The Big BangThe Big Bang

Thursday, January 17

Doppler shiftDoppler shift tells you if an object is coming toward you or moving away.

Blueshift: distance decreasing.

Redshift: distance increasing.

All distant galaxies have redshifts.

But wait, there’s more!....

The amountamount by which the wavelength is shifted tells us the radial velocityradial velocity of the object, in kilometers/second.

A light source is at rest: it emits light with a wavelength λ0.

If distance to light source is changingchanging, Doppler shift will

change the wavelength to λ ≠ λ0 .

Size of Doppler shift is proportional to radial velocity:

c

V

0

0

λ = observed wavelength

λ0 = wavelength if source isn’t at rest

V = radial velocity of moving source

c = speed of light

Hydrogen absorbs light with λ0 = 656.3 nm.

You observe a star with a hydrogen absorption line at λ = 656.2 nm.

656.3 nm ↓

Thinking locally: stars within 3 parsecs of the Sun.

Proxima Centauri

Equal numbers of redshifts and

blueshifts.

Typical radial velocity V = 30 km/second

(70,000 mph).

Thinking more globally: galaxies within 30 million parsecs of the Milky Way.

Almost all redshifts rather than blueshifts.

Typical radial velocity V = 1000 km/second

How do we know the distances How do we know the distances to stars and galaxies?to stars and galaxies?

No No sensesense of depth! of depth!

Climbing the “cosmic distance ladder”.

Can’t use the same technique to find distance to everyevery astronomical object.

Use one technique within Solar System (1st “rung” of ladder); another for

nearby stars (2nd “rung”), etc...

11stst rung rung of the distance ladder: distances within the Solar System.

Distances from Earth to nearby planets are found by radarradar.

Radar distance measurement:

Send out a strong radio pulse, wait until the faint reflected pulse returns.

Measured round-tripround-trip travel time = t

(typically several minutes)

One-way One-way travel time = t/2

DistanceDistance = speed × one-way travel time

Since radio waves are a form of light, distance = c t / 2

Using fancy technical methods, round-trip travel time can be

measured with great accuracy.

Thus, we know distances within the Solar System very well indeed.

1 astronomical unit (average distance from Sun’s center to Earth’s center) =

149,597,870,690 meters (plus or minus 30 meters).

22ndnd rung: rung: distances to nearby stars within the Milky Way Galaxy.

Distances from Solar System to nearby stars are found by parallaxparallax.

← Proxima Centauri

1 parsec = distance at which a star has a parallax of 1 arcsecond.

1 parsec = 206,000 astronomical units = 3.26 light-years

Not to scale

Flashback slide!

↓observed starobserver→

parallax angle

Measured parallax angle is inversely inversely proportional to a star’s distance.

p

parsec 1 Distance (p = parallax angle,

in arcseconds)

First star to have its parallax angle measured: 61 Cygni (in the year 1838).

Parallax angle = 0.287 arcseconds

Distance = 1 parsec / 0.287 =

3.48 parsecs

With the Hipparcos satellite, astronomers measured parallax angles with an accuracy of 0.001 arcseconds.

Parallax too small to measure for stars more than 1000 parsecs away.

33rdrd rung: rung: distances to galaxies beyond our own.

Distances from Milky Way to nearby galaxies are found with standard candlesstandard candles.

In the jargon of astronomers, a “standard candle” is a light

source of known luminosity.

LuminosityLuminosity is the rate at which light source radiates away energy

(in other words, it’s the wattage).

Sun’s luminosity = 4 × 1026 watts = 4 × 1033 ergs per second

When we measure the light from a star, we aren’taren’t measuring the luminosity.

To do that, we’d have to capture allall the light from the star.

When we measure the light from a star, we are measuring the fluxflux.

The flux is the wattage received perper square metersquare meter of our telescope lens.

At distance d from star of luminosity L,

the luminosity is spread over an area

4πd2.

Flux = luminosity / area

F = L / ( 4 π d2 )

What’s this got to do with finding the distance?

You knowknow luminosity (L) of a standard candle. You measuremeasure the flux (F).

You computecompute the distance (d):

F4

L d

2d4

LF

π

Climbing the distance ladder.

1) Measure flux of two standard candles: one near, one far.

2) Find distance to near standard candle from its parallax.

3) Compute luminosity of near standard candle: L = 4 π d2 F.

4) Assume far standard candle has same luminosity as the near.

5) Compute the distance to the far standard candle:

F4

L d

A good standard candle: Cepheid variable stars

Cepheid stars vary in brightness with a period that depends on their average

luminosity.

Observe Cepheid.

Measure period.

Look up luminosity.

Measure flux.

Compute its distance!

F4

L d

In 1929, Edwin HubbleEdwin Hubble looked at the relation between radial velocity and

distance for galaxies.

Hubble’s result: Radial velocity of a galaxy is

linearly proportional to its distance.

Modern data

1 Mpc = 1 million parsecs

Hubble’s law (that radial velocity is

proportional to distance) led to

acceptance of the Big Big BangBang model.

Big Bang model: universe started in an extremely dense state, but

became less dense as it expanded.