Reverberation Mapping

Basic idea

• Spectrum from AGN/quasar
  • Strong continuum: accretion onto black hole (BH)
  • Broad emission lines: gas excited by continuum radiation
• Gas near BH has high Doppler motions \Rightarrow broad line regions (BLRs)
• Changes in continuum level take time (time delay $\tau$, $R_{\mathrm{BLR}}=c\tau$) to reach BLRs
• Width of line \sigma is a measure of velocity of gas at $R_{\mathrm{BLR}}$
• BH mass $M_{\mathrm{BH}}\approx f{R}_{\mathrm{BLR}}{\sigma }^2/G$, $f$ is determined by geometry

Assumption and complication

• Virialized motions(there may be outflows, jets, winds, etc.)
• Unknown geometric factor $f$
• Adequate sampling to get accurate $\tau$
• BLRs may be contaminated by non-varying or slow varying narrow line regions (NLRs)
• Line blending (different $\tau$)
• Absorption along line of sight
• $L_{\mathrm{bol}}\ll L_{\mathrm{Edd}}$ $\Rightarrow$ gravity dominates

Comparison with other method

Result from RM method is often inconsistent with stellar dynamics with the same object A discrepancy in relation $M_{\mathrm{BH}}-L_{\mathrm{bulge}}$ exists $M_{\mathrm{BH}}-\sigma$ is much better correlation

High redshift case

• $\tau \sim$ days/months, even to a year $\Rightarrow$ hard to monitor
• Can use C IV transition as standard line
• RM at high z is OK, likely accurate to factor of $3-4$

BH evolution

• Extremely massive BHs already exist at $z=6$
• Supermassive BHs form first
• Host galaxies are not dynamically relaxed at high z, does $M_{\mathrm{BH}}-\sigma$ hold?