SED-fitting and Photometric Redshifts

Measurement of photometric redshifts and derived properties

Measurements of physical properties are necessary for virtually all galaxy evolution studies. The properties that are measurable from spectral energy distributions (SEDs) include photometric redshifts, star formation rates, stellar masses, dust attenuations and stellar metallicities. These properties are typically measured by comparing the observed photometry of individual galaxies to synthetic photometry from libraries of theoretical templates. The accuracy of the derived properties therefore depends on a number of factors, including the underlying population synthesis models, the filter sets utilised, the assumed dust attenuation laws, IMFs and star formation histories, the choice of model priors and the interpretation of the resulting probability distribution functions (see e.g. Salim et al. 2016).

Fig 1 shows the important impact of the u band filter for redshift estimation, assuming a survey at the nominal depth of LSST, and including magnitude and surface-brightness priors. In the nearby Universe, the redshifting of the Balmer break through the u filter enables the estimation of the photometric redshifts for z < 0.5 (where the break moves into the g and r bands). At higher redshift, the transition of the Lyman break into the u band filter increases the accuracy of the photometric redshifts for z > 2.5. This results in a reduced scatter in the redshift estimates at low redshift, improving studies of the properties of galaxies in the local Universe and reducing the number of catastrophic outliers by a factor of two (mistaking the Lyman break for the Balmer break results in a degeneracy between z = 0.2 and z = 3 galaxies). Removal of the u band results in a significant deterioration of the photometric redshifts for z < 0.5 to such an extent that they fail to meet the required LSST performance metrics.

In the redshift range 1.3 < z < 1.6, the photometric redshift constraints are most dependent upon the y filter. For z > 1.6 the Balmer break transitions out of the y band and hence the photometric redshifts are only poorly constrained until the Lyman break enters the u band at z > 2.5.

Photometric redshift algorithms have commonly used galaxy fluxes and/or colours alone to estimate redshifts. However, information on a galaxy's morphology, size, shape, overall surface brightness, or detailed surface brightness profile can provide additional information that can aid in constraining the redshift and/or type of a galaxy, breaking potential degeneracies that occur when using colours alone. Gains can be substantial at low redshift where LSST will resolve galaxies. Incorporating morphological information may help to improve joint predictions for galaxy properties and redshift. If sufficient training samples are available, priors for redshift and SED parameters, given a set of morphological parameters, p(z,SED|P), can be constructed. These can then be incorporated into Bayesian analyses of photometric redshifts and potentially lead to improved constraints on the redshift PDF (p(z|P,C) , where P represents observed morphological parameters, C represents observed flux/colour measurements, and SED represents one or more parameters representing the rest-frame SED of a galaxy. LSST GSC efforts that use advanced techniques (e.g. machine learning) to efficiently measure morphological properties will therefore be important for this endeavour.

Fig 2 shows the expected photometric redshift performance for bright galaxies observed in the LSST ugrizy system, derived using simulated photometry that reproduces the distribution of galaxy colours and luminosities as a function of redshift, as observed by the COSMOS, DEEP2 and VVDS surveys. The simulations include the effects of evolution in the stellar populations, redshift, type-dependent luminosity functions, type-dependent reddening and photometric errors.

Training SED fitting infrastructure

Spectroscopic training sets for photometric redshifts

Accurate photometric redshift estimates will require deep spectroscopic redshift data in order to help train algorithms, either directly in the case of machine-learning based algorithms, or to train Bayesian priors and adjust zero points, transmission curves, or error models for template-based methods. A detailed study of spectroscopic training needs and potential spectroscopic instruments that will be available in the coming years was undertaken by Newman et al. (2015). An immediate concern for galaxy science is to obtain spectroscopic samples for populations that will fundamentally underpin the LSST GSC science effort e.g. low-surface-brightness and dwarf galaxies. Spectroscopic campaigns from highly multi-plexed instruments, e.g. 4MOST, MOONS and PFS, will be crucial for providing the training samples that are necessary for building photometric redshift pipelines in the LSST era.

Simulations with realistic galaxy properties

As representative samples of spectroscopic redshifts could be difficult to compile for LSST, even using the next generation of spectrographs, cosmological simulations could play a key role in calibrating estimates of physical properties such as galaxy stellar mass and star formation rate. The current generation of LCDM-based cosmological simulations (e.g. Vogelsberger et al. 2014, Schaye et al. 2015, Kaviraj et al. 2017) perform well in reproducing the aggregate properties of the galaxy population, such as luminosity and stellar-mass functions, the redshift evolution of the star formation main sequence and the cosmic star formation history (see Figs 3, 4 and 5), at least for massive galaxies observed in wide-area surveys. This makes these simulations good testbeds for training photometric redshift pipelines, at least for the mass range that is well-resolved by the models. On the assumption that the simulations reliably model the galaxy formation physics outside these mass ranges, their utility could also be extended to other subsets, like dwarf and low-surface-brightness galaxies which form a significant fraction of the discovery space that will be opened up by LSST.