J/A+A/676/A50ivo://CDS.VizieR/J/A+A/676/A50doi:10.26093/cds/vizier.36760050CDSLazzarotto A.Hui-Bon-Hoa A.Rieutord M.2024-11-28T20:04:51Z2023-08-07T08:42:25ZCDS support team

CDS, Observatoire de Strasbourg, 11 rue de l'Universite, F-67000 Strasbourg, France

cds-question@unistra.frastronomical-modelsstellar-activityspectroscopyIntermediate-mass stars are often fast rotators, and hence are centrifugally flattened and notably affected by gravity darkening. To analyse this kind of stars properly, one must resort to 2D models to compute the visible radiative flux and to take the geometrical effect of the star inclination into account. Assuming a given stellar age and chemical composition, our aim is to derive the mass and rotation rates of main sequence fast rotating stars, along with their inclination, from photometric quantities influenced by gravity darkening. We chose three observables that vary with mass, rotation, and inclination: the temperature derived by the infrared flux method TIRFM, the Stroemgren c1 index, and a second index c2 built in the same way as the c1 index, but sensitive to the UV side of the Balmer jump. These observables are computed from synthetic spectra produced with the PHOENIX code and rely on a 2D stellar structure from the ESTER code. These quantities are computed for a grid of models in the range 2 to 7M_{sun}_ and rotation rates from 30% to 80% of the critical rate. Then, for any triplet (TIRFM, c1, c2), we try to retrieve the mass, rotation rate, and inclination using a Levenberg-Marquardt scheme, after a selection step to find the most suitable starting models. Hare-and-hound tests showed that our algorithm can recover the mass, rotation rate, and inclination with a good accuracy. The difference between input and retrieved parameters is negligible for models lying on the grid and is less than a few percent otherwise. An application to the real case of Vega showed that the u filter is located in a spectral region where the modelled and observed spectra are discrepant, and led us to define a new filter. Using this new filter and subsequent index, the Vega parameters are also retrieved with satisfactory accuracy. This work opens the possibility to determine the fundamental parameters of rapidly rotating early-type stars from photometric space observations.2023A&A...676A..50Lhttps://cdsarc.cds.unistra.fr/viz-bin/cat/J/A+A/676/A50CatalogResearchIsServedByTAP VizieR generic servicehttps://cds.unistra.fr/vizier-org/licences_vizier.htmlhttps://vizier.cds.unistra.fr/viz-bin/VizieR-2?-source=J/A+A/676/A50https://vizier.iucaa.in/viz-bin/VizieR-2?-source=J/A+A/676/A50http://vizieridia.saao.ac.za/viz-bin/VizieR-2?-source=J/A+A/676/A50https://vizier.cds.unistra.fr/viz-bin/votable?-source=J/A+A/676/A50https://vizier.iucaa.in/viz-bin/votable?-source=J/A+A/676/A50http://vizieridia.saao.ac.za/viz-bin/votable?-source=J/A+A/676/A50GETtext/xml+votablehttps://tapvizier.cds.unistra.fr/TAPVizieR/tapdefaultJ/A+A/676/A50/info_solSolar ESTER model informationrecnoRecord number assigned by the VizieR team. Should Not be used for identification.meta.recordintopaOpacityphys.absorption.coeffcharMassMassgphys.massdoubleRotRateRotation rate given as percentagephys.veloc.rotatintRpPolar radiuscmphys.size.radiusdoubleReEquatorial radiuscmphys.size.radiusdoubleepsFlatnesssrc.morph.paramfloatLLuminosity (erg/s)1e-07Wphys.luminositydoubleTeffPPolar effective temperatureKphys.temperature.effectivefloatTeffEEquatorial effective temperatureKphys.temperature.effectivefloatlog(geff)PLogarithm of the polar effective gravitylog(cm.s**-2)phys.gravityfloatlogg(eff)ELogarithm of the equatorial effective gravitylog(cm.s**-2)phys.gravityfloatveqEquatorial velocitykm/sphys.velocdoubleOmegaPPolar rotational speedrad/sphys.veloc.rotatdoubleOmegaEEquatorial rotational speedrad/sphys.veloc.rotatdoubleOmegaCCritical rotational speedrad/sphys.veloc.rotatdoublePeriodP? Polar period (- for infinity)dtime.perioddoublenullablePeriodE? Equatorial period (- for infinity)dtime.perioddoublenullablePeriodC? Critical period (- for infinity)dtime.perioddoublenullableLzAngular momentum (erg*s)1e-07J.sphys.angMomentumdoublejLz/Mcm**2.s**-1phys.angMomentumdoubleIzAxial moment of inertiag.cm**2stat.variance;phys.size.axisRatiodoubleIcCentral moment of inertiag.cm**2stat.variance;em.wl.centraldoubleJ2First multipolar coefficient of the gravitational field from inertia momentsstat.fit.paramdoubleJ2-bisFirst multipolar coefficient of the gravitational field direct calculationstat.fit.paramdoubleTKinetic energy1e-07Jphys.energydoubleT/WRatio between rotational kinetic energy and gravitational binding energyphys.energydoubleTkhKelvin-Helmoltz timeyrtime.epochdoubleMcMass of the coregphys.massdoubleRpcPolar radius of the corecmphys.size.radiusdoubleRecEquatorial radius of the corecmphys.size.radiusdoubleepscFlatness of the coresrc.morph.paramfloatLzcAngular momentum of the core (erg*s)1e-07J.sphys.angMomentumdoubleXcFraction of the hydrogen abundance present in the convective core. Hydrogen abundance in the core is thus X=X0.Xcphys.abund.X;arith.ratiofloatTcCentral temperatureKphys.temperaturedoublerhocCentral densityg.cm**-3phys.densitydoublepcCentral pressuredyn.cm**-2phys.pressuredoubleX0Mass fraction of hydrogenphys.abund.XfloatY0Mass fraction of heliumphys.abund.YfloatZ0Mass fraction of metalsphys.abund.ZfloatndomNumber of domainsmeta.numberintndomcNumber of domains in convective coremeta.numberintnptsNumber of points in each domainsmeta.numberintnrNumber of radial points in external domainmeta.numberintnthNumber of latitudinal pointsmeta.numberintnexNumber of radial points in external domainmeta.numberintnucType of nuclear reactionsmeta.notecharatmType of atmospheremeta.notecharsurffIf different from unity, coefficient modifying boundary conditions to truncate the stellar modelstat.fit.paramfloatcore-convec[0/1] values enable/disable convection in corestat.fit.paramintmin-core-sizeImpose a minimum core sizecmstat.fit.paramdoubleenv-convec[0/1] values enable/disable convection in envelopestat.fit.paramintVirial-testNormalized residual resulting from the Virial theoremstat.fit.paramdoubleEnergy-testRelative difference between the luminosity of the star obtained as the integral over the volume of the energy generation rate and that obtained as the integral of the energy flux at the surfacestat.fit.paramdoubleeosEquation of statephys.eoscharJ/A+A/676/A50/info_vegVega ESTER model informationndomNumber of domainsmeta.numberintatmType of atmospheremeta.notecharsurffIf different from unity, coefficient modifying boundary conditions to truncate the stellar modelstat.fit.paramfloatcore-convec[0/1] values enable/disable convection in corestat.fit.paramintmin-core-sizeImpose a minimum core sizecmstat.fit.paramdoubleenv-convec[0/1] values enable/disable convection in envelopestat.fit.paramintVirial-testNormalized residual resulting from the Virial theoremstat.fit.paramdoubleopaOpacityphys.absorption.coeffcharXcFraction of the hydrogen abundance present in the convective core. Hydrogen abundance in the core is thus X=X0.Xcphys.abund.X;arith.ratiofloatrecnoRecord number assigned by the VizieR team. Should Not be used for identification.meta.recordintMassMassgphys.massdoubleRotRateRotation rate given as percentagephys.veloc.rotatintRpPolar radiuscmphys.size.radiusdoubleReEquatorial radiuscmphys.size.radiusdoubleepsFlatnesssrc.morph.paramfloatLLuminosity (erg/s)1e-07Wphys.luminositydoubleTeffPPolar effective temperatureKphys.temperature.effectivefloatTeffEEquatorial effective temperatureKphys.temperature.effectivefloatlog(geff)PLogarithm of the polar effective gravitylog(cm.s**-2)phys.gravityfloatlogg(eff)ELogarithm of the equatorial effective gravitylog(cm.s**-2)phys.gravityfloatveqEquatorial velocitykm/sphys.velocdoubleOmegaPPolar rotational speedrad/sphys.veloc.rotatdoubleOmegaEEquatorial rotational speedrad/sphys.veloc.rotatdoubleOmegaCCritical rotational speedrad/sphys.veloc.rotatdoublePeriodP? Polar period (- for infinity)dtime.perioddoublenullablePeriodE? Equatorial period (- for infinity)dtime.perioddoublenullablePeriodC? Critical period (- for infinity)dtime.perioddoublenullableLzAngular momentum (erg*s)1e-07J.sphys.angMomentumdoublejLz/Mcm**2.s**-1phys.angMomentumdoubleIzAxial moment of inertiag.cm**2stat.variance;phys.size.axisRatiodoubleIcCentral moment of inertiag.cm**2stat.variance;em.wl.centraldoubleJ2First multipolar coefficient of the gravitational field from inertia momentsstat.fit.paramdoubleJ2-bisFirst multipolar coefficient of the gravitational field direct calculationstat.fit.paramdoubleTKinetic energy1e-07Jphys.energydoubleT/WRatio between rotational kinetic energy and gravitational binding energyphys.energydoubleTkhKelvin-Helmoltz timeyrtime.epochdoubleMcMass of the coregphys.massdoubleRpcPolar radius of the corecmphys.size.radiusdoubleRecEquatorial radius of the corecmphys.size.radiusdoubleepscFlatness of the coresrc.morph.paramfloatLzcAngular momentum of the core (erg*s)1e-07J.sphys.angMomentumdoubleTcCentral temperatureKphys.temperaturedoublerhocCentral densityg.cm**-3phys.densitydoublepcCentral pressuredyn.cm**-2phys.pressuredoubleX0Mass fraction of hydrogenphys.abund.XfloatY0Mass fraction of heliumphys.abund.YfloatZ0Mass fraction of metalsphys.abund.ZfloatndomcNumber of domains in convective coremeta.numberintnptsNumber of points in each domainsmeta.numberintnrNumber of radial points in external domainmeta.numberintnthNumber of latitudinal pointsmeta.numberintnexNumber of radial points in external domainmeta.numberinteosEquation of statephys.eoscharnucType of nuclear reactionsmeta.notecharEnergy-testRelative difference between the luminosity of the star obtained as the integral over the volume of the energy generation rate and that obtained as the integral of the energy flux at the surfacestat.fit.paramdoubleJ/A+A/676/A50/obs_solObservable according inclination for model with solar composition and agerecnoRecord number assigned by the VizieR team. Should Not be used for identification.meta.recordintMassStar masssolMassphys.massfloatRotRateRotaion rate given as percentagephys.veloc.rotatfloatiInclinaitiondegsrc.orbital.inclinationfloatTirfmEffective temperature computed with Infrared Method FluxKphys.temperature.effectivedoublec1Stromgren color indexmagphot.colordoublec1pStromgren color index with shifter u-filtermagphot.colordoublec2Color index build with HST filtersmagphot.colordoubleFileNameFile name in subdirectory filesmeta.id;meta.filecharJ/A+A/676/A50/obs_vegObservable according inclination for model with Vega composition and agerecnoRecord number assigned by the VizieR team. Should Not be used for identification.meta.recordintMassStar masssolMassphys.massfloatRotRateRotaion rate given as percentagephys.veloc.rotatfloatiInclinaitiondegsrc.orbital.inclinationfloatTirfmEffective temperature computed with Infrared Method FluxKphys.temperature.effectivedoublec1Stromgren color indexmagphot.colordoublec1pStromgren color index with shifter u-filtermagphot.colordoublec2Color index build with HST filtersmagphot.colordoubleFileNameFile name in subdirectory filesmeta.id;meta.filechar