Acoustic perturbations to stellar envelopes can lead to the formation of weak shock waves via nonlinear wave-steepening. Close to the stellar surface, the weak shock wave increases in strength and can potentially lead to the expulsion of part of the stellar envelope. While accurate analytic solutions to the fluid equations exist in the limits of low amplitude waves or strong shocks, connecting these phases generally requires simulations. We address this problem using the fact that the plane parallel Euler equations, in the presence of a constant gravitational field, admit exact Riemann invariants when the flow is isentropic. We obtain exact solutions for acoustic perturbations and show that after they steepen into shock waves, Whitham's approximation can be used to solve for the shock's dynamics in the weak to moderately strong regimes, using a simple ordinary differential equation. Numerical simulations show that our analytic shock approximation is accurate up to moderate ($\sim$ few--15) Mach numbers, where the accuracy increases with the adiabatic index.
We study the stellar mass function (SMF) and the co-evolution with dark matter halos via abundance matching in the largest redshift range to date $0.2<z<12$ in $0.53 \, {\rm deg}^2$ imaged by JWST from the COSMOS-Web survey. At $z>5$, we find increased abundances of massive (log$\, M_{\star}/M_{\odot}>10.5$) implying integrated star formation efficiencies (SFE) $\epsilon_{\star}\equiv M_{\star}\, f_{\rm b}^{-1} M_{\rm halo}^{-1} \gtrsim 0.5$. We find a flattening of the SMF at the high-mass end that is better described by a double power law at $z>5.5$. At $z \lesssim 5.5$ it transitions to a Schechter law which coincides with the emergence of the first massive quiescent galaxies in the Universe. We trace the cosmic stellar mass density (SMD) and infer the star formation rate density (SFRD), which at $z>7.5$ agrees remarkably with recent \JWST{} UV luminosity function-derived estimates. However, at $z \lesssim 3.5$, we find significant tension ($\sim 0.3$ dex) with the cosmic star formation (SF) history from instantaneous SF measures, the causes of which remain poorly understood. We infer the stellar-to-halo mass relation (SHMR) and the SFE from abundance matching out to $z=12$, finding a non-monotonic evolution. The SFE has the characteristic strong dependence with mass in the range of $0.02 - 0.2$, and mildly decreases at the low mass end out to $z\sim3.5$. At $z\sim3.5$ the SFE increases sharply from $\sim 0.1$ to approach high SFE of $0.8-1$ by $z\sim 10$ for log$(M_{\rm h}/M_{\odot})\approx11.5$, albeit with large uncertainties. Finally, we use the SHMR to track the SFE and stellar mass growth throughout the halo history and find that they do not grow at the same rate -- from the earliest times up until $z\sim3.5$ the halo growth rate outpaces galaxy assembly, but at $z>3.5$ halo growth stagnates and accumulated gas reservoirs keep the SF going and galaxies outpace halos.
The dearth of high quality spectroscopy of dusty star-forming galaxies (DSFGs) -- the main drivers of the assembly of dust and stellar mass at the peak of activity in the Universe -- greatly hinders our ability to interpret their physical processes and evolutionary pathways. We present JWST/NIRSpec observations from RUBIES of four submillimeter-selected, ALMA-detected DSFGs at cosmic noon, $z\sim2.3-2.7$. While photometry uniformly suggests vigorous ongoing star formation for the entire sample in line with canonical DSFGs, the spectra differ: one source has spectroscopic evidence of an evolved stellar population, indicating a recent transition to a post-starburst phase, while the remainder show strong spectroscopic signatures of ongoing starbursts. All four galaxies are infrared-luminous (log$_{10}$$L_{\rm{IR}}$/L$_{\rm \odot}$ $>12.4$), massive (log$_{10}\,M_\star$/M$_{\rm \odot}$ $>11$), and very dust-obscured ($A_V\sim3-4$ ABmag). Leveraging detections of multiple Balmer and Paschen lines, we derive an optical attenuation curve consistent with Calzetti overall, yet an optical extinction ratio $R_V\sim2.5$, potentially indicating smaller dust grains or differences in star-dust geometry. This case study provides some of the first detailed spectroscopic evidence that the DSFGs encompass a heterogeneous sample spanning a range of star formation properties and evolutionary stages, and illustrates the advantages of synergistic JWST and ALMA analysis of DSFGs.