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 1: Impact of using the u filter to improve measurement and resolve degeneracies in photometrically determined redshifts. On the left is the correlation between the photometric redshifts and spectroscopic redshifts with the full complement of LSST filters. The right panel shows the photometric redshift relation for data excluding the u filter. The addition of u-band data reduces the scatter substantially for z < 0.5 and removes degeneracies over the full redshift range. Adapted from Figure 3.16 of the LSST Science Book.
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.
Fig 2: The photometric redshift performance as a function of apparent magnitude and redshift, for a simulation based on the LSST filter set (ugrizy). Red points and curves correspond to the 'gold sample' defined by i < 25, and blue points and curves to a subsample with i < 24. The photometric redshift error is defined as ez = (zphoto −zspec)/(1+zspec). Top left: ez vs. photometric redshift. The two histograms show redshift distributions of the simulated galaxies. Top right: the root-mean-square scatter (rms, determined from the interquartile range) of ez as a function of photometric redshift. The horizontal dashed line shows the science driven design goal. Middle left: ez vs. observed i band magnitude. Two histograms show the logarithmic differential counts (arbitrary normalization) of simulated galaxies. The two horizontal cyan lines show the 3σ envelope around the median ez (where σ is the rms from the top right panel). Middle right: the fraction of 3σ outliers as a function of redshift. The horizontal dashed line shows the design goal. Bottom left: the median value of ez (bias) as a function of apparent magnitude. The two dashed lines show the design goal for limits on bias. Bottom right: the median value of ez (i.e., the bias in estimated redshifts) as a function of redshift. The two dashed lines show the design goal for this quantity. Adapted from Fig 3.17 of the LSST Science Book.
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.
Fig 3: The predicted stellar mass function from the Horizon-AGN simulation (grey; Kaviraj et al. 2017) vs observational data at 0<z<6. The pink dashed curves indicate predictions from Horizon-noAGN, a twin simulation without AGN feedback.
Fig 4: The predicted star formation main sequence from the Horizon-AGN simulation (2D histogram, with darker shades indicating lower galaxy density) vs observations in the redshift range 0<z<6.
Fig 5: Comparison of the predicted cosmic SFH in Horizon-AGN (Kaviraj et al. 2017) to observational data (Hopkins & Beacom 2006) in the redshift range 0 < z < 6. The red curve shows predictions from Horizon-AGN, while the grey shaded region indicates the parameter space covered by the observational data.
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.