1. 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

2. 2 A long time ago, in a galaxy far, far away…

3. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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)

13. 13 Comparisons Einstein Chandra

14. 14 Comparisons  Einstein, within 240 kpc of center: 1.7x10 13 M  < M * (r) < 4.0x10 13 M   Chandra, within 32 kpc of center: M * (r) ≈ 2.7x10 12 M  M BH ≈ 3x10 9 M 

15. 15 Extra Slide 1: The Einstein Observatory (HEAO-2) Giacconi, R. et al. 1979, Ap.J. 230,540 http://library01.gsfc.nasa.gov/gdprojs/images/heao_b.jpg