A New Empirical Method to Infer the Starburst History of the Universe from Local Galaxy Properties

The centers of bulges are formed dissipationally via gas inflows over short timescales: the 'starburst' mode of star formation (SF). Recent work has shown that detailed observations can be used to separate the stellar mass profile of these 'burst relic' components in local systems. Together with the assumption that some Kennicutt-Schmidt law holds, and that the burst was indeed a dissipational gas-rich event, we show that the observed profiles can be inverted to obtain the time and space-dependent SF history of each burst. Performing this with a large sample of well-studied spheroids, we show that the implied bursts scale in magnitude, mass, peak SFR, and spatial extent with galaxy mass in simple manner, and provide fits to these correlations. Burst masses are ~10% the total spheroid mass; timescales a mass-independent ~10^8 yr; peak SFR ~M_burst/t_burst; and they decay in power-law fashion ~t^-2.4. Sizes are ~0.1 R_e(spheroid), but grow with time. Combined with measurements of the nuclear stellar population ages of these systems (i.e. burst times), it is possible to re-construct the burst contribution to the distribution of SFRs and IR luminosity functions at all redshifts. The burst LF agrees well with observed IR LFs at the brightest luminosities, at z=0-2. At low-L, bursts are always unimportant; the transition to their importance increases from ULIRG luminosities at z~0 to HyLIRG luminosities at z~2. At all redshifts, bursts are a small fraction (~5-10%) of the total SFR density. We discuss possible implications of tension between maximum relic stellar mass densities in massive systems, and estimated number counts of brightest sub-millimeter galaxies.