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X-Ray Measurements of M87: Mass Distribution Analysis

Explore how x-ray surface brightness data of M87 is used to determine its mass distribution. The study, presented in 1980, delves into the density and temperature profiles of the hot gas responsible for the x-ray emission. By analyzing the gas's response to M87's gravitational potential, researchers derive insights into the radial mass distribution. The study emphasizes hydrostatic equilibrium as a key principle in understanding the mass distribution within M87.

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X-Ray Measurements of M87: Mass Distribution Analysis

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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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