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spectra.rst

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Fitting Spectra

There are several extra considerations that come up when fitting spectroscopy.

Wavelength range, resolution, and linespread function

Prospector is based on FSPS, which uses stellar spectral libraries with given resolution. The empirical MILES library has a resolution of ~2.5A FWHM from 3750AA - 7200AA restframe, and much lower (R~200 or so, but not actually well defined) outside this range. Higher resolution data (after including both velocity dispersion and instrumental resolution) or spectral points outside this range cannot yet be fit.

Prospector includes methods for FFT based smoothing of the spectra, assuming a Gaussian LSF (in either wavelength or velocity space). There is also the possibility of FFT based smoothing for wavelength dependent Gaussian dispersion (i.e. sigma_lambda = f(lambda) with f possibly a polynomial of lambda). In practice the smoothed model spectra will be a combination of the library resolution plus whatever FFT smoothing is applied. Hopefully this can be made to match your actual data resolution, which is a combination of the physical velocity dispersion and the instrumental resolution. The smoothing is controlled by the parameters sigma_smooth, smooth_type, and fftsmooth

For undersampled spectra, a special :py:class:`UnderSampledSpectrum` class exists that will integrate the model (smoothed by velocity dispersion and intrumental resolution) over the supplied pixels.

Instrumental Response & Spectrophotometric Calibration

There are various options for dealing with the spectral continuum shape depending on how well you think your spectra are calibrated and if you also fit photometry to tie down the continuum shape. You can optimize out a polynomial "calibration" vector, or simultaneously fit for a polynomial and marginalize over the polynomial coefficients (this allows you to place priors on the accuracy of the spectrophotometric calibration). Or you can just take the spectrum as perfectly calibrated.

Particular treatments can be implemented using different mix-in classes for the :py:class:`Spectrum` observational data, e.g. for optimization of a 5th order polynomial calibration vector at each likelihood call, use :py:class:`PolyOptCal` as follows

from prospect.observation import Spectrum, PolyOptCal
class PolySpectrum(PolyOptCal, Spectrum):  # order matters
    pass

spec = PolySpectrum(wavelength=np.linspace(3000, 5000, N),
                    flux=np.zeros(N),
                    uncertainty=np.ones(N),
                    polynomial_order=5)

Nebular emission

While prospector/FSPS include self-consistent nebular emission, the treatment is probably not flexible enough at the moment to fit high S/N, high resolution data including nebular emission (e.g. due to deviations of line ratios from Cloudy predictions or to complicated gas kinematics that are different than stellar kinematics). Thus fitting nebular lines should take adavantage of the nebular line amplitude optimization/marginalization capabilities. For very low resolution data this is less of an issue.