Modeling Long-term Variability in Stellar-compact Object Binary Systems for Mass Determinations

Abstract

This work models the effects of gravitational lensing, Doppler boosting, and ellipsoidal variations on eccentric eclipsing binary-system light curves. This is accomplished using a Newtonian orbital-motion code that simulates the orbital velocities and separation of the binary components as a function of time. Improving on previous literature, we examine the effects of orbital eccentricity and period, as well as stellar limb darkening on the expected light curves. Whether lensing, Doppler boosting, or ellipsoidal variation is dominant in the light curves is a function of the separation between the binary components; thus, the combination of all three effects allows for a unique mass-determination method that greatly expands the parameter space for the discovery of compact objects. This suggests the exciting possibility of revealing a large population of nonaccreting compact objects in galactic binary systems. At the same time, the model can be used on systems exhibiting any subset of these effects. In a case study, we fit our model to optical data from the ellipsoidal variable binary system Cygnus X-1, and we compare our determinations with those previously found by different modeling techniques.

The First TESS Self-lensing Pulses: Revisiting KIC 12254688

“…As described in Sorabella et al (2022b), we use our post-Newtonian orbital motion code derived from the Paczynski-Wiita potential to find the velocities and binary separation of the two stars in time. In this modeling effort, we exclude additional effects analyzed in Sorabella et al (2022a), such as relativistic Doppler boosting and ellipsoidal variations. While these effects are expected in some stellar-compact binary systems, they become significant only in systems with shorter orbital periods (smaller separations) than that of KIC 1225488 (Masuda & Hotokezaka 2019).…”

“…In the self-lensing models of KIC 12254688, the prior function allows us to constrain EMCEE by the known properties of the free parameters adopted in this study: (a) ranges for the mass and the radius of the primary star based on spectroscopic results (KIC DR25; Mathur et al 2017); (b) a plausible range for the mass of the WD companion (Figures 1, 3, and 6 in Kepler et al 2007); (c) a range for the orbital inclination (Figure 8 in Sorabella et al 2022a); and (d) the range for the limb-darkening coefficient, which is set to (0, 1) by its definition. The priors for the RV model are based closely on those used by KMM18, while the parameters not found in the KMM18 (or were derived parameters) were given, within reason, wide priors.…”

“…Self-lensing binary systems are a subset of eclipsing binary systems in which at least one component is a compact object, such as a white dwarf (WD), neutron star (NS), or black hole (BH). When the compact object transits in front of its (typically noncompact) companion, it gravitationally lenses the companion's surface, resulting in a symmetric flare in the system's light curve (Maeder 1973;Witt & Mao 1994;Marsh 2001; Rahvar et al 2011;Sorabella et al 2022a). Self-lensing pulses can be very useful in estimating binary parameters, as the pulse profile depends on the masses of the compact object and star, their separation during the transit, the impact parameter, and the orbital inclination of the system.…”

False-positive Self-lensing Events: TESS Observing Asteroid-crossing Events in Disguise

“…A self-lensing stellar binary system is home to a star with a compact-object companion such as a white dwarf, neutron star, or black hole. In these systems, the compact object eclipses its stellar counterpart, gravitationally lensing the star, resulting in a sharp increase in the binary system's apparent luminosity (Maeder 1973;Witt & Mao 1994;Marsh 2001; Rahvar et al 2011;Sorabella et al 2022a). From the profile of this lensing pulse, combined with its observed frequency, one could determine the system's binary parameters such as the orbital period, stellar radius, and the masses of the binary components.…”