We present two elementary derivations of the formula for the Toeplitz determinant generated by a pure Fisher-Hartwig singularity.

Albrecht Boettcher Harold Widom

Detection of the first stars has remained elusive so-far but their presence may soon be unveiled by upcoming JWST observations. Previous studies have not investigated the entire possible range of halo masses and redshifts which may help in their detection. Motivated by the prospects of detecting galaxies up to $z\sim 20$ in JWST early data release, we quantify the contribution of Pop III stars to high-redshift galaxies from $6 \leq z \leq 30$ by employing the semi-analytical model A-SLOTH, which self-consistently models the formation of Pop III and Pop II stars along with their feedback. Our results suggest that the contribution of Pop III stars is the highest in low-mass halos of $\rm 10^7-10^9~M_{\odot}$. While high-mass halos $\rm \geq 10^{10}~M_{\odot}$ contain less than 1\% Pop III stars, they host galaxies with stellar masses of $\rm 10^9~M_{\odot}$ as early as $z \sim 30$. Interestingly, the apparent magnitude of Pop~III populations gets brighter towards higher redshift due to the higher stellar masses, but Pop~III-dominated galaxies are too faint to be directly detected with JWST. Our results predict JWST can detect galaxies up to $z\sim 30$, which may help in constraining the IMF of Pop III stars and will guide observers to discern the contribution of Pop~III stars to high-redshift galaxies.

Shafqat Riaz Tilman Hartwig Muhammad A. Latif

High redshift quasars at z>6 have masses up to ~$10^9$ M$_\odot$. One of the pathways to their formation includes direct collapse of gas, forming a supermassive star, precursor of the black hole seed. The conditions for direct collapse are more easily achievable in metal-free haloes, where atomic hydrogen cooling operates and molecular hydrogen (H2) formation is inhibited by a strong external UV flux. Above a certain value of UV flux (J_crit), the gas in a halo collapses isothermally at ~$10^4$ K and provides the conditions for supermassive star formation. However, H2 can self-shield, reducing the effect of photodissociation. So far, most numerical studies used the local Jeans length to calculate the column densities for self-shielding. We implement an improved method for the determination of column densities in 3D simulations and analyse its effect on the value of J_crit. This new method captures the gas geometry and velocity field and enables us to properly determine the direction-dependent self-shielding factor of H2 against photodissociating radiation. We find a value of J_crit that is a factor of two smaller than with the Jeans approach (~2000 J_21 vs. ~4000 J_21). The main reason for this difference is the strong directional dependence of the H2 column density. With this lower value of J_crit, the number of haloes exposed to a flux >J_crit is larger by more than an order of magnitude compared to previous studies. This may translate into a similar enhancement in the predicted number density of black hole seeds.

Tilman Hartwig Simon C. O. Glover Ralf S. Klessen Muhammad A. Latif Marta Volonteri

The bulk irradiation of materials with 10-30 MeV protons promises to advance the study of radiation damage for fission and fusion power plants. Intermediate energy proton beams can now be dedicated to materials irradiation within university-scale laboratories. This paper describes the first such facility, with an Ionetix ION-12SC cyclotron producing 12 MeV proton beams. Samples are mm-scale tensile specimens with thicknesses up to 300 um, mounted to a cooled beam target with control over temperature. A specialized tensile tester for radioactive specimens at high temperature (500+ {\deg}C) and/or vacuum represents the conditions in fission and fusion systems, while a digital image correlation system remotely measures strain. Overall, the facility provides university-scale irradiation and testing capability with intermediate energy protons to complement traditional in-core fission reactor and micro-scale ion irradiation. This facility demonstrates that bulk proton irradiation is a scalable and effective approach for nuclear materials research, down-selection, and qualification.

S. J. Jepeal A. Danagoulian L. A. Kesler D. A. Korsun H. Y. Lee N. Schwartz B. N. Sorbom E. Velez Lopez Z. S. Hartwig

Twisted generalized Weyl algebras (TGWAs) $A(R,\sigma,t)$ are defined over a base ring $R$ by parameters $\sigma$ and $t$, where $\sigma$ is an $n$-tuple of automorphisms, and $t$ is an $n$-tuple of elements in the center of $R$. We show that, for fixed $R$ and $\sigma$, there is a natural algebra map $A(R,\sigma,tt')\to A(R,\sigma,t)\otimes_R A(R,\sigma,t')$. This gives a tensor product operation on modules, inducing a ring structure on the direct sum (over all $t$) of the Grothendieck groups of the categories of weight modules for $A(R,\sigma,t)$. We give presentations of these Grothendieck rings for $n=1,2$, when $R=\mathbb{C}[z]$. As a consequence, for $n=1$, any indecomposable module for a TGWA can be written as a tensor product of indecomposable modules over the usual Weyl algebra. In particular, any finite-dimensional simple module over $\mathfrak{sl}_2$ is a tensor product of two Weyl algebra modules.

Jonas T. Hartwig Daniele Rosso

The collapse of supermassive primordial stars in hot, atomically-cooled halos may have given birth to the first quasars at $z \sim$ 15 - 20. Recent numerical simulations of these rapidly accreting stars reveal that they are cool, red hypergiants shrouded by dense envelopes of pristine atomically-cooled gas at 6,000 - 8,000 K, with luminosities $L$ $\gtrsim$ 10$^{10}$ L$_{\odot}$. Could such luminous but cool objects be detected as the first stage of quasar formation in future near infrared (NIR) surveys? We have now calculated the spectra of supermassive primordial stars in their birth envelopes with the Cloudy code. We find that some of these stars will be visible to JWST at $z \lesssim$ 20 and that with modest gravitational lensing Euclid and WFIRST could detect them out to $z \sim$ 10 - 12. Rather than obscuring the star, its accretion envelope enhances its visibility in the NIR today by reprocessing its short-wavelength flux into photons that are just redward of the Lyman limit in the rest frame of the star.

Marco Surace Daniel J. Whalen Tilman Hartwig Erik Zackrisson S. C. O. Glover Samuel Patrick Tyrone E. Woods Alexander Heger Lionel Haemmerlé

Fisher-Hartwig asymptotics refers to the large $n$ form of a class of Toeplitz determinants with singular generating functions. This class of Toeplitz determinants occurs in the study of the spin-spin correlations for the two-dimensional Ising model, and the ground state density matrix of the impenetrable Bose gas, amongst other problems in mathematical physics. We give a new application of the original Fisher-Hartwig formula to the asymptotic decay of the Ising correlations above $T_c$, while the study of the Bose gas density matrix leads us to generalize the Fisher-Hartwig formula to the asymptotic form of random matrix averages over the classical groups and the Gaussian and Laguerre unitary matrix ensembles. Another viewpoint of our generalizations is that they extend to Hankel determinants the Fisher-Hartwig asymptotic form known for Toeplitz determinants.

P. J. Forrester N. E. Frankel

Asymptotically, we analytically derive the form of eigenvectors for two Fisher-Hartwig symbols besides those which were previously investigated in a $2016$ work due to Movassagh and Kadanoff, in which the authors characterized the eigenpairs of Toeplitz matrices generated by Fisher-Hartwig symbols with one singularity. To perform such computations, we extend their methods which consists of formulating an eigenvalue problem, obtained by a Wiener-Hopf method, from which a suitable winding number is defined for passing to Fourier space, and introducing a factorization dependent upon the winding number, for other Fisher-Hartwig symbols which have previously been defined in the literature. Following the computations required for the proof after obtaining the asymptotic approximation of the eigenvectors, we provide a table from which eigenvalues of one Fisher-Hartwig symbol for different complex valued functions $b$ can be inferred.

Pete Rigas

The leading contenders for the seeds of the first quasars are direct collapse black holes (DCBHs) formed during catastrophic baryon collapse in atomically-cooled halos at $z \sim$ 20. The discovery of the Ly$\alpha$ emitter CR7 at $z =$ 6.6 was initially held to be the first detection of a DCBH, although this interpretation has since been challenged on the grounds of Spitzer IRAC and Very Large Telescope X-Shooter data. Here we determine if radio flux from a DCBH in CR7 could be detected and discriminated from competing sources of radio emission in the halo such as young supernovae and H II regions. We find that a DCBH would emit a flux of 10 - 200 nJy at 1.0 GHz, far greater than the sub-nJy signal expected for young supernovae but on par with continuum emission from star-forming regions. However, radio emission from a DCBH in CR7 could be distinguished from free-free emission from H II regions by its spectral evolution with frequency and could be detected by the Square Kilometer Array in the coming decade.

Daniel J. Whalen Mar Mezcua Avery Meiksin Tilman Hartwig Muhammad A. Latif

Supermassive primordial stars in hot, atomically-cooling haloes at $z \sim$ 15 - 20 may have given birth to the first quasars in the universe. Most simulations of these rapidly accreting stars suggest that they are red, cool hypergiants, but more recent models indicate that some may have been bluer and hotter, with surface temperatures of 20,000 - 40,000 K. These stars have spectral features that are quite distinct from those of cooler stars and may have different detection limits in the near infrared (NIR) today. Here, we present spectra and AB magnitudes for hot, blue supermassive primordial stars calculated with the TLUSTY and CLOUDY codes. We find that photometric detections of these stars by the James Webb Space Telescope (JWST) will be limited to $z \lesssim$ 10 - 12, lower redshifts than those at which red stars can be found, because of quenching by their accretion envelopes. With moderate gravitational lensing, Euclid and the Wide-Field Infrared Space Telescope (WFIRST) could detect blue supermassive stars out to similar redshifts in wide-field surveys.

Marco Surace Erik Zackrisson Daniel J. Whalen Tilman Hartwig S. C. O. Glover Tyrone E. Woods Alexander Heger