Rigidity of p-adic cohomology classes of congruence subgroups of GL(n, Z)

We extend the work of Ash and Stevens [Ash-Stevens 97] on p-adic analytic families of p-ordinary arithmetic cohomology classes for GL(N,Q) by introducing and investigating the concept of p-adic rigidity of arithmetic Hecke eigenclasses. An arithmetic eigenclass is said to be "rigid" if (modulo twisting) it does not admit a nontrivial p-adic deformation containing a Zariski dense set of arithmetic specializations. This paper develops tools for explicit investigation into the structure of eigenvarieties for GL(N). We use these tools to prove that known examples of non-sefldual cohomological cuspforms for GL(3) are rigid. Moreover, we conjecture that for GL(3), rigidity is equivalent to non-selfduality.Comment: 23 page

Supermassive Black Holes from Ultra-Strongly Self-Interacting Dark Matter

We consider the cosmological consequences if a small fraction ($f\lesssim 0.1$) of the dark matter is ultra-strongly self-interacting, with an elastic self-interaction cross-section per unit mass $\sigma\gg1\ \mathrm{cm^{2}/g}$. This possibility evades all current constraints that assume that the self-interacting component makes up the majority of the dark matter. Nevertheless, even a small fraction of ultra-strongly self-interacting dark matter (uSIDM) can have observable consequences on astrophysical scales. In particular, the uSIDM subcomponent can undergo gravothermal collapse and form seed black holes in the center of a halo. These seed black holes, which form within several hundred halo interaction times, contain a few percent of the total uSIDM mass in the halo. For reasonable values of $\sigma f$, these black holes can form at high enough redshifts to grow to $\sim10^9 M_\odot$ quasars by $z \gtrsim 6$, alleviating tension within the standard $\Lambda$CDM cosmology. The ubiquitous formation of central black holes in halos could also create cores in dwarf galaxies by ejecting matter during binary black hole mergers, potentially resolving the "too big to fail" problem.Comment: submitted to Ap

Factors governing water condensation in the Martian atmosphere

Modeling results are presented suggesting a diurnal condensation cycle at high altitudes at some seasons and latitudes. In a previous paper, the use of atmospheric optical depth measurements at the Viking lander site to show diurnal variability of water condensation at different seasons of the Mars year was described. Factors influencing the amount of condensation include latitude, season, atmospheric dust content and water vapor content at the observation site. A one-dimensional radiative-convective model is used herein based on the diabatic heating routines under development for the Mars General Circulation Model. The model predicts atmospheric temperature profiles at any latitude, season, time of day and dust load. From these profiles and an estimate of the water vapor, one can estimate the maximum occurring at an early morning hour (AM) and the minimum in the late afternoon (PM). Measured variations in the atmospheric optical density between AM and PM measurements were interpreted as differences in AM and PM condensation