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On Detecting 21-cm Signal from EoR using Drift Scandata from MWA
Akash Kumar PatwaSupervisors:
Prof. Shiv Sethi & Prof. K. S. Dwarakanath
Astronomy and AstrophysicsRaman Research Institute (RRI)
Bengaluru, India
Science At Low Frequencies - VNagoya University, Japan
5th Dec 2018
Akash Kumar Patwa (RRI) EoR study with Drift Scan Strategy SALF-V, 2018 1 / 27
The Redshifted HI 21cm Signal from EoR:
Robertson et al (2010)
By z ∼ 30 density perturbations grow sufficiently to collapse and formfirst luminous sources. (Cosmic Dawn)
These sources ionize the nearby neutral hydrogen (HI) clouds. (Epochof Reionization)
By z ∼ 6, EoR ends.
In our study the data we use corresponds to z ∼ 8.2.
Akash Kumar Patwa (RRI) EoR study with Drift Scan Strategy SALF-V, 2018 2 / 27
What do we need for the detection?
The HI signal is ∼ 5 orders of magnitude weaker than foregroundcontaminations. For detection we need:
system stability
smooth bandpass
high precision calibration without ruining the signal (requires highresolution)
treatment of foreground;
avoidance (low SNR)subtraction (better SNR but prone to contaminating ‘EoR window’)suppression
minimum number of operations in the data analysis? (very highdynamic range and limited floating point precision may lead to roundoff errors)
around thousand hours of data integration to reduce thermal noise
Akash Kumar Patwa (RRI) EoR study with Drift Scan Strategy SALF-V, 2018 3 / 27
Why do we do Drift Scan?
In contrast with tracking mode observation, in drift scan:
sky drifts with respect to fixed phase center of the telescope
primary beam and systematics remain stationary in the entire run ofthe observation
sky intensity is not distorted (due to sky curvature) because region isnot tracked
smaller w -term in zenith drift scan
slightly better SNR (lower cosmic variance) and reduction in totalrequired data integration (Trott 2014)
The EoR study using drift scan was explored in “Study of Redshifted HIfrom the Epoch of Reionization with Drift Scan” Paul, S., Sethi, S.K., etal. (2014).We extend the formalism to delay space and apply it to MWA drift scandata.
Akash Kumar Patwa (RRI) EoR study with Drift Scan Strategy SALF-V, 2018 4 / 27
Drift Scan Formalism for HI power spectrum
In drift scan, visibility Vν(uν ,wν , t) and fluctuating component of HIspecific intensity ∆Iν(θ, t) are related by:
Vν(uν ,wν , t) =
∫d2θ
nAν(θ)∆Iν(θ, t)e−2πi(uν ·θ+wν(n−1))
2-point correlation function of visibilities in delay space:⟨Vτ (u0,w0, t)V ′∗τ (u′0,w
′0, t′)⟩
(u, v , τ) space is the natural domain of the HI signal.
HI power spectrum is proportional to the HI visibility correlationfunction.
Akash Kumar Patwa (RRI) EoR study with Drift Scan Strategy SALF-V, 2018 5 / 27
Properties of HI visibility correlation:
0 10 20 30 40 50 60t [min]
50
100
150
200
250u2 0
+v2 0
0.0
0.2
0.4
0.6
0.8
1.0
Akash Kumar Patwa (RRI) EoR study with Drift Scan Strategy SALF-V, 2018 6 / 27
HI Weights
HI weights are defined as:
W (u0,u′0,w0,w
′0,∆t) =
⟨Vτ (u0,w0, t)V ′∗τ (u′0,w
′0, t′)⟩
⟨Vτ (u0,w0 = 0, t)V ′∗τ (u′0,w
′0 = 0, t)
⟩Each correlating visibility pair is divided by corresponding weight, sothat while averaging we get coherant addition of power. [Paul et al (2016)]
Weights take care of the decorrelation due to different, non-zerow -terms and time intervals.
Akash Kumar Patwa (RRI) EoR study with Drift Scan Strategy SALF-V, 2018 7 / 27
Power Spectrum Eastimator:
Grids are populated with visibilitiesand are cross correlated.
HI weights ensure coherant addition ofpower.
Noise bias is avoided by i 6= j .
In each grid, following quantities arecomputed:
Paul et al (2016)
T 2B PHI (k) ∝
⟨Vτ (u0,w0, t)V ′∗τ (u′0,w
′0, t′)⟩
=
∑i 6=j
1σ2ij
(V iτ (u0,w0,t)V ′∗jτ (u0,w ′0,t
′)Wij
)∑i 6=j
1σ2ij
σg =
∑i 6=j
σ−2ij
−0.5
(σij = σ/Wij)
Akash Kumar Patwa (RRI) EoR study with Drift Scan Strategy SALF-V, 2018 8 / 27
MWA Drift Scan Data
Zenith drift scan, declination = -26.7deg
Phase I : RA = (4.1 – 116.7)deg, obs time = 7.5hrs
Phase II : RA = (349.0 – 70.3)deg, obs time = 5.5hrs
Bandwidth = 10.24MHz, centered at ν0 = 154.24MHz
Channel width ∆ν = 40kHz, time resolution = 10s
Data preprocessing:
COTTER: [raw data (40kHz, 0.5s)]→ MS tables (40kHz, 10s) →CASAManually flagging some channels and bad antennasCalibration: Flux and bandpass calibration with Pictor A(S150MHz = 382Jy , α = −0.76 [Jacobs, D. et al. 2013] )No Imaging: Imaging/CLEANing and foreground subtraction are NOTdone because error propagation in the process is not well understoodand it may ruin the embedded signal.Export visibility data out of CASA for further analysis.
Akash Kumar Patwa (RRI) EoR study with Drift Scan Strategy SALF-V, 2018 9 / 27
Point source simulation
Akash Kumar Patwa (RRI) EoR study with Drift Scan Strategy SALF-V, 2018 10 / 27
2D Power spectra P(k⊥, k‖)
Akash Kumar Patwa (RRI) EoR study with Drift Scan Strategy SALF-V, 2018 11 / 27
Noise Characterisation in Data
All visibilities falling in a grid are cross correlated without anyconstraint. HI weights are NOT used.
RMS is computed using all uv-cells.
For comparision with both data sets, simulation with Gaussian noise(GN) visibilities is also performed with zero mean.
Cross correlation (∼ VV ∗) would have RMS ∝ 1/√Ncorr . Ncorr ∝ t2
Thus RMS ∝ 1/t
Akash Kumar Patwa (RRI) EoR study with Drift Scan Strategy SALF-V, 2018 12 / 27
Noise Characterisation in DataPhase I & II
100 101 102 103
Drift time [min]
107
109
1011
1013
1015
(mK)
2 (h
1 Mpc
)3
Phase I: GN (Simulation)RMS
100 101 102 103
Drift time [min]
107
109
1011
1013
1015
(mK)
2 (h
1 Mpc
)3
Phase II: GN (Simulation)RMS
100 101 102 103
Drift time [min]
107
109
1011
1013
1015
(mK)
2 (h
1 Mpc
)3
Phase I: XXRMS
100 101 102 103
Drift time [min]
107
109
1011
1013
1015
(mK)
2 (h
1 Mpc
)3
Phase II: XXRMS
Akash Kumar Patwa (RRI) EoR study with Drift Scan Strategy SALF-V, 2018 13 / 27
Noise Characterisation in DataPhase I & II: Cut at 100λ
100 101 102 103
Drift time [min]
107
109
1011
1013
1015
(mK)
2 (h
1 Mpc
)3
Phase I: GN (Simulation)RMS
100 101 102 103
Drift time [min]
107
109
1011
1013
1015
(mK)
2 (h
1 Mpc
)3
Phase II: GN (Simulation)RMS
100 101 102 103
Drift time [min]
107
109
1011
1013
1015
(mK)
2 (h
1 Mpc
)3
Phase I: XXRMS
100 101 102 103
Drift time [min]
107
109
1011
1013
1015
(mK)
2 (h
1 Mpc
)3
Phase II: XXRMS
Akash Kumar Patwa (RRI) EoR study with Drift Scan Strategy SALF-V, 2018 14 / 27
Summary
Drift scan analysis is a promising tool to study HI 21-cm signal.
For detection we require system stability, smooth bandpass, highprecision calibration, minimum number of operations.
Drift scan is favoured because: small w terms, stability of the system,better SNR.
HI Weights take care of the decorrelation due to different parameters.It ensures coherant addition of HI power within a grid.
As expected from simulations, foreground are confined in wedge.
As demonstrated using data, EoR window is noise dominated.
Using all uv-cells:
RMS in clean modes behave like noise and fall as 1/t.Galactic plane does not affect clean modes.
Akash Kumar Patwa (RRI) EoR study with Drift Scan Strategy SALF-V, 2018 15 / 27
Akash Kumar Patwa (RRI) EoR study with Drift Scan Strategy SALF-V, 2018 16 / 27
Drift Scan Formalism
In drift scan, visibility Vν(uν ,wν , t) and fluctuating component of HIspecific intensity ∆Iν(θ, t) are related by;
Vν(uν ,wν , t) =
∫d2θ
nAν(θ)∆Iν(θ, t)e−2πi(uν ·θ+wν(n−1))
∆Iν(θ, t) as a function of HI density δHI (k):
∆Iν (θ, t) = Iν
∫d3k
(2π)3δHI (k)e irν(k‖+k⊥·(θ−ϑ(t)))
2-point correlation function of δHI (k) defines HI power spectrumPHI (k). ⟨
δHI (k)δ∗HI (k′)⟩
= (2π)3δ3(k− k′)PHI (k)
Akash Kumar Patwa (RRI) EoR study with Drift Scan Strategy SALF-V, 2018 17 / 27
Assumptions:Approximations used:d2θn ≈ d2θ and wν(n − 1) ≈ − 1
2wν
(l2 + m2
)Frequency depandance of rν ,uν , Iν and Aν(θ) is ignored. It is justifiedfor 10MHz bandwidth. Using these numbers at the center of the bandintroduces < 10% error in their values. [Paul, S., Sethi, S. K., et al(2016)]
2-point correlation function of visibilities in delay space:⟨Vτ (u0,w0, t)V ′∗τ (u′0,w
′0, t′)⟩≈ I 2
0
B
|r0|
∫d2k⊥(2π)2
PHI (k)e ir0k⊥1 cosφ∆H
×Q1(k⊥1, k⊥2, u0,w0,∆H = 0)Q2(k⊥1, k⊥2, v0,w0,∆H = 0)
×Q∗1 (k⊥1, k⊥2, u′0,w
′0,∆H)Q∗2 (k⊥1, k⊥2, v
′0,w
′0,∆H)
Q-integrals set relevant correlation scales and also influence strengthof the desired signal.
HI power spectrum is proportional to the HI visibility correlationfunction.
Akash Kumar Patwa (RRI) EoR study with Drift Scan Strategy SALF-V, 2018 18 / 27
Q-integrals
Form of Q-integral:
Q(x , y) =
∫ 1
−1dlAν(l)exp
[−2πi
(lx − 1
2l2y
)]Aν(l) = sinc2(πLν l)
Correlation scales: k⊥1 = 2πr0u0; k⊥2 = 2π
r0v0; k‖ = 2π
|r0|τ
If u0 = 100 then k⊥1 = 0.1hMpc−1
If τ = 100B−1 then k‖ = 5.3hMpc−1 (B = 10.24MHz)
Akash Kumar Patwa (RRI) EoR study with Drift Scan Strategy SALF-V, 2018 19 / 27
Q-integrals
Q1 and Q2 integrals are;
Q1(k⊥1, k⊥2, u0,w0,∆H) =
∫ 1
−1dlAν(l)exp
[− 2πi(
l(u0 −
r02π
(k⊥1 + k⊥2 sinφ∆H))− 1
2l2(w0 +
r02π
k⊥1 cosφ∆H))]
Q2(k⊥1, k⊥2, v0,w0,∆H) =
∫ 1
−1dmAν(m)exp
[− 2πi(
m(v0 −
r02π
(k⊥2 − k⊥1 sinφ∆H))− 1
2m2(w0 +
r02π
k⊥1 cosφ∆H))]
Correlation scales: k⊥1 = 2πr0u0; k⊥2 = 2π
r0v0; k‖ = 2π
|r0|τ
If u0 = 100 then k⊥1 = 0.1hMpc−1
If τ = 100B−1 then k‖ = 5.3hMpc−1 (B = 10.24MHz)
Akash Kumar Patwa (RRI) EoR study with Drift Scan Strategy SALF-V, 2018 20 / 27
Q(x , y) =
∫ 1
−1dlAν(l)exp
[−2πi
(lx − 1
2l2y
)]Q(−x , y) = Q(x , y), Q(x ,−y) = Q∗(x , y)
Aν(l) = sinc2(πLν l)
Akash Kumar Patwa (RRI) EoR study with Drift Scan Strategy SALF-V, 2018 21 / 27
Defining HI Power Spectrum
HI power spectrum is defined for:t = t ′,∆H = 0,w0 = 0,w ′0 = 0,u0 = u′0.
T 2B PHI (k) ∝
∫d2k⊥(2π)2
PHI (k) |Q1|2 |Q2|2
T 2B PHI (k) ∝
⟨Vτ (u0,w0 = 0, t)V ′∗τ (u0,w
′0 = 0, t)
⟩First and second equations are used to calculate HI power spectrumfrom simulation and data respectively.
Simulation is okay but data (visibilities) may not have same/zerow -terms or same baseline vectors. So we introduce HI Weights foreach pair of correlating visibilities.
Akash Kumar Patwa (RRI) EoR study with Drift Scan Strategy SALF-V, 2018 22 / 27
UV Field Gridding
|u0| ≤ 250λ, |v0| ≤ 250λ; gridsize = 0.5λ
Phase I: No. of filled grids ' 3300; max no. of vis in a grid = 3
Phase II: No. of filled grids ' 5200; max no. of vis in a grid = 53
In both data sets, |w0| ≤ 3λ
Akash Kumar Patwa (RRI) EoR study with Drift Scan Strategy SALF-V, 2018 23 / 27
Phase I & II
100 101 102 103
Drift time [min]
107
109
1011
1013
1015
(mK)
2 (h
1 Mpc
)3
Phase I: XXMean
100 101 102 103
Drift time [min]
107
109
1011
1013
1015
(mK)
2 (h
1 Mpc
)3
Phase II: XXMean
100 101 102 103
Drift time [min]
107
109
1011
1013
1015
(mK)
2 (h
1 Mpc
)3
Phase I: XXRMS
100 101 102 103
Drift time [min]
107
109
1011
1013
1015
(mK)
2 (h
1 Mpc
)3
Phase II: XXRMS
Akash Kumar Patwa (RRI) EoR study with Drift Scan Strategy SALF-V, 2018 24 / 27
1D Power Spectra ∆2(k)
Akash Kumar Patwa (RRI) EoR study with Drift Scan Strategy SALF-V, 2018 25 / 27
Point source simulation
Akash Kumar Patwa (RRI) EoR study with Drift Scan Strategy SALF-V, 2018 26 / 27
Noise Characterisation in DataPhase I & II: averaging in 2 stages (100 grids)
100 101 102 103
Drift time [min]
107
109
1011
1013
1015
(mK)
2 (h
1 Mpc
)3
Phase I: GN (Simulation)RMS
100 101 102 103
Drift time [min]
107
109
1011
1013
1015
(mK)
2 (h
1 Mpc
)3
Phase II: GN (Simulation)RMS
100 101 102 103
Drift time [min]
107
109
1011
1013
1015
(mK)
2 (h
1 Mpc
)3
Phase I: XXRMS
100 101 102 103
Drift time [min]
107
109
1011
1013
1015
(mK)
2 (h
1 Mpc
)3
Phase II: XXRMS
Akash Kumar Patwa (RRI) EoR study with Drift Scan Strategy SALF-V, 2018 27 / 27