on detecting 21-cm signal from eor using drift scan data ... · on detecting 21-cm signal from eor...

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.


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


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.


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.


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


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.


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)


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.


Point source simulation


2D Power spectra P(k⊥, k‖)


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


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


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


100 101 102 103

Drift time [min]

107

109

1011

1013

1015

(mK)

2 (h

1 Mpc

)3


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


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.


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)


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.


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)


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)


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)


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.


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


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


1D Power Spectra ∆2(k)


Point source simulation


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


100 101 102 103

Drift time [min]

107

109

1011

1013

1015

(mK)

2 (h

1 Mpc

)3


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


on detecting 21-cm signal from eor using drift scan data ... · on detecting 21-cm signal from eor...

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