Sagittarius A* (Sgr A*) is a compact radio source in the nucleus of the Milky Way galaxy (Galaxy). This radio source is interesting in that its estimated high mass and low bolometric luminosity are suggestive of a black hole residing at the center of our Galaxy. A two-temperature optically thin advection-dominated accretion flow (ADAF) model developed by Narayn, Yi, Mahadevan (1995) can be utilized to model Sgr A*. The model suggests that Sgr A* is a black hole.
Very near the dynamical center of the Milky Way galaxy (Galaxy) is compact radio source Sagittarius A* (Sgr A*). This non-thermal radio source is less than 0.1 arcsec in diameter and is located within the Sgr A West region of the Galaxy at galactic coordinates 17.42.29, 29.59.18 at a distance of about 8.5 kpc from Earth. Sgr A* may be a quasar that now is mostly dormant but for power supplied by a black hole (Frank, King & Raine, 2002).
Sgr A* has a mass of M = (2.5+/- 0.4) x 10^6 solar masses (Narayan et al., 1998), which suggests that it may be associated with a black hole. This mass is contained within about 0.1 pc of the Galaxy’s center, based on dynamical measurements (Haller et al., 1996). There are also many 2.2 (mu)m infrared emission sources surrounding Sgr A* (Zeilik, 1998).
Another estimate of the central mass at the center of the Galaxy is M = (3.7 +/- 1.5) x 10^6 solar masses. This estimate is based on high-resolution imaging of two-thirds of the orbit of star S2, which came within 10-20 mas of Sgr A* in spring 2002 (Schodel et al., 2002). These data rule out a dark cluster model of stellar objects at the Galaxy’s center.
Sgr A* has an unusual emission that spans wavelengths from the radio to above X-ray part of the spectrum, and a lower than expected luminosity based on estimates of its mass accretion rate (Narayan et al., 1998). Based on its mass and mass accretion rate, Sgr A* is expected to have peak emission in the near-infrared part of the spectrum (Frank, King & Raine, 1992).
Narayan et al. (1998) suggests a mass of (2.5 +/- 0.04) x 10^6 solar masses and a mass accretion rate of greater than or equal to about 10^-6 solar masses per year for Sgr A*. Based on these estimates, Sgr A*’s luminosity is expected to be greater than 10^40 erg^-1. However, its observed bolometric luminosity is less than 10^37 ergs^-1.
Compact radio source Sgr A* is important because of what it may tell us about the mass located at the center of our Galaxy. What is the mechanism of the active nucleus of the Milky Way? Is the compact radio source Sgr A* really a quiescent quasar that indicates the presence of a black hole? What we learn about Sgr A* can help us understand our own Galaxy and also be applied to models of more distant active galactic nuclei (AGN).
Locating Sgr A* in infrared images of the central region can be accomplished by detecting silicon monoxide (SiO) and/or water (H2O) maser emissions. M-type supergiant stars within one parsec of the galactic center have detectable maser emissions. Karl Menten and Mark Reid et al. (1997) suggest that these maser emissions can be used to accurately locate Sgr A* to within a milliarcsecond (mas) in infrared images.
The technique is to compare absolute positions of maser radio emissions that originate from the stellar infrared sources relative to Sgr A*’s continuum emission (Menten, Reid et al., 1997). Using this technique, Menten & Reid et al. have accurately registered several SiO masers that emanate from supergiant M-type stars in the infrared at 2.2 (mu)M relative to Sgr A*’s radio continuum to within 0.03 arcsec, with an uncertainty in measurement of about 20 mas.
The detection of SiO maser proper motion can also be used to find a lower limit on the mass enclosed within a radius of 0.2-2 pc of Sgr A* (Reid et al., 2003). The mass enclosed is greater than or equal to V^2total x Rproj/2G, where Vtotal is the three-dimensional speed of the maser, Rproj is the projected distance of star from Sgr A*, and G is the gravitational constant.
A lower limit to the mass enclosed within a radius of 0.33 pc from Sgr A* was found to be 4.5 x 10^6 solar masses (Reid et al., 2003). This mass value suggests that current models underestimate the mass within the enclosed radius of 0.33 pc or that this particular star is not bound to Sgr A*.
Sgr A*’s spectrum can be attributed to the way in which plasma accretes onto it. Sgr A* emits from the radio to the Xray part of the spectrum (Melia, Bromley, Liu & Walker, 2001). The compact radio source is brightest in the radio part of the spectrum and is weakly detected in the X-ray part of the spectrum (Predehl & Trumper, 1994). X-ray emission from Sgr A* is partially diffuse (Pessah & Melia, 2003). One explanation for the diffuse X-ray emission is that it is produced by a cluster of old neutron stars (Pessah & Melia, 2003).
Sgr A*’s spectrum from centimeter to millimeter wavelengths follows the power law S2(nu)^(alpha), Where (alpha) is about 0.19-0.34. Sgr A* has also been detected in the X-ray part of the spectrum (Bagonoff et al., 2003).
The spectra from Sgr A* contains peaks and bumps due to a synchrotron radiation peak in the infrared, two Compton peaks in the extreme ultraviolet (EUV) to soft X-ray range from scattering of synchrotron photons, and a peak in the hard X-ray range from bremsstrahlung radiation (Frank, King & Raine, 2002).
Narayan, Yi and Mahadevan (1995) constructed a model spectrum which fit the Sgr A* spectrum over ten decades of frequency. Their model is known as the advection-dominated accretion flow (ADAF) model.
An advection-dominated accretion flow (ADAF) model (Narayan, Yi & Mahadevan, 1995) attempts to model accretion flows around black holes. The ADAF model includes the effects of viscous hydrodynamics and radiation processes in modeling the behavior of a two-temperature optically thin accretion disk plasma. This model predicts that ADAFs with lower-than-expected bolometric luminosities based on mass accretion rates may signify the existence of a black hole (Frank, King & Raine, 2002).
The ADAF model is important because it takes into account advective energy transport as well as bremsstrahlung, synchrotron emission and Comptonization radiation processes in modeling the spectrum of Sgr A*. In the specific case of Sgr A*, its accretion rate is small and its optical depth is low, and an optically thin advection-dominated solution has been adopted.
Several assumptions have been made in applying the ADAF model to accretion flows around black holes; a steady state axially symmetric accretion flow; viscous heating of the accretion disk; inefficient radiative cooling; energy dissipation by way of advection into the central source; and local solutions to spectral calculations that are accurate to the marginally stable orbit (Narayan, Kato & Honma, 1997).
Equations used in the ADAF model are the continuity equation d/dR(2*pi*R)*(2*H*rho*v) = 0, where R is the cylindrical radius, H is half the vertical thickness of the disk, rho is the gas density, and v is the radial velocity (Narayan, Kato & Honma, 1997), the mass accretion rate (Mdot) = -4*pi*R*H*rho*v. The mass accretion rate of Sgr A* is about (2-5) x 10^-6 solar masses per year when calculated using the ADAF model (Manmoto, Mineshige & Kusunose, 1997). The disk’s vertical thickness H is given by H = (5/2)^1/2 Cs/wk, where the isothermal sound speed of the gas is Cs and the Keplerian angular velocity is wk.
A central black hole gravitational potentisl is given by phi(R) = -GM/(R-Rg), Rg = 2GM/c^2, where M is the black hole’s mass and Rg is the gravitational radius. wk^2 = GM/(R-Rg)^2R is the Keplerian angular velocity.
The equation of steady state angular momentum, taking into account viscosity, is v(d/dR)(wR^2) = (1/rho*R*H)(d/dR)(nu*pho*R^3*H*dw/dR), where nu, the kinematic coefficient of viscosity can be written as nu = (alpha)(Cs^2wk), where alpha is a constant. The Schwarzchild radius is Rs = 2GM/c^2. The radiative efficiency is epsilon = Lbol/Mdot*c^2 = 5 x 10^-6 f is about 1 is the advection parameter.
Solving these equations results in a series of solutions based on values of alpha ranging from 0.001 to 0.3 (Narayan, Kato & Honma, 1997). They find that the viscosity increases as the sound speed increases, which in turn causes an increase in the radial velocity of the accretion. The high radial velocity causes the density in the disk to drop, and the cooling rate decreases. As the cooling rate decreases, material is advected into the central source. They also find subsonic radial velocity for all values of alpha.
The ADAF model is a good fit to the observed fluxes in Sgr A*, except for the radio spectrum below 86 GHz and in the gamma ray part of the spectrum above 100 MeV. The model also predicts that the lower than expected luminosity of Sgr A* can be explained by means of advection (Narayan et al., 1998).
The most important finding of the ADAF model is that accretion is regulated by angular momentum and the rate of viscous transport because the gas can only be advected toward the central source by losing angular momentum (Narayan, Kato & Honma, 1997). Without viscosity and loss of angular momentum there would be only spherical accretion.
The advected energy must go somewhere. The ADAF model indicates that an event horizon exists inside the accretion disk (Narayan et al., 1998) and that the advected energy is consumed. This is good evidence that Sgr A* is in fact a black hole.
It is interesting to note that when alpha is set to 0.1 in the ADAF model, X-ray emission from the Galactic center can no longer be accounted for. There remains the possibility that X-rays are coming from a source other than Sgr A* (Manmoto, Mineshige & Kusunose, 1997). The center of the Galaxy is crowded, so the X-ray emission could be coming from a nearby source instead of from Sgr A*. An X-ray burster located within 1.3 arcsec of Sgr A* may be the source of the X-ray emission (Koyama et al., 1996).
Viscosity in accretion disks is not well understood and is an area of uncertainty in understanding the dynamics of Sgr A*. However, the Sgr A* spectrum predicted by the ADAF model is largely unaffected by changes in the viscosity parameter alpha.
The compact radio source Sgr A* is most likely a black hole or a quasar remnant that is powered by a black hole. Predictions of the mass contained at the center of the Milky Way galaxy is about 10^6 solar masses.
Emissions from Sgr A* are observed over decades of wavelength from radio waves in the low frequency to gamma rays at high frequencies. The luminosity of Sgr A* is lower than predicted. Its low luminosity can be explained by the ADAF model.
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