J/MNRAS/442/805 T(tau) relations code (Trampedach+, 2014)
Improvements to stellar structure models, based on a grid of 3D convection
simulations. I. T(tau)-relations.
Trampedach R., Stein R.F., Christensen-Dalsgaard J., Nordlund A., Asplund M.
<Mon. Not. R. Astron. Soc. 442, 805 (2014)>
=2014MNRAS.442..805T 2014MNRAS.442..805T
ADC_Keywords: Models, atmosphere ; Stars, late-type
Keywords: convection - stars: atmospheres - stars: interiors
Abstract:
Relations between temperature, T, and optical depth, τ, are often
used for describing the photospheric transition from optically thick
to optically thin in stellar structure models. We show that this is
well justified, but also that currently used T(τ)-relations are
often inconsistent with their implementation. As an outer boundary
condition on the system of stellar structure equations,
T(τ)-relations have an undue effect on the overall structure of
stars. In this age of precision asteroseismology, we need to re-assess
both the method for computing and for implementing T(τ)-relations,
and the assumptions they rest on.
We develop a formulation for proper and consistent evaluation of
T(τ)-relations from arbitrary 1D or 3D stellar atmospheres, and
for their implementation in stellar structure and evolution models.
We extract radiative T(τ)-relations, as described by our new
formulation, from 3D simulations of convection in deep stellar
atmospheres of late-type stars from dwarfs to giants. These
simulations employ realistic opacities and equation of state, and
account for line-blanketing. For comparison, we also extract
T(τ)-relations from 1D MARCS model atmospheres using the same
formulation.
T(τ)-relations from our grid of 3D convection simulations display
a larger range of behaviours compared with those of conventional
theoretical 1D hydrostatic atmosphere models based on the
mixing-length theory for convection. The use of scaled solar
T(τ)-relations is therefore questionable. Files with
T(τ)-relations for our grid of simulations is made available to
the community, together with routines for interpolating in this
irregular grid.
Description:
Radiative T(τ)-relations, in the form of generalised Hopf
functions, computed from a grid of 37, solar metallicity, realistic,
3D convection simulations with radiative transfer.
File Summary:
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FileName Lrecl Records Explanations
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ReadMe 80 . This file
TtauFeH0.dat 456 88 Calibrated Mixing-Length Theory (MLT)
α-values
TtauIntp.pro 80 275 IDL function for reading and interpolating in
TtauFeH0.dat
TtauIntp.f 80 188 Fortran 77 routine for reading and
interpolating in TtauFeH0.dat
624.f 69 5650 *General code for triangulation and
interpolation in irregularly gridded data
sample.f 72 41 Sample program for calling s/r TtauIntp
Makefile 71 34 Makefile for compiling sample.x
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Note on 624.f : From Renka, 1984, ACM Trans on Math. Softw, 10, 440
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Description of file: TtauFeH0.dat
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Line 1:
1- 12 A12 --- --- Description of line
13- 36 2I12 --- Ntau,Nsims Dimensions of table
Line 2:
1- 12 A12 --- Teff/[K] Description of line
13-456 37F12.3 K Teff Effective temperatures for the simulations.
Line 3:
1- 12 A12 --- logg Description of line
13-456 37F12.3 [cm/s2] logg Surface gravities for the 37 simulations.
Line 4:
1- 12 A12 --- [Fe/H] Description of line
13-456 37F12.3 --- [Fe/H] Metallicities the 37 simulations.
Line 5:
1- 12 A12 --- alpha Description of line
13-456 37F12.3 --- alpha MLT parameters for the 37 simulations.
Lines 6- 87:
1- 12 f12.8 [-] logtau Logarithmic Rosseland mean optical depth for
82 depths-points of the simulations
13-456 37f12.3 --- q(tau) Radiative Hopf functions for the 37
simulations, as function of optical depth
--------------------------------------------------------------------------------
Description of file: TtauIntp.pro
IDL function to read and interpolate in the table of MLT parameters α,
and T(τ)-relations derived from realistic, 3D convective, stellar
atmospheres Trampedach et al., (2013ApJ...769...18T 2013ApJ...769...18T, 2014MNRAS.442..805T 2014MNRAS.442..805T).
See Trampedach et al. (2013ApJ...769...18T 2013ApJ...769...18T) for details on the
implementation in stellar structure calculations.
Details on the arguments and return values can be found in the file.
Description of file: TtauIntp.f
Fortran 77 equivalent of the IDL function TtauIntp.pro. A routine to read
and interpolate in the table of MLT parameters α, and
T(τ)-relations derived from realistic, 3D convective, stellar
atmospheres Trampedach et al., (2013ApJ...769...18T 2013ApJ...769...18T, 2014MNRAS.442..805T 2014MNRAS.442..805T).
See Trampedach et al. (2013ApJ...769...18T 2013ApJ...769...18T) for details on the
implementation in stellar structure calculations.
Details on the arguments and return values can be found in the file.
Description of file: 624.f
Collection of Fortran 77 routines for performing a Delanuy triangulation
of and interpolation between irregularly gridded data.
The routines are written in single precision. To work with double precision
code 624.f needs to be compiled 64bits as the default size for real numbers.
With the Intel compilers the following can be added to a Makefile:
FLAG64b= -real-size 64
624.o: 624.f
$(FC) $(FFLAGS) $(FLAG64b) -c 624.f
See the sample Makefile.
Description of file: sample.f
Sample program to illustrate the use of subroutine TtauIntp.f.
The program prints out the mixing-length parameter, α, and the
radiative Hopf function for Teff=5000K and logg=3.0.
This file also lists the expected values for this set of parameters.
Can be compiled with the provided Makefile.
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Acknowledgements:
Regner Trampedach, trampeda(at)lcd.colorado.edu
References:
Trampedach et al., 2013ApJ...769...18T 2013ApJ...769...18T,
A grid of three-dimensional stellar atmosphere models of solar metallicity.
I. General properties, granulation, and atmospheric expansion.
(End) Regner Trampedach [JILA, CO, USA], Patricia Vannier [CDS] 24-Jun-2014