J/A+A/543/A67 WDA and WDB apsidal-motion constants (Claret, 2012)
The internal structure of neutron stars and white dwarfs, and the
Jacobi virial equation
Claret A.
<Astron. Astrophys. 543, A67 (2012)>
=2012A&A...543A..67C 2012A&A...543A..67C
ADC_Keywords: Models, evolutionary ; Stars, white dwarf ; Pulsars
Keywords: binaries: eclipsing - stars: interiors - stars: evolution -
stars: rotation - white dwarfs - neutron stars
Abstract:
The internal structure constants kj 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☉ and for
neutron star models covering a mass range from 1.0 up to
2.183M☉, in 0.1 mass step. We show that, contrary to previously
established opinion, the product of the form-factors β and
α, 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 αβ at the pre main-sequence phase
(∼0.4). These results may have important consequences for the
investigation of the Jacobi virial equation.
File Summary:
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FileName Lrecl Records Explanations
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ReadMe 80 . This file
table1.dat 106 388 WDA model, M=0.52 solar masses
table2.dat 106 423 WDA model, M=0.57 solar masses
table3.dat 106 429 WDA model, M=0.84 solar masses
table4.dat 106 389 WDA model, M=1.00 solar masses
table5.dat 106 508 WDB model, M=0.52 solar masses
table6.dat 106 462 WDB model, M=0.57 solar masses
table7.dat 106 384 WDB model, M=0.84 solar masses
table8.dat 106 448 WDA model, M=1.00 solar masses
table9.dat 84 14 Neutron star models, M=1.00-2.183 solar masses
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See also:
J/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)
Byte-by-byte Description of file: table[1-8].dat
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Bytes Format Units Label Explanations
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1- 16 E16.8 yr Age Age of the models
19- 26 F8.5 Msun Mass [0.52/1] Initial mass
29- 36 F8.5 [Lsun] log(L) Log(Total luminosity)
39- 46 F8.5 [K] log(Te) Log(Effective temperature)
49- 56 F8.5 [cm/s2] log(g) Log (Surface gravity)
59- 66 F8.5 [---] logK2 Log(Apsidal motion constant (j=2))
69- 76 F8.5 [---] logK3 Log(Apsidal motion constant (j=3))
79- 86 F8.5 [---] logK4 Log(Apsidal motion constant (j=4))
89- 96 F8.5 --- alpha α=-Ω.R/GM2 (Newtonian)
form-factor of gravitational potential energy
99-106 F8.5 --- beta β=fractional gyration radius (Newtonian)
defined as I(moment of intertia)=M(βR)2
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Byte-by-byte Description of file: table9.dat
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Bytes Format Units Label Explanations
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1- 7 F7.4 Msun Mass [1/2.183] Initial mass
9- 20 E12.6 cm Rad Radius of the models
22- 28 F7.4 [cm/s2] log(g) Log (Surface gravity)
30- 36 F7.4 [---] logK2 Log(Apsidal motion constant (j=2))
38- 44 F7.4 [---] logK3 Log(Apsidal motion constant (j=3))
46- 52 F7.4 [---] logK4 Log(Apsidal motion constant (j=4))
54- 60 F7.4 --- alpha α=-Ω.R/GM2 (Newtonian)
62- 68 F7.4 --- beta β=fractional gyration radius (Newtonian)
70- 76 F7.4 --- alphaGR αGR (General Relativity value)
78- 84 F7.4 --- betaGR βGR (General Relativity value)
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Acknowledgements:
Antonio Claret, claret(at)iaa.es
(End) Patricia Vannier [CDS] 04-Jun-2012