Gas Dynamics in Galaxies

Danail Obreschkow

Cambridge, 6 Sep 2013

International Centre for Radio Astronomy Research University of Western

Australia

Historical conundrum

Star  Forma)on  Rate  

Atomic  Hydrogen  

0 1 2 3 4 5Redshift z

7 986 100

10

5

15

SF History (Hopkins & Beacom 2006); HI from DLAs (Prochaska+ 2005)

ΩHI  

ρSFR  

Molecular H2 (~1%)

Atomic HI (~2%)

Stars (~7%)

Ionized HII (~90%)

Cosmic food chain

HI HII stars H2 2 Gyr 0.5-5 Gyr

Redshift

ρ(SFR)

0 1 2 3 4

ΩHI

ΩH2

ρSFR (Hopkins & Beacom 2006), DLAs (Prochaska 2005), THINGS CO z=0 (Leroy 2008), COLD GASS CO z=0 (Saintonge 2011), PHIBSS SMG CO z~2 (Tacconi 2013)

Pressure

THINGS (Leroy 2008)

DraftversionJune30,2012

Preprintty

pesetusingLATEX

style

emulateapjv.11/10/09

AMEASURE

OFCOSMIC

FILAMENTARIT

YFOR

‘POST

POW

ER-SPECTRUM’COSMOLOGY

D.Obresc

hkow

and

C.Power

TheUniversity

ofW

estern

Australia,

ICRAR,35

StirlingHwy,

Crawley,

WA

6009

,Australia

(Dated

:Ju

ne30

,20

12)

DraftversionJune30,2012

ABSTRACT

Weintrod

uce

ameasure

µ(r)of

cosm

iclarge-scalestructure,whichis

statisticallyindep

endentof

the2-point

correlation⇠

2(r)an

dthepow

er-spectrum.Thismeasure

naturallyem

ergesfrom

fourbasic

requ

irem

ents:statisticalhom

ogen

eity

andisotropy

;indep

enden

ceof

spectral

amplitudes;nu

merical

conv

ergence;an

dsimplicity.Phy

sically,

µ(r)canbeinterpretedas

ameasure

ofcosm

icfilamentarity,

whichis

truly

scale-invarian

tan

dparam

eter-free.

Bycalculatingµ(r)forasuiteof

synthetic

den

-sity

fieldsproducedby

N-bod

ySPH-sim

ulation

s,wedem

onstrate

that

thelate-tim

euniverse

holdsa

sign

ificant

amou

ntof

inform

ationin

µ(r).

Asan

exam

ple,wethen

show

that

thecosm

olog

ical

param

-etersxan

dyareconstrained

1.8-times

betterby

combiningµ(r)an

d⇠

2(r)than

byusing⇠

2(r)alon

e.µ(r)thereforepaves

theway

toan

enhan

cedan

alysis

ofexistingan

dupcomingredshiftsurveys.

1.IN

TRODUCTIO

N

⌃H

2/⌃

HI/

p

0.8

(1)

Themod

elof

aflat

andnearlyscale-free

universe

dom

-inated

bydarken

ergy

andcold

darkmatter(⇤

CDM),

passedstringent

empirical

testsof

thenew

millennium.

Thesix

free

mod

elparam

eterswerefound

simultan

e-ou

slyconsistent(K

omatsu

etal.20

11)withthetemper-

ature

fluctuationsin

thecosm

icmicrowavebackg

round

(CMB,Larsonet

al.20

11)measuredby

theW

ilkinson

MicrowaveAnisotropy

Probe(W

MAP,Ben

nettet

al.

2003

a,b),thebaryonacou

stic

oscillations(B

AOs)

inthe

late-tim

elarge-scalestructure

(LSS)derived

from

galaxy

redshiftsurveys(SDSS:P

ercivaletal.2

010;

seealso

2dF-

GRS:Percivalet

al.20

07;W

iggleZ

:Blake

etal.20

11),

andredshift–distance

measurements

based

ontypeIa

su-

pernovae

(SNe,

Hickenet

al.20

09;Kessler

etal.20

09).

This

phen

omen

alsuccessof

the

⇤CDM

cosm

olog

ystronglycontrastswithou

rignoran

cerega

rdingthena-

ture

ofitsdarkconstituents.Crucial

properties

ofthese

constituents,such

asthetemperature

ofdarkmatter,are

covertly

imprinted

inthefine-tuningof

theLSS(Smith&

Markovic20

11).

Yet,this

inform

ationis

not

read

ilyac-

cessible

tomeasurements.For

onething,

theLSSis

not

directlyob

servab

ledueto

theinvisibilityof

darkmat-

ter,

redshiftdistortions(B

onvin&

Durrer

2011

),gravi-

tation

allensing(Jainet

al.20

00),an

dinstrumentallim-

itations.

For

another,theinform

ationin

theLSSissub-

stan

tially

maskedby

apurely

random

compon

ent.

To

filter

outthis

random

compon

entob

served

and

mod

elled

den

sity

fieldsare

passed

through

statistical

measures.

Thoseareindep

endentof

cosm

icrandom

ness

upto

avolume-dep

endentshot

noise,called

‘cosmicvari-

ance’.

Inthecase

ofastatistically

hom

ogen

eousan

disotropic

universe

(see

Section

2),theinfinitefamilyof

isotropic

n-point

(n�

2)correlationfunctionsgets

rid

ofallrandom

nessupto

cosm

icvarian

ce,butpreserves

allinform

ation(Fry

1985

).How

ever,today

nofiniteset

ofstatisticalmeasuresis

know

n,whichexclusively

and

exhau

stivelydescribes

theinform

ationof

thecosm

icden

-sity

field.Mostcu

rrentstudiesby

passthisissueby

con-

sideringbuttheisotropic

2-point

correlationfunctionor,

equivalently,

theisotropic

pow

erspectrum.In

doingso,

important

inform

ationmight

belost;e.g.,subtlestruc-

turalfeatures,such

ascosm

icfilaments,becom

eindistin-

guishab

lefrom

spherical

features.

Som

estudiesim

prove

onthosedrawbacks

byconsideringhigher-order

corre-

lation

s(Fry

&Peebles19

78;Suto

&Matsubara19

94;

Takad

a&

Jain

2003

)an

dalternativestatisticalm

easures,

such

asthefractalcorrelation

dim

ension

(Scrim

geou

ret

al.20

12),

void

distribution

functions(W

hite19

79),

andfilamentfinders(Smithet

al.20

12).

How

ever,the

additional

ben

efitof

thesemeasuresremainscu

mbersome

forthey

alldep

endon

the2-point

correlation.

Hen

ce,theob

jectiveof

thisworkisto

introd

uce

anew

statisticalmeasure

ofthecosm

icden

sity

field,whichis

strictly

indep

endentof

any2-point

correlation,i.e.which

only

dep

endson

‘phasecorrelations’.This

requ

irem

ent

naturally

lead

sto

ameasure,which

wewillcall

the

isotropic

hyper-correlation

functionµ(r).

Weshow

that,

inalimited

sense,this

function

can

beinterpreted

asa

measure

ofcosm

ic‘filamentary’on

lengths2r.

By

calculatingµ(r)forvariou

ssimulatedden

sity

fieldswe

findthat

µ(r)holdsasign

ificant

amou

ntof

cosm

olog

ical

inform

ation.

This

implies

that

the2-point

correlation

overlook

sasubstan

tial

amou

ntof

inform

ation.Wethen

dem

onstrate

that

combiningµ(r)withthe2-point

corre-

lation

functionconstrainsthecosm

olog

ical

param

etersx

andyat

unprecedentedaccu

racy.

Thisworkfocu

sses

onmathem

atical

andphy

sicalcon-

cepts,whichwedem

onstrate

andverify

usingsimulated

den

sity

fields.

Anap

plication

toob

served

dataisbeyon

dthescop

eof

thiswork,

since

wewishto

separateconcep-

tual

develop

ments

from

additional

challengesattributed

toob

servations(butseediscu

ssionin

Section

5).

Thearticleproceed

sas

follow

s.Section

2summa-

rizesestablished

concepts

rega

rdingcosm

icstructure

and

clarifies

the

meaning

ofn-point

correlation

functions

andpoly-spectra.

Section

3form

ally

defi

nes

thehy

per-

correlationfunctionan

dpresentsseveralinterpretation

sof

this

statisticalmeasure.A

range

ofcosm

olog

ical

ap-

plication

sisthen

considered

inSection

4.Thoseillustra-

tion

srely

onsimulatedden

sity

fields,

obtained

through

Draft version June 30, 2012Preprint typeset using LATEX style emulateapj v. 11/10/09

A MEASURE OF COSMIC FILAMENTARITY FOR ‘POST POWER-SPECTRUM’ COSMOLOGY

D. Obreschkow and C. PowerThe University of Western Australia, ICRAR, 35 Stirling Hwy, Crawley, WA 6009, Australia

(Dated: June 30, 2012)Draft version June 30, 2012

ABSTRACT

We introduce a measure µ(r) of cosmic large-scale structure, which is statistically independent ofthe 2-point correlation ⇠2(r) and the power-spectrum. This measure naturally emerges from four basicrequirements: statistical homogeneity and isotropy; independence of spectral amplitudes; numericalconvergence; and simplicity. Physically, µ(r) can be interpreted as a measure of cosmic filamentarity,which is truly scale-invariant and parameter-free. By calculating µ(r) for a suite of synthetic den-sity fields produced by N -body SPH-simulations, we demonstrate that the late-time universe holds asignificant amount of information in µ(r). As an example, we then show that the cosmological param-eters x and y are constrained 1.8-times better by combining µ(r) and ⇠2(r) than by using ⇠2(r) alone.µ(r) therefore paves the way to an enhanced analysis of existing and upcoming redshift surveys.

1. INTRODUCTION

⌃H2/⌃HI / p

0.8 (1)

The model of a flat and nearly scale-free universe dom-inated by dark energy and cold dark matter (⇤CDM),passed stringent empirical tests of the new millennium.The six free model parameters were found simultane-ously consistent (Komatsu et al. 2011) with the temper-ature fluctuations in the cosmic microwave background(CMB, Larson et al. 2011) measured by the WilkinsonMicrowave Anisotropy Probe (WMAP, Bennett et al.2003a,b), the baryon acoustic oscillations (BAOs) in thelate-time large-scale structure (LSS) derived from galaxyredshift surveys (SDSS: Percival et al. 2010; see also 2dF-GRS: Percival et al. 2007; WiggleZ: Blake et al. 2011),and redshift–distance measurements based on type Ia su-pernovae (SNe, Hicken et al. 2009; Kessler et al. 2009).This phenomenal success of the ⇤CDM cosmology

strongly contrasts with our ignorance regarding the na-ture of its dark constituents. Crucial properties of theseconstituents, such as the temperature of dark matter, arecovertly imprinted in the fine-tuning of the LSS (Smith &Markovic 2011). Yet, this information is not readily ac-cessible to measurements. For one thing, the LSS is notdirectly observable due to the invisibility of dark mat-ter, redshift distortions (Bonvin & Durrer 2011), gravi-tational lensing (Jain et al. 2000), and instrumental lim-itations. For another, the information in the LSS is sub-stantially masked by a purely random component.To filter out this random component observed and

modelled density fields are passed through statisticalmeasures. Those are independent of cosmic randomnessup to a volume-dependent shot noise, called ‘cosmic vari-ance’. In the case of a statistically homogeneous andisotropic universe (see Section 2), the infinite family ofisotropic n-point (n � 2) correlation functions gets ridof all randomness up to cosmic variance, but preservesall information (Fry 1985). However, today no finite setof statistical measures is known, which exclusively andexhaustively describes the information of the cosmic den-sity field. Most current studies bypass this issue by con-

sidering but the isotropic 2-point correlation function or,equivalently, the isotropic power spectrum. In doing so,important information might be lost; e.g., subtle struc-tural features, such as cosmic filaments, become indistin-guishable from spherical features. Some studies improveon those drawbacks by considering higher-order corre-lations (Fry & Peebles 1978; Suto & Matsubara 1994;Takada & Jain 2003) and alternative statistical measures,such as the fractal correlation dimension (Scrimgeouret al. 2012), void distribution functions (White 1979),and filament finders (Smith et al. 2012). However, theadditional benefit of these measures remains cumbersomefor they all depend on the 2-point correlation.Hence, the objective of this work is to introduce a new

statistical measure of the cosmic density field, which isstrictly independent of any 2-point correlation, i.e. whichonly depends on ‘phase correlations’. This requirementnaturally leads to a measure, which we will call theisotropic hyper-correlation function µ(r). We show that,in a limited sense, this function can be interpreted asa measure of cosmic ‘filamentary’ on lengths 2r. Bycalculating µ(r) for various simulated density fields wefind that µ(r) holds a significant amount of cosmologicalinformation. This implies that the 2-point correlationoverlooks a substantial amount of information. We thendemonstrate that combining µ(r) with the 2-point corre-lation function constrains the cosmological parameters xand y at unprecedented accuracy.This work focusses on mathematical and physical con-

cepts, which we demonstrate and verify using simulateddensity fields. An application to observed data is beyondthe scope of this work, since we wish to separate concep-tual developments from additional challenges attributedto observations (but see discussion in Section 5).The article proceeds as follows. Section 2 summa-

rizes established concepts regarding cosmic structure andclarifies the meaning of n-point correlation functionsand poly-spectra. Section 3 formally defines the hyper-correlation function and presents several interpretationsof this statistical measure. A range of cosmological ap-plications is then considered in Section 4. Those illustra-tions rely on simulated density fields, obtained through

Physical model ra

dius

Redshift

HST (Bowens 2004)

Density decreases Pressure dictates molecularity

Draft version June 30, 2012Preprint typeset using LATEX style emulateapj v. 11/10/09

A MEASURE OF COSMIC FILAMENTARITY FOR ‘POST POWER-SPECTRUM’ COSMOLOGY

D. Obreschkow and C. PowerThe University of Western Australia, ICRAR, 35 Stirling Hwy, Crawley, WA 6009, Australia

(Dated: June 30, 2012)Draft version June 30, 2012

ABSTRACT

We introduce a measure µ(r) of cosmic large-scale structure, which is statistically independent ofthe 2-point correlation ⇠2(r) and the power-spectrum. This measure naturally emerges from four basicrequirements: statistical homogeneity and isotropy; independence of spectral amplitudes; numericalconvergence; and simplicity. Physically, µ(r) can be interpreted as a measure of cosmic filamentarity,which is truly scale-invariant and parameter-free. By calculating µ(r) for a suite of synthetic den-sity fields produced by N -body SPH-simulations, we demonstrate that the late-time universe holds asignificant amount of information in µ(r). As an example, we then show that the cosmological param-eters x and y are constrained 1.8-times better by combining µ(r) and ⇠2(r) than by using ⇠2(r) alone.µ(r) therefore paves the way to an enhanced analysis of existing and upcoming redshift surveys.

1. INTRODUCTION

⌃H2

⌃HI/ p

0.8 (1)

The model of a flat and nearly scale-free universe dom-inated by dark energy and cold dark matter (⇤CDM),passed stringent empirical tests of the new millennium.The six free model parameters were found simultane-ously consistent (Komatsu et al. 2011) with the temper-ature fluctuations in the cosmic microwave background(CMB, Larson et al. 2011) measured by the WilkinsonMicrowave Anisotropy Probe (WMAP, Bennett et al.2003a,b), the baryon acoustic oscillations (BAOs) in thelate-time large-scale structure (LSS) derived from galaxyredshift surveys (SDSS: Percival et al. 2010; see also 2dF-GRS: Percival et al. 2007; WiggleZ: Blake et al. 2011),and redshift–distance measurements based on type Ia su-pernovae (SNe, Hicken et al. 2009; Kessler et al. 2009).This phenomenal success of the ⇤CDM cosmology

strongly contrasts with our ignorance regarding the na-ture of its dark constituents. Crucial properties of theseconstituents, such as the temperature of dark matter, arecovertly imprinted in the fine-tuning of the LSS (Smith &Markovic 2011). Yet, this information is not readily ac-cessible to measurements. For one thing, the LSS is notdirectly observable due to the invisibility of dark mat-ter, redshift distortions (Bonvin & Durrer 2011), gravi-tational lensing (Jain et al. 2000), and instrumental lim-itations. For another, the information in the LSS is sub-stantially masked by a purely random component.To filter out this random component observed and

modelled density fields are passed through statisticalmeasures. Those are independent of cosmic randomnessup to a volume-dependent shot noise, called ‘cosmic vari-ance’. In the case of a statistically homogeneous andisotropic universe (see Section 2), the infinite family ofisotropic n-point (n � 2) correlation functions gets ridof all randomness up to cosmic variance, but preservesall information (Fry 1985). However, today no finite setof statistical measures is known, which exclusively andexhaustively describes the information of the cosmic den-

sity field. Most current studies bypass this issue by con-sidering but the isotropic 2-point correlation function or,equivalently, the isotropic power spectrum. In doing so,important information might be lost; e.g., subtle struc-tural features, such as cosmic filaments, become indistin-guishable from spherical features. Some studies improveon those drawbacks by considering higher-order corre-lations (Fry & Peebles 1978; Suto & Matsubara 1994;Takada & Jain 2003) and alternative statistical measures,such as the fractal correlation dimension (Scrimgeouret al. 2012), void distribution functions (White 1979),and filament finders (Smith et al. 2012). However, theadditional benefit of these measures remains cumbersomefor they all depend on the 2-point correlation.Hence, the objective of this work is to introduce a new

statistical measure of the cosmic density field, which isstrictly independent of any 2-point correlation, i.e. whichonly depends on ‘phase correlations’. This requirementnaturally leads to a measure, which we will call theisotropic hyper-correlation function µ(r). We show that,in a limited sense, this function can be interpreted asa measure of cosmic ‘filamentary’ on lengths 2r. Bycalculating µ(r) for various simulated density fields wefind that µ(r) holds a significant amount of cosmologicalinformation. This implies that the 2-point correlationoverlooks a substantial amount of information. We thendemonstrate that combining µ(r) with the 2-point corre-lation function constrains the cosmological parameters xand y at unprecedented accuracy.This work focusses on mathematical and physical con-

cepts, which we demonstrate and verify using simulateddensity fields. An application to observed data is beyondthe scope of this work, since we wish to separate concep-tual developments from additional challenges attributedto observations (but see discussion in Section 5).The article proceeds as follows. Section 2 summa-

rizes established concepts regarding cosmic structure andclarifies the meaning of n-point correlation functionsand poly-spectra. Section 3 formally defines the hyper-correlation function and presents several interpretationsof this statistical measure. A range of cosmological ap-plications is then considered in Section 4. Those illustra-

Obreschkow+2009 (MNRAS 394, ApJ 698, ApJL 696)

Comparison to observations

Redshift

ρ(SFR)

Hopkins & Beacom 2006

0 1 2 3 4

ΩH2 = (1+z)1.6 ΩHI

•  How to model the cosmic evolution of ΩHI? •  How do individual galaxies evolve? •  Effects of mergers, SB & AGN feedback, … ?

ΩHI

Cosmological model

Cosmic    structure  (N-­‐body  simula)on)  

Galaxy    evolu2on  (semi-­‐analy)cs)  

Split  HI  from  H2  (analy)c  post-­‐processing)  

Springel 2005, Croton 2006, De Lucia 2007, Obreschkow 2009

Pressured disk model for HI and H2

Obreschkow et al. 2009 (MNRAS 394 and ApJ 698); Leroy et al. 2008 (AJ 136)

Central H2/HI ratio Depends on Mstars, Mgas, r0

Observa2onally  mo2vated  assump2ons:  •     HI  and  H2  form  a  flat,  axially  symmetric  disk  •     ΣH2/  ΣHI  scales  as  power  of  pressure  •     ΣHI(r)+ΣH2(r)  is  an  exponen)al  profile  

 •     Scale  radius  of  stars  is  half  that  of  cold  gas  •     Velocity  dispersion  of  stars  varies  as  (Σstars)0.5  

•     Velocity  dispersion  of  gas  is  constant  

HI saturates at 10 Msun/pc2

Virtual sky of HI and CO lines

1 deg Ian Heywood

1 arcmin

HI CO(5–4) CO(1–0)

Obreschkow et al. 2009 (ApJ 703)

Modelling of emission lines

Vcbulge

0 5 radius [kpc]10 15

0 100–100–200 200

!HI

Vctotal

Vchalo

Vcdisk

observed velocity

(b)

(c)

(a)

Obreschkow et al. 2013 (ApJ 766)

HI emission line

HI surface density

Rotation velocity

Velocity function

CDM

SN

observations

UV

AGN

WDM

Mass

Sp

ace

den

sity

⇒ Baryon mass is a bad tracer of dark matter mass.

Rotation velocity

HIPASS mocks

Five HIPASS volumes inside the Millennium box.

Obreschkow et al. 2013 (ApJ 766)

beam

W50

100%

50%

0%

sky view spectrum

beam

W50

100%

50%

0%

sky view spectrum

Simulation versus observation

W50 [km s-1

]

101

102

103

104

50 100 200 500

dN

/ d

ex

Measurement

Model CDM!

Model WDM 1 keV c–2

!

Model WDM 0.5! keV c–2

Obreschkow et al. 2013 (ApJ 766)

Cold gas mass functions

z=2  z=0  

z=10  

z=5  z=0  z=2  

z=5  

z=10  

BzK-­‐4171  BzK-­‐21000  

Obreschkow et al. ApJ 696 (2009); Zwaan et al., MNRAS 359 (2005), Keres et al., ApJ 582 (2003), Daddi 2009

Evolution of the H2 / HI ratio

Obreschkow et al. ApJ 696 (2009); Popping (2013); Fu et al., MNRAS 409 (2010); Lagos et al., MNRAS 418 (2011); Pontzen et al., MNRAS 390 (2008); Tacconi et al., Nature 463 (2010)

Millennium resolution misses most of ΩHI at z>2 – accounted for by Lagos 2011 via Monte-Carlo extension of merger trees.

Tacconi+ 2010

Milky Way (based on 2000 scenarios)

80  kpc  

H2  

HI  

Milky Way (based on 2000 scenarios)

80  kpc  

500  M¤/pc2  

H2  

HI  

Milky Way (based on 2000 scenarios)

ALMA band 3 has a 50% chance of detecting a MW progenitor at z=3 in 24h.

5

10

15

20

0 1 2 3 4 5 6 7 8

Redshift z

0

108

109

1010

H2

HI

H2

HI

Ma

ss [

M

]H

alf

-ma

ss r

ad

ius

[kp

c]10

11

Stars

5

10

15

20

0 1 2 3 4 5 6 7 8

Redshift z

0

108

109

1010

H2

HI

H2

HI

Mass

[M

]

Half

-mass

rad

ius

[kp

c]

1011

Stars

Obreschkow, Heywood and Rawlings, 2011 (ApJ 743)

High gas fractions => giant clumps

Clump cluster galaxies (z=2) Marginally stable disks (Toomre Q=1):

Elmegreen & Elmegreen 2005, Elmegreen D. M., 2007 (ApJ, 670), Bournaud 2013

(see review Glazebrook 2013)

Clumps migrate to the bulge

Bournaud 2013 [Ramses AMR hydro simulation with stellar feedback]

3  kpc  

200  Myr   300  Myr  

500  Myr  400  Myr  

=> Q ~ j/M is important for bulge growth

Baryon angular momentum

Specific angular momentum

Regular spirals in THINGS (Leroy 2008)

B/T

M-j-B/T relation

Obreschkow 2013 (coming soon)

B/T

Unbarred spirals Barred spirals

The simplest model of galaxy formation

Mutch, Croton, Poole 2013

1012   1013  1011   Mvir  [Msun]  

The second simplest model of galaxy formation

•  Key to time-dependence (without invoking z) •  Size distribution at all z •  Morphology at all z •  ISM state at all z

Summary

Cosmic evolution in gas fraction (=> clumps & dispersion at z>1) Cosmic evolution of H2/HI

(=> declining cosmic SFR)

Angular momentum is the key