Transforms

These classes and functions are used to manipulate stellar spectra. Users are not expected to directly call these methods unless they are playing around with spectrums or creating custom methods.

Starfish.transforms.resample(wave, flux, new_wave)

Resample onto a new wavelength grid using k=5 spline interpolation

Parameters

• wave (array_like) – The original wavelength grid

• flux (array_like) – The fluxes to resample

• new_wave (array_like) – The new wavelength grid

Raises

ValueError – If the new wavelength grid is not strictly increasing monotonic

Returns

The resampled flux with the same 1st dimension as the input flux

Return type

numpy.ndarray

Starfish.transforms.rescale(flux, scale)

Rescale the given flux via the following equation

\[f \cdot \Omega\]

Parameters

• flux (array_like) – The input fluxes

• scale (float or array_like) – The scaling factor. If an array, must have same shape as the batch dimension of flux

Returns

The rescaled fluxes with the same shape as the input fluxes

Return type

numpy.ndarray

Starfish.transforms.renorm(wave, flux, reference_flux)

Renormalize one spectrum to another

This uses the rescale() function with a log_scale of

\[\log \Omega = \left. \int{f^{*}(w) dw} \middle/ \int{f(w) dw} \right.\]

where \(f^{*}\) is the reference flux, \(f\) is the source flux, and the integrals are over a common wavelength grid

Parameters

• wave (array_like) – The wavelength grid for the source flux

• flux (array_like) – The flux for the source

• reference_flux (array_like) – The reference source to renormalize to

Returns

The renormalized flux

Return type

numpy.ndarray

Starfish.transforms.doppler_shift(wave, vz)

Doppler shift a spectrum according to the formula

\[\lambda \cdot \sqrt{\frac{c + v_z}{c - v_z}}\]

Parameters

• wave (array_like) – The unshifted wavelengths

• vz (float) – The doppler velocity in km/s

Returns

Altered wavelengths with the same shape as the input wavelengths

Return type

numpy.ndarray

Starfish.transforms.instrumental_broaden(wave, flux, fwhm)

Broadens given flux by convolving with a Gaussian kernel appropriate for a spectrograph’s instrumental properties. Follows the given equation

\[f = f * \mathcal{F}^{\text{inst}}_v\]

\[\mathcal{F}^{\text{inst}}_v = \frac{1}{\sqrt{2\pi \sigma^2}} \exp \left[-\frac12 \left( \frac{v}{\sigma} \right)^2 \right]\]

This is carried out by multiplication in the Fourier domain rather than using a convolution function.

Parameters

• wave (array_like) – The current wavelength grid

• flux (array_like) – The current flux

• fwhm (float) – The full width half-maximum of the instrument in km/s. Note that this is quivalent to \(2.355\cdot \sigma\)

Raises

ValueError – If the full width half maximum is negative.

Returns

The broadened flux with the same shape as the input flux

Return type

numpy.ndarray

Starfish.transforms.rotational_broaden(wave, flux, vsini)

Broadens flux according to a rotational broadening kernel from Gray (2005) 1

Parameters

• wave (array_like) – The current wavelength grid

• flux (array_like) – The current flux

• vsini (float) – The rotational velocity in km/s

Raises

ValueError – if vsini is not positive

Returns

The broadened flux with the same shape as the input flux

Return type

numpy.ndarray

1

Gray, D. (2005). The observation and Analysis of Stellar Photospheres.

Cambridge: Cambridge University Press. doi:10.1017/CB09781316036570

Starfish.transforms.extinct(wave, flux, Av, Rv=3.1, law='ccm89')

Extinct a spectrum following one of many empirical extinction laws. This makes use of the extinction package. In general, it follows the form

\[f \cdot 10^{-0.4 A_V \cdot A_\lambda(R_V)}\]

Parameters

• wave (array_like) – The input wavelengths in Angstrom

• flux (array_like) – The input fluxes

• Av (float) – The absolute attenuation

• Rv (float, optional) – The relative attenuation (the default is 3.1, which is the Milky Way average)

• law (str, optional) – The extinction law to use. One of {‘ccm89’, ‘odonnell94’, ‘calzetti00’, ‘fitzpatrick99’, ‘fm07’} (the default is ‘ccm89’)

Raises

• ValueError – If law does not match one of the availabe laws

• ValueError – If Rv is not positive

Returns

The extincted fluxes, with same shape as input fluxes.

Return type

numpy.ndarray

Starfish.transforms.chebyshev_correct(wave, flux, coeffs)

Multiply the input flux by a Chebyshev series in order to correct for calibration-level discrepancies.

Parameters

• wave (array-lioke) – Input wavelengths

• flux (array-like) – Input flux

• coeffs (array-like) – The coefficients for the chebyshev series.

Returns

The corrected flux

Return type

numpy.ndarray

Raises

ValueError – If only processing a single spectrum and the linear coefficient is not 1.