Heated Poles on the Companion of Redback PSR J2339 − 0533
D. Kandel, Roger W. Romani, Alexei V. Filippenko, Thomas G. Brink, WeiKang Zheng
DDraft version September 10, 2020
Typeset using L A TEX twocolumn style in AASTeX63
Heated Poles on the Companion of Redback PSR J2339 − D. Kandel , Roger W. Romani , Alexei V. Filippenko ,
2, 3
Thomas G. Brink, and WeiKang Zheng Department of Physics, Stanford University, Stanford, CA, 94305, USA Department of Astronomy, University of California, Berkeley, CA, 94720, USA Miller Senior Fellow, Miller Institute for Basic Research in Science, University of California, Berkeley, CA 94720, USA (Received 2020 July 11; Revised 2020 August 30; Accepted 2020 September 8)
Submitted to ApJABSTRACTWe analyze photometry and spectra of the “redback” millisecond pulsar binary J2339 − i = 69 . ◦ ± . ◦ , together with the center-of-mass velocity (from the radial-velocityfits) K C = 347 . ± . − , give a fairly typical neutron star mass of 1 . ± . M (cid:12) . Keywords: pulsars: general pulsars: individual (PSR J2339 − INTRODUCTIONUsing optical imaging, Romani & Shaw (2011) andKong et al. (2012) discovered a binary system with P B = 0 .
193 d coincident with one of the brightestunidentified
Fermi /LAT sources, inferring that it wasthe tidally locked, heated companion of a millisecondpulsar (MSP). Radio observations (Ray et al. 2014,2020) found a 2.9 ms pulsar at this position, which wasgenerally obscured by a particularly powerful compan-ion wind, but occasionally visible at 820 MHz. Theconnection with the gamma-ray source was confirmedvia gamma-ray pulsations (Pletsch & Clark 2015); thesource is an ˙ E = 2 . × erg s − “redback”-type MSPwith a low-mass main-sequence companion. This andthe extreme spectroscopic variation (from mid ∼ ∼ Corresponding author: D. [email protected] allow a detailed fit for the orbital parameters. Herewe report on a new analysis of precision photometry,which shows highly significant asymmetries in the or-bital light curves. Such asymmetry has been observedin other heated companions (e.g., Stappers et al. 2001;Schroeder & Halpern 2014), and it has been suggestedthat these distortions may arise from asymmetric heat-ing from the system’s intrabinary shock (IBS; Romani& Sanchez 2016) or from hot-spots on the companionmagnetic poles created by precipitating IBS particles(Sanchez & Romani 2017). Recently, Kandel & Romani(2020, herafter KR20) have described a model in whichglobal winds may advect the direct pulsar heating, alsoproducing light-curve distortions. Each of these predictssomewhat different heating patterns. Our photometry,which includes four epochs over eight years, also indi-cates that the distortions are not constant. We findthat a hot-spot which shifts location can reproduce theselight curves, with consistent (and constant) geometricparameters for the binary. We combine this geometricinformation with a reanalysis of the RS11 Hobby-EberlyTelescope (HET) spectroscopic data to infer the neutronstar mass as 1 . ± . M (cid:12) . We conclude with a dis-cussion of the nature of the hot-spot asymmetry and a r X i v : . [ a s t r o - ph . H E ] S e p Kandel et al. recommendations for future observations that seek tomeasure the mass of such binaries. OBSERVATIONSOur principal new photometric dataset is derived froman analysis of archival grizJHK photometry of PSRJ2339 − ×
145 s for the optical exposuresover the two observing sessions, the data covered 1.89orbits. We downloaded the image frames and associ-ated bias, flat, and dark frames. After standard IRAFprocessing and combination of the subexposures in theinfrared (IR) frames, we extracted aperture photome-try at the pulsar position measured near orbital maxi-mum brightness. The instrumental magnitudes were cal-ibrated against Sloan Digital Sky Survey (SDSS) mea-surements of field stars in the optical and against Two-Micron All-Sky Survey (2MASS) stars in the near-IR.Unfortunately, with the limited GROND field of view,only a handful of calibration stars were available. Theseeing during these observations was poor and variable,with full width at half-maximum intensity (FWHM)1 . − . (cid:48)(cid:48) , and the airmass was as large as ∼ .
6, leadingto large apertures and low signal-to-noise ratio (S/N) de-tections near orbital minimum brightness. Nevertheless,the photometry was quite stable, with useful detectionsthroughout the orbit. We also extracted the IR-channeldata, calibrating against a single nearby 2MASS star.We find that the J -band light curve is of good quality,and H shows the heating effect, but the combinationof limited S/N, large background uncertainties, and low T eff sensitivity made the K s GROND data nearly use-less.This photometry can be compared with more limiteddata taken at other epochs. First, optical imaging ofJ2339 was obtained at the WIYN 3.5 m telescope withthe MiniMo imager on Sep. 27-28, 2011 (5 ×
240 s + 2 ×
180 s in Gunn g , 9 ×
120 s + 240 s in Gunn r , 7 ×
120 s +300 s in Gunn i ). We also examined BV RI photometryfrom Sep. 22 to Oct. 7, 2011, taken by the OISTERcollaboration (Yatsu et al. 2015) and kindly shared bythose authors. Next, photometry at the SOAR 4.2 mtelescope using the GHTS in direct imaging mode onAugust 12, 2013, was collected: 3 ×
180 s + 300 s inSDSS u (cid:48) , 4 ×
120 s + 300 s in SDSS g (cid:48) , 4 ×
120 s + 60 sin SDSS r (cid:48) , 4 ×
120 s + 300 s in SDSS i (cid:48) , and 4 ×
600 sin H α . For all SOAR and WIYN frames, standard CCDreductions were made and the fluxes were calibrated toSDSS stars in the field using u (cid:48) , g (cid:48) , r (cid:48) (for Gunn r andH α ), and i (cid:48) magnitudes. For the WIYN data, the seeing image quality was good (0 . (cid:48)(cid:48) FWHM), and we can see(Fig. 1, left) that a faint extended source lies near thepulsar counterpart.Most recently, on Oct. 28, 2019, we obtained eight600 s exposures with the Keck-I 10 m telescope plus theLow Resolution Imaging Spectrometer (LRIS; Oke et al.1995) in long-slit mode, using the 5600 ˚A dichroic, the400 line mm − (blazed at 4000 ˚A) blue grism, and the400 line mm − (blazed at 8500 ˚A) red grating, coveringthe binary orbital minimum brightness. This gave usspectra in the approximate range 3300–10,500 ˚A, withdispersions of 0.63 ˚A pixel − (blue) and 1.2 ˚A pixel − (red). The atmospheric dispersion corrector (ADC) al-lowed us to not have the slit aligned along the parallacticangle (Filippenko 1982), instead rotating the 1 (cid:48)(cid:48) -wideslit so that we could simultaneously observe a nearbybrighter G0 star. This enabled us to monitor the sys-tem throughput and to detect small shifts in the wave-length solution between frames. In addition, since thiscomparison (“comp”) star has known and stable SDSSmagnitudes, we are able to integrate the extracted pul-sar and comp-star spectra over the appropriate wave-length ranges to get accurate relative photometry. Thisgives the pulsar magnitudes in broad-band filters, up toa possible small grey shift (due to different companionand comparison star slit losses) across the eight expo-sures. These spectra were followed by two g/I imagepairs, which served to check comp-star placement andstability. Thus, we have ten Keck photometric measure-ments in g and i/I and eight in other filters.Of course, the spectral velocity information is also di-rectly useful, and we augment the new Keck spectrawith a reanalysis of 48 600 s exposures taken with theHET/LRS as described by RS11 to extract a new radial-velocity curve of the companion.Although severely blended with the pulsar counter-part in the low-resolution GROND data, we have mea-sured the spectral energy distribution (SED) of thenearby extended source and find it consistent with agalaxy at redshift z ≈ . PHOTOMETRIC FITTINGUsing a recent recomputation of the gamma-rayephemeris (An et al. 2020) which provides excellentpulse-phase aligned timing throughout the
Fermi mis-sion, including the epochs of all observations describedin this paper, we determine the binary phase fromthe barycentered time of the exposure midpoints. The edback PSR J2339 − Figure 1.
Left: WIYN Gunn r image near orbital minimum, showing the pulsar companion and the contaminating galaxy ∼ (cid:48)(cid:48) SE. Right: The SED of the contaminating source (magenta points), compared with the excess to the best-fit GRONDmodel at minimum (black points). SEDs for elliptical galaxies at redshift z = 0 .
75 (cyan line), z = 0 . z = 0 . M a g n i t ud e HSDH WHWH − . . g . . r . . i . . . . . . . Binary Phase . . z Cycle 1 Cycle 2 Cycle 3
Figure 2.
Light curves ( griz ) of J2339. Three periods are plotted with φ B = 0 at pulsar TASC (ascending node). The solidcurves in all three cycles show the best-fit hot-spot model (Table 2, row 3). The dotted curve of cycle 1 shows the DH modelwith an arbitrary phase shift (fits without a phase shift are completely unacceptable). The dotted curve of cycle 2 illustratesthe wind model. Lower panels show fit residuals from the three models, with the hot-spot model (cycle 3) having the smallestresiduals. GROND dataset is densely sampled with nearly uniform phase coverage, so we fit these data to best constrain thebinary parameters.
Kandel et al.
Table 1.
Parameters DH + Phase Shift WH HS i (deg) 58 . +0 . − . . +0 . − . . +2 . − . f c . +0 . − . . +0 . − . . +0 . − . L P / (10 erg s − ) 2 . +0 . − . . +0 . − . . +0 . − . T N (K) 3183 +28 − +28 − +64 − d (kpc) 1 . +0 . − . . +0 . − . . +0 . − . (cid:15) ... 0 . +0 . − . ... θ c (deg) ... 55 . +2 . − . ...∆ φ − . +0 . − . ... ... χ / DoF 1388 /
553 877 /
552 671 / The GROND griz light curves (Fig. 2) are well sam-pled and quite smooth. First, the optical maximumbrightness is shifted significantly later in phase than pul-sar superior conjunction. Any model which does not ac-count for this is completely unacceptable. Accordingly,our minimal direct heating (DH) model must include anarbitrary (not physically justified) phase shift ∆ φ . Also,the light curve shows significant asymmetry, with excessemission on the leading side, especially in the bluer col-ors. This a clear sign of heat redistribution from thesubpulsar point.We also fit for an extra background flux in each band,since the large-aperture GROND extractions (3 . (cid:48)(cid:48) inthe optical, 5 (cid:48)(cid:48) in the IR) guarantee contamination bythe nearby galaxy. The best-fit contamination fluxes dofollow the red galaxy spectrum in the optical (Fig. 1).The IR fluxes are somewhat larger; this may be due tothe larger photometric aperture, but may also implicatea red nonphotospheric contribution from J2339 itself.The best-fit parameters of this DH model are given inTable 1. With a large χ per degree of freedom (DoF) of2.51, it is unable to explain the asymmetric light curve,as can be seen in the fit residuals of Figure 2.One way to produce light-curve phase shifts and asym-metry is via a global circulation, as in the model devel-oped by KR20, where an equatorial wind redistributesheat from the subpulsar point. This wind is charac-terized by (cid:15) ≡ τ rad ω adv , the ratio of radiation time toadvection time at the equator (prograde for (cid:15) > θ c , the angle from the equator at which the flow(with the same (cid:15) ) changes sign. Hydrodynamical mod-els of such flows can show more complex patterns, andVoisin et al. (2020) have recently developed a similarmodel also incorporating heat diffusion, but our simple prescription captures the bulk heat redistribution withsufficient freedom to use in model fits. The fit withthis wind-heating (WH) model implies a super-rotatingequatorial wind resulting in the overall phase shift ofthe light-curve maxima by ∆ φ max ≈ − .
03. The χ decrease of this model is large, with strong statisticalpreference over the DH model.However, there is good reason to expect that the low-mass stellar companions of redbacks are significantlymagnetized so that the companion field can channel en-ergetic pulsar particles to heat its surface at magneticcaps formed by the field foot-points (Sanchez & Romani2017). Thus, we also fit with a single hot-spot (HS)model having a simple Gaussian excess on the compan-ion surface, characterized by amplitude A hs , radial size r hs , and angular position θ hs , φ hs . The binary parame-ters for this model are listed in Table 1. The hot-spotparameters (Table 2) indicate a substantial (32%) tem-perature excess in a large-radius (47 ◦ ) pole. This poleis located in the companion’s “southern” hemisphere(across the equator from Earth’s line of sight) and leadsthe subpulsar point near L . The fit is superior to that ofboth the DH and WH models. The χ / DoF approaches1 and the fit residuals reduce greatly (Fig. 2, panel 3),showing that the model reproduces the observed asym-metry quite well. One should note that i is substantiallyhigher (and L p is lower) for the HS model than for theDH and WH models. The other binary parameters aresimilar. SHIFTING HOT-SPOTSArmed with the binary parameters determined by thefit to the GROND data, we can check consistency withthe partial light curves provided by our other datasets,which span eight years. First, the sparse WIYN 2011data show a minimum appreciably brighter than theGROND model curve, with the minimum closer to φ =0 .
25 than the GROND data. Near this epoch (Septem-ber 22 – October 7, 2011), observations were made usingthe Optical and Infrared Synergetic Telescopes for Ed-ucation and Research (OISTER). Originally presentedby Yatsu et al. (2015), this dataset has good phase cov-erage and shows a phase shift. We have elected to fitthese datasets together for the 2011 epoch; if fit sepa-rately, both indicate a hot-spot at similar θ hs and φ hs .Next, 2013 SOAR photometry covered only maximumbrightness, but also show a peak slightly later in phasethan for GROND. Perhaps the best comparison, though,is with the 2019 Keck data. With the spectral points wehave multicolor coverage of the orbital minimum, plusa few late g/I points. This minimum is distinctly bluer edback PSR J2339 − .
00 0 .
25 0 .
50 0 .
75 1 .
00 1 .
25 1 .
50 1 .
75 2 . Binary Phase M a g n i t ud e SOAR modelGROND modelSOAR data Keck modelKeck data
Figure 3.
Left: 2013 ugri
SOAR photometric observations,compared with the best-fit HS model (solid curves, Table 2,row 2). Right: 2019 ugriz
Keck photometry and best-fit HSmodel (solid curves, Table 2, row 4). For comparison, thedotted griz curves in both panels are the best-fit HS modelfor the GROND epoch solid curves of Fig. 2 (Table 2, row3). . . . . . . Binary Phase . . . . . . . F l u x ( e r g / s / H z / c m ) × − OISTERdataWIYNdata
Figure 4.
BVRI
OISTER photometry from Yatsu et al.(2015) and best-fit HS model (solid curves, Table 2, row 1).The WIYN g (green), r (black), and i (magenta) points atsimilar epoch are overlaid. than in the GROND data, with a flat minimum wellcentered on φ = 0 . φ hs <
0, across theequator from the Earth line-of-sight), and (iii) spots onthe “day” (pulsar) side ( θ hs < ◦ ) are more stronglyheated (larger fractional temperature increase A hs ) thanthe Keck example, which is on the back “night” side. Ifthe hot-spots are heated by precipitation of IBS parti-cles ducted to the companion, as in the model of Sanchez& Romani (2017), then fewer particles are captured byfield lines extending away from the pulsar, so the weakerheating fit for the Keck example is natural.As for all redbacks, this companion is a low-mass star,fully convective in the core with a short spin period im-posed by tidal locking, so we expect a strong α − Ω dy-namo as well as a strong and frequently refreshed mag-netic field. So, magnetic pole hot-spots are natural andchanges in the dipole axis are plausible. Of course, theregenerated field may assume a random orientation un-der each regeneration – this is a nominal conclusion fromour fit spot locations. However, it is intriguing that allfour epochs are consistent with φ hs ≈ − ◦ to − ◦ ; inthis case, we might infer that the magnetic axis is rela-tively stable, but that the differing θ hs could representa drifting interior dipole. Such a motion may explainthe shifting light curve of redback PSR J1723 − A hs for the two hemispheres.For the GROND epoch, we refit the full model; reas-suringly, all fit binary parameters are within the uncer-tainty of single-spot fit values. We find A / A ≈
10. Forthe Keck epoch the flux ratio is relatively unconstrained,1 . (cid:46) A / A (cid:46) .
5, but the brighter (northern) hemi-sphere pole is poorly constrained mostly because of thelack of data around the light-curve maxima. It will beinteresting if future intensive studies can test the ex-pectation that heated poles will have the largest powerwhen closest to the companion nose. SPECTRAL ANALYSISWe can compare the Keck spectroscopy with the pho-tometric fit model. Figure 5 shows the Keck flux aver-
Kandel et al.
Table 2.
Best-fit hot-spot parameters for different epochs (in chronological order).
Dataset Obs MJD θ hs (deg) φ hs (deg) A hs r hs (deg) Ref.WIYN + OISTER 55826 - 55841 65 . ± . − . ± . . ± .
10 31 . ± . . ± . − . ± . . ± .
20 40 . ± . . ± . − . +5 . − . . +0 . − . . +4 . − . Fig. 2Keck 58784 124 . ± . − . +26 . − . . +0 . − . . ± . Figure 5.
J2339 Keck spectrum, averaged over the fourexposures at minimum brightness (red). This is comparedwith the model composite spectrum (blue) as well as a sin-gle night-side base temperature model (green). The modelspectra include extra flux toward the red: i = 2 . ± . µ Jyand z = 5 . ± . µ Jy. The average colors synthesized fromthe spectrum with the sbands routine for the SDSS bands(faint dotted curves) are shown by the magenta points. aged over the four spectra at the light-curve minimum.For comparison, we show the composite model spectrum(blue) and a single-temperature T N model averaged overthe same four Keck nighttime phases. The compositespectrum is computed using the ICARUS code (Bretonet al. 2012) for a model with reduced γ -ray heating, ashifted hot-spot (Table 2, row 4), and excess IR flux at-tributed to the background galaxy (Fig. 1, left). Thegeneral agreement is reasonable, with an M3–M1-classspectrum, but the composite model is too blue. Thecompanion also has a strong H α line, with weaker H β visible in some spectra.Since they are dominated by molecular bands, theKeck spectra at minimum brightness do not providegood radial velocities. The first spectrum at φ B = 0 . α line provides good velocities for allspectra. We have also compared with the HET spec-tra of RS11, remeasuring the radial velocities by fittingwith a K1 template while excluding 100 ˚A ranges aroundthe Balmer absorption features that dominate near op-tical maximum. No evidence for H α emission is seenin the lower-S/N, lower-resolution HET data. Retain-ing only the HET points with strong cross-correlationpeaks (from the day phases), we obtain the radial-velocity curve of Figure 6. The HET spectra seem tohave a wavelength offset, which introduced a substan-tial Γ ≈ −
80 km s − in RS11; we have chosen to matchthe Keck velocity solution for the K1 fits, which resultin a small positive Γ.As emphasized by Linares et al. (2018) and discussedby KR20, different line species have varying tempera-ture sensitivities and so are differently distributed acrossthe face of the companion. By fitting with K1 tem-plates (and excluding the Balmer-line wavelengths), weare most sensitive to the metal lines. SYSTEM MODELING AND DISCUSSIONFor a given heating model, the radial-velocity data canbe used to infer the companion center-of-mass (CoM)motion. Adopting the GROND-epoch light-curve model(Table 1), we can compute the equivalent width (EW)-weighted radial velocity at each orbital phase, for a givenline species. Here, since we use a K1 template to mea-sure the radial velocities, we are most sensitive to thecommon metal absorption lines. Using a set of archivalstandard dwarf spectra, we have computed the temper-ature dependence of the EWs of the strongest Fe, Mg I,and Na I optical lines. Averaging, a simple power-lawfit gives EW( T ) = (3 . /T ) . . With this prescrip-tion, we compute the metal-line radial-velocity curve fora given model and can fit to the spectroscopic data todetermine the CoM radial velocity K and Γ. Althoughwe do not perform a simultaneous fit with photomet-ric data, the spectroscopic fits are marginalized over thegeometrical parameters from the end of the GRONDphotometric Markov Chain Monte Carlo chains, sam-pling 2 σ uncertainties. Thus, the mass errors include edback PSR J2339 − Figure 6.
J2339 radial-velocity measurements, from metallines (K1 template) and H α emission. The best-fit curve,employing the Keck-epoch host-spot illumination, is shown. Table 3.
Radial-velocity fit results for J2339
Parameters Phase Shift WH HS K C (km s − ) 351 . +3 . − . . +3 . − . . +3 . − . Γ (km s − ) 22 . +2 . − . . +2 . − . . +2 . − . M NS ( M (cid:12) ) 2 . +0 . − . . +0 . − . . +0 . − . M C ( M (cid:12) ) 0 . +0 . − . . +0 . − . . +0 . − . χ / DoF 23 /
19 22 /
19 23 / all uncertainties in the model fitting, spectroscopic andphotometric.The fit results are given in Table 3 while the best-fitradial-velocity curve is shown Figure 6. For our basemodel (HS model) this gives a companion CoM velocityamplitude K C = 347 . ± . − , a relatively modestneutron star mass of 1 . ± . M (cid:12) , and a companionmass of 0 . ± . M (cid:12) . Note that this companion massis consistent with its observed spectral class and fit basetemperature of ∼ . ± . − , 349 . ± . − , and348 . ± . − for Keck, WIYN + OISTER, andSOAR, respectively. Such differences lead to mass shifts of ∼ ± . M (cid:12) . This shows that although the differ-ent heating models do imply small differences in theCoM radial-velocity amplitude K c and hence mass, thelargest differences arise from the different inclinationsof the fit models. The other (deprecated) heating mod-els give substantially different masses. For the phase-shift or WH model, one would infer large ( (cid:38) . M (cid:12) )masses. Some systems may indeed have such largemasses (see KR20), but here the smaller mass HS so-lution is clearly statistically preferable. Additional sup-port can be drawn from the fact that the high-mass mod-els have M C > . M (cid:12) , inconsistent with the low T N ofthe light-curve fits.The connection between the H α radial velocities andthe underlying CoM velocity is unclear. Interestingly,the largest departures from the model radial-velocitycurve are near the inferred hot-spot phase. However,the relative redshift of the emission line is a puzzle. Ifit represented outflow from the companion surface, ablueshift would be expected at these phases. Additionalspectroscopy with good S/N might follow this line emis-sion into the day side of the orbit, giving clues to itsorigin.Note that here we have determined the radial veloc-ities by adopting a cross-correlation fit dominated bymetal lines and then using the model surface temper-ature distribution to map the EW-weighted radial ve-locity. A more complete analysis would be to gener-ate model spectra for each phase and to cross-correlatethese spectra with the data to find the radial-velocityshifts uniformly fit from all spectral features (using arange of species with different T dependence). For ob-jects such as J2339 with a large ( > × ) range in thesurface temperature, this would be the best way to con-nect back- (night) side molecular band shifts with theday-side Balmer line velocities. We plan to pursue suchan analysis in upcoming papers.Our evidence for secular light-curve variations joinsthat for other redbacks. It seems that this is a quitecommon feature of these systems and we speculate thatit is associated with time-varying magnetic dipoles onthe active companion, heated by precipitating IBS parti-cles. We encourage high-quality multiband light curvesof these systems at few-month separations over severalyears to probe the physical origin of these variations.We thank the anonymous referee for a very detailedand careful reading of the manuscript. We are grate-ful for the excellent assistance of the staffs of the ob-servatories where data were taken. Some of the datapresented herein were obtained at the W. M. Keck Ob-servatory, which is operated as a scientific partnership Kandel et al. among the California Institute of Technology, the Uni-versity of California, and NASA; the observatory wasmade possible by the generous financial support of theW. M. Keck Foundation. D.K. and R.W.R. were sup- ported in part by NASA grants 80NSSC17K0024 and80NSSC17K0502. A.V.F.’s group is grateful for gener-ous financial assistance from the Christopher R. RedlichFund, the TABASGO Foundation, and the Miller Insti-tute for Basic Research in Science (UC Berkeley).REFERENCESamong the California Institute of Technology, the Uni-versity of California, and NASA; the observatory wasmade possible by the generous financial support of theW. M. Keck Foundation. D.K. and R.W.R. were sup- ported in part by NASA grants 80NSSC17K0024 and80NSSC17K0502. A.V.F.’s group is grateful for gener-ous financial assistance from the Christopher R. RedlichFund, the TABASGO Foundation, and the Miller Insti-tute for Basic Research in Science (UC Berkeley).REFERENCES