Radiative Processes & Magneto Hydrodynamics (MHD)

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  • RadiativeProcesses&MagnetoHydrodynamics(MHD)

    Overview(0)

    TotalC.F.U.=9(8CFULect.+1Ex.)76hr

    Lectures@AULA1onMondays(1416)Tuesdays(1416)Thursdays(1013)

    Contact:daniele.dallacasa@unibo.itontuesdays&thursdays15:3017:30

    Exam:2datesinJanuaryFebruarythenagainfromJune,about1date/monthashortadmissiontestwillbecarriedout

    ZEMAX

  • RadiativeProcesses&MagnetoHydrodynamics(MHD)

    Overview(0.5)

    whytheadmissiontest

    1829

    01.0112.312006 01.0112.312011

    fail

    30

  • RadiativeProcesses&MagnetoHydrodynamics(MHD)

    Overview(0.75)

    whattheadmissiontestis

    Duration:1hTypically:4questions(one/twoarejuststatememts)AllowedconsultationofBooksLecturenotesSlides

    possibleresults:Adm.,Adm.w.R.,NotAdm.

  • RadiativeProcesses&MagnetoHydrodynamics(MHD)

    Overview(1)

    Aimsofthecourse:

    provideaPANCHROMATICAPPROACH

    toAstrophysics

    provideaall(mostof)thetoolstounderstandwhat

    weobserve(radiation)intheUniverse

  • 408MHz21cm

    rays

    TheSkyatvariouswavelengthss

  • Individualobjects:images(1)

  • RadiativeProcesses&MagnetoHydrodynamics(MHD)

    CONTENTS(Part1)

    MHD:Statics

    HD

    MHD&Plasmaphysics

    FluidInstabilities

  • RadiativeProcesses&MagnetoHydrodynamics(MHD)

    CONTENTS(Part2)

    Radiativeprocesses:

    Continuousradiationfromachargedparticle(Fundamentalphysicsofastrophysicalplasmas)

    0BlackBody

    1.Bremsstrahlung

    2.Synchrotron

    3.Diffusionprocesses

    4.CosmicRays

  • RadiativeProcesses&MagnetoHydrodynamics(MHD)

    CONTENTS(Part3)

    TheInterstellarmediumPlasma,Neutralmedium,Dust&Molecules

    Atomic&moleculartransitions

    Einstein'sCoefficientsAtoms(molecules)asoscillatorspermitted&forbiddenlines

    Radiative.vs.collisional(de)excitation

    ThephasesoftheISMdiagnostics

    Acasestudy:HIandtherotationcurveinspiralgalaxies

  • RadiativeProcesses&MagnetoHydrodynamics(MHD)

    Bibliography:

    Clarke&CarswellPrinciplesofAstrophysicalFluidDynamics

    Rybicki&LightmanRadiativeProcessesinAstrophysics

    PadmanabanTheoreticalAstrophysics(VolIAstrophysicalprocesses)

    VietriAstrofisicadelleAlteEnergie

    Dopita&SutherlandAstrophysicsoftheDiffuseUniverse

    copyoftheslidesareavailableathttp://www.ira.inaf.it/~ddallaca/PRAD.html

    theyarejustlecturenotes,notsufficientforaproperstudy

    http://www.ira.inaf.it/~ddallaca/P-RAD.html

  • Hydrodynamics(fluidmechanics)

    Fluidsareinformofeitherliquidorgaseousbodies.

    Fluidsareidealmacroscopicbodieswithcontinuousproperties.

    Hydrostaticsisdefinedbytheidealgasequationstate(P,,T).

    Hydrodynamicsrequirestoknowalsotheinstantaneousvelocity(P,,[T],v)v(x,y,z,t)isthevelocityvectorofafluidvolumeelement,andnotthatofindividualfluidparticles.

    Descriptionbasedon1.studythefluidflowingacrossagivenplace/surface[Eulerianview]2.studyavolumeelementinitsflow/motion[Lagrangianview]

    Atfirstthemagneticfieldisnotconsidered.ItwillbeinMHD(MagnetoHydroDynamics)

  • Basicmathematicaltoolsrequiredforunderstanding:

    gradientofascalar:

    thevectorisperpendiculartothesurfacewherethescalarisconstant

    divergenceofavector

    curlofavector

    2

    x

    i y

    j z

    k

    h x

    hx y h y z

    hz

    h i j kx y zhx hy hz 2

    2

    x 2

    2

    y 2

    2

    z 2

  • Basicmathematicaltoolsrequiredforunderstanding(2):

    Gauss'theorem

    Stokes'theorem

    surface V Gn dS = Volume G dV

    Gd l = surface G dS

  • Mathematicaltools[3]:

    approximaterelationshipsbetweenoperatorsandpracticalquantities:

    U = velocity ; L = length ; T = time x

    1L

    t

    1T

    UL

    1L

    1L

    2 1L2

  • Astrophysicalfluids

    Extensionofthephysicalconcept.

    Largescale:Gas/dust(ISM)inspiral(elliptical)galaxies

    Starsingalaxies

    Galaxies(&clusters)&IGMintheUniverse

    Smallscale:Stellarwinds

    Accretiondiscs&Jets,Stars,gas/dustclouds

    Ingeneral,thegaseousfluidismoreappropriate(liquidfluiddescribeshighpressureenvironments,e.g.planetary&starsurfacesandinteriors)sincethetypicaldensitiesareverysmall.Ingeneralthefluidisinhomogeneous(TP),accordingtoitslocation

    HIM,WIM,WMN,CNMThereareothercompactbodieslikeWD&NS,wheretheequationofstateisfundamentaltodefinethefluidproperties

  • Astrophysicalfluids(2)

    Basicconcept:

    Eachvolumeelementmustbe

    smallenoughtopreserveasinglevalueforrelevantquantities:

    largeenoughtobestatisticallyrepresentative(largenumberofparticles)

    Incasethefluidelementhas

    thenparticlesredistributeinformationandthefluidistermedcollisional.Allthisimpliesthatanumberofstatisticallawshold.

    L fluidLscale~qq

    q=generic quantity

    n Lfluid3 1 n=number density

    L fluidmfp mfp=mean free path

  • Idealfluid

    1.nointernalfriction

    2.changesinshapedonotrequirework(Vremainsconstant)

    3.(incompressible)

    4.continuous,microscopicvolumes(dV)stillcontainlargeamountsofparticles

    Astrophysicalexamples:

    thevastmajorityofthecelestialbodies(andthespacebetweenthem)canbephysicallydescribedwith(magneto)hydrodynamics:

    stars,plasma,stellarwinds,supernovae,insterstellargas,cosmicrays,galaxies,galacticwinds,intergalacticspace(e.g.hotgasinclustersofgalaxies),radiosources,etc.

  • Fluidstatics.vs.Fluiddymanics

    Fluidstaticsstudiesequilibrium

    localthermodynamicconditionsareallyouneed:

    stateequation(e.g.PV=nRT)aliasP=f(n/V,T)=f(,T)

    Dynamicsinsteadstudies/considersmotionsofvolumesincaseofmotion,velocitymustbetakenintoaccount,inaddition,andagivenquantity,likepressureis

    P = f , v ,T

  • Fluidstatics

    1.PascalPrinciple:Inafluidatrest,w/oanyvolumetricforces(e.g.gravity),Pisconstantwithinthefluid.AsmallforceF

    1becomesstronginF

    2

    2.Archimede'sPrinciple:asolidbodywithinafluidissubjecttoalltheforcesoveritssurfacefromthe

    fluidpressure.(A.'spushup:=weightoftheliquiddisplacedbythebody)

  • Fluidstatics(2)

    3.Stevino'slaw:

    e.g.atmosphericpressure:thereisaforce(gravity)actingonvolume:ithasacomponentalongz[i.e.g=(0,0,g

    z)]

    P z = g zconstant

    dPdz

    =g where = N = PkT

    .

    for an isothermal atmospheredPP

    = gkT

    dz = mean molecular mass

    P = P o eg z /kT = o e

    g z /kT

    P o = 1.033 dynecm2 = 1.013105 Nm2Pa

    o = 1.29103 gcm3 = 1.29 kgm3

  • Fluidstatics(3)aircompositionand

    .

  • Fluidmechanics(1)equationofcontinuity(massconservation)

    masswithinsomegivenvolumeVois:

    massflowingperunittimethroughasurfacedSis:

    totalmassouflowingVois:

    thedecreaseperunittimeofthemassfluidinVois:

    andequating(1)and(2)

    V o dV

    vd S = vn dS [ 0 outflowing V o ]

    vd S = V o v dV 1 Gauss ' theorem

    ddt V o dV = V o

    t

    dV 2

    V o t

    dV = V o v dV

    V o [ t v ]dV = 0

  • Fluidmechanics(2)equationofcontinuity

    theequationmustholdforanyvolumethentheintegrandmustvanish:

    thequantityisalsoknownasmassfluxdensity.

    Ifweintroducetheconvectivederivative**theequationofcontinuitycanalsobewrittenas

    **itislikeweconcentrateoutattentiontoacertainmass(volume)elementfollowingitsmotion.Suchderivativerepresentthevariationofthedensityascomovingwithit.

    t

    v = 0

    t

    v v = 0 Eulerian

    j = vDDt

    t

    v

    D Dt

    v = 0 Lagrangian

  • Fluidmechanics(3)equationofcontinuityapplication(1):duringtthefluidmovesofacertainamountx1=v1tinS1andofx2=v2tinS2withamassmotionof

    m1=1S1x1=1S1v1tm2=S2x2=2S2v2t

    incaseofmassconservationm1=m2namely1S1v1=2S2v2i.e.Sv=constantincaseofincompressiblefluids(=constant)

    Sv=constant=Q

    incaseofvariablecrosssectionofthetube:

    i.e.velocityincreaseswhenthecrosssectionnarrows

    S1

    S2

    v 1S

  • Fluidmechanics(4)equationofcontinuityapplication(2):gravityplaysarole!

    foreq.of.c.dm1=dm2=dm

    if=constantS1v1=S2v2

    thereisavariationofkineticenergy

    S1

    S 2

    z 2

    z1

    z

    K = 12

    dm v 22v 12 = Lp Lg

    Lg = dm g z 1z 2Lp = p1S1v 1dtp2S 2 v 2dt=p1Vp 2V

    12

    dm v 22v 12 = dm g z 1z 2p1p 2V but V

    dm

    12

    v 12

    g

    p 1g

    z 1 =12

    v 22

    g

    p2g

    z 2 [Bernoulli ' s equation ]

    stopheight

    piezometricheight

    height

    dm

    dm

  • DanielBernoulli(17001782)

    Fluidmechanics(5)equationofcontinuity

    itfollowsthat:

    (otherformsofBernoulli'sequation)

    S1

    S 2

    z 2

    z1

    z

    12

    v 2

    g p

    gz = const

    12

    v 2 p g z = const

    dm

    dm

  • Fluidmechanics(6)Euler'sequationEuler'sequation(momentumconservation)(equivalenttoF=ma)

    alongx,consideringalltheactingforces:

    andwemustconsidertheforcesfxactingonthevolume(i.e.gravity)andonthesurface(i.e.pressure)

    andfrom(1)and(2)

    thesamealsoalongyandz;thenusingthevectorformalism

    dVx

    dS

    dF x = dmdv xdt

    = dVdv xdt

    1

    dF x = dV f x[p x p xdx ]dS = f xdpdx dV 2

    dVdv xdt

    = f xdpdx dV i.e. dv xdt = 1 f x1 dpdx d vdt

    =[ 1 f ] 1 p 3

  • d vdt

    = [ 1 f ] 1 p

    Fluidmechanics(7)Euler'sequation

    theLagrangianviewfollowsthefluidelementduringthemotiontheEulerianviewstudiesthevelocityfield

    itreferstotherateofchangeofagivenfluidvolumedVasitmovesaboutinspace(whichisthegoal)andnottherateofchangeoffluidvelocityatafixedpoin