Satellite Halo Tidal Heating Rates

Class providing models of tidal heating rates in satellite halos. Specifically, the integrated, normalized (i.e. the energy divided by radius squared) tidal heating energy, \(Q_\mathrm{tidal}\).

Default implementation: satelliteTidalHeatingRateZero

Methods

heatingRate → double precision

Return the satellite tidal heating rate for node (in units of (km/s/Mpc)\(^2\)/Gyr).

  • type(treeNode), intent(inout) :: node

satelliteTidalHeatingRateGnedin1999

A satellite tidal heating rate class which uses the formalism of Gnedin et al. (1999) to compute the heating rate:

\[\dot{Q}_\mathrm{tidal}=\frac{1}{3}\epsilon\left[1+\left(\frac{T_\mathrm{shock}}{T_\mathrm{orb}}\right)^2\right]^{-\gamma} g_{ij} G^{ij}\]

where \(T_\mathrm{orb}\) and \(T_\mathrm{shock}\) are the orbital period and shock duration, respectively, of the satellite, \(\epsilon=\)[epsilon] and \(\gamma=\)[gamma] are model parameters, \(g_{ij}\) is the tidal tensor, and \(G_{ij}\) is the integral with respect to time of \(g_{ij}\) along the orbit of the satellite. Upon tidal heating, a mass element at radius \(r_\mathrm{i}\) expands to radius \(r_\mathrm{f}\), according to the equation

\[\frac{1}{r_\mathrm{f}}=\frac{1}{r_\mathrm{i}}-\frac{2r_\mathrm{i}^3Q_\mathrm{tidal}}{\mathrm{G}M_\mathrm{sat}(<r_\mathrm{i})}.\]

Parameters

  • [epsilon] (default 3.0d0) — Parameter, \(\epsilon\), controlling the tidal heating rate of satellites in the Gnedin1999 method.

  • [gamma] (default 2.5d0) — Parameter, \(\gamma\), controlling the tidal heating rate of satellites in the Gnedin1999 method.

satelliteTidalHeatingRateZero

A satellite tidal heating rate class which implements a tidal heating rate model in which the heating rate is always zero.

(Default implementation)