A new line on the wide binary test of gravity. (arXiv:1902.01857v1 [astro-ph.GA])
<a href="http://arxiv.org/find/astro-ph/1/au:+Banik_I/0/1/0/all/0/1">Indranil Banik</a>
The relative velocity distribution of wide binary (WB) stars is sensitive to
the law of gravity at the low accelerations typical of galactic outskirts. I
consider the feasibility of this wide binary test using the `line velocity’
method. This involves considering only the velocity components along the
direction within the sky plane orthogonal to the systemic proper motion of each
WB. I apply this technique to the WB sample of Hernandez et. al. (2018),
carefully accounting for large-angle effects at one order beyond leading. Using
Monte Carlo trials, the uncertainty in the one-dimensional velocity dispersion
is $approx 100$ m/s when using sky-projected relative velocities. Using line
velocities reduces this to $approx 30$ m/s because these are much less
affected by distance uncertainties. My analysis does not support the Hernandez
et. al. (2018) claim of a clear departure from Newtonian dynamics beyond a
radius of $approx 10$ kAU, partly because I use $2sigma$ outlier rejection to
clean their sample first. Nonetheless, the uncertainties are small enough that
existing WB data are nearly sufficient to distinguish Newtonian dynamics from
Modified Newtonian Dynamics. I estimate that $approx 1000$ WB systems will be
required for this purpose if using only line velocities. In addition to a
larger sample, it will also be important to control for systematics like
undetected companions and moving groups. This could be done statistically. The
contamination can be minimized by considering a narrow theoretically motivated
range of parameters and focusing on how different theories predict different
proportions of WBs in this region.
The relative velocity distribution of wide binary (WB) stars is sensitive to
the law of gravity at the low accelerations typical of galactic outskirts. I
consider the feasibility of this wide binary test using the `line velocity’
method. This involves considering only the velocity components along the
direction within the sky plane orthogonal to the systemic proper motion of each
WB. I apply this technique to the WB sample of Hernandez et. al. (2018),
carefully accounting for large-angle effects at one order beyond leading. Using
Monte Carlo trials, the uncertainty in the one-dimensional velocity dispersion
is $approx 100$ m/s when using sky-projected relative velocities. Using line
velocities reduces this to $approx 30$ m/s because these are much less
affected by distance uncertainties. My analysis does not support the Hernandez
et. al. (2018) claim of a clear departure from Newtonian dynamics beyond a
radius of $approx 10$ kAU, partly because I use $2sigma$ outlier rejection to
clean their sample first. Nonetheless, the uncertainties are small enough that
existing WB data are nearly sufficient to distinguish Newtonian dynamics from
Modified Newtonian Dynamics. I estimate that $approx 1000$ WB systems will be
required for this purpose if using only line velocities. In addition to a
larger sample, it will also be important to control for systematics like
undetected companions and moving groups. This could be done statistically. The
contamination can be minimized by considering a narrow theoretically motivated
range of parameters and focusing on how different theories predict different
proportions of WBs in this region.
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