ShantanuT01/DACTYL-Pretraining huggingface dataset:
The accreting black-hole binary XTE J1752--223 was observed in a stable hard state for 25 d by RXTE, yielding a 3--140 keV spectrum of unprecedented statistical quality. Its published model required a single Comptonization spectrum reflecting from a disk close to the innermost stable circular orbit. We studied that model as well as a number of other single-Comptonization models (yielding similarly low inner radii), but found they violate a number of basic physical constraints, e.g., their compactness is much above the maximum allowed by pair equilibrium. We also studied the contemporaneous 0.55--6 keV spectrum from the Swift/XRT and found it well fitted by an absorbed power law and a disk blackbody with the innermost temperature of 0.1 keV. The normalization of the disk blackbody corresponds to an inner radius of $\gtrsim$20 gravitational radii and its temperature, to irradiation of the truncated disk by a hot inner flow. We have also developed a Comptonization/reflection model including the disk irradiation and intrinsic dissipation, but found that it does not yield any satisfactory fits. On the other hand, we found that the $\leq$10 keV band from RXTE is much better fitted by a reflection from a disk with the inner radius $\gtrsim$100 gravitational radii, which model then underpredicts the spectrum at $>$10 keV by $<$10%. We argue that the most plausible explanation of the above results is inhomogeneity of the source, with the local spectra hardening with the decreasing radius. Our results support the presence of a complex Comptonization region and a large disk truncation radius in this source.
In this paper we present some compactness results, showing how they can be applied in dealing with "zero mass" problems by a variational approach. In particular we use our results in two different situations: we look for complex valued solutions of a very classical elliptic equation, and we study an elliptic problem on an axially symmetric unbounded domain.
An effective action is obtained for the $N=1$, $2D-$induced supergravity on a compact super Riemann surface (without boundary) $\hat\Sigma$ of genus $g>1$, as the general solution of the corresponding superconformal Ward identity. This is accomplished by defining a new super integration theory on $\hat\Sigma$ which includes a new formulation of the super Stokes theorem and residue calculus in the superfield formalism. Another crucial ingredient is the notion of polydromic fields. The resulting action is shown to be well-defined and free of singularities on $\sig$. As a by-product, we point out a morphism between the diffeomorphism symmetry and holomorphic properties.
A class of generalized exclusion processes parametrized by the maximal occupancy, $k\geq 1$, is investigated. For these processes with symmetric nearest-neighbor hopping, we compute the diffusion coefficient and show that it is independent on the spatial dimension. In the extreme cases of $k=1$ (simple symmetric exclusion process) and $k=\infty$ (non-interacting symmetric random walks) the diffusion coefficient is constant; for $2\leq k<\infty$, the diffusion coefficient depends on the density and the maximal occupancy $k$. We also study the evolution of a tagged particle. It exhibits a diffusive behavior which is characterized by the coefficient of self-diffusion which we probe numerically.
We develop the theory of Hodge ideals for Q-divisors by means of log resolutions, extending our previous work on reduced hypersurfaces. We prove local (non-)triviality criteria and a global vanishing theorem, as well as other analogues of standard results from the theory of multiplier ideals, and we derive a new local vanishing theorem. The connection with the V-filtration is analyzed in a sequel.
By means of a recent variational technique, we prove the existence of radially monotone solutions to a class of nonlinear problems involving the $p$-Laplace operator. No subcriticality condition (in the sense of Sobolev spaces) is required.
We present the Image-based Tapered Gridded Estimator (ITGE) to measure the angular power spectrum $(C_{\ell})$ of the sky signal directly from the visibilities measured in radio-interferometric observations. The ITGE allows us to modulate the sky response through a window function which is implemented in the image plane, and it is possible to choose a wide variety of window functions. In the context of the cosmological HI 21-cm signal, this is useful for masking out the sky signal from specific directions which have strong residual foregrounds. In the context of the ISM in external galaxies, this is useful to separately estimate the $C_{\ell}$ of different parts of the galaxy. The ITGE deals with gridded data, hence it is computationally efficient. It also calculates the noise bias internally and exactly subtracts this out to give an unbiased estimate of $C_{\ell}$. We validate the ITGE using realistic VLA simulations at $1.4 {\rm GHz}$. We have applied the ITGE to estimate the $C_{\ell}$ of HI 21-cm emission from different regions of the galaxy NGC 628. We find that the slope of the measured $C_{\ell}$ in the outer region is significantly different as compared with the inner region. This indicates that the statistical properties of ISM turbulence possibly differ in different regions of the galaxy.
We review Hodge structures, relating filtrations, Galois Theory and Jordan-Holder structures. The prototypical case of periods of Riemann surfaces is compared with the Galois-Artin framework of algebraic numbers.
We discuss a category of graphs, recursive clique trees, which have small-world and scale-free properties and allow a fine tuning of the clustering and the power-law exponent of their discrete degree distribution. We determine relevant characteristics of those graphs: the diameter, degree distribution, and clustering parameter. The graphs have also an interesting recursive property, and generalize recent constructions with fixed degree distributions.
This paper describes the construction of the first explicitly known widely digitally delicate prime.
We develop a minimal theory for the recently observed metal-insulator transition (MIT) in two-dimensional (2D) moir\'e multilayer transition metal dichalcogenides (mTMD) using Coulomb disorder in the environment as the underlying mechanism. In particular, carrier scattering by random charged impurities leads to an effective 2D MIT approximately controlled by the Ioffe-Regel criterion, which is qualitatively consistent with the experiments. We find the necessary disorder to be around $5$-$10\times10^{10}$cm$^{-2}$ random charged impurities in order to quantitatively explain much, but not all, of the observed MIT phenomenology as reported by two different experimental groups. Our estimate is consistent with the known disorder content in TMDs.
We prove nonexistence of nontrivial bounded solutions to some nonlinear problems involving nonlocal operators of the form \[Lu(x)=\sum a_{ij}\partial_{ij}u+{\rm PV}\int_{\R^n}(u(x)-u(x+y))K(y)dy.\] These operators are infinitesimal generators of symmetric L\'evy processes. Our results apply to even kernels $K$ satisfying that $K(y)|y|^{n+\sigma}$ is nondecreasing along rays from the origin, for some $\sigma\in(0,2)$ in case $a_{ij}\equiv0$ and for $\sigma=2$ in case that $(a_{ij})$ is a positive definite symmetric matrix.   Our nonexistence results concern Dirichlet problems for $L$ in star-shaped domains with critical and supercritical nonlinearities (where the criticality condition is in relation to $n$ and $\sigma$).   We also establish nonexistence of bounded solutions to semilinear equations involving other nonlocal operators such as the higher order fractional Laplacian $(-\Delta)^s$ (here $s>1$) or the fractional $p$-Laplacian. All these nonexistence results follow from a general variational inequality in the spirit of a classical identity by Pucci and Serrin.
We clarify the recently proposed method to compute a Special K\"ahler metric on a Calabi-Yau complex structures moduli space that uses the fact that the moduli space is a subspace of specific Frobenius manifold. We apply this method to computing the Special K\"ahler metric in a two-moduli non-Fermat model which has been unknown until now.
Supernovae of Type IIb contain large fractions of helium and traces of hydrogen, which can be observed in the early and late spectra. Estimates of the hydrogen and helium mass and distribution are mainly based on early-time spectroscopy and are uncertain since the respective lines are usually observed in absorption. Constraining the mass and distribution of H and He is important to gain insight into the progenitor systems of these SNe.   We implement a NLTE treatment of hydrogen and helium in a three-dimensional nebular code. Ionisation, recombination, (non-)thermal electron excitation and H$\alpha$ line scattering are taken into account to compute the formation of H$\alpha$, which is by far the strongest H line observed in the nebular spectra of SNe IIb. Other lines of H and He are also computed but are rarely identified in the nebular phase. Nebular models are computed for the Type IIb SNe 1993J, 2001ig, 2003bg and 2008ax as well as for SN 2007Y, which shows H$\alpha$ absorption features at early times and strong H$\alpha$ emission in its late phase, but has been classified as a SN Ib. We suggest to classify SN 2007Y as a SN IIb. Optical spectra exist for all SNe of our sample, and there is one IR nebular observation of SN 2008ax, which allows an exploration of its helium mass and distribution.   We develop a three-dimensional model for SN 2008ax. We obtain estimates for the total mass and kinetic energy in good agreement with the results from light-curve modelling found in the literature. We further derive abundances of He, C, O, Ca and $^{56}$Ni. We demonstrate that H$\alpha$ absorption is probably responsible for the double-peaked profile of the [O {\sc i}] $\lambda\lambda$ 6300, 6363 doublet in several SNe IIb and present a mechanism alternative to shock interaction for generating late-time H$\alpha$ emission of SNe IIb.
We present far-infrared (FIR) analysis of 68 Brightest Cluster Galaxies (BCGs) at 0.08 < z < 1.0. Deriving total infrared luminosities directly from Spitzer and Herschel photometry spanning the peak of the dust component (24-500um), we calculate the obscured star formation rate (SFR). 22(+6.2,-5.3)% of the BCGs are detected in the far-infrared, with SFR= 1-150 M_sun/yr. The infrared luminosity is highly correlated with cluster X-ray gas cooling times for cool-core clusters (gas cooling time <1 Gyr), strongly suggesting that the star formation in these BCGs is influenced by the cluster-scale cooling process. The occurrence of the molecular gas tracing Ha emission is also correlated with obscured star formation. For all but the most luminous BCGs (L_TIR > 2x10^11 L_sun), only a small (<0.4 mag) reddening correction is required for SFR(Ha) to agree with SFR_FIR. The relatively low Ha extinction (dust obscuration), compared to values reported for the general star-forming population, lends further weight to an alternate (external) origin for the cold gas. Finally, we use a stacking analysis of non-cool-core clusters to show that the majority of the fuel for star formation in the FIR-bright BCGs is unlikely to originate form normal stellar mass loss.
We compute the two-loop master integrals for non-leptonic heavy-to-heavy decays analytically in a recently-proposed canonical basis. For this genuine two-loop, two-scale problem we first derive a basis for the master integrals that disentangles the kinematics from the space-time dimension in the differential equations, and subsequently solve the latter in terms of iterated integrals up to weight four. The solution constitutes another valuable example of the finding of a canonical basis for two-loop master integrals that have two different internal masses, and assumes a form that is ideally suited for a subsequent convolution with the light-cone distribution amplitude in the framework of QCD factorisation.
Narrow, elongated regions of very low polarized intensity -- so-called canals -- have recently been observed by several authors at decimeter wavelengths in various directions in the Milky Way, but their origin remains enigmatic. We show that the canals arise from depolarization by differential Faraday rotation in the interstellar medium and that they represent level lines of Faraday rotation measure RM, a random function of position in the sky. Statistical properties of the separation of canals depend on the autocorrelation function of RM, and so provide a useful tool for studies of interstellar turbulence.
We present B, R, and Halpha images for a total of 114 nearby galaxies (v_helio<4000km/s) that, with exception of 9 objects, are classified as Blue Compact Dwarfs (BCDs). BR integrated magnitudes, Halpha fluxes and Halpha equivalent widths for all the objects in the sample are presented. A new set of quantitative, observational criteria for a galaxy to be classified as a BCD is proposed. These criteria include a limit on the K-band luminosity (i.e. stellar mass; M_K>-21mag), peak surface brightness (mu_B,peak<22mag/arcsec^2), and color at the peak surface brightness (mu_B,peak-mu_R,peak<~1). Halpha emission is detected in all but three sample galaxies. Typical color, absolute magnitude, and Halpha luminosity are (B-R)=0.7+/-0.3mag, M_B=-16.1+/-1.4mag, and log(L_Halpha)=40.0+/-0.6(erg/s). Galaxies morphologically classified as nE and iE BCDs within our sample show lower Halpha equivalent widths and redder colors, on average, than the iI and i0-type BCDs. For most of the galaxies the presence of an evolved stellar population is required to explain their observed properties; only the most metal-poor BCDs (e.g. IZw18, Tol65) are still compatible with a pure, young burst. The flux-calibrated and WCS-compliant images in this Atlas are individually available through the NASA/IPAC Extragalactic Database (NED) image server and collectively through a dedicated web page at http://nedwww.ipac.caltech.edu/level5/Sept02/Palco_BCD/frames.html
The linearly polarized Gowdy $T^3$ model can be regarded as compact Bianchi I cosmologies with inhomogeneous modes allowed to travel in one direction. We study a hybrid quantization of this model that combines the loop quantization of the Bianchi I background, adopting the improved dynamics scheme put forward by Ashtekar and Wilson-Ewing, with a Fock quantization for the inhomogeneities. The Hamiltonian constraint operator provides a resolution of the cosmological singularity and superselects separable sectors. We analyze the complicated structure of these sectors. In any of them the Hamiltonian constraint provides an evolution equation with respect to the volume of the associated Bianchi I universe, with a well posed initial value problem. This fact allows us to construct the Hilbert space of physical states and to show that we recover the standard quantum field theory for the inhomogeneities.
The goal of the current text is to study non-archimedean analytic derived de Rham cohomology by means of formal completions. Our approach is inspired by the deformation to the normal cone provided in \cite{Gaitsgory_Study_II}. More specifically, given a morphism $f \colon X \to Y$ of (derived) $k$-analytic spaces we construct the \emph{non-archimedean deformation to the normal cone} associated to $f$. The latter can be thought as an $\mathbf A^1_k$-parametrized deformation whose fiber at $1 \in \mathbf A^1_k$ coincides with the formal completion of $f$ and the fiber at $0 \in \mathbf A^1_k$ with the (derived) normal cone associated to $f$. We further show that such deformation can be endowed with a natural filtration which spreads out the usual Hodge filtration on the (completed shifted) analytic tangent bundle to the formal completion. Such filtration agrees with the $I$-adic filtration in the case where $f$ is a locally complete intersection morphism between (derived) $k$-affinoid spaces. Along the way we develop the theory of (ind-inf)-$k$-analytic spaces or in other words $k$-analytic formal moduli problems.
We study the coupled equations describing fluctuations of scalars and the metric about background solutions of N=8 gauged supergravity which are dual to boundary field theories with renormalization group flow. For the case of a kink solution with a single varying scalar, we develop a procedure to decouple the equations, and we solve them in particular examples. However, difficulties occur in the calculation of correlation functions from the fluctuations, presumably because the AdS/CFT correspondence has not yet been properly implemented in the coupled scalar-gravity sector. Some new examples of correlators of operators dual to simpler uncoupled bulk scalars are given and are satisfactory. As byproducts of our study we make some observations relevant to the stability of domain walls in the brane-world scenario and to the Hamilton-Jacobi formulation of holographic RG flows.
We consider a special class of mean field SDEs with common noise which depend on the image of the solution (i.e. the conditional distribution given noise). The strong well-posedness is derived under a monotone condition which is weaker than those used in the literature of mean field games, the Feynman-Kac formula is established to solve Schr\"ordinegr type PDEs on $\scr P_2$, and the ergodicity is proved for a class of measure-valued diffusion processes.
We briefly review the beginnings of HI astronomy, proceed to an assessment of our current capabilities in this area, and continue by considering what will be necessary to push back the frontier to cosmological distances. We then consider how such a leap in performance might be realized.
We present updated constraints on the free-streaming of warm dark matter (WDM) particles derived from an analysis of the Lya flux power spectrum measured from high-resolution spectra of 25 z > 4 quasars obtained with the Keck High Resolution Echelle Spectrometer (HIRES) and the Magellan Inamori Kyocera Echelle (MIKE) spectrograph. We utilize a new suite of high-resolution hydrodynamical simulations that explore WDM masses of 1, 2 and 4 keV (assuming the WDM consists of thermal relics), along with different physically motivated thermal histories. We carefully address different sources of systematic error that may affect our final results and perform an analysis of the Lya flux power with conservative error estimates. By using a method that samples the multi-dimensional astrophysical and cosmological parameter space, we obtain a lower limit mwdm > 3.3 keV (2sigma) for warm dark matter particles in the form of early decoupled thermal relics. Adding the Sloan Digital Sky Survey (SDSS) Lya flux power spectrum does not improve this limit. Thermal relics of masses 1 keV, 2 keV and 2.5 keV are disfavoured by the data at about the 9sigma, 4sigma and 3sigma C.L., respectively. Our analysis disfavours WDM models where there is a suppression in the linear matter power spectrum at (non-linear) scales corresponding to k=10h/Mpc which deviates more than 10% from a LCDM model. Given this limit, the corresponding "free-streaming mass" below which the mass function may be suppressed is 2x10^8 Msun/h. There is thus very little room for a contribution of the free-streaming of WDM to the solution of what has been termed the small scale crisis of cold dark matter.
Rapid advances in additive manufacturing over the past decade have kindled widespread interest in the rational design of metamaterials with unique properties. However, many applications require multi-physics metamaterials, where multiple properties are simultaneously optimized. This is challenging, since different properties, such as mechanical and mass transport properties, typically impose competing requirements on the nano-/micro-/meso-architecture of metamaterials. Here, we propose a parametric metamaterial design strategy that enables independent tuning of the effective permeability and elastic properties. We apply hyperbolic tiling theory to devise simple templates based on which triply periodic minimal surfaces (TPMS) are partitioned into hard and soft regions. Through computational analyses, we demonstrate how the decoration of hard, soft, and void phases within the TPMS substantially enhances their permeability-elasticity property space and offers high tunability in the elastic properties and anisotropy, at constant permeability. We also show that this permeability-elasticity balance is well captured using simple scaling laws. We then proceed to demonstrate the proposed concept through multi-material additive manufacturing of representative specimens. Our approach, which is generalizable to other designs, offers a route towards multi-physics metamaterials that need to simultaneously carry a load and enable mass transport, such as load-bearing heat exchangers or architected tissue-substituting meta-biomaterials.
Using the 0.9--4.4~$\mu$m imaging data from the James Webb Space Telescope (JWST) Early Release Observation in the SMACS J0723.3-7327 galaxy cluster field, we discuss the properties of three submillimeter galaxies (SMGs) detected by the Atacama Large Millimeter Array. These sources are magnified by 1.4--2.1$\times$due to gravitational lensing. This is the first time that SMG host galaxies are resolved in the rest-frame near-infrared (NIR). One source was previous undetected by HST, while the remaining two are disk galaxies with S\'ersic indices of $\sim 0.9$ and star formation rates on or just below the star formation "main sequence". Their submillimeter emission originates from the inner parts of the hosts, suggesting that their dust contents are concentrated towards the center. The host half-light radii measured in the rest-frame NIR are $\sim$1.5$\times$ smaller than those measured in the rest-frame optical, consistent with a concentrated dust distribution. The more severe extinction that optical light suffers towards the center makes it seemingly less concentrated. Therefore, we expect that the optically-based determination of the stellar mass distribution within host galaxies could still be severely biased by dust. Interestingly, these two disk galaxies are dramatically different in their outer regions, with one being star forming and the other being quiescent. Upcoming JWST observations of statistically significant samples of SMGs will allow us to understand the correlation between the dusty star forming regions and their hosts.
Recent advances in N-body simulations of dark matter halos have shown that three-parameter models, in particular the Einasto profile characterized by d ln {\rho}(r)/d ln r / r with a shape parameter {\alpha} < 0.3, are able to produce better fits to the 3D spatial density profiles than two-parameter models like the Navarro, Frenk and White (NFW), and Moore et al. profiles.   In this paper, we present for the first time an analytically motivated form for the 2D surface mass density of the Einasto family of dark matter haloes, in terms of the 3D spatial density parameters for a wide range of the shape parameter 0.1 < {\alpha} < 1. Our model describes a projected (2D) Einasto profile remarkably well between 0 and (3 - 5) r_{200}, with errors less than 0.3 per cent for {\alpha} < 0.3 and less than 2 per cent for {\alpha} as large as 1. This model (in 2D) can thus be used to fit strong and weak lensing observations of galaxies and clusters whose total spatial (3D) density distributions are believed to be Einasto-like. Further, given the dependence of our model on the 3D parameters, one can reliably estimate structural parameters of the spatial (3D) density from 2D observations. We also consider a Sersic-like parametrization for the above family of projected Einasto profiles and observe that fits with a Sersic profile are sensitive to whether one fits the projected density in linear scale or logarithmic scale and yield widely varying results. Structural parameters of Einasto-like systems, inferred from fits with a Sersic profile, should be used with caution.