# Measuring the Black Hole Mass in Markarian 6 using Reverberation Mapping

• Title: BLR kinematics and Black Hole Mass in Markarian 6
• Authors: V.T. Doroshenko, S.G. Sergeev, S.A. Klimanov, V.I. Pronik, Yu.S. Efimov
• First Author’s Institution: Crimean Astrophysical Observatory, Ukraine

Background: Black Holes and Galaxies
It is now well established that supermassive black holes exist at the centers of most, if not all, large galaxies. Not only do the black holes exist at the centers of galaxies, but there also appears to be a number of black hole-host galaxy scaling relations. For example, the MBH relation provides a correlation between the mass of the central black hole and the velocity dispersion of the spheroidal component (either a galaxy bulge or an entire elliptical galaxy) of galaxies. There are a number of other quantities that scale with the central black hole mass including the mass and the luminosity of the spheroidal component. For a more in depth discussion of galaxy scaling relations, see this astrobite.

The existence of black hole-galaxy scaling relations is important for two reasons. First of all, these relations suggest there may be a link between galaxy formation and black hole growth. If we didn’t know these relations existed, there would be no reason to expect the mass of black holes at the centers of galaxies to correlate with galaxy properties. This is because the radius of influence of the black hole, or the region where the black hole mass dominates the gravitational dynamics of the system, only extends outwards on the scale of parsecs or tens of parsecs. In contrast, the host galaxy properties are measured on kiloparsec scales. The second reason black hole-galaxy scaling relations are important is because of their predictive power. These relations mean that if we can measure a galaxy property such as the velocity dispersion or the luminosity of the spheroidal component, we get the central black hole mass for free. This is fantastic, because measuring black hole masses is tough! However, in order to properly calibrate these scaling relations, we need accurate central black hole mass measurements in some galaxies.

Figure 1. The accretion disk is shown in blue and the BLR is shown in green. The figure shows the time delay between light which reaches us directly from the central continuum source (the blue arrow) and the light which is emitted due to recombination in the BLR (the green arrow).

Measuring Black Hole Masses
There are two primary methods by which we measure black hole masses. The first relies on directly measuring the Doppler shifts of material orbiting the central black hole. This can be done using stellar kinematics, gas kinematics, or masers. The limitation of this method is that you have to be able to resolve the inner region of the galactic nucleus. In other words, the galaxy must be nearby. The second method to directly measure black holes is called reverberation mapping.

Reverberation mapping relies on the nature and geometry of active galactic nuclei (AGNs), so before we go any further, we should briefly discuss some details of AGNs. At their very centers, AGNs, like many galaxies, contain a supermassive black hole. The defining characteristic of an AGN is that this black hole is accreting material at a high rate. Before it is accreted, material collects in a disk surrounding the black hole (an accretion disk). As the material nears the black hole it loses gravitational potential energy and radiates it away in the form of electromagnetic radiation, which causes the AGN to be very luminous. Further away from the black hole, there is another region of gas known as the broad line region (BLR). This region gets photoionized by the continuum source (the accretion disk) at the center. As the gas recombines, it emits light at characteristic wavelengths such as H-alpha. The BLR takes its name because the high velocity gas moving both towards and away from us broadens the peaks of the emission lines through Doppler broadening. I have just barely grazed the variety and features of AGNs and their host galaxies, so if you are interested in learning more you should check out our galaxy and AGN glossary and this astrobite.

Figure 2 (from Peterson 2001). This figure shows the time delay between the continuum source flux and the BRL flux.

Reverberation Mapping
Reverberation mapping relies on the fact that the light emitted by the BLR is reprocessed from the central continuum source, and that the central continuum source is variable (see figure 1). Given these two facts, and diligent monitoring of an AGN, we can measure the time delay between the variability of the continuum source and the variability of the BLR. An example of this is shown in figure 2. The time delay analysis can tell us the distance between the central black hole and the BLR. If we then examine the Doppler broadening of the lines more carefully, we can also obtain the velocity dispersion of the gas. Given a velocity and a distance, we can use Kepler’s laws to tell us the mass interior to that orbit, or the black hole mass. This gives,

M_{\rm{BH}} = \frac{fR_{\rm{BLR}}\ \sigma^2}{G}

where $R_{\rm{BLR}}$ is the radius of the BLR, $\sigma$ is the velocity dispersion measured by the line broadening, $G$ is the gravitational constant, and $f$ is a dimensionless filling factor which depends upon the structure, kinematics, and inclination of the system. To date, ~40 systems have had black hole masses measured via reverberation mapping.

Observations
Doroshenko et al. present spectral and photometric observations of Markarian 6 taken from 1998 to 2008 on the 2.6 meter Shajn telescope at the Crimean Astrophysical Observatory. These observations allow the authors to determine the time delay between the variability of the continuum source and the variability of the BLR and the velocity dispersion of the BLR gas, thus allowing them to determine the central black hole mass.

Results
Doroshenko et al. determine the supermassive black hole in Markarian 6 has a mass of (1.8 ± 0.2) × 108 M. Furthermore, they find that the luminosity changes in the blue wings of the broad line peaks lag slightly behind the luminosity changes in the red winds of the broad line peaks. This lag indicates that the motion of the BLR gas is a combination of orbital velocity and infall towards the central black hole. The detection of gas inflow could have important implications for large-scale mass flow in AGNs, but inflows and outflows have only been detected in the BLR in a few other cases (e.g. Denney et al. 2009, Bentz et al. 2009), so it is not possible to make any statistically signifigant statements about these inflows yet.

#### About Kim Phifer

I am currently a first year graduate student at UCLA. I work with Andrea Ghez to study the dynamics of the old stars in the Galactic Center. Last year, I earned a M.Phil (Master of Philosophy) in astronomy at the University of Cambridge. While there, I studied the (theoretical) progenitors of electron capture supernovae with Chris Tout. I completed my undergraduate degree at Butler University where I studied the dynamics of galactic nuclei with Brian Murphy.

# 1 Comment

1. Thanks for this post, very clear and interesting. It helped me a lot 😉