The Opacity of the Intergalactic Medium Measured Along Quasar Sightlines at z∼6z\sim 6

We publicly release a new sample of $34$ medium resolution quasar spectra at $5.77\leq z_{\rm em}\leq6.54$ observed with the Echellette Spectrograph and Imager (ESI) on the Keck telescope. This quasar sample represents an ideal laboratory to study the intergalactic medium (IGM) during the end stages of the epoch of reionization, and constrain the timing and morphology of the phase transition. For a subset of $23$ of our highest signal-to-noise ratio spectra (S/N$>7$, per $10\,{\rm km\,s^{-1}}$ pixel), we present a new measurement of the Lyman-$\alpha$ (Ly$\alpha$) forest opacity spanning the redshift range $4.8\lesssim z\lesssim6.3$. We carefully eliminate spectral regions that could be causing biases in our measurements due to additional transmitted flux in the proximity zone of the quasars, or extra absorption caused by strong intervening absorption systems along the line of sight. We compare the observed evolution of the IGM opacity with redshift to predictions from a hydrodynamical simulation with uniform ultraviolet background (UVB) radiation, as well as two semi-numerical patchy reionization models, one with a fluctuating UVB and another with a fluctuating temperature field. Our measurements show a steep rise in opacity at $z\gtrsim5.0$ and an increased scatter and thus support the picture of a spatially inhomogeneous reionization process, consistent with previous work. However, we measure significantly higher optical depths at $5.3\lesssim z\lesssim5.7$ than previous studies, which reduces the contrast between the highest opacity Gunn-Peterson troughs and the average opacity trend of the IGM, which may relieve some of the previously noted tension between these measurements and reionization models.Comment: accepted for publication at Ap

On a counterexample to a conjecture by Blackadar

Blackadar conjectured that if we have a split short-exact sequence 0 -> I -> A -> A/I -> 0 where I is semiprojective and A/I is isomorphic to the complex numbers, then A must be semiprojective. Eilers and Katsura have found a counterexample to this conjecture. Presumably Blackadar asked that the extension be split to make it more likely that semiprojectivity of I would imply semiprojectivity of A. But oddly enough, in all the counterexamples of Eilers and Katsura the quotient map from A to A/I is split. We will show how to modify their examples to find a non-semiprojective C*-algebra B with a semiprojective ideal J such that B/J is the complex numbers and the quotient map does not split.Comment: 6 page

Disordered Topological Insulators via C∗C^*-Algebras

The theory of almost commuting matrices can be used to quantify topological obstructions to the existence of localized Wannier functions with time-reversal symmetry in systems with time-reversal symmetry and strong spin-orbit coupling. We present a numerical procedure that calculates a Z_2 invariant using these techniques, and apply it to a model of HgTe. This numerical procedure allows us to access sizes significantly larger than procedures based on studying twisted boundary conditions. Our numerical results indicate the existence of a metallic phase in the presence of scattering between up and down spin components, while there is a sharp transition when the system decouples into two copies of the quantum Hall effect. In addition to the Z_2 invariant calculation in the case when up and down components are coupled, we also present a simple method of evaluating the integer invariant in the quantum Hall case where they are decoupled.Comment: Added detail regarding the mapping of almost commuting unitary matrices to almost commuting Hermitian matrices that form an approximate representation of the sphere. 6 pages, 6 figure

First Spectroscopic Study of a Young Quasar

The quasar lifetime $t_{\rm\,Q}$ is one of the most fundamental quantities for understanding quasar evolution and the growth of supermassive black holes (SMBHs), but remains uncertain by several orders of magnitude. In a recent study we uncovered a population of very young quasars ($t_{\rm Q}\lesssim10^4-10^5$ yr), based on the sizes of their proximity zones, which are regions of enhanced Ly$\alpha$ forest transmission near the quasar resulting from its own ionizing radiation. The presence of such young objects poses significant challenges to models of SMBH formation, which already struggle to explain the existence of SMBHs at such early cosmic epochs. We conduct the first comprehensive spectroscopic study of the youngest quasar known, $\rm SDSS\,J1335+3533$ at $z=5.9012$, whose lifetime is $t_{\rm Q}<10^4$ yr ($95\%$ confidence). A careful search of our deep optical and near-infrared spectra for HI and metal absorption lines allows us to convincingly exclude that its small proximity zone results from an associated absorption system rather than a short lifetime. We use the MgII emission line to measure its black hole mass $M_{\rm BH}=(4.09\pm0.58)\times 10^9 M_{\odot}$, implying an Eddington ratio of $0.30\pm0.04$ -- comparable to other co-eval quasars. We similarly find that the relationship between its black hole mass and dynamical mass are consistent with other $z\sim6$ quasars. The only possible anomaly associated with youth are its weak emission lines, but larger samples are needed to shed light on a potential causal connection. We discuss the implications of short lifetimes for various SMBH growth scenarios, and argue that future observations of young quasars with JWST could distinguish between them.Comment: 13 pages, submitted to Ap