J/A+A/543/A67ivo://CDS.VizieR/J/A+A/543/A67doi:10.26093/cds/vizier.35430067CDSClaret A.2017-06-26T11:49:58Z2012-06-27T15:44:15ZCDS support team

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

cds-question@unistra.frstellar-evolutionary-modelswhite-dwarf-starspulsarsThe internal structure constants k_j_ and the radius of gyration are useful tools for investigating the apsidal motion and tidal evolution of close binaries and planetary systems. These parameters are available for various evolutionary phases but they are scarce for the late stages of stellar evolution. To cover this gap, we present here the calculations of the apsidal-motion constants, the fractional radius of gyration, and the gravitational potential energy for two grids of cooling evolutionary sequences of white dwarfs and for neutron star models. The cooling sequences of white dwarfs were computed with LPCODE. An additional alternative to the white dwarf models was also adopted with the MESA code which allows non-stop calculations from the pre main-sequence (PMS) to the white dwarf cooling sequences. Neutron star models were acquired from the NSCool/TOV subroutines. The apsidal-motion constants, the moment of inertia and the gravitational potential energy were computed with a fourth-order Runge-Kutta method. The parameters are made available for four cooling sequences of white dwarfs (DA and DB types): 0.52, 0.57, 0.837 and 1.0M_{sun}_ and for neutron star models covering a mass range from 1.0 up to 2.183M_{sun}_, in 0.1 mass step. We show that, contrary to previously established opinion, the product of the form-factors {beta} and {alpha}, which are related to the moment of inertia, and gravitational potential energy, is not constant during some evolutionary phases. Regardless of the final products of stellar evolution (white dwarfs, neutron stars and perhaps black holes), we found that they recover the initial value of product {alpha}{beta} at the pre main-sequence phase (~0.4). These results may have important consequences for the investigation of the Jacobi virial equation.2012A&A...543A..67Chttps://cdsarc.cds.unistra.fr/viz-bin/cat/J/A+A/543/A67CatalogResearchIsServedByTAP VizieR generic servicerelated-toJ/A+A/541/113 : PMS gravity-darkening exponents & apsidal-motion (Claret 2012)J/A+A/424/919 : New grids of stellar models I (Claret, 2004)J/A+A/440/647 : New grids of stellar models II (Claret, 2005)J/A+A/453/769 : New grids of stellar models III (Claret, 2006)J/A+A/467/1389 : New grids of stellar models IV (Claret, 2007)https://cds.unistra.fr/vizier-org/licences_vizier.htmlhttps://vizier.cds.unistra.fr/viz-bin/VizieR-2?-source=J/A+A/543/A67https://vizier.iucaa.in/viz-bin/VizieR-2?-source=J/A+A/543/A67http://vizieridia.saao.ac.za/viz-bin/VizieR-2?-source=J/A+A/543/A67https://vizier.cds.unistra.fr/viz-bin/votable?-source=J/A+A/543/A67https://vizier.iucaa.in/viz-bin/votable?-source=J/A+A/543/A67http://vizieridia.saao.ac.za/viz-bin/votable?-source=J/A+A/543/A67GETtext/xml+votablehttps://tapvizier.cds.unistra.fr/TAPVizieR/tapRadiodefaultJ/A+A/543/A67/wdaWDA model, M=0.52, 0.57, 0.84 and 1M_{sun}_recnoRecord number assigned by the VizieR team. Should Not be used for identification.meta.recordintAgeAge of the modelsyrtime.agedoubleMass[0.52/1] Initial masssolMassphys.massdoublelog(L)Log(Total luminosity)log(solLum)phys.luminositydoublelog(Te)Log(Effective temperature)log(K)arith.zpdoublelog(g)Log (Surface gravity)log(cm.s**-2)arith.zpdoublelogK2Log(Apsidal motion constant (j=2))stat.paramdoublelogK3Log(Apsidal motion constant (j=3))stat.paramdoublelogK4Log(Apsidal motion constant (j=4))stat.paramdoublealpha{alpha}=-{Omega}.R/GM^2^ (Newtonian) form-factor of gravitational potential energystat.paramdoublebeta{beta}=fractional gyration radius (Newtonian) defined as I(moment of intertia)=M({beta}R)^2^stat.paramdoubleJ/A+A/543/A67/wdbWDB model, M=0.52, 0.57, 0.84 and 1M_{sun}_recnoRecord number assigned by the VizieR team. Should Not be used for identification.meta.recordintAgeAge of the modelsyrtime.agedoubleMass[0.52/1] Initial masssolMassphys.massdoublelog(L)Log(Total luminosity)log(solLum)phys.luminositydoublelog(Te)Log(Effective temperature)log(K)arith.zpdoublelog(g)Log (Surface gravity)log(cm.s**-2)arith.zpdoublelogK2Log(Apsidal motion constant (j=2))stat.paramdoublelogK3Log(Apsidal motion constant (j=3))stat.paramdoublelogK4Log(Apsidal motion constant (j=4))stat.paramdoublealpha{alpha}=-{Omega}.R/GM^2^ (Newtonian) form-factor of gravitational potential energystat.paramdoublebeta{beta}=fractional gyration radius (Newtonian) defined as I(moment of intertia)=M({beta}R)^2^stat.paramdoubleJ/A+A/543/A67/table9Neutron star models, M=1.00-2.183 solar massesrecnoRecord number assigned by the VizieR team. Should Not be used for identification.meta.recordintMass[1/2.183] Initial masssolMassphys.massfloatRadRadius of the modelskmphys.size.radiusfloatlog(g)Log (Surface gravity)log(cm.s**-2)arith.zpfloatlogK2Log(Apsidal motion constant (j=2))stat.paramfloatlogK3Log(Apsidal motion constant (j=3))stat.paramfloatlogK4Log(Apsidal motion constant (j=4))stat.paramfloatalpha{alpha}=-{Omega}.R/GM^2^ (Newtonian)stat.paramfloatbeta{beta}=fractional gyration radius (Newtonian)stat.paramfloatalphaGR{alpha}_GR_ (General Relativity value)stat.paramfloatbetaGR{beta}_GR_ (General Relativity value)stat.paramfloat