MWA超低周波電波のデータ解析
SHINTARO YOSHIURA
B. Pindor, C.M. Trott, K. Takahashi and MWA EoR teamAll results are preliminary「銀河進化と遠方宇宙」2019 (第五回) @ 神奈川大学 Using MWA presentations templateIntroduction
Credit : K Hasegawa

21cm line「銀河進化と遠方宇宙」2019 (第五回) @ 神奈川大学

221cm line
Hyperfine structure :energy difference due tothe spins of proton and electron.
An atom emits a photon witha wavelength of 21cm via
the spin-flip transition.
During the EoR and the CD,
the 21cm line is a good tracer of the IGM.
21cm brightness temperature<latexit sha1_base64="(null)">(null)</latexit>

Tb / xHI (1 + m )(1TCMB TS 1 )「銀河進化と遠方宇宙」2019 (第五回) @ 神奈川大学

32

Global signal

and δb will be relevant for the details of the signal, bu
provide a glimpse of the Universe at z ! 12
are not required to get the broad features of the signalrough a narrow field of view and are unlikely
on which we focus here.
on redshifts z ! 20. As we will show, 21
xperiments could potentially provide crude
21cm
Globalsignalat:a much lower cost.
n evenhigher
redshifts
ture of this paper is as follows. In §II, we 1
cribing21
the basic physics
the evoHI that drivesrad
Dark-Ages
S21 cm global signature and drawing atteney observable features. We follow this in §III
EDGES is designed for measuring
sion of the foregrounds, which leads into ourReionization
the21cm
emission
andabsorption.
Fisher matrix formalism for predicting obonstraints in §IV. In §V and §VI we apply
m to the signal from reionization and theespectively. After a brief discussion in §VII
ects for detecting the signal from the dark
Heating bytar formation, we conclude in §VIII.
X-ray photon.
ut this paper where cosmological parameters
we use the standard set of values Ωm = 0.3,WF effectΩb = 0.046, H = 100h km s−1 Mpc−1 (with= 0.95, and σ8 = 0.8, consistent with therements [14].

T<latexit sha1_base64="(null)">(null)</latexit>/ x (1TTICS OF THE 21 CM GLOBAL SIGNAL)

Pritchard & Loeb 2012

FIG. 1: Evolution of the 21 cm global signal for diﬀeren

cs of the「銀河進化と遠方宇宙」2019
cosmological 21 cm signal
has@beenTS ≫(第五回)
神奈川大学scenarios. Solid blue curve: no stars; solid red curve:
4
detail by a number of authors [15, 16] andTγ ; black dotted curve: no heating; black dashed curve: noToo strong absorption

ETTER
Measured δTb is -500 mK at z=17, and T_K need to be less than 3.2K.
the minimum
T_K should be 6 K at z=17 in standard
cosmology.
Age of the Universe(Myr)vity toHowever,possible calibration
errorsonModelled
error level

Recoveredamplitude (K)0.1 dB
20 ps
0.02 dB
20 ps
N/A
N/A

1.0 dB
100 ps
0.2 dB100 ps
N/A
N/A

0.51
0.48
0.50
0.48
0.51
0.48

nty for each case is based on empirical values from laboratory
eatability tests. Modelled error levels were chosen conservatively toger than the estimated uncertainties for the phases and magnitudes,
oise amplifier; S11, input reflection coefficient; N/A, not applicable.

150

0.2

Brightness temperature, T21 (K)deelay)nitudee (delay)

Estimateduncertainty

200

250

300

0–0.2
H1–0.4LowestinH2
standardmodel
H3

Bowman+2018
H4ng restricted spectral bandsCredit
yield :nearlyidentical
H5
rption profiles, with the highest signal-to-noise ratio–0.6
H6ig. 2 we show representative cases of these fits.
numerous hardware and processing tests to validate
P8
he 21-cm absorption profile is observed in data that
26
24
22
20
18
16
14
years and can be extracted at all local solar times andCredit : Bowman+2018
Redshift, z
eal times. It is detected by two identically designed
rated at the same site and located 150 m apart, and Figure 2 | Best-fitting 21-cm absorption profiles for each hardware case.
l hardware modifications to the instruments, includ- Each profile for the brightness temperature T21 is added to its residuals andrientations of one of the antennas. Similar results for plotted against the redshift z and the corresponding age of the Universe.
The thick black line is the model fit for the hardware and analysis
profile are 「銀河進化と遠方宇宙」2019
obtained by using two independent(第五回) @pro神奈川大学
5, which we tested using simulated data. The profile is configuration with the highest signal-to-noise ratio (equal to 52; H2;

see Methods), processed using 60–99 MHz and a four-term polynomial

New physics? Need more data
EDGES low band : detection a powerful absorption
Inspired papers :Barkana 2018, Fialkov+2018, Berlin+2018,Fraser+2018, Hirano&Bromm 2018, SY +2018, Minoda+2019, etc
・early decouple of gas and radiation ?
・Hotter CMB ?
・High baryon density ?
・Radio background ?
・Did some exotic physics cool the HI gas ?
> baryon and dark-matter interaction? Barkana 2018, Nature Letter.
We need to observe the frequency using other instruments !
e.g. Power spectrum with interferometers「銀河進化と遠方宇宙」2019 (第五回) @ 神奈川大学

6ifbothof expression
the spin temperatureand theneutral fraction
spectrum,andintheaboveforthebrightness
temperature
given
pected to belargerthanthatinmatterfluctuations.
(Forotherprob
thestatistics
ofthe
brightness
temperaturefluctuations
if bothsuchof thespin temperatureand theneutralfraction are completely
as Minkowski
functionals,see[49,78,60].)
densityfluctuations
δm . However,in the completely
era of CD andE
the statistics of thebrightness
temperaturefluctuations
followtemperatureand theneutralfractionshouldinhdensity fluctuationsδm . However,in theera of
CD andEoR,beitspatiallyis expectedthebespatialfluctuationsof thosequantities
would be highly・Ideally,21cm linewill
imaged.
temperatureandtheneutralfractionshouldbespatially
inhomogeneousand t
6.2 Formulation
and
setup
astrophysicaleﬀects.
Accordingly,
the statisticsof the brig
the spatialanalysis
fluctuationsof thosequantities
wouldofbeongoinghighlynon-Gaussiandue・Statisticalis required
to increase
sensitivity
telescopes.
would
deviate fromthepure Gaussianand it should
be imastrophysicaleﬀects.
Accordingly,
thestatistics
ofthebrightness
temperatur
ETTER
6.2.1 Formulation
forthe21 cmbebispectrum
Gaussian
featureoftheandbrightness
fluctuations
would deviate fromthe pure
Gaussianit shouldtemperatureimportant
to invest
featurecan beinvestigatedthroughthe skewnessof theof
the brightness
AlthoughsuchoneaaGaussian
21-cm
intensity
Baryon–darkmatter velocity
Wefeature
have introduced
theb 21temperature
cm power
influctuations.
eq.(6.1) as follows:
done in [118],
thescale-dependentfeaturehas been integra
Powerspectrum
2.2
feature can be investigated–100 through the skewness of the one-point distributio′′
2.0
hand, the higher
ordercorrelation
functionsin Four3
done in [118], the otherscale-dependenthas
been
integrated
outtheskew⟨δfeature
(k)δ
(k)⟩
=(2π)
δ(k+k)Pin
21
21
21 (k),
1.8–200
and a trispectrum
characterize
the innon-Gaussianfeaturesan1.6
other hand, the higher
order correlation
functions
Fourierspacesuch asinformation.
Here,in order to see
the1.4non-Gaussianfeatur–300
and a trispectrum
characterizethenon-Gaussianfeatures
andalsohave
the scwhere,1.2
δ21 , weon the bispectrum
which i1.0
information. Here,fluctuations
in orderthefocus
non-Gaussianfeatureof oftheδ21brightnes–400 to see
Bispectrum
0.8
δ21 (x) of≡ δδT− ⟨δTfluctuations δ21 , we focus on the bispectrum
whichis givenb ⟩.3 by21b (x)0.6–500⟨δ21 (k1 )δ21 (k2 )δ21 (k3 )⟩0.4= (2π) δ(k1 + k2 +Statistical approachv/vrmsT21 (mK)

100 Mpc

0.2⟨δ21 (k1 )δof–600(k2 )δ
(2π)3 δ(k1 + kfluctuations, kpureIf the statisticsbrightness
Ga
21the21 (k3 )⟩ = temperature
2 + k3 )B(k1is2 , k3 ).
Inorder to characterize
the shape of model
the isbispectrum
in k-sBarkana
ed 21-cm intensity usinga modelwith 2018
baryon–dark
basedon a semi- charlikely observed
value5). This astrophysicalinformationon the brightness
temperature
shouldbecompletely15(indefinedMethods).
patterna, The 21-cm-transition brightness temperature
T21
numerical
simulation
whichisask=k(seek = The
αkspatial≥ 1/2).
Foranexa1
2 =3 (α21-cm-signalInordertocharacterizetheshapeofthebispectrum
ink-space,weuse
isspectrum,
and
in
the
above
expressionforthebrightness
temperatur
wo-dimensional slice (thickness of 3 Mpc) of a simulated
is determined by the baryon–dark matter relative velocity left over fromshapeofWethe
bispectrum
is≥
often
calledassqueezedtype
orwloverse withwhich
sides of 384
Mpc(all lengthsas
co-moving).
earlycosmicevolution
beforerecombination.
b, Distribution
ofin
theisdefinedk==k=αk(α1/2).
For
examples,case
if
bothofthespinandtheneutral
fractionarecom
13−20 k22 temperature= 78.9 MHz), where this model (with σ1 = 8 × 10 cm
baryon–dark matter relative velocity (in the same simulated volume as thatcalledasequilateral
type,and in case
with
α=1/2
itcaseisby calw
GeV)reaches
its maximum
article massmχ = 0.3of
shown
in a, assuming
adiabatic initial
densityfluctuations),
normalized
shape
the
bispectrum
isoftencalledassqueezed
type
or
local
type,
in
the
statistics
ofthebrightness
temperaturefluctuations
completel「銀河進化と遠方宇宙」2019(第五回)@ 神奈川大学
71,010.
rption depthof −504 mK (roughly matching
the most
its r.m.s. value of 29condition
km s−1 at 1 + z =because
relaxtheconfiguration
wecalculate
thecalled as
equilateral
type, andcase with in
α=1/2
is called
as EoR,foldedittype.
densityfluctuations
δ in. However,theerait ofCD andis e

In this talkInstrument : MWA phase I (128 tiles)
Bandpass : 74-100MHz ( 18 > z > 13)
Observation time : ~5hours
Showing foregrounds and systematics
Calculating power spectrum and bispectrum
Predict future detectability
Credit: Natasha Hurley-Walker

Software : RTS (calibration): CHIPS (power spectrum estimator)
Objectives ・detection of 21cm power spectrum at Cosmic Dawn
・the study MWA systematics and foreground at ultralow
・validation of EDGES result「銀河進化と遠方宇宙」2019 (第五回) @ 神奈川大学

8Data property
Obstacles at ultralow frequency
・powerful thermal noise

ULUL
midLow
BandHighBand・high RFI contamination
・(too) bright foregrounds
・(too) wide field of view
EDGES
FM

「銀河進化と遠方宇宙」2019 (第五回) @ 神奈川大学

9

EoR1 field at ultralow bandBefore subtraction, after clean using WSCLEAN
Phase center : EoR1(RA,Dec) = (4h,-30deg)
Beam size : 40*40 deg2

FornaxA

PictorA

Jy/beam「銀河進化と遠方宇宙」2019 (第五回) @ 神奈川大学

10Extended sources
Fornax A・extended source
・modeling with shape-let

86

7.6

1625

33

3167

103

139

42

50

59

Jy/beam6776

8

Pictor A
・extended source
・modeling with 2D gaussian

6「銀河進化と遠方宇宙」2019 (第五回) @ 神奈川大学

176

212

248

Jy/beam

285

321

3511

Peeling
Results of point source subtraction
Quiet ionosphere dataIonosphere could have influenceon subtraction of point sources「銀河進化と遠方宇宙」2019 (第五回) @ 神奈川大学

12Peeling
Results of point source subtraction
Active ionosphere dataIonosphere could have influenceon subtraction of point sources「銀河進化と遠方宇宙」2019 (第五回) @ 神奈川大学

13

EoR1 field at ultralow band
After subtraction
Phase center : EoR1
(RA,Dec) = (4h,-30deg)
Beam size : 40*40 deg2
calculate power spectrum
using the data afterpoint source subtraction.

Jy/beam「銀河進化と遠方宇宙」2019 (第五回) @ 神奈川大学

14

2D power spectrum
Using ultraCHIPS, good ionosphere, lower RMS
75MHz< ν <87MHz「銀河進化と遠方宇宙」2019 (第五回) @ 神奈川大学

87MHz< ν <100MHz

15

1D power spectrum
1D Power - D2(k) = (k3P(k)/2p2) (mK2)1011

log10 D2(k) (mK2)1010

75MHz< ν <87MHz
4 * 107 mK2

109
108
107
87MHz< ν <100MHz< 107 mK2

106
105
0.1

1.0
-1

log10 k (h Mpc )「銀河進化と遠方宇宙」2019 (第五回) @ 神奈川大学

16

FoldedBispectrum
culated using HB, ULmid, UL data from left to right. The solid line is B

tot with XX polariza

ed line is Bdiff with XX polarization, and dot-dashed line is Bdiff with YY polarization.
Choose three vector in Fourier space|k1 |/2 = |k2 | = |k3 |<latexit sha1_base64="(null)">(null)</latexit>

me as Fig. 3, but for Folded type of Bispectrum.

「銀河進化と遠方宇宙」2019@ 神奈川大学
alow data
isin Fig.(第五回)??directone.

17Signal prediction
Publications of the Astronomical Society of Japan, (2014), Vol. 00, No. 0

To compare the data, we perform the 21cmFAST

and refer Fialkov+2018

ed lines are the 21cm global signal of Model A and Model B. The 21cm signal is simulated by using 21CMFAST. change line typenoise like feature. sign! Note that theighly changeable this indicates the meated by the error. The non-gaussianity ofhan the error.

B/|B|. The sign is not stable at any scales, and the result indicates a weak non-Gaussianity of the bispectrum, dominated by
the foregrounds.

The diff data should be dominated by the noise since thetime independent astronomical emission is cancelled. The rightfolded type shows similar behavior topanel of the Figs. 7 is fairly consistent with the model of thermal
lateral type as represented in the Fig. 4.
noisewhich@is 神奈川大学
shown in the Fig. ??, and the noise is reduced at
the BFG drasticallydecreases at k ≈「銀河進化と遠方宇宙」2019(第五回)
k⊥ < 0.01 due to a large number of weights since the MWA hasr, this could be coincidence due to theFialkov+201818

Power spectrum

PS[mK2]Upper limits : 107 mK2
Need to remove foreground (1~2 orders) and add more data

21cmFAST「銀河進化と遠方宇宙」2019 (第五回) @ 神奈川大学

Fialkov+2018

19

Bispectrum forecast
Assumptions
・MWA PhaseII・1000hours observation
・FGRM 2 orders of magnitude

EDGES?

MWA can measure
the bispectrum at high band
MWA might validate
the EDGES results

Fig. 11. Redshift evolution of the folded type of Bis「銀河進化と遠方宇宙」2019 (第五回) @ 神奈川大学

20Summary
Analyzing the MWA Ultralow data (75-100MHz)
Objectives
Deep analysis on UL datavalidation of the EDGES strong absorption
Correct limits
Power spectrum 107 mK2 at 0.1 Mpc-1
Bispectrum 1024 mK3Mpc6 at 0.1 Mpc-1
MWA Phase II might validate the EDGES absorption
Requirements
observation of 1000hours
foreground removal more than 2 orders of magnitude in Kelvin
Next steps
Using more data,Attempting to foreground removal,
Selecting clean data
Note : all results are preliminary「銀河進化と遠方宇宙」2019 (第五回) @ 神奈川大学

21

2D power spectrum
Using ultraCHIPS, good ionosphere, lower RMS
75MHz< ν <87MHz「銀河進化と遠方宇宙」2019 (第五回) @ 神奈川大学

87MHz< ν <100MHz

22

1D power spectrum
1D Power - D2(k) = (k3P(k)/2p2) (mK2)1011

log10 D2(k) (mK2)

1010
109

75MHz< ν <87MHz
3 * 107 mK2

108
107

87MHz< ν <100MHz< 107 mK2

106
105
0.1

1.0-1

log10 k (h Mpc )「銀河進化と遠方宇宙」2019 (第五回) @ 神奈川大学

23Beambetter resolution?

ਤ 20

Expected beam respons「銀河進化と遠方宇宙」2019 (第五回) @ 神奈川大学

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R.M.S of visibilitylog(rms)

Weird data should be removed

various observations

Before calculate power spectrum,
check the visibility r.m.sfrequency bin「銀河進化と遠方宇宙」2019 (第五回) @ 神奈川大学

25

pip install cthulhu. To run, one needs to do, e.g.

cthulhu wrapper.py rts nid00165 20180206 094607 node001.log -p
Ionosphere. Then, ionosphere metric and plots are produced. The list of ionosphere metric o

can be found in name. In Fig. 3 shows the averaged ionosphere oﬀsets and PCA“cthulhu” (C.Jordan+2017)
observation.
Note that analysis
the oﬀset value is scales as if it is measured at 200MH: python software
for ionosphereis fairlyisconsistent
the Fig.1 of theChris’s
paper ref.
However,compareto theIonosphere offset
measuredwith
by comparison
observed
positionof point
sourcesusing listed
high band
data,catalogue
the result has more tiny oﬀset data (e.g. oﬀset is smaller t
and the position
in radiomight indicates some non-Gaussianity of the ionosphere or the ionosphere conditi
the high band data fortunately (private conversation with Chris).

ਤ 3 Sameplotof Fi.1 of Jordan+2017, but using ionosphere data measured
usin「銀河進化と遠方宇宙」2019(第五回)@ 神奈川大学
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Data quality
For now,choose data with・quiet ionosphere・lower r.m.s「銀河進化と遠方宇宙」2019 (第五回) @ 神奈川大学

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ਤ 24

Gain

5.6 Averaged Gain and Phasegainwater roof?

ਤ「銀河進化と遠方宇宙」2019 (第五回) @ 神奈川大学

28

cotterPlot before after, output file has the occupancy as a function of fine channel every coarse band. In the Fig
examples of occupancies are shown.

ਤ4

Examples of cotter occupancy. X-axis is fine channel. Color represents diﬀerent coarse band.

「銀河進化と遠方宇宙」2019 (第五回) @ 神奈川大学

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Click to add title• Click to add text
• Text• Bullet 1• Bullet 2• Bullet 3

Image credit: John Goldsmith, 2012

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