Calibration of the mixing-length parameter $alpha$ for the MLT and FST models by matching with CO$^5$BOLD models. (arXiv:1811.05229v1 [astro-ph.SR])
<a href="http://arxiv.org/find/astro-ph/1/au:+Sonoi_T/0/1/0/all/0/1">T. Sonoi</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Ludwig_H/0/1/0/all/0/1">H.-G. Ludwig</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Dupret_M/0/1/0/all/0/1">M.-A. Dupret</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Montalban_J/0/1/0/all/0/1">J. Montalbán</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Samadi_R/0/1/0/all/0/1">R. Samadi</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Belkacem_K/0/1/0/all/0/1">K. Belkacem</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Caffau_E/0/1/0/all/0/1">E. Caffau</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Goupil_M/0/1/0/all/0/1">M.-J. Goupil</a>
The CoRoT and Kepler missions provided a wealth of high-quality data for
solar-like oscillations. To make the best of such data for seismic inferences,
we need theoretical models with precise near-surface structure, which has
significant influence on solar-like oscillation frequencies. The mixing-length
parameter, $alpha$, is a key factor for the near-surface structure. In the
convection formulations used in evolution codes, the $alpha$ is a free
parameter that needs to be properly specified. We calibrated $alpha$ values by
matching entropy profiles of 1D envelope models with those of 3D CO$^5$BOLD
models. For such calibration, previous works concentrated on the classical
mixing-length theory (MLT). Here we also analyzed the full spectrum turbulence
(FST) models. For the atmosphere part in the 1D models, we use the Eddington
grey $T(tau)$ relation and the one with the solar-calibrated Hopf-like
function. For both the MLT and FST models with a mixing length $l=alpha H_p$,
calibrated $alpha$ values increase with increasing $g$ or decreasing $T_{rm
eff}$. For the FST models, we also calibrated values of $alpha^*$ defined as
$l=r_{rm top}-r+alpha^*H_{p,{rm top}}$. $alpha^*$ is found to increase with
$T_{rm eff}$ and $g$. As for the correspondence to the 3D models, the solar
Hopf-like function gives a photospheric-minimum entropy closer to a 3D model
than the Eddington $T(tau)$. The structure below the photosphere depends on
the convection model. However, not a single convection model gives the best
correspondence since the averaged 3D quantities are not necessarily related via
an EOS. Although the FST models with $l=r_{rm top}-r+alpha^*H_{p,{rm top}}$
are found to give the frequencies closest to the solar observed ones, a more
appropriate treatment of the top part of the 1D convective envelope is
necessary.
The CoRoT and Kepler missions provided a wealth of high-quality data for
solar-like oscillations. To make the best of such data for seismic inferences,
we need theoretical models with precise near-surface structure, which has
significant influence on solar-like oscillation frequencies. The mixing-length
parameter, $alpha$, is a key factor for the near-surface structure. In the
convection formulations used in evolution codes, the $alpha$ is a free
parameter that needs to be properly specified. We calibrated $alpha$ values by
matching entropy profiles of 1D envelope models with those of 3D CO$^5$BOLD
models. For such calibration, previous works concentrated on the classical
mixing-length theory (MLT). Here we also analyzed the full spectrum turbulence
(FST) models. For the atmosphere part in the 1D models, we use the Eddington
grey $T(tau)$ relation and the one with the solar-calibrated Hopf-like
function. For both the MLT and FST models with a mixing length $l=alpha H_p$,
calibrated $alpha$ values increase with increasing $g$ or decreasing $T_{rm
eff}$. For the FST models, we also calibrated values of $alpha^*$ defined as
$l=r_{rm top}-r+alpha^*H_{p,{rm top}}$. $alpha^*$ is found to increase with
$T_{rm eff}$ and $g$. As for the correspondence to the 3D models, the solar
Hopf-like function gives a photospheric-minimum entropy closer to a 3D model
than the Eddington $T(tau)$. The structure below the photosphere depends on
the convection model. However, not a single convection model gives the best
correspondence since the averaged 3D quantities are not necessarily related via
an EOS. Although the FST models with $l=r_{rm top}-r+alpha^*H_{p,{rm top}}$
are found to give the frequencies closest to the solar observed ones, a more
appropriate treatment of the top part of the 1D convective envelope is
necessary.
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