ORBIT N1 N2 N3 N4 FIX KXLO KXHI NKX KYLO KYHI NKY GALO GAHI NGA
FRLO FRHI NFR VSLO VSHI NVS TAPER EPS OPTION FLO FHI FILE SET
Solves for orbital parameters of binary motion using Bayesian
analysis of cross-correlation or 'skew mapping'. The orbit is fit with
V = Gamma - Kx cos(2*pi*phi) + Ky sin(2*pi*phi)
and the routine can optimise GAMMA, Kx, Ky, the orbital frequency
FREQ (cycles/day) and the rotational broadening VSINI.
Parameters:
N1 -- First object spectrum
N2 -- Last object spectrum
N3 -- First template spectrum
N4 -- Last template spectrum
FIX -- String controlling operations of maximisation stepping
etc.
0 = allow parameter to be maximised.
1 = parameter will be fixed at one value.
2 = parameter will be stepped but maxmised.
The parameters have the order Kx, Ky, Gamma, orbital
frequency and Vsini (=GXYFV) e.g. 00012 allows KX, KY, GAMMA,
to vary but holds VSINI fixed at a single value while stepping in
FREQ. This would go through a series of frequencies, optimising
KX, KY and Gamma each time.
The parameters to be stepped or optimised need a grid of values to be
specified. If they are to be optimised, a maximum is hunted by first
locating the highest point on a regularly spaced grid.
Fixed Free
KX or KXLO, KXHI, NKX -- Kx (km/s)
KY or KYLO, KYHI, NKY -- Ky (km/s)
GAMMA or GALO, GAHI, NGA -- systemic velocity (km/s).
FREQ or FRLO, FRHI, NFR -- Orbital frequency (cycles/day)
VSINI or VSLO, VSHI, NVS -- V sin i (km/s)
TAPER-- Amount to taper at ends to reduce end effects
EPS -- limb darkening for broadening
OPTION- Two possible Bayesian models according to whether we allow
the veiling factors or f-values (which indicate the
fraction of flux from the Xcor target) to be independent
for each spectrum or to have 1 value only.
* 1 -- independent f-values for eachs. Suited to
eclipsing binaries and other cases where f may vary.
2 -- for single f-value (equivalent to Smith's skew
mapping and probably best for very difficult cases
FLO, FHI Lower and upper limits to fraction of light contributed
by secondary star. Comes into the integral over the
f-values used in the Bayesian computation.
FILE - File to store values on stepped grid. This is
a FIGARO file. You will only be prompted for it if
you step at least one parameter. <CR> not to bother.
SET - Yes to set mask pixels in target spectra. The template
spectra are assumed to be OK.
Details:
The spectra and templates should be normalised and continuum subtracted.
The parameter Vsini should only be changed if absolutely necessary as
this entails a large computational cost.
The routine initially looks for a maximum with a grid search over user
defined ranges. The values here should be chosen carefully. For example
if you tried 100 points in each of 5 parameters you would end trying to
compute the probability over 10**10 points, which would take forever.
You may want to start without searching over Vsini and perhaps Gamma to
reduce the burden. The probability function has many peaks which is why
this expensive strategy is needed. One can expect peaks to be separated
by of order the velocity resolution in Gamma, Kx, and Ky so this should
give some idea of suitable values. However, it would probably be best to
experiment with different grid sizes until the results do not change.
The variation in Vsini is likely to less complex and just a few points
will probably do if you really have to vary it.
The search in period is made in frequency because constant step sizes are
more suited to frequency as the following considerations show. If you have
observations spread over a baseline T then you should step in frequency such
that the relative phases of start and end do not alter by more than FRAC of
a cycle (FRAC=0.1 is a plausible choice). You then require a frequency
stepsize of FRAC/T cycles/day, and therefore NFR = (FRHI-FRLO)*T/FRAC is
about the right order of mag. This can still give large values e.g. a 3 day
run with 1 spectrum/half hour would give T=2 days, FRLO=0.25 (no point
looking lower than 0.5 cycles over the whole run), FRHI=24 (Nyquist
frequency), and so NFR = 500. Obviously FRAC and FRHI are quite important
here and you may wish to experiment. Any information on the period from
other sources could be a great help.
The zero point of the orbital phase is loaded from the D header parameter
HJDO or from the first HJD if the former is not found.
This command belongs to the classes: binary .