Presentation on theme: "X-Ray Measurements of the Mass of M87 D. Fabricant, M. Lecar, and P. Gorenstein Astrophysical Journal, 241: 552-560, 15 October 1980 Image:"— Presentation transcript:
X-Ray Measurements of the Mass of M87 D. Fabricant, M. Lecar, and P. Gorenstein Astrophysical Journal, 241: 552-560, 15 October 1980 Image: http://chandra.harvard.edu/photo/2004/m87.jpg Presented by David Riethmiller 17 October 2007
3 Procedure Overview Measure M87’s x-ray surface brightness (0.7-3.0 keV), indicates density profile Determine temperature profile of hot gas responsible for x-ray emission Gas responds to M87’s gravitational potential Then density and temperature profiles are somehow indicative of radial mass distribution
4 Measuring Surface Brightness Contour Plot: Isophotes represent separation factor of 1.5 in surface brightness. Surface brightness function shown here has no particular physical significance other than fitting the data. I o = central surface brightness r = radius (arcmin) b, c, d, n = fit parameters
5 Density Profile Assuming isothermality, can invert surface brightness profile numerically to obtain density profile Then density profile follows same form: ρ o = mass density normalization r = radius (arcmin) b’, c’, d’, n’ = fit parameters
6 Temperature Profile Search for temperature gradient in spectral data as projected along line of sight Instruments on board Einstein Observatory lack sensitivity to trace temperature profile as surface brightness falls below peak levels Uncertainty on final results mostly due to uncertainty in temperature profile
7 Mass Distribution: Hydrostatic Equilibrium Believe gas is in H.E. because: Cooling time for gas everywhere is much longer than the dynamical (freefall) time
8 Mass Distribution: Hydrostatic Equilibrium Believe gas is in H.E. because: The temperature does not increase inward as would be expected if the gas were settling or expanding adiabatically.
9 Mass Distribution: Hydrostatic Equilibrium Believe gas is in H.E. because: Density profile of x-ray emitting gas is not as steep as expected for freely expanding or falling gas Freely falling/expanding gas (blue): Observed (red): Density vs. Radius (Not to scale)
10 Mass Distribution: Hydrostatic Equilibrium Then can combine condition for (spherically symmetric) H.E. with ideal gas law: After some math (not shown): P gas = pressure of gas ρ gas = gas density K = Boltzmann constant T gas = gas temperature (constant) μ = mean molecular weight M * (r) = M87 mass (interior to r) M H = mass of H atom
11 Results Substitution of parameters specific to M87 leads to a mass that far outweighs the mass of its visible matter Implies the existence of a dark halo
12 More Results Within radius of ~50 arcmin (~240 kpc), 1.7x10 13 M < M * (r) < 4.0x10 13 M Uncertainties mostly due to lack of sensitivity in determining temperature profile Core radius of visible matter: ~10 arcsec (0.8 kpc)
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