Modeling magnetohydrodynamics and non equilibrium SoHO/UVCS line emission of CME shocks

0.36 MB·English

by  P. Pagano

Astronomy&Astrophysicsmanuscriptno.CMEshockpaper c ESO2008
(cid:13)
February2,2008
Modeling magnetohydrodynamics and non equilibrium
SoHO/UVCS line emission of CME shocks
P.Pagano1,2,3,J.C.Raymond2,F.Reale1,3,andS.Orlando3
1 DipartimentodiScienzeFisicheedAstronomiche,SezionediAstronomia,Universita`diPalermo,PiazzadelParlamento1,90134
8 Palermo,Italy
0 2 Harvard-SmithsonianCenterforAstrophysics,60GardenStreet,Cambridge,MA02138
0 3 INAF-OsservatorioAstronomicodiPalermo,PiazzadelParlamento1,90134Palermo,Italy
2
16november2007

n
a ABSTRACT
J

7 Aims.WeprovideaguidelinetointerprettheUVCSemissionlines(inparticularOVIandSiXII)duringshockwavepropagationin
1 theoutersolarcorona.
Methods.Weuseanumerical MHDmodel performingasetof simulationsof shockwavesgenerated inthecorona andfromthe

] resultwecomputetheplasmaemissionfortheOVIandSiXIIincludingtheeffectsofNEI.Weanalyzetheradiativeandspectral
h
propertiesofourmodelwiththesupportofadetailedradiationmodelincludingDopplerdimmingandananalyticalmodelforshocks,
p and,finally,wesynthesizetheexpectedOVI1032A˚ lineprofile.
- Results.WeexplainseveralspectralfeaturesoftheobservationsliketheabsenceofdiscontinuitiesintheOVIemissionduringthe
o
shockpassage,thebrighteningofSiXIIemissionandthewidthofthelines.Weuseourmodelalsotogiveverysimpleandgeneral
r
t predictionsforthestrengthofthelinewingsduetotheionsshockheatingandonthelineshapeforLimbCMEsorHaloCMEs.
s
Conclusions.Theemissioncomingfrompost-shockregioninthesolarcoronaroughlyagreeswiththeemissionfromasimpleplanar
a
[ andadiabaticshock,buttheeffectofthermalconductionandthemagneticfieldmaybeimportantdependingontheeventparameters.
DopplerdimmingsignificantlyinfluencestheOVIemissionwhileSiXIIlinebrightensmainlybecauseoftheshockcompression.

1 SignificantshockheatingisresponsibleforthewideandfaintcomponentoftheOVIlineusuallyobservedwhichmaybetakenasa
v shocksignatureinthesolarcorona.
5
Keywords.CME;MHD;SolarCorona
0
7
2
. 1. Introduction that they are shocks withoutthe supportof deeper diagnostics.
1
0 ForinstanceVourlidasetal.(2003)supporttheidentificationof
8 Strong shock waves are expectedto developfromfast Coronal shocksinSoHO/LASCOobservationsthankstoanMHDmodel
0 Mass Ejections (CME). According to the most popular idea where a shock was needed to fit the observational constraints.
: aboutthe structure of CMEs, an expandingmagnetic flux rope Sometimes the shock is detected without uncertainness by the
v
propagatesin the solar corona and this leads to the creation of presence of a Type II radio burst that gives a reliable estima-
i
X theCMEleadingedgeandtothecreationofshocks,aswell.Itis tion of the post-shock density, but not of speed and location.
r widelyacceptedthatthefrontsidehaloCMEsarestronglycor- However,spectralanalysisisthemostgeneralwaytodetectand
a related with geomagnetic disturbances (Brueckneretal. 1998; describetheshockinthesolarcorona.
Caneetal. 2000; Gopalswamyetal. 2000; Webbetal. 2000; The UltraViolet Coronograph Spectrometer (UVCS)
Zhangetal. 2003). Thus, the detection of CME related shocks (Kohletal. 1995) on board the Solar and Heliospheric
is a crucialtopicin space weatherresearch.However,it is also Observatory (SoHO) (Domingo&Poland 1988) gave a strong
a difficultproblem,because it cannotbe confirmedfrom white impulse to this research topic. Ciaravellaetal. (2006) pointed
light images alone. A further problem is to describe the shock out the correlation between the shocks and several spectral
and figure out whether the environment or the CME core ex- properties of the post-shock emission. Overall, they found
pansion determine the shock wave properties, since they influ- that the shock emission is comparable or weaker than the
encetheaccelerationofenergeticparticlesastheshockevolves, backgroundcoronalemission.TheOVI1032A˚ lineisusually
whichisagainakeyquestioninspaceweatherresearch. broad, but its intensity does not increase. Instead the Si XII
All proposed hypothesesagree that the shock wave, when- brightens significantly and it is common that the intensity of
everexists,staysontheleadingedgeoftheCME(Hundhausen thelinedoubles,andtheLyαfades.Thisgeneraldescriptionis
1987;Wagner&MacQueen1983)thoughitmaybetoofaintto based on several studies made on different CME events which
beeasilyseen.Theleadingedge,asobservedinwhitelightim- reachedsimilar conclusion.For instance, broadO VI lines and
ages, could be either plasma compressed by a shock or denser more intense Si XII line have been observed in 2000 June 28
material in magnetic loops ejected from near the solar surface. (Ciaravellaetal. 2005), 2000 September 12 (Suleimanetal.
Several shocks have been detected during CME front propa- 2005)and2000October24(Ciaravellaetal.2006)event.Inthe
gationwith differentdiagnostics(Ciaravellaetal. 2006). Sharp shock related to the CME event on June 11, 1998 the derived
edges in white light images have been taken as evidence of compression and ionization appear modest with respect to the
shocks at the CME leading edge, but it is impossible to prove inferred shock strength (Raymondetal. 2000). Signatures of
2 P.Paganoetal.:ModelingmagnetohydrodynamicsandnonequilibriumSoHO/UVCSlineemissionofCMEshocks
shockhavebeenobservedduringthe2000March3CMEevent aim,weneedtomodeltheevolutionofboththeplasmaandthe
(Mancusoetal. 2002). They pointed out that the Oxygen tem- magnetic field and, to computeemission, also of the ion abun-
perature(T )wasmuchlargerthantheprotontemperature(T ) dances.
O p
andthatthecoronalOVIemissionduringashockiswellfitted We consider the solar gravity, the radiative losses (e.g.
by a narrow component which comes from the quiet corona Raymond&Smith(1977),aphenomenologicalcoronalheating
andabroadcomponentwhichcomesfromtheshockedplasma. termandthefield-orientedthermalconduction(Spitzer1962)as
Actually,particlesofdifferentspeciescanbeheatedbydifferent importantphysicaleffects.ThefullMHDequationwesolveare:
amounts in a collision-less shock, since there is not enough
∂ρ
time for Coulomb collisions to bring the temperatures into +∇ (ρv)=0 (1)
equilibrium.Observationsofshocksinthesolarwindgenerally ∂t ·
show that electrons are weakly heated (Schwartzetal. 2000) ∂ρv (∇ B) B
and that minor ions of mass m have higher temperaturesthan +∇ (ρvv)= p+ × × +ρg (2)
i ∂t · −∇ 4π
protons, perhaps as high as T = (m /m )T (Korrecketal.
i i p p
2007). Observations of supernova remnants instead show ∂u
Te Ti forrelativelyslowshocksandTe Ti forfastshocks ∂t +∇·[(u+p)v]=ρg·v−n2P(T)+H0−∇·Fc (3)
∼ ≪
(Ghavamianetal. 2001) and T T for slow shocks and
TO 8Tp fora fast one(RaymOond∼etapl.2003b;Korrecketal. ∂B =∇ (v B) (4)
2004∼). ∂t × ×
Since the whole sample of events amounts to 10 shocks 1
∼ u= ρv2+E (5)
linked to CMEs and only few of them have good enough data
2
to do detailed analysis, questions aboutthe line emission from
shockedplasmaarestillopen.Overallitisimportanttolinkall p=(γ 1)E (6)
−
the observed features listed above with models, at least quali-
withtheconstraintgivenby:
tatively. Because of the large number of parameters that could
characterize the evolution of a CME it is quite impossible and B =0 (7)
∇·
even useless to model quantitatively one single event. On the
where t is the time, ρ is the density, n the number density, p
otherhand,manyrecenteffortshavefocusedonthetheoretical
the thermal pressure, T the temperature (T = T = T in
modelingofthesolarcorona,withthegoaltoproperlydescribe e p i
thismodel),v the plasmaflow speed,u the totalenergy(inter-
the processes that lead to eruption and activity in the corona.
We think that modeling should be linked as much as possible nalenergyE pluskinetic),g thegravityacceleration,Fc isthe
conductive flux according to Spitzer (1962) and corrected for
to observables, because several assumptions lay between the
the saturation effect (Cowie&McKee 1977), P(T) the radia-
physics that the model describes and the actual emission that
tivelossesperunitemissionmeasure(Raymond&Smith1977),
couldbeinferredfromthatmodel.Asanimmediateimplication,
H = n2P(T )isaconstantheatingtermwhoseonlyroleisto
any attempt to model observables in shock wave propagation 0 0 0
keepsteadytheunperturbedcoronabybalancingexactlyitsra-
cannot neglect that the highly dynamic plasma can be easily
diative losses, with n (r) = n(r,t = 0) and T = T(t = 0)
in Non Equilibrium of Ionization (NEI) (Spadaroetal. 1994), 0 0
(Paganoetal. 2007). We do not include plasma resistivity ef-
since the time scales are too short to allow the ionization state
fects, which can be considered globally negligible on large
oftheplasmatorelax.
scalesinthesolarcorona.
Theaimofthisworkistofindunambiguousspectralshocksig-
We solve numerically the set of the ideal full MHD
natures,andto provideaguidefortheinterpretationofgeneral
equations with the MHD module of the advanced par-
featuresthatcouldappearinUVCSobservations.Ourapproach
allel FLASH code, basically developed by the ASC /
is to model in detail and diagnose the propagation of a shock
Alliance Center for Astrophysical Thermonuclear Flashes in
wave generated from a supersonic fragment of a CME in the
Chicago (Fryxelletal. 2000), with Adaptive Mesh Refinement
magnetizedcorona.WeuseanumericalMagnetohydrodynamic
(PARAMESH, MacNeiceetal. 2000). We include the FLASH
(MHD) model (Paganoetal. 2007) to describe the MHD
module for the anisotropic thermal conduction (Spitzer 1962)
evolutionandfromthe resultwe computethe plasma emission
implementedbyPaganoetal.(2007),andimprovedforthesat-
fortheOVIandSiXIIlineswhicharediagnosticallyimportant
urationeffectsbyOrlandoetal.(2005)
in UVCS observations of shock waves including the effects
Wecomputetheionizationstateoftheplasmafromthehis-
of NEI. As a guideline to interpret the results, we support the
tory and distribution of v, n and T obtained with the MHD
study with a simple analytical model of a Rankine-Hugoniot e
model.ThisisdoneasynchronouslyoftheMHDcomputations;
planarandadiabatic shockwave.From the radiationmodelwe
we can do this safely because we sample the solution on time
synthesizeobservablequantities,suchastheprofilesofspectral
bins( 25s)shorterthanatypicalUVCSexposuretime( 120
lines.
∼ ∼
s) and than the shock passage time scales ( 500 s for a scale
In Section 2 we describe our model, Sec.3 includes the results
length of 5 109 cm and a typical sound∼speed of 107 cm/s)
discussedinSec.4.
×
and because we do not expect effects from small scale mix-
ing by turbulent motion in the presence of the magnetic field
2. Themodel andofthethermalconduction.Theionizationstateiscomputed
considering the lagrangian transport of ions, and the ioniza-
We use a full MHD model of the solar corona tuned to inves-
tion/recombination processes, i.e. we are not assuming ioniza-
tigate the coronalemission visible from UVCS during a shock
tionequilibriumduringthesimulation.Thevariationoftheion-
wave propagation.We modela supersonicCME core fragment
izationfractionofeachionspeciesisgovernedbytheequation:
moving upward in a magnetohydrostatic solar corona. During
itspropagation,thefastcloudgeneratesaseriesofshockwaves, ∂nZ
and we study how the waves perturb the quiet corona. To this ∂ti =−∇·nZi v+ne[nZi+1αZi+1+nZi−1qiZ−1−nZi (αZi +qiZ)](8)
P.Paganoetal.:ModelingmagnetohydrodynamicsandnonequilibriumSoHO/UVCSlineemissionofCMEshocks 3
wherenZisthedensityoftheelementZinthei-thionization thecentralaxis.Onthisbasicconfiguration,webuildvariousse-
i
levelinunitsofcm−3,n istheelectronnumberdensityandαZ tupsof the otherparameterandinitialconditions.As reference
e i
and qZ are respectively the recombinationand ionization rates setup,theCMEfragmenthasaninitialvelocityvc =1000km/s
i
fortheelementZinthei-thionizationlevelinunitsofcm3/s. and is 10 times denser than the surroundings(i.e. nc/n0 = 10
The ionization state evolution explicitly depends on elec- andtemperature:Tc =1.5 105K).Theintensityofthedipole
×
tron and ion densities and the bulk velocity of the plasma, and ischosentogiveβ 1attheinitialheightoftheCMEfragment
∼
implicitly on the temperature through αZ and qZ. In Eq. (8) center.Theothersimulationsthatwepresentdifferonlyforone
i i
the first term on the right hand side is the advection term, and parameter, and in particular, β = 10, β = 0.1, nc/n0 = 4,
the second is the variation due to ionization and recombina- vc =700km/s
tion processes that take place at the temperature of the plasma Simulationsβ01 and β10 are devotedto investigatethe ef-
element. We solve this equation numerically for each relevant fectofthemagneticfield ontheglobalstructureofthe shocks,
species and ions, assuming initial ionization equilibrium, and i.e. whether a stronger (weaker) magnetic field could lead to
treating explicitly the advection term with a Godunov scheme less (more) compression and, ultimately, to less (more) emis-
(Godunov1959)andimplicitlythesecondtermwithionization sion. Simulation nc4 and v700 explore situations in which the
ratesgivenbyCox&Raymond(1985)andrecombinationones initialshockingfragmentcarrieslessmomentum(lessmassthe
byBryansetal.(2006).Theevolutionoftheelectrondensityand former,lessvelocitythelatter).
oftheplasmamotionthroughoutthedomainaretakenfromthe Thesimulationsareallperformedina3-Dcartesiandomain
MHD modelresults (sampled every25 s). A Godunovscheme (x,y,z) that is (8 8 16) 1010 cm large, for the duration
× × ×
is applied to compute the ion transfer through the cells due to neededbytheshocktopropagatewellabove2R⊙ whichisthe
thebulkmotionoftheplasma,andtheionizationfractionisup- height where we put a hypothetical UVCS observations. The
datedconsideringtheionizingandrecombiningcollisions(sec- timeis 1000swhentheinitialvelocityofthefragmentis1000
∼
ondterminEq.(8))betweenelectronsandions. km/sand 1500swhenitis700km/s.
∼
Theintensityofthelinesiscomputedasthesumofthecolli-
sional(Ic)andradiative(Ir)contributions(seetheAppendixA 3. Results
formoredetails):
We now discuss our reference simulation and later the others
I =I (n ,nZ,T)+I (nZ,T,v) (9) which differ from it by just one parameter of the initial condi-
c e i r i
tions(i.e.:β,initialvelocityofthecloud,densityofthecloud).
Wemodeltheevolutionofadensecloudmovingupwardsu-
personically in the outer coronal atmosphere as shown in Fig.
3.1. Thereferencesimulation
1. The center of the cloud (i.e. the CME fragment) is initially
In Fig. 2 the density and the temperature of the plasma after
1000 s of evolution are shown (for the reference simulation).
Log10(Temperature) Log10(Density number)
In all the simulations shock fronts depart from the upper part
Time = 0 s
12 12 of the high speed cloud. Here we address the shock evolution
only,andnotthecloudevolution.Thecloudcontinuouslyshocks
thesurroundingmedium,sinceitsspeedremainsfasterthanthe
10 10
soundspeed(atleastduringthetimeofoursimulation),itcools
down during the motion because of the radiative losses and its
8 8 corebecomesthermallyunstable.
m) m)
10 z (10 c 6 10 z (10 c 6 Log10(Temperature) Log10(Density number)
Time = 1000 s
12 12
4 4
10 10
2 2
8 8
-5 -4 -3 -2 -1 1 2 3 4 5
x (1010 cm) x (1010 cm)
m) m)
4.00 5.00 6.00 7.00 6.00 6.50 7.00 7.50 8.00 8.50 10 z (10 c 6 10 z (10 c 6
Fig.1.Initialconditionofthemodel.Thepanelshowsasection
4 4
aty =0ofthetemperatureanddensitynumberspatialdistribu-
tions.Thethemagneticfieldlinesarealsoshown(whitelines).
2 2
positionedat0.15R⊙abovethephotosphereandhasanupward
-5 -4 -3 -2 -1 1 2 3 4 5
initialvelocity.Itisdenserthanthesurroundings,butinpressure x (1010 cm) x (1010 cm)
equilibriumwith them (i.e. colder than the surroundingsatmo-
sphere).The atmosphereis isothermalat 1.5MK and stratified 4.00 5.00 6.00 7.00 6.00 6.50 7.00 7.50 8.00 8.50
by gravity in such a way to have n = 108cm−3 at the initial Fig.2.AsinFig.1,butatt=1000sinthereferencesimulation.
CMEfragmentcenterheight.Thebackgroundmagneticfieldis
modeledasadipolelayinginthecenteroftheSunandseenfrom
4 P.Paganoetal.:ModelingmagnetohydrodynamicsandnonequilibriumSoHO/UVCSlineemissionofCMEshocks
Table1.Numericalsimulations
Name β nc/n0 vc(km/s)
REF 1 10 1000
β01 0.1 10 1000
β10 10 10 1000
nc4 1 4 1000
v700 1 10 700
3.1.1. TheShock
In thereferencesimulation,the shockpropagatesradiallyfrom
thecloud.Severalshockfrontsaregeneratedduringthepassage
of the cloud and finally they merge in a bow shock edge ex-
pandingintime.After1000sofevolutionthecloudhasreached
the height of 2.5R⊙ and the producedshock edge has trav-
∼
eled 0.4R⊙ from the originating cloud. Behind the edge of
∼
the shock wave, the structure of the shocked gas is due to the
interactionandsuperpositionofthedifferentshockwaves.
Since this work addresses the signatures of a shock transi-
tionduringaCME,wefocusourattentionontheshockingedge
whichdrivesthedisturbanceofthequietoutercoronaratherthan
ontheinnerstructureoftheshock.Thecloserinxdirectionthe
shockedplasmaistotheshockingcloud,thelesstheshockhas
propagatedinthecorona,thestrongeristheshock,andthemore
thebulkvelocityofthepost-shockplasmaisperpendiculartothe
solarsurface.Thecloudvelocityremainssuperalfve´nicandthe
magneticfieldisshockedaswell.Forthisreasonthepost-shock
magneticfieldtendstobeparalleltotheshockfront.Theplasma
β isrelativelyhighintheuppercorona( 15inoursimulation
∼
at2R⊙),andsothemagneticfieldpressureisnegligiblewithre-
specttotheplasmacompression,whilethemagneticfieldorien- Fig.3. Evolution of the emission of O VI (upperpanel) and Si
tationinfluencesthethermalpropertiesoftheshockand,ascon- XII (lower panel) expected along an UVCS slit positioned at
sequence,theionizationstate.Sincetheshockedmagneticfield 2R⊙integratedalongthelineofsight.Theevolutionissampled
isparalleltotheshockfrontwhichishotterthanthesurrounding every25s.Thewhitelinesmarktheshockedge.
atmosphere, the thermal conduction toward pre-shock regions
is ineffectiveand the shockedplasma doesnotcooldown.The
shockheatstheplasma,theionizationisenhancedandtheion- peaktemperaturefortheOVI,theemissionbecomesfainterand
izationstatechanges.Immediatelybehindtheshocktheplasma fainterbehindtheshockwhiletheionsapproachequilibrium,i.e.
isfarfromtheionizationequilibriumattheshocktemperature, atlatertime.TheshockheatingmakestheSiXIIabundancein-
and the ionization equilibrium is approached farther from the crease, because the Si XII peak temperature is higher than the
shockfront,wherethetemperaturehasbeennolongerchanging temperatureofthequietatmosphere(1.5MK).Becauseofthis,
muchandtheplasmaisslowlyrelaxing. alargefractionoftheSiXIIemissioncomesfromtheinnerpart
oftheshockedregion.
As mentionedabove,fordiagnostic purposes,we focusthe
3.1.2. OVIandSiXIIshockemission
analysisatacharacteristicheightfortheUVCSobservationsand
WeapplyourgeneralradiationmodeltoOVIandSiXIIlines, forshockformation(Raymondetal.2003a),i.e.2R⊙.Itshould
that are importantfor the CME shock front diagnostics. Fig. 3 be noted,that, in spite of the formationof the shock,the CME
shows the evolution of the line intensity across the UVCS slit may either accelerate or decelerate that far from the solar sur-
computedfrom the full MHD simulation and consideringnon- faceandthatlongaftertheignitionphase.Inordertoinvestigate
equilibriumofionization.Theintensityjumpacrosstheshockis the role of the non-equilibriumionization state, of the thermal
sharperintheSiXIIlinethanintheOVIline.Ourmodelshows conduction,andofthemagneticfield,wecomparetheintensity
that the shocked plasma is far from ionization equilibrium; in oftheplasmabehindtheshockobtainedfromtheMHDsimula-
fact,theheatingtimeduetotheshockismuchshorterthanthe tionwith the onepredictedbya simple modelofadiabatic and
ionizationequilibriumtimeandthereisnotenoughtimeforthe locally planar shock according to the Rankine-Hugoniot jump
ionizationstate to changeas soonas theshockhasreachedthe relations of density, temperature and velocity as a function of
plasma.Forinstance,theionizationtimefortheOVIatthepost- the post-shockvelocityof the plasma.For furtherdetailsabout
shock temperature (T 3 MK) is roughly τ 400 s (see this analytical model see the Appendix B. This simple model
eq
∼ ∼
AppendixB),significantlylongerthantheheatingtime.Wecan isa roughapproximationforourshocks,since theshockisnot
estimate the actual heating time (τ ) from the speed of the propagatingin a very low beta plasma (neglectthe momentum
heat
shock and the gyroradius of the particles. Considering a mag- fluxduetotheLorentzforce),thethermalconductionismostly
neticfieldofB 0.5G,atemperatureof 2MKandtheve- inhibitedbythemagneticfield(adiabaticplasma)andtheshock
locityofthesho∼ck( 500km/s)wegetτ∼ 10−5s.Since heatingismuchfasterthantheplasmaionizationandrecombina-
heat
∼ ∼
thetemperatureintheregionbehindtheshockishigherthanthe tion(theionizationfractiondoesnotchangeattheshockfront).
P.Paganoetal.:ModelingmagnetohydrodynamicsandnonequilibriumSoHO/UVCSlineemissionofCMEshocks 5
Significantdeparturesfromthisapproximationmaybesignature
thatsomeoftheassumptionslistedabovedonothold. 2.0
Tocomparethedetailedsimulationwiththeanalyticalmodel
so asto evaluatethe deviations,in Fig.4 we plotthe ratiosbe-
tween the post-shocked and pre-shocked density and tempera- 1.5
tureasfunctionofthepost-shockvelocityoftheplasmaforthe mission
MqabnuyHdawnDttheimitstieiepmseliurnfaloeatrustiritoenhnejFuaismngidm.p3)uf.oalarretitohcneoma(inp.aeul.tyeptdiocasattl-tsmhheoocdshkeol.vcTeklhoeecdigptyeo,,smtd-esanhrskoiectdyk mission over quiet e1.0
VI e
O
0.5
6
0.0
0 1 2 3 4
Post-shock plasma velocity (107 cm/s)
T/T0
4 n/n0 20
15
2 mission over quiet emission10
0 XII e
0 1 Post-sh2ock plasma velocity (1307 cm/s) 4 5 Si 5
Fig.4. Ratio between post-shock and pre-shock temperature
(solid lines) and density (dashed) as a function of the post-
0
shock plasma velocity. Thick lines mark results obtained from 0 1 2 3 4
Post-shock plasma velocity (107 cm/s)
theMHDsimulation,andthinlinesfromananalyticalmodelof
Rankine-Hugoniotrelations Fig.5.Ratiobetweenpost-shockandpre-shockemissioninthe
onanadiabaticandplanarshock. OVI(upperpanel)andSiXII(lowerpanel)linesasafunction
ofthepost-shockplasmavelocity.ResultsfromtheMHDsimu-
lation(thicklines)andfromtheanalyticalmodel(thinlines)are
The front of the bow shock begins to cross the UVCS slit
shown. In the latter case we consider approximated ionization
field of view at 675 s. UVCS detects first the upper and
∼ stateformulaeassumingτ = 0(solidline)orτ = 100(dashed
fastestpartofthisfrontandlatertheflanks.Asmentionedabove,
line)andourradiationmodel(seeAppendixA).
the shock strength decreases in time duringthe crossing of the
UVCS slit field of view and at t=700 s the plasma is acceler-
atedto 500km/sbecauseoftheshockandto 250km/sat
∼ ∼
t = 1000s(seeFig.4).AsshowninFig.4thedensityjumpin
thesimulationroughlyagreeswiththatoftheanalyticalmodel,
meaning that the magnetic field has little relevance in this dy-
namic regime. The temperatures agree with less accuracy be- unperturbed plasma, but it completely vanishes because of the
causethethermalconductionisnotcompletelyineffective,and Dopplerdimmingintheregionbehindtheshock.Theradiative
theshockcancooldownforthat.Forinstance,thethermalcon- contributionto O VI 1032is 4 times thatof O VI 1037(in the
ductioniseffectiveintheregionwheretheshockisstronger,i.e. absence of other pumping), while the collisional componentis
where the shock propagation is not perpendicular to the post- a factor of 2 brighter. The shock compression makes the colli-
shockmagneticfield.Here(i.e.x 2 1010sandz 10 1010 sional contribution of the line increase, whereas the shock ac-
∼ × ∼ ×
cminFig.2),theanglebetweenthemagneticfieldandthether- celerationmakestheradiativecontributiondecreaseatthesame
mal gradient is 30◦. Considering the thermal gradient, the time.Forthisreason,theshockshowsanemissionfainterthan,
∼
temperatureandthelengthscaleinvolved,weestimateathermal or at most comparable with, the quiet corona, as usually ob-
conductiontimescaleof 5stobecomparedtothedynamical served (Ciaravellaetal. 2005, 2006), i.e. O VI emission ratio
∼
(expansion)timeonthesamelengthscalewhichis 100s.The 1 in Fig. 5. The weight of the radiative part dependson the
thermalconductionisthereforeveryeffectiveandl∼eadstotem- n∼on-shocked plasma density and in our model considering an
peratures lower than those predicted by the Rankine-Hugoniot unperturbeddensityof 2 106cm−3,itis85%oftheemis-
relations. sionandincreasesasthe∼unp×erturbeddensitydecreases.Instead,
Fromthejumpinthedensityandthetemperaturewederive since the radiative part of the Si XII is negligible, the total in-
the jump in the emission for O VI and Si XII with our radia- tensity of the post-shock line emission jumps significantly and
tionmodel.ItisplottedinFig.5asafunctionofthepost-shock relativelytothestrengthoftheshock,asplottedinFig.5(lower
plasma velocity (O VI upperpaneland Si XII lower panel).In panel).Asaconsequence,theSiXIIlineclearlybrightens,while
the O VI line the radiativepartof the line is significantfor the theOVIlinedoesnot,asCiaravellaetal.(2006)pointedout.
6 P.Paganoetal.:ModelingmagnetohydrodynamicsandnonequilibriumSoHO/UVCSlineemissionofCMEshocks
3.2. Comparisonwithothersimulations thosesimulationsandthetopofthecloudneeds600sand875s
toreachtheheightof2R⊙,inthesimulationwithn/n0=4and
3.2.1. Differentβ
in the one with v = 700 km/s respectively. During the travel
0
As anticipated above, we perform two more simulations con- of the cloud in the corona, the shock departs from it radially
sidering different intensities of the magnetic field, with a less reaching a final distance from the cloud of 0.6R⊙ in the x
∼
(β 10) and more (β 0.1) intense magnetic field than in direction.Thefinalbowshapeoftheshockfrontissimilartothe
the∼referencesimulation,∼respectively.Fig. 6 shows the density oneinthereferencecase.Ofcourse,thesmallertheenergyofthe
cloud,thelesstheshockstrengthatanytime,sothattheplasma
is never accelerated over 300 km/s. The velocity relative to
∼
thecloudis30%smallerandthatleadstoacorrespondingdelay
6 in the detectionat2R⊙. Thisdelayallowsthe plasmato better
approachionizationequilibrium.
T/T0 3.3. OVIlineprofile
4 n/n0
Tofurtherinvestigatetheobservationalconstraintsfortheshock
propertiesweshowherethelineprofileoftheOVIlinessynthe-
sized from our reference model. This line is analyzed in detail
by Mancusoetal. (2002) who indicate shock diagnostics from
2
UVCS observations. Here we try to provide further insight to
that analysis, but our synthesis of the line profile is very gen-
eralandcouldbeappliedalsototheSiXIIlineaftertuningthe
appropriateparameters.
0
0 1 2 3 4 5
Post-shock plasma velocity (107 cm/s)
Fig.6. Ratio between post-shock and pre-shock temperature
(solid lines) and density (dashed lines) as functionof the post-
shockplasmavelocity.Thethicknessofthelineisinverselypro-
portionaltotheinitialβ ofthesimulation,(β = 0.1,β = 1and
β =10).Thethinnestlinesisfortheratiocomputedanalytically
fromRankine-Hugoniotrelations
.
andtemperaturejumpacrosstheshockforthesimulationswith
differentvaluesofβ.Thesimulationwithβ = 10showsavery
similarbehaviourandtheshockpropertiesdonotdepartsignif-
icantly from the reference case already discussed. This is not
surprising,sincewehavealreadyshownthatthemagneticfield
hasnorelevancefortheshockdynamicsinthisregime.
Inastrongermagneticfield(Fig.6),theshockissignificantly
influencedbythemagneticpressure.Accordingtothetheoryof
MHD shocks the compression due to the shock is splitted be-
Fig.7. Line profile of the O VI line synthesized from our ref-
tweenmagneticfieldandplasmaand,asresult,theplasmaden-
erence model if observed as a limb CME at t 500 s (point-
sityjumpisweakerthaninanormalHDshock(Bazer&Ericson ∼
dashedthickline)andatt 900s(solidthickline),i.e.before
1959). This effect characterizes our simulation with a stronger ∼
andaftertheshockcrossedtheUVCSfieldofview,respectively.
field.Thedensityjumpfromthepre-shocktothepost-shockre-
The emission is averaged on time bins of 150 s and on space
gionis 5%lessthanreferencecase,butthetemperaturedoes
∼ bins of 9’ along the UVCS slit throughwhich the CME is ob-
not show any significant departure since the energetics of the
served.Theprofileisnormalizedtothepeak.Wealsoshowthe
shockisnotinfluencedbythemagneticfieldexceptforthepar-
twocomponentswhichcombinetoformthelineatt 900:the
tialthermalinsulationwhichactsregardlessoftheβ value.The ∼
oneemittedbytheshockedplasma( >1,solidthinline)and
radiative properties of this case descend from these considera- M
theoneemittedbytheunshockedplasma( < 1,dashedthin
tions. Theemission of the O VI andSi XII line is weakerthan M
line).
inthereferencecase,becausethedensityislower.Theradiative
part of the line vanishes because of the Doppler dimming,and
the intensity of the line is weaker than the referencecase is by Wetakeintoaccountthethermalbroadeningofthelineand
10%. the Dopplershiftdueto the plasmamotionprojectedalongthe
∼
lineofsight,butnottheinstrumentalbroadening.Toapproacha
realistic UVCS observationwe averagethe spectrumovertime
3.2.2. Weakercloud
bins of 150 s and over space bins of 9’. We also consider in-
Wenowdiscussthepropagationofshockingcloudsthatinitially tegrations along two different lines of sight: one mimicking a
carrieslessmomentum,i.e.withinitialdensitycontrastn/n0= limbCME,theotherahaloCME.Finallywediscusstheeffect
4,insteadofn/n0=10,orinitialcloudvelocityv =700km/s, of the differential Oxygen/protons shock heating on the Limb
0
insteadofv = 1000km/s.Theshockpropagationisslowerin CMElineprofile.
0
P.Paganoetal.:ModelingmagnetohydrodynamicsandnonequilibriumSoHO/UVCSlineemissionofCMEshocks 7
3.3.1. LimbCME
In Fig. 7 we plot the profile of the O VI line for the reference
modelasifitwereobservedasalimbCMEbeforeandafterthe
shockpassed the UVCS slit. For the momentwe assume equal
proton,electronandiontemperature.Aftertheshockthecentral
partofthelinehasnotchangedbecauseitisemittedbythatpart
oftheplasmaneverinvolvedintheshockpassage.Evidenceof
the passage of the shock across the UVCS slit can instead be
found in the wings of the later line. They are more prominent
thaninthequietline,becauseofthelineshiftduetothelineof
sightcomponentoftheshockvelocity.Theresultinglineprofile
isthesumoftheemissioncontributionfromun-shockedplasma
and shockedplasma. The un-shockedplasma emits only a nar-
rowcomponent(Fig.7, <1line),whilesuperpositionofthe
M
lines emitted by the shocked plasma gives both a central com-
ponentandsignificantwings.Thesetwoemissioncontributions
mergeinatwocomponentline.Thefirstisanarrowandbright
Fig.8. As in Fig. 7, but considering different Oxygen-electron
component,thesharppeakemittedbytheunshockedcoronaand
plasmatemperatureratio,asindicatedinthelegend.Alltheline
bytheshockedplasmathatmovesperpendicularlytothelineof
profilesarecomputedatt 900s.
sight; the second componentis due to the shocked plasma that ∼
hasasignificantcomponentofthevelocityparalleltothelineof
sight,sothatitemitsthermallybroadenedlinescenteredfarfrom
1032A˚. The relative weight of the two componentsis strongly
sensitivetothebackgroundemission,whichseriouslyinfluence
thenarrowcomponent.Mancusoetal.(2002)indeedobserveda
similarlineprofileandconcludedthatashockwascrossingthe
fieldofviewoftheUVCSslitduringtheobservation.Weargue
that a two component line profile, as shown in Fig. 7, may in
generalbeasignatureofthepresenceofashock.
3.3.2. Oxygenshockheating
Weexpectthatthewingsofthelineprofilebecomemorepromi-
nent if the shock heating mechanism is more effective on the
heavy ions than on the protons, because the thermal broad-
ening becomes larger right in the Doppler-shifted components
of the ion lines. To test this consideration, already made by
Fig.9.FractionoftheOVIlineemittedinthewingsasfunction
Korrecketal. (2004) and Raymondetal. (2003b), we check
ofOxygen-electronplasmatemperatureratio.Thethinsolidline
what happens if we artificially increase the O VI temperature
isconsideringonlytheDopplereffect(temperatureoftheatmo-
obtainedfromourMHD modelby agivenfactor.Fig.8 shows
spherenotchanged),thedashedlineonlythethermalbroaden-
theOVIlineprofile,obtainedbyincreasingthetemperatureby
ing,thethicksolidlinebothofthem.
a factor 8 (Korrecketal. 2004; Raymondetal. 2003b) and 16
(oxygen atomic mass). Because of the temperature decoupling
between electrons and ions, the FWHM of the line emitted by
theshockedplasmaincreasesfrom 0.2A˚ upto 1A˚. the assertions of those papers that TO/Tp was large. Our ap-
∼ ∼ proach, when applied to specific events, can give reliable and
Thewingsofthelineprofilebrightenifa greaterT /T
OVI p
alternative measurements on the actual T /T , once measured
ratioissupposed.Fig.9showstheratiobetweenthetotalemis- i p
sion of the wings(i.e. emission outof the range1032 0.3A˚) the post-shockelectron temperature,and of the componentsof
± the velocity, since the value of the wing/center ratio uniquely
and that of the center of the line (i.e. inside that range). It in-
correspondstoacertainiontemperature.
creasesfrom0.1(T =T )upto0.24(T =16T ).The
OVI e OVI e
trendismostlydueto theincreasingthermalbroadeningofthe
emission from the post-shock plasma (Fig. 9, dotted line), but
3.3.3. HaloCME
itislimitedbythepresenceoftheotherbroadeningcomponent
whichisindependentofthetemperature(Fig.9,thinsolidline). Fig. 10showsthe resultsforthe referencemodelif orientedas
Thesumofthetwoeffectsgivesthetotalstrengthofthewings a HaloCMEexpelledtowardtheobserver,notconsideringany
intheobservedlines(Fig.9,thicksolidline).Thestrongeristhe temperatureincreasefortheions.Inthelineprofilethereisonly
shock,thestrongerarethewings.Thereforeat 575s,whenthe onetailontheblueside.Thelineofsightisappropriatetodetect
∼
firstpartoftheshockcrossestheUVCSslitfieldofviewandthe theDopplershiftduetotheglobalfrontmotion,ratherthanthat
shockisthestrongest,thewing/centerratiois 0.6andlater,at duetofrontexpansion,detectedfortheLimbCMElineofsight.
∼
1000s,itdecreasesdownto0.24(showninFig.9).Itshould Atincreasingdistancefromtheshockcentralaxistheblue-shift
∼
be noted that Fig. 8 shows that T /T = 16 resembles the is progressively reduced due to the projection effect. The total
O p
profiles shown by Raymondetal. (2003b) and Mancusoetal. line profile consists of the superpositionof radiation with con-
(2002) far better than the lower temperature ratios, supporting tinuouslyvaryingblue-shift.Fig.10showsthelinedetectedby
8 P.Paganoetal.:ModelingmagnetohydrodynamicsandnonequilibriumSoHO/UVCSlineemissionofCMEshocks
of the wings of the O VI line as possible diagnostics for ion
shockheating.
Wehavechosenasareferencecasetheshockfrontoriginat-
ingfromaCMEfragment10timesdenserthanthesurrounding
1.5MKmagnetized(β 1)coronaexpelledataspeedof1000
≈
km/s. The ambientmagnetic field is a large scale dipole. Then
we have explored other cases with higher and lower magnetic
field,withlessdensecloudandwithslowercloud.Foreachsim-
ulationwehavecomputedtheemissionintheselectedlinesand
derivedthelineprofileswithadetailedradiationmodelinclud-
ingtheradiativeandcollisionalcontributionsandtheeffectsof
non-equilibriumofionization.
Fromthereferencesimulationwefindthatsomeofthedis-
tinctiveshockfeaturesdetectableinOVIandSiXIIlinesarise
fromtherelativebrightnessofthecollisionalandradiativecon-
tributions in the unperturbed corona. Since, the radiative con-
tribution is actually negligible for Si XII, but important for O
Fig.10.LineprofileoftheOVIlinesynthesizedfromourrefer- VI, theintensity jumpacrosstheshockis sharperin the SiXII
encemodelifobservedasanHaloCMEatt 900s,i.e.after linethanintheOVIline.TheintensityoftheSiXIIlinescales
the shockcrossed the UVCS field ofview. Th∼eemission is av- roughlyasthesquareofthecompression,whiletheoneoftheO
eragedovertime binsof 150s and overspace binsof 9’ along VIscalesmoresmoothlybecauseitsemissionisstronglybiased
theUVCSslitthroughwhichtheCMEisobserved.Theprofile bytheradiativecontribution.IntheOVIlinetheradiativepart
isnormalizedtothepeak.Forthesolidlinetheslitis 5′apart completely vanishesin the regionbehind the shock because of
fromthecenteroftheSun, 7′forthedashedone. ∼ the Doppler dimming, while the shock compressionmakes the
∼ collisionalcontributionofthelineincrease.Thetwoeffectsare
competitive and comparable,so that the shock shows an emis-
theslitpointingat 5′ (solidline)and 7′ (dashedline)from sionfainterthanorcomparablewiththequietcoronainthisline.
∼ ∼ IntheSiXIIline,theshocksproduceonlythegrowthofthecol-
the center of the Sun. The closer the field of view to the Sun
lisionalcontribution.ThisexplainswhyatthesametimetheSi
disk,thelargeristhelineofsightcomponentofthepost-shock
XIIlineclearlybrightens,whiletheshockhaslittleinfluenceon
bulkvelocityandthemoreblue-shiftedistheemission.Theline
the O VI line. These considerations explain past observations.
presentsaverybrightquietemissionandanenvelopeofshifted
lines extendingto 1A˚ from the quite line (see Fig. 10, solid Ciaravellaetal. (2005) found that during the shock passage in
∼ the2000June28eventtheO VIemissionwasweakerorcom-
line).Althoughthedetailsofthestructureofthelinearestrongly
parabletothequietcoronaemission.Ciaravellaetal.(2006)ex-
relatedtothestructureandgeometryoftheshock,theverypres-
aminedseveraleventsandshowedthatitoccurscommonlythat
enceofthissmoothandasymmetriccomponentofthelinecould
whenashockisdetectedtheOVIdoesnotbrighten,andtheSi
be a distinctive feature, although such observations are techni-
XIIbrightenssignificantly.
cally unfeasible for UVCS, because the slit is too close to the
Theionizationfractionsofoxygenandsilicondonotchange
centeroftheSun,wemayequallyhopetodetectthisfeaturein
in shock transitionsbecause the shock heating and passage are
realobservations.Infact,sincetheshockfrontismorethan16’
muchfasterthatthe ionization/recombinationprocesses.In our
wide,if theCME is notexpelledperfectlyalongthe Sun-Earth
simulations the shocks are not extremely strong, so that they
line,partoftheshockfrontcouldbevisibleoutoftheSundisk
represent realistic situations, typically observed. For this rea-
ina realistic UVCSfieldofview.Thisconclusionwouldapply
to the halo CME shocks observed by Ciaravellaetal. (2006). son,weexpectthattheconditionsofionizationnon-equilibrium
are commonlyfoundand thatthe ionizationfractionsare com-
Moreover, as we already claim above (Section 3.2.2), a shock
parable to those of the quiet corona. Behind the shock front
frontcouldextendovera wider angleif the shockingfragment
islessdense. the plasma should slowly approach the ionization equilibrium
atpost-shocktemperature.
Finally,forCMEsexpelledindirectionsinbetweentheex-
The effect of the magnetic field on the shocks depends on
tremecasesconsideredhereweexpecttodetectboththebroad-
the strengthof the field. In high β plasma the role of the mag-
eningeffectduetothethermalbroadeningoftheshockedplasma
netic field is only to thermally insulate the shocked plasma. It
(Limb CME) and the one due to the Doppler shifted emission
happensbecauseinthisregimetheshockissuperalfve´nicandit
fromfastplasmamovingtowardtheobserver.
isresponsibleforthereorientationofthemagneticfieldparallel
totheshockfront,i.e.perpendiculartothethermalgradient.In
lowβplasma,themagneticfieldinfluencesalsothecompression
4. Discussionandconclusions
of the plasma. In thisregime(also superalfve´nic)the compres-
In this work we study the shock fronts departing from super- sionduetotheshockissplitbetweenthemagneticfieldandthe
sonicCMEfragmentswithdetailedMHDmodeling.Weaddress plasma; therefore, the density (and the line intensity) is lower
thediagnosticsobtainablewithUVCSobservations,whichhave than in a high β regime. Raymondetal. (2000) argued that a
beenwidelyanalyzedinthisframework,andinparticulartheO relatively strong magnetic field could in principle be responsi-
VIandSiXIIemissionlines.Asaresult,weareabletoexplain bleformodestcompressionswithrespecttotheobservedshock
mostofthespectralsignaturesoftheshocksrevealedbytheob- speed.
servations,andwestepforwardtopredictmoreshockproperties. Differencesin the kineticenergyof the CME could lead to
Inparticularweindicatethemaindifferencesinthelineshapes differentextentof the shockfront. We find thatthe weaker the
expectedbetweenhaloCMEsandlimbCMEs andthe strength CMEcore,themoreextendedandslowistheshockpropagation.
P.Paganoetal.:ModelingmagnetohydrodynamicsandnonequilibriumSoHO/UVCSlineemissionofCMEshocks 9
When we observetheshockpropagatingfroma limbCME useforthetwolinesofinterestforthispaper(i.e.OVI1032A˚
weexpecttoobserveaprofileoftheOVIlineconsistingontwo andSiXII499A˚):
distinctoverlappingcontributions.Theunperturbedplasmathat
liesalongtheline ofsightemitsa narrowline andtheshocked Q(T) =QOVIe−TcOutVI/T ln kbT (A.3)
plasmaemitsa widerline. Thiscombinationisthe kindofline OVI 0 √T OVI
E
shapethatRaymondetal.(2000)andMancusoetal.(2002)ob-
servedduringtheCMEevents.Theyusedthedoublecomponent Q(T) =QSiXIIe−TcSuitXII/T ln kbT (A.4)
line profile as signature of the shock. In our simulation we get SiXII 0 √T SiXII
E
the same line profile shape after the shock passage. Therefore
where QOVI and QSiXII are two normalization factors
weconfirmthatthisspectralfeatureisareliablesignatureofthe 0 0
usefulto matchthe emission atthe ionizationequilibriumwith
shockpresence.
theoneprescribedbytheCHIANTIdatabase(Landietal.2006),
In oursimulation we have a line of sight componentof the
TOVI =139.000KandTSiXII =288.000Karethetemper-
velocity of 200km/s, leading to a line shift of 0.7 A˚. cut cut
The shock h∼eating T = T leads to a line shift of∼ 0.2 A˚. ature forO VI andSi XII respectivelyand EOVI = 11.99eV
TheaccelerationofthOeplasmpaisresponsibleforthepr∼esenceof andESiXII =14.8eV arethethresholdenergyrespectivelyfor
OVIandSiXII.
the wings and higher T /T leads to more significant wings.
O p
For this reason, diagnostic of the ion shock heating could be
basedonmeasuringtherelativeimportanceofthewingsofthe A.2. Radiativecontribution
O VI line and on estimating the post-shock electron tempera-
Theradiativecontributionis:
ture, and the components of the velocity. Here we present an
exampleofprotonandoxygenenhancedheating(Korrecketal. I (nZ,T,v)=IrnZσ (A.5)
r i 0 i D
2004;Raymondetal.2003b).Itwillbeinterestinginthefuture
where Ir is the intensity emitted from the Sun disk that
toapplythiskindofdiagnosticsoftheionsshockheatingtoone 0
reaches the height r to be scattered by the coronal ions, σ is
particularevent.
the cross section of the scattering, and is the Doppler dim-
Finally, we expect to see an asymmetric O VI line profile D
ming factor. The radiative contributionis computedonlyfor O
with a smooth tail on the blue-side, when the shock propagat-
VI,sinceitisnegligibleforSiXII.Ir iscomputedby:
ingfromahaloCMEexpelledtowardtheobserverentersinthe 0
UVCSfieldofview.Aconditionforthedetectabilityofthisef- R2
fectoutofthe solardisk area largelineof sightcomponentof Ir =IOVI 10322π 1 1 ⊙ (A.6)
theplasmavelocityandawideshockfront. 0 0 −r − r2 !
whereIOVI1032 =1.94phot/(cm2ssr)isthediskinten-
Acknowledgements. The authors thank Angela Ciaravella for fruitful discus- 0
sityandthefollowingfunctionofrissimplythedilutionfactor
sionandfeedbackonobservationalaspects.Theyacknowledgesupportforthis
work from Agenzia Spaziale Italiana (contract I/035/05/0), Istituto Nazionale duetothedistancefromthedisk.
diAstrofisicaandMinistero dell’Universita` eRicerca. P.Pagano’s stayatthe σiscomputed(forOxygen)by:
CenterforAstrophysicswassupportedbyNASAgrantNNG06GG78Gtothe
SmithsonianAstrophysicalObservatory.Thesoftwareusedinthisworkwasin vOVI
σ =σOVI disk (A.7)
partdevelopedbytheDOE-supportedASC/AllianceCenterforAstrophysical OVI 0
ThermonuclearFlashesattheUniversityofChicago,usingmodulesforthermal 3kbT
mO
conduction and optically thin radiation built at the Osservatorio Astronomico
q
di Palermo. The calculations were performed on the Exadron Linux cluster where vOVI = 30 105 cm/s is the wideness of the
at the SCAN (Sistema di Calcolo per l’Astrofisica Numerica) facility of the Oxygenlinedsieskmittedfrom×thedisk,andm =2.67 10−23g
OsservatorioAstronomicodiPalermoandontheIBM/SP5machineatCINECA O ×
istheOxygenmass.
(Bologna,Italy).Partofthesimulationswereperformedwithinakey-projectap-
iscomputed(forOxygen)by:
provedintheINAF/CINECAagreement2006-2007.CHIANTIisacollaborative
D
projectinvolvingtheNRL(USA),RAL(UK),MSSL(UK),theUniversitiesof
Florence(Italy)andCambridge(UK),andGeorgeMasonUniversity(USA). −( vrad )2 −((vrad−v0Lyβ))2
DOVI =(I0OVI 1032e vcOutVI +I0Lyβe vcHut )/I0OVI 1032(A.8)
where the second term accounts for pumping of O VI by
AppendixA: Theradiativeandcollisional
Lyβ (Raymond&Ciaravella 2004) and ILyβ = 4.13 1013
contribution phot/(cm2 s sr) is the disk intensity fo0r the Lyman×β line,
Theintensityofthelinesismodeledasthesumofthecollisional vLyβ = 18 107 cm/s is the distance between the center of
0 ×
(Ic) and radiative (Ir) contributions as functions of ne, nZi , T theOVI1032A˚ lineandtheLyβline,vrad istheradialveloc-
andv: ityoftheplasmaandv isthecutoffvelocityfortheDoppler
cut
dimmingwhichisgivenbytheoverlappingbetweenthediskline
I =I (n ,nZ,T)+I (nZ,T,v) (A.1) profileandthecoronallineprofile.ForOxygenandHydrogenit
c e i r i
isrespectively:
A.1. Collisional contribution 3k T
vOVI = vOVI + b (A.9)
Thecollisionalcontributionis: cut r disk mO
3k T
I (n ,nZ,T)=n nZQ(T) (A.2) vH = vH + b (A.10)
c e i e i cut disk m
r H
where Q(T)is the collisionalexcitationrate coefficientfor wherevH = 112 105 cm/s is the width forHydrogen
the ions which treats the collisionally induced emission of the lines emitteddisfkrom the d×isk, and m = 1.68 10−24 g is the
H
×
ions. Here we present the approximated formula for Q(T) we Hydrogenmass.
10 P.Paganoetal.:ModelingmagnetohydrodynamicsandnonequilibriumSoHO/UVCSlineemissionofCMEshocks
AppendixB: Analyticalshockmodel Fryxell,B.,Olson,K.,Ricker,P.,etal.2000,ApJS,131,273
Ghavamian,P.,Raymond,J.C.,&Blair,W.P.2001,inAmericanInstituteof
From the Rankine-Hugoniot conditions for a planar adiabatic PhysicsConferenceSeries,Vol.565,YoungSupernovaRemnants,ed.S.S.
shockandourradiationmodelpresentedinAppendixA,wede- Holt&U.Hwang,189–192
velop an analytical model for the jump in the intensity of the Godunov,S.1959,Math.Sbornik,47,271
Gopalswamy,N.,Lara,A.,Lepping,R.P.,etal.2000,Geophys.Res.Lett.,27,
emissionlinesduetotheshock.
145
First, we computethe jumpin ne,nZi ,T andv as function Hundhausen,A.J.1987,inSixthInternationalSolarWindConference,ed.V.J.
oftheMachNumber,thenweusetheradiationmodelpresented Pizzo,T.Holzer,&D.G.Sime,181–+
inAppendixAtogetthejumpintheintensityoftheemission. Kohl,J.L.,Esser,R.,Gardner,L.D.,etal.1995,Sol.Phys.,162,313
Hereafter we indicate the pre-shockand post-shockquanti- Korreck,K.E.,Raymond,J.C.,Zurbuchen,T.H.,&Ghavamian,P.2004,ApJ,
615,280
ties respectively with the subscript 0 and 1. The jump in elec-
Korreck,K.E.,Zurbuchen,T.H.,Lepri,S.T.,&Raines,J.M.2007,ApJ,659,
tron density, temperature and velocity due to the shock are 773
(Landau&Lifshitz1966): Landau,L.D.&Lifshitz,E.M.1966,Hydrodynamik(Lehrbuchdertheoretis-
chenPhysik,Berlin:Akademie-Verlag,1966)
n (γ+1) 2 Landi,E.,DelZanna,G.,Young,P.R.,etal.2006,ApJS,162,261
e1 = M (B.1) MacNeice,P.,Olson,K.M.,Mobarry,C.,deFainchtein,R.,&Packer,C.2000,
ne0 2+(γ 1) 2 ComputerPhysicsCommunications,126,330
− M
Mancuso,S.,Raymond,J.C.,Kohl,J.,etal.2002,A&A,383,267
T 2γ(γ 1) 4 (γ2 6γ+1) 2 2(γ 1) Orlando,S.,Peres,G.,Reale,F.,etal.2005,A&A,444,505
1 = − M − − M − − (B.2) Pagano,P.,Reale,F.,Orlando,S.,&Peres,G.2007,A&A,464,753
T (γ+1)2 2
0 Raymond,J.C.&Ciaravella,A.2004,ApJ,606,L159
M
Raymond,J.C.,Ciaravella,A.,Dobrzycka,D.,etal.2003a,ApJ,597,1106
2 1 Raymond,J.C.,Ghavamian, P.,Sankrit, R.,Blair, W.P.,&Curiel, S.2003b,
v1 =2cs0 M − (B.3) ApJ,584,770
(γ+1)
M Raymond,J.C.&Smith,B.W.1977,ApJS,35,419
Raymond,J.C.,Thompson,B.J.,St.Cyr,O.C.,etal.2000,Geophys.Res.Lett.,
where istheMachnumberandc isthesoundspeed.
s 27,1439
M
The ionizationfractionis computedfromthe followingap- Schwartz,S.J.,Paschmann,G.,Sckopke,N.,etal.2000,J.Geophys.Res.,105,
proximated formula (Eq. (B.4)) in which pre-shock ionization 12639
equilibriumisassumed. Spadaro,D.,Leto,P.,&Antiochos,S.K.1994,ApJ,427,453
Spitzer,L.1962,PhysicsofFullyIonizedGases(PhysicsofFullyIonizedGases,
fiZ =FiZ(T1)+(FiZ(T0)−FiZ(T1))e−τeτq (B.4) SulNeiemwanY,orRk.:IMnt.e,rCscrioeonkceer(,2Nnd.eUd.i,tioRna)y,m19o6n2d), J. C., & van Ballegooijen, A.
2005,inIAUSymposium,Vol.226,CoronalandStellarMassEjections,ed.
wherefZ istheionizationfractionfortheionsZ inthei-th K.Dere,J.Wang,&Y.Yan,71–75
i
ionizationstate,FZ(T)istheequilibriumionizationfractionfor Vourlidas,A.,Wu,S.T.,Wang,A.H.,Subramanian,P.,&Howard,R.A.2003,
i ApJ,598,1392
the ions Z in the i-th ionizationstate at temperatureT, τ is an
Wagner,W.J.&MacQueen,R.M.1983,A&A,120,136
estimationofthetimeelapsedfromtheshockfrontpassage,and Webb,D.F.,Cliver,E.W.,Crooker,N.U.,Cry,O.C.S.,&Thompson,B.J.
τ isthetimescaleneededtogetionizationequilibriumwhich 2000,J.Geophys.Res.,105,7491
eq
isgivenby: Zhang,J.,Dere,K.P.,Howard,R.A.,&Bothmer,V.2003,ApJ,582,520
τ =(n q )−1 (B.5)
eq e eff
Because asingleratedominatesforbothoftheionsweare
interestedin,wecanapproximateq bythefastestrateinvolv-
eff
ingtheion.
Wecancomputetheionsdensityby:
nZ =n ASunfZ (B.6)
i e Z i
whereASunisthesolarabundanceoftheionZ.
Z
Throughthiscomputationwegetthevaluesforn ,nZ,T and
e i
v forthe post-shockregion,while we knowallofthem forthe
pre-shockregion.Atthispointwecomputethejumpintheemis-
sionlinesfromtheradiationmodelpresentedinAppendixA.
References
Bazer,J.&Ericson,W.B.1959,ApJ,129,758
Brueckner, G. E., Delaboudiniere, J.-P., Howard, R. A., et al. 1998,
Geophys.Res.Lett.,25,3019
Bryans,P.,Badnell,N.R.,Gorczyca,T.W.,etal.2006,ApJS,167,343
Cane,H.V.,Richardson,I.G.,&Cyr,O.C.S.2000,Geophys.Res.Lett.,27,
3591
Ciaravella,A.,Raymond,J.C.,&Kahler,S.W.2006,ApJ,652,774
Ciaravella,A.,Raymond,J.C.,Kahler,S.W.,Vourlidas,A.,&Li,J.2005,ApJ,
621,1121
Cowie,L.L.&McKee,C.F.1977,ApJ,211,135
Cox,D.P.&Raymond,J.C.1985,ApJ,298,651
Domingo, V.&Poland, A.I.1988,SOHO:anobservatory tostudythesolar
interiorandthesolaratmosphere,Tech.rep.