Explanatory note on the extrapolated spectra to 300 microns
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Deliveries:
      Stellar composite spectra extrapolated to long wavelengths in      
      support of ISOPHT calibration.  Range is 25--300 um.

Attached:
      Spectral energy distributions of stellar composites extended to
      300 um (by request of PHT these extrapolations encompass the
      longest PHT bandpasses (e.g. the C-180 and C-200 filters of the 
      C200 detector) which attain zero response by 259 um.

Methods and background to this effort:
      Each stellar composite was treated in the same fashion by fitting
      the shape of an appropriate red giant branch model to the longest
      wavelength reliable observations of that star.  The SiO fundamental
      absorption was avoided in setting the starting wavelength of this
      fitting region.  The onset of large noise in the observations, and
      the beginning of any Engelke function (a theoretical construct used
      to supplant noisy data or extend adequate data out to 35 um), were
      both avoided, in determining the ending wavelength of the fitting
      region.  In this manner one can be sure that only real observations
      guide the actual fitting of the model shape.

Stellar files:
     Each file consists of a minimal header identifying its provenance and
     comes with four columns: the first is wavelength (in um); the second
     the monochromatic specific intensity, F(lambda), in units of W/cm2/um;
     the third, the F(nu) equivalent flux density in Jy; the fourth, an
     estimate of the total fractional uncertainty associated with the 
     predicted far-IR continua (the latter is treated as wavelength-
     independent: see below).

     If this is not adequate wavelength coverage or resolution, then you can 
     achieve adequate results from these by linearly interpolating (onto your
     own wavelength grids) in the quantities (lambda^4)*F-lambda [2nd column] 
     and (lambda^2)*F-nu [3rd column].  The model spectra are strictly not
     Rayleigh-Jeans, particularly for the shorter wavelengths of C1_90, but the
     interpolation in lambda^4*F-lambda (or its frequency equivalent quantity)
     is robust and will track the "true" (model) spectrum.


Uncertainties:
    The procedure used to fit the models to the composite spectra involves:
    (i) the removal of the global bias associated with the composite from 
    the total uncertainty in the fitting interval (i.e. using just the
    uncorrelated component of error); (ii) the assignment of 5% global error 
    (wavelength independent) to each model spectrum to perform the splice of
    the model shape to the observed spectrum; (iii) assignment of a wavelength-
    independent uncertainty of 4.8% due to typical uncertainties in effective
    temperature of stars (+/-100K), gravity (+/-0.5 dex is reasonable for 
    cool giants), metallicity (+/-0.2 dex), presence of chromospheres and the 
    probable influence of all these uncertainties in the fundamental stellar 
    parameters on the opacities calculated in the far-infrared, any remaining 
    uncertainty in our knowledge of the H-minus free-free absorption opacity 
    (which is the dominant source of opacity in these cool giant atmospheres)
    and effects upon the temperature structure; and (iv) these elements were 
    all root-sum-squared, adding 3% arising from the fact that the models are
    currently only CONTINUUM calculations -- creation of a full-blown 
    self-consistent model structure and synthetic spectrum across the infrared
    is close to but still slightly beyond what is feasible, practical, and
    affordable even on CRAYs -- the concern here is the appreciable role that
    must be played by the roughly 40 million lines of water vapor known from
    laboratory work on both the temperature structure and the emergent 
    spectrum.  The combination of all these estimated errors leads to 
    predictions for the far-infrared that are good to about 6% total 
    precision: certainly, better than 10% PROVIDED ALWAYS THAT THERE IS 
    NOTHING PATHOLOGICAL ABOUT THE TEMPERATURE STRUCTURES AND ENVIRONS OF 
    THESE STARS.


					  Martin Cohen
				        January 12, 1996



PS: REFEREED DOCUMENTATION:
  A full description of the technique used to extrapolate stellar spectra, and
  of the stellar models used to provide the shapes for extrapolation, appeared
  in the November 1996 issue of The Astronomical Journal (AJ, 112, 2274, 1996:
  Paper VII in the calibration series of papers).