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
semimajoraxis(0)=2.04
eccentricity(0) =0.0
inclination(0)  =97.69
periastron(0)   =91.86	; of primary
apsidalmotion(0)=0.0
ascendingnode(0)=47.4
period(0)       =2.8673285
epoch(0)        =2441773.4894
; Fit to AB-C astrometry
component(1)    ='AB-C'
method(1)       =1
semimajoraxis(1)=94.6
eccentricity(1) =0.229
inclination(1)  =84.0
periastron(1)   =310.5
apsidalmotion(1)=0.0
ascendingnode(1)=312.3
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.

• System
  • Starid Star identifier. Character string, CCCNNNN, or CCCNNNNNN
  • RA Right Ascension. Needed for precession computation.
  • Dec Declination. Needed for precession computation.
  • Rv Systemic radial velocity in km/s
  • Wavelengths The wavelengths corresponding to elements of the magnitudes array in the stellar parameter section. Any number of elements is allowed. In microns.
• Star
  • Name/Component Single character string, 'A', 'B', etc.
  • WMC WMC designation of component, e.g. Aa
  • Type Integer, described in the following section
  • Model Kurucz atmosphere model to use, e.g. ip00k2.pck19, or name of Aufdenberg atmosphere (without .dat extension). In case of images, the filename.
  • SED Name of XDR file which restores wavelength $l$ and flux $f$ (in equal wavelength bins) if to be used to define the SED of a component.
  • Mass In units of the solar mass
  • Diameter In milliarcseconds
  • Ratio Axial ratio minor/major axis (elliptical components or CLEAN beam
  • PA Position angle of major axis
  • Hole Disk hole in milliarcseconds
  • Omega Ratio of axial rotation rate to breakup rate (type 14) or ratio of axial rotation rate to orbital rate (WD)
  • Tilt Inclination of rotation axis, zero is pole-on
  • Teff Effective temperature in K
    • 0 Set intrinsic flux to 1
    • $<0$ Use blackbody law
    • $>0$ Use model atmosphere
  • Logg Logarithm of surface gravity
  • gr Exponent in gravity darkening law, convective envelopes 0.3, radiative 1.0
  • albedo
  • alpha Temperature exponent in passive disks
  • magnitudes Apparent visual magnitude. These are converted to flux factors and applied to the fluxes derived from the effective temperature parameter.
• Binary
  • Component Name of component, character string
  • WDmode WD mode
  • Method
    • 1 Use orbital elements
    • 2 Use ($\rho$,$\theta$) parameters
    • 3 Use ($\rho$,$\theta$) parameters with orbital motion
    • 4 Interacting binary, use WD code
  • Semimajoraxis in milliarcseconds
  • Eccentricity
  • Inclination in degrees
  • Periastron in degrees, of primary
  • Apsidalmotion in degrees/year
  • Ascendingnode in degrees
  • Period in days
  • Epoch Full Julian date, periastron passage
  • Rho Separation, in milliarcseconds
  • Theta Position angle, in degrees

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.)