Sherpa, and the free parameters were theeffective temperature and the normalized radius. The PL model wasfitted using xspegpwrlw , with the photon index and flux as freeparameters. Figure 2 shows the X-ray spectra and best fits of the sixMSPs, and the best-fit models and parameters are given in Table 3.We used the Q-value, which is a measure of what fraction of simu-lated spectra would have a larger value of the reduced statistic thanthe observed one, if the assumed model and the best-fit parametersare true, to indicate the goodness of the fits. The Q-values in Table 3 See https://heasarc.gsfc.nasa.gov/xanadu/xspec/manual/XSappendixStatistics.html for more details.MNRAS000
10 mas . The observed M13fields contain stars included in Gaia DR2, so we use the defaultWCS information to set our absolute astrometry. We performed all spectral fits using ciao’s modeling and fittingapplication, Sherpa . X-ray emission from MSP A was only detectedin the latter observation (Obs ID: 5436) with just two photons. Wecannot determine whether the two photons originated from MSP A,or are just background emission. However, we fitted the spectrumof MSP A, and set the obtained fits as the upper limits, finding 𝐿 𝑋 < . × erg s − . The other five MSPs in M13 (MSPsB, C, D, E, and F) show faint and relatively soft X-ray emission(Figure 2), with X-ray luminosities ∼ × − erg s − . We https://archive.stsci.edu/contents/newsletters/may-2020/new-absolute-astrometry-for-some-hst-data-products Available at https://cxc.cfa.harvard.edu/sherpa/ adopted the WSTAT statistic , a Poisson log-likelihood functionincluding a Poisson background, within Sherpa to fit X-ray spectrawith few photons. In addition, we grouped the data to include atleast one photon in each bin due to the limited number of photons(Humphrey et al. 2009). For all six detected MSPs, we fitted thespectra by fixing the hydrogen column density ( 𝑁 H ) to the cluster.We estimated 𝑁 H from the known reddening (Harris 1996, 2010edition) and an appropriate conversion factor (Bahramian et al.2015) and obtained a value of 1 . × cm − , given that interstellarextinction 𝐸 ( 𝐵 − 𝑉 ) generally gives the best predictions of 𝑁 H (Heet al. 2013).We considered spectral models of the X-ray emission fromMSPs (Bogdanov et al. 2006) involving a blackbody (BB), a power-law (PL), and combinations of these. For the BB model, we usedthe xsbbodyrad model in Sherpa, and the free parameters were theeffective temperature and the normalized radius. The PL model wasfitted using xspegpwrlw , with the photon index and flux as freeparameters. Figure 2 shows the X-ray spectra and best fits of the sixMSPs, and the best-fit models and parameters are given in Table 3.We used the Q-value, which is a measure of what fraction of simu-lated spectra would have a larger value of the reduced statistic thanthe observed one, if the assumed model and the best-fit parametersare true, to indicate the goodness of the fits. The Q-values in Table 3 See https://heasarc.gsfc.nasa.gov/xanadu/xspec/manual/XSappendixStatistics.html for more details.MNRAS000 , 1–9 (2020)
Zhao, Zhao & Heinke
GO Exposure (s) Observation Start Instrument Filter10775 567 2006-04-02 10:41 ACS/WFC F606W (V )10775 567 2006-04-02 12:15 ACS/WFC F814W (I )12605 1281 2012-05-14 01:52 WFC3/UVIS F275W (UV )12605 1281 2012-05-17 03:54 WFC3/UVIS F275W (UV )12605 700 2012-05-14 02:24 WFC3/UVIS F336W (U )12605 700 2012-05-17 04:48 WFC3/UVIS F336W (U )12605 92 2012-05-14 01:49 WFC3/UVIS F438W (B )12605 92 2012-05-17 03:26 WFC3/UVIS F438W (B ) Table 2.
HST observations used in this work. are above 0.05, indicating that these are reasonable fits and hencethe Q-values themselves did not rule out any models.The spectra of all six MSPs in M13 are well described byeither a pure BB model or a pure PL model. (We tested BB+PL andBB+BB models, but these did not give better fits, so we only discusssimple one-component fits henceforth.) Although we cannot ruleout either model from Q-values alone, other fitting parameters, likeeffective temperature and photon index, provide reasons to excludemodels. For instance, if we fit the spectra of MSPs C, D, and Fusing a PL model, the obtained photon indices are nearly 4, whichare empirically not observed from MSPs, given the typical photonindices of MSPs Γ ∼ . Γ = . ± . . ± .
6, respectively. Given that MSP E is a “black widow”pulsar, the bulk of its observed non-thermal X-rays are likely to beproduced by interaction of the relativistic particle wind from thepulsar with matter lost from the companion. MSPs C, D, and F haveX-ray spectra well fitted with a pure blackbody spectrum, implyingno or little X-ray emission from a pulsar magnetosphere and/orintra-binary shock. Blackbody-like X-ray spectra are common fromMSPs (e.g. Bogdanov et al. 2006), and likely originate from smallhot spots at the magnetic poles heated by relativistic particles in thepulsar magnetosphere (e.g. Harding & Muslimov 2002).Particularly, since we only have two photons from MSP A, weneed to fix one more parameter to obtain at least one degree offreedom. In order to determine the upper limit of the luminosity ofMSP A, we fixed the effective temperature 𝑇 eff and photon index Γ for the BB and PL models in the fitting processes, respectively. Thevalue of the fixed 𝑇 eff was obtained by averaging the fitted 𝑇 eff ofMSPs C, D, and F, giving a value of 𝑇 eff = . × K, while thefixed Γ was given by the mean value of photon indices of MSPs Band E, providing Γ = . . × erg s − (0.3 − We use the dolphot software (version 2.0) to generate photometrycatalogues for the WFC3 and ACS images. dolphot is a photom-etry package based on HSTphot (Dolphin 2000) which providespipelines to perform aperture and PSF photometry on individualFLC images. We first choose the U and I drizzle-combined images as the reference frames for WFC3 and ACS, on whichdolphot runs a detection algorithm to find stars. The referenceimages also provide master coordinates ( 𝑥, 𝑦 ) to which stars on in-dividual FLC frames are transformed. In the next step, we maskthe flagged bad pixels in all FLC images using the wfc3mask and acsmask tools. These tools also multiply the FLC images and thepixel areas, converting the pixel units to electrons. The final pho-tometry routine runs on separate CCD chips, which are extractedfrom the FLC images by the splitgroups tool. These chip-specificimages are also needed for the calcsky tool to create correspond-ing sky images. With all these preparations, we finally run the dolphot routine for WFC3 and ACS, adapting a photometry aper-ture ( img _ RAper , in pixels) of 8, and a PSF radius ( img _ RPSF , inpixels) of 15, while defining a sky annulus ( img _ RSky , in pixels)with inner and outer radii of 9 and 14, respectively, for PSF photom-etry. The final magnitudes are calibrated to the VEGMAG systemusing updated photometry zeropoints for ACS (Sirianni et al. 2005)and WFC3 .We keep stars with S/N>5 and rule out non-star objects, leavingcleaned catalogues to make colour-magnitude diagrams (CMDs;Figure 3, 4). These catalogues are used to compare the potentialcounterpart’s photometry with the bulk of stars of the cluster. Since the radio timing solution provides much more accurate local-isation ( ∼ mas; Wang et al. 2020) than the Chandra imaging (errorradius ∼ . (cid:48)(cid:48) ), we expect potential counterparts in the vicinity ofthe corresponding radio position. We therefore search around the ra-dio timing positions for optical counterparts in the drizzle-combinedimages; this leads to the discovery of optical/UV counterparts to twoof the 6 MSPs: MSP D and F, both of which are very close ( ≈ . (cid:48)(cid:48) )to the radio positions. We report their photometric properties in thefollowing paragraphs. The counterpart to MSP D is a faint star 15 mas north from theradio timing position (Figure 5). Although the counterpart is visibleby visual inspection in the V -band image (Figure 5), it was notmeasured by dolphot. We hereby make a rough estimate of its Note that the drizzle-combined images used here are in their native pixelscales. https://acszeropoints.stsci.edu/ MNRAS , 1–9 (2020) illisecond pulsars of M13 MSP Spectral Model a 𝑅 effb 𝑇 eff Photon Index Reduced Stat c /Q-value 𝐹 𝑋 (0.3 − K) (10 − erg cm − s − )A BB 0 . + . − . [ . ] d − . + . − . PL − − [ . ] d . + . − . B BB 0 . +∞− . . +∞− . − . +∞− . PL − − . ± . . + . − . C BB 0 . + . − . . + . − . − . + . − . PL − − . ± . . + . − . D BB 0 . + . − . . + . − . − . + . − . PL − − . ± . + . − . E BB 0.07 + . − . . + . − . − . + . − . PL − − . ± . . + . − . F BB 0 . + . − . . + . − . − . + . − . PL − − . ± . + . − . Table 3.
Spectral fits for the M13 MSPs. a) PL = power-law, BB = blackbody. The hydrogen column density was fixed to 𝑁 H = . × cm − . Alluncertainties are 1 𝜎 . b) 𝑅 eff calculated assuming a distance of 7.1 kpc. c) Reduced statistic, calculated by the fit statistic divided by the degrees of freedom.d) Obtained by averaging the best spectral fits of other MSPs. See section 3.1 for more details. e) Bounds unavailable. f) Model reached lower bound. magnitude by performing aperture photometry, using an aperture of0 . (cid:48)(cid:48) to enclose most of the PSF of the star. Since the counterpartis in the vicinity of a very bright star, we also estimate backgroundcounts with the same aperture size in a nearby source-free region.The background-subtracted counts are then calibrated to dolphotmagnitude by V = − . ( net counts )+ .
31, giving V ≈ .
63. We set a lower limit on the I band magnitude at 3 times thelocal background counts, which gives I (cid:38) .
03. The upper limiton the V − I colour is on the red side of the main sequence. We found a faint star ≈
22 mas east from the radio timing position(Figure 5). The counterpart to MSP F appears to be bluer thanthe main sequence on all three CMDs (Figure 3, 4), and overlapsthe white dwarf cooling sequence on the UV − U CMD.This is expected in MSPs descended from binary evolution witha giant companion (e.g., Stairs 2004), wherein the NS exhauststhe companion’s envelope via continued mass accretion, resultingin a WD companion (e.g., Sigurdsson et al. 2003; Splaver et al.2005; Cadelano et al. 2019). After submission of this manuscript,we became aware of Cadelano et al. (2020), which independentlyidentified the optical counterpart to the MSP M13 F, and usedphotometry in additional
HST filters to characterize the companionas a 0.23 𝑀 (cid:12) He-core white dwarf. Our optical counterpart analysisis consistent with theirs, though not as constraining.
We estimate the number of chance coincidences ( 𝑁 𝑐 ) by dividingthe cluster field into concentric annuli centered on the cluster, andcalculating the probability of a coincidence within our search area.The radio position offers a much smaller search area than the X-ray position, so we use the radio error circle to assess the chancecoincidence rate. The uncertainty in the radio position comes fromthe uncertainty in the radio timing position from Wang et al. (2020),which we estimate to be 3 mas at most (noting that the uncertaintyin declination is missing from M13 F in Wang et al. 2020’s Table2), and from the uncertainty in HST ’s absolute astrometry (10 mas,see §2.2), giving a total uncertainty in the radio position in the
HST frame of ∼
10 mas. Based on the UV − U CMD, we count numbers of ob-jects that align with the main sequence and the white dwarf sequencewithin each annulus. We did not apply proper-motion cleaning tothe CMD, since we are comparing the estimated counts to actualobserved numbers of sources in each search area. The counts arethen divided by the annulus areas to give the 𝑁 𝑐 per unit area, whichis then multiplied by the search area of MSP D and MSP F (10 masof radius) to give the 𝑁 𝑐 per search area. We estimate ≈ ≈ × − WDs in the search region of MSP F. Both counterparts to theseMSPs are therefore very unlikely to be chance coincidences.
The majority of X-ray emission from most isolated MSPs is thermalradiation with blackbody-like spectra (e.g. Bogdanov et al. 2006;Forestell et al. 2014), which is believed to result from polar capheating from inverse Compton scattering (e.g. Harding & Muslimov2002). The observed spectrum of MSP C is a typical example ofthose of isolated MSPs. However, some relatively young MSPs withhigh spin-down power, like B1821 −
24 in the globular cluster M28(Saito et al. 1997; Bogdanov et al. 2011a), produce pulsed non-thermal radiation generated by relativistic particles accelerated inthe pulsar magnetosphere.Intriguingly, given the upper limit of X-ray luminosity of 1 . × erg s − (0.3 − 𝐿 𝑋 < erg s − .Only one MSP among 23 studied in X-rays in 47 Tuc (Bogdanovet al. 2006; Ridolfi et al. 2016; Bhattacharya et al. 2017), namelyPSR J0024 − − 𝐿 𝑋 between 1 . × forM28 D, and 10 erg s − for M28 A, with three upper limits due toconfusing, brighter sources. Four other nearby globular clusters Bogdanov et al. (2011a) report an upper limit < . × erg s − forM28 I, but the position of M28 I used there proved to be incorrect, and theMNRAS000
24 in the globular cluster M28(Saito et al. 1997; Bogdanov et al. 2011a), produce pulsed non-thermal radiation generated by relativistic particles accelerated inthe pulsar magnetosphere.Intriguingly, given the upper limit of X-ray luminosity of 1 . × erg s − (0.3 − 𝐿 𝑋 < erg s − .Only one MSP among 23 studied in X-rays in 47 Tuc (Bogdanovet al. 2006; Ridolfi et al. 2016; Bhattacharya et al. 2017), namelyPSR J0024 − − 𝐿 𝑋 between 1 . × forM28 D, and 10 erg s − for M28 A, with three upper limits due toconfusing, brighter sources. Four other nearby globular clusters Bogdanov et al. (2011a) report an upper limit < . × erg s − forM28 I, but the position of M28 I used there proved to be incorrect, and theMNRAS000 , 1–9 (2020) Zhao, Zhao & Heinke
MSP A MSP BMSP C MSP DMSP E MSP F
Figure 2.
X-ray spectra and best fits for five MSPs in M13. The data are binned with 1 count/bin, and fitted using the WSTAT statistic. have deep X-ray and radio observations, with known MSPs: M22,NGC 6397, M71, and M4. Those four clusters each contain one,brighter, MSP (Grindlay et al. 2001; Bassa et al. 2004; Elsner et al.2008; Amato et al. 2019). Thus, among 47 detectable MSPs in true 𝐿 𝑋 of M28 I in its pulsar mode is 1 − × erg s − Papitto et al.(2013); Linares et al. (2014). these eight well-studied clusters, MSP A is one of the faintest fourin X-rays (along with 47 Tuc aa, NGC 6752 E, and M28 D), andpossibly the faintest. We cannot rule out either X-ray spectral model,by either Q-values or the fitted parameters, for MSP A. We prefer,however, the BB model, as MSP A is an isolated MSP. MSP A mayhave a relatively small spindown power, producing its relativelysmall X-ray luminosity. We cannot calculate its characteristic ageor spindown power, due to its acceleration within the gravitational
MNRAS , 1–9 (2020) illisecond pulsars of M13 UV U UV U B U MSP F MSP F
Figure 3. UV − U and U − B CMDs of M13. The red squaremarks the location of the counterpart to MSP F, which is bluer than the mainsequence, consistent with the white dwarf cooling sequence. . . . . . . V I V MSP F MSP D
Figure 4. V − I CMD of M13. Red squares mark the counterparts toMSP D and MSP F. The former was not detected in I , so only a 3 𝜎 upper limit is put on its V − I colour. potential of M13, which produces an observed negative spin periodderivative. Alternatively, MSP A may appear to have a low X-rayluminosity due to an unfavorable inclination of its spin axis withrespect to Earth, with one or both hot spots on the far side fromEarth (Riley et al. 2019 and Miller et al. 2019 showed that PSRJ0030+0451 has both hot spots in a single hemisphere). MSPs B, D, E, and F are in binary systems, with orbital periodsranging from 0.1 to 1.4 days (Wang et al. 2020). The X-ray spectraof MSPs B and E are well described by a pure power-law model, in-dicating that the X-rays from them are predominantly non-thermal.Non-pulsed non-thermal emission is anticipated for MSP E, since ithas been identified as an eclipsing black widow pulsar. In eclipsingspider pulsar systems, X-rays are thought to originate from intra-binary shocks, driven by the interaction of the relativistic pulsarwind with matter from its companion star (e.g. MSPs J0023 − − (cid:12) (assuming apulsar mass of 1 . (cid:12) , Wang et al. 2020), is not clear yet. The best-fit spectral model (a power-law of photon index 1.8 ± .
7) requireseither a magnetospheric origin (and thus a relatively high spindownenergy loss rate to produce this), or an intrabinary shock origin, inwhich case (given the companion mass) MSP B would be a redbacksystem. We consider the 21 MSPs in the globular cluster 47 Tucwith X-ray spectra that can be individually fit (Bogdanov et al.2006; Ridolfi et al. 2016; Bhattacharya et al. 2017). The 17 systemsthat are not black widows and redbacks are all best fit by thermalblackbody spectra, while two of the three black widows (47 TucJ,O,R), and the redback (47 Tuc W) all showed dominant power-lawcomponents to their spectra. Thus, it seems likely that MSP B is aredback system. No eclipses were detected in the radio observationsof MSP B (Wang et al. 2020), which could be due to a relativelylow inclination, as observed in the black widows 47 Tuc I and P(Freire et al. 2003). As intra-binary shocks are expected to emitX-rays in all directions (though not isotropically), the non-thermalX-rays may be detected at any inclination.The optical counterparts to MSPs D and F were found with
HST observations (Figure 5). According to the position of the coun-terpart to MSP F on the CMDs of M13 (Figure 3), as well as theminimum companion mass of ∼ .
18 M (cid:12) , a white dwarf is the mostlikely companion star of MSP F. We also found a plausible opticalcounterpart to MSP D, which is only detected in the V band. Wecannot identify the nature of MSP D’s companion star definitively,due to its very faint magnitude leading to a large uncertainty of itslocation on the CMD (see Figure 4). The observed magnitudes areconsistent with the rather broad expectations of MSP white dwarfcompanions (van Kerkwijk et al. 2005).The X-ray spectrum of MSP D is well described by a pureblackbody model, implying that emission from the neutron starsurface dominates, and that there is no intra-binary shock. Sinceall known redback binary systems show hard non-thermal X-rayemission (Bogdanov 2018), this indicates that MSP D is probablynot in a redback binary. With a minimum companion mass of ∼ .
18 M (cid:12) , we suggest that the companion star of MSP D is also ahelium-core white dwarf.
In this report, we have presented X-ray and optical studies of the sixMSPs in the globular cluster M13 by using archival
Chandra and
HST observations. Five of the six MSPs are firmly detected (MSPsB, C, D, E, and F) by
Chandra , with X-ray luminosities 𝐿 𝑋 ∼ × − erg s − (0.3 − . × erg s − . The MNRAS000
Chandra , with X-ray luminosities 𝐿 𝑋 ∼ × − erg s − (0.3 − . × erg s − . The MNRAS000 , 1–9 (2020)
Zhao, Zhao & Heinke .0 0.2 0.6 1.4 3.0 6.1 12.4 25.0 50.2 100.2 199 .0 0.2 0.6 1.4 3.0 6.1 12.4 25.0 50.2 100.2 199
E N
MSP D MSP F
Figure 5. V finding charts for MSP D (left) and MSP F (right), showing a 1 . (cid:48)(cid:48) × . (cid:48)(cid:48)
65 square region centred on the X-ray position. North is up, and eastis to the left. The blue cross in each chart indicates the centre of the X-ray position error circle, while the blue circle shows the 95% error region given theX-ray counts (Hong et al. 2005). The red cross marks the radio timing position from Wang et al. (2020), and the optical counterparts are indicated with yellowcrosshairs. uncommonly X-ray-faint properties of MSP A may imply that oneor both its hot spots are on the far side from Earth.The X-ray spectra of the six MSPs are well-described by eithera single blackbody or a single power-law model. As expected, thespectra of two isolated MSPs, MSPs A and C, are well fitted by apure blackbody model, indicating thermal X-ray emission from thesurface of these two objects. The identified black widow binarysystem, MSP E (Hessels et al. 2007; Wang et al. 2020), emitsprincipally non-thermal X-rays which are likely generated fromintra-binary shock. Similarly, the X-ray emission from MSP B, abinary system with a companion of mass ∼ . (cid:12) (Wang et al.2020), is non-thermal as well. Based on its non-thermal spectralproperties and companion mass, we suggest MSP B is a redbackbinary system.We searched for the optical counterparts to the four MSP bi-nary systems in M13 using HST archival data in the vicinity of therespective radio timing positions, and discovered optical counter-parts to MSPs D and F. The position of the counterpart to MSP Fon color-magnitude diagrams shows that the companion star is mostlikely a white dwarf. The counterpart to MSP D is faint and onlyobserved in V band, resulting in a large uncertainty of its positionon color-magnitude diagrams. However, given MSP D’s blackbody-like X-ray spectrum and companion mass of ∼ . (cid:12) (Wang et al.2020), we argue that the counterpart to MSP D is also likely to bea helium-core white dwarf. To our knowledge, this is the first useof the X-ray properties of a radio millisecond pulsar to predict thenature of its companion star. ACKNOWLEDGEMENTS
COH acknowledges support from NSERC Discovery Grant RGPIN-2016-04602. This research has made use of data obtained from the Chandra Data Archive and the Chandra Source Catalog, and soft-ware provided by the Chandra X-ray Center (CXC) in the applicationpackages CIAO and Sherpa. This research has made use of NASA’sAstrophysics Data System. This research is based on observationsmade with the NASA/ESA Hubble Space Telescope obtained fromthe Space Telescope Science Institute, which is operated by theAssociation of Universities for Research in Astronomy, Inc., underNASA contract NAS 5–26555.
DATA AVAILABILITY
The
Chandra data used in this paper are available in the ChandraData Archive ( https://cxc.harvard.edu/cda/ ) by searchingthe Observation ID listed in Table 1 in the Search and Retrievalinterface, ChaSeR ( https://cda.harvard.edu/chaser/ ). The
HST data used in this work can be retrieved from the Mikul-ski Archive for Space Telescope (MAST) Portal ( https://mast.stsci.edu/portal/Mashup/Clients/Mast/Portal.html ) bysearching the proposal IDs listed in Table 2.
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