A Likely Redback Millisecond Pulsar Counterpart of 3FGL J0838.8-2829

A major achievement of the Large Area Telescope on the Fermi Gamma-ray Observatory is the detection of many recycled millisecond pulsars (MSPs), some of which are accomplished with the help of prior radio ephemerides, but most of them are new ones that are found in successful radio-pulsar searches of its unidentified γ-ray source error circles. Of the 205 pulsars detected by Fermi so far, 92 are recycled.³ Most interesting among the Fermi MSP discoveries are the black widow (BW) and "redback" binary systems (Roberts 2013). BWs have companions of substellar mass, while redbacks have $\gt 0.1\,{M}_{\odot }$ bloated companions that are usually close to filling their Roche lobes. Both BWs and redbacks are compact binaries with orbital periods ≲1 day. Their properties connect BWs and redbacks to their long-supposed low-mass X-ray binary progenitors, which spin them up by accretion (Alpar et al. 1982). A direct link was forged by the three redbacks that have been observed to transition between radio-pulsar and accreting states on timescales of years: PSR J1023+0038 (Archibald et al. 2009), XSS J12270−4859 (Bassa et al. 2014; Roy et al. 2015), and PSR J1824−2452I, in the globular cluster M28 (Papitto et al. 2013). Currently, $\approx 60$ BW and redback pulsars are known that are almost equally divided between globular clusters and Galactic field populations.⁴

In addition to the BW and redback systems that are certified radio MSPs, it has become possible through X-ray and optical follow-up of Fermi source error circles to identify counterparts that are almost certainly MSP binaries, even without obtaining a radio-pulsar detection. Their distinctive optical and X-ray light curves, spectroscopic orbital parameters, and positional coincidence with a γ-ray source allow some objects to be classified as BW or redback pulsars whose spin parameters are not yet known. Fermi sources that have been identified in this way are 3FGL J0212.1+5320 (Li et al. 2016; Linares et al. 2017), 1FGL J0523.5−2529 (Strader et al. 2014), 2FGL J1311.7−3429 (Kataoka et al. 2012; Romani 2012; Romani et al. 2012, 2015), 2FGL J1653.6−0159 (Kong et al. 2014; Romani et al. 2014), 3FGL J2039.6−5618 (Romani 2015; Salvetti et al. 2015), and 1FGL J2339.7−0531 (Romani & Shaw 2011; Kong et al. 2012). Radio pulsations at 2.88 ms were subsequently detected from 1FGL J2339.7−0531/PSR J2339−0533 by Ray et al. (2014), and 2.56 ms pulsations were found in γ-rays from 2FGL J1311.7−342/PSR J1311−3430 (Pletsch et al. 2012) with the help of its optical orbital ephemeris.

Complementing the above list of sources, 3FGL J0427.9−6704 (Strader et al. 2016) and 3FGL J1544.6−1125 (Bogdanov & Halpern 2015) have X-ray/optical counterparts that appear to be transitional MSPs in the accreting state. A related discovery is 3FGL J1417.5−4402/PSR J1417−4402, with a giant companion in a 5.4 day orbit (Strader et al. 2015) and 2.66 ms radio pulsations (Camilo et al. 2016). It is thought to be a typical MSP observed in the late stages of recycling, one that will end its evolution with a white dwarf companion in a several day orbit. The difficulty of detecting radio pulsations over most of the orbit of PSR J1417−4402, as well as from most redbacks, is apparently due to the absorption by the winds from their companions. This suggests that some γ-ray pulsars may be completely enshrouded most of the time (as proposed by Tavani 1991) and will remain as only putative MSPs unless their pulsations can be found in X-rays or γ-rays.

Several authors have performed systematic analyses of the spectral and temporal properties of unidentified Fermi sources using machine learning techniques to assign the tentative classifications as active galactic nuclei, young pulsars, or MSPs (Ackermann et al. 2012; Lee et al. 2012; Mirabal et al. 2012, 2016; Saz Parkinson et al. 2016). In particular, Mirabal et al. (2016) classified 3FGL J0838.8−2829 among the high-confidence MSPs. In Halpern et al. (2017, Paper I), we identified a candidate binary MSP counterpart for 3FGL J0838.8−2829 from an XMM-Newton X-ray and optical study of its error circle (see also Rea et al. 2017), as well as in our own ground-based optical data. In this paper, we report on new optical and radio observations that characterize the source, XMMU J083850.38−282756.8. Section 2 describes time-series photometry that determines its 5.15 hr orbital period and characterizes the orbital light curve. Section 3 reports spectroscopy that yields a radial velocity curve for the secondary, and reveals variable, broad Hα emission lines. Section 4 presents tentative inferences about the binary parameters, distance, and luminosity, and discusses the heating light curve and flaring activity and possible interpretations of the Hα emission line. Section 5 summarizes the main conclusions.

Over three months in 2016–2017 we obtained six nights of time-series photometry of XMMU J083850.38−282756.8, the MSP candidate for 3FGL J0838.8−2829 from Paper I and Rea et al. (2017), using either the MDM Observatory 2.4 m Hiltner telescope and Ohio State Multi-Object Spectrograph (OSMOS; Martini et al. 2011) in imaging mode, or a robotic 1 m telescope at the CTIO node of the Las Cumbres Observatory (LCO) with its Sinistro imager (Brown et al. 2013). A log of the observations is given in Table 1. An SDSS $r^{\prime}$ filter was used in each case with an exposure time of 300 s. Run lengths ranged between 5 and 6 hours. The goals of this single-filter observing program were to obtain a precise orbital ephemeris, to monitor for rapid flaring as was seen in one of the XMM-Newton observations (Paper I), and to characterize any other variability of the light curve.

Table 1.  Log of Time-series Photometry^a

Telescope/Instrument	Date (UTC)	Time (UTC)
MDM 2.4 m/OSMOS	2016 Dec 24	07:27–12:29
MDM 2.4 m/OSMOS	2016 Dec 27	07:02–12:41
LCO 1 m/Sinistro	2017 Jan 2	02:00–07:56
MDM 2.4 m/OSMOS	2017 Jan 28	05:01–09:57
MDM 2.4 m/OSMOS	2017 Feb 25	02:57–08:20
LCO 1 m/Sinistro	2017 Mar 27–28	23:27–05:33

Note.

^aAll exposures are 300 s in the $r^{\prime}$ filter.

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The optical position listed in Table 2 was derived from a 2.4 m image using stars from the USNO B1.0 catalog (Monet et al. 2003) for an astrometric solution, and is consistent with the optical position given in Paper I. The $0\buildrel{\prime\prime}\over{.} 3$ error indicated in each coordinate includes the nominal uncertainty of the catalog coordinates.

Table 2.  Photometric Orbital Ephemeris

Parameter	Value
R.A. (J2000)	${08}^{{\rm{h}}}{38}^{{\rm{m}}}50\buildrel{\rm{s}}\over{.} 44(2)$
Decl. (J2000)	$-28^\circ 27^{\prime} 57\buildrel{\prime\prime}\over{.} 3(3)$
Time span (MJD)	57746–57840
Epoch T0 (MJD TDB)a	57781.2524(8)
Orbital period ${P}_{\mathrm{orb}}$ (day)	0.214507(5)

Note.

^aEpoch of the ascending node of the putative pulsar $\phi =0$ in Figure 1.

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Differential photometry and magnitude calibration were performed with respect to a calibrated comparison star. Images were inspected for cosmic-ray contamination, and a few points were rejected for cosmic-ray hits. The six resulting light curves are shown in Figure 1 as a function of orbital phase, the determination of which is described below. Here we adopt the convention in which phase zero is the ascending node of the pulsar, $\phi =0.25$ is the inferior conjunction of the companion, and $\phi =0.75$ is the superior conjunction. The shape of the light curve is characteristic of the heating of the side of the companion facing the pulsar, with a maximum brightness of $r^{\prime} \approx 19.5$ and a minimum of $r^{\prime} \approx 20.6$.

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There is occasional flaring, which is most easily visible in the 2017 January 28 and February 25 light curves in Figure 1. A quiescent state, if one can be recognized in the data, is perhaps best represented by the smooth light curve on 2016 December 27. It shows a sloping maximum that is not symmetric about the expected phase 0.75 of peak heating, but is rising up to $\phi =0.90$. Such behavior is not uncommon among redbacks (Woudt et al. 2004; Li et al. 2014; Deneva et al. 2016), indicating that the heating of the companion is frequently not symmetric about the line connecting the stars.

In order to derive an orbital ephemeris in the presence of flaring and other possible sources of variable asymmetry of the light curve, we use the epoch of minimum in the light curve as $\phi =0.25$, the fiducial phase, presuming that the timing of the minimum would be least affected by variability. Mid-times of each exposure were converted to barycentric dynamical time (TDB) using the utility of Eastman et al. (2010). Approximately 25 points around each minimum were fitted to a quadratic, and the calculated epochs of minimum were fitted to a constant orbital period, ${P}_{\mathrm{orb}}=5.14817\pm 0.000012\,\mathrm{hr}$. The precise parameter values are listed in Table 2, with the epoch of pulsar ascending node T₀ taken to be at $\phi =0$. The average residual of the epochs of minimum from the fitted ephemeris is $\approx 2$ minutes. For the ephemeris presented here we did not use the first observation (2016 December 24) as its minimum was poorly determined due to bad seeing, although its inclusion does not change the results within their errors.

We performed spectroscopy on four different nights, from 2017 February 3 to April 24 (UT), with the Goodman spectrograph (Clemens et al. 2004) on the Southern Astrophysical Research (SOAR) telescope. On the first night spectra were taken with a 1200 l mm⁻¹ grating and a $1\buildrel{\prime\prime}\over{.} 03$ wide slit over the wavelength range of 7700–8700 Å, yielding a resolution of 1.6 Å. The remaining observations all used a 400 l mm⁻¹ grating and a $1.^{\prime\prime} 03$ slit over the wavelength range of 4800–8830 Å, giving a resolution of 5.4 Å. The exposure times ranged from 900 to 1500 s, depending on the brightness of the source and the seeing. The spectra were reduced in the standard manner. Molecular bands indicate that the companion star is a late K or early M type, probably M0–M1 on the night side, and slightly hotter on the illuminated side.

We derived barycentric radial velocities through cross-correlation with bright stars taken with the same setup. Generally we used the region of the Ca ii near-infrared triplet, but we substituted the region around Mgb for spectra with low signal-to-noise in the Ca ii triplet region. The respective epochs for each spectrum are given as Modified Julian Day (MJD) in the TDB system. Given the faintness of the star, the formal radial velocity uncertainties are themselves uncertain, but the final results are nevertheless robust (see below). The radial velocity data are listed in Table 3.

Table 3.  Barycentric Radial Velocities

UT Date	MJD (TDB)	Exposure	vr	$\sigma ({v}_{r})$
		(s)	(km s−1)	(km s−1)
2017 Feb 3	57787.1650	900	342.3	25.6
2017 Feb 3	57787.1756	900	316.8	25.0
2017 Feb 12	57796.1260	1200	339.2	25.5
2017 Feb 12	57796.1444	1200	465.9	22.5
2017 Mar 28	57840.1192	1200	436.0	28.3
2017 Mar 28	57840.1332	1200	431.3	37.7
2017 Mar 28	57840.1513	1200	407.9	27.1
2017 Mar 28	57840.1653	1200	377.1	32.4
2017 Mar 28	57840.1839	1200	125.4	25.7
2017 Apr 24	57867.0436	1200	−222.4	21.2
2017 Apr 24	57867.0576	1200	−184.7	23.5
2017 Apr 24	57867.0756	1200	−117.3	24.0
2017 Apr 24	57867.0896	1200	20.2	21.6
2017 Apr 24	57867.1269	1500	289.0	20.5

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Since the orbital period and time of ascending node are determined with more precision from the photometry than what is possible from the presently limited spectroscopy, we adopted the photometric values of ${P}_{\mathrm{orb}}$ and T₀ from Table 2, nonetheless finding that the photometric values fall within the uncertainties resulting from an independent fit to the radial velocities only. Given the short period and presumed long history of the system, we also assume zero eccentricity. Hence, the only free parameters are the velocity semi-amplitude of the secondary K₂ and the systemic velocity ${v}_{\mathrm{sys}}$. Using a circular Keplerian fit, we find best-fit values of ${K}_{2}=315\pm 17$ km s⁻¹ and ${v}_{\mathrm{sys}}=129\pm 15$ km s⁻¹, with the uncertainties determined via bootstrap. This immediately yields a mass function of $0.69\pm 0.11{M}_{\odot }$ for the compact object. If we instead assume that all radial velocities have the same uncertainties, the best-fit K₂ and ${v}_{\mathrm{sys}}$ do not change. The best-fit radial velocity curve is shown in Figure 2.

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In addition to the radial velocities, a notable feature of the optical spectra is the variable Balmer-line emission. The spectra on 2017 February 12 show remarkably broad, asymmetric Hα emission (this is the only night where Hβ emission, which is similarly broad, is clearly present). On 2017 March 28 the Hα emission is present, but weak. In the last set of data, from 2017 April 24, the emission is stronger, though still not as strong as on 2017 February 12. Figure 3 shows the Hα emission lines on the days when it was strongest. The maximum observed equivalent width was $\approx 90\,\mathring{\rm A}$. The FWHM ranges from 550–1510 km s⁻¹, accounting for the spectral resolution. The line is generally asymmetric and sometimes double-peaked, with peak separations of 520–770 km s⁻¹. It is difficult to trace the velocities of the emission line due to the changing strengths of its multiple components. While they are shifted from the absorption-line radial velocities, there is no clear pattern with respect to orbital phase. However, there is often a peak in the line at or near the radial velocity of the companion, as marked in Figure 3.

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4.1. Binary Parameters, Distance, and Luminosity

4.2. Heating Light Curve

4.3. Optical and X-Ray Flares

Definite flaring behavior is present during some of the observations, most notably during $0.6\lt \phi \lt 0.85$ on 2017 January 28 and February 25. In the BW PSR J1311−3430, bright flares have been seen in optical and X-rays, which, because they appear to exceed the spin-down power of the pulsar, could be coming from stored energy in the companion's magnetic field (Romani et al. 2015). The same may be true of the occasional flares seen from PSR J1048+2339 in the Catalina Real Time Transient Survey (Deneva et al. 2016), which are difficult to account for assuming isotropic pulsar-wind heating. We do not know the pulsar parameters for XMMU J083850.38−282756.8, so it is not yet possible to make such a quantitative comparison for it.

XMMU J083850.38−282756.8 is the first non-accreting MSP binary in which a simultaneous X-ray and optical flare was observed (Paper I). The optical ephemeris of Table 2 is precise enough to extrapolate to the epoch of the XMM-Newton light curve of 2015 December 2 (ObsID 079018010), enabling us to examine the orbital dependence of the X-ray variability. The phase uncertainty of the extrapolation is $\sigma (\phi )\approx 0.05$. Figure 4 is a reproduction of Figure 10 from Paper I, now plotted as a function of orbital phase. The dramatic 1.2 hr long flare spans $-0.05\lt \phi \lt 0.19$, with peaks at $\phi =-0.03,0.06$ and 0.17. The flare's final and highest peak has a maximum luminosity of $\approx 1\times {10}^{33}\,{(d/1\mathrm{kpc})}^{2}$ erg s⁻¹ in a single 100 s bin. Since it occurs close to $\phi =0.25$, either the flaring region must not be very close to the heated photosphere where it could be occulted, or the inclination angle of the orbit must not be very large. In redbacks there is often a broad dip in the X-ray emission centered around $\phi =0.25$, which is attributed to the occultation of an intrabinary shock that is very close to the companion (Bogdanov et al. 2014a, 2014b; Gentile et al. 2014; Hui et al. 2015; Roberts et al. 2015; Romani & Sanchez 2016). There is no evidence for such orbital modulation of the "quiescent" emission in Figure 4, which instead may be dominated by low-level flaring.

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The simultaneous flare in the XMM-Newton optical monitor (Figure 4, bottom), for which B = 19.5 averaged over the 4400 s exposure time is an increase of $\approx 1.5$ mag over the quiescent level, is more intense than any of the smaller flares that we have seen in 33 hours of $r^{\prime}$-band photometry. This implies either that the flares are very blue, or that emission at the level of the XMM-Newton flare is relatively rare.

4.4.  $H\alpha$ Emission

A photometric and spectroscopic study of the previously suggested X-ray counterpart of the Fermi source 3FGL J0838.8−2829 reveals a 5.15 hr orbit with a heating light curve and an M dwarf companion characteristic of a redback MSP system. X-ray and γ-ray fluxes are compatible with an MSP identification at a typical distance and spin-down power for Fermi MSPs. Following on similar discoveries of this distinctive class of MSP binary in positional coincidence with γ-ray sources, we conclude that XMMU J083850.38−282756.8 is the redback counterpart of 3FGL J0838.8−2829 even though its pulsations have not yet been detected. This source adds to a growing sample of redbacks that have asymmetric heating light curves and strong flaring activity in X-ray and optical that are not well fitted by existing models of heating meditated by an intrabinary shock between the pulsar wind and the companion's wind. This suggests that magnetic fields intrinsic to the companion shape the light curve, both by channeling the pulsar wind directly to its photosphere and by tapping its own energy in transient reconnection events.

Variable Hα emission may be coming from the wind driven from the companion, which could be responsible for the absence (so far) of detected radio pulsations due to free–free absorption or dispersion. Nevertheless, sensitive searches are warranted for radio pulsations at a number of epochs and at all orbital phases, since the uncertain configuration and possibly variable column density of the absorbing plasma may allow rare windows of transparency. A search of the Fermi γ-rays for pulsations may also be feasible with the aid of the optical ephemeris, to be refined in the future.

We thank the anonymous referee for excellent suggestions. Jessica Klusmeyer obtained two of the optical light curves at the MDM Observatory. MDM Observatory is operated by Dartmouth College, Columbia University, the Ohio State University, Ohio University, and the University of Michigan. This work makes use of observations from the LCO network and the SOAR telescope, which is a joint project of the Ministério da Ciência, Tecnologia, e Inovação (MCTI) da República Federativa do Brasil, the U.S. National Optical Astronomy Observatory (NOAO), the University of North Carolina at Chapel Hill (UNC), and Michigan State University (MSU). Support for this work was provided by the National Aeronautics and Space Administration through Chandra Award Number SAO GO6-17027X issued by the Chandra X-ray Observatory Center, which is operated by the Smithsonian Astrophysical Observatory for and on behalf of the National Aeronautics Space Administration under contract NAS8-03060. J.S. acknowledges support from NASA grant NNX15AU83G and a Packard Fellowship. This investigation also uses observations obtained with XMM-Newton, an ESA science mission with instruments and contributions directly funded by ESA Member States and NASA.