Evolution of solar-type stellar wind

0.18 MB·English

by  Takeru K. Suzuki

AstronomischeNachrichten,14January2013
Evolution of solar-type stellar wind
TakeruK.Suzuki1,⋆
DepartmentofPhysics,NagoyaUniversity,Furo-cho,Chikusa,Nagoya,Aichi,606-8602,Japan
ReceivedXXXX,acceptedXXXX
PublishedonlineXXXX
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0 Keywords Magnetohydrodynamics(MHD),solarwind,stars:chromospheres,stars:winds,waves,turbulence.
2
Byextendingourself-consistentMHDsimulationsforthesolarwind,westudytheevolutionofstellarwindsofsolar-type

n stars from early main sequence stage to red giant phase. Young solar-type stars are active and the mass loss rates are
a largerbyupto ∼100timesthanthatof thepresent-day sun. Weinvestigatehow thestellarwindisaffectedwhenthe
J magneticfieldstrengthandfluctuationamplitudeatthephotosphereincrease.Whilethemasslossratesensitivelydepends

0 ontheinput energyfromthesurfacebecauseoftheglobal instabilityrelatedtothereflectionandnonlineardissipation
1 ofAlfve´nwaves,itsaturatesat∼100timesbecausemostoftheenergyisusedupfortheradiativelossesratherthanthe
kineticenergyofthewind.Aftertheendofthemainsequencephasewhenthestellarradiusexpandsby∼10times,the
] steadyhotcorona withtemperature 106 K,suddenly disappears. Chromospheric materials,withhot bubblesembedded
R
owingtothermalinstability,directlystreamout;theredgiantwindisnotasteadystreambutstructuredoutflow.
S
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h
p
-
o 1 Introduction hoc ‘coronal base’ or ‘upper chromosphere’ but the pho-
r tosphere where there are much observationalinformation1
t
s Theoriginoftheenergywhichdrivesthesolarwindisbe- (e.g.Fujimura&Tsuneta2009;Matsumoto&Kitai2010).
a
lieved to be in the surfaceconvectionzone.Turbulentmo- Therefore,mass loss rate can be directly determinedas an
[
tionassociatedwiththeconvectionexcitesvariousmodesof outputofthesurfaceproperties.

1 wavesthatpropagateupwardly.Magneticfieldlines,which Thistypeofwindisnotuniquetothesolarwind.Main
v
arealsoaconsequenceofdynamoprocessesinthesurface sequence stars with mass comparable to or less than the
9
5 convectivemotion(e.g.Yoshimura1975;Parker1993),play solar mass possess surface convection zones, and the stel-
3 as a guideforthe upgoingwaves.Amongvarioustypesof larwindsemanatingfromthesestarsbysimilarmechanism
2 waves,theAlfve´nwaveisthemostreliablecandidatewhich (e.g.Cranmer&Saar2011).Observationsofasterospheres
1. transferstheenergyfromthesurfaceconvectionto theup- oflow-masstointermediate-massstarsshowthatthemass
0 perregionwherethesolarwindisacceleratedbecauseitcan lossratesofyoungstarsaremuchlargerupto ∼100times
3 travelalongerdistanceduetotheincompressivenature(e.g. ofthepresentsolarvalue(Woodetal.2002,2005).
1 Alazraki&Couturier1971;Belcher1971;Hollweg1973).
Redgiantstarsalsohavesurfaceconvectionzones.Alfve´n
:
v Alfve´nwaveshavebeenextensivelystudiedinthe con- wavespossiblyplayaroleindrivingthestellarwindsfrom
Xi textofdrivingthesolarwind.ThedissipationofAlfve´n red giantstars (e.g. Hartmann& MacGregor1980;Holzer
waves is a key to understand the acceleration of the solar etal.1983).
r
a wind because it controlsthe energyand momentum trans- Inthispaper,wediscussstellarwindsoriginatingfrom
ferfrom the waves to the gas. Varioustypesof dissipation
surfaceconvectionzones.Inparticularwefocusonhowthe
mechanisms have been investigated such as ion-cyclotron
masslossrateisdeterminedfromthephotosphericproper-
resonance(e.g.Axford&McKenzie1992;Kohletal.1998),
ties,basedonourMHDsimulations.
turbulentcascade(e.g.Matthaeusetal.1996;Verdini&Velli
2007), and the nonlinear mode conversion to compressive
modes (e.g. Kudoh & Shibata 1999) by using steady-state 2 Ourprevious works forthepresent-day
models(e.g.Cranmer&vanBallegooijen2007)ordynam- solarwind
icalsimulations(e.g.Suzuki&Inutsuka2005).
Among others, we have carried out magnetohydrody- Inthissection,webrieflysummarizeourMHDsimulations
namical(MHD)simulationscoveringfromthephotosphere forthesolarwind.In Suzuki& Inutsuka(2005,2006),we
to the sufficiently outer region where the solar wind is al- performedself-consistentone-dimensional(1D)simulations
readyaccelerated(Suzuki&Inutsuka2005,2006;Matsumoto that handle the propagation, reflection, and dissipation of
& Suzuki 2012).One of the greatest advantage of our dy- MHDwavesinanindividualsuper-radiallyopenmagnetic
namicalsimulationsisthattheinnerboundaryisnotanad
1 Recentsteady-statecalculations(e.g.Verdini&Velli2007;Cranmer
⋆ Correspondingauthor:e-mail:[email protected] &vanBallegooijen2007)alsoincludethephotosphere.
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2 TakeruK.Suzuki:Evolutionofstellarwind
fluxtubefromthephotospheretothesolarwindregion.We 1000
tookintoaccountradiativecoolingandthermalconduction
toexaminethecoronalheatingwithoutadhocassumptions
andthreecomponentsofmagneticfieldandvelocitytotreat 100
Alfve´nwaves. We injected transverse fluctuationsfrom the s)
m/
photosphereand run the simulationsuntilthe quasi-steady k
v( 10
states were achieved.A main result of these papersis that
the input of the transverse fluctuations with ∼ 1 km/s at
thephotospherenaturallydrivesthesolarwindwhichisob- Young Sun
1
reference
servedtoday.
1 10
TheAlfve´nwaveswhichareexcitedfromthephotosphere
R/R⊙
aremostlyreflectedbackdownwardbecauseofthechange
oftheAlfve´nspeed(Moore1991),butroughly10%ofthe 10-6
Young Sun
initialPoyntingfluxassociatedwiththeAlfve´nwavespene- 10-8 reference
tratestothecoronaandcontributestotheheatingoftheso- 10-10
larwind.ThemainchannelofthedissipationoftheAlfve´n
10-12
wavesisthegenerationofcompressivewaves,particularly 3cm) 10-14
slowMHDwaves(Kudoh&Shibata1999).Thesteepening g/
ρ( 10-16
of the wave fronts leads to the shock dissipation of these
excitedcompressivewaves.Ingeneral,however,inthe1D 10-18
simulationstheshockdissipationtendstobeoverestimated 10-20
becausethewavesareconfinedintheindividualfluxtubes 10-22
10-4 10-3 10-2 10-1 100 101
withoutleakage.
(R-R⊙)/R⊙
InMatstumoto&Suzuki(2012),weextendedtotwodi-
mensional(2D) simulations. The biggest differenceis that
we can treat the leakage of the waves to neighboring flux 106
tubes. Cascading Alfve´nicturbulence can be also handled,
althoughit isrestrictedto the 2Dspace. Inthe 2D simula-
tion, the effect of compressive waves is suppressed, while K)105
theturbulentcascadebecomescomparablyimportantinthe T(
dissipationoftheAlfve´nwaves.Theoveralldissipationrate
of the Alfve´nwavesis comparableto that of the 1D cases, 104
andasaresult,the1Dand2Dsimulationsgivesimilarmass Young Sun
reference
lossratesandterminalvelocities.
10-4 10-3 10-2 10-1 100 101
In the following sections, we extend these simulations (R-R⊙)/R⊙
from the present-day solar wind to more active solar-type
stars (§3)and red giantstars (§4).Because the 2D and 1D Fig.1 Comparisonofthewindstructures.Thesolidlines
simulationsyieldsimilarglobalpropertiesofthewinds,we arethewindstructurefortheactivecase (seetext)andthe
usethe1Dsimulationstosavecomputationaltime. dashed lines are the wind structure of the reference case.
From top to bottom,velocity,density, and temperatureare
displayed.
3 Mass lossfrom youngactivesolar-type
stars
photosphereandasuper-radialexpansionfactor f = 1000
Youngsolar-typestarsaregenerallyveryactive.TheX-ray tomatchrecentHINODEobservations(Tsunetaetal.2009;
fluxisupto∼1000timeslargerthanthepresentSun(e.g. Ito et al. 2010), and inject fluctuations, δv = 1.4 km s−1
Gu¨del 2004), and the transition region flux is also much fromthephotosphere.Thisreferencecase wellreproduces
larger (Ayres 1997). Observation of young main sequence theaverageglobalpropertiesofthepresent-daysolarwind.
starsshowverystrongmagneticfieldswithanorderofkG Weperformmorethan30simulationrunswithdifferentB0,
orevenlarger(e.g.,Donati&CollierCameron1997;Saar& f,andδv.
Brandenburg1999).Themasslossrateisalsomuchhigher Figure1 showsthe stellarwindstructurewhich adopts
butseemssaturatedaround∼100timesofthepresentsolar B0 = 2kG,δv = 2.8kms−1,andf = 1000(solidlines,
level(Woodetal.2002;2005). labeled as ‘Young Sun’) in comparison with the reference
Inthissection,weinvestigatehowthesolaratmosphere case (dashed lines). This active case gives the mass loss
reactstoincreasesofmagneticfieldstrengthandfluctuation rate,M˙ =4×10−13M⊙/yr,whichis20timeslargerthan
amplitudeatthephotoshere.Asthereferencecasewesetup 2×10−14 M⊙/yrobtainedfromthereferencecase(≈the
a magnetic flux tube with field strength B0 = 1 kG at the presentvalue).SincetheinjectedPoyntingflux(∝ B0δv2)
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ANheaderwillbeprovidedbythepublisher 3
0.1 1
Q (cid:17)3
(cid:17)3
2M/dt)v/2Lwave 0.01 (cid:17)(cid:17)(cid:17)(cid:17)(cid:17) Qs L/LUV+Xwave 0 0.0.11 (cid:17)(cid:17)(cid:17)(cid:17)(cid:17)
d
(
0.001 0.001
1028 1029 1030 1031 1032 1028 1029 1030 1031 1032
L (erg/s) L (erg/s)
wave wave
Fig.2 Energeticsofstellarwindderivedfromthesimulations;eachdatapointindicateseachrun.Theleftpanelshows
thefractionsofthekineticenergyfluxesonthetotalinputPoyntingfluxesfromthephotospheres,andtherightpanelshows
thefractionsofthetotalradiativelossesfromthetransitionregionsandcoronaeonthetotalinputPoyntingfluxes.
in the active case is only 8 times larger,the mass loss rate 100
quite sensitively depends on the energy input. This is be-
cause of the global instability involved with the reflection (cid:0)(cid:18) PPPq
andnonlineardissipationofAlfve´nwaves(seeSuzuki2012 un) 10 (cid:0)(cid:0)
S
fordetails). nt (cid:0)
e
The location of the transition region in the active case es 1 (cid:0)
pr (cid:0)
isat≈ 1.1R⊙,whichismuchhigherthantheheightofthe dt(/
transition region of the reference case (≈ 1.003R⊙). This dM/ 0.1
is becausein theactivecase morematerialis liftedupdue
tothelargerenergyinjectionfromthephotosphereandthe
temperature cannot increase easily owing to the larger ra- 0.01
103 104 105 106 107 108
diativecooling.Hence,thechromosphereextendstohigher F (erg/cm2s)
TR+Corona
altitude in the active case. Interestinglyenough,the obser-
vation of a young solar-like star, CoRot-2a, by using the Fig.3 Mass loss rate normalized by the present solar
Rossiter-McLaughlin effect shows that this star possesses valueonradiativefluxfromtransitionregionandcorona.
anextendedchromosphereofupto1.16timesofthestellar
radius(Czeslaetal.2012).
al.(2002,2005).AsexpectedfromFig.2,themasslossrate
Figure2displaysthefractionsofthekineticenergyflux
ofthe stellarwind,M˙ v2, (left)andtheradiativelossfrom ispositivelycorrelatedwithradiativefluxinitially,whileit
2
eventually saturates, or even slightly decreases. The main
the transitionregionandcorona(right)ofeachrunagainst
reasonofthesaturationisthatmostoftheinputenergiesare
thetotalinjectedPoyntingenergyassociatedwithAlfve´n
exhaustedfortheradiativelossesbesidesreflectioninthese
waves,Lwave,fromthephotosphere.Bothpanelsshowlarge saturatedcases.Namely,theincreaseof M˙ ismainlydone
scatters in the vertical direction, reflecting varieties of f.
bytheincreaseofdensity,whichenhancesradiativelosses.
Thesumsofthesetwofractionsaremuchlessthanunityin
Finally, no more energy remains for the kinetic energy of
alltheruns,becausemostoftheinputenergiesarereflected
the stellar wind. We discuss this saturation mechanism in
backdownward.
more detail in a forthcomingpaper (Suzukiet al. 2012, in
Theleftpanelshowsthatthefractionofthekineticen-
preparation).
ergy flux initially increases with increasing input energy;
theincreaseofthekineticenergyofthestellarwindismore
rapidthanlinearontheinputenergy,whichisrelatedwith 4 Masslossfrom redgiants
the global instability owing to the reflection and nonlin-
eardissipationofAlfve´nwavesasexplainedabove(Suzuki Afterthe hydrogenin the core is exhausted,a star evolves
2012).However,iteventuallysaturatesanddecreasesonin- to a red giant stage. Because red giant stars have surface
creasingLwave.Ontheotherhand,theradiativelossshows convectionzones,itisexpectedthatthefluctuationsthesur-
saturationaswellbuttheoverturningtrendisnotsodistinc- faceswouldgiveasignificantcontributiontothestellarwinds.
tive. On the other hand, the expansion of the radius largely af-
Combiningthesetwopanels,wecangettherelationbe- fectsthedynamicsthroughthechangeofthesurfacegravity.
tween radiativefluxandmassloss rate(Fig.3),whichcan We have carriedoutMHD simulationsforredgiantwinds
bedirectlycomparedwiththefigurespresentedinWoodet (Suzuki2007),ofwhichwebrieflysummarizetheresults.
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4 TakeruK.Suzuki:Evolutionofstellarwind
because the onset locations of the winds are around sev-
eral stellar radii (Harper et al.2009). Through the stellar
evolution, the mass loss rate increases due to the increase
of the stellar surface (∝ R2) and the increase of the den-
sity.Fromthemainsequencestartothereadgiantstarwith
R⋆ =31R⊙,themasslossrateincreases105−106times.
Acknowledgements. Thiswork wassupported inpart byGrants-
in-AidforScientificResearchfromtheMEXTofJapan,22864006.
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The densities of the winds increase with stellar evolu-
tion due to the decrease of the surface gravity. The wind
velocitiesaremuchsmallerthanthesurfaceescapespeeds,
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