The Big Bang Thursday January 17 Doppler shift

The Big Bang Thursday, January 17

Doppler 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 amount by which the wavelength is shifted tells us the radial velocity of the object, in kilometers/second.

A light source is at rest: it emits light with a wavelength λ 0. If distance to light source is changing, changing Doppler shift will change the wavelength to λ ≠ λ 0.

Size of Doppler shift is proportional to radial velocity: λ = observed wavelength λ 0 = wavelength if source isn’t at rest V = radial velocity of moving source c = speed of light

Hydrogen absorbs light with λ 0 = 656. 3 nm ↓ You observe a star with a hydrogen absorption line at λ = 656. 2 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 to stars and galaxies? No sense of depth!

Climbing the “cosmic distance ladder”. Can’t use the same technique to find distance to every astronomical object. Use one technique within Solar System (1 st “rung” of ladder); another for nearby stars (2 nd “rung”), etc. . .

1 st rung of the distance ladder: distances within the Solar System. Distances from Earth to nearby planets are found by radar

Radar distance measurement: Send out a strong radio pulse, wait until the faint reflected pulse returns.

Measured round-trip travel time = t (typically several minutes) One-way travel time = t/2 Distance = 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).

2 nd rung: distances to nearby stars within the Milky Way Galaxy. ← Proxima Centauri Distances from Solar System to nearby stars are found by parallax

Flashback slide! 1 parsec = distance at which a star has a parallax of 1 arcsecond. ↓observed star observer→ parallax angle Not to scale 1 parsec = 206, 000 astronomical units = 3. 26 light-years

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

3 rd rung: distances to galaxies beyond our own. Distances from Milky Way to nearby galaxies are found with standard candles

In the jargon of astronomers, a “standard candle” is a light source of known luminosity. Luminosity 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’t measuring the luminosity. To do that, we’d have to capture all the light from the star.

When we measure the light from a star, we are measuring the flux The flux is the wattage received per square meter of our telescope lens.

At distance d from star of luminosity L, the luminosity is spread over an area 4πd 2. Flux = luminosity / area F=L/(4π 2 d )

What’s this got to do with finding the distance? You know luminosity (L) of a standard candle. You measure the flux (F). You compute the distance (d):

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 d 2 F. 4) Assume far standard candle has same luminosity as the near. 5) Compute the distance to the far standard candle:

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!

In 1929, Edwin 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 Bang model: universe started in an extremely dense state, but became less dense as it expanded.