3. Statistical Properties of Galaxies

3.1. Luminosity Functions

  • For reasons we don’t totally understand, the distribution of galaxies as a function of luminosity and mass can be modeled as a Schecter function:

Φ(L)dL=Φ(LL)αeL/L d(LL)
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  • L is the inflection point of the function

  • α is the faint end slope

  • Φ is a normalization with units of number per volume

  • For faint galaxies, we have a power low behavior in α

  • For bright galaxies, we have an exponential decline in the number of galaxies

  • In the local volume, the Milky Way is an L galaxy of roughly 1010L

  • Note that individual galaxy types do not necessarily obey Schecter functions, but the sum of galaxies do.

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3.1.1. Challenges of Observation

  • You need distances – redshifts in particular for low z galaxies do reflect both the distance the peculiar motion

  • For the same luminosity and z, low-surface brightness galaxies are harder to detect

  • Malmquist bias: brighter galaxies can be traced to larger distances than fainter galaxies. Solutions:

    • Only consider a range in luminosity and distance for which you are complete

    • Apply volume corrections for each observed luminosity

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3.1.2. Luminosity Functions vs. Color

  • Redder galaxies dominate the bright end of the luminosity function – they’re the biggest and brightest. Blue galaixes dominate the faint end.

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3.1.3. Luminosity Functions vs. Environment

  • There are more galaxies in denser environments. Also, the faint end slope gets steeper in low density environments – that means there are more low mass galaxies in dense environments.

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3.1.4. Physical Origin of the Luminosity Function

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3.2. Mass Functions

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  • Remember that redder galaxies have larger mass-to-light ratios. Thus, the red galaxy mass functions moves to the right compared to the blue function when moving from luminosity to mass space.

3.2.1. Evolution of the Mass Function

  • The mass function normalization changes in time.

    • We can use the mass function to trace the building of mass over cosmic history. Near z of 2 or so, the blue and red galaxy mass functions are nearly on top of each other, whereas they have bifurcated today.

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3.3. UV Luminosity Function

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  • We can trace the SFR density over cosmic time by looking at the UV luminosity function.

  • At high redshift, we have a low number density of galaxies because galaxies have not formed yet!

  • Integrating the UV luminosity function, we can get the SFR density over cosmic time.

    • SFR peaks near z2 or 3, and declines steeply at high redshift. The peak epoch was around 2 or 3 billion years after Big Bang.

  • To make these measurements, we fit Schecter functions to UV luminosity functions at each redshift bin. We integrate for the total UV luminosity at that time, and use a stellar population model to infer the # of stars, masses, and SFRs.

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