A finite temperature chandrasekhar model: Determining the parameters and calculation of the characteristics of degenerate dwarfs

Abstract

We suggest a generalization of the standard Chandrasekhar model for degenerate dwarfs. We apply an equation of state for a degenerate ideal electron gas in the form of a Sommerfeld expansion in the parameter k B T (r)/m 0 c 2 . The radial temperature distribution T (r) is modeled taking into account the presence of the isothermal core. The model has four dimensionless parameters, two microscopic (the relativistic parameter at the stellar center x 0 and the chemical-composition parameter μ e = A/Z) and two macroscopic (the dimensionless temperature T * 0 = k B T c /m 0 c 2 and dimensionless radius ξ 0 = R c /R of the core, where R c and R are the radii of the core and dwarf). We found x 0 , μ e , and T * 0 for about 3000 DA white dwarfs, based on their masses, radii, and effective temperatures from the Sloan Digital Sky Survey Data Release 4; ξ 0 was treated as a free parameter. The influence of temperature effects on the macroscopic characteristics is analyzed, in particular, the minimum mass and maximum radii of the stars. Based on our computed energy-radius dependence, we suggest an interpretation of the observed radius distribution for these dwarfs.

Planar and non-planar nucleus-acoustic solitary waves in warm degenerate multi-nucleus plasmas

“…The works highlighted above are valid only for absolutely cold degenerate plasma species, but are not valid for degenerate plasma species at finite temperature, particularly for hot white dwarfs (Dufour et al 2008(Dufour et al , 2011Werner & Rauch 2015;Werner, Rauch & Reindl 2019;Koester, Kepler & Irwin 2020). To overcome this limitation in previously published works (Mamun et al 2016(Mamun et al , 2017Zaman et al 2017Zaman et al , 2018Chowdhury et al 2018;Jannat & Mamun 2018a,b;Das & Karmakar 2019), the equation of state for a degenerate plasma at finite temperature (Manfredi 2005;Vavrukh & Smerechynskyi 2012;Hossain & Mandal 2019) is derived by quantum field theory (Hossain & Mandal 2019) and by introducing two parameters, namely σ j = m j c 2 /E Fj and σ Tj = k B T j /E Fj , where E Fj (T j ) is the the Fermi energy (temperature) of species j with k B being the Boltzmann constant. The equation of state (1.1) for plasma species j at finite temperature T j can, therefore, be modified as…”

“…2018; Jannat & Mamun 2018 a , b ; Sultana & Schlickeiser 2018; Sultana et al. 2018; Das & Karmakar 2019), the equation of state for a degenerate plasma at finite temperature (Manfredi 2005; Vavrukh & Smerechynskyi 2012; Hossain & Mandal 2019) is derived by quantum field theory (Hossain & Mandal 2019) and by introducing two parameters, namely and , where () is the the Fermi energy (temperature) of species with being the Boltzmann constant. The equation of state (1.1) for plasma species at finite temperature can, therefore, be modified as where arises due to the effect of finite temperature , and is given by (Hossain & Mandal 2019) in which and .…”

The structure and stability of massive hot white dwarfs

“…The temperature influence on the structure of white dwarfs has been investigated under diverse conditions. Among them, for example, in the Newtonian framework, to optimize the temperature effects, Vavrukh & Smerechynskyi (2012) assume the thermal energy proportional to the kinetic energy of the electrons. Considering the Fermi-Dirac equation of state (EOS)-with the Sommerfeld (1928) expansion-authors found that the static equilibrium configurations derived from their model are within the results estimated by the observational data.…”

Consideration of the Competing Factors in Calculations of the Characteristics of Non-Magnetic Degenerate Dwarfs

“…It turned out that the degenerate dwarfs are characterized by the same variety of characteristics like stars of other types. The most striking fact indicating the limitation of applying Chandrasekhar's model is the distribution of dwarfs with small and medium masses on the "mass-radius" plane [11], which is a manifestation of the incomplete degeneration of the subsystem of electrons, since the effective temperatures of the photosphere of some dwarfs reach 10 5 K. However, the influence of temperature effects on the characteristics of massive dwarfs is very small. In the case of massive non-magnetic dwarfs, the main factors of the structure formation are interparticle Coulomb interactions and the axial rotation, which are competing ones.…”