orbit

 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.  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 class: binary


Tom Marsh, Warwick