DOI: 10.5061/dryad.dncjsxkzt
title: Numerical code and data for the stellar structure and dynamical instability analysis of generalised uncertainty white dwarfs

description: The enclosed code and dataset correspond to the numerical
 solution of  Tolman Oppenheimer Volkoff (TOV) equation (3.3) and
 (3.4) and the dynamical instability scheme given by equations
 4.13 to 4.16 in the research article ``Existence of Chandrasekhar's
 limit in generalized uncertainty white dwarfs'' by the same
 authors. The dataset is generated for a wide range of central Fermi
 momentum $xi_c$ supplemented by the equation of state (2.6) and (2.11)
  parametrized by the Fermi momentum $\xi$. For a given value of
 central Fermi momentum, the solution gives the total mass and radius of
 the white dwarfs. These solutions facilitate the evaluation of
 the integrals 4.14--4.16 giving the eigenfrequency of the
 fundamental mode in equation (4.13).
description: The research article entitled ``Existence of Chandrasekhar's
 limit in generalized uncertainty white dwarfs'' by the same
 authors requires a numerical solution of the Einstein equation for
 spherically symmetric white dwarf stars.   A single
 dataset in Figures (1) and (2) in the research article corresponds to
 solving Tolman Oppenheimer Volkoff (TOV) equations for a range central
 Fermi momenta with a particular choice of GUP parameter $\beta_0$.
 The first-order differential equations (see equations 3.3 and 3.4 in the
 article) are solved numerically with the aid of C programming using the
 fourth-order Runge-Kutta method with boundary conditions as described in
 the article.  The dataset for the eigenfrequency of the
 fundamental mode is obtained from the dynamical instability scheme as
 described in the article. Integrations in equations 4.14-4.16 carried
 out employing the Trapezoidal method. This yields the eigenfrequency
 corresponding to a range of central Fermi momentum (or central density)
 for a particular choice of the GUP parameter $\beta_0$.
description: There is a total of 17 datasets to produce all the Figures in the
 article. There are mainly two different data files: GUP White Dwarf
 Mass-Radius (GUPWD_M-R) data and GUP White Dwarf Profile (GUPWD_Profile)
 data.  The file GUPWD_M-R gives only the Mass-Radius
 relation with Radius (km) in the first column and Mass (solar mass) in the
 second. On the other hand GUPWD_Profile provides the
 complete profile with following columns. column 1:
 Dimensionless central Fermi Momentum $\xi_c$<br> column 2: Central
 Density $\rho_c$ ( Log10 [$\rho_c$ g cm$^{-3}$] )<br> column 3:
 Radius $R$ (km)<br> column 4: Mass $M$ (solar mass)<br> column
 5: Square of fundamental frequency $\omega_0^2$ (sec$^{-2}$)
 ===================================================================================== Figure 1 (a) gives Mass-Radius (M-R) curves for $\beta_0=10^{42}$, $10^{41}$ and $10^{40}$. <br> The filenames of the corresponding dataset are  GUPWD_M-R[Beta0=E42].dat<br> GUPWD_M-R[Beta0=E41].dat<br> GUPWD_M-R[Beta0=E40].dat ===================================================================================== Figure 1 (b) gives Mass-Radius (M-R) curves for the high value of $\beta_0=10^{44}$ which is <br> numerically obtained in the dataset with the filename  GUPWD_M-R[Beta0=E44].dat.  The Figure also plots analytically obtained M-R relation. For low $\xi_c$ values (inset), the mass-radius curve is given by the expression (3.9) and (3.12) in the article, the corresponding data is given in the file ''GUPWD_M-R_Asym_Low.dat''. Note that Mass-radius the curve is independent of the GUP parameter for low values of central Fermi momentum. For high $\xi_c$ values, the mass-radius curve is given by the expression (3.20), and it is a function of the value $\beta_0$. The corresponding data is given in the file ''GUPWD_M-R_Asym_High[Beta0=E44].dat'' for $\beta_0=10^{44}$. ===================================================================================== Figure 2 (a) plots Mass-Radius (M-R) curves for $\beta_0=6.3\times 10^{39}$, $6.0\times 10^{39}$, $5.38\times 10^{39}$, $5.0\times 10^{39}$ and $4.5\times 10^{39}$.  The filenames of the corresponding dataset are  GUPWD_M-R[Beta0=6.30E39].dat<br> GUPWD_M-R[Beta0=6.00E39].dat<br> GUPWD_Profile[Beta0=5.38E39].dat<br> GUPWD_Profile[Beta0=5.00E39].dat<br> GUPWD_M-R[Beta0=4.50E39].dat ===================================================================================== Figure 2 (b) plots Mass-Radius (M-R) curves for $\beta_0=10^{39}$,  $\beta_0=10^{38}$ and  $\beta_0=0$.  The filenames of the corresponding dataset are  GUPWD_M-R[Beta0=E39].dat<br> GUPWD_Profile[Beta0=1.00E38].dat<br> GUPWD_Profile[Beta0=0.0].dat ===================================================================================== Figure 3 plots the square of the eigenfrequency of the fundamental mode as the function of central density. The filenames for the corresponding dataset is GUPWD_Profile[Beta0=1.00E40].dat<br> GUPWD_Profile[Beta0=5.60E39].dat<br> GUPWD_Profile[Beta0=5.38E39].dat<br> GUPWD_Profile[Beta0=5.00E39].dat<br> GUPWD_Profile[Beta0=1.00E38].dat<br> GUPWD_Profile[Beta0=0.0].dat