Measuring the Orbital Parameters of Radial Velocity Systems in Mean Motion Resonance—a Case Study of HD 200964. (arXiv:1908.04789v1 [astro-ph.EP])

Measuring the Orbital Parameters of Radial Velocity Systems in Mean Motion Resonance—a Case Study of HD 200964. (arXiv:1908.04789v1 [astro-ph.EP])
<a href="http://arxiv.org/find/astro-ph/1/au:+Rosenthal_M/0/1/0/all/0/1">M. M. Rosenthal</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Jacobson_Galan_W/0/1/0/all/0/1">W. Jacobson-Galan</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Nelson_B/0/1/0/all/0/1">B. Nelson</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Murray_Clay_R/0/1/0/all/0/1">R. A. Murray-Clay</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Burt_J/0/1/0/all/0/1">J. A. Burt</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Holden_B/0/1/0/all/0/1">B. Holden</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Chang_E/0/1/0/all/0/1">E. Chang</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Kaaz_N/0/1/0/all/0/1">N. Kaaz</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Yant_J/0/1/0/all/0/1">J. Yant</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Butler_R/0/1/0/all/0/1">R. P. Butler</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Vogt_S/0/1/0/all/0/1">S. S. Vogt</a>

The presence of mean motion resonances (MMRs) complicates analysis and
fitting of planetary systems observed through the radial velocity (RV)
technique. MMR can allow planets to remain stable in regions of phase space
where strong planet-planet interactions would otherwise destabilize the system.
These stable orbits can occupy small phase space volumes, allowing MMRs to
strongly constrain system parameters, but making searches for stable orbital
parameters challenging. Furthermore, libration of the resonant angle and
dynamical interaction between the planets introduces another, long period
variation into the observed RV signal, complicating analysis of the periods of
the planets in the system. We discuss this phenomenon using the example of HD
200964. By searching through parameter space and numerically integrating each
proposed set of planetary parameters to test for long term stability, we find
stable solutions in the 7:5 and 3:2 MMRs in addition to the originally
identified 4:3 MMR. The 7:5 configuration provides the best match to the data,
while the 3:2 configuration provides the most easily understood formation
scenario. In reanalysis of the originally published shorter-baseline data, we
find fits in both the 4:3 and 3:2 resonances, but not the 7:5. Because the time
baseline of the data is less than the resonant libration period, the current
best fit to the data may not reflect the actual resonant configuration. In the
absence of a full sample of the longer libration period, we find that it is of
paramount importance to incorporate long term stability when fitting for the
system’s orbital configuration.

The presence of mean motion resonances (MMRs) complicates analysis and
fitting of planetary systems observed through the radial velocity (RV)
technique. MMR can allow planets to remain stable in regions of phase space
where strong planet-planet interactions would otherwise destabilize the system.
These stable orbits can occupy small phase space volumes, allowing MMRs to
strongly constrain system parameters, but making searches for stable orbital
parameters challenging. Furthermore, libration of the resonant angle and
dynamical interaction between the planets introduces another, long period
variation into the observed RV signal, complicating analysis of the periods of
the planets in the system. We discuss this phenomenon using the example of HD
200964. By searching through parameter space and numerically integrating each
proposed set of planetary parameters to test for long term stability, we find
stable solutions in the 7:5 and 3:2 MMRs in addition to the originally
identified 4:3 MMR. The 7:5 configuration provides the best match to the data,
while the 3:2 configuration provides the most easily understood formation
scenario. In reanalysis of the originally published shorter-baseline data, we
find fits in both the 4:3 and 3:2 resonances, but not the 7:5. Because the time
baseline of the data is less than the resonant libration period, the current
best fit to the data may not reflect the actual resonant configuration. In the
absence of a full sample of the longer libration period, we find that it is of
paramount importance to incorporate long term stability when fitting for the
system’s orbital configuration.

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