connecting 21 cm observations to theoretical models

CONNECTING 21 CM
OBSERVATIONS TO THEORETICAL
MODELS
Jonathan Pober
NSF Postdoctoral Fellow
Brown University
Preparing for the 21 cm Revolution
October 2, 2015
Photo Credit: Peter Wheeler, ICRAR
Connecting 21 cm Observations to
Theoretical Models
Observations
???
Theoretical
Models
Connecting 21 cm Observations to
Theoretical Models
Observations
Power
Spectrum
Theoretical
Models
Connecting 21 cm Observations to
Theoretical Models
Observations
Power
Spectrum
Theoretical
Models
So You Want To Constrain Some Theory
Real Space
Power Spectrum
Pober et al. (2014)
Foregrounds: Theory and Practice
23 July 2010
15:26
Observed
Predicted
k ll
1/frequency
resolution
| k | shells
Cosmic
evolution
∆ z ≈ 0.5
Foregrounds
k
1/ FoV
T
ARI
Max baseline
n of the k-space measurement space of an HI interferometer. The instrument measures the
n k-space cells, with the power spectrum (PS) intensity and uncertainty per cell described by
Morales & Wyithe 2010
16, 17, and 18. For epoch of reionization (EoR) measurements, the PS intensity is averaged within
Pober et al. 2013
The Wedge (To Scale)
0.5
•  Real instruments do not probe k|| and
k⊥ on equal scales
log10[P (k)]
15
•  300 m baseline è k⊥,max ~ 0.15 h/Mpc
k∥ [hMpc−1 ]
•  100 kHz resolution è k||,max ~ 5 h/Mpc
0.3
13
0.2
•  21 cm experiments probe line of sight
k modes
•  Wedge exacerbates issue
log10 [mK2 (h−1 Mpc)3 ]
0.4
0.1
0.0
0.00 0.06 0.12
k⊥ [hMpc−1 ]
11
Pober 2015
Pober 2015
The wedge bias
Line of Sight Modes
3
•  Observed power
1.0
spectrum is in redshift
space – not isotropic
xHI
0.8
0.6
0.4
0.2
8
z
9
10
Figure 3. The mass averaged mean neutral fraction as a function of redshift
in our simulations.
Jensen et al. 2015
µ = 0.5
µmin = 0.95
min
60
•  Anti-correlation between
density and ionization
fields can decrease line
of sight power
∆2s (mK2)
k(Mpc−1)
40
0.09
0.16
0.25
0.42
20
0
0.2
0.4
0.6
0.8
1.0 0.2
xHI
0.4
0.6
0.8
1.0
•  Potential for “wedge”
bias if not accounted for
(Jensen et al. 2015)
Connecting 21 cm Observations to
Theoretical Models
Observations
Power
Spectrum
Theoretical
Models
Parsons et al. 2014
Sensitivity Limits
•  Parsons et al. 2014:
Δ2(k) < 1681 mK2
(z = 7.7)
Limits require some degree
of IGM heating
Sensitivity Limits
•  Parsons et al. 2014:
Δ2(k) < 1681 mK2
(z = 7.7)
•  Ali et al. 2015:
Δ2(k) < 502 mK2
(z = 8.4)
Ali et al. 2015
Sensitivity Limits
Pober et al. 2015
•  Parsons et al. 2014:
Δ2(k) < 1681 mK2
(z = 7.7)
•  Ali et al. 2015:
Δ2(k) < 502 mK2
(z = 8.4)
Quantitative limits on IGM
temperature: Tspin > 10 K
Sensitivity Limits
Pober et al. 2015
•  Parsons et al. 2014:
Δ2(k) < 1681 mK2
(z = 7.7)
•  Ali et al. 2015:
Δ2(k) < 502 mK2
(z = 8.4)
Potential that observed
galaxies cannot heat IGM
to level required
Sensitivity Limits
•  Parsons et al. 2014:
Δ2(k) < 1681 mK2
(z = 7.7)
•  Ali et al. 2015:
Δ2(k) < 502 mK2
(z = 8.4)
•  HERA 331:
Δ2(k) ≤ 1 mK2
adapted from Mesinger, Ewall-Wice & Hewitt 2014
Sensitivity Limits
•  Parsons et al. 2014:
Δ2(k) < 1681 mK2
(z = 7.7)
•  Ali et al. 2015:
Δ2(k) < 502 mK2
(z = 8.4)
•  HERA 331:
Δ2(k) ≤ 1 mK2
Pober et al. 2014
Sensitivity Limits
•  Parsons et al. 2014:
Δ2(k) < 1681 mK2
(z = 7.7)
•  Ali et al. 2015:
Δ2(k) < 502 mK2
(z = 8.4)
•  HERA 331:
Δ2(k) ≤ 1 mK2
adapted from Greig & Mesinger 2015
Sensitivity Limits
•  Parsons et al. 2014:
Δ2(k) < 1681 mK2
(z = 7.7)
•  Ali et al. 2015:
Δ2(k) < 502 mK2
(z = 8.4)
•  HERA 331:
Is there a near-term 21 cm science
“wasteland”?
Δ2(k) ≤ 1 mK2
adapted from Mesinger, Ewall-Wice & Hewitt 2014
discuss the validity of this assumption below, but first we outline the role of these t
in setting the power spectrum amplitude.
Intermediate Sensitivity Science
It is worthwhile to keep the brightness temperature contrast between the 21 c
CMB ( Tb ) in mind as we discuss the e↵ect of various parameters:


1
TCMB (z) H(z)/(1 + z)
Tb (⌫) ⇡ 9xHI (1 + )(1 + z) 2 1
mK,
TS
dvk /drk
where xHI is the global neutral hydrogen fraction, z is the redshift, TCMB is the
the cosmic microwave background, TS is the spin temperature, H(z) is the Hubble
Limitsalong
onthe
Tspin
dvk /drk is the gradient of the proper• velocity
line can
of sightonly
(Furlanetto
¯Tb
we define a fractional brightness temperature
perturbation,
x) ⌘ [ Tb (~x)
21 (~
improve
so much
spectrum, P (~k), is given by the ensemble average of the square of the spatial Fou
•  … and how cold do we
expect the IGM to be
any way?
Pober et al. 2015
Do We Know What To Do With A
Detection?
4253
21CMMC: astrophysics from the 21 cm EoR signal
esc
0.6
0.8
step forward
1.0
1.0
0.8
0.4
HERA 331
SKA
isocontours of
constant x̄HI
1σ
2σ
PDF(ζ 0 )
0.6
0.2
•  Framework for
0.8
0.6
0.4
0.2
0.0
0.0
1.0
20
18
16
14
12
10
8
6
4
2
0.8
0.6
0.4
0.2
0.4
x¯ HI
0.6
0.8
1.0
0.2
0.0
1.0
•  How well do ζ,
Tvir,min, & Rmfp
capture
reionization?
Feed
log10 (T vir
[K])
5.2
5.0
0.8
4.8
0.6
4.6
0.4
4.4
0.2
4.2
4.0
20
40
60
ζ0
80
100
2
4
6
8 10 12 14 16 18 20
R mfp (Mpc)
4.0
4.2
4.4 4.6 4.8 5.0
Feed
[K])
log10 (T vir
5.2
Feed
PDF(log10 (T vir
))
mfp
(Mpc)
0.0
R
incorporating other
constraints… but
what is the
common ground?
1.0
mfp )
0.4
PDF(R
f
0.05 0.2
PDF(x¯ HI )
•  21CMMC is a huge
0.0
Figure 3. The recovered constraints from 21CMMC on our three parameter EoR model parameters for a single (z = 9) 1000 h observation of the 21 cm PS
obtained with HERA (red curve) and the SKA (blue curve). In the diagonal panels, we provide the 1D marginalized PDFs for each of our EoR model parameters
Feed ), respectively) and we highlight our fiducial choice for each by the vertical dashed line. Additionally, we cast our ionizing efficiency,
(ζ 0 , Rmfp and log10 (Tvir
ζ 0 , into a corresponding escape fraction, fesc , on the top axis (simply using the fiducial values in equation 2). In the upper-right panel, we provide the 1D
PDF of the recovered IGM neutral fraction where the vertical dashed line corresponds to the neutral fraction of the mock 21 cm PS observation (x̄H I = 0.71).
Finally, in the lower-left corner we provide the 1 (thick) and 2σ (thin) 2D joint marginalized likelihood contours for our three EoR parameters (crosses denote
their fiducial values, and the dot–dashed curves correspond to isocontours for x̄H I of 20, 40, 60 and 80 per cent from bottom to top).
Greig & Mesinger 2015
First detection(s)
•  100 to 200 MHz
probes z ~ 6 – 13
•  Sky noise dominated
•  Tsky ∝ (freq.)-2.55
•  Power spectrum noise
(mK2) at 200 MHz is up
to 35 times larger than
at 100 MHz
Ø > 10σ detection at 50% ionization
Ø No significant detection of peak
explained by more
the noise level was
ciently rapid time i
infer the overall noi
Although one can
values of k and z, ou
6.2 × 104 mK2 at k
of observation, and
modes at higher k. Since we do not subtract a bias, even
these “detections” are upper limits on the cosmological
signal.
A number of barely significant detections are observed at
higher k. Though we excise bins associated with the k∥ ∼
0.45 h Mpc−1 line, the slight detections may be due to
leakage from that line. At higher z, the feature may be due
Would You Believe A Detection?
108
•  Every published
Parsons et al. 2014
6
10
5
z = 6.6 - 7.0
Paciga et al. 2014
∆ 2(k) (mK 2)
Ali et al. 2015
10
Dillon et al. 2015
z = 6.2 - 6.6
104
103
10
2
10
1
100
10
-1
-1
10
0
10
-1
k (h Mpc )
Downloaded from http://mnras.oxfordjournals.org/ at University of Washington on May 13, 2014
21 cm limit
detected
something
10
7
-1
10
0
k (h Mpc )
Beardsley
2015 (thesis)
2σ Errors and 20%-80% Window Functions
Even/Odd Cross ∆ (k)
2
!
Thermal Noise
8
Figure 11. Power as a function of the total wavenumber k = k⊥ 2 + k∥ 2 . Each point represents a different
10 (k⊥ , k∥ ) pair; there is no binning in k. Colours
indicate the number of SVD modes removed; 0 (blue), 4 (green), 8 (red), 16 (cyan) and 32 (purple) are shown. The boxed region at k ≈ 0.5 is shown inset,
FIG. 9 (color online). Finally, we can set confident limits on the 21 cm power spectrum at t
with nearby points each of the three marked k spread out slightly for clarity. The best limit at 2σ is (248 mK)2 at 0.50 h Mpc−1 achieved with four SVD modes
bandwidth
into three 10.24 MHz data cubes. The lowest k bins show the strongest “de
removed. The solid line shows the predicted 3D power spectrum from Iliev et al. (2008) assuming
a 30 mK signal.
5 CONCLUSION
Using an SVD as a foreground removal technique and a simulated
signal to quantify the loss of a real 21 cm signal the SVD may
cause, we have calculated an upper limit to the H I power spectrum
at z = 8.6 of (248 mK)2 at k = 0.50 h Mpc−1 . The k⊥ component
was found using the median power in annuli of the (u, v) plane,
while a Hermite window was used to sample the k∥ direction. This
is in contrast to our previous work with a piecewise-linear filter
∆ 2 x x ( mK 2 )
correction, making this measurement an upper limit on the actual
21 cm signal.
6
suprahorizon
10 emission [26] that we expect to appear because we only cut out the wedge and
also be
seeattributed
marginalin“detections”
at higher kassumptions
which are likely due to subtle bandpass calibratio
ence can likely
part to the simplifying
such error,
which
at bins
around
k∥ ∼ 0.45funch Mpc−1 and can be seen most clearly in Fi
necessary when
deriving
the occurs
analytical
Hermite
windowing
2
4
2
three
of these
plots.
Our
absolute
lowest
limitthan
requires
tion. We also
consider
the
current
result
to be more
robust
that Δ ðkÞ < 3.7 × 10 mK at 95% confid
4
10
and z ¼ in
6.8,
which
is consistent
withthepublished
limits [8,12–15]. We also include a simplis
reported previously
Paciga
et al.
(2011). While
previous limit
based lower,
on ourthis
observed
system temperature.
was considerably
can be accounted
for by manyThough
factors; it is not directly comparable to our me
it does
show
that most of
our several
measurements
the differentfunctions,
k scale, the
change
in foreground
filter,
minor are consistent with thermal noise. Fo
2
model
of
[71]
(which
predicts
that
reionization
ends before z ¼ 6.4) at the central redshif
changes in the analysis
10 pipeline detailed in Section 2 and most sigmagnitude
away
from
the
fiducial
model,
recall
that
nificantly the fact that this is the first time a transfer function hasthe noise in the power spectrum scales
square
been used to
correctroot.
for signal lost in the foreground filter. Without
such a correction, our best
upper limits with the SVD foreground
0
10 −1
filter may have been incorrectly
reported as low as (50 mK)2 .
10
Mp c − 1)
This limit still compares favourably to others establishedkin( hthe
0
10
Preparing for the 21 cm revolution
•  The future for 21 cm studies is bright
•  New techniques
•  Better understanding of systematics
•  Drastic sensitivity increases
•  First framework for recovering physics (21CMMC)
•  A detection would be transformative
•  What will it take to be conclusive?
•  What is the near term science?
•  Is there more to be learned from improved upper limits?
•  What is the science from a first detection?