The Expanding Universe

Getting the Distances to Galaxies is a “Big Industry”

solar system 10 A.U. radar ranging

Local Galaxy 100 pc stellar parallax

Across Galaxy 10,000 pc spectroscopic “parallax”

Nearby galaxies 15 Mpc Variable stars

Distant galaxies 200 Mpc Standard candle and “Tully-Fisher”

Location Distance Method

1 Mpc = 1 million parsecsWe have studied stellar parallax, and variable stars.

Spectroscopic parallax is simply comparison of brightness of identical stars.Standard candle is comparison of brightness of identical supernovae explosions.Tully-Fisher is a way to measure galaxy luminosity from its rotations speed. More …

The Distance Ladderd = constant x (L/B)1/2

Distance Measurements to Other Galaxies (1)

a) Cepheid Method: Using Period – Luminosity relation for classical Cepheids:

Measure Cepheid’s Period Find its luminosity Compare to apparent magnitude Find its distance

b) Type Ia Supernovae (collapse of an accreting white dwarf in a binary system):

Type Ia Supernovae have well known standard luminosities Compare to apparent magnitudes Find its distances

Both are “Standard-candle” methods:

Know absolute magnitude (luminosity) compare to apparent magnitude find distance.

Cepheid Distance Measurement

Repeated brightness measurements of a Cepheid allow the determination of the period and thus the absolute magnitude.

Distance

L = constant x (velocity)4

d = constant x (L/B)1/2

Tully-Fisher Distance IndicatorRecall, luminosity of stars scales with mass of stars… therefore, luminosity of galaxy scales with number of stars (and thus, mass of stars). Thus, luminosity of galaxy gives mass of galaxy.

Going backwards… measure the velocity to “weigh” the galaxy to obtain luminosity.

velocity

Doppler velocity map of galaxy.

The Extragalactic Distance Scale

• Many galaxies are typically millions or billions of parsecs from our galaxy.

• Typical distance units:

Mpc = Megaparsec = 1 million parsec

Gpc = Gigaparsec = 1 billion parsec

• Distances of Mpc or even Gpc The light we see left the galaxy millions or billions of years ago!!

• “Look-back times” of millions or billions of years

The Hubble Law

The problem is that 200 Mpc is nothing!

Well, it turns out that there is another indicator for extreme distances.

The Hubble LawThe further away a galaxy is, the greater is its redshift.

Red Blue

(As you can see, it is not perfect.)

Distance Measurements to Other Galaxies (2): The Hubble Law

E. Hubble (1913):

Distant galaxies are moving away from our Milky Way, with a recession velocity, vr, proportional to their distance d:

vr = H0*d

H0 ≈ 70 km/s/Mpc is the Hubble constant

• Measure vr through the Doppler effect infer the distance

Hubble Law Takes us All the Way Out

Implies that Galaxies are “flying away” and that the speed with which they are moving away is proportional to there distance away.

The further away the galaxy, the faster it is receding from us. (more on this later…)

The distance scale revisited.

velocity = constant x distance

The constant is called Hubble’s constant.It is designated as H0. Pronounced “H not”.

velocity = H0 x distance

Discovery of Expansion

1929: Edwin Hubble measured the distances to 25 galaxies:

• Compared distances and recession velocities• Calculated recession velocity by assuming the

redshift of spectral lines is due to the Doppler Effect

Discovered:• Recession velocity gets larger with distance.

Systematic expansion of the Universe.

Redshifted Spectral Lines

Increasing D

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Hubble’s Data (1929)

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Added more data :Hubble & Humason (1931)

10 20 30

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1929 Data

v = recession velocity in km/sec

d = distance in Mpc

H0 = expansion rate today (Hubble Parameter)

Measure Hubble Parameter by calculating slope of the linear relationship

Best value: H0 = 22 ± 2 km/sec/Mly

where Mly = Mega lightyear=1 million ly

Hubble’s Law

v = H0 x d

Interpretation

Hubble’s Law demonstrates that the Universe is expanding in a systematic way:

• The more distant a galaxy is, the faster it appears to be moving away from us.

• Hubble Parameter: Rate of expansion today.

Comments:• Empirical result - based only on data• Actual value of H0 is important. Allows us to get

a rough idea of the Age of the Universe (time elapsed since the Big Bang)

Age of the Universe (Analogy)

You leave Columbus by car for Florida, but leave your watch behind.

How long have you been on the road?• Your speed = 100 km/h• Your trip meter reads: distance = 300 km

Time since you left: T = distance speed• T = 300 km 100 km/h = 3.00 hours

The Hubble Time: T0

Hubble’s Law says• A galaxy at distance d away has a recession

speed, v = H0d

So as in the analogy:• T0 = d / v

• but since, v = H0d, T0 = d / H0d = 1 / H0

Hubble Time: T0 = 1 / H0

Estimate of the Age of the Universe

Best Estimate of the Age:

14.0 1.4 Gyr

This age is consistent with the ages of the oldest stars seen in globular clusters.

• 1 Gyr = 1 Gigayear = 1 billion years

Common Misconception of Universe Expansion

Milky Way

Common MisconceptionDescription:

• Galaxies are all moving away from each other through space

• Explosion of the Big Bang sent them flying• Big Bang sent all galaxies flying away from MW

because that is what we observe

Problems:• Why is the Milky Way the Center of the Universe?• Why is Hubble’s Law obeyed?

Should speed vs distance be linear?Does the galaxy movement have to be uniform?

Space Itself is Expanding: Hubble Flow

Correct ExplanationDescription:

• Galaxies typically have small (compared to Hubble flow), gravitationally influenced motions in any direction in space. (More on this later)

• SPACE ITSELF IS EXPANDING Distance between galaxies is growing, they only appear to be

moving away

Solutions:• Nothing special about the Milky Way. Every galaxy would

see the others receding from them (in the same manner)• Hubble’s Law follows naturally.

Galaxy A is 1 Mly from MW : dA=1 Mly. Galaxy B has dB=3 Mly

Expansion of universe doubles the scale of the coordinate system

Now: A distance is 2 Mly B distance is 6 MlyVA~ (2-1)=1 Mly = dA VB ~ (6-3)=3 Mly = dB V ~ d

Two Dimensional Analogy

Cosmological Redshift

Expansion of space stretches light:

• Wavelengths get stretched intoredder (longer) wavelengths

• The greater the distance,the greater the stretching

Result: • The redshift of an object

gets larger with distance.• Just what Hubble actually

measured

Two Dimensional Analogy

Time to be more preciseMost galaxies are found in groups & clustersGalaxies are held in them by gravity

It is the distance between clusters of galaxies that is getting bigger due to the expansion of the universe

Within a cluster, galaxies can have other motions due to the gravity produced by the total matter in the cluster. Gravitational Force is stronger on these “small” scales than the expansion.

For example, the Andromeda Galaxy and the Milky Way are on a collision course!

The Local Group

Group of 39 galaxies including the Milky Way and Andromeda:

• Size: ~1 Mpc• 5 bright galaxies (M31, MW, M33, LMC, IC10)• 3 Spirals (MW, M31, & M33)• 22 Ellipticals (4 small Es & 18 dEs)• 14 Irregulars of various sizes (LMC, SMC

nearest neighbors)

Total Mass ~5x1012 Msun

The Local Group

1 Megaparsec (Mpc)

Virgo Cluster

Nearest sizable cluster to the Local Group

Relatively loose cluster, centered on two bright Ellipticals: M87 & M84

Properties:• Distance: ~18 Mpc• Size: ~ 2 Mpc• 2500 galaxies (mostly dwarfs)• Mass: ~1014 Msun

Rich Clusters

Contain 1000’s of bright galaxies:• Extend for 510 Mpc

• Masses up to ~1015 Msun

• One or more giant Elliptical Galaxies at center• Ellipticals found near the center.• Spirals found at the outskirts.

1020% of their mass is in the form of a very hot (1078K) intracluster gas seen only atX-ray wavelengths.

Rich ClusterAbell 1689(Hubble Space Telescope)