X-Ray Measurements of the Mass of M87
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Transcript of X-Ray Measurements of the Mass of M87
X-Ray Measurements of the X-Ray Measurements of the Mass of M87Mass of M87
D. Fabricant, M. Lecar, and P. GorensteinD. Fabricant, M. Lecar, and P. GorensteinAstrophysical Journal, 241: 552-560, 15 October 1980Astrophysical Journal, 241: 552-560, 15 October 1980
Image: http://chandra.harvard.edu/photo/2004/m87.jpg
Presented by David Riethmiller
17 October 2007
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A long time ago, in a galaxy far, far away…
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Procedure OverviewProcedure Overview
Measure M87’s x-ray surface brightness (0.7-3.0 Measure M87’s x-ray surface brightness (0.7-3.0 keV), indicates density profilekeV), indicates density profile
Determine temperature profile of hot gas Determine temperature profile of hot gas responsible for x-ray emissionresponsible for x-ray emission
Gas responds to M87’s gravitational potentialGas responds to M87’s gravitational potential
Then density and temperature profiles are Then density and temperature profiles are somehow indicative of radial mass distributionsomehow indicative of radial mass distribution
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Measuring Surface BrightnessMeasuring Surface Brightness
Contour Plot:
Isophotes represent separation factor of 1.5 in surface brightness.
2 4 6( )
1
on
II r
br cr dr
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
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Density ProfileDensity Profile
Assuming isothermality, can invert surface Assuming isothermality, can invert surface brightness profile numerically to obtain brightness profile numerically to obtain density profiledensity profile
Then density profile follows same form:Then density profile follows same form:
'2 4 6( )
1 ' ' '
onr
b r c r d r
ρo = mass density normalizationr = radius (arcmin)b’, c’, d’, n’ = fit parameters
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Temperature ProfileTemperature Profile Search for temperature Search for temperature
gradient in spectral data gradient in spectral data as projected along line as projected along line of sightof sight
Instruments on board Instruments on board Einstein Observatory Einstein Observatory lack sensitivity to trace lack sensitivity to trace temperature profile as temperature profile as surface brightness falls surface brightness falls below peak levelsbelow peak levels
Uncertainty on final Uncertainty on final results mostly due to results mostly due to uncertainty in uncertainty in temperature profiletemperature profile
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Mass Distribution: Hydrostatic Mass Distribution: Hydrostatic EquilibriumEquilibrium
Believe gas is in H.E. because:Believe gas is in H.E. because:
Cooling time for gas everywhere is much longer than Cooling time for gas everywhere is much longer than the dynamical (freefall) timethe dynamical (freefall) time
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Mass Distribution: Hydrostatic Mass Distribution: Hydrostatic EquilibriumEquilibrium
Believe gas is in H.E. because:Believe gas is in H.E. because:
The temperature does not increase inward as would The temperature does not increase inward as would be expected if the gas were settling or expanding be expected if the gas were settling or expanding adiabatically.adiabatically.
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Mass Distribution: Hydrostatic Mass Distribution: Hydrostatic EquilibriumEquilibrium
Believe gas is in H.E. because:Believe gas is in H.E. because:
Density profile of x-ray emitting gas is not as steep as Density profile of x-ray emitting gas is not as steep as expected for freely expanding or falling gasexpected for freely expanding or falling gas
'2 4 6( )
1 ' ' '
onr
b r c r d r
2( )r r
Freely falling/expanding gas (blue): Observed
(red):
Density vs. Radius (Not to scale)
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Mass Distribution: Hydrostatic Mass Distribution: Hydrostatic EquilibriumEquilibrium
Then can combine condition for (spherically Then can combine condition for (spherically symmetric) H.E. with ideal gas law:symmetric) H.E. with ideal gas law:
*
2
( )gas gasdP GM r
dr r
gas gasgas
H
KTP
M
*
log( )
loggas gas
H
KT dM r r
G M d r
After some math (not shown):
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
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ResultsResults
Substitution of parameters specific to M87 Substitution of parameters specific to M87 leads to a mass that far outweighs the leads to a mass that far outweighs the mass of its visible mattermass of its visible matter
Implies the existence of a dark haloImplies the existence of a dark halo
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More ResultsMore Results
Within radius of ~50 arcmin (~240 kpc), Within radius of ~50 arcmin (~240 kpc),
1.7x101.7x101313 M M < M < M**(r) < 4.0x10(r) < 4.0x101313 M M
Uncertainties mostly due to lack of sensitivity in Uncertainties mostly due to lack of sensitivity in determining temperature profiledetermining temperature profile
Core radius of visible matter: ~10 arcsec (0.8 kpc)Core radius of visible matter: ~10 arcsec (0.8 kpc)
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ComparisonsComparisons
Einstein
Chandra
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ComparisonsComparisons
Einstein, within 240 kpc of center:Einstein, within 240 kpc of center:
1.7x101.7x101313 M M < M < M**(r) < 4.0x10(r) < 4.0x101313 M M
Chandra, within 32 kpc of center:Chandra, within 32 kpc of center:
MM**(r) (r) ≈≈ 2.7x10 2.7x101212 M M
MMBHBH ≈≈ 3x10 3x1099 M M
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Extra Slide 1:Extra Slide 1:The Einstein Observatory The Einstein Observatory
(HEAO-2)(HEAO-2)
Giacconi, R. et al. 1979, Ap.J. 230,540
http://library01.gsfc.nasa.gov/gdprojs/images/heao_b.jpg