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

22

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

33

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

44

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

55

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

66

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

77

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

88

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.

99

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)

1010

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

1111

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

1212

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)

1313

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

1515

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