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Stellar atmospheres a very short introduction Part I

Stellar atmospheres a very short introduction Part I. Ewa Niemczura Astronomical Institute , UWr eniem@astro.uni.wroc.pl. Stellar spectra. Stellar spectra. One picture is worth 1000 words, but one spectrum is worth 1000 pictures! Ivan Hubeny. What is a Stellar Atmosphere ?.

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Stellar atmospheres a very short introduction Part I

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  1. Stellaratmospheresa veryshortintroductionPart I Ewa Niemczura AstronomicalInstitute, UWr eniem@astro.uni.wroc.pl

  2. Stellar spectra

  3. Stellar spectra One picture is worth 1000 words, but one spectrum is worth 1000 pictures! Ivan Hubeny

  4. Whatis a StellarAtmosphere? Stellaratmosphere: • medium connectedphysically to a star; from this medium photonsescape to the surroundingspace • region where the radiationobservable by a distantobserveroriginates

  5. Whatis a StellarAtmosphere? Stellaratmosphere: • usually, a verythinlayer on the surface of the star • latestars: photosphere, chromosphere, corona

  6. Whatis a StellarAtmosphere? Stellaratmosphere: • usually, a verythinlayer on the surface of the star • latestars: photosphere, chromosphere, corona • earlystars: photosphere, expanding regions

  7. Whystudystellaratmospheres? „Why in the worldwouldanyone want to studystellaratmospheres? Theycontainonly 10-10 of the mass of a typical star! Surelysuch a negligiblefraction of a star mass cannotpossiblyaffectitsoverallstructure and evolution!” Question to D. Mihalas, about 50 years ago From the lecture of Ivan Hubeny

  8. Whystudystellaratmospheres? Atmospheresareall we see; we have to usethisinformation in the fullest. Stars: Stellaratmospheres: Determination of atmosphericparameters.

  9. Spectralclassification • Atmosphericparameters • Effectivetemperature Teff • Surfacegravitylogg • Chemical abundances • Metallicity [m/H] • Microturbulence, macroturbulence • Chemicalpeculiarities • Stratification of elements • RotationvelocityVsini • Stellar wind parameters • Magnetic field parameters Stellar spectraWhatcan we obtain?

  10. Stellarclassification • Atmosphericparameters • Chemicalpeculiarities • Stratification of elements • Rotationvelocity • Stellarwind parameters • Magneticfield parameters • Multiple systems • Variabilityinspectral lines • Radialvelocities • Orbit determination • Clustermembership • Pulsations • … Stellar spectraWhatcan we obtain?

  11. Whystudystellaratmospheres? Stars: Stellaratmospheres: Determination of primary (Teff, logg, chemicalcomposition) and secondaryatmosphericparameters (rotationvelocity, turbulence etc.) Stellarstructure and evolution: Determination of basicstellarparameters (M, R, L) Determination of the detailedphysicalstate; Boundry for the stellarstructure/evolutionmodels; Atmospheres do influence the stellarevolutionafterall (mass loss from the atmosphere).

  12. Whystudystellaratmospheres? Global context: Galaxiesaremade of stars (specialcase: verybrightstars in distantgalaxies); Sourcesof chemicalspecies; (…)

  13. Whystudystellaratmospheres? Methodologicalimportance: Radiationdetermines the physicalstructure of the atmosphere, and thisstructureisprobedonly by the radiation; Sophisticatedmodelingapproachneeded – stellaratmospheresareguides for modelingotherastronomicalobjects (e.g. accretiondiscs, planetarynebulae, planetaryatmospheres etc.).

  14. Models: typicalassumptionsGeometry • Plane-parallel symetryvery small curvature (e.g. main-sequencestars); • Typically for stellarphotospheres: • Sun: km • Photosphere: km; • Chromosphere: km; • Corona:

  15. Models: typicalassumptionsGeometry • Plane-parallel symetryvery small curvature (e.g. main-sequencestars); • Sphericalsymetrysignificantcurvature (e.g. giants, supergiants); • …

  16. Models: typicalassumptionsHomogeneity • We assume the atmosphere to be homogeneous. • But it’s not always the case, e.g. sunspots, granulations, non-radialpulsations, magneticAp-stars (stellarspots), clumps and shocks in hot star winds etc.

  17. Models: typicalassumptionsStationarity • We assume the atmosphere to be stationary • In most casesthisassumptioncan be accepted • Exceptions: pulsatingstars, supernovae, mass transfer in closebinaries etc.

  18. Models: typicalassumptionsConservation of momentum and mass • We assumehydrostaticequilibrium; • plane-parallel geometry: • spherical geometry: • Exceptions: effects of magneticfields, interaction in binarysystems etc. • no hydrostaticequilibrium:

  19. Models: typicalassumptionsConservation of energy • Nuclearreactions and production of energy: stellarinteriors • Stellaratmospheres: negligibleproduction of energy • We assumethat the energyfluxisconservedatany radius:

  20. Differentstars – differentatmospheres Temperature: • MS stars, T~2000 – 60,000K • Brown dwarfs, T < 2000K • Hot, degenerateobjects, T~104 – 108 K • White dwarfs, T < 100,000K • Neutron stars, T~107K Density: • MS stars, N~1010 – 1015 cm-3 • WD, N~1021– 1026 cm-3

  21. Basic StructuralEquations Stellar atmosphere: plasmacomposed of particles (atoms, ions, freeelectrons, molecules, dustgrains) and photons. Conditions: temperatures: ~103 – ~105 K; densities: 106 – 1016 cm-3. Starting point for physicaldescription: kinetictheory Distribution function(most generalquantitywhichdescribes the system): - number of particles in a volume of the phasespaceatposition, momentum, and timet.

  22. Basic StructuralEquations Kinetic (Boltzmann) equation(describes a development of the distributionfunction): – nabladifferentialoperators with respect to the position and momentumcomponents – particlevelocity – externalforce – collisional term (describescreations and destructions of particles of type with the position () and momentum (). Kineticequation – completedescription of the system Problem – number of unknowns (e.g. differentexcitationstates of atoms etc.) Simplification– moments of the distributionfunction– integralsovermomentumweighted by variouspowers of

  23. Basic StructuralEquations Moment equations: (moment equations of the kineticequation, summedoverallkinds of particles; hydrodynamicequations): Continuityequation (1): Momentumequation (2): Energybalanceequation (3): – macroscopicvelocity – total mass density – pressure – externalforce – internalenergy , – radiation and conductiveflux

  24. Basic StructuralEquations Additionalequation (zeroth-order moment equation): conservationequationfor particles of type: – numberdensity (oroccupationnumber, orpopulation)of particles of type.

  25. Basic StructuralEquations Significant simplification of the system: Stationary, static medium (), 1-D (allquantitiesdepend on one coordinate): Statistical equilibriumequation (0): Hydrostaticequilibriumequation (2; assumption): Radiativeequilibriumequation (3; assumption):

  26. Basic StructuralEquations Convection: transport of energy by rising and fallingbubbles of material with propertiesdifferent from the local medium; non-stationary and non-homogeneousprocess. In 1-D stationaryatmosphere, simplification – mixing-lengththeory; Radiativeequilibriumequation with convection: – convectiveflux; specifiedfunction of basicstateparameters

  27. TE and LTE • TE – thermodynamicequilibrium: • simplification; particle velocitydistribution and the distribution of atomsoverexcitation and ionisationstatesarespecified by twothermodynamicvariables: absolutetemperature and totalparticlenumberdensity (or the electronnumberdensity). • stellaratmosphereis not in TE – we seea star – photonsareescaping – therearegradients of stateparameters.

  28. TE and LTE • LTE – localthermodynamicalequilibrium: • simplification; standard thermodynamical relations areemployedlocally for localvalues of , or, despite of the gradientsthatexist in the atmosphere. • equilibriumvalues of distributionfunctionsareassigned to massiveparticles, the radiation field candepart from equilibrium (Planckian) distributionfunction.

  29. LTE LTE ischaracterised by threedistributions: 1. Maxwellianvelocitydistribution of particles: – particle mass and velocity – Boltzmann constant

  30. LTE 2. Boltzmann excitationequation statistical weight of levels – levelenergies (measured from the groundstate)

  31. LTE 3. Sahaionisationequation – totalnumberdensity of ionisationstage – ionisationpotential of the ion – partitionfunctiondefined by (cgs) In LTE the same temperatureapplies to allkind of particles and to allkinds of distributions.

  32. LTE • Maxwell, Saha, Boltzmann equations – LTE from macroscopic point of view • Microscopically – LTE isholdifallatomicprocessesare in detailedbalance • the number of processedisexactlybalanced by the number of inverseprocesses, • – anyparticlestatebetweenwhichthereexists a physicallyreasonabletransition. • e.g. – isan atom in anexcitedstate, the same atom in anotherstate, etc.

  33. LTE vs. non-LTE • non-LTE (NLTE) – anystatethatdeparts from LTE (usuallyitmeansthatpopulations of someselectedenergylevels of someselectedatoms/ionsareallowed to depart from their LTE value, but velocitydistributions of allparticlesareassumed to be Maxwellian, with the same kinetictemperature).

  34. LTE vs. non-LTE When we have to take non-LTE intoaccount? • LTE breaks down if the detailedbalance of atleast one transitionbreaks down • Radiativetransitions– interactioninvolvesparticles and photones • Collisionaltransitions – interactionsbetweentwoormoremassiveparticles • Collisionstend to maintain LTE (theirvelocitiesareMaxwellian) • Validity of LTE depends on whether the radiativetransitionsare in detailedbalanceor not.

  35. LTE vs. non-LTE Departures from LTE: • Radiativerates in animportantatomictransitiondominateover the collisionalrates and • Radiationis not in equilibrium (intensitydoes not havePlanckiandistribution) Collisionalratesareproportional to the particledensity – in high densitiesdepartures from LTE will be small. Deep in the atmospherephotons do not escape and intensityisclose to the equilibriumvalue – departures from LTE are small evenif the radiativeratesdominateover the collisionalrates.

  36. LTE vs. non-LTE non-LTE if: rate of photonabsorptions >> rate of electroncollisions LTE if: lowtemperatures and high densities non-LTE if: high temperatures and lowdensities

  37. LTE vs. non-LTE LTE if: lowtemperatures and high densities non-LTE if: high temperatures and lowdensities R. Kudritzki lecture

  38. Transport of energy Mechanisms of energy transport: • radiation: (most important in allstars) • convection: (important especially in cool stars) • conduction: e.g. in the transition between solar chromosphereand corona • radial flow of matter: corona and stellar wind • sound and MHD waves: chromosphereand corona

  39. Intensity of Radiation specificintensityof radiationatposition, travelling in direction, with frequencyattime – the amount of energytransported by radiation in the frequencyrange, acrossanelementaryareainto a solid angle in a timeinterval: – anglebetween and the normal to the surface. specificintensity, proportionalityfactor; dimention: erg cm-2 sec-1 hz-1 sr-1 dS

  40. Intensity of Radiation Photon distributionfunction – number of photons per unit volumeatlocation and time, with frequencies in the rangepropagating with velocity in the direction. Number of photonscrossingan element in time is: Energy of photons: where:

  41. Intensity of Radiation From the comparison of energy of photons: with definedbefore: Relation betweenspecificintensity and photondistributionfunction: Using thisrelation we definemoments of the distributionfunction (specificintensity): energydensity, flux and stress tensor.

  42. Intensity of Radiation Energy densityof the radiation (is the number of photons in anelementaryvolume, is the energy of photon): Energyfluxof the radiation (is the vectorvelocity); how much energyflowstrough the surface element: Ratiationstresstensor: Photonmomentumdensity(momentum of anindividualphotonis):

  43. Absorption and EmissionCoefficient The radiative transfer equationdescribes the changes of the radiation field due to itsinteraction with the matter. Absorptioncoefficient– removal of energyfrom the radiation field by matter: Element of matterial of cross-section and length remove from a beam of specificintensityanamount of energy The dimention of is cm-1

  44. Absorption and EmissionCoefficient The radiative transfer equationdescribes the changes of the radiation field due to itsinteraction with the matter. Absorptioncoefficient– removal of energyfrom the radiation field by matter: – dimention of length; measures a characteristicdistance a photoncantravelbeforeitisabsorbed – a photonmeanfreepath.

  45. Absorption and EmissionCoefficient Emission coefficient– the energyreleased by the material in the form of radiation. Elementaryamount of material of cross-section and lengthreleasesinto a solid anglein directionwithin a frequency band anamount of energy: The dimentionis erg cm-3 hz-1 sec-1 sr-1 dS

  46. Absorption and EmissionCoefficient Microscopicphysics– allcontributions from microscopicprocessesthatgiverise to anabsorptionoremission of photons with specifiedproperties. True absorption and scattering: True (thermal) absorption – photonisremoved from a beam and isdestroyed. Scattering – photonisremoved from a beam and immediately re-emitted in a differentdirectionwith slightlydifferentfrequency.

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