  The mass of super massive black holes at the centre of galaxies is tightly
correlated with the mass of the galaxy bulges which host them. This observed
correlation implies a mechanism of joint growth, but the precise physical
processes responsible are a matter of some debate. Here we report on the growth
of black holes in 400 local galactic bulges which have experienced a strong
burst of star formation in the past 600Myr. The black holes in our sample have
typical masses of 10^6.5-10^7.5 solar masses, and the active nuclei have
bolometric luminosities of order 10^42-10^44erg/s. We combine stellar continuum
indices with H-alpha luminosities to measure a decay timescale of ~300Myr for
the decline in star formation after a starburst. During the first 600Myr after
a starburst, the black holes in our sample increase their mass by on-average 5%
and the total mass of stars formed is about 1000 times the total mass accreted
onto the black hole. This ratio is similar to the ratio of stellar to black
hole mass observed in present-day bulges. We find that the average rate of
accretion of matter onto the black hole rises steeply roughly 250Myr after the
onset of the starburst. We show that our results are consistent with a simple
model in which 0.5% of the mass lost by intermediate mass stars in the bulge is
accreted by the black hole, but with a suppression in the efficiency of black
hole growth at early times plausibly caused by supernova feedback, which is
stronger at earlier times. We suggest this picture may be more generally
applicable to black hole growth, and could help explain the strong correlation
between bulge and black hole mass.
