Seb Oliver

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Distant Universe

• Seb Oliver
• Lecture 10 Luminosity Functions

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Main Topics

• Standard Hot Big Bang Model
• Classical Observational Cosmology
• Galaxy Evolution
• The Hunt for the First Galaxies
• Background Light
• Structure Formation

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Galaxy Evolution

• K-Corrections
• Luminosity Functions
• V/Vmax test of Evolution
• Passive Stellar Evolution
• Number Counts
• The Global History of Star-Formation

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The Luminosity Functions

• To study galaxy evolution we need to compare
  galaxies today with galaxies in the past
• To perform a fair comparison we need to compare
  the emitted power at the same wavelengths, hence
  K-corrections (Lect. 9)
• We cannot observe the same galaxy at different
  times, so we must look at the statistical
  properties of galaxies as populations, hence we
  study luminosity functions

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Luminosity Functions
The luminosity function characterises the number
density of galaxies as a function of the
luminosity Ln
Luminosity function, usually written ?(L), is
defined as the co-moving number density (number
of objects per co-moving volume) in some range of
luminosity (usually logarithmic)
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Luminosity Functions1/VA Estimator
Object Too Faint
Given a single object, X, visible within some
volume, VA
Object Detectable
For a number of objects i
Too Big
This 1/VA estimator is a maximum likelihood
estimator
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Luminosity Functions1/VA Estimator
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Luminosity Functions1/VA Estimator zmax
Observe fn and z over some area ?2 down to some
flux density limit, fn,min
can be estimated for different galaxy types
using T for type and L for cosmology
calculated numerically
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Luminosity Functions1/VA Estimator Vmax
Assume for simplicity that the zmax is constant
across the survey area, and that the survey is
only limited at zmax i.e. zmin0, though
generalisations not difficult
co-moving volume
Matter dominated
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Luminosity Functions

• Luminosity functions are different and should be
  estimated separately for different
• Galaxy Types
• Ellipticals
• Spirals
• AGNs
• Dwarfs

• Emission Wavelengths
• ?-/X-ray through radio
• Environments
• Clusters
• Field
• Redshifts
• Evolution

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Normal galaxy Types
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EnvironmentCluster
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Environment Field
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Luminosity Functions

• In order to allow easy comparison between
  different determinations of luminosity functions
  and luminosity functions of different types it is
  usual to use simple parameterisations
• Schecter - common for galaxies
• Two-Power-Law - common for AGN
• Power - Law with exponential cut-off - infrared
  galaxies

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Luminosity Functions

• Schecter Function - common for galaxies

Exponential Cut-off
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Luminosity Functions
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SDSS Luminosity Function
Blanton et al. 2001 AJ 121, 2358
www.sdss.org
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SDSS Luminosity Function
Blanton et al. 2001 AJ 121, 2358
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Parametric Evolution of Luminosity Functions
Pure density evolution
Density Evolution
Luminosity Evolution
Pure Luminosity evolution
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Parametric Evolution of Luminosity Functions
typical estimate of
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IR Evolution of AGN (ELAIS)
Matute et al. 2002 MNRAS 332 11
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Luminosity Function from 2dF Quasar Survey
www.2dfquasar.org
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Luminosity Function from 2dF Quasar Survey
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Luminosity Function from 2dF Quasar Survey
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Luminosity Function from 2dF Quasar Survey
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V/Vmax Evolution Test
For objects of fixed luminosity, L, in a redshift
survey there is a maximum volume in which the
object could have been seen, Vmax(zmax)
We can compare this to the volume in which the
object actually was seen V(z)
Thus V could be between 0 and Vmax
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V/Vmax Evolution Test
If there was no change in co-moving number density
Since the number density does not change the
probability of an object appearing in a survey
volume V, P(ltV)
dP is probability in range V to VdV
i.e. constant (independent of V) thus V/Vmax
distributed uniformly between 0 and 1 thus
ltV/Vmaxgt is 0.5
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V/Vmax Evolution Test
For a real survey with n galaxies our estimate of
ltV/Vmaxgt has some uncertainty associated with it
and it can be shown that in the absence of
evolution
Thus a measured value of ltV/Vmaxgt that differed
significantly from 0.5 demonstrates that
evolution has occurred
galaxies more numerous in past
galaxies less numerous in past
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Expected Evolution from SWIRE
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AGN Galaxy Connection

• MBH ? Mspheroid
• (Magorrian)
• Both evolve strongly
• closer connections at higher z ?
• Strong SED evolution for LIRGs ULIRGs?

Tyson