Detailed numerical implementation of the wide binary test. (arXiv:2109.03827v1 [astro-ph.GA])
<a href="http://arxiv.org/find/astro-ph/1/au:+Banik_I/0/1/0/all/0/1">Indranil Banik</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Pittordis_C/0/1/0/all/0/1">Charalambos Pittordis</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Sutherland_W/0/1/0/all/0/1">Will Sutherland</a>
The observed flat rotation curves of galaxies are among a number of
astrophysical phenomena which require a larger acceleration than can be
provided by the Newtonian gravity of the detected baryons. The main proposed
solutions are additional undetected mass in the form of dark matter, or a
low-acceleration modification to Newtonian gravity known as Milgromian dynamics
(MOND). It is possible to directly test MOND using wide binary stars in the
Solar neighbourhood, as these systems should contain a dynamically
insignificant amount of dark matter even if it comprises most of the Galaxy.
However, local wide binaries in MOND should orbit each other $approx 20%$
faster than in Newtonian dynamics. We describe the detailed plan for how this
wide binary test will be conducted, focusing especially on stages with a high
numerical cost. The computational costs and memory requirements are estimated
for the main stages in the plan. Our overall assessment is that the critically
important cost function can be evaluated deterministically at a marginal cost
of a few seconds, giving the absolute binomial likelihood of a model. This will
allow the cost function to be embedded within a Markov Chain Monte Carlo
sampler, or a less expensive gradient descent stage designed to reveal the
best-fitting model parameters. Therefore, the wide binary test should be
feasible using currently available technology.
The observed flat rotation curves of galaxies are among a number of
astrophysical phenomena which require a larger acceleration than can be
provided by the Newtonian gravity of the detected baryons. The main proposed
solutions are additional undetected mass in the form of dark matter, or a
low-acceleration modification to Newtonian gravity known as Milgromian dynamics
(MOND). It is possible to directly test MOND using wide binary stars in the
Solar neighbourhood, as these systems should contain a dynamically
insignificant amount of dark matter even if it comprises most of the Galaxy.
However, local wide binaries in MOND should orbit each other $approx 20%$
faster than in Newtonian dynamics. We describe the detailed plan for how this
wide binary test will be conducted, focusing especially on stages with a high
numerical cost. The computational costs and memory requirements are estimated
for the main stages in the plan. Our overall assessment is that the critically
important cost function can be evaluated deterministically at a marginal cost
of a few seconds, giving the absolute binomial likelihood of a model. This will
allow the cost function to be embedded within a Markov Chain Monte Carlo
sampler, or a less expensive gradient descent stage designed to reveal the
best-fitting model parameters. Therefore, the wide binary test should be
feasible using currently available technology.
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