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Distribution of Maximal Luminosities of Galaxies in SDSS

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…

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Distribution of Maximal Luminosities of Galaxies in SDSS

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  1. Distribution of Maximal Luminosities of Galaxies in SDSS Manuchehr Taghizadeh-Popp (JHU) Zoltán Rácz, Alex Szalay, Katalin Ozogany, Enikö Regös

  2. 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?

  3. 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.

  4. Pencil-Beams Need 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.

  5. -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

  6. Comparing Data to Standard Gumbel Distribution -Histograms of standarized extreme Luminosities. Some good finite correction fits, but some some cases correction has opposite sign.  Influence of variable number of Luminosities in the pencil beams? Current status: Trying simulations…..

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