1. Luminosity Functions from the 6dFGS Heath Jones ANU/AAO

2. 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

3. Background Working in the Near-Infrared 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 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

4. Stellar Mass Function Does the total stellar mass in the present-day universe support cosmic star formation history observed at higher redshift? log (M stars /h -2 M  ) Cole et al (2001) Star Formation History of the Universe

5. Sky completeness b J -band K-band

6. Magnitude Completeness Galaxies grouped according to the completeness of the field to which they belong

7. Total and Isophotal Magnitudes Total mags (K tot ) are preferred to isophotal (K iso ) because total luminosity is the physical quantity we ultimately seek The K tot mags provided for the 2MASS XSC become unreliable at low |b| However, the K iso are reliable, and so we use these (and the mean surface brightness within u K20 = 20) to provide a ‘corrected’ total magnitude: K tot =K iso - 1.5 exp1.25(u K20 - 20) Above: (K iso -K tot ) versus the average surface brightness Simple exponential disc model (solid) and adopted correction (upper dashed)

8. Number Counts 2MASS isophotal magnitudes and 6dFGS total magnitudes

9. 6dF Luminosity Function: The 1/V max Method 1/V max 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

10. 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 K-band LF 2MASS + 2dF ~17000 galaxies 600 sq deg 2MASS + ZCAT ~4000 galaxies 7000 sq deg 2MASS + SDSS ~12000 galaxies 400 sq deg 6dFGS: ~63500 galaxies, 9500 sq deg

11. K-band LF Schechter fit is only a close fit around M* to (M*+4) 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

12. Suppose V(z) as the survey volume within a redshift z z i is redshift of galaxy i z max,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(z i )/V(z max,i ) is uniformly distributed in the interval 0 to 1 V/V max statistic

13. K-band 1/V max 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 6dFGS STY fit is virtually identical to Schechter function fit to 1/V max LF

14. Correction for Virgo and Great Attractor Infall Model of Burstein et al (1989) No infall correction: cz correction goes beyond 10% for galaxies M K > -19 Corrected:

15. J-band LF: 1/V max and STY General agreement with 2dFGRS+2MASS study of Cole et al (2001)

16. J and H-band LF: STY In general, STY follows Schechter fit to 1/V max to high precision

17. b J and r F -bands: 1/V max Faint end rises as we move towards optical passbands

18. 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