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X-Ray Measurements of the Mass of M87

X-Ray Measurements of the Mass of M87. D. Fabricant, M. Lecar, and P. Gorenstein Astrophysical Journal, 241: 552-560, 15 October 1980. Presented by David Riethmiller 17 October 2007. Image: http://chandra.harvard.edu/photo/2004/m87.jpg. A long time ago, in a galaxy far, far away….

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X-Ray Measurements of the Mass of M87

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  1. X-Ray Measurements of the Mass of M87 D. Fabricant, M. Lecar, and P. Gorenstein Astrophysical Journal, 241: 552-560, 15 October 1980 Presented by David Riethmiller 17 October 2007 Image: http://chandra.harvard.edu/photo/2004/m87.jpg

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

  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. Io = 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: ρo = 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. 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 Mass Distribution: Hydrostatic Equilibrium Density vs. Radius (Not to scale) Freely falling/expanding gas (blue): Observed (red):

  10. Mass Distribution: Hydrostatic Equilibrium • Then can combine condition for (spherically symmetric) H.E. with ideal gas law: Pgas = pressure of gas ρgas = gas density K = Boltzmann constant Tgas = gas temperature (constant) μ= mean molecular weight M*(r) = M87 mass (interior to r) MH = mass of H atom After some math (not shown):

  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), 1.7x1013 M < M*(r) < 4.0x1013 M • Uncertainties mostly due to lack of sensitivity in determining temperature profile • Core radius of visible matter: ~10 arcsec (0.8 kpc)

  13. Comparisons Einstein Chandra

  14. Comparisons • Einstein, within 240 kpc of center:1.7x1013 M < M*(r) < 4.0x1013 M • Chandra, within 32 kpc of center:M*(r) ≈ 2.7x1012 MMBH≈ 3x109 M

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

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