Minimum-entropy constraints on galactic potentials
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arXiv
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| Main Authors: | , , , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909764272783360 |
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| author | Silva, Leandro Beraldo e Valluri, Monica Vasiliev, Eugene Hattori, Kohei Pedra, Walter de Siqueira Daniel, Kathryne J. |
| author_facet | Silva, Leandro Beraldo e Valluri, Monica Vasiliev, Eugene Hattori, Kohei Pedra, Walter de Siqueira Daniel, Kathryne J. |
| contents | A tracer sample in a gravitational potential, starting from a generic initial condition, phase-mixes towards a stationary state. This evolution is accompanied by an entropy increase, and the final state is characterized by a distribution function (DF) that depends only on integrals of motion (Jeans' theorem). We present a method to constrain a gravitational potential assuming a stationary (phase mixed) sample by minimizing the entropy the sample would have if it were allowed to phase-mix in trial potentials. This method avoids modeling the DF, and is applicable to any sets of integrals. We provide expressions for the entropy of DFs depending on energy, $f(E)$, energy and angular momentum, $f(E,L)$, or three actions, $f(\vec{J})$, and investigate the bias and statistical uncertainties in their estimates. We show that the method correctly recovers the parameters for spherical and axisymmetric potentials. We also present a methodology to characterize the posterior probability distribution of the parameters with an Approximate Bayesian Computation, indicating a pathway for application to observational data. Using $10^4$ tracers with $10\% (20\%)$-uncertainties in the 6D coordinates, we recover the flattening parameter $q$ of an axisymmetric potential with $σ_q/q\sim 5\% (10\%)$. The python module for the entropy estimators, \texttt{tropygal}, is made publicly available. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_07947 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Minimum-entropy constraints on galactic potentials Silva, Leandro Beraldo e Valluri, Monica Vasiliev, Eugene Hattori, Kohei Pedra, Walter de Siqueira Daniel, Kathryne J. Astrophysics of Galaxies A tracer sample in a gravitational potential, starting from a generic initial condition, phase-mixes towards a stationary state. This evolution is accompanied by an entropy increase, and the final state is characterized by a distribution function (DF) that depends only on integrals of motion (Jeans' theorem). We present a method to constrain a gravitational potential assuming a stationary (phase mixed) sample by minimizing the entropy the sample would have if it were allowed to phase-mix in trial potentials. This method avoids modeling the DF, and is applicable to any sets of integrals. We provide expressions for the entropy of DFs depending on energy, $f(E)$, energy and angular momentum, $f(E,L)$, or three actions, $f(\vec{J})$, and investigate the bias and statistical uncertainties in their estimates. We show that the method correctly recovers the parameters for spherical and axisymmetric potentials. We also present a methodology to characterize the posterior probability distribution of the parameters with an Approximate Bayesian Computation, indicating a pathway for application to observational data. Using $10^4$ tracers with $10\% (20\%)$-uncertainties in the 6D coordinates, we recover the flattening parameter $q$ of an axisymmetric potential with $σ_q/q\sim 5\% (10\%)$. The python module for the entropy estimators, \texttt{tropygal}, is made publicly available. |
| title | Minimum-entropy constraints on galactic potentials |
| topic | Astrophysics of Galaxies |
| url | https://arxiv.org/abs/2407.07947 |