Multiwavelength Observations of a New Redback Millisecond Pulsar 4FGL J1910.7−5320

We downloaded and reanalyzed the optical data of 4FGL J1910.7−5320 from the CRTS (Drake et al. 2009) to confirm, and perhaps improve, the period from the CRTS catalog. The phased light curves were also investigated to see if they are consistent with that of a pulsar binary. In addition, the spectral energy distribution (SED) in the optical band obtained from the VizieR Photometry viewer ⁸ was used to estimate the color temperature of the source as well as the distance to the system.

The CRTS observations were taken from 2005 August 1 to 2013 June 21, and the variable source is located at R.A.(J2000) = 19^h10^m4912, decl.(J2000) = $-53^\circ 20^{\prime} 57\buildrel{\prime\prime}\over{.} 1$. We fit the CRTS data with a sinusoidal function and found that the period is 0.3484776(10) days (roughly 8.36 hr) with a mean magnitude of 19.08 ± 0.01 mag and an amplitude of 0.54 ± 0.02 mag. We note that the period in the CRTS catalog is 0.697 days (twice our best-fit period; Drake et al. 2017), and at this period, the folded light curve shows a double-peaks feature. Given that the 0.697 days period is inconsistent with the SOAR observations (see Section 3.2), we conclude that the 8.36 hr period is the real one. More detailed investigations will be discussed in the next subsection.

For the SED, we included data from Gaia (Gaia Collaboration et al. 2016; Brown et al. 2018; Gaia Collaboration 2020), the Galaxy Evolution Explorer (Bianchi et al. 2011), POSS (Lasker et al. 2008), VISTA (McMahon et al. 2013), and the Wide-field Infrared Survey Explorer (Marocco et al. 2021), and corrected for the absorption using the extinction function from Cardelli et al. (1989) with the total absorption in magnitudes of A_v = 0.1857 mag and the ratio of total to selective absorption of R_v = 3.1 (Schlegel et al. 1998). Then we used a blackbody radiation model to fit the SED data (Figure 1). The best-fit color temperature is T = 5154 ± 164 K, and the inferred distance is $D={5.8}_{-0.4}^{+0.5}$ (R/R_☉) kpc where R is the companion radius.

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Assuming that the companion nearly fills up the Roche lobe, we used the approximate formula from Eggleton (1983), which is

$\begin{eqnarray}&&R=a\times \frac{0.49{q}^{2/3}}{0.6{q}^{2/3}+\mathrm{ln}(1+{q}^{1/3})},\end{eqnarray} \tag{ 1 }$

where q = M_C /M_MSP (M_C : mass of companion; M_MSP: mass of MSP) and a is the distance between the binary members, to calculate the Roche lobe radius. By assuming the masses of the MSP and the companion are 1.4 and 0.4 M_☉, respectively, and using Kepler's Third Law to calculate a, we find R ≲ 0.7 R_☉, and hence, D ≲ 4.1 kpc. If we assumed the companion size is similar to that of a black widow (i.e., M_C = 0.03 M_☉), then R ≲ 0.3 R_☉ and D ≲ 1.8 kpc.

Nevertheless, the SED data employed were not obtained simultaneously while the optical source is strongly variable. To check whether the effect is huge, we tried to find the blackbody model parameters using only the VISTA J- and K-band data (McMahon et al. 2013), which were taken nearly simultaneously. Similar to our original results, the parameters are T = 4550 K, D = 5.2 (R/R_☉) kpc. The distance is D ≲ 3.6 kpc by assuming the system is redback-like, i.e., R ≲ 0.7 R_☉.

We also searched the Gaia Catalog DR3 (Gaia Collaboration 2020; Moss et al. 2022) for further distance information, but the parallax is not well constrained (Bailer-Jones et al. 2021).

We obtained optical spectroscopy of the candidate counterpart to 4FGL J1910.7−5320 using the Goodman Spectrograph (Clemens et al. 2004) on the SOAR telescope over six nights from 2022 April 10 to 2022 June 10, typically taking multiple spectra per night. For all spectra we used a 12 slit and a 400 l mm⁻¹ grating covering a wavelength range of ∼3950–7850 Å, giving a resolution of about 7.3 Å for the FWHM. The spectra were reduced and optimally extracted using standard routines in IRAF (Tody 1986). We obtained 20 total usable spectra in this setup (Table 1).

The spectra generally appear consistent with a late G-/early K-type star (Figure 2). The most prominent absorption lines are Mgb and Na D, along with several Fe lines. Hα and Hβ are present in absorption in some of the SOAR spectra, while in others Hα is weak or absent. There are no clear emission lines in any spectra.

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We derived barycentric radial velocities (RVs) through cross correlation with a high signal-to-noise template spectrum in the region of Mgb. We fit a circular Keplerian model to the velocities. As the fitting spectroscopic period is consistent with the photometric period, we fix it to the latter as the time span of the photometry is much longer than that of the spectroscopy.

The model parameters of the fitting model are K_2,obs = 219 ± 14 km s⁻¹, γ = − 17 ± 12 km s⁻¹, and T₀ = BJD 2459700.8091(41), where K_2,obs is semiamplitude, γ is systemic velocity, and T₀ is the ascending node of the pulsar in Barycentric Julian Date (BJD). This fit has a χ²/ degree of freedom (dof) of 38/17 and an rms of 30.9 km s⁻¹, suggesting an imperfect fit. Two of the most negative velocity measurements seem to be unexpected outliers and could have underestimated uncertainties; if these points were excluded, the quality of the fit would be substantially improved. But we have no specific justification for such a change, so we retain the full data set, and acknowledge this is a preliminary characterization that could be improved with more data in the future.

We refit both the CRTS and SOAR data assuming a pulsar heating scenario (i.e., the CRTS light curve leads the SOAR RV curve by $\tfrac{\pi }{2}$). The best-fit parameters are an orbital period of 0.34847592(21) days, a mean CRTS magnitude of 19.015 ± 0.018 mag, a CRTS amplitude of 0.506 ± 0.029 mag, K_2,obs = 218 ± 8 km s⁻¹, γ = − 17 ± 6 km s⁻¹, and the phase zero at BJD 2453584.0121(31). We use the best-fit parameters of P = 0.34847592 days and phase zero at BJD 2453584.0121 to fold both the CRTS light and the RV curves, which are plotted in Figures 3 and 4, respectively.

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It is clear that we have incomplete phase coverage of the source in Figure 3; missing data around ϕ = 0.25 when the secondary is the faintest. This is not solely chance, but reflects the observational biases induced by the observational window available. Nonetheless, the main orbital parameters are relatively well constrained.

Because of irradiation, K_2,obs is not necessarily the same as the center of mass K₂, though no extreme changes are observed in the optical spectra at different phases. The observed mass function implied by the optical spectroscopy is f = 0.37 ± 0.02 M_⊙, which is a typical value for a spider binary. Even accounting for the uncertainty in the true K₂ value, this mass function (which approximately represents the minimum mass of the primary) implies that an edge-on binary inclination for a neutron star is ruled out, and instead an intermediate inclination is more likely.

The γ-ray source 4FGL J1910.7−5320 was observed with Chandra (Weisskopf et al. 2002) for 12.6 ks on 2019 November 20, and we used the Chandra data to check whether the CRTS source has an X-ray counterpart. If so, the X-ray data can constrain the X-ray spectral shape and X-ray variability for the putative X-ray counterpart to 4FGL J1910.7−5320.

We used CIAO (version 4.13; Fruscione et al. 2006) to extract the source and background spectra from the Chandra data. We made an auxiliary response file (for both source and background), which is an effective area calibration file where we also applied an energy-dependent point-source aperture correction. We generated a response matrix file to map between the properties of the incoming photons and the electronic signals obtained from the detector. After performing a spectral binning with at least 20 counts per bin, we used XSPEC ⁹ (version 12.12.0; Arnaud 1996) from HEASARC to measure the hydrogen column density (which will be a fixed parameter in our spectral model) and the photon index of the X-ray source assuming an absorbed power-law model. We also used the dmextract task to generate the light curve with a 2'' radius circular region and 2000 s bin time. Barycentric corrections were performed using axbary. In Figure 3, we folded the X-ray light curve using the optical period of P = 0.34847592 days.

A significant X-ray counterpart was detected at the optical position of the variable CRTS source. Its location is at R.A.(J2000) = 19^h10^m4910 and decl.(J2000) = $-53^\circ 20^{\prime} 57\buildrel{\prime\prime}\over{.} 2$ with a 90% uncertainty of 08. This is only 017 from the CRTS variable described in Section 3.1, strongly suggesting that they are the same source. There are 106 source counts in a 2'' radius aperture and 164 counts in a nearby source-free circular background region with a radius of 10''. We fit the X-ray spectrum with an absorbed power-law model with the Galactic hydrogen column density of N_H = 5.22 × 10²⁰ cm⁻² (fixed; Blackburn et al. 1999; HI4PI Collaboration et al. 2016). ¹⁰ The best-fit parameters to the X-ray spectrum (Figure 5) are a photon index of Γ = 1.0 ± 0.4 and an energy flux of F_0.3–7keV = (1.7 ± 0.2) × 10⁻¹³ erg cm⁻² s⁻¹ (χ²/d. o. f. = 3.7/3). The 0.3–7 keV X-ray luminosity is L_x ≲ (3.4 ± 0.4) × 10³² erg s⁻¹ by assuming D ≲ 4.1 kpc.

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We also fit the spectrum with a blackbody model, and the result is F_0.3–7keV = (1.26 ± 0.15) × 10⁻¹³ erg cm⁻² s⁻¹ and a temperature of kT = 0.9 ± 0.1 keV (χ²/dof = 13.2/3). The absorbed power-law model is statistically preferred by comparing the χ² values.

Here, we used Fermitools (version v11r5p3; Fermi Science Support Development Team 2019) from the Fermi Science Support Center (FSSC) ¹¹ with the 4FGL-DR3 (Abdollahi et al. 2022) and Pass8 data (P8R3) to refine the γ-ray position and the γ-ray spectral properties of 4FGL J1910.7−5320.

We downloaded the LAT event files and spacecraft data from FSSC. The P8R3 data downloaded starts from 2008 August 4 to 2021 November 9 with energies in 0.1–300 GeV. We chose the SOURCE class events (FRONT and BACK) with a zenith angle smaller than 90°. The center of the 14° × 14° region of interest is at (α, δ) = (287705, − 53349): the 4FGL-DR3 position of 4FGL J1910.7−5320. We used the 4FGL-DR3 cataloged sources located within 10° from the target to establish the spatial and spectral model of the γ-ray emission. The model includes the latest Galactic interstellar (gll_iem_v07.fits) and isotropic (iso_P8R3_SOURCE_V3_v1.txt) diffuse components. We employed a LogParabola model for 4FGL J1910.7−5320 as suggested in the 4FGL-DR3, which is

$\begin{eqnarray}&&\displaystyle \frac{{dN}}{{dE}}={N}_{0}{\left(\displaystyle \frac{E}{{E}_{b}}\right)}^{-(\alpha +\beta \mathrm{log}(\tfrac{E}{{E}_{b}}))},\end{eqnarray} \tag{ 2 }$

where α characterizes the photon index and β defines the degree of curvature for the LogParabola model. There is a total of 33 free parameters from the source in the emission model by allowing the background diffuse components and the sources inside a 5° radius circle from 4FGL J1910.7−5320 to vary. We performed a binned likelihood analysis with 37 logarithmically uniform energy bins, which gives a test statistic (TS) value, the significance of a certain source, of 146 (∼11.7σ detection significance with 3 extra parameters), a 0.1–100 GeV energy flux of F_{0.1–100 GeV} = (2.6 ± 0.4) × 10⁻¹² erg cm⁻² s⁻¹, α = 2.2 ± 0.2, and β = 0.3 ± 0.2 (Figure 6). The 0.1–100 GeV γ-ray luminosity is L_γ ≲ (5.3 ± 0.8) × 10³³ erg s⁻¹ by assuming D ≲ 4.1 kpc. Using gtfindsrc, we refined the 68% error circle of 4FGL J1910.7−5320 to a circular region with 21 radius centered at (α, δ) = (287°.691, −53330), which includes the CRTS optical source (Figure 7).

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As we mentioned in Section 3.3 and Figure 3, the X-ray and optical sources probably are the counterparts to 4FGL J1910.7−5320. This association can be further confirmed, if the X-ray and optical phased light curves have any relation.

In order to explore the X-ray modulation, we folded the Chandra X-ray light curve on the orbital period P = 0.34847592 days (Figure 3). Although the observation does not cover a complete orbit, the folded light curve shows a possible dip at phase 0.75 (Figure 3). If the X-ray orbital modulation is real, it could be due to the Doppler boosting effect in the intrabinary shock (Li et al. 2014; Takata et al. 2014; Kong et al. 2017). At phase 0.75 (Figure 3), the stellar companion is behind the presumed pulsar as seen from Earth. If the momentum flux of the pulsar wind is stronger than that of the stellar wind from the companion, the intrabinary shock can wrap the companion. This means the shocked wind does not point toward Earth, and the X-ray emission therefore decreases, consistent with the Chandra light curve of 4FGL J1910.7−5320. Furthermore, the intrabinary shock could produce synchrotron X-ray emission that can be described by a power-law spectral model. This naturally explains the observed Chandra X-ray emission, which appears nonthermal with Γ = 1.0 ± 0.4. Unfortunately, the current X-ray and optical data sets do not allow a detailed investigation. Deeper and longer observations in X-rays and the optical band (with color information) are required in the future.

From Figure 3, the optical phased light curve of 4FGL J1910.7−5320 shows an obvious one-peak signature. Since the pulsar heating effect is usually more prominent for black widows than for redbacks, this light curve feature is more consistent with that of a black widow. The optical peak and X-ray peak are shifted by half an orbit, which is similar to the original black widow PSR B1957 + 20 (Fruchter et al. 1988). However, there are also several black widow examples that show zero phase shift between the optical and X-ray peaks, such as PSR J1124−3653, PSR J1653−0158, and PSR J2256−1024 (Gentile et al. 2014; Long et al. 2022). Therefore, the evidence is not particularly strong to say that 4FGL J1910.7−5320 is a black widow candidate.

In Section 3.1, we assumed the size of the companion in the case of the redback (i.e., R ≲ 0.7 R_☉) and black widow (i.e., R ≲ 0.3 R_☉) based on a Roche lobe description, and estimated the distance to be D ≤ 4.1 kpc and 1.8 kpc, respectively. If the system is a black widow MSP, it will be relatively close to us. In fact, the system will be much closer if it is a black widow, because the companion size of a black widow is generally smaller than the Roche lobe radius (Draghis et al. 2019). We also performed another independent distance estimation by comparing the magnitude and the distance of 4FGL J1910.7−5320 to the original black widow, PSR B1957 + 20, of which the distance is D = 1.5–2.5 kpc (Taylor & Cordes 1993; Cordes & Lazio 2002; van Kerkwijk et al. 2011) and the minimum optical magnitude in the R band is 24.6 mag (Reynolds et al. 2007). In 4FGL J1910.7−5320, the minimum best-fit magnitude in the CRTS catalog is 19.62 mag (∼20.5 for the faintest data), which is about ∼5 mag brighter than the minimum magnitude of PSR B1957 + 20. This implies that if 4FGL J1910.7−5320 is a black widow MSP similar to PSR B1957 + 20, the distance to 4FGL J1910.7−5320 is D ∼ 0.15–0.25 kpc, which is extremely close to us. At this short distance, Gaia should be able to measure the parallax, and hence, the distance of 4FGL J1910.7–5320 easily. However, the parallax is not well constrained in the Gaia Catalog DR3 (Gaia Collaboration 2020). Therefore, interpreting 4FGL J1910.7−5320 as a redback MSP system is favored.

We notice that the irradiation signature is relatively strong (the amplitude is over 1 mag) compared to other redbacks. To check this phenomenon systematically, we used the CRTS catalog (Drake et al. 2009) to find the modulation amplitude of other known redback systems. We find that there are only two redbacks, PSR J2215 + 5135 (Breton et al. 2013) and PSR J2339−0533 (Romani & Shaw 2011) that have a high irradiation signature (amplitude > 1 mag) among the 14 known redbacks (Hui & Li 2019; Strader et al. 2019). A dedicated statistical study of irradiation signatures of redbacks will be published elsewhere.

We found a variable optical source inside the 95% error ellipse of 4FGL J2029.5−4237 and speculated that it is another MSP binary candidate. In the 11.7 ks Chandra observation, we found no significant X-ray source spatially coincident with the optical variable, with a 3σ flux upper limit of 2.4 × 10⁻¹⁴ erg cm⁻² s⁻¹ (0.3–7 keV). The corresponding luminosity is L = 3.8 × 10³⁰ erg s⁻¹ by using the Gaia distance of 1.14 kpc (Gaia Collaboration 2020), which is considerably lower than in many other MSPs. The optical source is also outside the updated 95% LAT error circle (Figure 8). These results strongly suggest that the variable optical source is probably not the counterpart to 4FGL J2029.5−4237 and unlikely a redback MSP.

While we were in the late stages of preparing this paper, TRAPUM discovered the radio pulsations associated with 4FGL J1910.7−5320 (i.e., PSR J1910−5320; C. Clark 2022, private communication), ¹³  and confirms that 4FGL J1910.7−5320 is a redback MSP. They also found that 4FGL J2029.5−4237 is an isolated MSP, which is unrelated to the optical source reported in this paper.