Luminosity Functions from the 6dFGS

Heath JonesANU/AAO

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

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

Stellar Mass Function Does the total stellar mass

in the present-day universe support cosmic star formation history observed at higher redshift?

log (Mstars/h-2M)

Cole et al (2001)

Star Formation Historyof the Universe

Sky completeness

bJ-band

K-band

Magnitude Completeness

Galaxies grouped according to the completeness of the field to which they belong

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:

Ktot=Kiso - 1.5 exp1.25(uK20-20)

Above: (Kiso-Ktot) versus the average surface brightnessSimple exponential disc model (solid) and adopted correction (upper

dashed)

Number Counts

2MASS isophotal magnitudes and 6dFGS total magnitudes

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

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 galaxies600 sq deg2MASS + ZCAT~4000 galaxies 7000 sq deg

2MASS + SDSS~12000 galaxies400 sq deg

6dFGS:~63500 galaxies, 9500 sq deg

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

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

V/Vmax statistic

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

6dFGS STY fit is virtually identical to Schechter function fit to 1/Vmax LF

Correction for Virgo and Great Attractor Infall

Model of Burstein et al (1989)

No infall correction:

cz correction goes beyond 10% for galaxies MK> -19

Corrected:

J-band LF: 1/Vmax and STY

General agreement with 2dFGRS+2MASS study of Cole et al (2001)

J and H-band LF: STY

In general, STY follows Schechter fit to 1/Vmax to high precision

bJ and rF-bands: 1/Vmax

Faint end rises as we move towards optical passbands

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