Post on 16-Apr-2018
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