Systematic Errors in the Estimation of Black Hole Masses by Reverberation Mapping

By Julian Krolik. 2000

143 citations recorded by the source corpus.

The mass of the central black hole in many active galactic nuclei has been estimated on the basis of the assumption that the dynamics of the broad emission line gas are dominated by the gravity of the black hole. The most commonly employed method is to estimate a characteristic size-scale r* from reverberation mapping experiments and combine it with a characteristic velocity v* taken from the line profiles; the inferred mass is then estimated by r*v/G. We critically discuss the evidence supporting the assumption of gravitational dynamics and find that the arguments are still inconclusive. We then explore the range of possible systematic error if the assumption of gravitational dynamics is granted. Inclination relative to a flattened system may cause a systematic underestimate of the central mass by a factor of ~(h/r)2, where h/r is the aspect ratio of the flattening. The coupled effects of a broad radial emissivity distribution, an unknown angular radiation pattern of line emission, and suboptimal sampling in the reverberation experiment can cause additional systematic errors as large as a factor of 3 or more in either direction.

Subfields: Astronomy and Astrophysics

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Citations in the corpus

CONSTRAINTS ON BLACK HOLE GROWTH, QUASAR LIFETIMES, AND EDDINGTON RATIO DISTRIBUTIONS FROM THE SDSS BROAD-LINE QUASAR BLACK HOLE MASS FUNCTION (2010, background): “…it possible to estimate MBH for BLQSOs (e.g., Vestergaard & Peterson 2006; Kelly & Bechtold 2007), albeit with considerable statistical uncertainty of ∼0.4 dex and various systematic effects (e.g., Krolik 2001; Vestergaard & Peterson 2006; Greene & Ho 2006; Marconi et al. 2008; Denney et al. 2009).”
Central Masses and Broad-Line Region Sizes of Active Galactic Nuclei. II. A Homogeneous Analysis of a Large Reverberation-Mapping Database (2004, background): “Unfortunately, there is a significant systematic uncertainty (Krolik 2001) in AGN reverberation masses embodied in the scaling factor f in eq.”
Supermassive Black Holes in Galactic Nuclei: Past, Present and Future Research (2004, background): “However, systematic uncertainties can in principle be a factor of several or more (Krolik 2001).”
Systematic effects in measurement of black hole masses by emission-line reverberation of active galactic nuclei: Eddington ratio and inclination (2006, unknown): “For instance, Krolik (2001) pointed out that if the BLR is a thin disk, it would lead to an underestimation of the mass by one or two orders of magnitude for objects seen at low inclination.”
THE RADIATIVE EFFICIENCY OF ACCRETION FLOWS IN INDIVIDUAL ACTIVE GALACTIC NUCLEI (2010, unknown): “A thorough discussion of systematic errors, including inclination dependence, is provided by Krolik (2001).”
The Mass Function of Active Black Holes in the Local Universe (2007, methodology): “Although relying on the physics of the BLR to estimate BH masses is fraught with danger (e.g., Krolik 2001), it is possible to directly compare virial masses with the measurements of bulge stellar velocity dispersions, and calibrate them with theMBH − σ∗ relation.”
Active Galactic Nucleus Black Hole Masses and Bolometric Luminosities (2002, background): “…that broad-line clouds are virialized, for which there has been increasing evidence (Krolik et al. 1991; Wandel, Peterson, & Makkan 1999; cf. Krolik 2001), the black hole mass can be estimated as MBH ¼ RBLRv2G 1 : ð1Þ The virial assumption may not be correct, however; radiation pressure…”
DWARF GALAXIES WITH OPTICAL SIGNATURES OF ACTIVE MASSIVE BLACK HOLES (2013, background): “Then there is the danger that we are not measuring the velocities at the same radius as probed with reverberation mapping (Krolik 2001).”
An expanded Mbh–σ diagram, and a new calibration of active galactic nuclei masses (2010, background): “Thin discs, thickened discs or composites of planar and random motions have all been modelled by various groups (see discussions by Krolik 2001; Collin et al. 2006; Labita et al. 2006; Decarli et al. 2008b).”
The cosmological evolution of quasar black hole masses (2003, unknown): “Krolik 2001).”
Biases in Virial Black Hole Masses: An SDSS Perspective (2007, background): “We also note that there might be other systematic errors associated with virial BH masses or reverberation mapping masses in general (Krolik 2001).”
On the Relationship between Radio Emission and Black Hole Mass in Galactic Nuclei (2001, background): “Notwithstanding this and other possible systematic uncertainties (Krolik 2001), reverberation mapping appears capable of delivering for AGNsMBHwith an accuracy of a factor of D2È3.”
THE LICK AGN MONITORING PROJECT 2011: SPECTROSCOPIC CAMPAIGN AND EMISSION-LINE LIGHT CURVES (2015, background): “More worrying is the possibility that the BLR dynamics might be affected by outflows or other nongravitational motions, in which case simple virial mass estimates might be entirely misleading (Krolik 2001).”
On the black hole–bulge mass relation in active and inactive galaxies (2001, background): “Indeed, uncertainty about the exact geometry of the broad-line region (BLR) in AGNs has the potential to produce large systematic errors in linewidth-based black hole mass estimates (see Krolik 2001 for a discussion).”
Accretion disk wind in the AGN broad-line region: Spectroscopically resolved line profile variations in Mrk 110 ? (2003, background): “But one has to keep in mind that there are further systematic uncertainties in the mass determination (e.g. Krolik 2001).”
The Effect of Radiation Pressure on Virial Black Hole Mass Estimates and the Case of Narrow-Line Seyfert 1 Galaxies (2008, background): “This possibility has generated a debate about thereliability of virial BH masses (e.g. Peterson & Wandel 2000; Krolik 2001; Onken & Peterson 2002; Collin et al. 2006; Vestergaard & Peterson 2006) which is beyond the scope of this paper.”
Determining Central Black Hole Masses in Distant Active Galaxies and Quasars. II. Improved Optical and UV Scaling Relationships (2002, background): “The factor f is on the order of unity and depends on the geometry and the details of the kinematics (see, e.g., Peterson & Wandel 1999, 2000; Fromerth &Melia 2000; Krolik 2001;McLure &Dunlop 2001).”
A New Sample of Low-Mass Black Holes in Active Galaxies (2007, methodology): “Although BH masses derived from reverberation mapping are susceptible to large systematic errors (due to uncertainties in the BLR geometry and kinematics; e.g., Krolik 2001), remarkably they have been shown to agree withσ∗, in those cases for which σ∗ can be measured.”
A long hard look at MCG–6-30-15 with XMM-Newton (2002, methodology): “In this case the rms velocity width of the line (σ) is determined by its proximity to the SMBH (r/ rg) and the geometry according to: r/ rg ∼ (c/σ)2/q (whereq depends on the geometry; Krolik 2001).”