THE ORBIT AND COMPANION OF PROBABLE γ-RAY PULSAR J2339−0533

The Large Area Telescope (LAT) on the Fermi satellite has revolutionized our understanding of the γ-ray sky, with particular success in detecting spin-powered pulsars and blazars. After only three months of observation, a preliminary 0FGL "bright source list" of 205 objects detected at >10σ significance was presented in Abdo et al. (2009a). Remarkably, over 95% of these sources now have been associated with lower energy counterparts (Ackerman et al. 2011). Moreover, comparison with the γ-ray properties of the identifications make it possible to classify many of the remaining sources; likely blazars show significant variability, while likely pulsars are steady, but show strongly curved spectra, with cutoffs above a few GeV.

At present, there are two 0FGL sources at |b| > 1° with pulsar-like properties and no identification. One, 0FGL J2339.8−0530 was a ∼12σ detection with steady, hard spectrum emission. It has been the subject of both radio pulsar counterpart searches and "blind" searches for γ-ray pulsations (e.g., Abdo et al. 2009b). To date no pulsed emission has been seen and the source remains unidentified in the latest catalog (Abdo et al. 2011). There it is listed as 2FGL J2339.6−0532, localized to l = 81.357 ± 0.03, b = −62.467 ± 0.02, with a variability index of 15.7 (indicating steady emission) and a flux of 3.0  ±  0.2 × 10⁻¹¹ erg cm⁻² s⁻¹, with a hard Γ = 1.96 spectrum showing 6σ evidence of a spectral cutoff. It thus remains one of the best unidentified pulsar candidates. Indeed, Kong et al. (2011a, 2011b have drawn attention to this source, finding that there was an optically variable star coincident with a CXO source in the LAT uncertainty region, arguing that this was likely a "radio-quiet" millisecond pulsar (MSP) and suggesting that it may be a low-mass X-ray binary (LMXB) in quiescence, similar to the LAT-associated LMXB/MSP transient FIRST J102347.6+003841 (Archibald et al. 2010; Tam et al. 2010). We report here on optical imaging and spectroscopy of this source which support the MSP hypothesis, but instead show that this is a "black widow" type pulsar, evaporating a low-mass companion, similar to the original of such systems, PSR B1957+20, but 2–3× closer at d ∼ 1 kpc. We suggest that strong outflow in this evaporating system inhibits detection of radio pulsations. If the pulsed emission can be detected in the LAT photons, the resulting orbital information will make this a double-line spectroscopic binary and should allow an unusually precise determination of the neutron star mass, comparable to the important high M_PSR = 2.40 ± 0.12 M_☉ determination recently made for PSR B1957+20 (van Kerkwijk et al. 2011).

Examination of plots of white light CCD photometry made on 2010 October 31 and November 1 with the 1 m Lulin Telescope (Taiwan) and on 2010 November 11 with the 0.81 m Tenagra Telescope (Arizona) allowed us to infer an orbital period of ∼0.19 days. The source appears in the Sloan Digital Sky Survey (SDSS) DR8 data release with colors u = 20.85, g = 19.00, r = 18.61, i = 18.25, and z = 18.23, suggesting a G-type spectral class. Optical extinction at this high latitude is very small (A_V ≈ 0.1 from the Schlegel et al. 1998 dust maps). Based on the large (>2.5 mag) variation it seemed likely that this is a nearby, short-period black-widow-type pulsar, with a strongly heated companion and thus a suitable target for detailed optical spectroscopy.

2.1. HET, SSO, and WIYN Photometry

The 9.2  m Hobby–Eberly Telescope (HET) has a spherical primary with a tracking corrector and can follow a source for ∼1 hr per night during a transit. This is a small fraction of the estimated 4.6 hr orbital period. However the HET is dynamically queue scheduled (Shetrone et al. 2007), and with an ephemeris one can obtain full orbital coverage. During HET Low Resolution Spectrograph (LRS) observations one obtains short direct images for target acquisition. We used these 3–15 s "pre" images, augmented by "post" images in several cases, to monitor the flux of J2339−0533. These images, through a Schott GG385 long-pass filter, approximate the "white light" of the 2010 photometry. We measured simple differential aperture magnitudes, calibrated to the SDSS r' magnitudes of nearby stars. These photometric data covering 2011 August 5–September 6 confirmed the dramatic optical modulation of J2339−0533. Conditions were variable, but detections were always of high signal-to-noise ratio (S/N), even at the r' ∼ 21 minimum.

Since the target is very bright, we obtained additional photometry with the 0.61 m Cassegrain telescope at the Stanford Student Observatory (SSO) on 2011 August 28 (MJD 55801.287–.399) and 2011 October 20 (MJD 55855.140–.381). Using 300 s unfiltered CCD exposures with an Apogee AP8 camera, we made differential flux measurements, again normalized to SDSS r' magnitudes. These data helped in absolute phasing and improving the binary period estimate.

Finally, we obtained SDSS g'r'i' frames at the 3.6 m WIYN telescope using the MiniMo camera on 2011 September 27 (55832.290–.424). These data, covering inferior conjunction (IC), were used to constrain the color variation through minimum (IC).

After converting exposure midpoint times to the solar system barycenter, we minimized residuals to obtain an accurate orbital period (Table 1, errors from bootstrap). The epoch (jointly fit with the radial velocity data, see below) defines superior conjunction (SC; approximately maximum light). The photometric data folded at this period are shown in Figure 1.

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Table 1. J2339−5033 System Parameters

Parameter	ELC Fit Value
R.A. (J2000)	23:39:38.75
Decl. (J2000)	−05:33:05.3
Pb (days)	0.19309790 ± 1 × 10−7
T0 (MJD-TDB)	55500.4833 ± 0.0002
M1 (M☉)	0.075 ± 0.007
M2 (M☉)	1.40 ± 0.04
i (deg)	57.4 ± 0.5
f1	0.90 ± 0.01
T1 (K)	2800 ± 50
log[LX] (erg s−1)	33.5 ± 0.1

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2.2. Archival X-Ray Light Curve

We used this ephemeris to extract an X-ray light curve from the archival 21 ks CXO ACIS-I exposure of the 0FGL J2339.8−0530 field taken on 2009 December 13 (MJD 55117.54, obs. 11791, PI: T. Cheung), covering 1.25 orbits. Figure 2 shows the exposure-corrected light curve. The source is clearly modulated, with a relatively constant emission from phase −0.25 to 0.25, and a deep minimum at IC (phase 0.5). The source is, however, detected at minimum.

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A simple absorbed power-law fit to the phase-averaged data gives a hard index Γ = 1.09^+0.40_{− 0.13} and no significant absorption N_H < 1.6 × 10²¹ cm⁻² with a (0.5–8 keV) flux 2.3^+1.2_{− 0.3} × 10⁻¹³ erg cm⁻² s⁻¹ (all 90% errors). Lacking counts for a phase-resolved spectral analysis, we can extract a simple hardness ratio. Intriguingly, this is lowest at ϕ = 0.5 (IC), suggesting that the hard spectrum source dominates near SC, but is deeply absorbed or eclipsed revealing a softer component at IC. Deeper X-ray observations are clearly needed to probe the orbital spectral variations.

2.3. Spectroscopy

For the spectroscopic exposures we used the HET LRS, employing grism 2, with a GG385 filter and a 1.5 arcsec slit. This covered λλ4283–7265, at a resolution of 1.99 Å pixel⁻¹, for an effective R ∼ 1000–1200. All observations were taken with the slit at the parallactic angle and we limited exposures to 600 s to minimize velocity smearing to <35 km s⁻¹. The HET pupil varies as the corrector tracks across the primary, so significant changes in the point spread function and hence in the line profile of stellar sources occurs at the extrema of the tracks. Since we are seeking maximal radial velocity accuracy, velocities from observations very early or late in a transit may be compromised. For most HET visits, we were able to obtain three–four 600 s exposures; however a few exposures were taken far from the track center and were omitted from the orbital velocity fits. J2339−0533 lies relatively near the HET's decl. = −11° southern limit. It is thus possible to extend visit times by resetting the telescope azimuth during the exposure sequence. On 2011 September 1, we obtained such a "long track" re-setting the azimuth twice and allowing 9 × 600 s exposure to be obtained (spanning ∼2 hr or 0.42 of orbital phase) with only modest tracker excursion. Thus, under favorable circumstances, the HET can obtain extended integrations during a single visit at the cost of queue efficiency. In total 48× 600 s exposure were obtained during one month of queue observations under variable conditions, equivalent to a full night of classical observation.

Data reduction was performed with the IRAF package (Tody 1986; Valdes 1986) using standard techniques. Biases, dome flats, and arc lamp exposures were obtained nightly. All data were bias subtracted, and flat fields were applied after removal of the lamp response. Arc exposures were used for wavelength calibration. Checks of the sky lines showed that these solutions were stable to ∼0.3 Å  during a single visit and ∼0.7 Å  night to night; sky lines were monitored to subtract out these residual shifts, leading to an estimated stability of 0.1 Å  for the wavelength scale. Spectra were optimally extracted (Valdes 1992) and visually cleaned of residual cosmic rays. Spectrophotometric calibration was performed using standard stars from Oke (1990) and Bohlin (2007). Occasionally, appropriate standards were not measured during a given night; data from a neighboring queue night were then employed. The fluxing was not reliable for ∼20 Å  at the ends of the spectra and these were generally excluded from the final analysis. Spectra were corrected for atmospheric extinction using the KPNO extinction tables. Telluric templates were generated from the standard star observations in each night, with separate templates for the oxygen and water line complexes. We corrected separately for the telluric absorptions of these two species. We found that most telluric features divided out well, with significant residuals only apparent in spectra with the highest S/N.

The final cleaned, calibrated spectra were averaged to study the companion spectrum at various orbital phase bins (Figure 3). Although the LRS does not cover much of the far blue used for traditional MK classification, there are clear continuum and line dominance trends through the orbit. Comparison with the Gray online atlas² and with sample spectra from the SDSS DR8 SEGUE Spectroscopic Parameter Pipeline³ (Lee et al. 2008) allows reasonably accurate temperature classification. The spectrum evolves from a ∼6900 K F3 type continuum at flux maximum to a ∼2900 K M5 class spectrum near flux minimum. In general, the bright phase spectra show stronger metal line absorptions than the corresponding continuum spectral class; Na i D at the stellar radial velocity is particularly strong at all phases away from IC.

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Velocity shifts of individual exposures were computed by cross-correlation against dwarf star spectral templates (from the SDSS spectral library) using the IRAF rvsao package. Templates from F0 through M5 were used. We found that K0 templates provided the largest cross-correlation amplitude for most phases, despite continuum colors matching hotter spectral classes near maximum—we attribute this to the fact that the effective spectrum is composite.

Near phase 0.5 the spectrum is increasingly dominated by molecular bands and the best cross-correlations (and effective spectral class) move through M0 to M5. At these phases, the spectra are very red and improved correlation was often found when the data were trimmed by 500–1000 Å  in the blue. Even at flux minimum we obtained cross-correlation coefficients R > 3, except for a few poorly exposed spectra at large tracker offset (small effective telescope aperture). These were dropped from the radial velocity study. Typical correlations had R ∼ 15–25 and radial velocity errors 8–12 km s⁻¹. The radial velocity points and errors are shown in the bottom panel of Figure 1, with symbol type indicating the highest correlation spectral class.

Normally for pulsar binaries we have a precision mass function and orbital ephemeris from the radio arrival times, which greatly restrict the range of viable model solutions. However, even without a pulse detection, we can still use our HET/SSO/WIYN photometry and spectroscopy to place preliminary constraints on the orbital parameters of the J2339−0533 system, using the ELC code of Orosz & Hauschildt (2000). This code includes the effect of companion illumination "X-ray heating" and estimates light curves based on the low temperature "NextGen" atmosphere tables. A table adapted for SDSS filters and white light photometry was kindly generated by J. Orosz. As found by Reynolds et al. (2007) for PSR B1957+20, the low T_eff atmospheres were essential to allowing the model to produce reasonable light curves; the blackbody approximation produced models too bright at orbital minimum. For the fits we adjusted the companion unheated (backside) effective temperature T₁ and Roche lobe fill factor f₁, the pulsar heating flux L_x, the orbital semimajor axis a, mass ratio q, inclination i, and phase of superior conjunction.

The best-fit parameters (Table 1, light curve and radial velocity models in Figure 1) indicate a cool companion, intermediate inclination, and moderate X-ray heating. This solution suggests a mass ratio q = 18.5 ± 1 and a relatively massive companion M₁ = 0.075 M_☉. The errors quoted are statistical only. Figure 1 also shows the companion center-of-mass velocity; note the substantial decrease in amplitude and small shape distortions of the center-of-light curve. We caution that, with reduced χ² ≈ 3, systematic errors are substantial and secondary minima exist.

Overall, the good agreement with the "black widow" picture is encouraging. For all fits the models remain slightly too hot (g' too bright and i' too faint) at pulse minimum, suggesting amendments to the passbands or the heating and albedo model are needed. Also, the best-fit epoch from the radial velocities alone shifts δϕ ∼ 0.005(δT₀ = 0.001 days) from that of the full fit, implying that improvements in the spectral weighting could be helpful. Additional color photometry and especially a pulsar mass function and phase measurement should tighten up the fits considerably.

Our data also give some constraint on the distance and spin-down luminosity of the putative pulsar. At phase 0.25 the companion is half-illuminated, with T_eff ≈ 4800 ± 200 K. Adopting the companion fit radius R₂ = 0.24 R_☉ and scaling from a main-sequence star gives an expected M_r = 8.7 ± 0.3. The observed m_r = 18.8 ± 0.2 then indicates a distance of 1.1 ± 0.3 kpc. The CXO flux gives a pulsar X-ray luminosity of ≈3 × 10³¹ erg s⁻¹ d²_kpc. This is substantially less than the 3 × 10³³ erg s⁻¹ heating effect observed from the companion. Note, however, that Becker (2009) has found that pulsars have $L_X \approx 10^{-3}{\dot{E}}$ so that we would infer a spin-down luminosity of ∼3 × 10³⁴d² erg s⁻¹. Thus, again, like PSR B1957+20, we find that a substantial fraction of ∼0.1–0.3 of the expected spin-down luminosity goes into heating the companion. We can obtain an additional estimate of the pulsar spin-down luminosity from the observed F_γ = 3 × 10⁻¹¹ erg s⁻¹, since a heuristic γ-ray luminosity $L_{\gamma,{\rm heu}} \approx ({\dot{E}}\, \times \, 10^{33}\ {\rm erg \ s^{-1}})^{1/2}$ has been found for other γ-ray pulsars (Abdo et al. 2010), where $L_\gamma = 4\pi f_\Omega F_\gamma d^2$ and $f_\Omega$ should be in the range 0.7–1.3 Watters et al. (2009). This gives an estimate ${\dot{E}} \approx 1.3 \times 10^{34} f_\Omega ^2 d^4 \,{\rm erg \,s^{-1}}$. All of these estimates support the identification with an ${\dot{E}} \approx 2 \times 10^{34} \,{\rm erg\, s^{-1}}$ pulsar, somewhat less luminous and closer than PSR B1957+20, but consistent with the other BW-type pulsars recently discovered in the direction of Fermi sources (Roberts 2011).

We conclude that the γ-ray source is an energetic pulsar evaporating a low-mass companion. Our preliminary photometry and model fits suggest a somewhat larger companion mass than for the original black widow pulsar PSR B1957+20. Our present estimate of i ∼ 57° implies that we should not see a γ-ray eclipse. However, the substantial drop of the X-ray flux at phase 0.3–0.6 suggests a strong wind absorbing much of the X-ray emission.

To date no γ-ray MSP has been discovered in a blind search of the LAT photons, since the ∼ms periods require many trials in pulsar spin frequency and position space. Since most MSP are in binaries the additional trials needed to cover binary acceleration makes the searches prohibitively expensive. One of our prime motivations in this project has been to reduce the binary phase space of trials needed to search J2339−0533 and enable such a discovery. Our data tightly constrain the period and phase of the pulsar reflex motion and suggest an amplitude a₂sini ≈ 0.16 lt-s. These constraints are insufficient for a direct fold, but greatly restrict the number of binary trials needed.

If a γ-ray (or radio) pulse detection is made, this system provides an excellent opportunity for study of the pulsar mass and binary evolution. The resulting precise mass ratio q will restrict the fit space, improving mass estimates for PSR J2339−0533 and its companion. Further optical and X-ray spectroscopy of this bright system can measure the surface heating in more detail and probe the density of the evaporative wind. If highly eclipsed radio emission is discovered, this suggests radio beams closely coincident with the γ-ray emission. Conversely, if no pulsed radio emission is found while viewing at relatively clear orbital phases and folding at a known pulsar period, this could represent the first truly "radio-quiet" MSP. As it is, we have built such a strong circumstantial case that it is fair to refer to J2339−0533 as a probable MSP; all we are missing is the spin period itself.

We wish to thank Albert Kong for drawing our attention to recent progress on identifying the counterpart and for sharing plots of the Lulin optical photometry. Jerome Orosz and Jeff Coughlin kindly supplied copies of the ELC code. We also particularly wish to thank the Hobby–Eberly Telescope RA team of Matthew Shetrone, John Caldwell, Steve Odewan, and Sergiy Rostopchin, for their excellent efforts in obtaining good orbital phase coverage of this short-period binary.

This work was supported in part by NASA Grants NNX10AD11G and NNX11AO44G.

The Hobby–Eberly Telescope (HET) is a joint project of the University of Texas at Austin, the Pennsylvania State University, Stanford University, Ludwig-Maximilians-Universitaet Muenchen, and Georg-August-Universitaet Goettingen. The HET is named in honor of its principal benefactors, William P. Hobby and Robert E. Eberly. The Marcario Low Resolution Spectrograph is named for Mike Marcario of High Lonesome Optics, who fabricated several optics for the instrument but died before its completion. The LRS is a joint project of the Hobby–Eberly Telescope partnership and the Instituto de Astronoma de la Universidad Nacional Autonoma de Mexico.