Evidence of violation of Case B recombination in Little Red Dots

TL;DR

This work tests Case B recombination in Little Red Dots by analyzing Balmer line ratios ($H\alpha$, $H\beta$, $H\gamma$, $H\delta$) from JWST/NIRSpec data and decomposing each line into narrow and broad components. A three-component line-profile model captures a narrow core, an unscattered broad core, and a broad scattered component due to electron scattering in a dense gas cocoon, with nested sampling via Dynesty and LM optimization used to derive fluxes and extinctions; most broad components are consistent with Case B when dust extinction is included ($A_V\sim4$), while narrow components are largely dust-free, though two objects show unusually flat decrements ($H\alpha/H\beta\approx1.8$) that could indicate density-bounded gas or unresolved absorption. One broad component (RUBIES-EGS-49140) deviates from Case B with $H\gamma/H\alpha$ and especially $H\delta/H\alpha$ suppressed beyond extinction predictions, pointing to optically thick Balmer lines and self-absorption in a dense broad-line cocoon. These findings support a two-component picture with a heavily reddened BLR near the SMBH and a relatively dust-free NLR or star-forming host, implying that extinction is local to the LRD rather than arising from the host ISM and potentially biasing virial BH mass estimates if Case B does not hold. The results motivate deeper spectroscopic campaigns to detect higher-order Balmer lines and to perform detailed radiative-transfer modelling of high-density gas in LRDs.

Abstract

Little Red Dots (LRDs) are a new class of compact extragalactic objects, with a v-shaped optical spectral energy distribution breaking close to the Balmer break wavelength, and broad, typically exponentially-shaped lines. They are believed to be supermassive black holes surrounded by very dense, ionized gas, leading us to explore for any departures from Case B recombination by examining the ratios of multiple hydrogen Balmer lines: $Hα$, $Hβ$, $Hγ$, and $Hδ$. We analyze a dozen high-S/N LRDs with JWST/NIRSpec, measuring Balmer ratios in the seven objects with coverage of at least three lines. We decompose the line ratios into their respective broad and narrow components. Broad line ratios are consistent with Case B plus dust extinction in all objects but one, RUBIES EGS-49140, which departs from Case B expectations by more than $5σ$. The narrow components are consistent with minimal dust attenuation, while two objects exhibit narrow $Hα$/$Hβ\approx 1.8$. Such low decrements are observed in highly ionized density bounded nebulae, associated with starburst environments. Nevertheless, both flat decrement cases can be reconciled assuming an unresolved absorption feature. RUBIES EGS-49140, shows a high broad $Hα$/$Hβ$, but $Hγ$/$Hα$ and $Hδ$/$Hα$ ratios are lower than expected for extinction-modified Case B, hinting at an unphysically steep dust law. These line ratios may be due to increased optical depth in the Balmer lines, as a direct effect of high density (log$n_e$ > 9) gas surrounding the black hole. If Case B recombination does hold in most LRDs, they must be moderate-to-heavily dust obscured ($A_V\simeq1-8$) while the host-galaxy should be dust-free, suggesting that the extinction in the broad lines is local to the LRD and not due to the general ISM of the host galaxy.

Figures (19)

• Figure 1: The best-fit solutions for the H$\alpha$, H$\beta$, H$\gamma$ and H$\delta$ of JADES-GN-68797 (ID A), as noted in their respective panels. The separate components that make up the line profile are also shown. We note that there is no narrow emission detected in JADES-GN-68797.
• Figure 2: Balmer line ratio diagram showing total line H$\alpha$/H$\beta$ vs. H$\gamma$/H$\alpha$. The black shaded regions mark the intrinsic Case B ratios across a range of reasonable values, while the colored dashed lines show the LMC lmc, SMC Gordon2024-SMC and Milky Way mw extinction laws, derived using the dust_extinction package Gordon2024-dust_ext. The arrow indicates the direction of increasing dust attenuation.
• Figure 3: Balmer line ratio diagrams showing the narrow and broad H$\alpha$/H$\beta$ vs. H$\gamma$/H$\alpha$ (left) and H$\alpha$/H$\beta$ vs. H$\delta$/H$\alpha$ (right) ratios. Broad ratios are shown as brown circles and narrow ratios as black squares. The black shaded regions mark the intrinsic Case B ratios across a range of reasonable values. The colored dashed lines show the LMC lmc, SMC Gordon2024-SMC, and Milky Way mw extinction laws, derived using the dust_extinction package Gordon2024-dust_ext. The arrows indicate the direction of increasing dust attenuation.
• Figure 4: Left: The H$\delta$ line of Object E (RUBIES-EGS-49140). The data are shown with a yellow fill and the best fit with a black line, the modeled H$\delta$ line profile based on the 5$\sigma$ upper limit of its flux as a brown line, and the predicted H$\delta$ line profile under Case B recombination assumptions as a blue line. The best fit solution yields $\chi^2_\nu = 1.08$, while the $5\sigma$ and the Case B predicted solutions yield $\chi^2_\nu = 1.15$ and $\chi^2_\nu = 1.27$ respectively. Right: The H$\delta$/H$\alpha$ flux ratio posterior distribution. The black and brown lines represents the 2 and 5$\sigma$ upper limits respectively. The blue line indicates the expected line ratio under Case B recombination and the $A_V = 3.52$ derived from the H$\alpha$/H$\beta$ ratio. Assuming a steeper curve, or a higher intrinsic H$\alpha$/H$\beta$ ratio increases the expected H$\delta$/H$\alpha$ ratio, making the deviation even more significant.
• Figure 5: Balmer line ratio diagrams showing the narrow and broad H$\gamma$/H$\beta$ vs. H$\delta$/H$\beta$ ratios for our sources. Broad ratios are shown as brown circles and narrow ratios as black squares. The black shaded regions mark the intrinsic Case B ratios across a range of reasonable values. The colored dashed lines show the LMC lmc, SMC Gordon2024-SMC, and Milky Way mw extinction laws, derived using the dust_extinction package Gordon2024-dust_ext. The arrows indicate the direction of increasing dust attenuation.