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Observational Cosmology 6. Galaxy Number Counts
It is a capital mistake to theorise before one
has data. Insensibly one begins to twist facts to
suit theories instead of theories to suit facts.

    Sherlock Holmes.
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6.1 Why Study Source Counts

• Why Study Source Counts - How many galaxies are
  there in the Universe ?

Why Study Galaxy Source Counts ?

• To count the numbers of galaxies in the Universe
• Numbers of galaxies
• Density of galaxies and the Universe
• Fainter and fainter galaxies at higher and
  higher redshift
• To determine the Geometry of the Universe
• Faint source counts depend on the geometry of
  the Universe
• low density / cosmological constant ? faster
  expansion ? larger volumes ? more galaxies
• To investigate the contribution of different
  galaxy populations to the Universe
• investigate optical mix of morphological types
• local infrared - spirals
• bright radio - ellipticals
• X-rays - AGN
• To investigate the evolution of galaxies
• Compare galaxies today with galaxies in the past
  
• Quantify and constrain the evolution in the
  galaxy populations
• Discriminate the nature of the evolution

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6.1 Why Study Source Counts

• Why Study Source Counts - The Geometry of the
  Universe

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6.1 Why Study Source Counts

• Why Study Source Counts - Population Contributions

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6.1 Why Study Source Counts

• Why Study Source Counts - Evolution

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6.2 Source Counts Derivation

• Simple Euclidean Case

How many galaxies are there in the Universe

• For flat, non expanding Universe filled with
  uniformly distributed galaxies of same luminosity
• (A Euclidean Universe)
• Galaxy number density n
• Galaxy luminosity L
• Number of galaxies to distance ( d ) N

• Nearby Galaxies generally follow this
  distribution
• More complex when we look to greater distances
• We have to consider the cosmology galaxy
  evolution
• Have to consider a range of galaxy types and
  luminosities

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6.2 Source Counts Derivation

• Derivation of Source Counts

SOURCE COUNT MODEL
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6.2 Source Counts Derivation

• Cosmology

Number of galaxies, N (seen to sensitivity, S)
number density galaxies x volume (for all
luminosities)
Galaxy number density (all luminosities) -
Luminosity Function
Volume depends on cosmology (Ho, Wo, L) Wo 0,
1 easiest
The farthest galaxies you can see depends on the
sensitivity
The Distance also depends on the cosmology (Ho,
Wo, L) Wo 0, 1 are the easiest.
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6.2 Source Counts Derivation

• Luminosity Function

LUMINOSITY FUNCTION Galaxy number density as a
function of their luminosity
Depends on 4() parameters
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6.2 Source Counts Derivation

• Luminosity Function

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6.2 Source Counts Derivation

• Calculation of Luminosity Function (1/Vmax method)

In 2-D
In 3-D
Pi probability of object staying in sample such
that if the probability of dropping out is 1/2
then we require 2x the weight This will be an
unbiased estimator of the underlying value
Vmax,I volume enclosed at maximum redshift
zmax,i at which the ith object can be
observed. Vlimit arbitrary large volume into
which the flux limited sample is embedded
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6.2 Source Counts Derivation

• Calculation of Luminosity Function (Maximum
  Likelihood method)

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6.2 Source Counts Derivation

• K-Correction

Want compare luminosities at the same wavelengths
? K-Correction

• Due to redshift effect s, the true galaxy SED
  and that seen from Earth are different
• Need to know about emission from sources at one
  single wavelength but we have ensemble le lo/
  (1z)
• Need a CORRECTION ? This correction is called
  the K-CORRECTION
• The significance of the correction depends on
  the shape of the galaxy SED

Observed flux at observed frequency, no, (cnl)
Corresponding to the luminosity at ne
The K-Correction depends on the assumed Spectral
Energy Distribution (SED)
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6.2 Source Counts Derivation

• Evolution

• LUMINOSITY EVOLUTION
• Galaxies in the past were more luminous

• DENSITY EVOLUTION
• Galaxies in the past were more numerous

Parameterize luminosity evolution
f(z) Parameterize density evolution g(z)
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6.2 Source Counts Derivation

• Evolution

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6.2 Source Counts Derivation

• V/Vmax Test for Evolution

For a galaxy with luminosity, L, in a redshift
survey there is a maximum volume within which the
object can be detected, Vmax(zmax)
Compare with volume in which galaxy was actually
detected V(z), 0 lt V(z) lt Vmax
If there was no change in co-moving number density
independent of V ? V/Vmax uniformly distributed
between 0 - 1 ? ltV/Vmaxgt 0.5
? ltV/Vmaxgt significantly deviates from 0.5 ?
evolution
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6.3 Source Counts Results

• Integral and Differential Source Counts

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6.3 Source Counts Results

• Number Redshift Distributions

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6.3 Source Counts Results

• Back Ground Contributions and Confusion

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6.4 Multiwavelength Source Counts

• Optical Source Counts

Faint blue galaxies (relatively low luminosity)
were more numerous in the past and may dominate
the faint source counts
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6.4 Multiwavelength Source Counts

• Optical Morphological Evolution

Redshift Distributions as function of
morphological type

• Bright Fluxes - More ellipticals , less
  Irregular
• Faint Fluxes - Few Ellipticals, more Irregular

• The Butcher Oemler Effect
• Low redshift Clusters have more red galaxies than
  blue galaxies,
• Higher redshift Clusters have higher fraction of
  blue galaxies
• The morphology Density Relationship
• Denser regions of clusters have higher proportion
  of red galaxies than less dense regions

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6.4 Multiwavelength Source Counts

• Near-Infrared Source Counts

• Near-infrared
• Emission from cool stars
• Old populations dominate
• Bright Fluxes E/S0 50
• Tracing Stellar Mass

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6.4 Multiwavelength Source Counts

• Far-Infrared Source Counts

The Dusty Universe Infrared Emission UV
emission from young hot OB stars Absorbed by
dust Reprocessed and emitted at IR wavelength
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6.4 Multiwavelength Source Counts

• Far-Infrared Source Counts

• Infra Red Astronomy Satellite
• Launched 1983
• All sky survey 12, 25, 60, 100mm

• The importance of DUST.
• For normal galaxies LIR/Lopt - 30.
• For Starburst LIR/Lopt - 50-90.
• ULIG - A new population LIR/Lopt - 90-99
• IR - Strong Evolution - High Star Formation.
• 50-60 Star Formation in the Universe is in IR.

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6.4 Multiwavelength Source Counts

• Far-Infrared Source Counts

Infrared Space Observatory ISO, 11/1995-5/1998

• The ISO Universe
• Source counts 7-200mm
• Strong Evolution
• Dominant LIG/ULIG pop.

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6.4 Multiwavelength Source Counts

• Far-Infrared Source Counts

Infrared Space Observatory ISO, 11/1995-5/1998

• The ISO Universe
• Source counts 7-200mm
• Strong Evolution
• Dominant LIG/ULIG pop.

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6.4 Multiwavelength Source Counts

• Submillimetre Source Counts

• 850mm SCUBA JCMT
• Re-emission from dust of Starlight at sub-mm
  wavelengths
• Many line emission from rotational transitions
  of CO
• Large negative K-corrections ? access high z
  Universe

• LBOL ? 1012Lo SFRgt102-103Mo/yr (Arp220 like
  ULIG sources)
• 50 detected sources
• Strong Evolution
• Assembly of an Elliptical Galaxy in lt 1Gyr
• SCUBA beam 15 ? I.D.s difficult ? few
  redshifts
• Median redshift 2.5

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6.4 Multiwavelength Source Counts

• Radio Source Counts

• Radio Sources separated into 2 populations
• Bright radio fluxes (S1.4GHz gt mJy)
• ? Radio Loud Ellipticals
• Black Hole Power Source
• power law emission S1.4GHz ? n-a a 0.3
• Faint radio sources (S1.4GHz lt mJy)
• ? Star Forming Galaxies (STFG)
• SNR synchrotron emission
• ? Star Formation Power Source
• S1.4GHz ? n-a a 0.8

• Bright radio fluxes - Ellipticals Dominate
• sub-mJy fluxes - Emergence of new population
  (Starburst Galaxies)
• ltzgt0.3 ? higher redshift counterpart of IRAS
  STFG
• Follow well known Radio-FIR relation (S60mm 90
  S1.4GHz)
• Radio fluxes lt 35mJy - Spectral slope flattens
  to a 0.7 ? STFG dominate over AGN
• zlt1.5 optically red star forming galaxies

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6.4 Multiwavelength Source Counts

• X-Ray Source Counts

Bright (0.5-2keV) X-ray Fluxes Dominant
Population - Quasars S (0.5-2keV) lt 10-14 ergs
cm-2 s-1 ? new faint population of sources
NELGs (Starbursts / AGN) Densities
1000-2000/sq.deg.
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6.5 The Star Formation History

• Background Light

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6.6 Future Prospects

• The Future

• Spitzer
• GALLEX
• ASTRO-F
• UKIDSS
• VISTA
• Herschel
• SCUBA-2
• WISE
• ALMA
• JWST
• SPICA
• SKA

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6.7 Summary

• Summary

• Study Galaxy source counts to
• investigate the contribution of different galaxy
  populations to the Universe
• compare the evolution of galaxies today with
  those in the past
• constrain Geometry of the Universe
• Source counts depend on
• Cosmology
• Luminosity Function
• K-Correction
• Evolution
• Source counts are a function of observing
  wavelength
• Different wavelengths are dominated by different
  classes of sources
• To understand the star formation and
  evolutionary history ? multiwavelength analysis
• Present and next generation surveys
• Larger areas to greater depths
• increase statistical samples by orders of
  magnitudes!

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6.7 Summary

• Summary

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Observational Cosmology 6. Galaxy Number Counts
Observational Cosmology 7. The Evolving Universe
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