Luminosity Functions from the 6dFGS

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Luminosity Functions from the 6dFGS
Heath Jones ANU/AAO
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Background

• Luminosity functions of NIR-selected galaxies are
  effective tracers of the stellar mass function of
  collapsed structures
• Light from the near-infrared is dominated by the
  older and cooler stars that make up the bulk of
  the stellar mass.
• Early attempts were limited to small sky areas
  and/or sample sizes in the hundreds
• With the advent of 2MASS, more recent attempts
  have exploited the power of wide-field redshift
  surveys like 2dFGRS, SDSS and ZCAT
• Of these, 6dFGS has the largest 2MASS overlap to
  date

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Background

• Luminosity functions of NIR-selected galaxies are
  effective tracers of the stellar mass function of
  collapsed structures
• Light from the near-infrared is dominated by the
  older and cooler stars that make up the bulk of
  the stellar mass.
• Early attempts were limited to small sky areas
  and/or sample sizes in the hundreds
• With the advent of 2MASS, more recent attempts
  have exploited the power of wide-field redshift
  surveys like 2dFGRS, SDSS and ZCAT
• Of these, 6dFGS has the largest 2MASS overlap to
  date

Working in the Near-Infrared

• Extinction is minimal at longer wavelengths
• Mass-to-light ratios are better constrained in
  near-infrared passbands (e.g. Bell de Jong
  2001).
• Cosmological k-corrections are small
• 2MASS affords digital (as opposed to
  photographic) photometry over the wide sky areas
  now spanned by redshift surveys

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Stellar Mass Function
Cole et al (2001)

• Does the total stellar mass in the present-day
  universe support cosmic star formation history
  observed at higher redshift?

log (Mstars/h-2M?)
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Sky completeness
K-band
bJ-band
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Magnitude Completeness
Galaxies grouped according to the completeness of
the field to which they belong
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Total and Isophotal Magnitudes
Total mags (Ktot) are preferred to isophotal
(Kiso) because total luminosity is the physical
quantity we ultimately seek
The Ktot mags provided for the 2MASS XSC become
unreliable at low b
However, the Kiso are reliable, and so we use
these (and the mean surface brightness within
uK20 20) to provide a corrected total
magnitude KtotKiso - 1.5 exp1.25(uK20-20)
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Number Counts
2MASS isophotal magnitudes and 6dFGS total
magnitudes
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6dF Luminosity Function The 1/Vmax Method

• 1/Vmax straightforward to implement and does not
  assume a functional form for the LF
  (non-parametric)
• Very robust with respect to apparent magnitude
  incompleteness ---- good for samples with poorly
  characterised magnitude incompleteness functions

• However, assumes survey volume is homogeneous
• ---- biased if the galaxy distribution is
  clustered

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K-band LF
6dFGS 63500 galaxies, 9500 sq deg

• 6dFGS K-band LF goes 1.5 to 2 mags better at
  both the bright and faint ends
• Agrees with previous measures within the
  differences between magnitude systems employed
• The smaller redshift surveys have larger
  uncertainties about the normalisation

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K-band LF

• Schechter fit is only a close fit around M to
  (M4)
• Fails to turn over sufficiently rapidly for the
  bright end
• Faint end also drops off
• Simple 3-parameter function insufficient to
  properly characterise the luminosity distribution
  galaxies over this range of 10,000x in luminosity

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V/Vmax statistic
Suppose V(z) as the survey volume within a
redshift z zi is redshift of galaxy i zmax,i
is the maximum redshift that same galaxy could
have and still satisify the survey selection
criteria If sample is complete and of uniform
density, then V(zi)/V(zmax,i) is uniformly
distributed in the interval 0 to 1
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K-band 1/Vmax and STY together

• STY does not need to assume that the LF is
  independent of local density, therefore is
  insensitive to clustering in the sample
• STY does not require binning
• However, is parametric, and must assume some
  functional form for the LF

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Correction for Virgo and Great Attractor Infall
No infall correction
cz correction goes beyond 10 for galaxies MKgt
-19
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J-band LF 1/Vmax and STY
General agreement with 2dFGRS2MASS study of Cole
et al (2001)
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J and H-band LF STY
In general, STY follows Schechter fit to 1/Vmax
to high precision
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bJ and rF-bands 1/Vmax
Faint end rises as we move towards optical
passbands
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Current and Future Work

• StepWise Maximum-Likelihood Currently working on
  our SWML fits to the 6dFGS data. (SWML is a
  non-parametric maximum-likelihood LF estimator,
  that is also insensitive to clustering).
• Normalisation Want to examine the change in the
  mean number density in the 6dFGS over redshift
  shells of increasing volume.
• Stellar Mass Function Derive stellar masses for
  these galaxies from their NIR photometry, fit the
  SMF and derive the total stellar mass content of
  the local universe.
• Blue and Red Galaxies Demarcate the sample along
  lines of extreme (b-K) colour and examine the LF
  shape relative to the basic LFs