ShantanuT01/DACTYL-Pretraining huggingface dataset:
In this paper we describe the Bayesian link between the cosmological mass function and the distribution of times at which isolated halos of a given mass exist. By assuming that clumps of dark matter undergo monotonic growth on the time-scales of interest, this distribution of times is also the distribution of `creation' times of the halos. This monotonic growth is an inevitable aspect of gravitational instability. The spherical top-hat collapse model is used to estimate the rate at which clumps of dark matter collapse. This gives the prior for the creation time given no information about halo mass. Applying Bayes' theorem then allows any mass function to be converted into a distribution of times at which halos of a given mass are created. This general result covers both Gaussian and non-Gaussian models. We also demonstrate how the mass function and the creation time distribution can be combined to give a joint density function, and discuss the relation between the time distribution of major merger events and the formula calculated. Finally, we determine the creation time of halos within three N-body simulations, and compare the link between the mass function and creation rate with the analytic theory.
We show that torsion points of certain orders are not on a theta divisor in the Jacobian variety of a hyperelliptic curve given by the equation $y^2=x^{2g+1}+x$ with $g \geq 2$. The proof employs a method of Anderson who proved an analogous result for a cyclic quotient of a Fermat curve of prime degree.
WL measurements have well-known shear estimation biases, which can be partially corrected for with the use of image simulations. We present an analysis of simulated images that mimic HST/ACS observations of high-redshift galaxy clusters, including cluster specific issues such as non-weak shear and increased blending. Our synthetic galaxies have been generated to match the observed properties of the background-selected samples in the real images. First, we used simulations with galaxies on a grid to determine a revised signal-to-noise-dependent correction for multiplicative shear measurement bias, and to quantify the sensitivity of our bias calibration to mismatches of galaxy or PSF properties between the real data and the simulations. We studied the impact of increased blending and light contamination from cluster and foreground galaxies, finding it negligible for $z>0.7$ clusters, whereas there is an effect at the $\sim 1\%$ level for lower redshift clusters. Finally, we studied the impact of fainter neighbours and selection bias mimicking the positions and magnitudes of galaxies in CANDELS data. The initial SExtractor object detection causes a selection bias of $-0.028 \pm 0.002$, reduced to $-0.016 \pm 0.002$ by further cuts. We compared our CANDELS-based estimate to a grid-based analysis, with added clustered galaxies reaching even fainter magnitudes, yielding a refined estimate of $\sim -0.013$. Our pipeline is calibrated to an accuracy of $\sim 0.015$, which is fully sufficient for current and near-future weak lensing studies of high-redshift clusters. As an application, we used it for a refined analysis of three highly relaxed clusters from the SPT-SZ survey, including measurements down to $r>200$ kpc. Compared to previously employed scales, this tightens the cluster mass constraints by a factor 1.38 on average.
In this article we study the existence of solutions for the Dirac systems \begin{equation}\label{e:0.1} \left\{ \begin{array}{c}   Pu=\frac{\partial H}{\partial v}(x,u,v) \quad\hbox{on} \ M,   Pv=\frac{\partial H}{\partial u}(x,u,v) \quad\hbox{on} \ M,   B_{\text{CHI}}u= B_{\text{CHI}}v=0\quad\hbox{on} \ \partial M \end{array} \right. \end{equation} where $M$ is an $m$-dimensional compact oriented Riemannian spin manifold with smooth boundary $\partial M$, $P$ is the Dirac operator under the boundary condition $B_{\text{CHI}}u= B_{\text{CHI}}v=0$ on $\partial M$, $ u,v\in C^{\infty}(M,\Sigma M)$ are spinors. Using an analytic framework of proper products of fractional Sobolev spaces, the solutions existence results of the coupled Dirac systems are obtained for nonlinearity with superquadratic growth rates.
Currently, both the g factor measurement of the muon as well as the Lamb shift 2S-2P measurement in muonic hydrogen are in disagreement with theory. Here, we investigate possible theoretical explanations, including proton structure effects and small modifications of the vacuum polarization potential. In particular, we investigate a conceivable small modification of the spectral function of vacuum polarization in between the electron and muon energy scales due to a virtual millicharged particle and due to an unstable vector boson originating from a hidden sector of an extended standard model. We find that a virtual millicharged particle which could explain the muonic Lamb shift discrepancy alters theoretical predictions for the muon anomalous magnetic moment by many standard deviations and therefore is in conflict with experiment. Also, we find no parameterizations of an unstable virtual vector boson which could simultaneously explain both "muonic" discrepancies without significantly altering theoretical predictions for electronic hydrogen, where theory and experiment currently are in excellent agreement. A process-dependent correction involving electron screening is evaluated to have the right sign and order-of-magnitude to explain the observed effect in muonic hydrogen. Additional experimental evidence from light muonic atoms and ions is needed in order to reach further clarification.
If $\mathfrak{p} \subseteq \mathbb{Z}[\zeta]$ is a prime ideal over $p$ in the $(p^d - 1)$th cyclotomic extension of $\mathbb{Z}$, then every element $\alpha$ of the completion $\mathbb{Z}[\zeta]_\mathfrak{p}$ has a unique expansion as a power series in $p$ with coefficients in $\mu_{p^d -1} \cup \{0\}$ called the Teichm\"uller expansion of $\alpha$ at $\mathfrak{p}$. We observe three peculiar and seemingly unrelated patterns that frequently appear in the computation of Teichm\"uller expansions, then develop a unifying theory to explain these patterns in terms of the dynamics of an affine group action on $\mathbb{Z}[\zeta]$.
This article extends classical one variable results about Euler products defined by integral valued polynomial or analytic functions to several variables. We show there exists a meromorphic continuation up to a presumed natural boundary, and also give a criterion, a la Estermann-Dahlquist, for the existence of a meromorphic extension to $\C^n.$ Among applications we deduce analytic properties of height zeta functions for toric varieties over $\Q$ and group zeta functions.
Context. X-shaped radio galaxies (XRGs) exhibit a pair of bright primary lobes and a pair of weak secondary lobes (wings), which are oriented with an angle that gives the structure a cross-like shape. Though several theoretical models have been proposed to explain their origin, there is currently not a general consensus on a formation scenario. Aims. We analysed new multifrequency Karl G. Jansky Very Large Array (JVLA) radio data at 1.5, 5.5, 6, and 9 GHz of the candidate XRG in Abell 3670 (A3670) in order to characterise and classify it for the first time and to investigate its origin. Methods. We produced flux, spectral index, and radiative age maps of A3670 by means of the new radio data. We investigated the connection between the radio galaxy and its host, a brightest cluster galaxy (BCG) with two optical nuclei classified as a dumbbell galaxy. Finally we discussed the literature models and compared them to the observed properties of A3670. Results. We classify A3670 as a Fanaroff-Riley I-type XRG and measured a 1.4 GHz radio power of 1.7 x 10^25 W Hz-1. By estimating the radiative age of the various source components, we find that the wings are 20 Myr older than the lobes. We verified that the lobes and wings are aligned with the major and minor axes of the optical galaxy, respectively, and we estimated a black hole mass of 10^9 Msun , which is in agreement with the typical properties of the XRGs. Conclusions. Among the discussed scenarios, the jet-shell interaction model may best reproduce the observed properties of A3670. The gas of a stellar shell is responsible for the deflection of the jets, thus forming the wings. The presence of stellar shells in A3670 is plausible, but it needs further optical observations to be confirmed.
We investigate the possibility of the existence of the exotic torus configuration in the high-spin excited states of $^{40}$Ca. We here consider the spin alignments about the symmetry axis. To this end, we use a three-dimensional cranked Skyrme Hartree-Fock method and search for stable single-particle configurations. We find one stable state with the torus configuration at the total angular momentum $J=$ 60 $\hbar$ and an excitation energy of about 170 MeV in all calculations using various Skyrme interactions. The total angular momentum J=60 $\hbar$ consists of aligned 12 nucleons with the orbital angular momenta $\Lambda=+4$, +5, and +6 for spin up-down neutrons and protons. The obtained results strongly suggest that a macroscopic amount of circulating current breaking the time-reversal symmetry emerges in the high-spin excited state of $^{40}$Ca.
In this paper, we show that if $X$ is a smooth variety of general type of dimension $m \geq 3$ for which the canonical map induces a triple cover onto $Y$, where $Y$ is a projective bundle over $\mathbf P^1$ or onto a projective space or onto a quadric hypersurface, embedded by a complete linear series, then the general deformation of the canonical morphism of $X$ is again canonical and induces a triple cover. The extremal case when $Y$ is embedded as a variety of minimal degree is of interest, due to its appearance in numerous situations. This is especially interesting as well, since it has no lower dimensional analogues.
We study iPTF14hls, a luminous and extraordinary long-lived Type II supernova, which lately has attracted much attention and disparate interpretation. We present new optical photometry that extends the light curves until more than 3 yr past discovery. We also obtained optical spectroscopy over this period, and furthermore present additional space-based observations using Swift and HST. After an almost constant luminosity for hundreds of days, the later light curve of iPTF14hls finally fades and then displays a dramatic drop after about 1000 d, but the supernova is still visible at the latest epochs presented. The spectra have finally turned nebular, and the very last optical spectrum likely displays signatures from the deep and dense interior of the explosion. The high-resolution HST image highlights the complex environment of the explosion in this low-luminosity galaxy. We provide a large number of additional late-time observations of iPTF14hls, which are (and will continue to be) used to assess the many different interpretations for this intriguing object. In particular, the very late (+1000 d) steep decline of the optical light curve, the lack of very strong X-ray emission, and the emergence of intermediate-width emission lines including of [S II] that likely originate from dense, processed material in the core of the supernova ejecta, are all key observational tests for existing and future models.
Using the renewal approach we prove exponential inequalities for additive functionals and empirical processes of ergodic Markov chains, thus obtaining counterparts of inequalities for sums of independent random variables. The inequalities do not require functions of the chain to be bounded and moreover all the involved constants are given by explicit formulas whenever the usual drift condition holds, which may be of interest in practical applications e.g. to MCMC algorithms.
We examine scaling relations of dispersion-supported galaxies over more than eight orders of magnitude in luminosity by transforming standard fundamental plane parameters into a space of mass (M1/2), radius (r1/2), and luminosity (L1/2). We find that from ultra-faint dwarf spheroidals to giant cluster spheroids, dispersion-supported galaxies scatter about a one-dimensional "fundamental curve" through this MRL space. The weakness of the M1/2-L1/2 slope on the faint end may imply that potential well depth limits galaxy formation in small galaxies, while the stronger dependence on L1/2 on the bright end suggests that baryonic physics limits galaxy formation in massive galaxies. The mass-radius projection of this curve can be compared to median dark matter halo mass profiles of LCDM halos in order to construct a virial mass-luminosity relationship (Mvir-L) for galaxies that spans seven orders of magnitude in Mvir. Independent of any global abundance or clustering information, we find that (spheroidal) galaxy formation needs to be most efficient in halos of Mvir ~ 10^12 Msun and to become inefficient above and below this scale. Moreover, this profile matching technique is most accurate at the high and low luminosity extremes (where dark matter fractions are highest) and is therefore quite complementary to statistical approaches that rely on having a well-sampled luminosity function. We also consider the significance and utility of the scatter about this relation, and find that in the dSph regime observational errors are almost at the point where we can explore the intrinsic scatter in the luminosity-virial mass relation. Finally, we note that purely stellar systems like Globular Clusters and Ultra Compact Dwarfs do not follow the fundamental curve relation. This allows them to be easily distinguished from dark-matter dominated dSph galaxies in MRL space. (abridged)
Numerous cosmological simulations have been performed to study the formation of the first objects. We present the results of high resolution 3-D cosmological simulations of primordial objects formation using the adaptive mesh refinement code FLASH by including in an approximate manner the radiative transfer effects of Lyman alpha photons. We compare the results of a Lyman alpha trapping case inside gas clouds with atomic and molecular hydrogen cooling cases.The principal objective of this research is to follow the collapse of a zero metallicity halo with an effective equation of state (that accounts for the trapping) and to explore the fate of a halo in each of the three cases, specifically, the impact of thermodynamics on fragmentation of halos.Our results show that in the case of Lyman alpha trapping, fragmentation is halted and a massive object is formed at the center of a halo. The temperature of the gas remains well above $10^{4}$ K and the halo is not able to fragment to stellar masses. In the atomic cooling case, gas collapses into one or two massive clumps in contrast to the Lyman alpha trapping case. For the molecular hydrogen cooling case, gas cools efficiently and fragments.The formation of massive primordial objects is thus strongly dependent on the thermodynamics of the gas. A salient feature of our results is that for the formation of massive objects, e.g. intermediate mass black holes, feedback effects are not required to suppress $H_{2}$ cooling, as molecular hydrogen is collisionally dissociated at temperatures higher than $10^{4}$ K as a consequence of Lyman alpha trapping.
We consider a sum of the derivatives of Dirichlet $L$-functions over the zeros of Dirichlet $L$-functions. We give an asymptotic formula for the sum.
Thin highly epitaxial BiFeO$_3$ films were prepared on SrTiO$_3$ (100) substrates by reactive magnetron co-sputtering. Detailed MOKE measurements on BiFeO$_3$/Co-Fe bilayers were performed to investigate the exchange bias as a function of the films thicknesses and Co-Fe stoichiometries. We found a maximum exchange bias of H$_{\mathrm{eb}}$=92 Oe and a coercive field of H$_{\mathrm{c}}$=89 Oe for a 12.5 nm thick BiFeO$_3$ film with a 2 nm thick Co layer. The unidirectional anisotropy is clearly visible in in-plane rotational MOKE measurements. AMR measurements reveal a strongly increasing coercivity with decreasing temperature, but no significant change in the exchange bias field.
We have explored the impact of sterile neutrino dark matter on core-collapse supernova explosions. We have included oscillations between electron neutrinos or mixed $\mu,\tau$ neutrinos and right-handed sterile neutrinos into a supernova model. We have chosen sterile neutrino masses and mixing angles that are consistent with sterile neutrino dark matter candidates as indicated by recent x-ray flux measurements. Using these simulations, we have explored the impact of sterile neutrinos on the core bounce and shock reheating. We find that, for ranges of sterile neutrino mass and mixing angle consistent with most dark matter constraints, the shock energy can be significantly enhanced and even a model that does not explode can be made to explode. In addition, we have found that the presence of a sterile neutrino may lead to detectable changes in the observed neutrino luminosities.
The variational quantum eigensolver (VQE) is an algorithm to compute ground and excited state energy of quantum many-body systems. A key component of the algorithm and an active research area is the construction of a parametrized trial wavefunction -- a so called variational ansatz. The wavefunction parametrization should be expressive enough, i.e. represent the true eigenstate of a quantum system for some choice of parameter values. On the other hand, it should be trainable, i.e. the number of parameters should not grow exponentially with the size of the system. Here, we apply VQE to the problem of finding ground and excited state energies of the odd-odd nucleus $^6$Li. We study the effects of ordering fermionic excitation operators in the unitary coupled clusters ansatz on the VQE algorithm convergence by using only operators preserving the $J_z$ quantum number. The accuracy is improved by two order of magnitude in the case of descending order. We first compute optimal ansatz parameter values using a classical state-vector simulator with arbitrary measurement accuracy and then use those values to evaluate energy eigenstates of $^6$Li on a superconducting quantum chip from IBM. We post-process the results by using error mitigation techniques and are able to reproduce the exact energy with an error of 3.8% and 0.1% for the ground state and for the first excited state of $^6$Li, respectively.
For $0<\alpha\leq2$, a super-$\alpha$-stable motion $X$ in $\mathsf{R}^d$ with branching of index $1+\beta\in(1,2)$ is considered. Fix arbitrary $t>0$. If $d<\alpha/\beta$, a dichotomy for the density function of the measure $X_t$ holds: the density function is locally H\"{o}lder continuous if $d=1$ and $\alpha>1+\beta$ but locally unbounded otherwise. Moreover, in the case of continuity, we determine the optimal local H\"{o}lder index.
While the slope of the dust attenuation curve ($\delta$) is found to correlate with effective dust attenuation ($A_V$) as obtained through spectral energy distribution (SED) fitting, it remains unknown how the fitting degeneracies shape this relation. We examine the degeneracy effects by fitting SEDs of a sample of local star-forming galaxies (SFGs) selected from the Galaxy And Mass Assembly survey, in conjunction with mock galaxy SEDs of known attenuation parameters. A well-designed declining starburst star formation history is adopted to generate model SED templates with intrinsic UV slope ($\beta_0$) spanning over a reasonably wide range. The best-fitting $\beta_0$ for our sample SFGs shows a wide coverage, dramatically differing from the limited range of $\beta_0<-2.2$ for a starburst of constant star formation. Our results show that strong degeneracies between $\beta_0$, $\delta$, and $A_V$ in the SED fitting induce systematic biases leading to a false $A_V$--$\delta$ correlation. Our simulation tests reveal that this relationship can be well reproduced even when a flat $A_V$--$\delta$ relation is taken to build the input model galaxy SEDs. The variations in best-fitting $\delta$ are dominated by the fitting errors. We show that assuming a starburst with constant star formation in SED fitting will result in a steeper attenuation curve, smaller degeneracy errors, and a stronger $A_V$--$\delta$ relation. Our findings confirm that the $A_V$--$\delta$ relation obtained through SED fitting is likely driven by the systematic biases induced by the fitting degeneracies between $\beta_0$, $\delta$, and $A_V$.
We consider a holographic fermionic system in which the fermions are interacting with a U(1) gauge field in the presence of a dilaton field in a gravity bulk of a charged black hole with hyperscaling violation. Using both analytical and numerical methods, we investigate the properties of the infrared and ultaviolet Green's functions of the holographic fermionic system. Studying the spectral functions of the system, we find that as the hyperscaling violation exponent is varied, the fermionic system possesses Fermi, non-Fermi, marginal-Fermi and log-oscillating liquid phases. Various liquid phases of the fermionic system with hyperscaling violation are also generated with the variation of the fermionic mass. We also explore the properties of the flat band and the Fermi surface of the non-relativistic fermionic fixed point dual to the hyperscaling violation gravity.
The rest-frame UV-optical (i.e., $NUV-B$) color is sensitive to both low-level recent star formation (specific star formation rate - sSFR) and dust. In this Letter, we extend our previous work on the origins of $NUV-B$ color gradients in star-forming galaxies (SFGs) at $z\sim1$ to those at $z\sim2$. We use a sample of 1335 large (semi-major axis radius $R_{\rm SMA}>0.''18$) SFGs with extended UV emission out to $2R_{\rm SMA}$ in the mass range $M_{\ast} = 10^{9}-10^{11}M_{\odot}$ at $1.5<z<2.8$ in the CANDELS/GOODS-S and UDS fields. We show that these SFGs generally have negative $NUV-B$ color gradients (redder centres), and their color gradients strongly increase with galaxy mass. We also show that the global rest-frame $FUV-NUV$ color is approximately linear with $A_{\rm V}$, which is derived by modeling the observed integrated FUV to NIR spectral energy distributions of the galaxies. Applying this integrated calibration to our spatially-resolved data, we find a negative dust gradient (more dust extinguished in the centers), which steadily becomes steeper with galaxy mass. We further find that the $NUV-B$ color gradients become nearly zero after correcting for dust gradients regardless of galaxy mass. This indicates that the sSFR gradients are negligible and dust reddening is likely the principal cause of negative UV-optical color gradients in these SFGs. Our findings support that the buildup of the stellar mass in SFGs at the Cosmic Noon is self-similar inside $2R_{\rm SMA}$.
Let $\left\lbrace a_{n}\right\rbrace_{n\geq 0}$ be the Narayana Sequence defined by the recurence $a_{n}=a_{n-1}+a_{n-3}$ for all $n\geq 3$ with intital values $a_{0}=0$ and $a_{1}=a_{2}=1$. In This paper, we fully characterize the $3-$adic valuation of $a_{n}+1$ and $a_{n}-1$ and then we prove that there are no integer solutions $(u,m)$ to the Brocard-Ramanujan Equation $m!+1=u^2$ where $u$ is a Narayana number.
We present several sequences of Euler sums involving odd harmonic numbers. The calculational technique is based on proper two-valued integer functions, which allow to compute these sequences explicitly in terms of zeta values only.
We propose a systematical approach to construct generic fractional quantum anomalous Hall (FQAH) states, which are generalizations of the fractional quantum Hall states to lattice models with zero net magnetic field and full lattice translation symmetry. Local and translationally invariant Hamiltonians can also be constructed, for which the proposed states are unique ground states. Our result demonstrates that generic chiral topologically ordered states can be realized in lattice models, without requiring magnetic translation symmetry and Landau level structure. We further generalize our approach to the time-reversal invariant analog of fractional quantum Hall states--fractional topological insulators, and provide the first explicit wavefunction description of fractional topological insulators in the absence of spin conservation.