Astr 1050     Fri., Nov. 22, 2002

   Today: Astronomy Articles

                 Review Homework #10

                 Finish Chapter 15, Cosmology

A great webpage tutorial on cosmology. Recommended! http://www.astro.ucla.edu/~wright/cosmolog.htm

Homework #10

Q 1: If we discover a type 1a supernova in a distant galaxy that at its brightest has an apparent magnitude of 17, how far away is the galaxy? (Assume the supernova has an absolute magnitude of -19.)

D = 10^(m-M+5)/5, so 160 Mpc

Q 2: If a galaxy has a radial velocity (redshift) of 5000 km/s, how far away is it? Assume a Hubble Constant of 70 km/s/Mpc.

V = HxD, so D=v/H, or 5000/70 Mpc = 71 Mpc

Q 3: A quasar is observed to have a redshift z=0.5. What recessional velocity does this correspond to?

v/c = ((z+1)²-1)/((z+1)² +1) = 1.25/3.25 = 38%

Q 4: If we take a spectrum of a quasar and see that the Lyman alpha line, observed in the laboratory at a wavelength of 121.6 nm, appears at a wavelength of 425.6 nm, what is the redshift of this quasar?

Z = Δλ/λ = (425.6 -121.6)/121.6 = (425.6/121.6) – 1 = 3.5 – 1 = 2.5

Q 5: Quasars can be 1000 times more luminous than an entire galaxy. The absolute magnitude of such a luminous quasar would be about M = -28.5. If the black hole in the center of our galaxy became a quasar, and obscuring gas and dust did not dim it, what would the apparent magnitude of the galactic core be? Think about the answer and what that would look like in the sky.

m – M = -5 +5logd, so m = -5 +5log8.5k + M = -13.9 (about like the full moon!)

Q 6: If Galaxy A is four times more distant than Galaxy B, then according to the Hubble Law, the recessional velocity of Galaxy A is larger than that of Galaxy B by what factor?

V = HxD which is a linear relationship, so V is 4 times larger.

First prediction from Big Bang model:
Cosmic Background Radiation

Look out (and back in time) to place where H became neutral

Beyond that the high density ionized H forms an opaque “wall”

Originally 3000 K blackbody radiation

The material that emitted it was moving away from us at extreme speed

That v produces extreme redshift (z=1000), so photons all appear much redder, so T appears cooler

With red shift, get 2.7 K Planck blackbody

Should be same in all directions

Cosmic Microwave Background Observations

First detected by Wilson and Penzias in 1960’s

Serendipitous detection – thought is was noise in their radio telescope but couldn’t find cause. Only later heard of theoretical predictions

Best spectrum observed by COBE satellite

Red curve is theoretical prediction

43 Observed data points plotted there
error bars so small they are covered by curve.

it is covered by curve.

Isotropy also measured by COBE

T varies by less than 0.01 K across sky

Small “dipole” anisotropy seen

Blue = 2.721 Red = 2.729

Caused by motion of Milky Way falling towards the Virgo supercluster.

Second prediction from Big Bang Model:
Abundance of the light elements

Big Bang Nucleosynthesis

T, r both high enough at start to fuse protons into heavier elements

T, r both dropping quickly so only have time enough to fuse a certain amount.

Simple models of expansion predict 25% abundance He

25% is the amount of He observed

Abundance of ²H, ³He, ⁷Li depends on r_{normal matter}

Suggests r_{normal matter} is only 5% of r_critical

But we need to also consider “dark matter” and its gravity

Main Tests of the Big Bang

Hubble Expansion (not a test really, inspiration)

Cosmic Microwave Background

Abundance of light elements

Refinements of Big Bang Still Being Tested

Possible “cosmological constant”

Very early history:

particle/antiparticle asymmetry

“inflation” -- Details of very early very rapid expansion

small r, T fluctuations which lead to galaxies

Will the expansion stop?

Is there enough gravity (enough mass) to stop expansion?

Consider an simple model as first step (full model gives same answer)

Treat universe as having center

Assume only Newtonian Gravity applies

Does a given shell of matter have escape velocity? Is v > v_esc ?

General Relativistic Description

What we call “gravity” is really bending of our 3-d space in some higher dimension.

Bending, or “curvature of space” is caused by presence of mass.

More mass implies more bending.

If bending is enough, space closes back on itself,
just like 2-d surface of earth is bent enough in 3rd dimension
to close back on itself.

Mass and the Curvature of Space

First consider case with little mass (little curvature)

Ant (in 2-d world) can move in straight line from point A to point B.

Add mass to create curvature in extra dimension invisible to the ant.

   In trying to go from point A to
   point B, fastest path is curved one
   which avoids the deepest part of the

   well.

Ant will be delayed by the extra

motion in the hidden third

dimension.

Both effects verified in sending photons past the sun:

Bending of starlight during solar eclipse

Delay in signals from spacecraft on
opposite side of the sun

How to test the amount of curvature

Measure the circumference of a circle as you get farther and farther from the origin:

Does it go up as expected from (2 p R)?

It goes up slower in a positively curved world.

How high is the density?

Not nearly enough normal matter to provide critical density

We keep seeing effects of gravity from “dark matter”

Higher rotation speeds in our own galaxy

Higher relative velocities of galaxies in clusters

Rate at which matter clumps together to form galaxy clusters

Gravitational lensing from galaxies, clusters

May be 10 to 100 times as much “dark matter” as visible matter

What might make up the “dark matter”? Possibilities include

MACHOs (massive compact halo objects) http://www.astro.ucla.edu/~wright/microlensing.html

but ²H, Li, Be abundance suggest no more than 5% can be “baryonic”

WIMPs (weakly interacting massive particles) predicted by some GUT’s

Mass of neutrinos

Mass equivalent of “cosmological constant” energy

Refining the Big Bang

Flatness Problem – why so close to a critical universe?

Horizon Problem – why is background all same T?

SOLVED BY AN “INFLATIONARY UNIVERSE”

“Grand Unified Theories” of combined Gravity/Weak/Electric/Nuclear forces predict very rapid expansion at very early time: “inflation”

When inflation ends, all matter moving away with v=v_escape (flat universe – curvature forced to zero)

Also solves horizon problem – everything was in causal contact

Implications of Slowing Expansion Rate

Our calculation of age T=1/H_o = 13.6 billion years assumed constant rate

Gravity should slow the expansion rate over time

If density is high enough, expansion should turn around

If expansion was faster in past, it took less time to get to present size

For “Flat” universe T = 2/3 * (1/H_o) = 9.3 billion years

contradiction with other ages if T is too small

Is the expansion rate slowing?

Look “into the past” to see if expansion rate was faster in early history.

To “look into the past” look very far away:

Find “H_o” for very distant objects, compare that to “H_o” for closer objects

Remember – we found H_o by plotting velocity (v_r) vs. distance

We found velocity v_r from the red shift (z)

We found distance by measuring apparent magnitude (m_v)
of known brightness objects

We can test for changing H_o by measuring m_v vs. z

Measuring deceleration using supernovae

Plot of m_v vs. z is really a plot of distance vs. velocity

If faint (Þdistant Þearlier) objects show slightly higher z
than expected from extrapolation based on nearby (present day) objects,
then expansion rate was faster in the past and has been decelerating

Surprise results from 1998 indeed do suggest accelerating expansion

May be due to “cosmological constant” proposed by Einstein

AKA “Dark energy” or “Quintessence”

“Cosmological constant”

General Relativity allows a repulsive term

Einstein proposed it to allow “steady state” universe

He decided it wasn’t needed after Hubble Law discovered

Is the acceleration right?

Could it be observational effect – dust dims distant supernova?

Could it be evolution effect – supernova were fainter in the past?

So far the results seem to stand up

Still being determined: 1) density, 2) cosmological constant

With cosmological constant included, can have a “flat universe” even with acceleration.

Given “repulsion” need to use relativistic “geometrical” definition of flatness, not the escape argument one given earlier.

Energy (and equivalent mass) from cosmological constant may provide density needed to produce flat universe.

Tests using
the Origin of Structure

Original “clumpiness” is a “blown up” version of the small fluctuations in density present early in the big bang and seen in the background radiation.

We can compare the structure implied to that expected from the “Grand Unification Theories”

Rate at which clumpiness grows depends on density of universe

Amount of clumpiness seems consistent with “flat universe” density

That means you need dark matter to make clumpiness grow fast enough

Acoustic Peaks in Background

Chapter 13: Galaxies

Family of Galaxies

Classification

Properties of Galaxies

Distance; The Hubble Law

Size and Luminosity

Mass (including Dark Matter)

Evolution of Galaxies

Clusters

Mergers

Chapter 11: Neutron Stars & Black Holes

Neutron Stars

Pulsars (Radio pulsation, lighthouse model)

Properties (size, density, composition)

Black holes

Schwarzschild Radius

Properties

Detection (Gravity, X-rays from Disks)

Review Chapter 12: Milky Way

The discovery of the Galaxy

Variable stars as distance indicators

Globular clusters

The size and overall structure of the Galaxy

21 cm Hydrogen emission

Motions in the galaxy

The Halo

The Disk population

Spiral Arms

The Nuclear Bulge

The Rotation curve and the Galaxy’s mass

The origin of the galaxy

The Galactic Center

Chapter 14: Galaxies with Active Nuclei

Discovery of Active Galactic Nuclei (AGN)

Seyfert Galaxies and Radio Sources

The Unified Model

Black Holes in Galaxies, disks, orientation, +

Quasars

Distances and Relativistic Redshifts

Quasars as extreme AGN

Evolution of Quasars/Galaxies

Gravitational Lensing

Chapter 15: Cosmology

The Hubble Expansion – review+

Olber’s paradox

The Big Bang

Refining the Big Bang

Details of the Big Bang

General Relativity

Cosmological Constant

Origin of Structure

Exam #3 on Mon., Nov. 25

20 multiple choice (3 pts each), 10 true/false (2 pts each), 2 essay (10 pts each).

A larger fraction of fact-based questions.

Two Essay questions drawn from these topics:

Falling into a Black Hole

The Milky Way galaxy

The Hubble Law

The Cosmic Microwave Background Radiation

The Unified Model of Active Galaxies

The Age of the Universe

Exam #3 on Mon., Nov. 25

Sample questions.

True/False:

The radio lobes of radio galaxies arise from 21 cm radiation.

The Milky Way galaxy is only a small member of the Local Group.

Neutron stars can be found in supernova remnants.

The Magellanic Clouds are irregular galaxies.

The Cosmic Microwave Background Radiation is blackbody radiation.

The more luminous a Cepheid variable star, the shorter its period.

Elliptical galaxies evolve into spiral galaxies.

Exam #3 on Mon., Nov. 25

Sample questions.

Multiple choice:

Which sequence below gives objects in order of decreasing size?

A. Red Giant -> the Sun -> the moon -> white dwarf

B. The Sun -> the Earth -> neutron star -> 3 solar mass black hole

C. Red Dwarf -> white dwarf -> the Sun -> neutron star

D. Red Giant -> white dwarf -> red dwarf -> neutron star

The assumption of Isotropy states that

A. The universe looks the same at all epochs.

B. The universe looks the same from all locations over large enough distances.

C. The universe looks the same in all locations over large enough distances.

D. All of the above.

E. None of the above.

Exam #3 on Mon., Nov. 25

Sample questions.

Multiple choice:

In order to determine the age of the universe, we require

A. The universe to be flat.

B. The amount of dark matter to be determined.

C. The redshifts of galaxies in the Local Group to be measured.

D. An accuration temperature of the background radiation.

E. The Hubble Constant and the density of the universe to be determined.

The center of our galaxy lies in the direction of the constellation of

A. Ursa Minor.

B. Ursa Major.

C. Sagittarius.

D. Orion.

E. Andromeda.


	Today: Astronomy Articles
	Review Homework #10
	Finish Chapter 15, Cosmology


	A great webpage tutorial on cosmology. Recommended! http://www.astro.ucla.edu/~wright/cosmolog.htm


	Q 1: If we discover a type 1a supernova in a distant galaxy that at its brightest has an apparent magnitude of 17, how far away is the galaxy? (Assume the supernova has an absolute magnitude of -19.)
		D = 10^(m-M+5)/5, so 160 Mpc
	Q 2: If a galaxy has a radial velocity (redshift) of 5000 km/s, how far away is it? Assume a Hubble Constant of 70 km/s/Mpc.
		V = HxD, so D=v/H, or 5000/70 Mpc = 71 Mpc
	Q 3: A quasar is observed to have a redshift z=0.5. What recessional velocity does this correspond to?
		v/c = ((z+1)²-1)/((z+1)² +1) = 1.25/3.25 = 38%
	Q 4: If we take a spectrum of a quasar and see that the Lyman alpha line, observed in the laboratory at a wavelength of 121.6 nm, appears at a wavelength of 425.6 nm, what is the redshift of this quasar?
		Z = Δλ/λ = (425.6 -121.6)/121.6 = (425.6/121.6) – 1 = 3.5 – 1 = 2.5
	Q 5: Quasars can be 1000 times more luminous than an entire galaxy. The absolute magnitude of such a luminous quasar would be about M = -28.5. If the black hole in the center of our galaxy became a quasar, and obscuring gas and dust did not dim it, what would the apparent magnitude of the galactic core be? Think about the answer and what that would look like in the sky.
		m – M = -5 +5logd, so m = -5 +5log8.5k + M = -13.9 (about like the full moon!)
	Q 6: If Galaxy A is four times more distant than Galaxy B, then according to the Hubble Law, the recessional velocity of Galaxy A is larger than that of Galaxy B by what factor?
		V = HxD which is a linear relationship, so V is 4 times larger.


	Look out (and back in time) to place where H became neutral
	Beyond that the high density ionized H forms an opaque “wall”
	Originally 3000 K blackbody radiation
	The material that emitted it was moving away from us at extreme speed
	That v produces extreme redshift (z=1000), so photons all appear much redder, so T appears cooler
	With red shift, get 2.7 K Planck blackbody
	Should be same in all directions


First detected by Wilson and Penzias in 1960’s
	Serendipitous detection – thought is was noise in their radio telescope but couldn’t find cause. Only later heard of theoretical predictions

Best spectrum observed by COBE satellite
	Red curve is theoretical prediction
	43 Observed data points plotted there error bars so small they are covered by curve.
	it is covered by curve.

Isotropy also measured by COBE
	T varies by less than 0.01 K across sky
	Small “dipole” anisotropy seen
		Blue = 2.721 Red = 2.729
		Caused by motion of Milky Way falling towards the Virgo supercluster.


Big Bang Nucleosynthesis
	T, r both high enough at start to fuse protons into heavier elements
	T, r both dropping quickly so only have time enough to fuse a certain amount.

	Simple models of expansion predict 25% abundance He
		25% is the amount of He observed
	Abundance of ²H, ³He, ⁷Li depends on r_{normal matter}
		Suggests r_{normal matter} is only 5% of r_critical
		But we need to also consider “dark matter” and its gravity


Hubble Expansion (not a test really, inspiration)
Cosmic Microwave Background
Abundance of light elements Refinements of Big Bang Still Being Tested
	Possible “cosmological constant”
	Very early history:
		particle/antiparticle asymmetry
		“inflation” -- Details of very early very rapid expansion
		small r, T fluctuations which lead to galaxies


	Is there enough gravity (enough mass) to stop expansion?
	Consider an simple model as first step (full model gives same answer)
		Treat universe as having center
		Assume only Newtonian Gravity applies
		Does a given shell of matter have escape velocity? Is v > v_esc ?


	What we call “gravity” is really bending of our 3-d space in some higher dimension.
	Bending, or “curvature of space” is caused by presence of mass.
	More mass implies more bending.

	If bending is enough, space closes back on itself, just like 2-d surface of earth is bent enough in 3rd dimension to close back on itself.


	First consider case with little mass (little curvature)

	Ant (in 2-d world) can move in straight line from point A to point B.

	Add mass to create curvature in extra dimension invisible to the ant.

	In trying to go from point A to point B, fastest path is curved one which avoids the deepest part of the
	well.

	Ant will be delayed by the extra
	motion in the hidden third
	dimension.

	Both effects verified in sending photons past the sun:
	Bending of starlight during solar eclipse
	Delay in signals from spacecraft on opposite side of the sun


	Measure the circumference of a circle as you get farther and farther from the origin:

	Does it go up as expected from (2 p R)?

	It goes up slower in a positively curved world.


Not nearly enough normal matter to provide critical density
We keep seeing effects of gravity from “dark matter”
	Higher rotation speeds in our own galaxy
	Higher relative velocities of galaxies in clusters
	Rate at which matter clumps together to form galaxy clusters
	Gravitational lensing from galaxies, clusters
	May be 10 to 100 times as much “dark matter” as visible matter


What might make up the “dark matter”? Possibilities include
	MACHOs (massive compact halo objects) http://www.astro.ucla.edu/~wright/microlensing.html
		but ²H, Li, Be abundance suggest no more than 5% can be “baryonic”
	WIMPs (weakly interacting massive particles) predicted by some GUT’s
	Mass of neutrinos
	Mass equivalent of “cosmological constant” energy


	Flatness Problem – why so close to a critical universe?
	Horizon Problem – why is background all same T?

	SOLVED BY AN “INFLATIONARY UNIVERSE”
		“Grand Unified Theories” of combined Gravity/Weak/Electric/Nuclear forces predict very rapid expansion at very early time: “inflation”
		When inflation ends, all matter moving away with v=v_escape (flat universe – curvature forced to zero)
		Also solves horizon problem – everything was in causal contact


	Our calculation of age T=1/H_o = 13.6 billion years assumed constant rate
	Gravity should slow the expansion rate over time
		If density is high enough, expansion should turn around











	If expansion was faster in past, it took less time to get to present size
	For “Flat” universe T = 2/3 * (1/H_o) = 9.3 billion years
		contradiction with other ages if T is too small


	Look “into the past” to see if expansion rate was faster in early history.

	To “look into the past” look very far away:
		Find “H_o” for very distant objects, compare that to “H_o” for closer objects

	Remember – we found H_o by plotting velocity (v_r) vs. distance
		We found velocity v_r from the red shift (z)
		We found distance by measuring apparent magnitude (m_v) of known brightness objects

		We can test for changing H_o by measuring m_v vs. z


	Plot of m_v vs. z is really a plot of distance vs. velocity
	If faint (Þdistant Þearlier) objects show slightly higher z than expected from extrapolation based on nearby (present day) objects, then expansion rate was faster in the past and has been decelerating









	Surprise results from 1998 indeed do suggest accelerating expansion
	May be due to “cosmological constant” proposed by Einstein
		AKA “Dark energy” or “Quintessence”


	General Relativity allows a repulsive term
		Einstein proposed it to allow “steady state” universe
		He decided it wasn’t needed after Hubble Law discovered

	Is the acceleration right?
		Could it be observational effect – dust dims distant supernova?
		Could it be evolution effect – supernova were fainter in the past?
		So far the results seem to stand up

	Still being determined: 1) density, 2) cosmological constant
		With cosmological constant included, can have a “flat universe” even with acceleration.
		Given “repulsion” need to use relativistic “geometrical” definition of flatness, not the escape argument one given earlier.
		Energy (and equivalent mass) from cosmological constant may provide density needed to produce flat universe.


	Original “clumpiness” is a “blown up” version of the small fluctuations in density present early in the big bang and seen in the background radiation.
		We can compare the structure implied to that expected from the “Grand Unification Theories”
	Rate at which clumpiness grows depends on density of universe
		Amount of clumpiness seems consistent with “flat universe” density
		That means you need dark matter to make clumpiness grow fast enough


	Family of Galaxies
		Classification
	Properties of Galaxies
		Distance; The Hubble Law
		Size and Luminosity
		Mass (including Dark Matter)
	Evolution of Galaxies
		Clusters
		Mergers


	Neutron Stars
		Pulsars (Radio pulsation, lighthouse model)
		Properties (size, density, composition)

	Black holes
		Schwarzschild Radius
		Properties
		Detection (Gravity, X-rays from Disks)


The discovery of the Galaxy
	Variable stars as distance indicators
	Globular clusters
The size and overall structure of the Galaxy
21 cm Hydrogen emission
Motions in the galaxy
	The Halo
	The Disk population
		Spiral Arms
	The Nuclear Bulge
	The Rotation curve and the Galaxy’s mass
The origin of the galaxy
The Galactic Center


	Discovery of Active Galactic Nuclei (AGN)
		Seyfert Galaxies and Radio Sources
	The Unified Model
		Black Holes in Galaxies, disks, orientation, +
	Quasars
		Distances and Relativistic Redshifts
		Quasars as extreme AGN
		Evolution of Quasars/Galaxies
		Gravitational Lensing


	The Hubble Expansion – review+
	Olber’s paradox
	The Big Bang
	Refining the Big Bang
	Details of the Big Bang
	General Relativity
	Cosmological Constant
	Origin of Structure


	20 multiple choice (3 pts each), 10 true/false (2 pts each), 2 essay (10 pts each).
	A larger fraction of fact-based questions.
	Two Essay questions drawn from these topics:
		Falling into a Black Hole
		The Milky Way galaxy
		The Hubble Law
		The Cosmic Microwave Background Radiation
		The Unified Model of Active Galaxies
		The Age of the Universe


	Sample questions.
	True/False:
		The radio lobes of radio galaxies arise from 21 cm radiation.
		The Milky Way galaxy is only a small member of the Local Group.
		Neutron stars can be found in supernova remnants.
		The Magellanic Clouds are irregular galaxies.
		The Cosmic Microwave Background Radiation is blackbody radiation.
		The more luminous a Cepheid variable star, the shorter its period.
		Elliptical galaxies evolve into spiral galaxies.


Sample questions.
Multiple choice:
	Which sequence below gives objects in order of decreasing size?
		A. Red Giant -> the Sun -> the moon -> white dwarf
		B. The Sun -> the Earth -> neutron star -> 3 solar mass black hole
		C. Red Dwarf -> white dwarf -> the Sun -> neutron star
		D. Red Giant -> white dwarf -> red dwarf -> neutron star

	The assumption of Isotropy states that
		A. The universe looks the same at all epochs.
		B. The universe looks the same from all locations over large enough distances.
		C. The universe looks the same in all locations over large enough distances.
		D. All of the above.
		E. None of the above.


Sample questions.
Multiple choice:
	In order to determine the age of the universe, we require
		A. The universe to be flat.
		B. The amount of dark matter to be determined.
		C. The redshifts of galaxies in the Local Group to be measured.
		D. An accuration temperature of the background radiation.
		E. The Hubble Constant and the density of the universe to be determined.

	The center of our galaxy lies in the direction of the constellation of
		A. Ursa Minor.
		B. Ursa Major.
		C. Sagittarius.
		D. Orion.
		E. Andromeda.