Spectral Uniformity of Little Red Dots: A Natural Outcome of Coevolving Seed Black Holes and Nascent Starbursts

The birth of seeds of massive black holes (BHs) and nascent galaxies at cosmic dawn takes place in dense gaseous environments, which play a crucial role in shaping their coevolution and radiation spectra. We investigate gas accretion during the assembly of massive halos with $M_{\rm h}\gtrsim 10^{10-11}~M_\odot$ at redshifts $z\simeq 4-10$, driving both rapid BH feeding and concurrent nuclear starbursts. As the BH grows to $\sim 10^{6-7}~M_\odot$ via super-Eddington accretion, the accretion power inflates a dense envelope whose effective temperature approaches the Hayashi limit at $T_{\rm eff}\simeq 5000~{\rm K}$, producing red optical emission, while a coeval young stellar population of $\sim 10^7~M_\odot$ provides blue UV emission. This early coevolving system naturally reproduces the characteristic spectral features of the so-called little red dots (LRDs), a population of broad-line active galactic nuclei (AGNs), including the V-shaped UV-to-optical spectra and weakness of X-ray, infrared, and radio emission. Massive stars in the nuclear starburst soon explode as supernovae, injecting energy and momentum that expel gas from the nucleus, quench gas supply to the BH envelope, and ultimately drive a transition into normal AGN phases. For individual LRDs, the optical-to-UV luminosity ratio remains nearly constant at $L_{\rm opt}/L_{\rm UV}\simeq 2-10$ from the onset of accretion bursts for $\simeq 15~{\rm Myr}$, one-third of the Salpeter time, until quenching by stellar feedback. While this ratio is sustained for the LRD population at $z\simeq 4-8$, it declines toward lower redshifts as BHs can no longer maintain red envelopes, thereby losing the LRD characteristics.