  It has been argued that recycled gas from stellar mass loss in galaxies might
serve as an important fuelling source for black holes (BHs) in their centers.
Utilizing spectroscopic samples of galaxies from the Sloan Digital Sky Survey
(SDSS) at $z = 0-0.35$ and the Large Early Galaxy Astrophysics Census (LEGA-C)
survey at $z = 0.6-1$ that have X-ray coverage from XMM-Newton or Chandra, we
test this stellar mass loss fuelling scenario by investigating how AGN activity
and BH growth vary with the break strength at 4000 $\r{A}$, $\rm D_{n}4000$
(which is closely related to the age of stellar populations), as younger
galaxies are considered to have higher stellar mass loss rates. We found that
when controlling for host-galaxy properties, the fraction of log $L_{\rm
X}$/$M_\star$ > 32 (which roughly corresponds to Eddington ratios $\gtrsim 1$%)
AGN and sample-averaged black hole accretion rate ($\rm \overline{BHAR}$)
decrease with $\rm D_{n}4000$ among $\rm D_{n}4000$ $\lesssim$ 1.9 galaxies,
suggesting a higher level of AGN activity among younger galaxies, which
supports the stellar mass loss fuelling scenario. For the oldest and most
massive galaxies at $z = 0-0.35$, this decreasing trend is not present anymore.
We found that, among these most massive galaxies at low redshift, the fraction
of low specific-accretion-rate (31 $<$ log $L_{\rm X}$/$M_\star$ $<$ 32) AGNs
increases with $\rm D_{n}4000$, which may be associated with additional
fuelling from hot halo gas and/or enhanced accretion capability.
