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The current cosmological paradigm asserts that dark matter halos provide the gravitational scaffolding for galaxy formation through a combination of hierarchical structure formation and non-linear local (g)astrophysical processes. This close relationship, known as the galaxy-halo connection, suggests that the growth and assembly of dark matter halos impact the properties of galaxies. While the stellar mass of galaxies correlates strongly with the mass of their halos, it is important to note that the galaxy-halo connection encompasses a broader distribution of galaxy and halo properties. This distribution can be constrained using data from astronomical observations and cosmological $N$-body simulations, a technique known as semi-empirical modeling. By operating at the intersection of observational data and the cosmological structure formation model, the semi-empirical modeling provides valuable insights into galaxy formation and evolution from a cosmological perspective. In this proceeding, we utilize a new sEM-emPIRical modEl, EMPIRE, to explore the star formation, SF, history of central galaxies across cosmic epochs, spanning from dwarfs to massive ellipticals. EMPIRE aims to constrain the multivariate distribution that links galaxy and halo properties. Our findings reveal distinct growth stages for progenitors of central massive galaxies. Evidence suggests that cold streams played a significant role in sustaining SF at higher $z$, while virial shock heating became more prominent at lower $z$. The maximum star formation efficiency, SFE, occurs at a factor of $\sim1.5-2$ below $M_{\rm vir \; shocks}$ for $z\lesssim1$. Furthermore, at higher redshifts, $z>1$, this peak tends towards higher masses, $M_{\rm vir}\sim 2\times 10^{12} M_{\odot}$. Notably, at redshifts higher than $z\sim2$, the peak of SFE aligns comfortably within the region characterized by cold streams., Comment: 16 pages, 7 figures. Extended contribution to the original proceeding for the XVII Latin American Regional IAU Meeting

We investigate the relation between galaxy structure and star formation rate (SFR) in a sample of $\sim2.9\times10^{4}$ central galaxies with $z<0.0674$ and axial ratios $b/a>0.5$. The star-forming main sequence (SFMS) shows a bend around the stellar mass of $M_\ast\leq{}M_c=2\times10^{10}{}M_{\odot}$. At $M_\ast\leq{}M_c$ the SFMS follows a power-law $\text{SFR}\propto{}M_\ast^{0.85}$, while at higher masses it flattens. $M_c$ corresponds to a dark matter halo mass of $M_\text{vir}\sim{}10^{11.8}M_{\odot}$ where virial shocks occurs. Some galaxy structure (e.g., half-light radius, $R_e$) exhibits a non-monotonic dependence across the SFMS at a fixed $M_\ast$. We find $\text{SFR}\propto{R_e^{-0.28}}$ at fixed $M_\ast$, consistent with the global Kennicutt-Schmidt (KS) law. This finding suggests that galaxy sizes contribute to the scatter of the SFMS. However, at $M_\ast>M_c$ the relationship between SFR and $R_e$ diminishes. Low-mass galaxies above the mean of the SFMS have smaller radii, exhibit compact and centrally concentrated profiles resembling green valley (GV) and quiescent galaxies at the same mass, and have higher $M_{\text{H}_2}/M_\text{HI}$. Conversely, those below the SFMS exhibit larger radii, lower densities, have no GV or quiescent counterparts at their mass and have lower $M_{\text{H}_2}/M_\text{HI}$. The above data suggest two pathways for quenching low-mass galaxies, $M_\ast\leq{}M_c$: a fast one that changes the morphology on the SFMS and a slow one that does not. Above $M_c$, galaxies below the SFMS resemble GV and quiescent galaxies structurally, implying that they undergo a structural transformation already within the SFMS. For these massive galaxies, CG are strongly bimodal, with SFMS galaxies exhibiting negative color gradients, suggesting most star formation occurs in their outskirts, maintaining them within the SFMS., Comment: 30 pages, 28 figures, submitted to MNRAS

We present a new cosmologically motivated mock redshift survey of the Dusty Star-Forming Galaxy population. Our mock survey is based on the Bolshoi-Planck dark-matter halo simulation and covers an area of 5.3 sq. degree. Using a semi-empirical approach, we generate a light cone and populate the dark-matter haloes with galaxies. Infrared properties are assigned to the galaxies based on theoretical and empirical relations from the literature. Additionally, background galaxies are gravitationally lensed by dark-matter haloes along the line-of-sight assuming a point-mass model approximation. We characterize the mock survey by measuring the star formation rate density, integrated number counts, redshift distribution, and infrared luminosity function. When compared with single-dish and interferometric observations, the predictions from our mock survey closely follow the compiled results from the literature. We have also directed this study towards characterizing one of the extragalactic legacy surveys to be observed with the TolTEC camera at the Large Millimeter Telescope: the 0.8 sq. degree Ultra Deep Survey, with expected depths of 0.025, 0.018 and 0.012 mJy beam$^{-1}$ at 1.1, 1.4 and 2.0 mm. Exploiting the clustering information in our mock survey, we investigate its impact on the effect of flux boosting by the fainter population of dusty galaxies, finding that clustering can increase the median boosting by 0.5 per cent at 1.1 mm, 0.8 per cent at 1.4 mm and, 2.0 per cent at 2.0 mm, and with higher dispersion., Comment: 17 pages, 12 figures

We measure the clustering of low-redshift SDSS galaxies as a function of stellar mass ($10.0<\log(M_*/M_\odot)<11.5$) and specific star formation rate (sSFR) and compare the results to models of the galaxy--halo connection. We find that the auto-correlation functions of central galaxies exhibit little dependence on sSFR, with the well-known stronger clustering of quiescent galaxies mainly attributable to satellites. Because halo assembly history is known to affect distinct halo clustering, this result implies that there is little net correlation between halo assembly history and central galaxy sSFR. However, cross-correlations with satellites are stronger for quiescent centrals than star-forming centrals, consistent with quiescent centrals having more satellites in their haloes at fixed $M_*$, as found in SDSS group catalogues. We model the galaxy--halo connection in an $N$-body simulation by assigning sSFRs to central galaxies in three different ways. Two of the models depend on halo assembly history (being based on halo accretion rate or concentration), while the third is independent of halo assembly history (being based on peak halo circular velocity, $V_\text{peak}$, a proxy for halo mass). All three models replicate the observed auto-correlations of central galaxies, while only the $V_\text{peak}$ model reproduces the observed cross-correlations with satellites. This further suggests that the effects of halo assembly history may not be easily seen in auto-correlations of centrals and implies that a more complete understanding of central galaxy clustering may require more than auto-correlations of centrals alone. Additionally, the good agreement with the $V_\text{peak}$ model supports the idea that quiescent galaxies reside in more massive haloes than star-forming galaxies at fixed $M_*$., Comment: MNRAS accepted, 26 pages