Photometry and Filters

Once it has generated a spectrum for a stellar population (see Stellar Atmospheres and Spectral Synthesis), SLUG can convolve that spectrum with filter response curves to produce predictions for photometry. The fundamental calculation that SLUG carries out to compute photometry is to evaluate the integral

\[\left\langle L_\lambda \right\rangle_R = \frac{\int_{-\infty}^\infty L_\lambda R_\lambda \,\mathrm{d}\ln\lambda}{\int_{-\infty}^\infty R_\lambda \,\mathrm{d}\ln\lambda}\]

where \(L_\lambda\) is the specific luminosity and \(R_\lambda\) is the response function of the filter, which describes the expected number of counts produced in the detector per incident photon of wavelength \(\lambda\). Which filter response function(s) are evaluated is determined by the filters keyword in the Photometry Keywords section of The SLUG Input Deck. See Filter Data and Ideal and Special Filters for a list of available filters in the standard data set, and Adding Additional Filters for instructions on how to add additional filter data.

Photometric Systems

The fundamental integral of the spectrum \(L_\lambda\) over a filter response function \(R_\lambda\) returns a mean specific luminosity over the filter in the same units as \(L_\lambda\): energy per unit time per unit wavelength. SLUG can automatically convert this output into a variety of other photometric systems, as specified by the system keyword in the Photometry Keywords section of The SLUG Input Deck. The allowed photometric systems are:

Flambda: the default, returns \(\left\langle L_\lambda \right\rangle_R\) directly
Fnu: returns a specific luminosity \(\left\langle L_\nu \right\rangle_R\) with units of energy per time per frequency, which is related to \(\left\langle L_\lambda \right\rangle_R\) by \(\left\langle L_\nu \right\rangle_R = (\lambda_R^2/c) \left\langle L_\lambda \right\rangle_R\), where \(\lambda_R\) is the pivot wavelength of the filter (see Filter Data)
ST: returns a magnitude in the ST system, which is related to \(\left\langle L_\lambda \right\rangle_R\) by \(\mathrm{mag}_\mathrm{ST} = -2.5 \log_{10}[\left\langle L_\lambda \right\rangle_R / (4\pi d^2) / F_\mathrm{ST,0}]\), where \(d = 10\) pc is the standard distance and \(F_\mathrm{ST,0} = 3.631\times 10^{-9}\,\mathrm{erg}/\mathrm{cm}^2/\mathrm{s}/\mathrm{Å}\) is the zero point of the ST magnitude system
AB: returns a magnitude in the AB system, which is related to \(\left\langle L_\nu \right\rangle_R\) by \(\mathrm{mag}_\mathrm{AB} = -2.5 \log_{10}[\left\langle L_\nu \right\rangle_R / (4 \pi d^2) / F_\mathrm{AB,0}]\), where \(d = 10\) pc is the standard distance and \(F_\mathrm{AB,0} = 3631.0\,\mathrm{Jy}\) is the zero point of the AB magnitude system
Vega: returns a magnitude in the Vega system, which is computed from \(\left\langle L_\lambda \right\rangle_R\) as \(\mathrm{mag}_\mathrm{Vega} = -2.5 \log_{10}[\left\langle L_\lambda \right\rangle_R / (4\pi d^2) / \langle F_\mathrm{Vega} \rangle_R]\), where \(\langle F_\mathrm{Vega}\rangle_R\) is the flux of Vega convolved with the response function \(R_\lambda\). The Vega flux is computed on-the-fly from a reference Vega spectrum stored in the repository as data/spectra/vega.h5.

slugpy also contains a tool, phot_convert, to convert between photometric systems after a simulation has been run.

Filter Data

SLUG’s default data includes response curves and pivot wavelengths for a standard set of filters, which are taken from the SVO Filter Profile Service. The list of filters available is stored in a registry file, data/filters/filters.toml, and the data themselves are stored in data/filters/filters.h5. SLUG follows the SVO naming convention where a filter name takes the form FACILITY.INSTRUMENT.FILTER, where FACILITY is the name of the facility for that filter (e.g., HST), INSTRUMENT is the name of the instrument on that facility (e.g., ACS_WFC), and FILTER is the name of the filter on that instrument (e.g., F435W). Thus to generate photometry in this filter, one would include HST.ACS_WFC.F435W in the list of filters supplied by the filters keyword in the Photometry Keywords section of The SLUG Input Deck.

Ideal and Special Filters

In addition to real astronomical filters, SLUG also provides “ideal” filters that can be used to compute photometric or photometric-like quantities from spectra. The following entries can be included in the filter list to produce these outputs:

ideal_energy_X_Y: a filter where the response function \(R_\lambda\) is a perfect tophat function that is unity for wavelengths between X and Y (in Angstrom) and 0 elsewhere
ideal_phot_X_Y: a filter that measures the total number of photons per unit time evaluated over the wavelength range from X to Y, by evaluating the integral \(\int_X^Y L_\lambda / (hc/\lambda) \, \mathrm{d}\lambda\). For filters of this type, Y can be “inf”, in which case the upper limit on the integral is taken to be infinity.
Q(<Elem><IonStage>), where <Elem> is the standard elemental symbol for some element (e.g., H, He) and <IonStage> is a Roman numeral giving the ionization stage of that element; this filter returns the number of photons emitted per unit time with energies high enough to ionize the given ion to one higher ionization state, e.g., “Q(HI)” gives the number of photons per second emitted capable of ionizing neutral hydrogen, “Q(CII)” gives the number of photons per second emitted capable of ionizing C+ to C++. This is equivalent to ideal_phot_0_Y with Y set to the wavelength that corresponds to the ionization potential of the ion in question.
Lbol: a “filter” that returns the total bolometric luminosity of the stellar population; this is not computed by integrating a spectrum at all, and instead is computed directly from the output of the Stellar Tracks.

Outputs for ideal_energy_X_Y-type filters use the same photometric system as real filters, while outputs for all the other ideal filter types use units of photons per time regardless of which photometric system is selected.

Adding Additional Filters

SLUG’s default data set contains all the filters hosted by SVO for the following facilities: 2MASS, CFHT, GALEX, HST, JWST, Paranal, SLOAN, SkyMapper, and Spitzer. It also provides the “Generic” facility filters (which includes the standard Bessell, Cousins, Johnson, and Stromgren filters). If you want to add filters from any other facility whose filter data are hosted on SVO, the repository contains a script data/tools/filters/fetch_filter_vo.py that can be used to add additional filters to the data/filters/filters.h5 filter catalogue and add corresponding registry entries to data/filters/filters.toml so that filters can be accessed by SLUG.

If you want to add filters from another source, you can do so by writing your own HDF5 file (or appending to the existing one) with a corresponding TOML registry file (or entries in the existing registry file).

The required format for HDF5 files containing filter data is as follows.

A filter data file is organized as a three-level nested group hierarchy that mirrors the facility/instrument/filter naming convention described above: one top-level group per facility (e.g. HST), containing one subgroup per instrument on that facility (e.g. ACS_WFC), containing one subgroup per filter on that instrument (e.g. F435W) – so a given filter’s data live at the HDF5 path <FACILITY>/<INSTRUMENT>/<FILTER>. The names given to these groups are exactly the FACILITY, INSTRUMENT, and FILTER names used to refer to the filter elsewhere (e.g. in the filters keyword of Photometry Keywords), so they must match the corresponding names used in the registry entry described below. Each filter’s own group must contain two 1D datasets of equal length:

wavelength: the wavelength grid, in Angstrom, on which the response function is tabulated. This need not be evenly spaced, but should be sorted in order of increasing wavelength.
transmission: the filter’s response function \(R_\lambda\) at each wavelength in wavelength – the expected number of counts produced in the detector per incident photon, as described at the start of this section.

A filter group may also carry additional HDF5 attributes (e.g. the Description, ZeroPoint, and DetectorType attributes written by data/tools/filters/fetch_filter_vo.py for filters fetched from SVO); SLUG itself never reads any of these, so they are optional and are included purely for reference.

The required format for registry entries for filters is as follows.

Unlike a track or spectra registry, which lists one entry per named track/atmosphere set, a single filter registry describes every facility, instrument, and filter in one file, and only ever points to a single HDF5 file. The registry must have a top-level file key (a string): the path to the HDF5 file described above, resolved relative to the directory containing the registry file itself, exactly as for a track or spectra registry’s own file key (see Standard Track Sets).

For every facility to be made available, the registry must also contain a top-level table of that facility’s name (e.g. [HST]) with an instruments key (an array of strings, the names of that facility’s instruments). For every one of those instruments, the registry must in turn contain a subtable (e.g. [HST.ACS_WFC]) with a filters key (an array of strings, the names of that instrument’s filters). Finally, for every one of those filters, the registry must contain a further subtable (e.g. [HST.ACS_WFC.F435W]) with the following required key:

wl_ref (a number): the filter’s pivot wavelength, in Angstrom – the \(\lambda_R\) used to convert between \(\left\langle L_\lambda \right\rangle_R\) and \(\left\langle L_\nu \right\rangle_R\) for the Fnu photometric system (see the Fnu entry under Photometric Systems above). Unlike a filter’s wavelength grid and response function, its pivot wavelength is read from this registry entry alone, not from the HDF5 file.

A filter’s subtable may also include any of the following optional keys, which SLUG itself never reads but which are included in the standard registry (as written by fetch_filter_vo.py) for documentation purposes:

description: A short, human-readable description of the filter.
source: A URL identifying where this filter’s data came from.

A registry may likewise include top-level name and Facilities keys (the latter listing every facility the registry describes); SLUG never reads either of these either, since it always looks a facility up by name directly, but both are included in the standard registry for documentation purposes.