MLT

Calibrating the mixing length

match_alpha_atmo_sun

Matching the adiabatic entropy of the solar model and 1D models with mixing length ranging from 1.5 to 2.5 (blue lines). The inlay shows the difference.

We calibrated the free mixing length parameter α with a 1D atmosphere code that employs the identical equation-of-state and opacities. We matched both the entropy of the adiabatic convection zone sbot and the entropy jump ∆s. For the Sun, we find values of 1.98 and 2.01 for α with sbot and ∆s, respectively.


 

Variation with stellar parameters

phrd_mltb_feh0

Hertzsprung-Russell diagram showing the variation of the mixing length for different stellar parameter with solar metallicity.

psgsp_mltj psgsp_mltb

We find the mixing length to vary systematically in the range of 1.7 − 2.4, in particular, α decreases towards higher effective temperature (Teff), lower surface gravity (log g) and higher metallicity ([Fe/H]). The calibration data is available in the file table.dat with the Readme. If you refer to our mixing length values, please use  Magic et al. 2015a as reference.


Functional fits

We performed functional fits of mixing length by converting the the stellar parameters firstScreen Shot 2015-09-11 at 13.28.23and then employing the following functional basis:

Screen Shot 2015-09-11 at 13.24.23

The coefficients are presented in the subsequent table:

alpha(sbot)
[Fe/H]   a0            a1            a2            a3            a4           a5             a6
---------------------------------------------------------------------------------------------------------
 +0.5    1.97373939   -0.13429013    0.16320105    0.03213152    0.04675864   -0.02560510    0.05287061
 +0.0    1.97607815   -0.11007132    0.17560548    0.00397791    0.10333613   -0.05869070    0.08055718
 -0.5    1.95635712   -0.13364510    0.13382454    0.02749096    0.04912460   -0.04804536    0.05795566
 -1.0    1.96994460   -0.14370964    0.14900418    0.00115447    0.05283657   -0.03347076    0.03782256
 -2.0    2.01099658    0.01230849    0.16089396   -0.04127175    0.18048579   -0.05957744    0.07440862
 -3.0    2.13397360    0.05330705    0.22228307   -0.19292034    0.22541197   -0.06493668    0.02723039
---------------------------------------------------------------------------------------------------------

alpha(ssj)
[Fe/H]   a0            a1            a2            a3            a4           a5             a6
---------------------------------------------------------------------------------------------------------
 +0.5    2.06006479   -0.07569695    0.18375048    0.01806064    0.16093068   -0.11088019    0.16478878
 +0.0    2.07706857   -0.07928257    0.15337647    0.04106182    0.09879519   -0.10897204    0.13737732
 -0.5    2.08065319   -0.11715591    0.13925005    0.10587439    0.06301484   -0.10459623    0.14323266
 -1.0    2.13189578   -0.13557833    0.19569437    0.03977120    0.10923155   -0.07456533    0.11053021
 -2.0    2.22904897   -0.06863265    0.24814114   -0.04372929    0.22952285   -0.08884621    0.11280482
 -3.0    2.32452703   -0.01166212    0.29351541   -0.17113568    0.30502114   -0.11259495    0.07783704
---------------------------------------------------------------------------------------------------------

alpha(mml)
[Fe/H]   a0            a1            a2            a3            a4           a5             a6
---------------------------------------------------------------------------------------------------------
 +0.5    1.79108894   -0.18378760    0.17911838   -0.02216346    0.09653585   -0.02823296    0.05483445
 +0.0    1.83234417   -0.17710495    0.16663390    0.01183489   -0.00241608   -0.03047223    0.01922494
 -0.5    1.85997987   -0.20880155    0.15448160    0.11192263   -0.00135705   -0.08921278    0.10582217
 -1.0    1.89792848   -0.20828377    0.17466573    0.03538898    0.02029307   -0.04590686    0.03108134
 -2.0    1.95997667   -0.25568783    0.18373927    0.03268370    0.00057016   -0.03213373    0.00039981
 -3.0    1.96079028   -0.20168570    0.20858072    0.03279546    0.10613903   -0.09538646    0.06592885
---------------------------------------------------------------------------------------------------------
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