jesterTOV.ptov module

The post-TOV (pTOV) module extends the standard TOV equations to include tidal deformability calculations.

jesterTOV.ptov.calc_k2(R, M, H, b)

jesterTOV.ptov.sigma_func(p, e, m, r, lambda_BL, lambda_DY, lambda_HB, gamma, alpha, beta)

jesterTOV.ptov.tov_ode(h, y, eos)

jesterTOV.ptov.tov_solver(eos, pc)

Mathematical Background

The post-TOV equations include additional perturbative equations for calculating the tidal Love number \(k_2\):

\[\frac{dH}{dr} = \beta(r) H + \alpha(r) b\]

\[\frac{db}{dr} = H + \gamma(r) b\]

where \(H\) and \(b\) are auxiliary functions related to the tidal deformation, and \(\alpha\), \(\beta\), \(\gamma\) are coefficients that depend on the background stellar structure.

The tidal Love number is then:

\[k_2 = \frac{8C^5}{5}(1-2C)^2[2 + 2C(y_R - 1) - y_R] \times \{2C[6-3y_R + 3C(5y_R-8)] + 4C^3[13-11y_R + C(3y_R-2) + 2C^2(1+y_R)] + 3(1-2C)^2[2-y_R + 2C(y_R-1)]\ln(1-2C)\}^{-1}\]

where \(C = GM/Rc^2\) is the compactness and \(y_R\) is related to the tidal response at the surface.