Astr 5460 Fri., Feb. 28, 2003

Today: Reminders/Assignments

Longair, Chapter 4, Clusters

Unless noted, all figs and eqs from Longair.

Reminders/Preliminaries

Astro-ph preprints:

http://xxx.lanl.gov/

Galaxy Spectra/Modeling Assignment

Reading Bennett et al. 2003 (MAP) paper

WIRO possible on Saturday? (WEBDA)

Galaxy Spectra assignment

The textbook is rather weak when it comes to observational properties like spectra – as budding young observers you need to know more!

Find and download the galaxy spectra templates of Kinney et al. (1996) – and read the paper!

Find and download the spectral synthesis population models of Bruzual and Charlot.

“Fit” the elliptical template and one spiral galaxy.

Show some plots indicating how broad-band colors change with redshift assuming not evolution (up to z=2).

Write up your results like you would for publication with clarity, citations, etc.

King Profiles

More complex version based on Fokker-Planck equation by King (1966). Assumes no particles present with escape velocity+.

Structures of Regular Clusters

Bahcall (1977) describes distributions as truncated isothermal distributions:

Where f(r) is the projected distribution normalized to 1 at r=0, and C is a constant that makes N(r) = 0 at some radius. Results in steepening distribution in outer regions vs. pure isothermal soultion.

R_1/2 = 150-400 kpc (220 kpc for Coma)

Structures of Regular Clusters

In central regions King profiles work well:

For these distributions N₀ = 2R_cρ₀.

De Vaucouleur’s law can also work.

Problem is observations do not constrain things quite tightly enough.

Rich Cluster Summary

Dark Matter in Galaxy Clusters

How do we know it is there?

Dynamical estimates of cluster masses

X-ray emission/masses

Sunyaev-Zeldovich Effect

Gravitational lensing

What is the dark matter???

Baryons vs. non-Baryons

Dark Matter in Galaxy Clusters

Dynamical estimates of cluster masses

Virial Theorem as we have discussed, but…

Very few clusters exist that can be well done!

E.g, which are cluster members?

Must measure many velocities

Case of Coma

Regular rich cluster, looks like isothermal sphere

Crossing time arguments OK

Virial mass issue for Coma first by Zwicky (1937)

Surface distribution, velocities in next figure…

Dynamic Properties of Coma

Dynamic Masses for Coma

Merritt (1987) analysis:

Assuming constant M/L ratio, then mass is 1.79 x 10¹⁵h^-1 solar masses, and M/L is 350 h^-1 in solar units (think about that!).

Typical M/L for ellipticals is 15 in solar units.

Differ by a factor of 20

Why should the dark matter have the same distribution as the light?

Why should the velocities even be isotropic?

X-ray Masses for Clusters

UHURU in 1970s:

Rich clusters very bright in X-rays!

Bremsstrahlung emission of hot intercluster gas

Very hot gas requires large potential to hold

Can use to estimate the cluster mass

X-ray Masses for Clusters

Fabricant, Lecar, and Gorenstein:

Assume spherical symmetry (as usual!)

Assume hydrostatic equilibrium (again!):

Perfect gas law:

X-ray Masses for Clusters

Fabricant, Lecar, and Gorenstein:

For ionized gas, cosmic abundances, μ = 0.6

Differentiating the gas law, and inserting into the hydrostatic equation:

So, the mass distribution can be found if the variation of pressure and temperature with radius are known (measured).

X-ray Masses for Clusters

Fabricant, Lecar, and Gorenstein:

Bremsstrahlung spectral emissivity:

Gaunt factor can be approximated:

X-ray Masses for Clusters

Fabricant, Lecar, and Gorenstein:

Bremsstrahlung spectrum is roughly flat up to X-ray energies, above which it cuts off exponentially. Cut-off is related to temperature. The measurement is a projection onto 2D space. Integrating emissivity and converting to intensity:

X-ray Masses for Clusters

So, from the spectrum we can get the temperature as a function of radius, and from the intensity we can get the emissivity and hence the density.

Chandra is great for this type of observation:

http://chandra.harvard.edu/photo/2002/0146/

http://chandra.harvard.edu/photo/0087/

http://www1.msfc.nasa.gov/NEWSROOM/news/photos/2002/photos02-037.html

Cooling flows are one possible complication.

X-ray Masses for Clusters

Textbook shows old ROSAT picture, which sucks compared to new Chandra images.

Important result is that the dark matter does follow the galaxies.

Typical masses then are 5x10^14-15 solar masses, only 5% visible light, 10-30% hot gas, rest is DM.

Sunyaev-Zeldovich Effect

Hot gas can also be studied by looking for decrements in the Cosmic Background radiation, resulting from Compton scattering by hot electrons. Net energy is slightly increased. Not a symmetric effect – in Rayleigh-Jeans region there is decrement but in Wein region there is an excess.

First predicted by Sunyaev and Zeldovich in 1969, and has been observed.

Sunyaev-Zeldovich Effect

Compton scattering optical depth:

Resulting decrement in R-J spectral region is:

Predicted to be on order of 1 part in 10000 given observed hot intercluster gas.

S-Z Effect for Clusters

Sunyaev-Zeldovich Effect

Note that the S-Z effect + X-ray observations over-constrain the physical conditions. With some assumptions then, the physical sizes of the clouds can be determined. Comparison of angular sizes then can give distances measured independent of redshift, and thus used to make estimates of Hubble’s constant.

Gravitational Lensing by Clusters

Mass bends space and hence light paths (Einstein 1915; General relativity).

Angular deflection by point mass is:

Where p is the “collision parameter.”

What happens when p goes to zero?

Gravitational Lensing by Clusters

Gravitational Lensing by Clusters

Previous derivation assumes Euclidean geometry (which WMAP says is OK!). Still OK if the distances are angular diameter distances (chapter 5).

Expressing the result in physical terms:

So, what is the typical size for clusters?

Gravitational Lensing by Clusters

Gravitational Lensing by Clusters

OK, but clusters are not point sources.

See discussion on P. 96-97.

For our isothermal gas sphere can derive the result that:

Gravitational Lensing by Clusters

Forms of Dark Matter???

We’re certain it is present.

Some is baryonic.

More is non-baryonic.

Baryonic Dark Matter

Protons, Neutrons, electrons (include black holes here too).

Text example of bricks (yes bricks!).

Brown dwarfs and the like.

BB nucleosynthesis constrains baryons to less than 0.036 h^-2 of closure density.

Baryonic Dark Matter

Black holes constrained by lensing effects (or lack thereof).

MACHOs (Alcock et al. 1993):

Baryonic Dark Matter

MACHOs:

http://www.owlnet.rice.edu/~spac250/coco/spac.html

MACHOs are rather massive, around half a solar mass, and can contribute up to half of the dark halo mass.

White dwarfs???

Non-Baryonic Dark Matter

I’m no expert on this stuff (and in some sense NO ONE is). Particle physicists play in this area more than astronomers.

Leading candidates include

Axions. Cold, low mass, avoid strong CP violation.

Neutrinos. Hot, low mass (getting better constrained), lots of them. SN helps.

WIMPs. Gravitino, photino, etc.

Mirror Matter. May use in my next novel.


	Today: Reminders/Assignments
	Longair, Chapter 4, Clusters



	Unless noted, all figs and eqs from Longair.


	Astro-ph preprints:
		http://xxx.lanl.gov/

	Galaxy Spectra/Modeling Assignment

	Reading Bennett et al. 2003 (MAP) paper

	WIRO possible on Saturday? (WEBDA)


	The textbook is rather weak when it comes to observational properties like spectra – as budding young observers you need to know more!
	Find and download the galaxy spectra templates of Kinney et al. (1996) – and read the paper!
	Find and download the spectral synthesis population models of Bruzual and Charlot.
	“Fit” the elliptical template and one spiral galaxy.
	Show some plots indicating how broad-band colors change with redshift assuming not evolution (up to z=2).
	Write up your results like you would for publication with clarity, citations, etc.


	More complex version based on Fokker-Planck equation by King (1966). Assumes no particles present with escape velocity+.


	Bahcall (1977) describes distributions as truncated isothermal distributions:

	Where f(r) is the projected distribution normalized to 1 at r=0, and C is a constant that makes N(r) = 0 at some radius. Results in steepening distribution in outer regions vs. pure isothermal soultion.
	R_1/2 = 150-400 kpc (220 kpc for Coma)


	In central regions King profiles work well:




	For these distributions N₀ = 2R_cρ₀.
	De Vaucouleur’s law can also work.
	Problem is observations do not constrain things quite tightly enough.


	How do we know it is there?
		Dynamical estimates of cluster masses
		X-ray emission/masses
		Sunyaev-Zeldovich Effect
		Gravitational lensing

	What is the dark matter???
		Baryons vs. non-Baryons


Dynamical estimates of cluster masses
	Virial Theorem as we have discussed, but…
		Very few clusters exist that can be well done!
		E.g, which are cluster members?
		Must measure many velocities

	Case of Coma
		Regular rich cluster, looks like isothermal sphere
		Crossing time arguments OK
		Virial mass issue for Coma first by Zwicky (1937)
		Surface distribution, velocities in next figure…


	Merritt (1987) analysis:
		Assuming constant M/L ratio, then mass is 1.79 x 10¹⁵h^-1 solar masses, and M/L is 350 h^-1 in solar units (think about that!).
		Typical M/L for ellipticals is 15 in solar units.
		Differ by a factor of 20

	Why should the dark matter have the same distribution as the light?
	Why should the velocities even be isotropic?


	UHURU in 1970s:
		Rich clusters very bright in X-rays!
		Bremsstrahlung emission of hot intercluster gas
		Very hot gas requires large potential to hold
		Can use to estimate the cluster mass


	Fabricant, Lecar, and Gorenstein:
		Assume spherical symmetry (as usual!)
		Assume hydrostatic equilibrium (again!):



		Perfect gas law:


	Fabricant, Lecar, and Gorenstein:
		For ionized gas, cosmic abundances, μ = 0.6
		Differentiating the gas law, and inserting into the hydrostatic equation:




		So, the mass distribution can be found if the variation of pressure and temperature with radius are known (measured).


	Fabricant, Lecar, and Gorenstein:
		Bremsstrahlung spectral emissivity:



		Gaunt factor can be approximated:


	Fabricant, Lecar, and Gorenstein:
		Bremsstrahlung spectrum is roughly flat up to X-ray energies, above which it cuts off exponentially. Cut-off is related to temperature. The measurement is a projection onto 2D space. Integrating emissivity and converting to intensity:


	So, from the spectrum we can get the temperature as a function of radius, and from the intensity we can get the emissivity and hence the density.
	Chandra is great for this type of observation:
	http://chandra.harvard.edu/photo/2002/0146/
	http://chandra.harvard.edu/photo/0087/
	http://www1.msfc.nasa.gov/NEWSROOM/news/photos/2002/photos02-037.html
	Cooling flows are one possible complication.


	Textbook shows old ROSAT picture, which sucks compared to new Chandra images.
	Important result is that the dark matter does follow the galaxies.
	Typical masses then are 5x10^14-15 solar masses, only 5% visible light, 10-30% hot gas, rest is DM.


	Hot gas can also be studied by looking for decrements in the Cosmic Background radiation, resulting from Compton scattering by hot electrons. Net energy is slightly increased. Not a symmetric effect – in Rayleigh-Jeans region there is decrement but in Wein region there is an excess.

	First predicted by Sunyaev and Zeldovich in 1969, and has been observed.


	Compton scattering optical depth:


	Resulting decrement in R-J spectral region is:



	Predicted to be on order of 1 part in 10000 given observed hot intercluster gas.


	Note that the S-Z effect + X-ray observations over-constrain the physical conditions. With some assumptions then, the physical sizes of the clouds can be determined. Comparison of angular sizes then can give distances measured independent of redshift, and thus used to make estimates of Hubble’s constant.


	Mass bends space and hence light paths (Einstein 1915; General relativity).
	Angular deflection by point mass is:



	Where p is the “collision parameter.”
	What happens when p goes to zero?


	Previous derivation assumes Euclidean geometry (which WMAP says is OK!). Still OK if the distances are angular diameter distances (chapter 5).
	Expressing the result in physical terms:



	So, what is the typical size for clusters?


	OK, but clusters are not point sources.
	See discussion on P. 96-97.
	For our isothermal gas sphere can derive the result that:



	We’re certain it is present.

	Some is baryonic.

	More is non-baryonic.


	Protons, Neutrons, electrons (include black holes here too).

	Text example of bricks (yes bricks!).

	Brown dwarfs and the like.

	BB nucleosynthesis constrains baryons to less than 0.036 h^-2 of closure density.


	Black holes constrained by lensing effects (or lack thereof).
	MACHOs (Alcock et al. 1993):


	MACHOs:
	http://www.owlnet.rice.edu/~spac250/coco/spac.html
	MACHOs are rather massive, around half a solar mass, and can contribute up to half of the dark halo mass.
	White dwarfs???


	I’m no expert on this stuff (and in some sense NO ONE is). Particle physicists play in this area more than astronomers.
	Leading candidates include
		Axions. Cold, low mass, avoid strong CP violation.
		Neutrinos. Hot, low mass (getting better constrained), lots of them. SN helps.
		WIMPs. Gravitino, photino, etc.
		Mirror Matter. May use in my next novel.