Chapter 27 Hubble’s Law and the Distance Scale Revised 2007

Determining Distances to Galaxies (In approximately the order that they were introduced); 1.Cepheids 2.Velocities 3.Supernovae

The Distance Ladder

Cepheids Henrietta Leavitt (1868 – 1921), working on the stellar spectra project at Harvard, discovered variable stars by inspecting photographic plates. She found 2400 Cepheids.

Cepheids undergo periodic changes in brightness

Which in turn is correlated with the stars luminosity – extremely useful as a distance indicator

So, the luminosity yields the absolute magnitude, M, which, combined with a measurement of the apparent magnitude, m, gives you the distance modulus m-M = 5logd – 5 Hence d

The Cepheids yielded distances to the Andromeda Galaxy, and other galaxies, which enabled Hubble to calibrate his new distance determination technique based on the recession velocities of galaxies.

Velocities

Redshifts are converted into recession velocities using the Doppler equation Doppler Equation z = v/c = 

The Hubble Law v = H o D

The Hubble Constant H o = 50 kms -1 /Mpc according to Sandage H o = 100 kms -1 /Mpc according to DeVaucouleurs H o = 75 kms -1 /Mpc according to modern measurements. The way to use the equation is to measure the recession velocity, and divide by H o to get D in Mpc.

Supernova Type Ia supernovae are regarded as “standard candles” because they all attain the same peak brightness (luminosity), plus, since they are so bright, they can be used to measure the Hubble flow at great distances.

Supernova attain approximately the same peak brightness

Different types of Supernovae, but the Type Ia’s are the best as they reach the same maximum brightness

Type Ib

Type Ic

Type II

Supernova light curves

Maximum brightness for a Type 1a supernova is M B = /- 0.2 mag Supernovae are so bright, they can be observed to great distances. Since we know their absolute magnitudes, we can get the distance From the apparent magnitude and m-M = 5logd – 5.

One Major Complication is Dust The major problem with all distance determinations is the extinction of starlight due to dust in our Galaxy and other galaxies.

The amount of dust extinction depends on which direction you look

The consequence of dust extinction is to make the “star” appear further away than it actually is, so to correct for this effect we add another term to the distance modulus equation m-M = 5logd – 5 + A v

A v is called the dust extinction coefficient, and has units of mag, and is a measure of the decrease in brightness of an object caused by intervening dust. A major problem is determining the correct value for A v. There is some hope however…..

Because the extinction changes the color of the object as well as making it fainter.

So, if you know what the intrinsic color of the object is you can figure out what the extinction coefficient is from the observed color. and the equation is A v = 3 E(B-V) where E(B-V) is called the color excess, or how much redder it is, (in magnitudes), due to the dust.

Solid green – flat universe,  = 0. Dashed Green – open universe,  Blue – flat universe,