The Hierarchical Stellar Systems Model Format

In a hierarchical stellar system, the separation between two neighboring stars is always much smaller than the separation of this pair from the next companion in the system, be it another pair or a single star. Hierarchical systems are dynamically stable, and therefore by far the most common type encountered. They are also numerically easier to handle than non-hierarchical systems, since each pair can be described with the standard orbital parameters, and each star with a small number of physical parameters. Because AMOEBA is designed to combine different data sets, the HSSMF eliminates parameters only specific to one dataset in favor of replacing them with physical parameters such as masses, luminosities, etc. It is important to not over determine the model, i.e. to allow one or more parameters to be functions of others. The following illustrates an example for a triple star, Algol.

; Global parameters:
starid          ='FKV0111'
wavelengths     =[0.550,0.800]
rv              =4.0
; Star parameters (for each star):
name(0)         ='A'
type(0)         =1
mass(0)         =3.67
diameter(0)     =0.98
omega(0)        =1.0
teff(0)         =0
gr(0)           =1.0
albedo(0)       =1.0
magnitudes(*,0) =[2.26,2.36]
name(1)         ='B'
type(1)         =1
mass(1)         =0.82
diameter(1)     =1.2
omega(1)        =1.0
teff(1)         =0
gr(1)           =0.3
albedo(1)       =0.5
magnitudes(*,1) =[5.23,4.26]
name(2)         ='C'
type(2)         =1
mass(2)         =1.88
diameter(2)     =0.58
magnitudes(*,2) =[5.1,4.8]
; Binary parameters (for each binary):
component(0)    ='A-B'
method(0)       =1
wdmode(0)       =5
eccentricity(0) =0.0
inclination(0)  =97.69
periastron(0)   =91.86	; of primary
period(0)       =2.8673285
epoch(0)        =2441773.4894
; Fit to AB-C astrometry
component(1)    ='AB-C'
method(1)       =1
eccentricity(1) =0.229
inclination(1)  =84.0
periastron(1)   =310.5
period(1)       =679.9966
epoch(1)        =2453731.4d0

The syntax of the model format is identical to the language, e.g. IDL. The individual lines are actually commands which are executed by AMOEBA upon reading the model file.

Model parameters are defined in the following. Please note that Julian Day epochs (model parameters and data) are stored internally with 2440000 days subtracted.

The model is checked upon reading to make sure all components are defined. All wavelength dependent parameters are defined at a set of wavelengths given in the global parameter section, and therefore all have to have the same number of elements. (Polynomials are used to interpolate intermediate values.)