Guide to parameters

Although many of the parameters in the params.txt file are self-explanatory and commented, this page aims to provide a description of the key additional parameters for ExoZvezda code. Some parameters are very similar as the ones used in the GRChombo code. The GRChombo parameter guide can be found here.

Single Boson Star Parameters

• central_amplitude_CSF - central amplitude of your boson star, $A(0)$. If simulating a binary, you will have a corresponding central_amplitude_CSF2 variable to set.
• phase - a constant phase offset $\delta \phi$. This parameter must be given in the form of a multiple of $\pi$. For example, if $\delta \phi = \pi$, then phase = 1.
• gridpoints - number of grid points used to compute the 1D BS solution. Usually one needs at least $\mathcal{O}(10^5)$ points, however $\mathcal{O}(10^6)$ is recommended. Default is $10^6$.
• BS_solver_psc - a guess for the central value of the conformal factor used in the computation of the BS metric in the isotropic gauge. This is not a feely specifiable variable and the initial guess is refined during the shooting method. Depending on the solution being computed, one may need to adjust their initial guess. Default is 2.0.
• BS_solver_omc - a guess for the central value of the lapse function used in the computation of the BS metric in the isotropic gauge. This is not a feely specifiable variable and the initial guess is refined during the shooting method. Depending on the solution being computed, one may need to adjust their initial guess. Default is 0.5.
• BS_solver_verbosity - a boolean to determine whether more information should be printed out when computing the BS solution in 1D. Default is false.
• enable_matching - a boolean to determine whether to enable matching to the asymptotic solution or not. If set to false, the solution is truncated smoothly to zero at radius where exponentially growing modes start to kick in. Default is true.
• niter - number of iterations used in the shooting method. Typically 'not too hard to find' solutions converge within 3 to 4 iterations. Default is 17.
• star_centre - $(x,y,z)$ location of the single star. In the binary context this corresponds to the coordinates of the center of mass. Defaults to the center of the grid.
• BS_mass - anticipated mass of the BS, useful for setting the initial guess for the apparent horizon finder. Default is 1.0.

Potential Parameters

• scalar_mass - the value of the scalar mass $\mu$. Default is 1.0.
• phi4_coeff - the value of $\lambda$ coefficient. Default is 0.0.
• solitonic - a boolean to determine whether you want to use a solitonic potential. Default is false.
• sigma_solitonic - the value of the $\sigma_0$ self-interaction term. Default is 0.2.

Binary Boson Star Parameters

• antiboson - a boolean to determine whether one of the stars in the binary should have a negative frequency. Default is false.
• BS_rapidity - rapidity (i.e. $atanh(v)$, where $v$ is the boost velocity in the $x$-direction) of a boson star. Default is 0.0.
• BS_separation - separation between the BSs in the $x$-direction. Default is 0.0.
• BS_impact_parameter - separation between the BSs in the $y$-direction. Default is 0.0.
• mass_ratio - mass ratio of the binary ($q \leq 1$). Given an unequal mass ratio, the two stars will be placed in the centre of mass frame automatically. Default is 1.0.

Parameters Specific to Unequal-mass Binary Initial Data

• radius_width1 - width of the weight function imposed around star A, see Eq.(24) of https://arxiv.org/abs/2212.08023. Default is 10.
• radius_width2 - the same as radius_width1, but for star B. Default is a random 20.
• conformal_factor_power - the power applied to the conformal factor in the construction of unequal-mass initial data, see Eq.(A.4) of https://arxiv.org/abs/2212.08023. Default is 4, which is what is recommended and used in the results of https://arxiv.org/abs/2212.08023 paper.

Star Tracking

• do_star_track - whether to do start tracking or not. Default is false.
• number_of_stars - number of stars. Default is 1.
• star_points - number of points to be used in the fitting of stars' positions. This would depend on the level you are tracking it on, usually 5-15 should be enough. Default is 11.
• star_track_width_A - the total coordinate length of the interval along which we are finding the stars' positions. Default is 3. When we are fitting along a fixed coordinated direction, e.g. $x$ with the previous center at $x_{\rm{BS}}$, to the left of $x_{\rm{BS}}$ we will consider the interval up to $(x_{\rm{BS}} - 1.5)$, whilst to the right an interval of $x_{\rm{BS}}+1.5$, therefore resulting in the total coordinate length of 3.
• star_track_width_B - the same as star_track_width_A, except for the other star in the binary.
• direction_of_motion - specify the directions along which you need the star positions. For example, for a head-on collision with stars being boosted along the $x$-axis, the star positions are expected to change only along $x$, so set direction_of_motion = "x". For a binary system evolving in the $x-y$ plane, set direction_of_motion = "xy". For all spatial directions to be fit for, set direction_of_motion = "xyz".
• star_track_level - level to track your star's positions on. Default is 5.

Other Diagnostics Parameters

• activate_mass_extraction - whether to extract the ADM mass. Default is 0.
• num_mass_extraction_radii - a number of extraction radii used for ADM mass extraction.
• mass_extraction_levels - a list of levels used for ADM mass extraction, e.g. 1 1 1.
• mass_extraction_radii - a list of radii used for ADM mass extraction, e.g. 30. 60. 90.
• num_points_phi_mass - number of angular $\phi$ points in the integration.
• num_points_theta_mass - number of angular $\theta$ points in the integration.
• mass_extraction_center - center around which to extract the ADM mass.
• calculate_noether_charge - whether to calculate the Noether charge as a function of time during the evolution. Default is false.