TOVSolver

TOVSolver#

Overview#

This entry contains all relevant information regarding Tolman-Oppenheimer-Volkov (TOV, [Tol39]) system of PDEs. In particular, one specifies here radius discretization, central energy density for IVP, \(P(\rho)\) EoS function discretization etc. In what follows we discuss all the possible settings under this entry.

This section is essential for any simulation and is therefore mandatory to include.

In order to refer to an example, see presupplied/APR4/RHMconfig.json and presupplied/APR4/APR_EOS_Acc_Fe_RHMstandard.dat.

Description#

  • "AdaptionLimit" (uint, [TOV, COOL, RH]) : Defines how many times TOV solver will try to adapt the radial step before concluding early termination. Defaults to 20.

Note

Early termination can be overwatched in “Debug” log.

  • "EoSInterpolation" (string, [TOV, COOL, RH]) : Interpolation kind to be used for \(\rho(P)\) dependence. Choose from [“Linear”, “Cubic”], with “Cubic” being default.

  • "DensityInterpolation" (string, [TOV, COOL, RH]) : Interpolation kind to be used for \(n_{bar}(P)\) dependence. Choose from [“Linear”, “Cubic”], with “Linear” being default.

Warning

“Cubic” mode strongly distorts the \(n_{bar}-M\) relation at phase transitions, even weak ones. Select on your own risk.

  • "RadialInterpolation" (string, [TOV, COOL, RH]) : Interpolation kind to be used for discretized \(m(r), P(r), \rho(r), ...\) dependences. Choose from [“Linear”, “Cubic”], with “Cubic” being default.

  • "LengthUnits" (string/double, [TOV, COOL, RH]) : Conversion factor from length to natural units (GeV powers). It must either be supplied as a choice from [“Gev-1”, “Km”, “M”, “Cm”], or as an actual multiplier. Used for “RadiusStep”

  • "RadiusStep" (double, [TOV, COOL, RH]) : Defines radius discretization step. Units are defined by “LengthUnits” entry.

  • "CenterPressure" : Defines central pressure for initial value problem.

    • "ProvidedAs" (string, [COOL, RH]) : The way the “CenterPressure” is provided. Choose from [“Same”, “LinspacedMinToMax”, “MassCached”]. “LinspacedMinToMax” linearly maps \([0,1] \rightarrow [P_{min}, P_{max}]\), while “Same” assumes same units as for “Pressure”. “MassCached” instead is fed with a star’s desired mass (solar mass units) and the corresponding pressure is calculated from cached TOV output.

    • "Value" (double, [COOL, RH]) : Value of central pressure. Interpretation depends on “ProvidedAs” entry.

    • "CachePath" (string, [COOL, RH]) : Path to the cached TOV output. Only used if “ProvidedAs” is set to “MassCached”. In order to produce cache, run

    ./bin/project/M-R_diagram/m_r_diagram.out --inputfile <path_to_inputfile> [OPTIONS] > <path_to_cache>

    , where options are inspectable via --help flag.

    Warning

    1. One is not enforced to have TOV output ordered by mass, since this may be complicated to achieve. Because of this, the code looks for the first interval containing the desired mass. To limit the possible range, use --left_fraction and --right_fraction flags during cache creation.

    2. The resulting mass is not guaranteed to coincide with the desired mass, since the value is linearly interpolated. Pass a bigger --selection_size to increase precision.

    3. Avoid mixing different EoSs with the same cache. This can either lead to out-of-range errors or to wrong mass values.

Note

Though this setting is a key value for TOV solver, it is not used for producing M-R curves, since M-R curves are parametrized by pressure. It, of course, does not undermine its importance during any simulation on a given pressure.

  • "SurfacePressure" : Defines surface pressure as an ultimate exit condition for TOV.

    • "ProvidedAs" (string, [TOV, COOL, RH]) : The way the “SurfacePressure” is provided. Choose from [“Same”, “LinspacedMinToMax”]. “LinspacedMinToMax” linearly maps \([0,1] \rightarrow [P_{min}, P_{max}]\), while “Same” assumes same units as for “Pressure”.

    • "Value" (double, [TOV, COOL, RH]) : Value of surface pressure. Interpretation depends on “ProvidedAs” entry.

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