Testing gravity with wide binary stars like α Centauri

Abstract

We consider the feasibility of testing Newtonian gravity at low accelerations using wide binary (WB) stars separated by 3 kAU. These systems probe the accelerations at which galaxy rotation curves unexpectedly flatline, possibly due to Modified Newtonian Dynamics (MOND). We conduct Newtonian and MOND simulations of WBs covering a grid of model parameters in the system mass, semi-major axis, eccentricity and orbital plane. We self-consistently include the external field (EF) from the rest of the Galaxy on the Solar neighbourhood using an axisymmetric algorithm. For a given projected separation, WB relative velocities reach larger values in MOND. The excess is ≈ 20% adopting its simple interpolating function, as works best with a range of Galactic and extragalactic observations. This causes noticeable MOND effects in accurate observations of ≈ 500 WBs, even without radial velocity measurements.We show that the proposed Theia mission may be able to directly measure the orbital acceleration of Proxima Centauri towards the 13 kAU-distant α Centauri. This requires an astrometric accuracy of ≈ 1 µas over 5 years. We also consider the long-term orbital stability of WBs with different orbital planes. As each system rotates around the Galaxy, it experiences a time-varying EF because this is directed towards the Galactic Centre. We demonstrate approximate conservation of the angular momentum component along this direction, a consequence of the WB orbit adiabatically adjusting to the much slower Galactic orbit. WBs with very little angular momentum in this direction are less stable over Gyr periods. This novel direction-dependent effect might allow for further tests of MOND.

Effect of the Solar dark matter wake on planets

“…Radio tracking data from Cassini has placed strong constraints on the MOND interpolating function, though some choices are still consistent with observations (Hees et al 2014(Hees et al , 2016. Nearby wide binary stellar systems could be even more important as the MOND circular velocity exceeds the Newtonian value by ≈ 20% (Banik & Zhao 2018). Such systems do appear to show a departure from Newtonian expectations , though it was later shown that the two can be reconciled with a more careful rejection of outliers (Banik 2019).…”

“…For MOND, the dynamics of wide binary stars is a promising 'experimentum crucis' in the near future (e.g. Banik & Zhao 2018). If the observed dynamical discrepancies are due to DM, then massive objects moving through the Galactic DM halo should experience dynamical friction (Chandrasekhar 1943).…”

Testing gravity with interstellar precursor missions

“…If a slightly heavier spacecraft can be launched, it might be possible to perform Cavendish-style gravitational experiments beyond the Sun's MOND radius. As discussed in Banik & Zhao (2018d, figure 1), the force between two point masses would exceed the Newtonian expectation by ≈ 30 − 60% depending on their heliocentric distance, orientation with respect to the Galactic external field and, to a smaller extent, their mass ratio (see their figure 8). In general, the force would not be parallel to the separation between the masses, causing the system as a whole to spontaneously undergo torsional oscillations.…”

“…The external field entering this equation is the Newtonianequivalent quantity g N,ext , the Newtonian gravity exerted by the rest of our Galaxy on the Solar System. As discussed in section 9.3.1 of Banik & Zhao (2018d), the Sun's location in the outskirts of the Galactic disk means that it is quite accurate to use the spherically symmetric relation between g N,ext and the actual external field gext.…”

“…For a definition of what it means to use the 'same' interpolating function in AQUAL and QUMOND, we refer the reader to section 7.2 ofBanik & Zhao (2018d).MNRAS 000, 1-9 (2019)…”