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The accretion disks of supermassive black holes (SMBHs) harboring in active galactic nuclei (AGN) are considered to be an ideal site for producing different types of gamma-ray bursts (GRBs). The detectability of these GRB phenomena hidden in AGN disks is highly dependent on the dynamical evolution of the GRB relativistic jets. By investigating the reverse and forward shock dynamics due to the interaction between the jets and AGN disk material, we find that the relativistic jets can successfully break out from the disks only for a sufficiently high luminosity and a long enough duration. In comparison, relatively normal GRB jets are inclined to be choked in the disks, unless the GRBs occur near an SMBH with relatively low mass (e.g., $\sim 10^6M_{\odot}$). For the choked jets, unlike normal GRB prompt and afterglow emission, we can only expect to detect emission from the forward shock when the shock is very close to the edge of the disks, i.e., the shock breakout emission and subsequent cooling of the shock., Comment: 9 pages, 6 figures

Wolf-Rayet stars in close binary systems can be tidally spun up by their companions, potentially leaving behind fast-spinning highly-magnetized neutron stars, known as ``magnetars", after core collapse. These newborn magnetars can transfer rotational energy into heating and accelerating the ejecta, producing hydrogen-poor superluminous supernovae (SLSNe). In this {\em{Letter}}, we propose that the magnetar wind of the newborn magnetar could significantly evaporate its companion star, typically a main-sequence or helium star, if the binary system is not disrupted by the {abrupt mass loss and} SN kick. The subsequent heating and acceleration of the evaporated star material along with the SN ejecta by the magnetar wind can produce a post-peak bump in the SLSN lightcurve. Our model can reproduce the primary peaks and post-peak bumps of four example observed multiband SLSN lightcurves, revealing that the mass of the evaporated material could be $\sim0.4-0.6\,M_\odot$ if the material is hydrogen-rich. {We propose that the magnetar could induce strongly enhanced evaporation from its companion star near the pericenter if the orbit of the post-SN binary is highly eccentric, ultimately generating multiple post-peak bumps in the SLSN lightcurves. This ``magnetar-star binary engine" model may offer a possible explanation for the evolution of polarization, along with the origin and velocity broadening of late-time hydrogen or helium broad spectral features observed in some bumpy SLSNe.} The diversity in the lightcurves and spectra of SLSNe may be attributed to the wide variety of companion stars and post-SN binary systems., Comment: Accepted by ApJL, 14 pages, 4 figures, 2 tables

The aim of this paper is to confirm an inequality predicted by Isaacs and Navarro in 1995, which asserts that for any $\pi'$-subgroup $Q$ of a $\pi$-separable group $G$, the number of $\pi'$-weights of $G$ with $Q$ as the first component always exceeds that of irreducible $\pi$-partial characters of $G$ with $Q$ as their vertex. We also give some sufficient condition to guarantee that these two numbers are equal, and thereby strengthen their main theorem on the $\pi$-version of the Alperin weight conjecture.

In this {\em{Letter}}, we explore the formation of the mass-gap black hole-neutron star (mgBHNS) merger detected in gravitational wave (GW) event, i.e., GW230529, from the isolated binary evolution channel, and study potential signatures of its electromagnetic counterparts. By adopting the `delayed' supernova prescription and reasonable model realizations, our population synthesis simulation results can simultaneously match the rate densities of mgBHNS and total BHNS mergers inferred from the population analyses, along with the population distribution of the BH mass in BHNS mergers reported by the LIGO-Virgo-KAGRA Collaboration. Because GW230529 contributes significantly to the inferred mgBHNS rate densities, we suggest that GW230529 can be explained through the isolated binary evolution channel. Considering the AP4 (DD2) equation of state, the probability that GW230529 can make tidal disruption is $12.8\%$ ($63.2\%$). If GW230529 is a disrupted event, its kilonova peak apparent magnitude is predicted $\sim23-24\,{\rm{mag}}$, and hence, can be detected by the present survey projects and LSST. Since GW230529 could be an off-axis event inferred from the GW observation, its associated gamma-ray burst (GRB) might be too dim to be observed by $\gamma$-ray detectors, interpreting the lack of GRB observations. Our study suggests the existence of mgBHNS mergers formed through the isolated binary evolution channel due to the discovery of GW230529, indicating that BHNS mergers are still likely to be multimessenger sources that emit GWs, GRBs, and kilonovae. Although mgBHNS mergers account for $\sim50\%$ cosmological BHNS population, we find that $\gtrsim90\%$ disrupted BHNS mergers are expected to originate from mgBHNS mergers., Comment: Submitted to ApJL, 15 pages, 5 figures, 4 tables, comments are welcome!

Over-/under-break excavation is a common phenomenon in shallow tunnelling, which is nonetheless not generally considered in existing complex variable solutions. In this paper, a new equilibrium mechanical model on over-/under-break shallow tunnelling in gravitational geomaterial is established by fixing far-field ground surface to form a corresponding mixed boundary problem. With integration of a newly proposed bidirectional composite conformal mapping using Charge Simulation Method, a complex variable solution of infinite complex potential series is subsequently derived using analytic continuation to tranform the mixed boundaries into a homogenerous Riemann-Hilbert problem, which is iteratively solved to obtain the stress and displacement in geomaterial. The infinite complex potential series of the complex variable solution are truncated to obtain numerical results, which is rectified by Lanczos filtering to reduce the oscillation of Gibbs phenomena. The bidirectional conformal mapping is discussed and validated via several numerical cases, and the subsequent complex variable solution is verified by examining the Lanczos filtering and solution convergence, and comparing with corresponding finite element solution and existing analytical solution. Further discussions are made to disclose possible defects of the proposed solution for objectivity.

The second brightest gamma-ray burst, GRB 230307A (with a duration $T_{90}$ ~ 40 s), exhibited characteristics indicative of a magnetar engine during the prompt emission phase. Notably, a suspected kilonova was identified in its follow-up optical and infrared observations. Here we propose that the origin of GRB 230307A is a neutron star-white dwarf (NS-WD) merger, as this could naturally interpret the long duration and the large physical offset from the center of its host galaxy. In the framework of such a NS-WD merger event, the late-time kilonova-like emission is very likely to be powered by the spin-down of the magnetar and the radioactive decay of $^{56}$Ni, rather than by the decay of r-process elements as these heavy elements may not be easy to be synthesized in a NS-WD merger. It is demonstrated that the above scenario can be supported by our fit to the late-time observational data, where a mass of ~ $10^{-3} \ \rm M_{\odot}$ $^{56}$Ni is involved in the ejecta of a mass of ~ $0.1 \ \rm M_{\odot}$. Particularly, the magnetar parameters required by the fit are consistent with those derived from the early X-ray observation., Comment: 9 pages; 4 figures; Accepted by ApJL

In this work, we investigate an alternative channel for the formation of fast-spinning black hole-neutron star (BHNS) binaries, in which super-Eddington accretion is expected to occur in accreting BHs during the stable mass transfer phase within BH-stripped helium (BH--He-rich) star binary systems. We evolve intensive \texttt{MESA} grids of close-orbit BH--He-rich star systems to systematically explore the projected aligned spins of BHs in BHNS binaries, as well as the impact of different accretion limits on the tidal disruption probability and electromagnetic (EM) signature of BHNS mergers. Most of the BHs in BHNS mergers cannot be effectively spun up through accretion, if the accretion rate is limited to $\lesssim10\,\dot{M}_{\rm Edd}$, where $\dot{M}_{\rm Edd}$ is the standard Eddington accretion limit. In order to reach high spins (e.g., $\chi_{\rm BH} \gtrsim 0.5$), the BHs are required to be born less massive (e.g., $\lesssim3.0\,M_\odot$) in binary systems with initial periods of $\lesssim0.2-0.3\,{\rm days}$ and accrete material at $\sim100\,\dot{M}_{\rm Edd}$. However, even under this high accretion limit, $\gtrsim6\,M_\odot$ BHs are typically challenging to significantly spin up and generate detectable associated EM signals. Our population simulations suggest that different accretion limits have a slight impact on the ratio of tidal disruption events. However, as the accretion limit increases, the EM counterparts from the cosmological BHNS population can become bright overall., Comment: 18 pages, 9 figures, 1 table, accepted for publication in ApJ

Super-Eddington accretion of neutron stars (NSs) has been suggested both observationally and theoretically. In this paper, we propose that NSs in close-orbit binary systems with companions of helium (He) stars, most of which systems form after the common-envelope phase, could experience super-Eddington stable Case BB/BC mass transfer (MT), and can sometimes occur accretion-induced collapses (AICs) to form lower mass-gap black holes (mgBHs). Our detailed binary evolution simulations reveal that AIC events tend to happen if the primaries NS have an initial mass $\gtrsim1.7\,M_\odot$ with an accretion rate of $\gtrsim300$ times the Eddington limit. These mgBHs would have a mass nearly equal to or slightly higher than the NS maximum mass. The remnant mgBH--NS binaries after the core collapses of He stars are potential progenitors of gravitational-wave (GW) source. Multimessenger observation between GW and kilonova signals from a population of high-mass binary NS and mgBH--NS mergers formed through super-Eddington stable MT are helpful in constraining the maximum mass and equation of state of NSs. S230529ay, a mgBH--NS merger candidate recently detected in the fourth observing run of the LIGO-Virgo-KAGRA Collaboration, could possibly originate from this formation scenario., Comment: MNRAS in press, 12 pages, 7 figures

A population of binary stellar-mass black hole (BBH) mergers are believed to occur embedded in the accretion disk of active galactic nuclei (AGNs). In this {\em Letter}, we demonstrate that the jets from these BBH mergers can propagate collimatedly within the disk atmosphere along with a forward shock and a reverse shock forming at the jet head. Efficient proton acceleration by these shocks is usually expected before the breakout, leading to the production of TeV$-$PeV neutrinos through interactions between these protons and electron-radiating photons via photon-meson production. AGN BBH mergers occurring in the outer regions of the disk are more likely to produce more powerful neutrino bursts. Taking the host AGN properties of the potential GW190521 electromagnetic (EM) counterpart as an example, one expects $\gtrsim1$ neutrino events detectable by IceCube if the jet is on-axis and the radial location of the merger is $R\gtrsim10^5R_{\rm{g}}$, where $R_{\rm{g}}$ is the gravitational radius of the supermassive BH. Neutrino bursts from AGN BBH mergers could be detected by IceCube following the observation of gravitational waves (GWs), serving as precursor signals before the detection of EM breakout signals. AGN BBH mergers are potential target sources for future joint GW, neutrino, and EM multi-messenger observations., Comment: Accepted by MNRAS Letters. Comments are welcome. 8 pages, 1 table, 3 figures, and 1 beautiful schematic figure in the appendix

Based on different neutron star-white dwarf (NS-WD) population models, we investigate the prospects of gravitational-wave (GW) detections for NS-WD mergers, with the help of early warnings from two space-borne decihertz GW observatories, DO-Optimal and DECIGO. We not only give quick assessments of the GW detection rates for NS-WD mergers with the two decihertz GW detectors, but also report systematic analyses on the characteristics of GW-detectable merger events using the method of Fisher matrix. With a sufficient one-day early-warning time, the yearly GW detection number for DO-Optimal is in the range of $ (1.5$-$1.9) \times 10^{3}$, while it is $ (3.3$-$4.6) \times 10^{4}$ for DECIGO. More importantly, our results show that most NS-WD mergers can be localized with an uncertainty of $O(10^{-2})\,\mathrm{deg}^2$. Given the NS-WD merger as a possible origin for a peculiar long-duration gamma-ray burst, GRB 211211A, followed with kilonova-like emissions, we further suggest that the GW early-warning detection would allow future electromagnetic telescopes to get prepared to follow-up transients after some special NS-WD mergers. Based on our analyses, we emphasize that such a feasible "wait-for" pattern can help to firmly identify the origin of GRB 211211A-like events in the future and bring excellent opportunities for the multimessenger astronomy., Comment: 14 pages, 7 figures; accepted by MNRAS

The formation of black hole-neutron star (BH-NS) or BH-BH systems may be accompanied with special supernova (SN) signals, due to the accretion feedback from the companion BH. The additional heating, which is mainly attributed to the Blandford-Payne mechanism, would disrupt the isotropic nature of the luminosity distribution on the surface of the SN ejecta, leading to the appearance of polarization. Here we develop a three dimensional (3D) Monte Carlo polarization simulation code (MCPSC) to conduct simulations for these special SNe. We find that the maximum polarization level of approximately \sim 2 occurs at the peak time of SN emission in the "close-binary" scenario, while in the "faraway-binary" case, maximum polarization (i.e. \sim 0.7) is observed at a considerably later time than the peak of the SN. The magnitude of polarization is dependent on the degree of unevenness in the luminosity distribution and the angle between the line of sight and the equatorial direction. When considering the geometric distortion of supernova ejecta at the same time, the magnitude of polarization may either increase (for a oblate ellipsoidal shape) or decrease (for a prolate ellipsoidal shape). The polarization signatures represent a promising auxiliary instrument to facilitate the identification of the companion-fed SNe. Moreover, by comparing the event rate of these special SNe with the event rate density of LIGO-Virgo detected BH-NS/BH systems could further help to distinguish the BH-NS/BH formation channel., Comment: 15 pages, 13 figures,accepted for publication in APJ

Let $Q$ be a $p$-subgroup of a finite $p$-solvable group $G$, where $p$ is a prime, and suppose that $\delta$ is a linear character of $Q$ with the property that $\delta(x)=\delta(y)$ whenever $x,y\in Q$ are conjugate in $G$. In this situation, we show that restriction to $p$-regular elements defines a canonical bijection from the set of those irreducible ordinary characters of $G$ with Navarro vertex $(Q,\delta)$ onto the set of irreducible Brauer characters of $G$ with Green vertex $Q$. Also, we use this correspondence to examine the behavior of lifts of Brauer characters with respect to normal subgroups.

A conjecture raised by Cossey in 2007 asserts that if $G$ is a finite $p$-solvable group and $\varphi$ is an irreducible $p$-Brauer character of $G$ with vertex $Q$, then the number of lifts of $\varphi$ is at most $|Q:Q'|$. This conjecture is now known to be true in several situations for $p$ odd, but there has been little progress for $p$ even. The main obstacle appeared in characteristic two is that all the vertex pairs of a lift are neither linear nor conjugate. In this paper we show that if $\chi$ is a lift of an irreducible $2$-Brauer character in a solvable group, then $\chi$ has a linear Navarro vertex if and only if all the vertex pairs of $\chi$ are linear, and in that case all of the twisted vertices of $\chi$ are conjugate. Our result can also be used to study other lifting problems of Brauer characters in characteristic two. As an application, we prove a weaker form of Cossey's conjecture for $p=2$ "one vertex at a time".

Extreme stripped-envelope supernovae (SESNe), including Type Ic superluminous supernovae (SLSNe), broad-line Type Ic SNe (SNe Ic-BL), and fast blue optical transients (FBOTs), are widely believed to harbor a newborn fast-spinning highly-magnetized neutron star (``magnetar''), which can lose its rotational energy via spin-down processes to accelerate and heat the ejecta. The progenitor(s) of these magnetar-driven SESNe, and the origin of considerable angular momentum (AM) in the cores of massive stars to finally produce such fast-spinning magnetars upon core-collapse are still under debate. Popular proposed scenarios in the literature cannot simultaneously explain their event rate density, SN and magnetar parameters, and the observed metallicity. Here, we perform a detailed binary evolution simulation that demonstrates that tidal spin-up helium stars with efficient AM transport mechanism in close binaries can form fast-spinning magnetars at the end of stars' life to naturally reproduce the universal energy-mass correlation of these magnetar-driven SESNe. Our models are consistent with the event rate densities, host environments, ejecta masses, and energetics of these different kinds of magnetar-driven SESNe, supporting that the isolated common-envelope formation channel could be a major common origin of magnetar-driven SESNe. The remnant compact binary systems of magnetar-driven SESNe are progenitors of some galactic systems and gravitational-wave transients., Comment: Main text (17 pages, 5 Figures) and Supplementary Information (18 pages, 6 Figures, 2 tables)

Despite the fact that the progenitor of fast blue optical transients (FBOTs) is still up for debate, FBOTs are sometimes suggested to originate from the core-collapse of ultra-stripped stars and be powered by a spinning-down neutron star. Following this consideration, it is expected that the late-time evolution of the progenitor stars can leave important imprints in the circumstellar material (CSM) of the FBOTs, due to the strong mass loss of the stars. The interaction of the FBOT ejecta with the CSM can drive a long-lasting shock to generate radio emission, which thus enables us to probe the CSM properties through radio observation although such observations are still rare. Within the framework of the magnetar-powered model, Liu et al.(2022) fitted the multi-band optical light curves of 40 FBOTs and, hence, the statistical distributions of the FBOT magnetar and ejecta parameters were obtained. Based on these FBOT population results, we investigate the dependence of the radio emission on the mass-loss rate of the progenitors and evaluate the detectability of radio emission from FBOTs with current and future telescopes. It is found that the distribution of the peak time and peak luminosity of the emission at 8.4 GHz are primarily in the regions of $t_{\rm{peak},\nu}=10^{2.12\pm0.63}$ days and $L_{\rm{peak},\nu}=10^{28.73\pm0.83}$ erg s$^{-1}$ Hz$^{-1}$, respectively. A joint detection of the Zwicky Transient Facility and Very Large Array could achieve success in about 8.7% FBOTs of $z\leq1$. Furthermore, if considering a joint observation of the Chinese Space Station Telescope and Square Kilometer Array, this fraction can be increased to about 23.9%., Comment: 10 pages, 5 figures, submitted to ApJ

Let $G$ be a finite $\pi$-separable group, where $\pi$ is a set of primes, and let $\chi$ be an irreducible complex character that is a $\pi$-lift of some $\pi$-partial character of $G$.It was proved by Cossey and Lewis that all of the vertex pairs for $\chi$ are linear and conjugate in $G$ if $2\in\pi$, but the result can fail for $2\notin\pi$. In this paper we introduce the notion of the twisted vertices in the case where $2\notin\pi$, and establish the uniqueness for linear twisted vertices under the conditions that either $\chi$ is an $\mathcal N$-lift for a $\pi$-chain $\mathcal N$ of $G$ or it has a linear Navarro vertex, thus answering a question proposed by them.

Various supernovae (SN), compact object coalescences, and tidal disruption events are widely believed to occur embedded in active galactic nuclei (AGN) accretion disks and generate detectable electromagnetic (EM) signals. We collectively refer to them as \emph{AGN disk transients}. The inelastic hadronuclear ($pp$) interactions between shock-accelerated cosmic rays and AGN disk materials shortly after the ejecta shock breaks out of the disk can produce high-energy neutrinos. However, the expected efficiency of neutrino production would decay rapidly by adopting a pure Gaussian density atmosphere profile applicable for stable gas-dominated disks. On the other hand, AGN outflows and disk winds are commonly found around AGN accretion disks. In this paper, we present that the circum-disk medium would further consume the shock kinetic energy to more efficiently produce high-energy neutrinos, especially for $\sim$\,TeV$-$PeV neutrinos that IceCube detects. Thanks to the existence of the circum-disk medium, we find that the neutrino production will be enhanced significantly and make a much higher contribution to the diffuse neutrino background. Optimistically, $\sim20\%$ diffuse neutrino background can be contributed from AGN disk transients., Comment: 12 Pages, 3 figures, and 2 tables; Accepted by ApJ

The LIGO, Virgo, and KAGRA (LVK) collaboration has announced 90 coalescing binary black holes (BBHs) with $p_{\rm astro} > 50\%$ to date, however, the origin of their formation channels is still an open scientific question. Given various properties of BBHs (BH component masses and individual spins) inferred using the default priors by the LVK, independent groups have been trying to explain the formation of the BBHs with different formation channels. Of all formation scenarios, the chemically homogeneous evolution (CHE) channel has stood out with distinguishing features, namely, nearly-equal component masses and preferentially high individual spins aligned with the orbital angular momentum. We perform Bayesian inference on the BBH events officially reported in GWTC-3 with astrophysically-predicted priors representing different formation channels of the isolated binary evolution (CEE: common-envelope evolution channel; CHE; SMT: stable mass transfer). Given assumed models, we report strong evidence for GW190517\_055101 being most likely to have formed through the CHE channel. Assuming the BBH events in the subsample are all formed through one of the isolated binary evolution channels, we obtain the lower limits on the local merger rate density of these channels at $11.45 ~\mathrm{Gpc^{-3}~yr^{-1}}$ (CEE), $0.18 ~\mathrm{Gpc^{-3}~yr^{-1}}$ (CHE), and $0.63 ~\mathrm{Gpc^{-3}~yr^{-1}}$ (SMT) at $90\%$ credible level., Comment: 13 pages, 4 figures, 1 table

Here we collect three unique bursts, GRBs\,060614, 211211A and 211227A, all characterized by a long-duration main emission (ME) phase and a rebrightening extended emission (EE) phase, to study their observed properties and the potential origin as neutron star-black hole (NSBH) mergers. NS-first-born (BH-first-born) NSBH mergers tend to contain fast-spinning (non-spinning) BHs that more easily (hardly) allow tidal disruption to happen with (without) forming electromagnetic signals. We find that NS-first-born NSBH mergers can well interpret the origins of these three GRBs, supported by that: (1) Their X-ray MEs and EEs show unambiguous fall-back accretion signatures, decreasing as $\propto{t}^{-5/3}$, which might account for their long duration. The EEs can result from the fall-back accretion of $r$-process heating materials, predicted to occur after NSBH mergers. (2) The beaming-corrected local event rate density for this type of merger-origin long-duration GRBs is $\mathcal{R}_0\sim2.4^{+2.3}_{-1.3}\,{\rm{Gpc}}^{-3}\,{\rm{yr}}^{-1}$, consistent with that of NS-first-born NSBH mergers. (3) Our detailed analysis on the EE, afterglow and kilonova of the recently high-impact event GRB\,211211A reveals it could be a merger between a $\sim1.23^{+0.06}_{-0.07}\,M_\odot$ NS and a $\sim8.21^{+0.77}_{-0.75}\,M_\odot$ BH with an aligned-spin of $\chi_{\rm{BH}}\sim0.62^{+0.06}_{-0.07}$, supporting an NS-first-born NSBH formation channel. Long-duration burst with rebrightening fall-back accretion signature after ME, and bright kilonova might be commonly observed features for on-axis NSBHs. We estimate the multimessenger detection rate between gravitational waves, GRBs and kilonovae from NSBH mergers in O4 (O5) is $\sim0.1\,{\rm{yr}}^{-1}$ ($\sim1\,{\rm{yr}}^{-1}$)., Comment: 15 pages, 5 figures, 2 tables, accepted by ApJL

We fit the multi-band lightcurves of 40 fast blue optical transients (FBOTs) with the magnetar engine model. The mass of the FBOT ejecta, the initial spin period and polar magnetic field of the FBOT magnetars are respectively constrained to $M_{\rm{ej}}=0.18^{+0.52}_{-0.13}\,M_\odot$, $P_{\rm{i}}=9.4^{+8.1}_{-3.9}\,{\rm{ms}}$, and $B_{\rm p}=7^{+16}_{-5}\times10^{14}\,{\rm{G}}$. The wide distribution of the value of $B_{\rm p}$ spreads the parameter ranges of the magnetars from superluminous supernovae (SLSNe) to broad-line Type Ic supernovae (SNe Ic-BL; some are observed to be associated with long-duration gamma-ray bursts), which are also suggested to be driven by magnetars. Combining FBOTs with the other transients, we find a strong universal anti-correlation as $P_{\rm{i}}\propto{M_{\rm{ej}}^{-0.45}}$, indicating them could share a common origin. To be specific, it is suspected that all of these transients originate from collapse of extreme-stripped stars in close binary systems, but with different progenitor masses. As a result, FBOTs distinct themselves by their small ejecta masses with an upper limit of ${\sim}1\,M_\odot$, which leads to an observational separation in the rise time of the lightcurves $\sim12\,{\rm d}$. In addition, the FBOTs together with SLSNe can be separated from SNe Ic-BL by an empirical line in the $M_{\rm peak}-t_{\rm rise}$ plane corresponding to an energy requirement of a mass of $^{56}$Ni of $\sim0.3M_{\rm ej}$, where $M_{\rm peak}$ is the peak absolute magnitude of the transients and $t_{\rm rise}$ is the rise time., Comment: 15 pages, 5 figures, 2 tables, accepted by ApJL

Learning visual representations from natural language supervision has recently shown great promise in a number of pioneering works. In general, these language-augmented visual models demonstrate strong transferability to a variety of datasets and tasks. However, it remains challenging to evaluate the transferablity of these models due to the lack of easy-to-use evaluation toolkits and public benchmarks. To tackle this, we build ELEVATER (Evaluation of Language-augmented Visual Task-level Transfer), the first benchmark and toolkit for evaluating(pre-trained) language-augmented visual models. ELEVATER is composed of three components. (i) Datasets. As downstream evaluation suites, it consists of 20 image classification datasets and 35 object detection datasets, each of which is augmented with external knowledge. (ii) Toolkit. An automatic hyper-parameter tuning toolkit is developed to facilitate model evaluation on downstream tasks. (iii) Metrics. A variety of evaluation metrics are used to measure sample-efficiency (zero-shot and few-shot) and parameter-efficiency (linear probing and full model fine-tuning). ELEVATER is a platform for Computer Vision in the Wild (CVinW), and is publicly released at at https://computer-vision-in-the-wild.github.io/ELEVATER/, Comment: NeurIPS 2022 (Datasets and Benchmarks Track). The first two authors contribute equally. Benchmark page: https://computer-vision-in-the-wild.github.io/ELEVATER/