bns_lorene Module

ADM mass of the system $[M_\odot]$

$x$ component of the angular momentum of the BNS system

$y$ component of the angular momentum of the BNS system

$z$ component of the angular momentum of the BNS system

Angular velocity $[{\rm rad/s}]$

Areal (or circumferential) radius of star 1 $[L_\odot]$ Note that these is the areal radius of the star in the binary system, which is different than that of an isolated star. The latter is used in the mass-radius diagrams, together with the gravitatonal mass

Areal (or circumferential) radius of star 2 $[L_\odot]$ Note that these is the areal radius of the star in the binary system, which is different than that of an isolated star. The latter is used in the mass-radius diagrams, together with the gravitatonal mass

Array containing the barycenters of the stars

Barycenter of star 1 $[L_\odot]$

Barycenter of star 2 $[L_\odot]$

Array containing the barycenters of the stars

1-D array storing the baryon mass density in the fluid frame [kg m^{-3}]

Identifier of the bnslorene object

C pointer to the \(\texttt{LORENE}\)'s \(\texttt{Bin_NS}\) object N.B. This variable is global. The pointer to the second \(\texttt{LORENE}\) \(\texttt{Bin_NS}\) object will overwrite the first one, and so on. This variable stores the pointer to the last defined \(\texttt{LORENE}\) \(\texttt{Bin_NS}\) object. That's why it is not freed in the destructor of a bns object. Presently, it has to be freed by the user at the end of the PROGRAM. See the last part of the PROGRAM in setup_lorene_id.f90, for example.

Array containing the centers of the stars

Stellar center of star 1 (origin of the LORENE chart centered on star 1) $[L_\odot]$

Stellar center of star 2 (origin of the LORENE chart centered on star 2) $[L_\odot]$

Timer that times the construction of the appropriate object

Distance $d$ between the points of maximum baryon density $[{\rm km}]$

Distance between the centers of mass $[L_\odot(=1.47662503825040{\rm km})]$

1-D array storing the energy density [kg c^2 m^{-3}]

Central energy density for star 1 $[M_\odot c^2 L_\odot^{-3}]$

Central energy density for star 2 $[M_\odot c^2 L_\odot^{-3}]$

Central enthalpy for star 1 $[c^2]$

Central enthalpy for star 2 $[c^2]$

Name of the equation of state (\(\mathrm{EOS}\)) of star 1

\(\texttt{SPHINCS_ID}\) identifier for the \(\mathrm{EOS}\) of star 1

\(\texttt{LORENE}\) identifier for the \(\mathrm{EOS}\) of star 1

Name of the equation of state (\(\mathrm{EOS}\)) of star 2

\(\texttt{SPHINCS_ID}\) identifier for the \(\mathrm{EOS}\) of star 2

\(\texttt{LORENE}\) identifier for the \(\mathrm{EOS}\) of star 2

Array of strings containing the names of the files containing the \(\mathrm{EOS}\) to be used for each matter object.

String containing the path to the files containing the table of the \(\mathrm{EOS}\) for star 1.

String containing the path to the files containing the table of the \(\mathrm{EOS}\) for star 2.

Pointer to a procedure that finalize the \(\mathrm{SPH}\) \(\mathrm{ID}\); for example, correct for the residual ADM linear momentum.

1-D array storing the xx component of the spatial metric [pure number]

1-D array storing the xy component of the spatial metric [pure number]

1-D array storing the xz component of the spatial metric [pure number]

1-D array storing the yy component of the spatial metric [pure number]

1-D array storing the yz component of the spatial metric [pure number]

1-D array storing the zz component of the spatial metric [pure number]

Piecewise polytrope: polytropic index $\gamma_0$ for star 1

Piecewise polytrope: polytropic index $\gamma_0$ for star 2

Piecewise polytrope: polytropic index $\gamma_1$ for star 1

Piecewise polytrope: polytropic index $\gamma_1$ for star 2

Piecewise polytrope: polytropic index $\gamma_2$ for star 1

Piecewise polytrope: polytropic index $\gamma_2$ for star 2

Piecewise polytrope: polytropic index $\gamma_3$ for star 1

Piecewise polytrope: polytropic index $\gamma_3$ for star 2

Single polytrope: polytropic index for star 1

Single polytrope: polytropic index for star 2

1-D array storing the xx component of the extrinsic curvature [c/MSun_geo]

1-D array storing the xy component of the extrinsic curvature [c/MSun_geo]

1-D array storing the xz component of the extrinsic curvature [c/MSun_geo]

1-D array storing the yy component of the extrinsic curvature [c/MSun_geo]

1-D array storing the yz component of the extrinsic curvature [c/MSun_geo]

1-D array storing the zz component of the extrinsic curvature [c/MSun_geo]

Piecewise polytrope: polytropic constant $\kappa_0$ for star 1 [pure number]

Piecewise polytrope: polytropic constant $\kappa_0$ for star 2 [pure number]

Piecewise polytrope: polytropic constant $\kappa_1$ for star 1 [pure number]

Piecewise polytrope: polytropic constant $\kappa_1$ for star 2 [pure number]

Piecewise polytrope: polytropic constant $\kappa_2$ for star 1 [pure number]

Piecewise polytrope: polytropic constant $\kappa_2$ for star 2 [pure number]

Piecewise polytrope: polytropic constant $\kappa_3$ for star 1 [pure number]

Piecewise polytrope: polytropic constant $\kappa_3$ for star 2 [pure number]

Single polytrope: polytropic constant for star 1 [pure number]

Single polytrope: polytropic constant for star 2 [pure number]

1-D array storing the lapse function

$x$ component of the ADM linear momentum of the system

$y$ component of the ADM linear momentum of the system

$z$ component of the ADM linear momentum of the system

Piecewise polytrope: Base 10 exponent of the pressure at the first fiducial density (between $\gamma_0$ and $\gamma_1$) $[{\rm dyne/cm^2}]$ for star 1

Piecewise polytrope: Base 10 exponent of the pressure at the first fiducial density (between $\gamma_0$ and $\gamma_1$) $[{\rm dyne/cm^2}]$ for star 2

Piecewise polytrope: Base 10 exponent of the first fiducial density (between $\gamma_0$ and $\gamma_1$) $[{\rm g/cm^3}]$ for star 1

Piecewise polytrope: Base 10 exponent of the second fiducial density (between $\gamma_1$ and $\gamma_2$) $[{\rm g/cm^3}]$ for star 2

Piecewise polytrope: Base 10 exponent of the second fiducial density (between $\gamma_1$ and $\gamma_2$) $[{\rm g/cm^3}]$ for star 1

Piecewise polytrope: Base 10 exponent of the second fiducial density (between $\gamma_1$ and $\gamma_2$) $[{\rm g/cm^3}]$ for star 2

Piecewise polytrope: Base 10 exponent of the third fiducial density (between $\gamma_2$ and $\gamma_3$) $[{\rm g/cm^3}]$ for star 1

Piecewise polytrope: Base 10 exponent of the third fiducial density (between $\gamma_2$ and $\gamma_3$) $[{\rm g/cm^3}]$ for star 2

mOmega= ( angular_vel$[{\rm km^{-1}}]$ ) $\times$ ( mass_grav1$[{\rm km}]$ + mass_grav2$[{\rm km}]$ ) [pure number]

Array containing the baryonic masses $[M_\odot]$

Baryonic mass of star 1 $[M_\odot]$

Baryonic mass of star 2 $[M_\odot]$

Array containing the gravitational masses $[M_\odot]$

Gravitational mass of star 1 $[M_\odot]$

Gravitational mass of star 2 $[M_\odot]$

Central baryon number density for star 1 $[L_\odot^{-3}]$

Central baryon number density for star 2 $[L_\odot^{-3}]$

Piecewise polytrope: Number of polytropic pieces for star 1

Piecewise polytrope: Number of polytropic pieces for star 2

1-D array storing the pressure

Central pressure for star 1 $[M_\odot c^2 L_\odot^{-3}]$

Central pressure for star 2 $[M_\odot c^2 L_\odot^{-3}]$

Array containing the signed radii of the stars

Radius of star 1, in the x direction, towards the companion $[L_\odot]$

Radius of star 1, in the x direction, opposite to companion $[L_\odot]$

Radius of star 1, in the y direction $[L_\odot]$

Radius of star 1, in the z direction $[L_\odot]$

Radius of star 2, in the x direction, towards the companion $[L_\odot]$

Radius of star 2, in the x direction, opposite to companion $[L_\odot]$

Radius of star 2, in the y direction $[L_\odot]$

Radius of star 2, in the z direction $[L_\odot]$

Central baryon mass density for star 1 $[M_\odot L_\odot^{-3}]$

Central baryon mass density for star 2 $[M_\odot L_\odot^{-3}]$

1-D array storing the x component of the shift vector [c]

1-D array storing the y component of the shift vector [c]

1-D array storing the z component of the shift vector [c]

1-D array storing the specific internal energy [c^2]

Central specific energy for star 1 $[c^2]$

Central specific energy for star 2 $[c^2]$

Array containing, for each matter object, a set of coordinates of some points modelling the surfaces.

Estimated time of the merger $[M_\odot]$ $$t_\mathrm{merger}=\dfrac{5}{256} \dfrac{d^4}{M^1_\mathrm{g}M^2_\mathrm{g}(M^1_\mathrm{g}+M^2_\mathrm{g})}$$ P. C. Peters, "Gravitational Radiation and the Motion of Two Point Masses", Phys. Rev. 136, B1224 (1964)

Array containing a tabulated \(\mathrm{EOS}\) for each matter object, when used.

1-D array storing the x component of the fluid 3-velocity with respect to

1-D array storing the y component of the fluid 3-velocity with respect to

1-D array storing the z component of the fluid 3-velocity with respect to

Finalizer (Destructor) of a bnslorene object

Allocates memory for the bnslorene member arrays

Checks that the given index is between 1 and n_matter, included. If not, it stops the execution of the program.

Constructs the \(\texttt{LORENE}\) \(\texttt{Bin_NS}\) object

Corrects the \(\mathrm{SPH}\) \(\mathrm{ID}\) so that the linear $\mathrm{ADM}$ momentum is zero

Deallocates memory for the bnslorene member arrays

Destructs the \(\texttt{LORENE}\) \(\texttt{Bin_NS}\) object

Estimate typical length scales, one per each matter object, by computing $\dfrac{f}{\partial f}$, where $f$ is a field given as input, and $\partial$ represent a derivative of it. Presently, the derivatives are computed separately along each spatial dimension, as 1D derivatives.

Finds the center of a matter object, as the point where the density is maximal.

Finds the surfaces of the stars, and prints them to a formatted file.

Finds the radius of a star, relative to a center and along a direction. The radius is determined as the first point where the density is zero.

Finds the surface of a star, using [[bnsbase::find_radius]] along many directions.

Returns adm_mass

Returns the angular momentum vector $($angular_momentum_x, angular_momentum_y, angular_momentum_z$)$

Returns angular_vel

Returns barycenter1_x

Returns barycenter2_x

Returns bns_identifier

Returns center1_x

Returns center2_x

Returns cold_system, the LOGICAL variable that specifies if the system is cold (no thermal component)

Returns distance

Returns distance_com

Returns energy_density_center1

Returns energy_density_center2

Returns ent_center1

Returns ent_center2

Returns eos1

Returns the \(\texttt{LORENE}\) identifier for the EOS of star 1

Returns eos1_loreneid

Returns eos2

Returns the \(\texttt{LORENE}\) identifier for the EOS of star 2

Returns eos2_loreneid

Returns eos1_id or eos2_id

Returns estimate_length_scale, the LOGICAL variable that specifies if a typical length scale, equal to the ratio of a field over its gradient, should be computed

Access the bnslorene-member arrays

GENERIC PROCEDURE, overloded to access the bnslorene-member variables as arrays and as values

Access the components of the bnslorene-member arrays

Returns gamma0_1

Returns gamma0_2

Returns gamma1_1

Returns gamma1_2

Returns gamma2_1

Returns gamma2_2

Returns gamma3_1

Returns gamma3_2

Returns gamma_1

Returns gamma_2

Returns mass_grav1

Returns mass_grav2

Returns kappa0_1

Returns kappa0_2

Returns kappa1_1

Returns kappa1_2

Returns kappa2_1

Returns kappa2_2

Returns kappa3_1

Returns kappa3_2

Returns kappa_1

Returns kappa_2

Returns the linear momentum vector $($linear_momentum_x, linear_momentum_y, linear_momentum_z$)$

Returns logP1_1

Returns logP1_2

Returns logRho0_1

Returns logRho0_2

Returns logRho1_1

Returns logRho1_2

Returns logRho2_1

Returns logRho2_2

Returns mass1

Returns mass2

Returns n_matter, the number of matter objects in the physical system

Returns nbar_center1

Returns nbar_center2

Returns npeos_1

Returns npeos_2

Returns one_lapse, the LOGICAL variable that determines if the lapse function $\alpha=1$, i.e., if the geodesic gauge is to be used

Returns pressure_center1

Returns pressure_center2

Returns radius1_x_comp

Returns radius1_x_opp

Returns radius1_y

Returns radius1_z

Returns radius2_x_comp

Returns radius2_x_opp

Returns radius2_y

Returns radius2_y

Returns rho_center1

Returns rho_center2

Returns specific_energy_center1

Returns specific_energy_center2

Returns the spatial extent of the physical system considered, as the array of 6 numbers $x_{\rm min},x_{\rm max},y_{\rm min},y_{\rm max},z_{\rm min},z_{\rm max}$

Returns zero_shift, the LOGICAL variable that determines if the shift $\beta^i=0$

This PROCEDURE calls the constructor of the idbase-extended type and the SUBROUTINE sanity_check afterwards. It is recommended to use this SUBROUTINE to construct objects of idbase-extended type since the sanity check is performed automatically.

Integrates the baryon mass density over a matter object, using spherical coordinates, and computes its radial profile inside the star

Procedure that does nothing. It is used to instantiate a deferred idbase procedure which is not needed in TYPE bnslorene. It also serves as a placeholder in case the idbase procedure will be needed in the future.

Prints the parameters of the \(\mathrm{BNS}\) to the standard output

Imports the parameters of the \(\mathrm{BNS}\) from \(\texttt{LORENE}\)

Stores the \(\mathrm{ID}\) in the bnslorene member arrays

Returns the \(\texttt{LORENE}\)'s mass density at the desired point

Returns the \(\texttt{LORENE}\)'s pressure at the desired point

Returns the \(\texttt{LORENE}\)'s conformally flat spatial ADM metric

Checks that n_matter and the sizes returned by return_spatial_extent and get_total_spatial_extent are acceptable. It is called by initialize, after the constructor of the derived type.

Sets cold_system, the LOGICAL variable that specifies if the system is cold (no thermal component)

Sets estimate_length_scale, the LOGICAL variable that specifies if a typical length scale, equal to the ratio of a field over its gradient, should be computed

Sets n_matter, the number of matter objects in the physical system, to a value

Sets one_lapse, the LOGICAL variable that determines if the lapse $\alpha=1$, i.e., if the geodesic gauge is to be used

Sets zero_shift, the LOGICAL variable that determines if the shift $\beta^i=0$

Returns 1 if the energy density or the specific energy or the pressure are negative