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The hydrogen Balmer decrement (e.g., $\rm H\alpha/H\beta$) is widely adoptedas an indicator of the internal reddening of active galactic nuclei (AGNs).This is challenged by some low-luminosity AGNs (LLAGNs) and changing-look AGNs(CLAGNs), which have steep Balmer decrement but without strong evidence forabsorption. We compile a sample of normal AGNs and CLAGNs with a widerdistribution of bolometric Eddington ratio ($\lambda_{\rm Edd}=L_{\rmbol}/L_{\rm Edd}$) and find a strong negative correlation between $\rmH\alpha/H\beta$ and $\lambda_{\rm Edd}$, which suggests that the Balmerdecrement is also accretion-rate dependent. We further explore the Balmerdecrement based on the photoionization model using the Cloudy code byconsidering spectral energy distribution (SED) from the accretion disk withdifferent accretion rates (e.g., disk/corona and truncated disk at high and lowEddington ratios, respectively). Both the standard disk and truncated diskpredict a negative correlation of $\rm H\alpha/H\beta-\lambda_{\rm Edd}$, wherethe relation is steeper in the case of the truncated disk. The negativecorrelations are also explored in two single CLAGNs. The measured negativecorrelation of $\rm H\alpha/H\beta$ -- $\lambda_{\rm Edd}$ is mainly caused bythe lower responsivity $({\rm dlog}L_{\rm line}/{\rm dlog}L_{\rm cont})$ in$\rm H\alpha$ relative to that in $\rm H\beta$, due to the larger optical depthin the former. We propose that the steep Balmer decrements inlow-Eddington-ratio AGNs (e.g., some Seyferts 1.5-1.9 and CLAGNs) are notsimply caused by absorption but mainly caused by the relatively low flux ofionizing photons.

Steep Balmer decrement in weak AGNs may be not caused by dust extinction: clues from low-luminosity AGNs and changing-look AGNs