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# 16.14 The Most Distant Galaxies

The Hubble relation is well tested out to distances of about 1000 Mpc. At that distance, if we assume a Hubble constant of 70 km/s/Mpc, the recession velocity is 70 × 100 = 72,000 km/s, or about two-tenths the speed of light (0.2c). What does a galaxy this far away — at a prodigious distance of 3.3 billion light years — look like? It looks small. At 1000 Mpc, a galaxy will look as small as a star image and so be difficult to resolve. It will only be detectable by a telescope of 4 meters size or larger.

Using the small angle equation, we can deduce that with images ½ arc second across, the smallest feature resolved by a ground-based telescope is about 0.5 × 1000 / 206,265 = 0.0024 Mpc or 2.4 kpc. So a galaxy like the Milky Way would only be 12 arc seconds across. Ten times farther away and it would be unresolved and indistinguishable from a star. Distant galaxies also appear dim. If astronomers make a deep image with a telescope in a direction away from the plane of the Milky Way, the faintest stars visible would be main sequence stars such as the Sun, about 10 kpc away. By the inverse square law of light, they have the same apparent brightness as a 1010 solar luminosity galaxy that was √1010 x 10 = 106 kpc, or 1000 Mpc distant. In other words, beyond about 1000 Mpc, a galaxy like the Milky Way is fainter than any star in our own galaxy. Astronomers who take deep images "run out" of stars and virtually every faint image is a distant galaxy!

Beyond about 1000 Mpc, the assumption that is generally used to characterize the red shift breaks down. The Doppler equation defines the recession velocity of a galaxy (v = zc) and the distance via the Hubble relation (d = zc / H0). In fact, the only true observable quantity is the cosmological red shift of spectral features in a galaxy, defined as z = Δλ / λ = (λ-λ0) / λ0. Rearranging this equation, the observed wavelength is one plus the red shift times the rest wavelength, λ = (1+z)λ0. This relationship can be used out to the largest distances that galaxies have been seen.

Galaxies are easily observed with a modest 3-4 meter telescope out to red shifts as high as z = 1. In other words, a spectral feature with a laboratory wavelength of λ0 = 327 nm (singly ionized oxygen) is observed at 654 nm, and a spectral feature with a laboratory wavelength of 656 nm (the Hα line of hydrogen) is observed at 1.3 microns. The highest red shift galaxies observable with a 6-8 meter telescope have z > 5. At this red shift, the oxygen line is observed at 2.0 microns and the hydrogen line is observed at 3.9 microns. Notice that very high red shift galaxies have most of their spectral features red shifted out of the optical window. Astronomers expect that the most distant galaxies will only be detectable at near infrared wavelengths. The red shift limit is about z = 9. At this prodigious distance the light is stretched by an order of magnitude in traveling across space to reach us. The strongest hydrogen line is in the mid infrared region, impossible to observe from the ground. Galaxies are no longer object with visible light to detect!

The distance to very high red shift galaxies is uncertain because it depends on the cosmological model. However, for the currently preferred values of cosmological parameters, the age of the universe is about 13.8 billion years. In this model, z = 1 corresponds to a distance of about 11 billion light years or a look back time of 57% of the age of the universe. The larger value of z = 5 corresponds to a distance of about 26 billion light years or a look back time of about 90% of the age of the universe. The highest red shift galaxies emitted the light we see within half a billion years of the big bang, when the universe was ten times hotter and a thousand times denser than it is today.

The Hubble Ultra Deep Field. Click here for original source URL.

Hubble Deep Field South. Click here for original source URL.

The Hubble Deep Field. Click here for original source URL.

The Hubble Deep Fields are the deepest images of the sky ever made. To achieve this, the Hubble Space Telescope stared at each small patch of sky for over a week. Each deep field contains about 2000 galaxies down to a level 4 billion times fainter than the naked eye can see. If we presume that the census of galaxies in these small patches of sky are representative of the entire sky, we can calculate the total number of galaxies visible to this depth. The answer is about 40 billion galaxies! Multiplying by the average number of stars in each galaxy gives roughly 1020. Hubble went back more recently with its newer detectors and made a new image for the Ultra Deep Field, increasing the galaxy census to 100 billion and the stellar census to 1021. Even though we have not observed them all individually, we infer that there are about 100 billion billion stars in the observable universe. We can see the Copernican idea taken to a dizzying level. Earth, the Sun, and the Milky Way are all lost in the amazing vastness of the universe.