A Comparison Between Physics-based and Polytropic MHD Models for Stellar Coronae and Stellar Winds of Solar Analogs

4.9 MB·

by  Ofer Cohen

Draft version January 6, 2017
PreprinttypesetusingLATEXstyleemulateapjv.5/2/11
A COMPARISON BETWEEN PHYSICS-BASED AND POLYTROPIC MHD MODELS FOR STELLAR
CORONAE AND STELLAR WINDS OF SOLAR ANALOGS
O. Cohen1,2
Draft version January 6, 2017
ABSTRACT
The development of the Zeeman-Doppler Imagine (ZDI) technique has provided synoptic observa-
tions of surface magnetic fields of low-mass stars. This led the Stellar Astrophysics community to
adopt modeling techniques that have been used in solar physics using solar magnetograms. However,
7 manyofthesetechniqueshavebeenneglectedbythesolarcommunityduetotheirfailuretoreproduce
1 solar observations. Nevertheless, some of these techniques are still used to simulate the coronae and
0 winds of solar analogs. Here we present a comparative study between two MHD models for the solar
2 corona and solar wind. The first type of model is a polytropic wind model, and the second is the
physics-basedAWSOMmodel. WeshowthatwhiletheAWSOMmodelconsistentlyreproducesmany
n
solarobservations,thepolytropicmodelfailstoreproducemanyoftheseobservationsandinthecases
a
J it does, its solutions are unphysical. Our recommendation is that polytropic models, which are used
to estimate mass-loss rates and other parameters of solar analogs, must be first calibrated with solar
4
observations. Alternatively, these models can be calibrated with models that capture more detailed

] physics of the solar corona (such as the AWSOM model), and that can reproduce solar observations
R in a consistent manner. Without such a calibration, the results of the polytropic models cannot be
S validated, but they can be wrongly used by others.
. Subject headings: planets and satellites: atmospheres
h
p
-
o 1. INTRODUCTION for recent review on the PFSS issues). Currently, the
r TheZeeman-DopplerImagine(ZDI)technique(Donati PFSSmethodismainlyusedtocalculatetheinitialstate
st & Semel 1990) has provided, for the first time, synop- of the magnetic field in Magnetohydrodynamic (MHD)
a models or to obtain a tentative description of the coro-
tic observations of surface magnetic fields of low-mass
[ nal field. Due to its limitations, the solar community is
stars(mostlyM,K,andG).Despiteofsomecriticismon
currently transitioning from using the PFSS method to
1 the uncertainty of these stellar ”magnetograms” (e.g.,
more sophisticated field extrapolation methods, such as
v Kochukhov et al. 2010; Reiners 2012), the growth in
thenon-linearforcefreetechnique(seereviewbyWiegel-
6 availability of stellar magnetograms (see Vidotto et al.
4 2014, for a summary of these observations) has led mann&Sakurai2012). Incontrast,thePFSSmethodis
1 the stellar astrophysics community to adopt techniques, usedmorefrequentlytoextrapolatestellarcoronalfields
1 which were used by the solar community to extrapolate based on the ZDI maps (see e.g., Jardine et al. 1999)
0 the three-dimensional coronal magnetic field. In partic- Following the pioneering coronal modeling work by
. Pneuman & Kopp (1971), modern, multi-dimensional
1 ular, ZDI data has been used to drive three-dimensional
MHDmodelsforthesolarcoronahavebeenfirstapplied
0 models for stellar coronae and stellar winds (in a sim-
athermallydriven,polytropicParkerwind(Parker1958)
7 ilar manner that solar magnetograms are used to drive
on top a a potential field (Linker et al. 1990; Usmanov
1 models for the solar corona and solar wind).
1993; Linker & Mikic 1995). The Parker wind solution
: The first approach, which was adopted from solar
v is obtained analytically assuming a (nearly) isothermal
physics is the so-called ”Potential Field Source Surface”
i radiallyexpandingflow. Asteady-stateisobtainedwhen
X (PFSS) method (Altschuler & Newkirk 1969). In the
a pressure balance between the Parker wind and the po-
PFSS model, the three-dimensional magnetic field is as-
r tential field is achieved. Despite of spacecraft conforma-
a sumedtobestatic(i.e.,thereisnoforcingonthefieldby
tion of the existence of super-Alfv´enic solar wind, the
electric currents) and as such, the field can be described
ParkerwindanditsimplementationintheseolderMHD
as a gradient of a scalar potential. This scalar potential
models have failed to reproduce the observation. In par-
can be obtained by solving the Laplace’s equation, as-
ticular, they could not produce the observed fast solar
suming that the field is purely radial above a spherical
wind. Thus, we should account for additional accelera-
surface - the ”Source Surface”, which is set at a random
tion missing from the Parker model.
distance. The potentiality of the solar coronal field has
Holzer (1977) and Usmanov et al. (2000) have pointed
been debated for some time among the solar community
out that in order to properly reproduce the solar corona
(see e.g., Riley et al. 2006). In particular, the validity
and the solar wind, MHD models need to include ad-
of a spherical source surface and the choice of its dis-
ditional momentum and energy terms beyond the set
tance have been challenged frequently (see Cohen 2015,
of ideal MHD equation. While the physical interpre-
1LowellCenterforSpaceScienceandTechnology,University tation of these terms is still under debate, these terms
ofMassachusetts,Lowell,MA01854,USA accountfortheobservedcoronalheatingandwindaccel-
2Harvard-SmithsonianCenterforAstrophysics,60GardenSt. eration. In an intermediate stage, the polytropic models
Cambridge,MA02138,USA
2
havebeenextendedtousevaryingpolytropicindex,γ,as the stellar corona except for the prescribe temperature
afunctionofsomelocalpropertiesofthegas(e.g.,Rous- of the gas and the adiabatic expansion. In other words,
sevetal.2003;Cohenetal.2007;Fengetal.2010;Jacobs thecoronainthismodelisassumedtobealreadyheated,
&Poedts2011). Inparticular,modelsweredevelopedto and the equations are relaxed to steady-state (when a
relate the local value of γ to the observed empirical rela- pressure balance is achieved). In this polytropic setting,
tionbetweenthesolarwindspeedandthemagneticflux we use a prescribed, non-uniform Cartesian grid with a
tube expansion geometry (Wang & Sheeley 1990; Mc- varying grid size ranging from ∆x = 0.02R near the
(cid:12)
Comas 2007). These models succesfully reproduced the inner boundary to ∆x=0.5R at the outer parts of the
(cid:12)
observedsolarwind. However,duetothelackofdetailed domain, which extends to 24R .
(cid:12)
thermodynamics,theydidnotprovideagoodagreement
with observations of the solar corona itself (i.e., compar- 2.2. The AWSOM Model
isonwithEUV/X-rayline-of-sightobservations). Recent
In the second setting of BATS-R-US, we use the re-
MHD models for the solar corona and solar wind adopt
cently developed Alfv´en Wave Solar Model (AWSOM)
a physics-based approach and include additional energy
(Sokolov et al. 2013; van der Holst et al. 2014). This
andmomentumsources,aswellasthermodynamicterms
model assumes a physics-based, self-consistent coronal
(heating and cooling), and multi-fluid approach to in-
heating and wind acceleration by Alfv´en waves. Thus, it
clude the separation between ions and electrons (e.g.,
introduces additional energy and momentum terms that
most recent models by Lionello et al. 2014b,a; van der
incorporate these physical processes. The energy spec-
Holst et al. 2014; Usmanov et al. 2016).
trumoftheAlfv´enwavesiscalculatedbyassumingatur-
Despite of this evolution in modeling the solar corona
bulent cascade between two, counter-propagating waves
and wind (and perhaps due to some possible disconnec-
alongthemagneticfieldlines,wheretwoadditionalequa-
tion by the Astrophysics community from solar physics
tions are introduced for these two Alfv´en waves. From
literature) recent models for stellar coronae of solar
thesetwoequations,thetotalenergydissipationandthe
analogs have returned to use the spherical polytropic
Alfv´en waves pressure gradient are then added to the
Parker wind imposed on a potential magnetic field.
MHD momentum and energy equations.
ThesemodelshaveusedavailableZDImapsorlow-order
The AWSOM model accounts for thermodynamic and
idealized magnetic fields to study and scale stellar mass-
radiative transfer processes, such as electron heat con-
lossratesandstellarspindownwithstellarageandrota-
duction and radiative cooling, and could also be run in
tion periods, as well as to characterize the coronae and
two-temperature mode, where the electrons and ions are
winds of planet-hosting stellar systems (e.g., Matt et al.
decoupled (not used here). Unlike the polytropic model,
2012; Vidotto et al. 2014; Matsakos et al. 2015; R´eville
at which the inner boundary is set at the coronal base,
et al. 2015; Strugarek et al. 2015), while they were not
the inner boundary of AWSOM is set at the chromo-
calibrated by solar input parameters and solar magne-
sphere. Finally, the Poynting Flux, which is specified at
togram data. Instead, some of the models have adopted
the base of model, is formulated so that it depends only
an idealized ”fiducial” solar case, which is represented
on the stellar radius square, assuming the observed rela-
bysolarmass,radius,rotationperiod,andadipolemag-
tion between the unsigned magnetic flux and the X-ray
netic field.
flux (Pevtsov et al. 2003). This feature provides a built-
Thegoalofthispaperistodemonstratethatthepoly-
in scaling from the model’s original parametrization for
tropicParkerwindimposedonapotentialfieldstruggles
the Sun to other, Sun-like stars.
to reproduce solar observations. We use high-resolution
In the AWSOM setting, we use a spherical grid, which
solar magnetograms to drive both a polytropic Parker
is stretched in the r coordinate, with the smallest grid
wind MHD model, and a physics-based MHD model for
size being ∆r = 0.015R near the inner boundary, and
the solar corona and solar wind, and compare the out- (cid:12)
the largest grid size being ∆r = 0.65 near the outer
putfromeachmodelwithsolarobservations. Inthenext
boundary. The angular resolution is about two degrees.
section we describe the models and the chosen input pa-
rameters,wepresentanddiscusstheresultsinSection3,
2.3. Models Parameters
and conclude our findings in Section 5.
In order to keep the two models as consistent which
2. MODEL DESCRIPTION eachotheraspossiblewesetbothmodelswiththesame,
magnetogram input data, the same initial conditions for
In this study, we compare the solutions of two types
the three-dimensional magnetic field (a PFSS extrapola-
of MHD models, both performed using the BATS-R-US
tion), the same initial density structure, and the same
MHD code (Powell et al. 1999; T´oth et al. 2012).
initial condition for the wind speed (a Parker solution
with T = 3MK). We also specify the boundary con-
2.1. Thermally-driven Polytropic MHD Model
ditions to be the same in both models, with the coronal
In the first setting of BATS-R-US, the set of ideal numberdensity,n=108 [cm−3],andthecoronaltemper-
MHD equations is solved with no source terms in the ature, T =3MK. We use this high coronal temperature
momentum and energy equations assuming a polytropic to obtain un upper limit of the wind speed in the poly-
gas,wherethevalueofγ isclosetounity(nearlyisother- tropic model. Figure 1 shows the initial conditions for
malgas). Thissolutionprovidessomeaccelerationofthe the number density and wind speed.
wind due to the pressure gradient between the solar sur- Despiteofthedifferentgridgeometriesusedinthetwo
face and space, where the chosen coronal temperature settings, we trust that the comparison presented here
determines the amount of gas expansion. This model is valid due to the fact that we are interested in com-
does not account for any thermodynamic processes in paring the overall wind acceleration via global proper-
3
ties,suchasthemaximumwindvelocityandtotalmass- Figure 3 shows a comparison between SOHO Extreme
loss rate, and the fact that the grid size near both the ultravioletImagineTelescope(EIT)3andYOHKOHSoft
inner and outer boundaries is comparable in both set- X-ray Telescope (SXT)4 full-disk imagesof the Sun, and
tings. For the Polytropic setting, we test three cases synthetic images produced by AWSOM. The EIT bands
with γ =1.01,1.05, and 1.1. We also test how the coro- are 171, 195, and 284 ˚A, and the X-ray images are in-
nal base density affects the solution by performing one tegrated over the 2.4−32 ˚A range. The synthetic im-
case with γ =1.05 and n=107 [cm−3].
ages are obtained by integrating the square of the elec-
tron density, n , multiplied by a response function for
2.4. Input Data e
a particular temperature bin, Λ(T) along the line-of-
In order to drive the two models, we use high-
sight(LOS)throughthethree-dimensionalsolution. The
resolution Michelson Doppler Imager (MDI) solar
response functions are calculated from the CHIANTI
magnetograms obtained from the Stanford Magne-
atomic database (see e.g., Dere et al. 1997; Landi et al.
togram repository (http://hmi.stanford.edu/data/ 2013) in a similar way that the actual observed images
synoptic.html). The magnetogram input data is used are produced, taking into account the particular instru-
in the form of spherical harmonics coefficient list calcu-
mentcalibration(seeDownsetal.2010;Oranetal.2015,
lated up to n=90 (this resolution enables to resolve ac-
for more details about the production of synthetic LOS
tive regions on the Sun). We perform simulations for so-
images in BATS-R-US).
larminimumperiod(quietSun)usingamagnetogramfor
The comparison in Figure 3 shows a very good agree-
Carrington Rotation (CR) 1916 (November-December
mentbetweentheobservationsandtheimagesproduced
1996), and for solar maximum period (active Sun) using
from AWSOM. The location and overall structure of the
a magnetogram for CR 1962 (April-May 2000). In addi-
active regions is well reproduced in the modeled images,
tion,werunthedifferentmodelcasesusingaZDImapof
as well as the location and size of the coronal holes (the
HD189733, which is reproduced from the data published
darkregionsassociatedwiththelowerdensityintheopen
in Fares et al. (2010). While this is a low-resolution
field regions). In the solar minimum case, the active re-
magnetogram, we still extrapolate it up to n = 90 for
gion at the center of the disk is reproduced, along with
constancy, and in order to maintain high-resolution grid
the active region close to the right limb. The active re-
forthePFSS extrapolationsince thisresolutionisdeter- gion in the center is blank in the 171 ˚A band, probably
mined by the order of harmonics.
because the model overheated the area with tempera-
3. RESULTS ture above the one, which responses to that particular
line. For solar maximum, the overall structure of the ac-
Figure 2 shows the results for the wind speed and
tive regions belts is reasonably reproduced, along with
temperature from the polytropic model with γ =
the coronal hole boundaries. We performed similar pro-
1.01,1.05,1.1, and from AWSOM. The wind speed in
cedure to produce synthetic EIT/SXT images from the
the polytropic solutions is quite uniform, with speeds
polytropic models. However, due to the lower coronal
ranging between 100 km s−1 to about 500 km s−1 for
plasma temperature and the low temperature contrast
γ =1.01, 100kms−1 to about 400kms−1 for γ =1.05,
all the LOS images are blank and do not show any fea-
and 100 km s−1 to about 300 km s−1 for γ = 1.1.
tures.
The fast/slow wind contrast is much more visible in the
The usage of ZDI maps to drive MHD models for the
AWSOM solutions, with clear regions of slow wind with
coronae and winds of cool stars is important in the con-
speed of about 300−400 km s−1, and regions of fast
text of stellar spindown and stellar evolution. Table 1
wind with speed above 600kms−1.
summarizes the maximum wind speed, the total mass-
The MHD solutions presented here use single fluid
loss rate, and total angular momentum loss rate of each
plasma,whichassumesthattheiontemperature,T ,and
i of the solutions.
the electron temperature, T , are equal, and that the
e
plasma temperature, T = (T +T )/2 = p/2ρ (where
p i e 4. DISCUSSION
p and ρ are the simulated pressure and density, respec-
The values from Table 1 show that the polytropic
tively). The plasma temperature is half the prescribed
models cannot produce consistent agreement with the
temperature in the initial Parker wind and the coronal
observed properties of the Sun. The solutions with
base temperature. Here we show this reduced tempera-
γ =1.05,1.1cannotproducethefast(above600kms−1)
tureasitrepresentsamorerealisticcoronaltemperature
wind, while the γ = 1.01 solution does produce a faster
(especiallyinthecontextofEUV/X-rayobservationsde-
wind, but it consistently overestimates the observed so-
scribed below).
The temperature plots show, as expected from an lar mass-loss rate of about M˙(cid:12) ≈2−3·10−14 M(cid:12) yr−1
isothermal solution, an almost uniform coronal temper- (Cohen 2011). Reducing the boundary density of the
ature of 1.5MK for the γ =1.01 cases. For the γ =1.05 γ =1.05solutionfrom108 to5·107 [cm−3]doesnotpro-
and γ =1.1 cases, the temperature contrast is more no- duce fast wind as well, while the overestimation of the
table and it follows the density and magnetic field struc- masslossrateisreduced. Reducingtheboundarydensity
ture. In particular, the temperature contrast clearly fol- even further to 107 [cm−3] leads to a much faster wind,
lows the helmet streamers (the close field regions) in the but too low mass-loss rate of 0.4 10−14 M yr−1. The
(cid:12)
solarminimumcase. IntheAWSOMsolutions, thetem- AWSOMsolutionproducesfastwindsabove600kms−1,
perature contrast is very clear, and the temperature is and mass-loss rates of 1.3−1.6 10−14 M yr−1, within
(cid:12)
much higher (over 2MK) in the helmet streamers. The
temperature does not exceed the prescribed, 1.5MK in 3 http://sohodata.nascom.nasa.gov
the polytropic solutions. 4 http://ylstone.physics.montana.edu/
4
a factor of 2 or so from the observed one. The two AW- resultmightbeduetothefactthatthepolytropicmodel
SOM solutions for the two solar epochs produce consis- is set uniformly, and it is driven and constrained exclu-
tentvaluesforthemass-lossandangularmomentumloss sively by the boundary conditions. Thus, the polytropic
rates, while the polytropic solutions slightly differ be- model is set by a small number of global constrains. The
tween solar minimum and solar maximum. Surprisingly, AWSOMmodelontheotherhand,accountsfortheheat-
the polytropic solutions overestimate the mass-loss rate ingandaccelerationateachpointofthedomainindivid-
but underestimate the angular momentum loss rate for ually,andthesourcesandsinksofenergyandmomentum
γ =1.01,1.05 comparing to the AWSOM solutions. The are defined in a local manner, while also taking into ac-
mass-loss rate is comparable between the γ = 1.1 and count more detailed processes. This difference seems to
the AWSOM solutions, but the angular momentum loss makeasignificantdifferenceonthelocationoftheAlfv´en
rate is overestimated by the γ =1.1 solution. point. FollowingLeer&Holzer(1980),itispossiblethat
The trends mentioned above can be explained by the sincetheAlfv´enpointinthepolytropicisratherlow,the
different in size of the Alfv´en surfaces in the different mass flux cannot be regulated much above it, resulting
solutions (shown in Figure 2). For the γ = 1.01,1.05, in an overestimation of the mass loss rate. The resulting
the Alfv´en surface is smaller than that in the AWSOM relatively high density above the Alfv´en point (compar-
solution. Thus, the overall mass-loss is higher due to ing to the AWSOM density at similar heights) prevents
thehigherdensityonthesurface(closertothesolarsur- the acceleration of the plasma to fast speeds as obtained
face),buttheangularmomentumlossrateissmallerdue by the AWSOM model.
totheshorterleverarmthatappliesatorqueonthestar. The results show that the AWSOM model agrees with
The Alfv´en surface is slightly bigger in the γ =1.1 solu- all elements of the observed solar properties – the wind
tionscomparingtotheAWSOMsolutions. Thisexplains speed, coronal temperature and density structure, and
thesimilarmass-lossratebutslightlylargerangularmo- total mass-loss rate (the total observed angular momen-
mentum loss rate. Nevertheless, the wind speeds and tum loss rate is harder to determine). Non of the poly-
temperatures of the γ =1.1 solutions do not agree with tropicsolutionscanprovidesuchaconsistencywithsolar
solar observations. observations, and some of the solutions might even be
Explanation for these trends can also be found in Fig- considered ”unphysical”, due to a maximum wind speed
ure 4, where we show the wind’s radial speed, number that is lower than the minimum observed solar wind
density, and temperature extracted along an open field speed. The choice of the coronal base number density,
lineswiththesamefootpointlocationfromallthediffer- n, in the models is crucial to get both agreement with
entsolutions. Figure4showsthatthewindisaccelerated the observed total mass-loss rate, and with the observed
much faster in the AWSOM solution to higher values, three-dimensional coronal density. Our work suggest
where the polytropic speeds do not exceed 400 km s−1. that this base density should be about n = 108 cm−3,
OnlyintheAWSOMsolution,thetemperaturefirstrises which is lower than the choice in other polytropic mod-
andthenfallsadiabatically,whileitonlyfallsinthepoly- els for stellar coronae (e.g., Vidotto et al. 2015; R´eville
tropic solutions. Finally, the density drops much faster et al. 2015).
in the AWSOM solutions comparing to the polytropic In order to extend this work to the stellar context, we
solutions. Figure 5 shows a similar extraction along the perform similar simulations to the planet-hosting star
same field lines for the Alfv´en Mach number, M , and HD 189733 using ZDI map which is taken from the
A
the local mass-loss rate, dM = ρ u 4πr2, where the in- published data by Fares et al. (2010). In the simula-
i i i i
dex i stands for the particular point along the field line. tion of HD189733, we use the same parameter setting
The plots show that the wind exceeds the Alfv´en speed as in the solar runs. Figure 6 shows the solution for
inthepolytropicsolutionswithγ =1.01,1.054−5solar HD189733, which shows overall similar range of wind
radiilowerthanintheAWSOMsolutions,whereM =1 speeds and coronal temperatures comparing to the so-
A
around r = 14−15R . The wind exceeds the Alfv´en lar results. The figure also shows the three-dimensional
(cid:12)
speed at higher radii for the γ =1.1 polytropic solution coronal magnetic field, colored with temperature con-
comparing to the AWSOM solution. The local mass-loss tours with hotter closed field lines (shown in red) and
ratetrendsaresimilartothoseofthedensity,wheredM colder open filed lines (shown in green/yellow). We also
is 5-10 times higher at the location of M = 1 for the show synthetic EIT/SXT images of HD189733, where
A
polytropicsolutionscomparingtotheAWSOMsolution. a good agreement is obtained between the location of
This explains the overestimation of the mass-loss rate the colder open field lines and the coronal holes in the
for γ = 1.01,1.05 comparing to AWSOM. This trend LOS images. Table 2 shows the global parameters of
of slower decline of the local mass-loss rate is compen- HD189733usingtheγ =1.01polytropicmodelandAW-
satedbythefurtherAlfv´enpointintheγ =1.1solution. SOM. The mass-loss rate is overestimated by the poly-
Therefore, this solution does not overestimate the mass- tropic model comparing to AWSOM, but the angular
lossrateoftheAWSOMsolutionasitaccountsforlower momentum loss rate is comparable. However, just like
mass-loss rate at further distance. in the solar case, the polytropic model cannot produce
Leer & Holzer (1980) found that if the energy deposi- a fast wind. The mass-loss rate for HD189733 is similar
tion occurs below the Alfv´en point it affects mostly the to the solar one in the AWSOM model, but the angular
mass flux, without affecting much the final wind speed. momentumlossrateismuchhigher,probablyduetothe
Alternatively, they found that energy deposition above difference in rotation period (about 12 days comparing
the Alfv´en point affects mostly the final wind speed, to the solar 25 days rotation period).
withoutaffectingmuchthemassflux. Inoursimulations,
the Alfv´en point seems to be closer to the surface in the
5. CONCLUSIONS
polytroic model comparing to the AWSOM model. This
5
Weperformacomparativestudybetweenapolytropic observations. Alternatively, these models can be cali-
wind MHD model and the physics-based AWSOM in or- bratedwithmodelsthatcapturemoredetailedphysicsof
der to test which model agrees better with solar obser- the solar corona (such as the AWSOM model), and that
vations. The AWSOM model produces a clear bi-model canreproducesolarobservationsinaconsistentmanner.
solar wind, with fast wind above 600 km s−1, a good Without such a calibration, the results of the polytropic
agreement (within a factor of 2) with the observed to- models cannot be validated, but they can be wrongly
tal solar mass-loss rate, and a good agreement with the used by others.
coronal temperature and density structure (validated by
solar full-disk LOS observations). The polytropic wind
model,withthreechoicesofthepolytropicindex,γ,fails
toproducesolutionsthatareconsistentwithsolarobser- We thank an unknown referee for his/her comments.
vations. In particular, the polytropic model cannot pro- The work presented here was funded by a NASA Living
duce the fast solar wind speed, and the coronal density withaStargrantnumberNNX16AC11G.Simulationre-
drops too slow in this type of model. This leads to in- sults were obtained using the Space Weather Modeling
consistency with the observed total mass-loss rate, solar Framework, developed by the Center for Space Environ-
wind speed, and the coronal base density. mentModeling,attheUniversityofMichiganwithfund-
Our recommendation is that polytropic models, which ing support from NASA ESS, NASA ESTO-CT, NSF
are used to estimate mass-loss rates and other parame- KDI, and DoD MURI. The simulations were performed
ters of solar analogs, must be first calibrated with solar on the Smithsonian Institute HYDRA cluster.
REFERENCES
Altschuler,M.D.,&Newkirk,G.1969,Sol.Phys.,9,131 Parker,E.N.1958,ApJ,128,664
Cohen,O.2011,MNRAS,417,2592 Pevtsov,A.A.,Fisher,G.H.,Acton,L.W.,Longcope,D.W.,
—.2015,Sol.Phys.,290,2245 Johns-Krull,C.M.,Kankelborg,C.C.,&Metcalf,T.R.2003,
Cohen,O.,Sokolov,I.V.,Roussev,I.I.,Arge,C.N.,Manchester, ApJ,598,1387
W.B.,Gombosi,T.I.,Frazin,R.A.,Park,H.,Butala,M.D., Pneuman,G.W.,&Kopp,R.A.1971,Sol.Phys.,18,258
Kamalabadi,F.,&Velli,M.2007,ApJ,654,L163 Powell,K.G.,Roe,P.L.,Linde,T.J.,Gombosi,T.I.,&de
Dere,K.P.,Landi,E.,Mason,H.E.,MonsignoriFossi,B.C.,& Zeeuw,D.L.1999,JournalofComputationalPhysics,154,284
Young,P.R.1997,A&AS,125 Reiners,A.2012,LivingReviewsinSolarPhysics,9
Donati,J.,&Semel,M.1990,Sol.Phys.,128,227 R´eville,V.,Brun,A.S.,Matt,S.P.,Strugarek,A.,&Pinto,
Downs,C.,Roussev,I.I.,vanderHolst,B.,Lugaz,N.,Sokolov, R.F.2015,ApJ,798,116
I.V.,&Gombosi,T.I.2010,ApJ,712,1219 Riley,P.,Linker,J.A.,Miki´c,Z.,Lionello,R.,Ledvina,S.A.,&
Fares,R.,Donati,J.,Moutou,C.,Jardine,M.M.,Grießmeier,J., Luhmann,J.G.2006,ApJ,653,1510
Zarka,P.,Shkolnik,E.L.,Bohlender,D.,Catala,C.,& Roussev,I.I.,Gombosi,T.I.,Sokolov,I.V.,Velli,M.,
Cameron,A.C.2010,MNRAS,406,409 Manchester,IV,W.,DeZeeuw,D.L.,Liewer,P.,T´oth,G.,&
Feng,X.,Yang,L.,Xiang,C.,Wu,S.T.,Zhou,Y.,&Zhong,D. Luhmann,J.2003,ApJ,595,L57
2010,ApJ,723,300 Sokolov,I.V.,vanderHolst,B.,Oran,R.,Downs,C.,Roussev,
Holzer,T.E.1977,J.Geophys.Res.,82,23 I.I.,Jin,M.,Manchester,IV,W.B.,Evans,R.M.,&
Jacobs,C.,&Poedts,S.2011,AdvancesinSpaceResearch,48, Gombosi,T.I.2013,ApJ,764,23
1958 Strugarek,A.,Brun,A.S.,Matt,S.P.,&R´eville,V.2015,ApJ,
Jardine,M.,Barnes,J.R.,Donati,J.,&CollierCameron,A. 815,111
1999,MNRAS,305,L35 T´oth,G.,vanderHolst,B.,Sokolov,I.V.,DeZeeuw,D.L.,
Kochukhov,O.,Makaganiuk,V.,&Piskunov,N.2010,A&A, Gombosi,T.I.,Fang,F.,Manchester,W.B.,Meng,X.,Najib,
524,A5 D.,Powell,K.G.,Stout,Q.F.,Glocer,A.,Ma,Y.-J.,&
Landi,E.,Young,P.R.,Dere,K.P.,DelZanna,G.,&Mason, Opher,M.2012,JournalofComputationalPhysics,231,870
H.E.2013,ApJ,763,86 Usmanov,A.V.1993,Sol.Phys.,146,377
Leer,E.,&Holzer,T.E.1980,J.Geophys.Res.,85,4681 Usmanov,A.V.,Goldstein,M.L.,Besser,B.P.,&Fritzer,J.M.
Linker,J.A.,&Mikic,Z.1995,ApJ,438,L45 2000,J.Geophys.Res.,105,12675
Linker,J.A.,vanHoven,G.,&Schnack,D.D.1990, Usmanov,A.V.,Goldstein,M.L.,&Matthaeus,W.H.2016,
Geophys.Res.Lett.,17,2281 ApJ,820,17
Lionello,R.,Velli,M.,Downs,C.,Linker,J.A.,&Miki´c,Z. vanderHolst,B.,Sokolov,I.V.,Meng,X.,Jin,M.,Manchester,
2014a,ApJ,796,111 IV,W.B.,To´th,G.,&Gombosi,T.I.2014,ApJ,782,81
Lionello,R.,Velli,M.,Downs,C.,Linker,J.A.,Miki´c,Z.,& Vidotto,A.A.,Fares,R.,Jardine,M.,Moutou,C.,&Donati,
Verdini,A.2014b,ApJ,784,120 J.-F.2015,MNRAS,449,4117
Matsakos,T.,Uribe,A.,&K¨onigl,A.2015,A&A,578,A6 Vidotto,A.A.,Gregory,S.G.,Jardine,M.,Donati,J.F.,Petit,
Matt,S.P.,MacGregor,K.B.,Pinsonneault,M.H.,&Greene, P.,Morin,J.,Folsom,C.P.,Bouvier,J.,Cameron,A.C.,
T.P.2012,ApJ,754,L26 Hussain,G.,Marsden,S.,Waite,I.A.,Fares,R.,Jeffers,S.,&
McComas,D.J.e.a.2007,ReviewsofGeophysics,45,1004 doNascimento,J.D.2014,MNRAS,441,2361
Oran,R.,Landi,E.,vanderHolst,B.,Lepri,S.T.,V´asquez, Wang,Y.-M.,&Sheeley,Jr.,N.R.1990,ApJ,355,726
A.M.,Nuevo,F.A.,Frazin,R.,Manchester,W.,Sokolov,I.,& Wiegelmann,T.,&Sakurai,T.2012,LivingReviewsinSolar
Gombosi,T.I.2015,ApJ,806,55 Physics,9
TABLE 1
Simulations Global Parameters of the Solar Corona
Case CR1916Parker CR1916Parker CR1916Parker CR1962Parker CR1962Parker CR1962Parker CR1916Parker CR1916Parker CR1916AWSOM CR1962AWSOM
γ=1.01 γ=1.05 γ=1.1 γ=1.01 γ=1.05 γ=1.1 γ=1.05n=107 γ=1.05n=5·107
MaximumSpeed[km/s] 460 350 275 518 440 520 1400 367 680 770
MJ˙˙[1[1002−81g4cMm(cid:12)2//sy2r]] 99..51 55..35 11..85 66..88 55..22 20..49 00..54 22..10 11..13 21..76
6
TABLE 2
Simulations Global Parameters of HD 189733
Case Parker γ=1.01 AWSOM
MaximumSpeed[km/s] 500 946
M˙ [10−14M(cid:12)/yr] 4.1 1.6
J˙[1028gcm2/s2] 4.1 1.7
Fig. 1.—Initialdistributionofthecoronalnumberdensity(left),andtheParkerwind(withT=3MK)usedforallsimulatedcases. The
initialplasmatemperatureisTp=1.5MKeverywhere.
Fig. 2.—Solarwindradialspeed(toptwopanels)andcoronaltemperature(bottomtwopanels)solutionsforCR1922andCR1962using
theParkermodelwiththreevaluesofγ (firstthreecolumns),andusingtheAWSOMmodel(rightcolumn). Alsoshownareselectedfield
linesandtheAlfv´ensurfaces(atthetoptwopanels).
7
Fig. 3.—SOHOEIT(171˚A,195˚A,and284˚A)andYOHKOHSXTimagescomparedwithsyntheticimagesproducedfromtheAWSOM
solutions for CR1916 (top two panels) and for CR1962 (bottom two panels). The white arrows mark the location of the coronal holes in
thesyntheticimages. SimilarimagesproducedfromtheParkerwindsolutionsareblankanddonotshowanyfeatures.
8
Fig. 4.— The wind’s radial speed (left), number density (middle), and temperature (right) extracted along an open filed line with the
samefootpointfromthedifferentsolutionsforsolarminimum(top)andsolarmaximum(bottom).
Fig. 5.—Thewind’sAlfv´enicMachnumber,MA (left),andlocalmasslossrate,dM (right)extractedalonganopenfiledlinewiththe
same footpoint from the different solutions for solar minimum (top) and solar maximum (bottom). Dashed red line marks the MA = 1
line.
9
Fig. 6.— Top: the surface radial magnetic field of HD18733 used here to drive the model (left), along with the AWSOM HD189733
solutions for the wind speed (middle) and the temperature (right) displayed in the same manner as in Figure 2. Bottom: the three-
dimensionalcoronalfieldofHD189733(left)coloredwithtemperaturecontourofhotter(red)andcolder(green/yellow)plasma,alongwith
EIT(middle),andSXT(right)syntheticimagesofHD189733. Whitearrowsmarkthecoronalholesassociatedwiththeopen,colderfield
lines.