There is a well-known strong correlation between the mass of a supermassive black hole and the velocity dispersion of its host galaxy’s bulge, known as the M-\(\sigma\) relation. This can not be explained through a direct relationship as the radius of gravitational influence of the black hole is much smaller than the radius of the host galaxy’s bulge. This suggests that there is some other form of feedback between the supermassive black hole and its host galaxy. The source of this feedback is unknown and an area of much active research. One way that these black hole masses are calculated is through reverberation mapping techniques.

The purpose of this computational exercise is to help students understand reverberation mapping. After completion of the project students will be able to calculate the cross correlation function for unevenly sampled time series data, they will be comfortable fitting emission lines for their velocity width, and they will be able to determine black hole mass estimates for reverberation mapping data.

The exercise begins with background information on reverberation mapping. Graphics are provided to instill visual understanding of a quasar’s accretion disk and broad line region. Continuum and Hβ light curves are provided, along with an interactive plotting tool that plots the continuum and emission light curves, as well as the cross correlation for different lag values. Once the time lag is extracted, the radius of the broad line region is determined. Next, students will use a spectral fitting tool to fit the rest frame optical spectrum to determine the Keplerian velocity. Once velocity and radius are determined, the black hole mass can be calculated.

Additional Information

Abbreviated Title: Reverberation Mapping

URL Reference: BLR

Type: Exercise Set

Course/Context: Astronomy/Astrophysics

Course Level: First Year of College, Beyond First Year

Author: Collin Dabbieri

This HTML is published online at collin-dabbieri.github.io/Lessons/

Learning Goals

After the completion of this project, students should be able to:

-Calculate the cross correlation function for unevenly sampled time series data

-Fit an emission line to determine its velocity width

-Determine black hole mass estimates for reverberation mapping data

Background Info

Quasars are the most luminous objects in the universe. They’re so bright that we can observe light from quasars that was emitted over 10 billion years ago. Quasars form when a supermassive black hole at the center of a galaxy draws gas from its host forming a disk that accretes onto the black hole. This disk emits thermal radiation that outshines the entire host galaxy. A diagram is given below.

Quasar Diagram

Quasar Diagram

The continuum light from the accretion disk emits like the sum of many blackbodies at different temperatures, and in practice is modelled as a power-law. The broad line region is illuminated by the accretion disk and gives off broad emission lines. An example synthetic spectrum is given below.

Quasar Spectrum

Quasar Spectrum

Galaxy Feedback

There’s a well-known correlation between the mass of a galaxy’s spheroidal component and the mass of the supermassive black hole at its center. For an elliptical galaxy, the spheroid is the whole galaxy, and for a spiral galaxy the spheroid is the central bulge. A plot illustrating this correlation is given below (Gültekin et al. (2009)).