The Slope of the Black Hole Mass versus Velocity Dispersion Correlation

Observations of nearby galaxies reveal a strong correlation between the mass of the central dark object MBH and the velocity dispersion σ of the host galaxy, of the form log(MBH/M☉) = α + β log(σ/σ0); however, published estimates of the slope β span a wide range (3.75-5.3). Merritt & Ferrarese have argued that low slopes (≲4) arise because of neglect of random measurement errors in the dispersions and an incorrect choice for the dispersion of the Milky Way Galaxy. We show that these explanations and several others account for at most a small part of the slope range. Instead, the range of slopes arises mostly because of systematic differences in the velocity dispersions used by different groups for the same galaxies. The origin of these differences remains unclear, but we suggest that one significant component of the difference results from Ferrarese & Merritt's extrapolation of central velocity dispersions to re/8 (re is the effective radius) using an empirical formula. Another component may arise from dispersion-dependent systematic errors in the measurements. A new determination of the slope using 31 galaxies yields β = 4.02 ± 0.32, α = 8.13 ± 0.06 for σ0 = 200 km s-1. The MBH-σ relation has an intrinsic dispersion in log MBH that is no larger than 0.25-0.3 dex and may be smaller if observational errors have been underestimated. In an appendix, we present a simple kinematic model for the velocity-dispersion profile of the Galactic bulge.

[1]  Heon-Young Chang,et al.  Current High Energy Emission Around Black Holes , 2002 .

[2]  P. T. de Zeeuw,et al.  The counterrotating core and the black hole mass of IC1459 , 2002, astro-ph/0202155.

[3]  M. Tremaine.  A time to say goodbye , 2002 .

[4]  D. Schlegel,et al.  Streaming motions of galaxy clusters within 12 000 km s−1 — III. A standardized catalogue of Fundamental Plane data , 2001 .

[5]  Dalia Chakrabarty,et al.  A Nonparametric Estimate of the Mass of the Central Black Hole in the Galaxy , 2001, astro-ph/0103467.

[6]  L. Ho,et al.  Evidence for a Supermassive Black Hole in the S0 Galaxy NGC 3245 , 2000, astro-ph/0012213.

[7]  J. Silk,et al.  Star Formation-Regulated Growth of Black Holes in Protogalactic Spheroids , 2000, astro-ph/0011511.

[8]  Gerard A. Luppino,et al.  The SBF Survey of Galaxy Distances. IV. SBF Magnitudes, Colors, and Distances , 2000, astro-ph/0011223.

[9]  T. Lauer,et al.  Evidence of a Supermassive Black Hole in the Galaxy NGC 1023 from the Nuclear Stellar Dynamics , 2000, astro-ph/0011204.

[10]  A. Koekemoer,et al.  Peering through the Dust: Evidence for a Supermassive Black Hole at the Nucleus of Centaurus A from VLT Infrared Spectroscopy , 2000, astro-ph/0011059.

[11]  J. Binney,et al.  Kinematics from spectroscopy with a wide slit: detecting black holes in galaxy centres , 2000, astro-ph/0010379.

[12]  L. Ho,et al.  Supermassive Black Holes in Bulges , 2000, astro-ph/0010240.

[13]  P. Salucci,et al.  Evidence for a massive dark object in ngc 4350 , 2000, astro-ph/0008429.

[14]  D. Merritt,et al.  The M•-σ Relation for Supermassive Black Holes , 2000, astro-ph/0008310.

[15]  G. Kauffmann,et al.  The Correlation between black hole mass and bulge velocity dispersion in hierarchical galaxy formation models , 2000, astro-ph/0007369.

[16]  Ralf Bender,et al.  A Relationship between Nuclear Black Hole Mass and Galaxy Velocity Dispersion , 2000, astro-ph/0006289.

[17]  D. Merritt,et al.  A Fundamental Relation between Supermassive Black Holes and Their Host Galaxies , 2000, astro-ph/0006053.

[18]  R. Bender,et al.  The Nuclear Dynamics of M32. I. Data and Stellar Kinematics , 2000, astro-ph/0005530.

[19]  C. Pichon,et al.  Stellar dynamics in the Galactic centre: Proper motions and anisotropy , 2000, astro-ph/0001428.

[20]  J. Ostriker,et al.  Collisional dark matter and the origin of massive black holes , 1999, Physical review letters.

[21]  S. Tremaine,et al.  Axisymmetric, Three-Integral Models of Galaxies: A Massive Black Hole in NGC 3379 , 1999, astro-ph/9912026.

[22]  K. Gebhardt,et al.  Obtaining Galaxy Masses Using Stellar Absorption and [O II] Emission-Line Diagnostics in Late-Type Galaxies , 1999, astro-ph/9911361.

[23]  R. Bender,et al.  The Double Nucleus and Central Black Hole of M31 , 1999 .

[24]  J. M. Moran,et al.  A geometric distance to the galaxy NGC4258 from orbital motions in a nuclear gas disk , 1999, Nature.

[25]  M. Dopita,et al.  A Survey of Planetary Nebulae in the Southern Galactic Bulge , 1999 .

[26]  A. Fabian,et al.  The mass density in black holes inferred from the X-ray background , 1999, astro-ph/9901121.

[27]  H. Ford,et al.  Nuclear Disks of Gas and Dust in Early-Type Galaxies and the Hunt for Massive Black Holes: Hubble Space Telescope Observations of NGC 6251 , 1998, astro-ph/9811319.

[28]  R. Bacon,et al.  Dynamical models of ngc 3115 , 1998, astro-ph/9810306.

[29]  E. Becklin,et al.  High Proper-Motion Stars in the Vicinity of Sagittarius A*: Evidence for a Supermassive Black Hole at the Center of Our Galaxy , 1998, astro-ph/9807210.

[30]  N. Cretton,et al.  Evidence for a Massive Black Hole in the S0 Galaxy NGC 4342 , 1998, astro-ph/9805324.

[31]  R. Bender,et al.  The Mass Distribution in the Elliptical Galaxy NGC 3377: Evidence for a 2 × 108 M☉ Black Hole , 1998, astro-ph/9803087.

[32]  W. Sparks,et al.  The Supermassive Black Hole of M87 and the Kinematics of Its Associated Gaseous Disk , 1997, astro-ph/9706252.

[33]  P. T. de Zeeuw,et al.  Improved Evidence for a Black Hole in M32 from HST/FOS Spectra. II. Axisymmetric Dynamical Models , 1997, astro-ph/9705081.

[34]  Timothy M. Heckman,et al.  The Nuclear Ionized Gas in the Radio Galaxy M84 (NGC 4374) , 1997, astro-ph/9710264.

[35]  H. Habing,et al.  The ATCA/VLA OH 1612 MHz survey. I. Observations of the galactic bulge Region , 1997 .

[36]  S. Tremaine,et al.  Spectroscopic Evidence for a Supermassive Black Hole in NGC 4486B , 1997, astro-ph/9703188.

[37]  C. Gwinn,et al.  VLBI Imaging of Water Maser Emission from a Nuclear Disk in NGC 1068 , 1997 .

[38]  S. Tremaine,et al.  Hubble Space Telescope Spectroscopic Evidence for a 1 × 109 M☉ Black Hole in NGC 4594 , 1996 .

[39]  Alfred Krabbe,et al.  The Dark Mass Concentration in the Central Parsec of the Milky Way , 1996 .

[40]  S. Tremaine,et al.  The centers of early-type galaxies with HST. IV. Central parameter relations , 1996, astro-ph/9610055.

[41]  H. Ford,et al.  Evidence for a Massive Black Hole in the Active Galaxy NGC 4261 from Hubble Space Telescope Images and Spectra , 1996 .

[42]  Oxford,et al.  The photometric structure of the inner Galaxy , 1996, astro-ph/9609066.

[43]  Matthew A. Bershady,et al.  Linear Regression for Astronomical Data with Measurement Errors and Intrinsic Scatter , 1996, astro-ph/9605002.

[44]  S. Tremaine,et al.  The Centers of Early-Type Galaxies with HST III: Non-Parametric Recovery of Stellar Luminosity Distributions , 1996, astro-ph/9604092.

[45]  S. Tremaine,et al.  Hubble Space Telescope Spectroscopic Evidence for a 2 × 109 M☉ Black Hole in NGC 3115 , 1996 .

[46]  I. Jørgensen,et al.  Spectroscopy for E and S0 galaxies in nine clusters , 1995 .

[47]  R. Rich,et al.  K Giants in Baade's Window. I. Velocity and Line-Strength Measurements , 1995, astro-ph/9508105.

[48]  Samuel Harvey Moseley,et al.  Morphology, near infrared luminosity, and mass of the galactic bulge from Cobe dirbe observations , 1995 .

[49]  K. Sellgren,et al.  M giant kinematics in off-axis fields between 150 and 300 parsecs from the galactic center , 1995, astro-ph/9503059.

[50]  S. Tremaine,et al.  Eccentric-Disk Models for the Nucleus of M31 , 1995, astro-ph/0307412.

[51]  Frank C. van den BoschRoeland P. van der Marel.  Dynamics of the nuclear gas and dust disc in the E4 radio galaxy NGC 7052 , 1994, astro-ph/9412041.

[52]  H. Ford,et al.  HST FOS spectroscopy of M87: Evidence for a disk of ionized gas around a massive black hole , 1994 .

[53]  H. Rix,et al.  Velocity profiles of galaxies with claimed black holes — I. Observations of M31, M32, NGC 3115 and NGC 4594 , 1994 .

[54]  Donald M. Terndrup,et al.  Radial Velocities of M Giants at 300 Parsec Projected Radius from the Galactic Center , 1994 .

[55]  William H. Press,et al.  Numerical recipes in C (2nd ed.): the art of scientific computing , 1992 .

[56]  S. Kent,et al.  Galactic structure from the Spacelab Infrared Telescope. III: A dynamical model for the Milky Way bulge , 1992 .

[57]  David Burstein,et al.  Spectroscopy and photometry of elliptical galaxies. II - The spectroscopic parameters , 1987 .

[58]  Andrzej Soƚtan,et al.  Masses of quasars , 1982 .

[59]  J. Bahcall,et al.  Models for the Galaxy and the Predicted Star Counts , 1979 .

[60]  P. Roberts.  On the Superpotential and Supermatrix of a Heterogeneous Ellipsoid. , 1962 .

[61]  T. Mahoney,et al.  The central KPC of starbursts and AGN : the la Palma connection : proceedings of a confernce held in Los Cancajos, la Palma, Spain, 7-11 May 2001 , 2001 .

[62]  Hugo Martel,et al.  26th Texas Symposium on Relativistic Astrophysics , 2001 .

[63]  R. Sanders.  CENTRAL PARSECS OF THE GALAXY , 1999 .

[64]  G. Gilmore,et al.  The Milky Way as a galaxy , 1990 .

[65]  John Skilling,et al.  Maximum Entropy and Bayesian Methods , 1989 .

[66]  Stephen F. Gull,et al.  Bayesian Data Analysis: Straight-line fitting , 1989 .

[67]  R. Ramaty,et al.  Tenth Texas Symposium on Relativistic Astrophysics , 1981 .