Astr 5460 Fri., Feb. 21, 2003

Today: Reminders/Assignments

Longair, Ch. 3,4-Galaxies

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 still pending…

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.

Galaxy Masses

Virial Theorem: A relationship between gravitational potential energy and velocities for a dynamically relaxed and bound system.

T = ½ |U|, where T is the total kinetic energy and U is the potential energy.

So, for a cluster of stars or a cluster of galaxies, measuring T (by measuring velocities) can give U and therefore M.

Properties of Ellipticals

Light Distribution, 1^st Hubble’s law:

Much better is the de Vaucouleur’s (1948) r^1/4 law:

r_e is the radius within which half the total light has been emitted.

Properties of Ellipticals

Then the total luminosity of an elliptical galaxy can be parameterized:

I_e is a surface brightness, and b/a is the apparent axis ratio of the galaxy.

Van der Kruit (1989)

Will discuss models and mass distribution in context of galaxy clusters in section 4.3.2.

Fundamental Plane

Luminosities, surface brightness, central velocity distribution, (and others), are correlated, hence the term “fundamental plane.” Ellipticals populate a plane in parameter space. BIG area of research – very useful tool and helps us understand galaxies.

Faber & Jackson (1976) is a classic in this area (you might want to look up and read this one):

L ~ σ^x where x ≈4

So, get dispersion from spectrum, get luminosity, and with magnitude get distance!

Fundamental Plane

Dressler et al. (1987) include all three of the plane parameters and find a tight relationship:

Can also substitute in a new variable Dn (a diameter chosen to match a surface brightness) which incorporates L and Σ.

Can get distances then to various accuracies.

Triaxial Elliptical Galaxies

So, are ellipticals simple to understand dynamically? Not so clear. We’re seeing a 2D picture of a 3D object.

Elliptical galaxies rotate too slowly for this to account for the flattening observed. In other words, their ratios of rotational to random kinetic energy is too low.

Triaxial Elliptical Galaxies

Spiral/Lenticular Galaxies

Light Distribution

Two components, spheroid + disk

Spheroid is like a mini-elliptical right down to a de Vaucouleur’s law distribution

Exponential disk component:

Where h is the disk scale length (3 kpc for the Milky Way), so total L is then 4πh²I_o.

Spiral/Lenticular Galaxies

Analogous relationship to the ellipticals’ Faber-Jackson relation is the Tully-Fisher relation:

The width of 21cm H I line, corrected for inclination, correlates with luminosity.

Again, can make a spectral measurement plus a magnitude to estimate a distance.

Spiral/Lenticular Galaxies

Tully-Fisher relation:

Original exponent = 2.5, later steeper, 3.5, and even steeper for near-IR H-band. Very tight near-IR correlation so great distance indicator (recall the Hubble assignment!).

Spiral/Lenticular Galaxies

Tully-Fisher relation interpretation:

Assuming mass follows light, then

Then most mass within r ~ h and the maximum of the rotation curve goes as the Keplerian velocity at radius h. Then making the same Newton/Kepler argument:

Combine the equations to eliminate h and you get that mass goes as V_max⁴, and for spirals M/L is roughly constant in the disk, so expect L ~ V_max⁴

Trends along Hubble Sequence

Roberts & Haynes 1994:

Trends along Hubble Sequence

Roberts & Haynes 1994:

Masses from S0 to Scd roughly constant, then decrease, and M/L roughly the same (recall these are all primarily luminous massive galaxies – why?)

H I not significant in ellipticals (< 1 in 10000), but is in spirals (0.01 to 0.15 from Sa to Sm)

Total surface density decreases, H I surface density increases

Ellipticals are red, spirals are blue…

H II regions frequency increases monotonically along the sequence (Kennicutt et al. 1989)

Star formation rates appear key to these relations

Trends along Hubble Sequence

Chapter 4: Galaxy Clusters

Large Scale Distribution of Clusters

Galaxy Distribution in Clusters

Dark Matter in Clusters

Forms of Dark Matter

Cluster Catalogs

Palomar Sky Survey using 48 inch Schmidt telescope (1950s)

Abell (1958) cataloged “rich” clusters – a famous work and worth a look

Abell, Corwin, & Olowin (1989) did the same for the south using similar plates

All original work was by visual inspection

Pavo Cluster

Cluster Selection Criteria (Abell)

Richness Criterion: 50 members brighter than 2 magnitudes fainter than the third brightest member. Richness classes are defined by the number in this range:

Cluster Selection Criteria (Abell)

Compactness Criterion: Only galaxies within an angular radius of 1.7/z arcmin get counted. That corresponds to a physical radius of 1.5 h^-1 Mpc. The redshifts are (were) estimated based on the apparent magnitude of the 10^th brightest cluster member.

Cluster Selection Criteria (Abell)

Distance Criteria: Lower redshift limit (z = 0.02) to force clusters onto 1 plate. Upper limit due to mag limit of POSS, which matches z of about 0.2. Distance classes based on magnitude of 10^th member:

More on Abell Clusters

Complete Northern Sample:

1682 Clusters of richness 1-5, distance 1-6.

Counts in Table 4.2 follow:

This is consistent with a uniform distribution*.

Space Density of Abell Clusters richer than 1:

For uniform distribution, cluster centers would be 50 h^-1 Mpc apart, a factor of ten larger than that of mean galaxies.

Clusters of Clusters

Based on Abell’s Northern Sample:

Spatial 2-point correlation function (Bahcall):

Scale at which cluster-cluster correlation function has a value of unity is 5 times greater than that for the galaxy-galaxy correlation function.

Clusters of Clusters

Peebles (1980) schematic picture:

Cloud of galaxies is basic unit, scale of 50 h^-1 Mpc

About 25% of galaxies in these clouds

All Abell Clusters are members of clouds (with about 2 per cloud), and contain about 25% of the galaxies in a cloud are in Abell Clusters (superclusters occur when several AC combine)

Remaining 75% follow galaxy-galaxy function

In terms of larger structures, galaxies hug the walls of the voids, clusters at the intersections of the cell walls.

Galaxies within Clusters

A range of structural types (Abell)

Regular indicates cluster is circular, centrally concentrated (cf. Globular clusters), and has mostly elliptical and S0 galaxies. Can be very rich with > 1000 galaxies. Coma is regular.

All others are irregular (e.g., Virgo).

I don’t know why he didn’t just call them type 1 and type 2…!

Galaxies within Clusters

A range of structural types (Oemler 1974)

cD clusters have 1 or 2 central dominant cD galaxies, and no more than about 20% spirals, with a E: S0: S ratio of 3: 4: 2.

Spiral-rich clusters have E : S0 : S ratios more like 1: 2: 3 – about half spirals.

Remainder are spiral-poor clusters. No dominant cD galaxy and typical ratio of 1: 2: 1.

Galaxies within Clusters

Galaxies differ in these types (Abell)

In cD clusters galaxy distribution is very similar to star distribution in globular clusters.

Spiral-rich clusters and irregular clusters tend not to be symmetric or concentrated.

Spiral-poor clusters are intermediate cf. above.

In spiral rich clusters, all galaxy types similarly distributed and no mass segregation, but in cD and spiral-poor clusters, you don’t see spirals in the central regions where the most massive galaxies reside.

cD Galaxies

Kormendy (1982) distinguishes these from being merely giant ellipticals.

Extensive stellar envelope up to 100 kpc

Only in regions of enhanced galaxy density (a factor of 100 denser than the average)

Mutiple nuclei in 25-50% of cDs (a very rare thing)

Regular cD clusters are systems that have relaxed into dynamical equilibirum.


	Today: Reminders/Assignments
	Longair, Ch. 3,4-Galaxies



	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 still pending…


	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.


	Virial Theorem: A relationship between gravitational potential energy and velocities for a dynamically relaxed and bound system.
	T = ½ \|U\|, where T is the total kinetic energy and U is the potential energy.
	So, for a cluster of stars or a cluster of galaxies, measuring T (by measuring velocities) can give U and therefore M.


	Light Distribution, 1^st Hubble’s law:

	Much better is the de Vaucouleur’s (1948) r^1/4 law:


	r_e is the radius within which half the total light has been emitted.


	Then the total luminosity of an elliptical galaxy can be parameterized:



	I_e is a surface brightness, and b/a is the apparent axis ratio of the galaxy.
	Van der Kruit (1989)
	Will discuss models and mass distribution in context of galaxy clusters in section 4.3.2.


	Luminosities, surface brightness, central velocity distribution, (and others), are correlated, hence the term “fundamental plane.” Ellipticals populate a plane in parameter space. BIG area of research – very useful tool and helps us understand galaxies.
	Faber & Jackson (1976) is a classic in this area (you might want to look up and read this one):
	L ~ σ^x where x ≈4
	So, get dispersion from spectrum, get luminosity, and with magnitude get distance!


	Dressler et al. (1987) include all three of the plane parameters and find a tight relationship:



	Can also substitute in a new variable Dn (a diameter chosen to match a surface brightness) which incorporates L and Σ.
	Can get distances then to various accuracies.


	So, are ellipticals simple to understand dynamically? Not so clear. We’re seeing a 2D picture of a 3D object.

	Elliptical galaxies rotate too slowly for this to account for the flattening observed. In other words, their ratios of rotational to random kinetic energy is too low.


	Light Distribution
		Two components, spheroid + disk
		Spheroid is like a mini-elliptical right down to a de Vaucouleur’s law distribution
		Exponential disk component:


		Where h is the disk scale length (3 kpc for the Milky Way), so total L is then 4πh²I_o.


	Analogous relationship to the ellipticals’ Faber-Jackson relation is the Tully-Fisher relation:
		The width of 21cm H I line, corrected for inclination, correlates with luminosity.
		Again, can make a spectral measurement plus a magnitude to estimate a distance.


	Tully-Fisher relation:


	Original exponent = 2.5, later steeper, 3.5, and even steeper for near-IR H-band. Very tight near-IR correlation so great distance indicator (recall the Hubble assignment!).


	Tully-Fisher relation interpretation:
		Assuming mass follows light, then

	Then most mass within r ~ h and the maximum of the rotation curve goes as the Keplerian velocity at radius h. Then making the same Newton/Kepler argument:


	Combine the equations to eliminate h and you get that mass goes as V_max⁴, and for spirals M/L is roughly constant in the disk, so expect L ~ V_max⁴


	Roberts & Haynes 1994:
		Masses from S0 to Scd roughly constant, then decrease, and M/L roughly the same (recall these are all primarily luminous massive galaxies – why?)
		H I not significant in ellipticals (< 1 in 10000), but is in spirals (0.01 to 0.15 from Sa to Sm)
		Total surface density decreases, H I surface density increases
		Ellipticals are red, spirals are blue…
		H II regions frequency increases monotonically along the sequence (Kennicutt et al. 1989)
	Star formation rates appear key to these relations


	Large Scale Distribution of Clusters
	Galaxy Distribution in Clusters
	Dark Matter in Clusters
	Forms of Dark Matter


	Palomar Sky Survey using 48 inch Schmidt telescope (1950s)
	Abell (1958) cataloged “rich” clusters – a famous work and worth a look
	Abell, Corwin, & Olowin (1989) did the same for the south using similar plates
	All original work was by visual inspection


	Richness Criterion: 50 members brighter than 2 magnitudes fainter than the third brightest member. Richness classes are defined by the number in this range:


	Compactness Criterion: Only galaxies within an angular radius of 1.7/z arcmin get counted. That corresponds to a physical radius of 1.5 h^-1 Mpc. The redshifts are (were) estimated based on the apparent magnitude of the 10^th brightest cluster member.


	Distance Criteria: Lower redshift limit (z = 0.02) to force clusters onto 1 plate. Upper limit due to mag limit of POSS, which matches z of about 0.2. Distance classes based on magnitude of 10^th member:


	Complete Northern Sample:
		1682 Clusters of richness 1-5, distance 1-6.
		Counts in Table 4.2 follow:

		This is consistent with a uniform distribution*.
		Space Density of Abell Clusters richer than 1:

		For uniform distribution, cluster centers would be 50 h^-1 Mpc apart, a factor of ten larger than that of mean galaxies.


	Based on Abell’s Northern Sample:
		Spatial 2-point correlation function (Bahcall):


		Scale at which cluster-cluster correlation function has a value of unity is 5 times greater than that for the galaxy-galaxy correlation function.


	Peebles (1980) schematic picture:
		Cloud of galaxies is basic unit, scale of 50 h^-1 Mpc
		About 25% of galaxies in these clouds
		All Abell Clusters are members of clouds (with about 2 per cloud), and contain about 25% of the galaxies in a cloud are in Abell Clusters (superclusters occur when several AC combine)
		Remaining 75% follow galaxy-galaxy function
		In terms of larger structures, galaxies hug the walls of the voids, clusters at the intersections of the cell walls.


	A range of structural types (Abell)
		Regular indicates cluster is circular, centrally concentrated (cf. Globular clusters), and has mostly elliptical and S0 galaxies. Can be very rich with > 1000 galaxies. Coma is regular.
		All others are irregular (e.g., Virgo).
		I don’t know why he didn’t just call them type 1 and type 2…!


	A range of structural types (Oemler 1974)
		cD clusters have 1 or 2 central dominant cD galaxies, and no more than about 20% spirals, with a E: S0: S ratio of 3: 4: 2.
		Spiral-rich clusters have E : S0 : S ratios more like 1: 2: 3 – about half spirals.
		Remainder are spiral-poor clusters. No dominant cD galaxy and typical ratio of 1: 2: 1.


	Galaxies differ in these types (Abell)
		In cD clusters galaxy distribution is very similar to star distribution in globular clusters.
		Spiral-rich clusters and irregular clusters tend not to be symmetric or concentrated.
		Spiral-poor clusters are intermediate cf. above.
		In spiral rich clusters, all galaxy types similarly distributed and no mass segregation, but in cD and spiral-poor clusters, you don’t see spirals in the central regions where the most massive galaxies reside.


	Kormendy (1982) distinguishes these from being merely giant ellipticals.
		Extensive stellar envelope up to 100 kpc
		Only in regions of enhanced galaxy density (a factor of 100 denser than the average)
		Mutiple nuclei in 25-50% of cDs (a very rare thing)

	Regular cD clusters are systems that have relaxed into dynamical equilibirum.