A binary pulsar in a 53-minute orbit

Abstract

Spider pulsars are neutron stars that have a companion star in a close orbit. The companion star sheds material to the neutron star, spinning it up to millisecond rotation periods, while the orbit shortens to hours. The companion is eventually ablated and destroyed by the pulsar wind and radiation^1,2. Spider pulsars are key for studying the evolutionary link between accreting X-ray pulsars and isolated millisecond pulsars, pulsar irradiation effects and the birth of massive neutron stars^3-6. Black widow pulsars in extremely compact orbits (as short as 62 minutes⁷) have companions with masses much smaller than 0.1 M_⊙. They may have evolved from redback pulsars with companion masses of about 0.1-0.4 M_⊙ and orbital periods of less than 1 day⁸. If this is true, then there should be a population of millisecond pulsars with moderate-mass companions and very short orbital periods⁹, but, hitherto, no such system was known. Here we report radio observations of the binary millisecond pulsar PSR J1953+1844 (M71E) that show it to have an orbital period of 53.3 minutes and a companion with a mass of around 0.07 M_⊙. It is a faint X-ray source and located 2.5 arcminutes from the centre of the globular cluster M71.

Fig. 1. Constraints on the mass and radius of the companion star.

a, A generic constraint on the companion mass as a function of inclination angle, i, on the basis of the measured mass function for different pulsar masses of 1.0, 1.4 and 2.0 M_⊙. If the orbital plane is randomly distributed, the integrated probability of inclination angle i from 90^o (edge-on) to 0^o (face-on) can be calculated as cos(i). The observed lower limit of a white dwarf (WD) mass is 0.16 M_⊙(light-blue dashed–dotted horizontal line). The probability of the companion being a white dwarf is smaller than 0.3%. b, Constraints on the mass and radius of the companion star. The red and green regions denote the mass–radius relations of the companion star at solar (LMX model) and zero (LMZ model) metallicities, respectively, with an evolution age of between 3 and 10 Gyr. Assuming a pulsar mass of 1.4 M_⊙ (M_p), the radius of the Roche lobe as a function of companion mass is plotted as the black curve, which serves as the upper limit of the allowed parameter space. The dotted regions are the allowed regions for the companion mass and radius.

Fig. 2. Location of M71E on the companion mass versus orbital period plane and comparison with binary evolutionary models.

Known short-period binary pulsars with companion masses (greater than 0.005 M_⊙) and orbital periods (less than 1 day) are plotted. The companions that may be either low-mass (LM) stars or white dwarfs (WDs) are represented as hollow circles with a dot inside. Owing to their very low mass function, the companions of J1653-0158 and J1518+0204C are marked as low-mass stars. The data are taken from the Australia Telescope National Facility Pulsar Catalogue. The mass ranges (grey horizontal lines) are calculated from the mass function, under the assumptions of a neutron star mass of 1.4 M_⊙ and an inclination angle of between 90 and 25.8 degrees (90% probability when assuming a random distribution). M71E with P_b = 53.3 minutes and companion mass (M_c approximately 0.05–0.10 M_⊙) is plotted as the red star with a black bar, with the median M_c = 0.07 M_⊙. For comparison, a horizontal grey line with a star at the lower left corner represents the mass range of M71E when the orbital inclination angle is between 90 and 25.8 degrees. Blue curves represent the typical evolution tracks of the binary models, with an initial metallicity of the donor star of Z = 0.02 (the solid line) or Z = 0.002 (the dashed line). The red dashed–dotted curve represents the typical evolution of a low-mass X-ray binary with an evolved main-sequence donor, which will evolve into an ultra-compact X-ray binary eventually. The initial neutron star mass is assumed to be 1.40 M_⊙ in these models and other initial binary parameters are listed in the legend.

Extended Data Fig. 1. Timing residuals and lack of eclipsing of M71E.

Panel a: Timing residuals of M71E, obtained by subtracting the best-estimated timing model shown in Table 1 from the time-of-arrivals. Panel b: timing residuals as a function of orbital phase, showing that there is no eclipsing events. Panel c and d: as an example, from the observation in December 4^th, 2021, the data were folded with timing solution. The observation covered more than 2 orbits, while no eclipsing was seen either for the whole FAST band (1.05–1.45 GHz,panel c), or the lowest 1.05–1.10 GHz subband (panel d). All the error bar are for ± 1 sigma.

Extended Data Fig. 2. Polarization pulse profile of M71E.

The intensity of the flux, linear polarization and circular polarization are presented as black solid, blue dashed and red dash-dotted curves, with polarization position angles with ± 1 sigma error bar above. The peak and mean flux of the total intensity of M71E was estimated to be 0.632 ± 0.002 and 0.092 ± 0.002 mJy, respectively. The RM used to obtain this pulse profile is −475 ± 2 rad m⁻².

Extended Data Fig. 3. Evolution of a binary system with an initial neutron star mass M_p,init = 1.40 M_⊙, an initial companion mass M_c,init = 0.40 M_⊙ and an initial orbital period P_b,init = 0.70 days.

Panel a: Evolution of donor mass and orbital period. The ages of the system at different epochs are indicated in the plot. Panel b: Evolution of mass transfer rate (red line) and total mass-loss rate (grey dashed line) as a function of time.

Extended Data Fig. 4. Details of the donor evolution.

Panel a: evolution of the donor star in the HR diagram; Panel b: evolution of mass transfer rate as a function of orbital period; Panel c: evolution of surface He abundance of the donor star as a function of donor mass. The initial binary parameters for this binary system are M_p,init = 1.40 M_⊙, M_c,init = 1.00 M_⊙ and P_b,init = 2.25 days. The red stars indicate the models with an orbital period same as the orbital period of M71E, i.e. 53 min.