LOSSCONE

This is a set of programs to deal with loss-cone problems – rates of capture of stars by supermassive black holes, in spherical, flattened, or triaxial geometry, accompanying the following papers:

E.Vasiliev, D.Merritt, `The loss-cone problem in axisymmetric nuclei', 2013, ApJ, 774, 87;

E.Vasiliev, `Rates of capture of stars by supermassive black holes in non-spherical galactic nuclei', 2014, Clas.Quant.Grav., 31, 244002 (updated version of the program applicable also for triaxial geometry)

K.Lezhnin, E.Vasiliev, `Suppression of tidal disruption rates by anisotropic initial conditions', 2015, ApJL, 808, 5 (another version that deals with a wider class of initial conditions, but does not consider draining in non-spherical cases)

To compute the total number of stars captured during a given time interval (~galactic age), one needs first to specify the mass model for the galaxy. This is achieved by tabulating the mass as a function of radius (a text file with two columns, the mass at r=0 corresponds to the black hole) and running the program `mkspher', which produces a much more detailed table where many dynamical quantities are given as functions of radius (in particular, distribution function and coefficients of diffusion).

This table is supplied as an input to a perl script (losscone.pl) which uses another auxiliary program `dif1d' to compute the solution of the time-dependent one-dimensional Fokker-Planck equation for each value of energy in the table file, and then sums up the captured mass at all energies.

The output consists of several quantities that are printed to console and written (appended) to the file `summary.txt', see the header of that file and comments in the end of losscone.pl to get more info.

One needs the GSL library to compile the two auxiliary programs (written in C++); the main script is written in perl.

Example runs (v1.1; see README in v1.2 for update):

1) d15bh1e-3.src is the source file for a mass model corresponding to gamma=1.5 Dehnen profile with a total mass and scale radius of unity, and a central point mass of 10^-3. d15bh1e-3.tab is the file obtained by running

> mkspher in=d15bh1e-1.src out=d15bh1e-3.tab

and contains all the necessary information to compute capture rates.

For instance, to scale this model to the Milky Way galaxy, one sets the total mass of 4e9 solar masses (so that the black hole is 4 million M_solar), and sets the scale radius of 200 pc (so that the density profile in the center is roughly rho = 1.5e5 M_sol/pc^3 * (r/1pc)^-3/2 ). Thus the model corresponds not to the entire galaxy, but rather to the central part of the bulge, encompassing the region around the influence radius which gives the dominant contribution to the capture rate. The tidal disruption radius for solar-type stars is roughly 3e-6 pc, ten times larger than the Schwarzschild radius. The capture rate is computed by running

> losscone.pl tab=d15bh1e-3.tab mass=4e9 rscale=200 rcapt=3e-6

for the spherical case, the same plus rsep=0.14 for the case of a flattened system with z/x axis ratio p=0.9 (see eqs. 1d,1e,8c,11b in the paper [Vasiliev&Merritt]), and the same plus triax for the triaxial geometry (assuming maximal triaxiality).

2) M87.src is the mass model for the giant elliptical galaxy M87 from Gebhardt&Thomas(2009), in units of solar masses and parsecs, so it does not need to be scaled:

> losscone.pl tab=M87.tab

the radius of loss cone is computed automatically as 4x Schwarzschild radius (i.e. direct capture, no tidal disruption).

3) Consider a series of galaxy models with black hole masses following the M-sigma relation, in the form log M_bh = 8 + 4.5 log(sigma/(200km/s)), and let them be represented by gamma=1 Dehnen models with a black hole of 10^-3 of total mass. The radius of influence in N-body units is 0.047 and the same radius in physical units is 35pc*(M_bh/10^8 M_sol)^0.56, so we need to set mass=1000*(M_bh/M_sol) and rscale=750*(M_bh/10^8 M_sol)^0.56. The script runmsigma.pl computes the rates for galaxies with black hole masses from 10^7 to 3*10^10 M_sol.

Download LOSSCONE: version 1.1 (for non-spherical geometry with isotropic initial conditions and draining), version 1.2 (for anisotropic initial conditions, draining not accounted for in non-spherical geometry).

© 2011–2015 Eugene Vasiliev, 2014–2015 Kirill Lezhnin

Any questions? email: eugvas@protonmail.com