Black hole growth by accretion
  We show that black holes grow substantially by accretion at close to Eddington rates. Using a complete sample of soft X-ray selected AGNs,   Grupe & Mathur (2004) have shown that narrow line Seyfert 1 galaxies, as a class, lie below the M_BH-sigma relation of normal galaxies. Some NLS1s, however, lie on or close to the M_BH-sigma relation. Here we show that not all NLS1s accrete at close to Eddington rates: those with low {L/L_{Eddington}} are close to the M_BH-sigma relation, and those with high {L/L_{Eddington}} are far. With various tests in this paper, we argue that black holes grow in mass substantially in their high-accretion phase and approach the M_BH-sigma relation over time. The mass growth in a low accretion phase, as in BLS1s and also in some NLS1s, appears to be insignificant. Any theoretical model attempting to explain the M_BH-sigma relation will have to explain the above observations. 
Smita Mathur & Dirk Grupe (Ohio State)