# Fluctuation of the background sky in the Hubble Extremely Deep Field (XDF) and its origin

## TL;DR

This study analyzes sky brightness fluctuations in the Hubble XDF, revealing large fluctuations likely caused by faint compact objects with properties suggesting they could be powered by black holes, contributing to the optical and infrared background.

## Contribution

It provides the first detailed fluctuation analysis of the Hubble XDF and proposes faint compact objects as the source of excess sky brightness, with constraints on their properties and origins.

## Key findings

- Detected large sky brightness fluctuations brighter than expected from galaxies.
- Faint compact objects have a surface density up to 2.6×10^3 per arcsec².
- FCOs are consistent with being powered by black hole gravitational energy.

## Abstract

We performed a fluctuation analysis of the Hubble Extremely Deep Field (XDF) at four optical wavelength bands and found large fluctuations that are significantly brighter than those expected for ordinary galaxies. Good cross-correlations with flat spectra are found down to 0.2 arcsec, indicating the existence of a spatial structure even at the 0.2 arcsec scale. The detected auto and cross-correlations provide a lower limit of 24 nW m$^{-2}$ sr$^{-1}$ for the absolute sky brightness at 700-900 nm, which is consistent with previous observations. We searched for candidate objects to explain the detected large fluctuation using the catalog of the Hubble Ultra Deep Field (UDF), and found that the surface number density of faint compact objects (FCOs) rapidly increases toward the faint end. Radial profiles of FCOs are indistinguishable from the PSF, and the effective radius based on de Vaucouleur's law is estimated to be smaller than 0.02 arcsec. The SEDs of FCOs follow a power law at optical wavelengths, but show greater emission and structure at $\lambda$ > 1 $\mu$m. Assuming that the FCOs are the cause of the excess brightness and fluctuations, the faint magnitude limit is 34.9 mag for the F775W band, and the surface number density reaches $2.6 \times 10^3$ (arcsec)$^{-2}$. Recent gamma-ray observations require that the redshift of FCOs must be less than 0.1, if FCOs are the origin of the excess optical and infrared background. Assuming that FCOs consist of missing baryons, the mass and luminosity of a single FCO range from $10^{2}$ to 1$0^{3}$ solar units, and mass-to-luminosity ratio is significantly lower than 1.0 solar unit. The maximum effective radius of an FCO is 4.7 pc. These results and the good correlation between near-infrared and X-ray background indicate that FCOs could be powered by the gravitational energy associated with black holes.