Astr 5460 Wed., Feb. 19, 2003

Today: Reminders/Assignments

Longair, Ch. 3-Galaxies

Unless noted, all figs and eqs from Longair.

Reminders/Preliminaries

On Friday Astro-ph preprints:

http://xxx.lanl.gov/

Galaxy Spectra/Modeling Assignment

Reading Bennett et al. 2003 (MAP) paper

Debrief Spacegrant proposals?

History of the Hubble Constant:

http://cfa-www.harvard.edu/~huchra/

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.

Galaxy Masses

Virial Theorem: T = ½ |U|

You do need to worry about the conditions of the theorem in an astrophysical context. For instance, comparing crossing times with the relevant timescale. Text examples are the sun’s orbital period and galaxies in Coma.

Galaxy Masses

Galaxy Masses

Astronomical context more complex. Cannot in general get all the 3D velocities. In exgal context, uncertain cosmology can translate into uncertain spatial dimensions. Usually only have position on sky plus radial velocities. Must make assumptions about velocity distribution to apply virial theorem.

Galaxy Masses

Isotropic case: <v²> = 3<v_r²> (why?)

If velocity dispersion independent of masses:

T = 3/2 M <v_r²>, where M is total mass

More complex if the above is not true. Assuming spherical symmetry and an observed surface distribution, get a weighted mean separation R_cl:

Galaxy Masses

More complex if the above is not true. Assuming spherical symmetry and an observed surface distribution, get a weighted mean separation R_cl:

Works for elliptical galaxies and yields mass to light ratios of 10-20 in solar units.

Galaxy Masses

Rotation Curves of Spiral Galaxies:

This just comes from Newton, by equating gravity to centripetal acceleration. This produces Kepler’s third law, and Keplerian orbital velocities around point sources fall off as r^-1/2.

The Galactic Rotation Curve

Keplerian fall-off near center indicates compact mass at center

Flat curve throughout disk indicates much distributed mass

Lack of fall-off beyond visible “edge” indicates “dark matter”

Galaxy Rotation Curves

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 4πr²I_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


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



	Unless noted, all figs and eqs from Longair.


	On Friday Astro-ph preprints:
		http://xxx.lanl.gov/
	Galaxy Spectra/Modeling Assignment
	Reading Bennett et al. 2003 (MAP) paper
	Debrief Spacegrant proposals?
	History of the Hubble Constant:
	http://cfa-www.harvard.edu/~huchra/


	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.


	Virial Theorem: T = ½ \|U\|
	You do need to worry about the conditions of the theorem in an astrophysical context. For instance, comparing crossing times with the relevant timescale. Text examples are the sun’s orbital period and galaxies in Coma.


	Astronomical context more complex. Cannot in general get all the 3D velocities. In exgal context, uncertain cosmology can translate into uncertain spatial dimensions. Usually only have position on sky plus radial velocities. Must make assumptions about velocity distribution to apply virial theorem.


	Isotropic case: <v²> = 3<v_r²> (why?)

	If velocity dispersion independent of masses:
		T = 3/2 M <v_r²>, where M is total mass

	More complex if the above is not true. Assuming spherical symmetry and an observed surface distribution, get a weighted mean separation R_cl:


	More complex if the above is not true. Assuming spherical symmetry and an observed surface distribution, get a weighted mean separation R_cl:


	Works for elliptical galaxies and yields mass to light ratios of 10-20 in solar units.


	Rotation Curves of Spiral Galaxies:



	This just comes from Newton, by equating gravity to centripetal acceleration. This produces Kepler’s third law, and Keplerian orbital velocities around point sources fall off as r^-1/2.


	Keplerian fall-off near center indicates compact mass at center
	Flat curve throughout disk indicates much distributed mass
	Lack of fall-off beyond visible “edge” indicates “dark matter”


	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 4πr²I_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