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Abstract:

Fast X-ray Transients (FXTs) are extragalactic bursts of soft X-rays first identified ≳10 yr ago. Since then, nearly 40 events have been discovered, although almost all of these have been recovered from archival Chandra and XMM-Newton data. To date, optical sky surveys and follow-up searches have not revealed any multiwavelength counterparts. The Einstein Probe, launched in 2024 January, has started surveying the sky in the soft X-ray regime (0.5–4 keV) and will rapidly increase the sample of FXTs discovered in real time. Here we report the first discovery of both an optical and radio counterpart to a distant FXT, the fourth source publicly released by the Einstein Probe. We discovered a fast-fading optical transient within the 3′ localization radius of EP 240315a with the all-sky optical survey ATLAS, and our follow-up Gemini spectrum provides a redshift, z = 4.859 ± 0.002. Furthermore, we uncovered a radio counterpart in the S band (3.0 GHz) with the MeerKAT radio interferometer. The optical (rest-frame UV) and radio luminosities indicate that the FXT most likely originates from either a long gamma-ray burst or a relativistic tidal disruption event. This may be a fortuitous early mission detection by the Einstein Probe or may signpost a mode of discovery for high-redshift, high-energy transients through soft X-ray surveys, combined with locating multiwavelength counterparts.

Abstract:

Context. Computing the matter power spectrum, P(k), as a function of cosmological parameters can be prohibitively slow in cosmological analyses, hence emulating this calculation is desirable. Previous analytic approximations are insufficiently accurate for modern applications, so black-box, uninterpretable emulators are often used.

Aims. We aim to construct an efficient, differentiable, interpretable, symbolic emulator for the redshift zero linear matter power spectrum which achieves sub-percent level accuracy. We also wish to obtain a simple analytic expression to convert A_s to σ₈ given the other cosmological parameters.

Methods. We utilise an efficient genetic programming based symbolic regression framework to explore the space of potential mathematical expressions which can approximate the power spectrum and σ₈. We learn the ratio between an existing low-accuracy fitting function for P(k) and that obtained by solving the Boltzmann equations and thus still incorporate the physics which motivated this earlier approximation.

Results. We obtain an analytic approximation to the linear power spectrum with a root mean squared fractional error of 0.2% between k = 9 &³Ù¾±³¾±ð²õ; 10⁻³â€…&³¾¾±²Ô³Ü²õ; 9 h M±è³¦⁻¹ and across a wide range of cosmological parameters, and we provide physical interpretations for various terms in the expression. Our analytic approximation is 950 times faster to evaluate than CAMB and 36 times faster than the neural network based matter power spectrum emulator BACCO. We also provide a simple analytic approximation for σ₈ with a similar accuracy, with a root mean squared fractional error of just 0.1% when evaluated across the same range of cosmologies. This function is easily invertible to obtain A_s as a function of σ₈ and the other cosmological parameters, if preferred.

Conclusions. It is possible to obtain symbolic approximations to a seemingly complex function at a precision required for current and future cosmological analyses without resorting to deep-learning techniques, thus avoiding their black-box nature and large number of parameters. Our emulator will be usable long after the codes on which numerical approximations are built become outdated.