The dramatic flow of data from the Kepler and K2 missions opens the opportunity to significantly improve our knowledge of stellar interiors, surface dynamics, and structure. However, interpretation of these observations is a challenging task because it depends on tiny effects that can be studied only with advanced first-principles modeling. We present results of 3D time-dependent radiative hydrodynamic simulations of stellar outer convection zones and atmospheres taking into account chemical composition, radiative transfer, turbulence effects, and a realistic equation of state for main sequence stars. We will discuss properties of convective structure and dynamics, convective overshoot, effects of magnetic fields and rotation, as well as the potential influence of turbulent surface dynamics on high-precision RV measurements

Kitiashvili, Irina

NASA Technical Reports Server

 3D rectangular geometry
 Fully conservative compressible MHD
 Fully coupled radiation solver:
LTE using 4 opacity-distribution-function bins
Ray-tracing transport by Feautrier method
18 ray (2 vertical, 16 slanted) angular 
quadrature
 Non-ideal (tabular) EOS
 4th order Padé spatial derivatives
 4th order Runge-Kutta in time
 LES-Eddy Simulation options (turbulence 
models):
LES: Smagorinsky model (and its dynamic 
procedure)
DNS + Hyperviscosity approach
MHD  subgrid turbulence models
3D Radiative Hydrodynamics Modeling of Convection of Stars
to Probe Their Interiors and Photospheric Properties 
The dramatic flow of data from the Kepler and K2 missions opens the opportunity to significantly improve our knowledge of stellar interiors, surface dynamics, and structure. However, interpretation of
these observations is a challenging task because it depends on tiny effects that can be studied only with advanced first-principles modeling. We present results of 3D time-dependent radiative
hydrodynamic simulations of stellar outer convection zones and atmospheres taking into account chemical composition, radiative transfer, turbulence effects, and a realistic equation of state for main-
sequence stars. We will discuss properties of convective structure and dynamics, convective overshoot, effects of magnetic fields and rotation, as well as the potential influence of turbulent surface
dynamics on high-precision RV measurements.
‘StellarBox’ code (Wray et al., 2018)

t  ui ,i  0ui
t  uiu j  Pij , j   ,i
Pij  p 23uk,k 
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The equations we solve are the grid-cell averaged
Conservation of mass:
Conservation 
of momentum:
Conservation of energy:
with
Conservation of magnetic flux 
Basic equations
Conclusions
Because of complexity of the physics of stellar surface and
subsurface layers, ‘ab initio’ (or ‘realistic’), numerical simulations
based on first principles are a primary tool of theoretical modeling.
Our investigation of main-sequence stars has shown that the
dynamics of stellar convection dramatically changes among stars
of different masses. The convection zone is shallower for more
massive stars, turbulent convection becomes more vigorous, with
plasma motions reaching supersonic speeds and multi-scale
convective cell structures appearing that can be quite different from
the granulation and supergranulation known from solar
observations. Convective downdrafts in intergranular lanes
between granulation clusters reach speeds of more than 20km/s,
Irina Kitiashvili, NASA Ames Research Center
Variation in the scales of granulation for different main-sequence
stars with increasing stellar mass. Distribution of the vertical velocity
is saturated for range +/- 6 km/s.
-40 -30 -20 -10 0
z, Mm
-0.10
-0.05
0.00
0.05
0.10   c 2 / c 2 
a)                                            b)                                             c)                                             d)
-0.10
-0.05
0.00
0.05
0.10    
-40 -30 -20 -10 0
z, Mm
0
-20
-10
0
10
20
 A*
-40 -30 -20 -10
z, Mm
-0.2
-0.1
0.0
0.1
0.2    
-40 -30 -20 -10 0
z, Mm
M=1.47M
0.04
0.02
0.00
-0.04
-0.02
0    0.2   0.4   0.6   0.8   1.0
r/R
  c 2 / c 2 0.02
0.01
0.00
-0.01
0    0.2   0.4   0.6   0.8   1.0
r/R
    0.04
0.02
0.00
-0.04
-0.02
0    0.2   0.4   0.6   0.8   1.0
r/R
 A* 0.004
0.002
0.000
-0.004
-0.002
0    0.2   0.4   0.6   0.8   1.0
r/R
   
e)                                             f)                                             g)                                             h)
SUN
2.0
1.5
1.0
0.5
0.0
1.7
1.6
1.5
1.4
1.3
1.2
1.1
T
 
 
1
0
 
,
 
K
x
5
-40            -30           -20           -10               0
z, Mm
-40            -30           -20           -10               0
z, Mm
-40            -30           -20           -10               0
z, Mm
-40            -30           -20           -10               0
z, Mm

a)                                                                            b)
c)                                                                            d)0.8
0.6
0.4
0.2
0.0
30
20
10
0
-10
-20
-30
d
l
o
g
T
/
d
l
o
g
P
A
 1.47M  , 3D model
 1.47M  , 1D model
HeII
ionization
H and HeII
ionization
convection zone
overshoot region
*
T
 
 
 
1
0
 
,
 
K
x
4
25
20
15
10
5
0
2.5
2.0
1.5
1.0
0.5

,
 
g
/
c
m
3
10
10
10
10
10
-4
-5
-6
-7
-8
M/M
1.00
1.01
1.12
1.17
1.35
1.47
M/M
1.00
1.01
1.12
1.17
1.35
1.47
M/M
1.00
1.01
1.12
1.17
1.35
1.47
M/M
1.00
1.01
1.12
1.17
1.35
1.47
-35     -30      -25       -20     -15     -10      -5          0 -4            -3                -2                -1             0
z, Mm z, Mm
-4            -3            -2               -1              0 -25       -20         -15          -10        -5           0
z, Mm z, Mm
p
,
 
g
/
(
c
m
 
s
 
)
2
10
10
10
10
10
10

1.7
1.6
1.5
1.4
1.3
1.2
8
7
6
5
4
3
  10x
4
-3        -2        -1         0
a)                                                                                   b)
c)                                                                                   d)
Models of interior structure of the stars obtained with a stellar
evolution code.
Deviations between the 3D simulation and a 1D 
model of a star with mass M=1.47 Msun as a 
function of depth, z=r-R,  for:  a) the squared 
sound speed, dcs2/cs2; b) density, drho/rho; c) the 
Ledoux parameter of convective stability, A*; and 
d) the adiabatic exponent, gamma. Panels e-h) 
show the corresponding deviations of the solar 
properties obtained by helioseismology inversion 
(Kosovichev 1999, 2011) from the  1D standard 
solar model (Christensen-Dalsgaard et al. 1996). 
Vertical dotted lines show the location of the 
bottom boundary of the convection zone.
Vertical slice for the modeled star (1.47Msun) shows: a) vertical velocity, b) density, c)
temperature, and d) sound speed perturbations from the radiative zone to the the stellar
photosphere. Large-scale density fluctuations in the radiative zone are caused by
internal gravity waves (g-modes) excited by convective overshooting. Depth z is defined
as: z=r-R.
Comparison of the 1D interior structure of a moderate mass star
(M=1.47Msun) calculated using mixing-length theory (dashed curves) and
from the 3D simulation (solid curves): a) temperature; b) adiabatic
exponent; c) temperature gradient; d) Ledoux parameter of convective
stability, A*. Vertical dotted lines indicate the bottom of the convection
zone and the extent of the overshoot region in the 3D simulation. The
mean profiles of the simulation are calculated by averaging in the
horizontal directions and over a 1 hour interval. The thin curve in panel
b) shows the value of the adiabatic exponent calculated from the mean
density and internal energy profiles of the 3D model
(Kitiashvili et. al. 2016).
Vertical profiles, obtained from the 3D numerical simulation of
a 1.47Msun F-type star (Kitiashvili et. al. 2016): a) rms of
velocity V (black), vertical Vz (red) and horizontal Vh (blue)
components of velocity; b) rms of temperature T’ (black) and
sound speed cs’ (blue) perturbations; c) enstrophy (black)
and helicity H (blue); d) rms of density (black) and gas
pressure P’ (blue) perturbations; e) turbulent Pturb (blue curve),
turbulent pressure of the vertical motions Pturb (black), and
the ratio of turbulent pressure Pturb to total pressure Pturb+P;
and f) convective energy flux Fconv (blue curve) and kinetic
energy flux Fkin (black), calculated according to the
formulation of Nordlund & Stein (2001). Vertical dashed lines
indicate the bottom boundary of the convection zone of the
corresponding 1D stellar model: zcz=-28.5 Mm.
-40          -30           -20           -10             0
z, Mm
-40          -30           -20           -10             0
z, Mm
-40          -30           -20           -10             0
z, Mm
-40          -30           -20           -10             0
z, Mm
-40          -30           -20           -10             0
z, Mm
-40          -30           -20           -10             0
z, Mm
10
8
6
4
2
0
10
10
10
10
10
5 x10
4 x10
3 x10
2 x10
1 x10
0
3000
2500
2000
1500
1000
500
0
3
2
1
0
V
 
 
 
 
,
 
k
m
/
s
r
m
s
r
m
s
V
V
V
z
h
T
 
 
 
 
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K
r
m
s
r
m
s
C
s
 
 
 
 
,
 
k
m
/
s
-3
-4
-5
-6
-7
10
10
10
10
4
3
2
1
10
10
10
10
10
7.5 x10
5.0 x10
2.5 x10
0
-2.5 x10
-5.0 x10
-7.5 x10
-7
-8
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
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s

P
 
 
 
 
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d
y
n
/
c
m
 
 
2
 
 
 
 
 
 
 
2

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r
m
s
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H
,
 
c
m
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s
H
2
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g
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c
m
F
l
u
x
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e
r
g
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c
m
 
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s
3
2
2
a)                                                                                       b)
c)                                                                                        d)
e)                                                                                     f)
6
5
4
p
 
 
 
 
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(
c
m
 
s
 
 
)
rms
rms
p    
t
u
r
b
Fconv
Fkin
Pturb
Pturb,z

rmsCs   

rmsT    

2
10
10
10
10
10
10
5
5
5
5
5
t
u
r
b
 
 
 
 
 
 
t
o
t
P
 
 
 
 
/
P
0.4
0.3
0.2
0.1
0.0
turb     totP   /P
Power spectrum of low-degree 
(radial) stellar oscillations for a 
1.47Msun star.
Slice of vertical velocity for a star with
mass 1.35 Msun.
Angular degree – frequency diagram, obtained 
from the 3D numerical simulations for a model 
of 1.47 Msun for different depth.
Angular degree – frequency diagram,
obtained from the 3D numerical
StellarBox simulations for a model of
1.35 Ms Kepler target star.
Power spectrum of low-degree (radial)
stellar oscillations for vertical velocity, gas
pressure, and temperature
Effects of rotation
x
y
R
R
R
X, rotation
M = 1.47 Msun,  Prot = 1day
30 deg
0 deg
X, rotation
C
o
n
v
e
c
t
i
o
n
z
o
n
e
3
5
 
M
m
R
a
d
i
a
t
i
v
e
z
o
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1
6
 
M
m
Vz
Vz
Vertical distribution of the velocity
components for two rotation rates
(Prot = 1 day and 14 days) and 3
latitudes: 0 deg (equator), 30 deg
and 60 deg. The vertical velocity
profiles are averaged over 1 hour.
References
can penetrate through the whole convection zone and hit the radiative zone, and form a
8Mm thick overshoot layer.
For stars with M > 1.35Ms the convection zone is relatively shallow, and high-resolution
simulation domains cover its entire depth, including a convectively stable layer of the
radiative zone. This allows us to investigate the physics of overshooting and turbulent
mixing, as well as excitation of internal gravity waves at the bottom of the convection
zone.
Including the effects of rotation reveals formation of roll-like structures at the bottom of
the convection zone that lead to the development of anti-solar differential rotation for a
star of 1.47 solar mass.
Christensen-Dalsgaard J. et al. 1996. Science 272, 1286.
Kitiashvili I. N. et. al. 2016. ApJ 821, article id. L17, 8.
Kosovichev A. G. 1999. J. Comput. Appl. Math., 109, 1.
Kosovichev A. G. 2011. In Lecture Notes in Physics, Vol. 
832. Berlin: Springer, 3-84.
Nordlund A. & Stein R. F. 2001. ApJ 546, 576
Wray A. A. et al. 2018. Realistic simulations of Stellar 
Radiative MHD. In Book: "Variability of the Sun and Sun-like 
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Sciences, 2018. p.39-62. ArXiv:1507.07999
https://ntrs.nasa.gov/search.jsp?R=20190027656 2019-09-26T20:02:22+00:00Z


3D Radiative Hydrodynamics Modeling of Convection of Stars to Probe Their Interiors and Photospheric Properties

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