Small Scale Structure in Voids Danny Pan Advisor: Michael Vogeley

Small Scale Structure in VoidsSmall Scale Structure in Voids

Danny PanDanny Pan

Advisor: Michael VogeleyAdvisor: Michael Vogeley

Motivation/GoalMotivation/Goal

LL-CDM models show small scale structure -CDM models show small scale structure in voidsin voids

Goal is to verify the small scale structure of Goal is to verify the small scale structure of voidsvoids

Possible results?Possible results?Structure exists, agree with modelsStructure exists, agree with modelsStructure does not exist, models may not tell Structure does not exist, models may not tell

the whole storythe whole story

Millenium Run SimulationMillenium Run Simulation

Simulated UniverseSimulated Universe

Gottlober (2003)Gottlober (2003)

OutlineOutline

IntroductionIntroductionResearch in VoidsResearch in VoidsVoidFinder (finds voids!)VoidFinder (finds voids!)Methods of AnalysisMethods of Analysis

Void StatisticsVoid StatisticsCorrelation FunctionCorrelation FunctionShapeFinderShapeFinder

Conclusion/ResultsConclusion/ResultsFuture WorkFuture Work

IntroductionIntroduction

The Universe contains objects, but it is The Universe contains objects, but it is mostly emptymostly empty

Modern cosmology tells us that evolution of Modern cosmology tells us that evolution of the Universe causes clumpinessthe Universe causes clumpinessDense regions stay dense and grow Dense regions stay dense and grow

asymmetricallyasymmetricallyUnderdense regions stay underdense and Underdense regions stay underdense and

grow symmetricallygrow symmetricallyResult is spherical voids with dense walls in the Result is spherical voids with dense walls in the

UniverseUniverse

Research in VoidsResearch in Voids

Gregory and Tifft (1976) first looked at Gregory and Tifft (1976) first looked at structure in Coma Superclusterstructure in Coma SuperclusterFound regions that seemed very emptyFound regions that seemed very empty

Kirshner et al (1982) found a 1,000,000 cu Kirshner et al (1982) found a 1,000,000 cu Mpc region in Bootes that was emptyMpc region in Bootes that was empty

Interest in voids grewInterest in voids grewRojas et al. (2004) observed differences in Rojas et al. (2004) observed differences in

void and wall galaxiesvoid and wall galaxies

VoidFinderVoidFinder

Used to determine sample of Void regions Used to determine sample of Void regions and Void galaxiesand Void galaxies

Volume limited sample from SDSSVolume limited sample from SDSS4783 square degrees of the sky4783 square degrees of the skymagnitude cut of 17.5magnitude cut of 17.5

approximately Lapproximately L** at furthest distance at furthest distance

radial cut of 100 and 300 hradial cut of 100 and 300 h-1-1 Mpc Mpc61,000 galaxies61,000 galaxies

GalaxiesGalaxies

3 Nearest Neighbors3 Nearest Neighbors

Potential Void GalaxiesPotential Void Galaxies

Walls OnlyWalls Only

Maximal SpheresMaximal Spheres

Void GalaxiesVoid Galaxies

VoidFinderVoidFinder

ResultsResults527 void regions527 void regions3369 void galaxies3369 void galaxies40% of the volume are voids40% of the volume are voids

Picture of VoidFinderPicture of VoidFinder

Methods of AnalysisMethods of Analysis

Void StatisticsVoid StatisticsCorrelation FunctionCorrelation FunctionShapeFinderShapeFinder

Void StatisticsVoid Statistics





Correlation FunctionCorrelation Function

Probability of two points separated by a Probability of two points separated by a distance r is:distance r is:

P r =n 2


Landy-Szalay (1993) equationLandy-Szalay (1993) equation

Correlation depends on data points as well as Correlation depends on data points as well as random pointsrandom points


ShapeFinderShapeFinder

Defined by Sahni et al. (1998) to assess Defined by Sahni et al. (1998) to assess shapes of objectsshapes of objects

Uses Minkowski Functionals to help Uses Minkowski Functionals to help determine shapesdetermine shapesVolume (V)Volume (V)Surface Area (S)Surface Area (S) Integrated Mean Curvature (C)Integrated Mean Curvature (C)Gaussian Curvature (G)Gaussian Curvature (G)

ShapeFinderShapeFinder

Can determine 3 phase space lengthsCan determine 3 phase space lengths L1 = V/SL1 = V/S L2 = S/CL2 = S/C L3 = CL3 = C

L1=L2<L3 FilamentL1=L2<L3 Filament L1<L2=L3 PancakeL1<L2=L3 Pancake

2 ShapeFinder statistics2 ShapeFinder statistics K1 = (L2-L1)/(L2+L1)K1 = (L2-L1)/(L2+L1) K2 = (L3-L2)/(L3+L2)K2 = (L3-L2)/(L3+L2)

K1=0, K2=0 SphereK1=0, K2=0 Sphere K1=1, K2=0 PancakeK1=1, K2=0 Pancake K1=0, K2=1 FilamentK1=0, K2=1 Filament

ShapeFinder ImagesShapeFinder Images

ShapeFinder ResultsShapeFinder Results

TABLE OF SHAPEFINDER RESULTS ON TABLE OF SHAPEFINDER RESULTS ON LARGEST VOIDSLARGEST VOIDS

ConclusionsConclusions

Void Statistics match other observational Void Statistics match other observational results as well as theoretical modelsresults as well as theoretical models

Radial density profiles match very well with Radial density profiles match very well with expected results, validates VoidFinderexpected results, validates VoidFinder

2 Point Correlation Function matches 2 Point Correlation Function matches various other samplesvarious other samples Implies correlation of underdense regions Implies correlation of underdense regions

mimic that of the entire samplemimic that of the entire sample

Future WorkFuture Work

ShapeFinder needs to be expanded to ShapeFinder needs to be expanded to accommodate for multiple “objects” within accommodate for multiple “objects” within each void regioneach void region

Analysis needs to be done on the Analysis needs to be done on the Millenium Run sample or another Lambda Millenium Run sample or another Lambda CDM model to compare resultsCDM model to compare results

AcknowledgementsAcknowledgements

Thank youThank youDr. Michael VogeleyDr. Michael VogeleyDr. Fiona HoyleDr. Fiona Hoyle

CommitteeCommitteeDr. Avijit GhoshDr. Avijit GhoshDr. Dave GoldbergDr. Dave GoldbergDr. Bhuvnesh JainDr. Bhuvnesh JainDr. Gordon RichardsDr. Gordon Richards

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Small Scale Structure in Voids Danny Pan Advisor: Michael Vogeley