Extragalactic fast X-ray transients (eFXTs) represent a rapidly growing class of high-energy phenomena, whose physical origins remain poorly understood. With its wide-field, sensitive all-sky monitoring, the Einstein Probe (EP) has greatly increased the discovery rate of eFXTs. The search and identification of the optical counterparts of eFXT are vital for understanding their classification and constraining their physical origin. Yet, a considerable fraction of eFXTs still lack secure classifications due to the absence of timely follow-up observations. We carry out a systematic search of publicly available optical survey data and transient databases (including the Zwicky Transient Facility, ZTF, and the Transient Name Server, TNS) for optical counterparts to eFXT candidates detected by EP. In this paper, we describe our ongoing program and report the first results. Specifically, we identified the eFXT EP240506a to be associated with a UV/optical counterpart, AT 2024ofs. Spectroscopy of its host galaxy with VLT yields a redshift of $z = 0.120 \pm 0.002$. By combining archival survey data with early-time multiwavelength observations, we find that the luminosity and light-curve evolution of AT~2024ofs are consistent with a core-collapse supernova origin. From detectability simulations, we estimate a local event rate density $\rho_{0}=8.8^{+21.2}_{-3.9}\ \mathrm{yr^{-1}\, Gpc^{-3}}$ for EP240506a-like events, and completeness-corrected rate of about $36$--$78\ \mathrm{yr^{-1}\ Gpc^{-3}}$ for EP-detected X-ray transients associated with supernovae. Our results demonstrate the potential of EP to uncover prompt high-energy emission from core-collapse supernovae and underscore the critical importance of timely follow-up of future eFXT events.
Precise measurements of cosmic microwave background polarization require rigorous control of instrumental systematics. For the South Pole Telescope's third-generation camera (SPT-3G), accurate characterization of the beam is critical for understanding the polarized mm-wave sky. Here, we present direct measurements of SPT-3G's polarized beam response using observations of 100 polarized extragalactic point sources. Previous SPT-3G CMB power spectrum analyses introduced a phenomenological parameter $\beta_\mathrm{pol}$ to describe the degree of polarization preserved in beam sidelobes. These analyses found evidence for significant depolarization driven by the requirement of polarization power spectrum consistency between different frequency bands. Our direct measurements yield $\beta_\mathrm{pol}=0.90\pm0.10$ at 95 GHz, $1.01\pm0.12$ at 150 GHz, and $0.81\pm0.29$ at 220 GHz, indicating minimal sidelobe depolarization. We validate these results through extensive systematic tests including Bayesian posterior sampling versus frequentist bootstrap resampling, real-space versus Fourier-space analysis, and variations on temperature-to-polarization leakage handling, covariance determination, and source selection. When compared to values inferred from previous cosmological analyses, which favored significant depolarization to resolve inter-frequency power spectrum inconsistencies, we find a mild tension of $1.9\sigma$. However, this apparent discrepancy is dependent on the beam modeling, as our point source-based analysis derives much of its constraining power on $\beta_\mathrm{pol}$ from higher multipoles than the power spectrum analysis. These measurements therefore admit three explanations for the frequency-dependent residuals observed in the power spectrum analysis: a statistical fluctuation, the need for more sophisticated polarized beam models, or systematics other than beam depolarization.
We propose a model-independent formalism for describing anisotropies in the stochastic gravitational wave background (SGWB) originating from primordial perturbations. Despite their diverse physical origins -- such as Sachs-Wolfe effects, integrated Sachs-Wolfe effects, or fossil effects from primordial non-Gaussianity -- SGWB anisotropies exhibit a universal angular structure. We show that this universality arises from a single vertex function, the Cosmological Form Factor (CFF), which encodes the information on how long-wavelength modes modulate the SGWB statistics. Two fundamental principles -- statistical isotropy and locality -- uniquely determine the angular dependence of the CFF, resulting in a universal multipole scaling of the SGWB anisotropies. The CFF formalism provides a common language for classifying SGWB anisotropies and offers a powerful framework for interpreting upcoming observations.
We revisit the spectral appearance of extended self-gravitating accretion disks around supermassive black holes. Using dust-poor opacity tables, we show that all optically thick disk solutions possess a universal outer effective temperature of $T_{\rm eff}\sim 4000-4500$K, closely resembling compact, high-redshift sources known as Little Red Dots (LRDs). Assuming the extended disk is primarily heated by stellar sources, this ``disk Hayashi limit" fixes the dominant optical continuum temperature of the disk spectrum independent of accretion rate $\dot{M}$, black hole mass $M_\bullet$, and disk viscosity $\alpha$, and removes the parameter-tuning required in previous disk interpretations of LRDs. We construct global self-gravitating accretion disk models with radially varying accretion rates, suggesting that burning of embedded stellar objects can both efficiently power the emission of the outer disk and hollow out the inner disk, strongly suppressing variable UV/X-ray associated with a standard quasar. The resulting disk emission is dominated by a luminous optical continuum while a separate, non-variable UV component arises from stellar populations on the nuclear to galaxy scale. We map the optimal region of parameter space for such systems and show that LRD-like appearances are guaranteed for $\dot{M}/\alpha \gtrsim 0.1 M_\odot /{\rm yr}$, a threshold insensitive to $M_\bullet$, below which the system may transition into classical non-self-gravitating AGN disks, potentially a later evolution stage. We expect this transition to be accompanied by the enhancement of metallicity and production of dust, giving rise to far infrared emission. This picture offers a physically motivated and quantitative framework connecting LRDs with AGNs and their associated nuclear stellar population.