Astrophysics with the highly
red-shifted 21 cm line
Jonathan Pritchard
(CfA-HCO)
Collaborators:
Steve Furlanetto (UCLA)
Avi Loeb (Harvard)
Adam Lidz (CfA)
Mario Santos (CENTRA - IST)
Alex Amblard (UCI)
Hy Trac (CfA)
Renyue Cen (Princeton)
Asantha Cooray (UCI)
STScI
MAR
2009
Overview
•Introduction
•Simulating the effect of
Lya and X-rays on the 21cm signal
•Non-gaussianity
z~30
z~12
z~7
2
STScI
MAR
2009
21 cm basics
•HI hyperfine structure
11S1/2
10S1/2
•Use CMB backlight to probe 21cm transition
TS
Tg
n1
3
Tb
HI
l=21cm
TK
n0
n1/n0=3 exp(-hn21cm/kTs)
z=13
f21cm=1.4 GHz
z=0
fobs=100 MHz
•3D mapping of HI possible - angles + frequency
•21 cm brightness temperature
•21 cm spin temperature
•Coupling mechanisms:
 Radiative transitions (CMB)
 Collisions
 Wouthuysen-Field
STScI
MAR
2009
Wouthuysen-Field effect
Hyperfine structure of HI
4
22P1/2
21P1/2
Effective for Ja>10-21erg/s/cm2/Hz/sr
Ts~Ta~Tk
21P1/2
20P1/2
W-F recoils
Field 1959
nFL J
Lyman a
11S1/2
Selection rules:
DF= 0,1 (Not F=0F=0)
10S1/2
l~21 cm
STScI
MAR
2009
Thermal History
5
e.g. Furlanetto
2006
Measure with
EDGES
STScI
MAR
2009
Brightness
temperature
21 cm fluctuations
Baryon
Density
Neutral
fraction
Gas
Temperature
6
W-F
Coupling
Velocity
gradient
Lya
sources
Cosmology
b
Cosmology
Reionization
Amount of
neutral hydrogen
X-ray
sources
Spin
temperature
Velocity
(Mass)
STScI
MAR
2009
Brightness
temperature
Temporal separation?
Baryon
Density
Neutral
fraction
Gas
Temperature
7
W-F
Coupling
Velocity
gradient
Lya
sources
Cosmology
b
Cosmology
Reionization
Dark Ages
X-ray
sources
Twilight
STScI
MAR
2009
Theoretical modeling
8
Ionization: Excursion set formalism
Furlanetto, Zaldarriaga,
Hernquist 2004
•
•
Three contributions to Lya flux:
continuum & injected from stars + x-ray
X-rays from mini-quasars, XB, IC
Lya: Barkana & Loeb 2005, Pritchard & Furlanetto 2006,
Chuzhoy & Shapiro 2006
X-ray:
Chen & Miralde-Escude 2006, Pritchard & Furlanetto 2007
Pritchard & Loeb 2008
• Source properties very uncertain
d
dV
STScI
MAR
2009
Reionization simulation
Simulation techniques for reionization well developed
Boxes well matched to typical bubble sizes ~1-10Mpc
L=100 Mpc/h
NDM=28803
Mhalo=108 Msol/h
RT on 3603 grid
Shin+ 2007
Trac & Cen 2007
Santos+ 2008
Resolves halos capable
of atomic cooling
9
STScI
MAR
2009
Including other radiation fields
• Problems:
 Lya and X-ray m.f.p > 100 Mpc
 Tracking radiation field numerically expensive
(Baek+ 2009 - Included Lya radiative transfer into course 100 Mpc box, no X-rays)
• Approach:
Santos, Amblard, JRP, Trac, Cen, Cooray 2008
 Implement semi-analytic procedure using SFR measured from
simulation
assume
mean IGM
 Lya very similar - account for all Lyman series photons
 Convolution can be evaluated quickly via FT
 Source parameters extrapolated from low z sources
10
STScI
MAR
2009
Simulation + Lya +X-rays
Santos, Amblard, JRP, Trac, Cen, Cooray 2008
11
STScI
MAR
2009
Full simulation
Movie courtesy of Mario Santos
12
STScI
MAR
2009
Comparison of Fluctuations
uniform
Lya
X-ray
13
STScI
MAR
2009
Evolution of signal
Mean signal
Power spectrum
TS
Tcmb
TK
w/ dT
TB
d only
• T fluctuations significantly shift mean TB at moderate z
• Different fluctuations important at different times
14
STScI
MAR
2009
Comparison w/ theory
Dotted
= d+xi
Dashed
= +X-ray
Dot-dashed = +Lya
Solid= All
theory
simulation
• Good agreement between simulation and ionization model
• Lya and X-ray predictions need further work
• X-rays important at z=10
15
STScI
MAR
2009
Higher order terms
• Ionization fluctuations are not small dXH~1
• Higher order (in X) terms modify P21 on all scales
- important to include in modeling
Green=full
Dashed = h.o.t.
Solid=standard
Lidz+ 2007
Santos+ 2008
16
STScI
MAR
2009
Non-Gaussianity
• Ionization field highly non-Gaussian
-> suggests statistics other than power spectrum
important
• How best to characterise non-Gaussianity?




One point function e.g. skewness
N-point function e.g. bispectrum
Minkowski Functionals
Wavelets
Harker+ 2008
Bharadwaj & Pandey 2005
17
STScI
MAR
2009
Bispectrum
18
• Advantages: Density bispectrum well understood
Formalism can be transferred
Extra information to constrain models
• Sensitivity?
Bharadwaj
& Pandey 2005
Mao+ 2008
• Choice of triangles?
 Equilateral
 Squeezed
 Cylindrical array geometry
Parallel k
Comparable sensitivity to 2- & 3-point fn
Perpendicular k
STScI
MAR
2009
21 cm bispectrum
19
•At simplest level, 21 cm signal from density and neutral fraction
STScI
MAR
2009
Bispectrum - density
20
• Bispectrum from gravitational collapse (nonlinearity)
fairly well understood from 2PT
• For galaxy surveys can get bias from bispectrum
Can we do something similar for 21 cm signal?
Scoccimarro
1998
STScI
MAR
2009
Bispectrum - reionization
Bharadwaj
& Pandey 2005
• Model reionization with random distribution of bubbles with
same size
• Bispectrum with power on large scales
• Need better models…
21
STScI
MAR
2009
Counting triangles
• Measure bispectrum from box by counting triangles
McQuinn+
(2007)
L=100 Mpc
NDM=10243
Mhalo=109 Msol
+subgrid
k resolution Dk~2/L ~0.06 Mpc-1
# k modes ~ (k/Dk)3~5000 (k/1 Mpc-1)3
# triangles ~ (#k modes)2~2107 (k/1 Mpc-1)6
• Many triangles - numerically expensive to count all of them
22
STScI
MAR
2009
Equilateral triangles
23
General triangles defined by three parameters
-> focus on equilateral triangles since easy to plot
density
Neutral fraction
Pritchard, Lidz,
Furlanetto (in prep.)
STScI
MAR
2009
21 cm bispectrum
Density dominates on small scales; bubbles on large
24
STScI
MAR
2009
21 cm bispectrum: z
• Complex scale evolution with redshift
25
STScI
MAR
2009
Array sensitivity
2PT density
• Extend P(k) calculation of Bowman+ (2004), McQuinn+ (2004)
•Take density only bispectrum as baseline signal
• Reasonable S/N achievable with MWA/MWA5000
26
STScI
MAR
2009
Conclusions
• Inclusion of X-ray and Lya fluctuations will be important for
interpretation of 21 cm power spectrum
• Simulation suggests X-ray heating leaves cold voids until
quite late -> temperature fluctuations important
• Ionization modeling good, but Lya & X-ray needs
improvement
• Non-gaussianity of ionization field affects power spectrum
• Higher order statistics contain extra information
• Simulations have reached point that we can begin to
calculate the signal
- more work needed to understand and interpret
• First arrays should be sensitive to bispectrum
27
STScI
MAR
2009
28
STScI
MAR
2009
Massive neutrinos
Massive neutrinos reduce density fluc. on small scales
- Matter-radiation equality delayed (relative to Mnu=0)
- Free-streaming neutrinos don’t clump
Precision measurements of P(k) at k>0.01 h Mpc-1 -> Mnu
QuickTime™ and a
TIFF (Uncompressed) decompressor
are needed to see this picture.
Lesgourgues
& Pastor 2006
QuickTime™ and a
TIFF (Uncompressed) decompressor
are needed to see this picture.
29
STScI
MAR
2009
Comparison with galaxy surveys
• Galaxies good on large scales
• 21 cm could extend to small
scales
QuickTime™ and a
TIFF (Uncompressed) decompressor
are needed to see this picture.
Pritchard & Pierpaoli 2008
30
STScI
MAR
2009
Neutrino mass
31
QuickTime™ and a
TIFF (Uncompressed) decompressor
are needed to see this picture.
QuickTime™ and a
TIFF (Uncompressed) decompressor
are needed to see this picture.
QuickTime™ and a
TIFF (Uncompressed) decompressor
are needed to see this picture.
QuickTime™ and a
TIFF (Uncompressed) decompressor
are needed to see this picture.
Q
TIFF (Uncom
are need
QuickTime™ and a
TIFF (Uncompressed) decompressor
are needed to see this picture.
Q
TIFF (Uncom
are need
Pritchard & Pierpaoli 2008
STScI
MAR
2009
Total mass constraints
QuickTime™ and a
TIFF (Uncompressed) decompressor
are needed to see this picture.
QuickTime™ and a
TIFF (Uncompressed) decompressor
are needed to see this picture.
32