Expansion of the Universe

How do we know that the universe is expanding?

Watch this video about redshift and Hubble's Law:

And this one, on the present uncertainty of the value of the Hubble constant:

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In Depth: Central Concepts

Atoms of each element in the periodic table can both emit and absorb specific wavelengths of electromagnetic radiation (EMR, commonly called "light"). This periodic table shows the emission spectra of all the elements. Absorption lines for each element have exactly the same positions as emission lines on an absorption spectrum (like the second figure).


Click to enlarge. To see spectral 
lines in great detail, click HERE.


Each spectrum is like a fingerprint of the element. In the complex spectra of stars and galaxies, computer algorithms can search the enormous number of absorption lines, and pick out element fingerprints, even if the lines are red-shifted by the motion of the star or galaxy. Here is a typical star spectrum. 

The sharp valleys are absorption lines; for example, the central one marked with a green band corresponds to the red hydrogen line (H-alpha, wavelength 656.281 nm) in the periodic table above (or better, here). If this star were moving rapidly away from us, this line would be redshifted -- that is, it would appear at a longer wavelength (remember, the computer algorithms can still find and identify them). The amount of redshift can tell us how fast it is moving.

Redshift

The numerical value of the redshift (called z) is the deviation of the line from its expected position (656.281 nm for H-alpha), divided by the expected wavelength:

(z: redshift; lambdas are observed (0)
and expected (e) wavelengths)

So z is simply the fraction of the normal wavelength by which the observed line is shifted. If, for example, the line is seen at 721.909 nm, the deviation is 721.909 - 656.281 = 65.628 nm. Then z is
65.628 ÷ 656.281 = 0.1. We say that the redshift of the light-emitting star or galaxy is 0.1.

Recession Velocity

The speed at which the emitting object is receding from us is related very simply to c, the speed of light. 


In the case above, v is simply 0.1 times c, or one-tenth the speed of light.

In short, the wavelength of all light from an object moving away from us at 1/10 the speed of light is longer by one-tenth of the normal wavelength. If, for example, another object is moving away at the speed of light, its redshift is 1.0.

Distance

If we know the inherent brightness (called luminosityL) of a light-emitting object, we can determine its distance by measuring the observed brightness (called fluxF) of the object, using this relationship:

Notice that this measurement is completely independent of redshift. It is purely a comparison of 1) how bright the object "really" is, with 2) how bright it appears to us from its distance. (If you square both sides of the equation and solve for F , you will see that F and L are related by an inverse-square law.*)

Using this method to measure distances requires finding objects whose luminosities are known. Such objects are called standard candles. Edwin Hubble's standard candles were pulsating stars called Cepheid variables. In the early 1900's Henrietta Swan Leavitt at Harvard College Observatory showed that luminosity of these stars can be accurately determined from the time-period of their pulsation. So it is possible to measure the period and thus compute L, and then use the measured to calculate d, the star's distance.

The Hubble Constant

Hubble is credited with recognizing that more distant objects (galaxies, their distances measured by the method described above), have greater redshifts. This suggests that the universe is expanding more or less uniformly. If distance and recession velocity (v or zc) are strictly proportional to each other, then their ratio is constant:

The purported constant H(0) is now known as the Hubble constant. Pursuit of its precise value (and any measurable inconstancy) continues today.

Hubble's Law


With the Hubble constant in hand (if ever), then all that's needed to determine the distance d to any object is its redshift. The measured value of the constant, based on thousands of measurements, is -- very roughly -- 70 [(km/s)/mpc]. The units mean that for every megaparsec (3.26 million light years) of distance to the object, its recession velocity is greater by 70 km/s.

Because of local gravitational effects, this relationship only works well for very large distances, such as the distances between galactic clusters. Within our own galactic cluster, for example, the Andromeda galaxy and the Milky Way are actually moving towards each other due to gravity. Light from Andromeda is slightly blue-shifted. (The shift is -0.001004, meaning that Andromeda is moving towards us at about 1/1000 times the speed of light, approximately 300 km/s.)

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*
The flux-luminosity equation, basis of distance measurements to standard candles:

This equation says that flux (measured brightness) decreases with the square of the distance to the shining object of luminosity L. This equation is solved for r in the section Distance above (is renamed d for distance there).