Dust in the Average Galaxy: Attenuation, Emission, and Opacity from 0<z<7

We present constraints on the dust emission and attenuation properties of galaxies across 0<z<7 using JWST imaging from the COSMOS-Web Survey combined with deep FIR/(sub)millimeter data from Spitzer, Herschel, SCUBA-2, NIKA-2 and ALMA. We analyze over 500,000 galaxies to independently constrain attenuation in the rest-frame UV/optical as well as dust emission from stacked FIR SEDs, enabling a direct comparison between the two. We find UV/optical attenuation systematically underpredicts IR luminosity by a factor of ~3x at 0.5<z<7 and up to an order of magnitude for $M_\star>10^{10.5}M_\odot$. We derive empirical relationships for the effective attenuation, dust temperature, fraction of star formation that is unobscured, and dust-to-stellar mass ratio as functions of redshift and stellar mass. We separate the first order effect of star/dust geometry from dust grain properties by combining constraints on the IR SED, UV SED, and dust mass surface density. Importantly, we measure over an order of magnitude decrease in $\kappa_{UV}/\kappa_{FIR}$--the ratio of dust mass absorption coefficients in the UV at 1600\AA\ and FIR at 500$\mu$m--from z~0 to z~7. A depressed $\kappa_{UV}/\kappa_{FIR}$ is consistent with a deficit of small dust grains, possibly attributable to the intense radiation fields of high-$z$ star formation; indeed, we find a redshift-invariant inverse relationship between $\kappa_{UV}/\kappa_{FIR}$ and $\Sigma_{SFR}$. Most evolution in the dust-to-stellar ratio is at $z<1$, the product of mild downward evolution in the dust-to-gas ratio combined with steep evolution in the gas-to-stellar ratio. The significant evolution and dynamic range of $\kappa_{UV}/\kappa_{FIR}$ and prevailing disconnect between the UV/optical and FIR regimes emphasize that direct dust constraints are irreplaceable for the majority of star-forming galaxies at z<7, not just the most extreme star-formers.