Distribution of Maximal Luminosities of Galaxies in SDSS

Manuchehr Taghizadeh-Popp (JHU)

Zoltán Rácz, Alex Szalay, Katalin Ozogany, Enikö Regös

Extreme Value Statistics (EVS)-Used in calculation of risk, stock market, structural failures, insurance claims, flooding, hurricanes…

-Distribution known for the extremes of N i.i.d. random variables (of parent distribution P(x) ) when N ∞.

3 Universal distributions depending on tail behavior of parent distribution P(x):

(1) P(x) ~ x^(-γ-1) (power law tail) ζ > 0 (Frechet distribution)

(2) P(x) ~ exp(-x^a) (exponential tail) ζ = 0 (Gumbel distribution)

(3) P(x) ~ (x0-x)^(γ-1) (finite cutoff tail) ζ < 0 (Weibull distribution)

-Motivation:

-Are Maximal Luminosities gumbel distributed? How good is Schechter fit for P(x)?

-Can we observe the appearance of the first order correction of Ф(x) due to finite N?

The Galaxy Samples from SDSS DR6 Use carefully the best photometry possible for:

- LRG (luminous red galaxies): 0.20 < redshift < 0.60 ( ~67000 galaxies) - MGS (Main Galaxy Sample): 0.05 < redshift < 0.15 (~280000 galaxies)

-Divide MGS in 2 populations: MGS blue and MGS red:-Fit bimodal gaussian to the Color Magnitude Diagram (CMD)-Use naive Bayes classifier for constructing optimal separating curve in the CMD.

Pencil-BeamsNeed N close-to-i.i.d. samples of Luminosities:

-Create N pencil-beams along redshift and sample the maximum Luminosity inside each of them.

-Use HEALPix tessellation (equal area cells in the sky) as the beams projections on the sky.

-Create high resolution HEALPix footprint inside SQL server using HTM ID’s ranges as a proxy.-Degrade HEALPix footprint to desired angular size of cell.-Use cells which have 98% of their area inside DR6 footprint.

-Distribution of Number of galaxies/Pencil Beam:

Reaching ~15 galaxies per beam at smallest cell size (~55’). Can’t go smaller.

-Estimating the Tail Index ζ using PEAKS OVER A THRESHOLD of extreme luminosities:

-Fit to GENERALIZED PARETO or use Pickands, DEdH estimators for ζ.

Looks like ζ ~ 0 Gumbel distribution is appropriate. no finite cutoff of the Luminosity function

at high Luminosities

Comparing Data to Standard Gumbel Distribution-Histograms of standarized extreme Luminosities.

Some good finite correctionfits, but some some cases correction has opposite sign.

Influence of variable number of Luminosities in the pencil beams?

Current status:Trying simulations…..