Astr 5460 Wed., Nov. 3, 2004

This week: Large Scale Structure

(Ch. 11, Combes et al., parts)

Unless noted, all figs from Combes et al.

Already talked about galaxy clusters a lot, and some distance ladder topics will be covered in more detail in Mike Pierce’s class next semester.

Some other issues

Discuss homework

Not as great as expected – just busier now? Can turn in problem 6 next week for extra credit – please write up the process!

Discuss Observing Project (briefly!)

Mid-term exam:

2 hours, take-home, on your honor, only calculator and constants/conversions

Some “basic knowledge” questions in addition to more analytic problems. Know terms, definitions, other intangible issues.

Large Scale Structure

Galaxy structure – how is the mass in the universe distributed (and recall gas can be important, too!)? Homogeneous? On what scale?

Text is a bit old (fine for history), but the best newest information will come from SDSS and 2dF. CHECK IT OUT!

Background radiation also of interest (discrete sources vs. true diffuse background).

Background “SED”

CMBR of special interest (as we will get to) and X-ray is a recent development (CXO).

Distance Scales

Parallax and Trigonometric Methods:

Distance Scales

Parallax and Trigonometric Methods

Distance Scales

Parallax and Trigonometric Methods

tan λ = Vt/Vr = μd/Vr

So then d = Vr tanλ/4.74μ [pc]

Where velocities are in km/s and proper motion μ is in arcseconds per year.

Should be something you can derive (it would be a good problem to work in your free time)

Distance Scales

Parallax and Trigonometric Methods – once Hyades distance known, can use main-sequence cluster fitting.

Distance Scales

Parallax and Trigonometric Methods – once Hyades distance known, can use main-sequence cluster fitting.

Then employ the distance modulus, basically a vertical shift on the CMD diagram, (m-M = 5 logd(pc) -5)

Distance Scales

Cepheids and Standard Candles

Various stars in the instability strip of the H-R diagram with Period-luminosity relations.

Distance Scales

Cepheids and Standard Candles

Various stars in the instability strip of the H-R diagram with Period-luminosity relations.

Figures for Cepheids from Horizons (Michael Seeds)

Distance Scales

The Tully-Fischer Relation

L = kΔV^α – where the index is ~ 4.

Better in the near-IR, as we discussed before, less star formation visible at H-band, so less distortion.

The velocity dispersion comes from either 21 cm or stellar optical absorption lines.

Distance Scales

This is where Combes et al. discusses the Hubble Law:

Vr = H_od where Ho is in km/s/Mpc

Hubble constant Ho is independent of direction in the sky (that’s important, think about it!)

Also recall Ho = h 100 km/s/Mpc

Distance Scales

The Tully-Fischer Relation

Distance Scales

Malmquist Bias:

Distance Scales

The Sunyaev-Zeldovich Effect:

Look toward hot intercluster medium in galaxy clusters…Thomson scattering can affect the CMBR seen through such a medium

Optical thickness is τ_T = ∫σ_Tn_e dl

Cluster properties can indeed “hamper” the CMBR

The CMBR is heated by the ICM, altering the frequency: Δν/ν = 4kT_e/m_ec², leading to:

ΔT/T = - ∫ 2kT_e/m_ec²dτ_T (hν << kT_e)

At low frequencies, REDUCES the temperature of the CMBR.

Can get distance estimates from S-Z effect.

Distance Scales

The Sunyaev-Zeldovich Effect

Measure the X-ray flux, the temperature fluctuations, and the temperature, and can get distance, and hence Ho.

Compton effect here

Distance Scales

Surface-Brightness Fluctuations

Surface brightness does not vary with distance – why?

How about, say, the number of stars per pixel as a function of distance? That does change, and the statistical uncertainty does vary with distance.

Distance Scales

Surface-Brightness Fluctuations

The “Third Dimension”

Galaxy distributions seen in images are 2-d projections on the sky.

Need distances…easiest way is to use the Hubble flow and redshifts, either photometric or spectra (best).

Reminder – SDSS and 2dF rule here now.

Huchra and Gellar’s “Z-machine” for the CfA survey as recounted in “Lonely Hearts of the Cosmos” by Dennis Overbye – Great!

The “Third Dimension”

Look at distance “slices” here.

The “Third Dimension”

The famous “man” in the distribution. Shows walls, voids, etc.

Why elongations, “finger of god” distributions pointing at “us?”

Statistical Methods

Correlation functions

How do you measure, quantitatively, the tendency of galaxies to cluster?

Following is specifically from Longair, but also present in Combes et al. with a different presentation.

Large-scale Distribution of Galaxies

Large-scale Distribution of Galaxies

On small scales, the universe is very inhomogeneous (stars, galaxies). What about larger scales?

Angular two-point correlation function w(θ):

Large-scale Distribution of Galaxies

This function w(θ) describes apparent clustering on the sky down to some magnitude limit.

More physically meaningful is the spatial two-point correlation function ξ(r) which describes clustering in 3-D about a galaxy:

Large-scale Distribution of Galaxies

w(θ) isn’t so hard to measure from various surveys – just need positions.

ξ(r) is harder – must have redshifts to do properly. Can make some assumptions however.

Large-scale Distribution of Galaxies

Large Scale Motions

Milky Way motion vs. CMBR, a “dipole” with velocity of about 1000 km/s (from COBE)

Large Scale Motions

“The Great Attractor”


	This week: Large Scale Structure

	(Ch. 11, Combes et al., parts)

	Unless noted, all figs from Combes et al.
	Already talked about galaxy clusters a lot, and some distance ladder topics will be covered in more detail in Mike Pierce’s class next semester.


	Discuss homework
		Not as great as expected – just busier now? Can turn in problem 6 next week for extra credit – please write up the process!
	Discuss Observing Project (briefly!)
	Mid-term exam:
		2 hours, take-home, on your honor, only calculator and constants/conversions
		Some “basic knowledge” questions in addition to more analytic problems. Know terms, definitions, other intangible issues.


	Galaxy structure – how is the mass in the universe distributed (and recall gas can be important, too!)? Homogeneous? On what scale?
	Text is a bit old (fine for history), but the best newest information will come from SDSS and 2dF. CHECK IT OUT!
	Background radiation also of interest (discrete sources vs. true diffuse background).


	CMBR of special interest (as we will get to) and X-ray is a recent development (CXO).


	Parallax and Trigonometric Methods
		tan λ = Vt/Vr = μd/Vr
		So then d = Vr tanλ/4.74μ [pc]
		Where velocities are in km/s and proper motion μ is in arcseconds per year.
		Should be something you can derive (it would be a good problem to work in your free time)


	Parallax and Trigonometric Methods – once Hyades distance known, can use main-sequence cluster fitting.


	Parallax and Trigonometric Methods – once Hyades distance known, can use main-sequence cluster fitting.
	Then employ the distance modulus, basically a vertical shift on the CMD diagram, (m-M = 5 logd(pc) -5)


	Cepheids and Standard Candles
		Various stars in the instability strip of the H-R diagram with Period-luminosity relations.


	Cepheids and Standard Candles
		Various stars in the instability strip of the H-R diagram with Period-luminosity relations.
		Figures for Cepheids from Horizons (Michael Seeds)


	The Tully-Fischer Relation
	L = kΔV^α – where the index is ~ 4.
	Better in the near-IR, as we discussed before, less star formation visible at H-band, so less distortion.
	The velocity dispersion comes from either 21 cm or stellar optical absorption lines.


	This is where Combes et al. discusses the Hubble Law:
		Vr = H_od where Ho is in km/s/Mpc
		Hubble constant Ho is independent of direction in the sky (that’s important, think about it!)
		Also recall Ho = h 100 km/s/Mpc


	The Sunyaev-Zeldovich Effect:
		Look toward hot intercluster medium in galaxy clusters…Thomson scattering can affect the CMBR seen through such a medium
		Optical thickness is τ_T = ∫σ_Tn_e dl
		Cluster properties can indeed “hamper” the CMBR
		The CMBR is heated by the ICM, altering the frequency: Δν/ν = 4kT_e/m_ec², leading to:
		ΔT/T = - ∫ 2kT_e/m_ec²dτ_T (hν << kT_e)
		At low frequencies, REDUCES the temperature of the CMBR.
		Can get distance estimates from S-Z effect.


	The Sunyaev-Zeldovich Effect
	Measure the X-ray flux, the temperature fluctuations, and the temperature, and can get distance, and hence Ho.
	Compton effect here


	Surface-Brightness Fluctuations
	Surface brightness does not vary with distance – why?
	How about, say, the number of stars per pixel as a function of distance? That does change, and the statistical uncertainty does vary with distance.


	Galaxy distributions seen in images are 2-d projections on the sky.
	Need distances…easiest way is to use the Hubble flow and redshifts, either photometric or spectra (best).
	Reminder – SDSS and 2dF rule here now.
	Huchra and Gellar’s “Z-machine” for the CfA survey as recounted in “Lonely Hearts of the Cosmos” by Dennis Overbye – Great!


	The famous “man” in the distribution. Shows walls, voids, etc.
	Why elongations, “finger of god” distributions pointing at “us?”


	Correlation functions
		How do you measure, quantitatively, the tendency of galaxies to cluster?
		Following is specifically from Longair, but also present in Combes et al. with a different presentation.


	On small scales, the universe is very inhomogeneous (stars, galaxies). What about larger scales?
	Angular two-point correlation function w(θ):


	This function w(θ) describes apparent clustering on the sky down to some magnitude limit.
	More physically meaningful is the spatial two-point correlation function ξ(r) which describes clustering in 3-D about a galaxy:


	w(θ) isn’t so hard to measure from various surveys – just need positions.
	ξ(r) is harder – must have redshifts to do properly. Can make some assumptions however.


	Milky Way motion vs. CMBR, a “dipole” with velocity of about 1000 km/s (from COBE)