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Studies of cosmology, galaxy evolution, and astronomical transients with current and next-generation wide-field imaging surveys like the Rubin Observatory Legacy Survey of Space and Time are all critically dependent on estimates of photometric redshifts. Capsule networks are a new type of neural network architecture that is better suited for identifying morphological features of the input images than traditional convolutional neural networks. We use a deep capsule network trained on ugriz images, spectroscopic redshifts, and Galaxy Zoo spiral/elliptical classifications of ∼400 000 Sloan Digital Sky Survey galaxies to do photometric redshift estimation. We achieve a photometric redshift prediction accuracy and a fraction of catastrophic outliers that are comparable to or better than current methods for SDSS main galaxy sample-like data sets (r ≤ 17.8 and zspec ≤ 0.4) while requiring less data and fewer trainable parameters. Furthermore, the decision-making of our capsule network is much more easily interpretable as capsules act as a low-dimensional encoding of the image. When the capsules are projected on a two-dimensional manifold, they form a single redshift sequence with the fraction of spirals in a region exhibiting a gradient roughly perpendicular to the redshift sequence. We perturb encodings of real galaxy images in this low-dimensional space to create synthetic galaxy images that demonstrate the image properties (e.g. size, orientation, and surface brightness) encoded by each dimension. We also measure correlations between galaxy properties (e.g. magnitudes, colours, and stellar mass) and each capsule dimension. We publicly release our code, estimated redshifts, and additional catalogues at https://biprateep.github.io/encapZulate-1.

We demonstrate how the total luminosity in satellite galaxies is a powerful probe of dark matter haloes around central galaxies. The method cross-correlates central galaxies in spectroscopic galaxy samples with fainter galaxies detected in photometric surveys. Using models, we show that the total galaxy luminosity, Lsat, scales linearly with host halo mass, making Lsat an excellent proxy for Mh. Lsat is also sensitive to the formation time of the halo. We demonstrate that probes of galaxy large-scale environment can break this degeneracy. Although this is an indirect probe of the halo, it yields a high signal-to-noise ratio measurement for galaxies expected to occupy haloes at

We present measurements of the redshift-dependent clustering of a DESI-like luminous red galaxy (LRG) sample selected from the Legacy Survey imaging data set, and use the halo occupation distribution (HOD) framework to fit the clustering signal. The photometric LRG sample in this study contains 2.7 million objects over the redshift range of 0.4 < z < 0.9 over 5655 deg2. We have developed new photometric redshift (photo-z) estimates using the Legacy Survey DECam and WISE photometry, with σNMAD = 0.02 precision for LRGs. We compute the projected correlation function using new methods that maximize signal-to-noise ratio while incorporating redshift uncertainties. We present a novel algorithm for dividing irregular survey geometries into equal-area patches for jackknife resampling. For a five-parameter HOD model fit using the MultiDark halo catalogue, we find that there is little evolution in HOD parameters except at the highest redshifts. The inferred large-scale structure bias is largely consistent with constant clustering amplitude over time. In an appendix, we explore limitations of Markov chain Monte Carlo fitting using stochastic likelihood estimates resulting from applying HOD methods to N-body catalogues, and present a new technique for finding best-fitting parameters in this situation. Accompanying this paper, we have released the Photometric Redshifts for the Legacy Surveys catalogue of photo-z's obtained by applying the methods used in this work to the full Legacy Survey Data Release 8 data set. This catalogue provides accurate photometric redshifts for objects with z < 21 over more than 16 000 deg2 of sky.

We measure how the properties of star-forming central galaxies correlate with large-scale environment, d, measured on 10 h-1 Mpc scales. We use galaxy group catalogues to isolate a robust sample of central galaxies with high purity and completeness. The galaxy properties we investigate are star formation rate (SFR), exponential disc scale length Rexp, and Sersic index of the galaxy light profile, nS. We find that, at all stellar masses, there is an inverse correlation between SFR and δ, meaning that above-average star-forming centrals live in underdense regions. For nS and Rexp, there is no correlation with δ at M* ≲ 1010.5 M⊙, but at higher masses there are positive correlations; a weak correlation with Rexp and a strong correlation with nS. These data are evidence of assembly bias within the star-forming population. The results for SFR are consistent with a model in which SFR correlates with present-day halo accretion rate, Mh. In thismodel, galaxies are assigned to haloes using the abundance-matching ansatz, which maps galaxy stellar mass onto halo mass. At fixed halo mass, SFR is then assigned to galaxies using the same approach, but Mh is used to map onto SFR. The best-fitting model requires some scatter in the Mh-SFR relation. The Rexp and nS measurements are consistent with a model in which both of these quantities are correlated with the spin parameter of the halo, λ. Halo spin does not correlate with δ at low halo masses, but for higher mass haloes, high-spin haloes live in higher density environments at fixed Mh. Put together with the earlier instalments of this series, these data demonstrate that quenching processes have limited correlation with halo formation history, but the growth of active galaxies, as well as other detailed galaxies properties, are influenced by the details of halo assembly.

Using group catalogues from the Sloan Digital Sky Survey (SDSS) Data Release 7, we measure galactic conformity in the local universe. We measure the quenched fraction of neighbour galaxies around isolated primary galaxies, dividing the isolated sample into star-forming and quiescent objects. We restrict our measurements to scales > 1 Mpc to probe the correlations between halo formation histories. Over the stellar mass range 109.7 ≥ M*/M⊙ = 1010.9, we find minimal evidence for conformity. We further compare these data to predictions of the halo age-matching model, in which the oldest galaxies are associated with the oldest haloes. For models with strong correlations between halo and stellar age, the conformity is too large to be consistent with the data. Weaker implementations of the age-matching model would not produce a detectable signal in SDSS data. We reproduce the results of Kauffmann et al., in which the star formation rates of neighbour galaxies are reduced around primary galaxies when the primaries are low star formers. However, we find this result is mainly driven by contamination in the isolation criterion; when removing the small fraction of satellite galaxies in the sample, the conformity signal largely goes away. Lastly, we show that small conformity signals, i.e. 2-5 per cent differences in the quenched fractions of neighbour galaxies, can be produced by mechanisms other than halo assembly bias. For example, if passive galaxies occupy more massive haloes than star-forming galaxies of the same stellar mass, a conformity signal that is consistent with recent measurements from PRIMUS (Berti et al.) can be produced.

We test whether halo age and galaxy age are correlated at fixed halo and galaxy mass. The formation histories, and thus ages, of darkmatter haloes correlate with their large-scale density ρ, an effect known as assembly bias. We test whether this correlation extends to galaxies by measuring the dependence of galaxy stellar age on ρ. To clarify the comparison between theory and observation, and to remove the strong environmental effects on satellites, we use galaxy group catalogues to identify central galaxies and measure their quenched fraction, fQ, as a function of large-scale environment. Models that match halo age to central galaxy age predict a strong positive correlation between fQ and ρ. However, we show that the amplitude of this effect depends on the definition of halo age: assembly bias is significantly reduced when removing the effects of splashback haloes - those haloes that are central but have passed through a larger halo or experienced strong tidal encounters. Defining age using halo mass at its peak value rather than current mass removes these effects. In Sloan Digital Sky Survey data, at M* ≳ 1010 M⊙ h-2, there is a ~5 per cent increase in fQ from low-to-high densities, which is in agreement with predictions of dark matter haloes using peak halo mass. At lower stellar mass there is little to no correlation of fQ with ρ. For these galaxies, age matching is inconsistent with the data across the range of halo formation metrics that we tested. This implies that halo formation history has a small but statistically significant impact on quenching of star formation at high masses, while the quenching process in low-mass central galaxies is uncorrelated with halo formation history.