Eclipse timing the Milky Way's gravitational potential

Abstract

We show that a small, but measurable shift in the eclipse mid-point time of eclipsing binary (EBs) stars of ∼ 0.1 seconds over a decade baseline can be used to directly measure the Galactic acceleration of stars in the Milky Way at ∼ kpc distances from the Sun. We consider contributions to the period drift rate from dynamical mechanisms other than the Galaxy's gravitational field, and show that the Galactic acceleration can be reliably measured using a sample of Kepler EBs with orbital and stellar parameters from the literature. Given the uncertainties on the formulation of tidal decay, our approach here is necessarily approximate, and the contribution from tidal decay is an upper limit assuming the stars are not tidally synchronized. We also use simple analytic relations to search for well-timed sources in the Kepler field, and find ∼ 70 additional detached EBs with low eccentricities that have estimated timing precision better than 1 second. We illustrate the method with a prototypical, precisely timed EB using an archival Kepler light curve and a modern synthetic HST light curve (which provides a decade baseline). This novel method establishes a realistic possibility for obtaining fundamental Galactic parameters using eclipse timing to measure Galactic accelerations, along with other emerging new methods, including pulsar timing and extreme precision radial velocity observations. This acceleration signal grows quadratically with time. Therefore, given baselines established in the near-future for distant EBs, we can expect to measure the period drift in the future with space missions like JWST and the Roman Space Telescope.

Snowmass2021 Cosmic Frontier White Paper: Dark Matter Physics from Halo Measurements

“…Line-of-sight accelerations of pulsars measured via their spins [365] and orbital periods [365,366] may already have hints of the local Galactic acceleration, with improvements possible in the future. It is also now imminently possible to measure the Galactic acceleration directly using eclipse timing, by measuring the small shift in the mid-point of the eclipse time over the past decade induced by the Galactic potential since the Kepler mission [367], using space-based observations from HST, and in the future with JWST and Roman observations. Gaia astrometric observations were also recently analyzed to measure the solar system acceleration [368,369], which is in agreement with prior measurements by VLBI [370]; given these measurements, it may be possible to use statistically aggregated astrometric accelerations of stars to measure the galactic potential [371], which would be aided further by astrometric missions beyond Gaia like Theia [372] or GaiaNIR [373].…”

Snowmass2021 Cosmic Frontier White Paper: Observational Facilities to Study Dark Matter

“…A complementary route to constrain the nature of dark matter with JWST can also be realized by measuring the accelerations of stars within the Milky Way. The Kepler mission observed eclipsing binaries [49,50] so precisely that the shift in the eclipse mid-point time induced by the Galactic Snowmass2021: Observational Facilities to Study Dark Matter potential in the intervening decade is in principle measurable today with JWST [51]. Although the shift in the eclipse mid-point induced by the Galactic potential is very small, ∼ 0.1 seconds, spacebased missions that afford exquisite photometric and timing precision for eclipsing binary stars can detect it with sources for which other dynamical effects are sub-dominant to the Galactic signal.…”

“…Although the shift in the eclipse mid-point induced by the Galactic potential is very small, ∼ 0.1 seconds, spacebased missions that afford exquisite photometric and timing precision for eclipsing binary stars can detect it with sources for which other dynamical effects are sub-dominant to the Galactic signal. For the sample of ∼ 200 eclipsing binaries for which Kepler established a very precise baseline a decade earlier, JWST can in principle now provide a new route for direct acceleration measurements and constraints on dark matter sub-structure [51].…”

“…These maps of the debris that remains after ∼ 13 Gyr of galaxy accretion and disruption will reveal significant samples of tidal streams [55,56] that can be used to constrain the existence of low mass dark matter halos [57]. Within the Milky Way, RST can enable even more precise measurements of accelerations by measuring the shift in the eclipse mid-point time [51] since the Kepler mission to provide unprecedented constraints on dark matter sub-structure. While these measurements are possible today with HST and JWST, like all acceleration measurements their precision improves significantly with time, and in this case quadratically with time.…”

Charting galactic accelerations – II. How to ‘learn’ accelerations in the solar neighbourhood

“…These can then be converted into absolute accelerations using a measurement of the Solar system acceleration, thus providing a small number of direct samples of the Galaxy's acceleration field (Bovy 2020 ;Chakrabarti et al 2021b ). In future, E-mail: aneesh.naik@nottingham.ac.uk greater statistical power will be afforded by complementary acceleration measurements, such as those derived from binary eclipse timing (Chakrabarti et al 2021a ) and those from future high-precision radial velocity spectrographs (Quercellini, Amendola & Balbi 2008 ;Ravi et al 2019 ;Silverwood & Easther 2019 ;Chakrabarti et al 2020 ).…”