Spectra

Spectroscopic observations are supported in sncosmo with the Spectrum class. A spectrum object can be created from a list of wavelengths and flux values:

>>> wave, flux, fluxerr = sncosmo.load_example_spectrum_data()
>>> spectrum = sncosmo.Spectrum(wave, flux)

By default, the wavelengths are assumed to be in angstroms and the flux values as a spectral flux density (erg / s / cm^2 / A).

Uncertainties

A spectrum can have associated uncertainties. This can be either uncorrelated uncertainties for each spectral element:

>>> spectrum = sncosmo.Spectrum(wave, flux, fluxerr)

or a full covariance matrix:

>>> fluxcov = np.diag(fluxerr**2) + 1e-5 * np.max(flux)**2
>>> spectrum = sncosmo.Spectrum(wave, flux, fluxcov=fluxcov)

All operations will take these uncertanties into account.

Synthetic photometry

Synthetic photometry can be calculated on a spectrum using any of the bandpasses available in sncosmo:

>>> spectrum.bandflux('sdssg')
6.417843339246818

Synthetic photometry can be calculated on multiple bands simultaneously:

>>> spectrum.bandflux(['sdssg', 'sdssr', 'sdssi'])
array([6.41784334, 5.37683496, 2.8626649 ])

If a zeropoint and magnitude system are specified, then the bandflux is returned in that system (otherwise it is in photons / s / cm^2 by default).

>>> spectrum.bandflux(['sdssg', 'sdssr', 'sdssi'], zp=25., zpsys='ab')
array([117413.72315598, 108956.25581652,  79592.47424074])

Optionally, the full covariance matrix between the bandfluxes can also be calculated:

>>> spectrum.bandfluxcov(['sdssg', 'sdssr', 'sdssi'], zp=25., zpsys='ab')
(array([117413.72315598, 108956.25581652,  79592.47424074]),
 array([[1546972.78077853,  874550.34470817, 1287550.14818921],
         [ 874550.34470817, 2479812.26652077, 2226272.0481113 ],
         [1287550.14818921, 2226272.0481113 , 3805168.84485814]]))

A band magnitude can be evaluated in a specific magnitude system:

>>> spectrum.bandmag(['sdssg', 'sdssr', 'sdssi'], magsys='ab')
array([12.32570285, 12.40686957, 12.74781999])

Rebinning a spectrum

A spectrum can be rebinned with arbitrary wavelength bins. This returns a new Spectrum object.

>>> binned_spectrum = spectrum.rebin(np.arange(3500, 6000, 100))

Rebinning introduces covariance between adjacent spectral elements if the bin edges in the original spectrum don’t line up with the bin edges in the rebinned spectrum. This covariance is properly propagated.

Fitting with spectra

Spectra can be used in fits. Any combination of spectra and photometry is allowed. To fit spectra, the times at which the spectra were taken must be specified. For example, to fit a single spectrum:

# Create the spectrum object, and specify the time at which it was taken.
>>> spectrum = sncosmo.Spectrum(wave, flux, fluxerr, time=20.)

# Fit a model to the spectrum.
>>> model = sncosmo.Model(source='hsiao-subsampled')
>>> sncosmo.fit_lc(model=model, spectra=spectrum,
...                vparam_names=['amplitude', 't0', 'z'],
...                bounds={'z': (0., 0.3)})
(      success: True
       message: 'Minimization exited successfully.'
         ncall: 108
         chisq: 576.7111360163605
          ndof: 597
   param_names: ['z', 't0', 'amplitude']
    parameters: array([9.96571945e-02, 1.80278503e+01, 1.00650322e-05])
  vparam_names: ['z', 't0', 'amplitude']
    covariance: array([[ 1.17946556e-07,  1.64336679e-05, -5.21279026e-12],
                       [ 1.64336679e-05,  1.70047614e-02, -4.60755668e-09],
                       [-5.21279026e-12, -4.60755668e-09,  2.91915780e-15]])
        errors: OrderedDict([('z', 0.00034343314287464677),
                             ('t0', 0.13040215158608248),
                             ('amplitude', 5.4029230945864686e-08)])
          nfit: 1
     data_mask: None,
<sncosmo.models.Model at 0x7fa30159a6d0>)

Other valid signatures are:

# photometry only
>>> sncosmo.fit_lc(photometry, model, ...)

# a single spectrum
>>> sncosmo.fit_lc(model=model, spectra=spectrum, ...)

# multiple spectra
>>> sncosmo.fit_lc(model=model, spectra=[spec_1, spec_2], ...)

# spectra and photometry simultaneously
>>> sncosmo.fit_lc(photometry, model, spectra=[spec_1, spec_2], ...)