1 INTRODUCTION
Millisecond pulsars (MSPs) form a special subclass of radio pulsars which is characterised by short (P < 30 ms) rotational periods, relatively small magnetic fields (B ~ 108 − 1010 G), and low spin-down rates (
$\dot{P}\sim 10^{-20}-10^{-19}$ s s−1). To date, about 350 MSPs have been discovered. This number is approximately 13% of the total number of known pulsarsFootnote 1. It is believed that short spin periods are caused by the accretion of matter from a donor star (Bisnovatyi-Kogan & Komberg Reference Bisnovatyi-Kogan and Komberg1974; Alpar et al. Reference Alpar, Cheng, Ruderman and Shaham1982). This ‘recycling’ hypothesis is consistent with the fact that most MSPs are found in binary systems. The hypothesis is strongly supported by discoveries of transient MSPs which show switching between the accretion and radio MSP stages, PSR J1023+0038, XSS J12270−4859, and PSR J1824−2452I (Archibald et al. Reference Archibald2009; Bassa et al. Reference Bassa2014; Roy et al. Reference Roy2015; Papitto et al. Reference Papitto2013).
Observed MSPs companions belong to various stellar classes: main sequence (MS) stars, white dwarfs (WDs), non-degenerate or partially degenerate stellar cores, and neutron stars (NSs) (e.g., Manchester Reference Manchester2017). This depends on initial parameters of the progenitor binary system, e.g., the mass of the donor star, the orbital separation, the environments where the system forms (e.g., the Galactic disc or a globular cluster), etc. The ‘fully’ recycled MSPs (P < 10 ms) most often have He-core WD companions (Tauris Reference Tauris, Schmidtobreick, Schreiber and Tappert2011).
Studies of binary MSPs allow one to probe different astrophysical phenomena including formation and evolution of binary systems and accretion processes. The unique rotational stability makes them precise celestial clocks. This can be used to test the accuracy of gravitational theories and to search for gravitational waves with a ‘pulsar timing array’ (Kramer Reference Kramer2016; Manchester Reference Manchester2017).
Masses of both components in a binary system can be obtained through a high-precision radio timing by measuring the Shapiro delay (Shapiro Reference Shapiro1964). However, this effect is most measurable if an orbit is highly inclined or a companion is massive. An alternative way to constrain masses and orbital parameters is optical observations (e.g., van Kerkwijk et al. Reference van Kerkwijk, Bassa, Jacoby, Jonker, Rasio and Stairs2005). In the case of a WD companion, its mass, spectral class, and temperature can be derived from comparison of photometric and/or spectroscopic data with predictions of WD cooling models. The derived WD mass together with the radio timing parameters then can be used to estimate the pulsar mass and in turn to constrain the equation of state of the superdense matter in NSs interiors (Lattimer & Prakash Reference Lattimer and Prakash2016). Optical observations also allow one to obtain the WD cooling age and, therefore, to constrain the binary system age independent of the pulsar characteristic age. This is important for studying the evolution of binary systems and pulsar spin evolution (e.g., Kiziltan & Thorsett Reference Kiziltan and Thorsett2010).
Binary MSP J0621+2514 (hereafter, J0621) was recently discovered in radio pulsation searches of Fermi unassociated sources with the Green Bank Telescope (Ray et al. Reference Ray2012; Sanpa-arsa Reference Sanpa-arsa2016). This led to detection of γ-ray pulsations in the Fermi data. The pulsar parameters obtained from timing analysis are presented in Table 1. Sanpa-arsa (Reference Sanpa-arsa2016) suggested that the system contains a WD companion. Here we report a likely identification of the pulsar companion using the results of optical surveys.
Table 1. Parameters of the J0621 system obtained from Sanpa-arsa (Reference Sanpa-arsa2016). The distances D YMW and D NE2001 are provided from the dispersion measure using the YMW16 (Yao, Manchester & Wang Reference Yao, Manchester and Wang2017) and NE2001 (Cordes & Lazio Reference Cordes and Lazio2002) models for the distribution of free electrons in the Galaxy, respectively.
2 The likely companion and its properties
We found a possible counterpart to J0621 using the Sloan Digital Sky Survey Data Release 14 (SDSS DR; Abolfathi et al. Reference Abolfathi2017) catalogue. The position of the point source SDSS J062110.86+251403.8 overlaps with J0621 at the 1σ significance. Its position and magnitudes in five filters are presented in Table 2 and the i′-band image of the pulsar field is shown in Figure 1. The source was also detected in three filters of the Panoramic Survey Telescope and Rapid Response System Survey (Pan-STARRS; Flewelling et al. Reference Flewelling2016). The probability to detect an unrelated source at the pulsar position is ~10−4 assuming the source magnitude r′ of 18–23.
Figure 1. SDSS i′-band image of the J0621 field. The white circle shows 5σ pulsar position uncertainty that accounts for the optical astrometric referencing and radio timing position uncertainties from Table 1.
Table 2. Magnitudes of the J0621 optical counterpart candidate SDSS J062110.86+251403.8 obtained from SDSS catalogue.
a Position uncertainties include centroiding and calibration errors and calculated as described in Theissen, West, & Dhital (Reference Theissen, West and Dhital2016).
In Figure 2, we show g′ − r′ vs. r′ diagram for sources from the SDSS database located within 3 arcmin from the J0621 position. One can see that the presumed pulsar companion is shifted bluewards from the MS population indicating that it is likely to be a WD.
Figure 2. Colour–magnitude diagram for sources from the SDSS database located within 3 arcmin of the J0621 position. The likely pulsar companion is shown in black.
To obtain dereddened colours of the optical source, we estimated the interstellar reddening E(B − V) utilising the dust model by Green et al. (Reference Green2018) which is based on the MS stars photometry in the Pan-STARRS 1 and the 2MASS surveys. The reddening was then transformed to the extinction correction values using conversion coefficients provided by Schlafly & Finkbeiner (Reference Schlafly and Finkbeiner2011). For the DM distance D YMW = 1.64 kpc, we obtained the reddening value E(B − V) = 0.25 + 0.02 − 0.03 (see Table 1). This implies the dereddened colours g′0 − r′0 = −0.12 + 0.14 − 0.17, r′0 − i′0 = −0.17 + 0.17 − 0.18, and absolute magnitude M r′ = 10.11 + 0.10 − 0.11 (the errors include uncertainties on the reddening and magnitudes).
We compared these values with various WD cooling tracks to check whether the optical source can be indeed a WD. The colour–magnitude and colour–colour diagrams are shown in Figures 3 and 4 where the model predictions for different classes of WDs from Panei et al. (Reference Panei, Althaus, Chen and Han2007), Holberg & Bergeron (Reference Holberg and Bergeron2006), Tremblay, Bergeron, & Gianninas (Reference Tremblay, Bergeron and Gianninas2011), Kowalski & Saumon (Reference Kowalski and Saumon2006), and Bergeron et al. (Reference Bergeron2011)Footnote 2 are presented. According to these diagrams, the optical source most likely belongs to a class of He-core WDs with a mass of ≲ 0.5M⊙. This is a rather young (the cooling age of ~0.2–0.5 Gyr) and hot (the effective temperature of ≈ 10000 ± 2000 K) WD. For the distance D NE2001=2.3 kpc, these estimates remain the same due to large colour uncertainties (see Figure 3; M r′ = 9.38 + 0.10 − 0.11).
Figure 3. Colour–magnitude diagram with various WD cooling tracks. Dash-dotted blue lines show tracks for He-core WDs with hydrogen atmospheres and masses 0.1869, 0.2026, and 0.2495 M⊙ (labelled as DA*; Panei et al. Reference Panei, Althaus, Chen and Han2007), solid blue lines—for WDs with hydrogen atmospheres and masses 0.3–0.8 M⊙ (labelled as DA; the step is 0.1 M⊙; Holberg & Bergeron Reference Holberg and Bergeron2006; Kowalski & Saumon Reference Kowalski and Saumon2006; Tremblay et al. Reference Tremblay, Bergeron and Gianninas2011), red dashed lines—for WDs with helium atmospheres and masses 0.2–0.7 M⊙ (labelled as DB; the step is 0.1 M⊙; Bergeron et al. Reference Bergeron2011). WD masses increase from upper to lower curves. Cooling ages are indicated by different symbols. The location of the J0621 companion is marked by the green triangles (the upper one is for the distance D NE2001 = 2.33 kpc and the lower one—for D YMW = 1.64 kpc).
Figure 4. Colour–colour diagram with various WD cooling tracks. The model predictions demonstrated in Figure 3 are labelled by the same symbols and colours. WD temperatures are indicated by different symbols. The location of the J0621 companion is marked by the green cross.
3 DISCUSSION AND CONCLUSIONS
We identified the likely optical counterpart for the binary MSP J0621. The source is different by its colours from the MS stars (see Figure 2) which supports its association with the pulsar. Comparing its absolute magnitudes and colours with WD cooling tracks, we found that the companion most likely belongs to the class of the He-core WDs with the temperature T ≈ 10000 ± 2000 K. The estimated companion mass M c is less than 0.5~M⊙. We compared the J0621 period P, the orbital period P b, and the companion mass M c with parameters of other known binary MSPs (see, e.g., Manchester Reference Manchester2017). This system lies in the M c–P and M c–P b planes among others with similar parameters.
From evolutionary tracks, we obtain the WD cooling age of ~0.2–0.5 Gyr. The latter is much shorter than the pulsar characteristic age of 1.8 Gyr. The situation is similar to PSRs J1012+5307, J1909−3744, and J1738+0333 and their WD companions, which also have large discrepancies between two ages (see, e.g., van Kerkwijk et al. Reference van Kerkwijk, Bassa, Jacoby, Jonker, Rasio and Stairs2005, and references therein). Two explanations of that have been suggested. At first, a pulsar age may be overestimated. If its initial period is similar to the current one, then its real age can be compatible with a short cooling age. J0621 is a rather energetic pulsar and we cannot exclude that it is young. Second, a WD cooling age may be underestimated. WDs can stay hot for a long time due to residual hydrogen burning in the thick hydrogen envelopes. The latter takes place for the extremely low-mass (ELM; M WD ≲ 0.2~M⊙; Panei et al. Reference Panei, Althaus, Chen and Han2007; van Kerkwijk et al. Reference van Kerkwijk, Bassa, Jacoby, Jonker, Rasio and Stairs2005) sources. Comparison between cooling tracks of ELM WDs with thin and thick hydrogen envelopes was recently provided by Calcaferro, Althaus & Córsico (Reference Calcaferro, Althaus and Córsico2018, see their Table 1). For example, a WD with M WD = 0.15~M⊙ and thin envelope cools down to an effective temperature of 9400 K in 0.03 Gyr in contrast with the 2 Gyr required by the thick envelope sequence. The latter case is in agreement with our results for the J0621+WD system. The alternative explanation of the WD high temperature is the low metallicity of its progenitor (Serenelli et al. Reference Serenelli, Althaus, Rohrmann and Benvenuto2002). CNO flashes in such stars are less intensive than in stars with solar metallicity and, therefore, even very old WDs remain relatively hot and bright.
At the estimated temperature and mass, spectra of WDs with hydrogen envelopes are characterised by a large number of Balmer lines. Spectroscopic observations may reveal such lines in the spectrum of J0621’s putative companion and allow one to better constrain its temperature, surface gravity, mass, and chemical composition. Radial velocity measurements would confirm the source relation to the pulsar and provide the mass ratio and, therefore, the pulsar mass. For a 22-mag source, this is feasible with 8–10-m class ground-based telescopes.
ACKNOWLEDGEMENTS
The authors thank the referee Scott Ransom for the useful comments which helped to improve the quality of the paper. AYuK and SVZ acknowledge PAPIIT grant IN-100617 for resources provided towards this research. Funding for the Sloan Digital Sky Survey IV has been provided by the Alfred P. Sloan Foundation, the U.S. Department of Energy Office of Science, and the Participating Institutions. SDSS-IV acknowledges support and resources from the Center for High-Performance Computing at the University of Utah. The SDSS web site is www.sdss.org. The Pan-STARRS1 Surveys (PS1) and the PS1 public science archive have been made possible through contributions by the Institute for Astronomy, the University of Hawaii, the Pan-STARRS Project Office, the Max-Planck Society and its participating institutes, the Max Planck Institute for Astronomy, Heidelberg and the Max Planck Institute for Extraterrestrial Physics, Garching, The Johns Hopkins University, Durham University, the University of Edinburgh, the Queen’s University Belfast, the Harvard-Smithsonian Center for Astrophysics, the Las Cumbres Observatory Global Telescope Network Incorporated, the National Central University of Taiwan, the Space Telescope Science Institute, the National Aeronautics and Space Administration under Grant No. NNX08AR22G issued through the Planetary Science Division of the NASA Science Mission Directorate, the National Science Foundation Grant No. AST-1238877, the University of Maryland, Eotvos Lorand University (ELTE), the Los Alamos National Laboratory, and the Gordon and Betty Moore Foundation.
