WHIM-hunting through cross-correlation of optical and SZ effect data in the Virgo cluster filaments

Context. The physical state of most of the baryonic matter in the local universe is unknown, which is commonly referred to as the ``missing baryon problem". It is theorized that at least half of these missing baryons are in a warm-hot, low-density phase outside of the virialized dark-matter halos. Aims. We make an attempt to find the signature of this warm-hot intergalactic medium (WHIM) phase in the filaments of the nearby Virgo cluster by using optical and Sunyaev-Zeldovich effect data. Methods. Specifically, we use a filament-galaxy catalog created from the HyperLeda database and an all-sky Compton-y map extracted from the Planck satellite data for 2-dimensional cross-correlation analysis by applying spherical harmonics transform. Significance test is based on the null-test simulations which exploits advanced cut-sky analysis tools for a proper map reconstruction. To place upper limits on the WHIM density in the Virgo filaments, realistic baryonic density modelling within the cosmic filaments is done based on state-of-the-art hydro-simulations, and it's done within the signal-boosting routine. Results. The cross-correlation signal is found to be too dim compared to the noise level in the Planck y-map. At 3$σ$ confidence level, the upper limit on volume-average WHIM density turns out to be $\left\langle n_e \right\rangle \lt 4\times10^{-4} cm^{-3}$, which is indeed consistent with the WHIM parameter space as predicted from simulations.