Too Quiet for Comfort: Local Little Red Dots Lack Variability over Decades

Several local ($z\lesssim 0.2$) metal-poor dwarf AGNs have remarkably similar properties to those of high-redshift Little Red Dots (LRDs), and are recently proposed to be local analogs of LRDs. We use long-term photometric and spectroscopic observations of three local LRDs spanning $\sim 20$ years to measure variability in their rest-frame optical continuum and broad H$\alpha$ emission lines. Using ZTF light curves over a rest-frame $\sim 5$ yr baseline, the $r$-band intrinsic rms variability is $(9\times 10^{-5})_{\rm -9E-5}^{+0.014}$ mag (J1022), $0.025\pm0.004$ mag (J1025) and $0.020\pm0.005$ mag (J1047), indicating low intrinsic variability ($<3-4\%$ at 3$\sigma$). These rms variability amplitudes are much lower than those for dwarf AGNs and more massive quasars. There is little structure in the optical variability structure functions for the three local LRDs, in contrast to normal AGN variability. Using available multi-epoch spectra, we constrain the broad H$\alpha$ line flux variability to be less than a few percent, without significant profile changes, over a rest-frame baseline of $\sim 15$ yrs in J1025 and J1047, respectively. The three LRDs stand out in the Balmer line properties compared with normal broad-line AGNs, with exceptionally large H$\alpha$ equivalent widths and H$\alpha$/H$\beta$ ratios far exceeding the Case B recombination value. In the context of recent theoretical models of LRDs as dense gas-enshrouded massive black holes with super-Eddington accretion, our results suggest that the photosphere emission is long-term stable and the broad Balmer lines are primarily collisonally excited. This scenario is consistent with the lack of variability, large H$\alpha$/H$\beta$ ratios and little dust extinction, as well as the expected high gas density. Virial black hole mass estimates using broad H$\alpha$ assuming photoionization are therefore highly questionable for LRDs.