PSR J1306--40: An X-ray Luminous Redback with an Evolved Companion

TL;DR

This paper presents detailed optical and X-ray observations of PSR J1306--40, a redback millisecond pulsar binary with an evolved companion, revealing its fundamental properties, high X-ray luminosity, and potential evolutionary significance.

Contribution

The study provides new optical photometry and spectroscopy data, constrains the system's component masses and inclination, and suggests PSR J1306--40 as a progenitor of typical pulsar-white dwarf binaries.

Findings

Minimum neutron star mass of 1.75 solar masses

High, nearly edge-on inclination angle

X-ray luminosity brighter than most known redbacks

Abstract

PSR J1306--40 is a millisecond pulsar binary with a non-degenerate companion in an unusually long $\sim$1.097 day orbit. We present new optical photometry and spectroscopy of this system, and model these data to constrain fundamental properties of the binary such as the component masses and distance. The optical data imply a minimum neutron star mass of $1.75\pm0.09\,M_{\odot}$ (1-sigma) and a high, nearly edge-on inclination. The light curves suggest a large hot spot on the companion, suggestive of a portion of the pulsar wind being channeled to the stellar surface by the magnetic field of the secondary, mediated via an intrabinary shock. The H$\alpha$ line profiles switch rapidly from emission to absorption near companion inferior conjunction, consistent with an eclipse of the compact emission region at these phases. At our optically-inferred distance of $4.7\pm0.5$ kpc, the X-ray luminosity is $\sim$10$^{33}$ erg s$^{\textrm{-1}}$, brighter than nearly all known redbacks in the pulsar state. The long period, subgiant-like secondary, and luminous X-ray emission suggest this system may be part of the expanding class of millisecond pulsar binaries that are progenitors to typical field pulsar--white dwarf binaries.

Tables

Table 1. Table 1 Barycentric Radial Velocities of PSR J1306–40

BJD	RV	err.
(d)	(km s-1)	(km s-1)
2457945.5419639	–119.5	6.5
2457945.6301728	–16.9	7.2
2457956.5212405	–123.1	6.8
2457956.5352468	–107.9	6.4
2457956.5546942	–95.8	8.1
2457956.5687017	–65.6	8.2
2457956.5948590	–57.2	7.0
2457956.6088705	–38.0	6.0
2457966.4981876	–27.2	7.6
2457966.5122271	–18.4	20.1
2457966.5399208	38.7	7.2
2457966.5608956	49.6	8.7
2457966.5914866	115.1	10.2
2457967.5998999	–1.5	12.8
2457996.4786139	231.8	8.4
2457996.4931540	238.7	8.0
2457996.5105239	228.8	9.4
2458001.4795192	–144.0	11.4
2458001.4935388	–124.6	10.2
2458139.7564130	–136.8	7.7
2458139.7704090	–117.1	6.8
2458140.7400266	–194.5	9.8
2458140.7540222	–166.4	8.3
2458140.7770050	–150.8	7.4
2458140.7910007	–158.5	8.2
2458161.6721983	–121.2	7.9
2458161.6872977	–107.7	7.3
2458202.5822163	177.8	8.5
2458202.5962046	197.7	9.6
2458202.8350917	190.9	7.4
2458202.8490793	176.1	7.6
2458223.5928781	231.9	7.7
2458223.8317433	41.2	8.4
2458223.8456941	32.1	14.9
2458243.6779211	–87.6	8.6
2458243.6919415	–112.3	10.5
2458243.7115353	–125.5	9.5
2458243.7263475	–141.9	10.2
2458243.7459698	–130.3	10.9
2458247.5062024	131.9	11.5
2458247.5435496	160.5	14.2
2458278.5472619	197.1	15.9
2458278.5613912	183.7	15.7

Table 2. Table 2 SMARTS Photometry of PSR J1306–40

BJD	Band	mag	err
(d)
2457962.46060	B	19.104	0.104
2457962.46769	V	18.212	0.029
2457962.47235	I	17.007	0.062
2457967.46273	B	19.357	0.099
2457967.46981	V	18.631	0.044
2457967.47448	I	17.461	0.095
2457968.46610	B	19.334	0.073
2457968.47319	V	18.426	0.037
2457968.47785	I	17.289	0.033
2457969.47164	B	19.140	0.062
…	…	…	…

Table 3. Table 3 Summary of ELC fits for PSR J1306–40

Parameters	No Spot	Hot Spot
incl (∘)	70.4${}_{-7.0}{}^{}{}_{}{}^{+16.7}$	83.5${}_{-4.8}{}^{}{}_{}{}^{+3.3}$
filling factor ($f_2$)	0.88${}_{-0.02}{}^{}{}_{}{}^{+0.06}$	0.94${}_{-0.05}{}^{}{}_{}{}^{+0.04}$
$T_{\text{eff}}$	4728${}_{-67}{}^{}{}_{}{}^{+77}$	4913${}_{-191}{}^{}{}_{}{}^{+198}$
$T_{\text{day}}$	5542${}_{-165}{}^{}{}_{}{}^{+275}$	6187${}_{-451}{}^{}{}_{}{}^{+397}$
$\Delta \varphi$	-0.0354${}_{-0.0019}{}^{}{}_{}{}^{+0.0016}$	-0.0228 $\pm$ 0.0039
${\lambda }_{\text{spot}}$(∘)aafootnotemark:	$\cdots$	2${}_{}{}^{+5}{}_{-2}{}^{}$
${\theta }_{\text{spot}}$(∘)bbfootnotemark:	$\cdots$	27${}_{}{}^{+14}{}_{-19}{}^{}$
$T_{\text{spot}}$ (K)	$\cdots$	11063${}_{}{}^{+306}{}_{-414}{}^{}$
$r_{\text{spot}}$(∘)	$\cdots$	52${}_{}{}^{+3}{}_{-4}{}^{}$
${\chi }^2$(d.o.f.)	370.3(275)	220.7(271)
$M_1$ ($M_{☉}$)	2.08${}_{-0.34}{}^{}{}_{}{}^{+0.35}$	1.77${}_{-0.03}{}^{}{}_{}{}^{+0.07}$
$M_2$ ($M_{☉}$)	0.59 $\pm$ 0.10	0.51${}_{-0.01}{}^{}{}_{}{}^{+0.02}$
$\text{log}g$ (cgs)	3.745${}_{-0.010}{}^{}{}_{}{}^{+0.025}$

Equations

$$v\text{sin}i=K_2\frac{0.49q^{2/3}(1+q)}{0.6q^{2/3}+\text{ln}(1+q^{1/3})}$$

Full text

††slugcomment: Accepted to ApJ - March 20, 2019

1. Introduction

Millisecond pulsars (MSPs) form in binary systems, where the central neutron star accretes matter and angular momentum from a non-degenerate companion, spinning it up to very rapid spin periods. Although this mass transfer process is expected to last hundreds of Myrs or more (Tauris99), most MSPs in the Galactic field have degenerate white dwarf companions in wide orbits ($P_{\textrm{orb}}\gtrsim$ 5 d), which represent the end stage of the recycling process (Tauris06).

Recent multiwavelength (optical, radio, and X-ray) follow-up observations of unidentified Fermi Large Area Telescope (LAT) $\gamma$-ray sources have revealed a substantial number of close neutron star binary systems that host hydrogen-rich secondaries rather than He white dwarfs. Unlike most field MSPs (as described above), these appear to be systems in which the standard recycling process is not yet complete (e.g., Benvenuto14), providing valuable insights into the spin-up process. These binaries are classified by the mass of the secondary: “redbacks” have non-degenerate, main sequence-like companions ($M_{c}\gtrsim$ 0.1 $M_{\sun}$), compared to the less massive ($M_{c}\lesssim$ 0.05 $M_{\sun}$), highly ablated, semi-degenerate “black widows” (Roberts11b). Both systems show radio eclipses due to ionized material from the secondary; these eclipses are typically more extensive for redbacks (e.g., DAmico01; Camilo15; Cromartie16).

A few redbacks have been observed to transition back and forth between an accretion-powered disk state and a rotationally-powered pulsar state. These “transitional millisecond pulsars” proved the suspected evolutionary link between some recycled MSPs and neutron star low-mass X-ray binaries (e.g., Archibald09; Papitto13; Bassa14). However, like the bulk of the redback population, the short orbital periods in these systems ($\lesssim$ 0.5 d) mean they are unlikely to end their lives as the wide-orbit MSP–He white dwarf binaries that dominate the observed population of MSPs in the field (Chen13). Instead, the progenitors to these canonical MSP–white dwarf systems are neutron stars with evolved red giant companions whose orbital periods are $>$ 1 day (Tauris99).

In this context, the MSP binary 1FGL J1417.7–4407 (PSR J1417–4402) was the first MSP binary discovered that is a likely progenitor to the typical MSP-white dwarf binaries (Strader15; Camilo16). Due to its long period, red giant companion, and inferred evolutionary track, a new “huntsman” subclass was coined to distinguish unique systems like these from the more common redbacks (Strader15; Swihart18).

Optical spectra of 1FGL J1417.7–4407 show a strong, persistent double-peaked H$\alpha$ emission profile that is unusual among redbacks in their pulsar states and reminiscent of a classic accretion disk. However, due to the small separation between the peak components, and the stationary profiles as a function of orbital phase in the rest frame of the secondary, this H$\alpha$ phenomenology is likely not due to a disk. Instead, the emission likely comes from a combination of material swept off the companion and a strong intrabinary shock (Camilo16; Swihart18). Another piece of evidence for an unusually luminous shock is the X-ray luminosity in this system ($\sim$ 1033 erg s${}^{\textrm{-1}}$), which is higher than other redbacks in the pulsar state. Swihart18 discuss the possibility that the shock luminosity in 1FGL J1417.7–4407 is enhanced over typical redbacks by a strong, magnetically driven wind from the tidally-locked red giant secondary. The candidate MSP binary 2FGL J0846.0+2820 shows many similarities to 1FGL J1417.7–4407, making it a possible second member of the huntsman subclass, though no radio pulsar has yet been confirmed in this system (Swihart17). Pending future evolution studies, it might be reasonable to include other long period redback-like systems with evolved companions in this class (e.g., PSR NGC 6397A).

The subject of this paper, PSR J1306–40, was discovered in the SUPERB survey (Keane17), where it was identified as a candidate redback binary. No pulsar timing solution was presented owing to the frequent eclipses. Linares18 found the X-ray spectrum of this source is a hard powerlaw typical of redbacks, and that the X-ray and optical light curves are modulated on the same orbital period, confirming the source as a likely redback. The orbital period is one of the longest known among compact MSP binaries ($P_{\textrm{orb}}\sim 1.097$ d).

Here we present the first optical spectroscopy and multi-band optical photometry of PSR J1306–40, and show that it has properties more similar to huntsman-type MSP binaries than classic redback systems. We detail our new optical spectroscopic and photometric observations of the system in §2. We model the optical light curves in §3, and examine the phase-resolved H$\alpha$ profiles in §LABEL:sec:Halpha. Finally, we make concluding remarks and discuss this system in the context of known redbacks and its connection to MSP–white dwarf progenitors in §LABEL:sec:discussion.

2. Optical Observations

2.1. SOAR Spectroscopy

We obtained spectra of the companion to PSR J1306–40 using SOAR/Goodman (Clemens04) from 2017 Jul 11 to 2018 Jun 9. All data used a 1200 l mm*-1* grating and a 0.95″ slit, giving a resolution of about 1.7 Å. Exposure times ranged from 15 to 30 min per spectrum, depending on weather conditions. The spectra covered a wavelength range of $\sim$ 5485–6740 Å. Barycentric radial velocities were determined through cross-correlation with bright standards taken with the same setup, primarily in the wavelength range 6050–6250 Å. The resulting 43 velocities are listed in Table 1. Observation epochs have been corrected to Barycentric Julian Date (BJD) on the Barycentric Dynamical Time system (Eastman10).

Even though the SUPERB survey has detected a pulsar in this system (Keane17), it has not yet been timed, so the ephemerides must be determined from our data. Using the custom Markov Chain Monte Carlo sampler TheJoker (Price17), we fit a circular Keplerian model to the data in Table 1 in order to determine the orbital period $P$, BJD time of the ascending node $T_{0}$, systemic velocity $\gamma$, and the semi-amplitude $K_{2}$. Here, and throughout the paper, uncertainties are given at 1-sigma. We find $P=1.097195(161)$ d, $T_{0}=2457780.8373(19)$ d, $\gamma=32.0\pm 1.8$ km s*-1*, $K_{2}=210\pm 2$ km s*-1*. (We note that the spectroscopic period we find here is fully consistent with the photometric period found in the discovery paper Linares18). A fit using these median values is shown in Figure 1. For the remainder of this work, we assume the period derived from our spectroscopy.

This fit has an rms scatter of 11 km s*-1* (compared to a median uncertainty among the velocities of about 8.4 km s*-1*) and a $\chi^{2}$/d.o.f of 74/39, perhaps suggesting the fit could be improved. However, we see no clear trends in the residuals. A fit with the eccentricity left free does not find a value significantly different from 0, so there is no evidence that the orbit is non-circular. It may just be that the velocity uncertainties are slightly underestimated. It would be useful to obtain additional radial velocities in the range $\phi=0.7-1.0$; it is challenging to get complete phase coverage for this system since its period is close to 1 d. Future pulsar timing should improve the ephemerides by orders of magnitude.

Our SOAR spectra also show resolved H$\alpha$ in emission in most, but not all epochs. We present an analysis of the H$\alpha$ morphology in §LABEL:sec:Halpha.

2.1.1 Determining the Mass Ratio

By assuming the secondary is tidally synchronized with the pulsar, we can estimate its projected rotational velocity ($v$ sin $i$) by comparing the rotationally broadened spectra with non-rotating template stars of similar spectral type. The assumption of synchronization is reasonable since this timescale is $\lesssim 1$ Myr for a system with the period of PSR J1306–40 and a typical redback mass ratio (Zahn77). Combined with our measurement of the orbital semi-amplitude, we use the $v$ sin $i$ value to constrain the mass ratio of the binary.

Following similar procedures as described in Strader14 and Swihart17, we obtained spectra of bright late-G to mid-K giant stars to use as templates and convolved these with a set of rotational convolution kernels reflecting a range of $v$ sin $i$ values (including limb darkening). After cross-correlating the broadened templates with the original, unbroadened spectra, we fit a relation between the full-width at half-maximum (FWHM) values and the input value of $v$ sin $i$. We then cross-correlated the spectra of the companion to PSR J1306–40 with that of the unconvolved standard stars and used the FWHM values to estimate the projected rotational velocity.

Our final estimate of $v$ sin $i$ derived in this manner is 75.5 $\pm$ 3.8 km s-1, where the uncertainty represents the standard deviation of the measurements among all templates and does not account for systematic uncertainties. Along with our measured value of the semi-amplitude, we use this equation, which uses the Roche lobe approximation of Eggleton83:

[TABLE]

where $q=M_{2}/M_{NS}$ is the mass ratio. This equation is valid assuming that the secondary fills its Roche lobe and is synchronized. We find that $q=0.290\pm 0.031$. This measurement can be directly tested once a timing solution for the pulsar is available.

2.1.2 The Minimum Neutron Star Mass

The binary mass function $f(M)=PK_{2}^{3}/2\pi G=M_{NS}\,\textrm{sin}^{3}(i)/(1+q)^{2}$. We have determined all of these quantities from the spectroscopy alone, except for the inclination. Propagating the uncertainties appropriately, we can determine the minimum neutron star mass $M_{NS}$   sin${}^{3}(i)$ = $1.75\pm 0.09\,M_{\odot}$. This quantity is independent of the light curve modeling we carry out in §3 and is a robust lower limit. Hence we see that, consistent with many other redbacks (Strader18), the mass of PSR J1306–40 is well in excess of the canonical $1.4\,M_{\odot}$.

2.2. Optical Photometry

We obtained optical $BVI$ photometry of the companion to PSR J1306–40 using ANDICAM on the SMARTS 1.3-m telescope at CTIO over 101 nights between 2017 Jul 17 and 2018 Apr 29 (UT). On each night, we took single 340 and 250 sec exposures in $V$ and $I$ bands, respectively, and two 250 sec exposures in $B$ that were merged during the reduction process. Data were reduced following the procedures in Walter12.

We performed differential aperture photometry to obtain instrumental magnitudes of the target source using fifteen nearby comparison stars as a reference. Absolute calibration was done with respect to the Landolt92 standard fields TPheD (2017 Jul 17 – Sep 03) and RU149 (2018 Jan 24 – Apr 29). After excluding measurements with large errors, our final dataset includes 92, 93, and 95 measurements in $B$, $V$, and $I$ bands, respectively. The mean observed magnitudes (not corrected for extinction) are $B=19.21$, $V=18.35$, and $I=17.20$, with median errors of $\sim$ 0.03 mag in $V$ and $I$ and $\sim$ 0.06 in $B$. The SMARTS photometry is listed in Table 2.

To determine the orbital phase of these observations, we folded the data on the orbital period and ephemeris derived from our spectroscopic observations, where $\phi$ = 0 corresponds to the ascending node of the pulsar (in this convention, the secondary is between the pulsar and Earth at $\phi$=0.25). We show the folded light curves in Figure 2.

The most obvious features of the light curves are the broad maxima centered near $\phi\sim 0.75$ and narrower minima at $\phi\sim 0.25$. A maximum at this phase suggests the tidally locked “day” side is being heated substantially, while the minimum corresponds to the “night” side of the secondary as we view it at inferior conjunction. As pointed out by Linares18, this heating plays a dominant role in shaping the optical light curve over the tidal deformation of the secondary (i.e., ellipsoidal modulations). If heating were not dominating the light curve, ellipsoidal modulations would result in two roughly equal maxima at $\phi$ = 0 and $\phi$ = 0.5, and two unequal minima at $\phi$ = 0.25 and $\phi$ = 0.75. The minimum at $\phi$ = 0.75 would be dimmer due to the effects of gravity and limb darkening when viewing along the axis connecting the primary and secondary. Overall, the shape and amplitude of the light curves appear broadly consistent with the unfiltered Catalina Sky Survey (Drake09) data presented by Linares18, suggesting no significant state change has occurred in this system since late-2005.

Another notable feature of the light curves is that the maxima are not symmetric about the expected $\phi$ = 0.75. Instead, the light curves slope downward between 0.5 $<\phi<$ 1.0, suggesting that the source of heating is asymmetric with respect to the rotational axis of the secondary. Similar asymmetric heating has been observed in a number of other redbacks and black widows, and may be common in these systems due to the effects of an asymmetric intrabinary shock, heating mediated by the magnetic field of the secondary, or other magnetic activity such as star spots (e.g., Stappers01; Breton13; Schroeder14; Romani15; Romani15b; Deneva16; Romani16; vanStaden16; Sanchez17; Cho18). We show below that asymmetric heating is a promising (though not unique) mechanism to explain the observed light curves of PSR J1306–40.

3. Light Curve Fitting

We modeled the $BVI$ light curves of PSR J1306–40 using the Eclipsing Light Curve (ELC; Orosz00) code. Given the recent pulsar detection, we assume there is no accretion disk; the light curves are dominated by a tidally distorted secondary that is being heated on its tidally locked day side. We also assume a circular orbit and fix the orbital period $P$, semi-amplitude $K_{2}$, and mass ratio $q$ to the values derived from our spectroscopy (§2.1). These values immediately set the scale for the system, giving an orbital separation of $\sim$ 6 R*⊙*.

In our most basic model, we fit for the orbital inclination $i$, the Roche lobe filling factor $f_{2}$, the intensity-weighted mean surface temperature of the secondary $T_{\textrm{eff}}$, the central isotropic irradiating luminosity from the pulsar, and a phase shift $\Delta\phi$. We characterize the irradiating luminosity indirectly through the most directly observed quantity: the maximum day side temperature of the heated secondary $T_{\textrm{day}}$. In Table LABEL:table:lcmodels, we summarize this model (“No Spot”) with the medians of the posterior distributions and corresponding 1$\sigma$ uncertainties for each parameter. We also plot this model along with the data in Figure 2 (dashed line). The best-fit inclination from these models is not all that well constrained ($i=70.4^{+16.7}_{-7.0}$), but implies a massive neutron star ($M_{1}=2.08^{+0.35}_{-0.34}$ $M_{\sun}$) that would be among the heaviest known. For the best-fit parameters, the formal $\chi^{2}$/d.o.f. = 370/275, suggesting the fit can be improved. In particular, this model overestimates the $I$-band flux at $\phi\sim$ 0.25 and underestimates the $B$-band flux at this same phase, indicating the temperature profile of the night side is not well-matched. This model also does a poor job of reproducing the asymmetric, downward sloping curves between 0.5 $<\phi<$ 1.0, as the only source of heating is symmetric around conjunction.