mw a lfd epoch of r eionization p ow er spectr um obser vations · 2007-09-18 · mw a !lfd epoch...
TRANSCRIPT
![Page 1: MW A LFD Epoch of R eionization P ow er Spectr um Obser vations · 2007-09-18 · MW A !LFD Epoch of R eionization P ow er Spectr um Obser vations Miguel F . M orales for the MW A](https://reader030.vdocuments.site/reader030/viewer/2022040807/5e49ca1ece1de5111971eb01/html5/thumbnails/1.jpg)
MWA–LFD Epoch of Reionization
Power Spectrum Observations
Miguel F. Morales for the MWA–LFD EOR power spectrum collaboration
December 16, 2006 @ Melbourne University
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Overview
• EOR power spectrum signal
• Building an EOR machine: MWA–LFD
• Foreground subtraction
0 (now)~6CMBBigBang
EOR
redshift
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EOR power spectrum signal
0 (now)~6CMBBigBang
EOR
redshift
![Page 4: MW A LFD Epoch of R eionization P ow er Spectr um Obser vations · 2007-09-18 · MW A !LFD Epoch of R eionization P ow er Spectr um Obser vations Miguel F . M orales for the MW A](https://reader030.vdocuments.site/reader030/viewer/2022040807/5e49ca1ece1de5111971eb01/html5/thumbnails/4.jpg)
H& during EOR
100
200
300
400
500
7
7.58
8.59
Mpc/h
z
sv_z8_zeta10_ME.fts_0
Oliver Zahn
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Statistical EOR detection
f
iy
ImageCube
ix
v
f
Visibilities
u
v
h
FourierRepresentation
u
FT SkyCoordinates
FTFrequency
Morales & Hewitt (2004)
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Spherical symmetry
v
u
h
Morales & Hewitt (2004)
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EOR power spectrum
k [Mpc-1 ]
(k3 P
/ 2π
2 )1/2 [M
pc-3
/2 J
y Hz
]
10-3 10-2 10-1 100 10110-1
100
101
102
103
Furlanetto, Zaldarriaga, Hernquist (2004a,b)Bowman, Morales & Hewitt (2005)
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EOR power spectrum
k [Mpc-1 ]
(k3 P
/ 2π
2 )1/2 [M
pc-3
/2 J
y Hz
]
10-3 10-2 10-1 100 10110-1
100
101
102
103
Furlanetto, Zaldarriaga, Hernquist (2004a,b)Bowman, Morales & Hewitt (2005)
![Page 9: MW A LFD Epoch of R eionization P ow er Spectr um Obser vations · 2007-09-18 · MW A !LFD Epoch of R eionization P ow er Spectr um Obser vations Miguel F . M orales for the MW A](https://reader030.vdocuments.site/reader030/viewer/2022040807/5e49ca1ece1de5111971eb01/html5/thumbnails/9.jpg)
EOR power spectrum
k [Mpc-1 ]
(k3 P
/ 2π
2 )1/2 [M
pc-3
/2 J
y Hz
]
10-3 10-2 10-1 100 10110-1
100
101
102
103
Furlanetto, Zaldarriaga, Hernquist (2004a,b)Bowman, Morales & Hewitt (2005)
![Page 10: MW A LFD Epoch of R eionization P ow er Spectr um Obser vations · 2007-09-18 · MW A !LFD Epoch of R eionization P ow er Spectr um Obser vations Miguel F . M orales for the MW A](https://reader030.vdocuments.site/reader030/viewer/2022040807/5e49ca1ece1de5111971eb01/html5/thumbnails/10.jpg)
EOR power spectrum
k [Mpc-1 ]
(k3 P
/ 2π
2 )1/2 [M
pc-3
/2 J
y Hz
]
10-3 10-2 10-1 100 10110-1
100
101
102
103
Furlanetto, Zaldarriaga, Hernquist (2004a,b)Bowman, Morales & Hewitt (2005)
![Page 11: MW A LFD Epoch of R eionization P ow er Spectr um Obser vations · 2007-09-18 · MW A !LFD Epoch of R eionization P ow er Spectr um Obser vations Miguel F . M orales for the MW A](https://reader030.vdocuments.site/reader030/viewer/2022040807/5e49ca1ece1de5111971eb01/html5/thumbnails/11.jpg)
EOR power spectrum
k [Mpc-1 ]
(k3 P
/ 2π
2 )1/2 [M
pc-3
/2 J
y Hz
]
10-3 10-2 10-1 100 10110-1
100
101
102
103
Furlanetto, Zaldarriaga, Hernquist (2004a,b)Bowman, Morales & Hewitt (2005)
Kaplinghat (2005)
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Building an EOR machine: the MWA–LFD
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Challenges 1: Foregrounds• Faint point sources
• Smooth galactic emission
• Galactic radio recombination lines
• RFI
• Others!
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Challenges 2: Ionosphere & Polarization
325 MHz polarized flux, 6° x 6°,4’ beam, 5 K peaks (de Bruyn)
Lonsdale (2004)
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Step 1: increase sensitivity
Survey speed with compact antenna distribution
1
Table 1.
At|dA At|NAdA|At B |u| t
Power Spectrum S/N A2t A
3/2t (dA)!1/2 ! FOV B1/2 |u| n(|u|) t
Note. — This table lists the scaling relationships of the key equations. In order, the variables in each column are: total array areaholding the size of each antenna constant At|dA (adding antennas), total array area holding the number of antennas and distributionconstant At|NA
(increasing antenna size), the size of each antenna with the total array area held constant dA|At (dividing area into moresmall antennas), the total bandwidth B, the sensitivity as a function of wavenumber length |u|, and the total observing time t.
1
Table 1.
At|dA At|NAdA|At B |u| t
Power Spectrum S/N A2t A
3/2t (dA)!1/2 ! FOV B1/2 |u| n(|u|) t
Note. — This table lists the scaling relationships of the key equations. In order, the variables in each column are: total array areaholding the size of each antenna constant At|dA (adding antennas), total array area holding the number of antennas and distributionconstant At|NA
(increasing antenna size), the size of each antenna with the total array area held constant dA|At (dividing area into moresmall antennas), the total bandwidth B, the sensitivity as a function of wavenumber length |u|, and the total observing time t.
Morales (2005)
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Step 2: systematics
0
10
20
30
40
50
60
0
10
20
30
40
50
60
!0.5
0
0.5
1
1.5
2
2.5
010
2030
4050
60
010
2030
4050
60−0.5
0
0.5
1
1.5
2
2.5
What we know about fitting algorithms is goodness-of-fit surface quality ö robustness
• Excellent instantaneous point spread function
• Data-rich observations & computation
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Realtime software team
S. Doeleman, J. Kasper, D. Mitchell, M. Morales, R. Sault, R. Wayth
R. Cappallo, L. Greenhill, C. Lonsdale, M. Tegmark, M. Zaldarriaga
Core:
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Laying down the math
m(v) = B(v,u!)F(u!, !!)A(!!, !)I(!) + n(v)
Observation:
(Tegmark, Zaldarriaga, Morales)
![Page 19: MW A LFD Epoch of R eionization P ow er Spectr um Obser vations · 2007-09-18 · MW A !LFD Epoch of R eionization P ow er Spectr um Obser vations Miguel F . M orales for the MW A](https://reader030.vdocuments.site/reader030/viewer/2022040807/5e49ca1ece1de5111971eb01/html5/thumbnails/19.jpg)
Laying down the math
m(v) = B(v,u!)F(u!, !!)A(!!, !)I(!) + n(v)
Observation:
true sky
(Tegmark, Zaldarriaga, Morales)
![Page 20: MW A LFD Epoch of R eionization P ow er Spectr um Obser vations · 2007-09-18 · MW A !LFD Epoch of R eionization P ow er Spectr um Obser vations Miguel F . M orales for the MW A](https://reader030.vdocuments.site/reader030/viewer/2022040807/5e49ca1ece1de5111971eb01/html5/thumbnails/20.jpg)
Laying down the math
m(v) = B(v,u!)F(u!, !!)A(!!, !)I(!) + n(v)
Observation:
true skyionosphericdistortion
(Tegmark, Zaldarriaga, Morales)
![Page 21: MW A LFD Epoch of R eionization P ow er Spectr um Obser vations · 2007-09-18 · MW A !LFD Epoch of R eionization P ow er Spectr um Obser vations Miguel F . M orales for the MW A](https://reader030.vdocuments.site/reader030/viewer/2022040807/5e49ca1ece1de5111971eb01/html5/thumbnails/21.jpg)
Laying down the math
m(v) = B(v,u!)F(u!, !!)A(!!, !)I(!) + n(v)
Observation:
true skyionosphericdistortion
Fouriertransform
(Tegmark, Zaldarriaga, Morales)
![Page 22: MW A LFD Epoch of R eionization P ow er Spectr um Obser vations · 2007-09-18 · MW A !LFD Epoch of R eionization P ow er Spectr um Obser vations Miguel F . M orales for the MW A](https://reader030.vdocuments.site/reader030/viewer/2022040807/5e49ca1ece1de5111971eb01/html5/thumbnails/22.jpg)
Laying down the math
m(v) = B(v,u!)F(u!, !!)A(!!, !)I(!) + n(v)
Observation:
true skyionosphericdistortion
integration overFourier modes to
measured visibilities
Fouriertransform
(Tegmark, Zaldarriaga, Morales)
![Page 23: MW A LFD Epoch of R eionization P ow er Spectr um Obser vations · 2007-09-18 · MW A !LFD Epoch of R eionization P ow er Spectr um Obser vations Miguel F . M orales for the MW A](https://reader030.vdocuments.site/reader030/viewer/2022040807/5e49ca1ece1de5111971eb01/html5/thumbnails/23.jpg)
Laying down the math
m(v) = B(v,u!)F(u!, !!)A(!!, !)I(!) + n(v)
Observation:
true skyionosphericdistortion
integration overFourier modes to
measured visibilities
Fouriertransform
noise
(Tegmark, Zaldarriaga, Morales)
![Page 24: MW A LFD Epoch of R eionization P ow er Spectr um Obser vations · 2007-09-18 · MW A !LFD Epoch of R eionization P ow er Spectr um Obser vations Miguel F . M orales for the MW A](https://reader030.vdocuments.site/reader030/viewer/2022040807/5e49ca1ece1de5111971eb01/html5/thumbnails/24.jpg)
Data analysis
m(v) = B(v,u!)F(u!, !!)A(!!, !)I(!) + n(v)
Observation:
I(!) =!
OTN
!1O
"!1
AT (!, !")FT (!",u")BT (u",v)
# $% &
OT
N!1
m(v)
Data reduction, v1:
measure-ment
noise covariancematrix
inversion/deconvolution
integrationpoint
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Ionospheric correctionA(!!, !) = "D[!! ! ! ! "!(!, t)]
A(u!,u) =
!d2!ei(u"u
!)·!+iu·"!(!,t)
A(u!,u) !
!d2!!ei(u"u
!)·!!
(1 + iu · "!(!!, t) + · · · )
! (2!)2"D[u " u!] + iu ·
!d2#ei(u"u
!)·!"#(#, t)
A(u!,u) = !D[u ! u!] + i
!
m
amu!D[u ! u!! bm] + cross terms
I(!) =!
OTN
!1O
"!1
AT (u,u")BT (u",v)
# $% &
OT
N!1
m(v)
Data reduction, v2:(Zaldarriaga & Morales; Morales et al.)
![Page 26: MW A LFD Epoch of R eionization P ow er Spectr um Obser vations · 2007-09-18 · MW A !LFD Epoch of R eionization P ow er Spectr um Obser vations Miguel F . M orales for the MW A](https://reader030.vdocuments.site/reader030/viewer/2022040807/5e49ca1ece1de5111971eb01/html5/thumbnails/26.jpg)
Correlator
Receiver
Node
Correlator Boards
Realtime Computer
Visibility Binner
Calibrate &
Integrate
Visibilities to
2-8 sec. in
baseline rings
(2 Gvis, 8 Gops)
Bin subset of
baselines at full
freq. & time
resolution to 2°
FOV (100 M u,v,f,p
cells, 250 Mops)
Combine vis.
in freq. to 32
kHz resolution
(500 Mvis, 1/2
Gops)
125 Mvis/s 0.5 GB/s
50 MB/s
EOR Realtime
System –
integrates to 10
min. and adds to
database
Sort into per
antenna sets [500]
& beamform each
in direction of 100
calibrators (25
Gops)
Mapper
Ionospheric
Calibration
ASM v1
Survey
Instrumental
Calibration
Faraday Rotation
Solar Imaging,
2° FOV, 32 kHz
every 8 sec.
(75 Mops)
1 GB/sec.
1.7
GB
/s~
1/2
Gvis
/s
125 M
vis
/s
Oversampled
map of primary
FOV, every 8
sec. (4 pol., 32
kHz, 3.6 Gcells
3.5 Gops)
Map to RA Dec
at array res.
(96 kHz, I pol.,
every 8 sec.,
0.5 Gops)
Map to RA Dec
at array res.
(32 kHz, 4 pol.,
every ~100
sec. 0.5 Gops)
GSM
Prediction
EOR Imaging
EOR Power
Spectrum
SurveyPostage
stamps towards
calibrators (4
pol. 32 kHz, <<
1 Mops)
Solar Imaging
Legend
Software Block
Hardware Block
Parallel Software
Block
Output Broadcast
IPS Power
Detection
Pulsar
Interface
16 GB/s – 2 Gvis every 1/2 sec.
Voltage
Beamformer
16 voltage beams, 2 pol., 1 GB/s
Monitor &
Control
Antenna
Beamformer
Bin to primary
beam FOV & 32
kHz channels
(1.8 G u,v,f,p cells,
~10 Gops)
Bin towards 100
calibrators, image
postage stamps, 1
pol. (outside
primary FOV) 25
Gops
Clock
IPS
Pulsars
Data Transport Layer
32 GB/s
Faraday Rotation
Solar Imaging
Realt
ime S
cie
nce
P
ack
ag
es
Offl
ine S
cie
nc
e
Pa
ck
ag
es
MWA-LFD Dataflow Diagram
Realtime Common Data Processing
Shadow indicates
workpackage
GPS
GSM
v2
System Diagram
![Page 27: MW A LFD Epoch of R eionization P ow er Spectr um Obser vations · 2007-09-18 · MW A !LFD Epoch of R eionization P ow er Spectr um Obser vations Miguel F . M orales for the MW A](https://reader030.vdocuments.site/reader030/viewer/2022040807/5e49ca1ece1de5111971eb01/html5/thumbnails/27.jpg)
Correlator
Receiver
Node
Correlator Boards
Realtime Computer
Visibility Binner
Calibrate &
Integrate
Visibilities to
2-8 sec. in
baseline rings
(2 Gvis, 8 Gops)
Bin subset of
baselines at full
freq. & time
resolution to 2°
FOV (100 M u,v,f,p
cells, 250 Mops)
Combine vis.
in freq. to 32
kHz resolution
(500 Mvis, 1/2
Gops)
125 Mvis/s 0.5 GB/s
50 MB/s
EOR Realtime
System –
integrates to 10
min. and adds to
database
Sort into per
antenna sets [500]
& beamform each
in direction of 100
calibrators (25
Gops)
Mapper
Ionospheric
Calibration
ASM v1
Survey
Instrumental
Calibration
Faraday Rotation
Solar Imaging,
2° FOV, 32 kHz
every 8 sec.
(75 Mops)
1 GB/sec.
1.7
GB
/s~
1/2
Gvis
/s
125 M
vis
/s
Oversampled
map of primary
FOV, every 8
sec. (4 pol., 32
kHz, 3.6 Gcells
3.5 Gops)
Map to RA Dec
at array res.
(96 kHz, I pol.,
every 8 sec.,
0.5 Gops)
Map to RA Dec
at array res.
(32 kHz, 4 pol.,
every ~100
sec. 0.5 Gops)
GSM
Prediction
EOR Imaging
EOR Power
Spectrum
SurveyPostage
stamps towards
calibrators (4
pol. 32 kHz, <<
1 Mops)
Solar Imaging
Legend
Software Block
Hardware Block
Parallel Software
Block
Output Broadcast
IPS Power
Detection
Pulsar
Interface
16 GB/s – 2 Gvis every 1/2 sec.
Voltage
Beamformer
16 voltage beams, 2 pol., 1 GB/s
Monitor &
Control
Antenna
Beamformer
Bin to primary
beam FOV & 32
kHz channels
(1.8 G u,v,f,p cells,
~10 Gops)
Bin towards 100
calibrators, image
postage stamps, 1
pol. (outside
primary FOV) 25
Gops
Clock
IPS
Pulsars
Data Transport Layer
32 GB/s
Faraday Rotation
Solar Imaging
Realt
ime S
cie
nce
P
ack
ag
es
Offl
ine S
cie
nc
e
Pa
ck
ag
es
MWA-LFD Dataflow Diagram
Realtime Common Data Processing
Shadow indicates
workpackage
GPS
GSM
v2
System Diagram
m(v)
![Page 28: MW A LFD Epoch of R eionization P ow er Spectr um Obser vations · 2007-09-18 · MW A !LFD Epoch of R eionization P ow er Spectr um Obser vations Miguel F . M orales for the MW A](https://reader030.vdocuments.site/reader030/viewer/2022040807/5e49ca1ece1de5111971eb01/html5/thumbnails/28.jpg)
Correlator
Receiver
Node
Correlator Boards
Realtime Computer
Visibility Binner
Calibrate &
Integrate
Visibilities to
2-8 sec. in
baseline rings
(2 Gvis, 8 Gops)
Bin subset of
baselines at full
freq. & time
resolution to 2°
FOV (100 M u,v,f,p
cells, 250 Mops)
Combine vis.
in freq. to 32
kHz resolution
(500 Mvis, 1/2
Gops)
125 Mvis/s 0.5 GB/s
50 MB/s
EOR Realtime
System –
integrates to 10
min. and adds to
database
Sort into per
antenna sets [500]
& beamform each
in direction of 100
calibrators (25
Gops)
Mapper
Ionospheric
Calibration
ASM v1
Survey
Instrumental
Calibration
Faraday Rotation
Solar Imaging,
2° FOV, 32 kHz
every 8 sec.
(75 Mops)
1 GB/sec.
1.7
GB
/s~
1/2
Gvis
/s
125 M
vis
/s
Oversampled
map of primary
FOV, every 8
sec. (4 pol., 32
kHz, 3.6 Gcells
3.5 Gops)
Map to RA Dec
at array res.
(96 kHz, I pol.,
every 8 sec.,
0.5 Gops)
Map to RA Dec
at array res.
(32 kHz, 4 pol.,
every ~100
sec. 0.5 Gops)
GSM
Prediction
EOR Imaging
EOR Power
Spectrum
SurveyPostage
stamps towards
calibrators (4
pol. 32 kHz, <<
1 Mops)
Solar Imaging
Legend
Software Block
Hardware Block
Parallel Software
Block
Output Broadcast
IPS Power
Detection
Pulsar
Interface
16 GB/s – 2 Gvis every 1/2 sec.
Voltage
Beamformer
16 voltage beams, 2 pol., 1 GB/s
Monitor &
Control
Antenna
Beamformer
Bin to primary
beam FOV & 32
kHz channels
(1.8 G u,v,f,p cells,
~10 Gops)
Bin towards 100
calibrators, image
postage stamps, 1
pol. (outside
primary FOV) 25
Gops
Clock
IPS
Pulsars
Data Transport Layer
32 GB/s
Faraday Rotation
Solar Imaging
Realt
ime S
cie
nce
P
ack
ag
es
Offl
ine S
cie
nc
e
Pa
ck
ag
es
MWA-LFD Dataflow Diagram
Realtime Common Data Processing
Shadow indicates
workpackage
GPS
GSM
v2
System Diagram
m(v)
BT (u!
,v)
![Page 29: MW A LFD Epoch of R eionization P ow er Spectr um Obser vations · 2007-09-18 · MW A !LFD Epoch of R eionization P ow er Spectr um Obser vations Miguel F . M orales for the MW A](https://reader030.vdocuments.site/reader030/viewer/2022040807/5e49ca1ece1de5111971eb01/html5/thumbnails/29.jpg)
Correlator
Receiver
Node
Correlator Boards
Realtime Computer
Visibility Binner
Calibrate &
Integrate
Visibilities to
2-8 sec. in
baseline rings
(2 Gvis, 8 Gops)
Bin subset of
baselines at full
freq. & time
resolution to 2°
FOV (100 M u,v,f,p
cells, 250 Mops)
Combine vis.
in freq. to 32
kHz resolution
(500 Mvis, 1/2
Gops)
125 Mvis/s 0.5 GB/s
50 MB/s
EOR Realtime
System –
integrates to 10
min. and adds to
database
Sort into per
antenna sets [500]
& beamform each
in direction of 100
calibrators (25
Gops)
Mapper
Ionospheric
Calibration
ASM v1
Survey
Instrumental
Calibration
Faraday Rotation
Solar Imaging,
2° FOV, 32 kHz
every 8 sec.
(75 Mops)
1 GB/sec.
1.7
GB
/s~
1/2
Gvis
/s
125 M
vis
/s
Oversampled
map of primary
FOV, every 8
sec. (4 pol., 32
kHz, 3.6 Gcells
3.5 Gops)
Map to RA Dec
at array res.
(96 kHz, I pol.,
every 8 sec.,
0.5 Gops)
Map to RA Dec
at array res.
(32 kHz, 4 pol.,
every ~100
sec. 0.5 Gops)
GSM
Prediction
EOR Imaging
EOR Power
Spectrum
SurveyPostage
stamps towards
calibrators (4
pol. 32 kHz, <<
1 Mops)
Solar Imaging
Legend
Software Block
Hardware Block
Parallel Software
Block
Output Broadcast
IPS Power
Detection
Pulsar
Interface
16 GB/s – 2 Gvis every 1/2 sec.
Voltage
Beamformer
16 voltage beams, 2 pol., 1 GB/s
Monitor &
Control
Antenna
Beamformer
Bin to primary
beam FOV & 32
kHz channels
(1.8 G u,v,f,p cells,
~10 Gops)
Bin towards 100
calibrators, image
postage stamps, 1
pol. (outside
primary FOV) 25
Gops
Clock
IPS
Pulsars
Data Transport Layer
32 GB/s
Faraday Rotation
Solar Imaging
Realt
ime S
cie
nce
P
ack
ag
es
Offl
ine S
cie
nc
e
Pa
ck
ag
es
MWA-LFD Dataflow Diagram
Realtime Common Data Processing
Shadow indicates
workpackage
GPS
GSM
v2
System Diagram
m(v)
BT (u!
,v)
AT (!, !!)FT (!!,u!)
![Page 30: MW A LFD Epoch of R eionization P ow er Spectr um Obser vations · 2007-09-18 · MW A !LFD Epoch of R eionization P ow er Spectr um Obser vations Miguel F . M orales for the MW A](https://reader030.vdocuments.site/reader030/viewer/2022040807/5e49ca1ece1de5111971eb01/html5/thumbnails/30.jpg)
Correlator
Receiver
Node
Correlator Boards
Realtime Computer
Visibility Binner
Calibrate &
Integrate
Visibilities to
2-8 sec. in
baseline rings
(2 Gvis, 8 Gops)
Bin subset of
baselines at full
freq. & time
resolution to 2°
FOV (100 M u,v,f,p
cells, 250 Mops)
Combine vis.
in freq. to 32
kHz resolution
(500 Mvis, 1/2
Gops)
125 Mvis/s 0.5 GB/s
50 MB/s
EOR Realtime
System –
integrates to 10
min. and adds to
database
Sort into per
antenna sets [500]
& beamform each
in direction of 100
calibrators (25
Gops)
Mapper
Ionospheric
Calibration
ASM v1
Survey
Instrumental
Calibration
Faraday Rotation
Solar Imaging,
2° FOV, 32 kHz
every 8 sec.
(75 Mops)
1 GB/sec.
1.7
GB
/s~
1/2
Gvis
/s
125 M
vis
/s
Oversampled
map of primary
FOV, every 8
sec. (4 pol., 32
kHz, 3.6 Gcells
3.5 Gops)
Map to RA Dec
at array res.
(96 kHz, I pol.,
every 8 sec.,
0.5 Gops)
Map to RA Dec
at array res.
(32 kHz, 4 pol.,
every ~100
sec. 0.5 Gops)
GSM
Prediction
EOR Imaging
EOR Power
Spectrum
SurveyPostage
stamps towards
calibrators (4
pol. 32 kHz, <<
1 Mops)
Solar Imaging
Legend
Software Block
Hardware Block
Parallel Software
Block
Output Broadcast
IPS Power
Detection
Pulsar
Interface
16 GB/s – 2 Gvis every 1/2 sec.
Voltage
Beamformer
16 voltage beams, 2 pol., 1 GB/s
Monitor &
Control
Antenna
Beamformer
Bin to primary
beam FOV & 32
kHz channels
(1.8 G u,v,f,p cells,
~10 Gops)
Bin towards 100
calibrators, image
postage stamps, 1
pol. (outside
primary FOV) 25
Gops
Clock
IPS
Pulsars
Data Transport Layer
32 GB/s
Faraday Rotation
Solar Imaging
Realt
ime S
cie
nce
P
ack
ag
es
Offl
ine S
cie
nc
e
Pa
ck
ag
es
MWA-LFD Dataflow Diagram
Realtime Common Data Processing
Shadow indicates
workpackage
GPS
GSM
v2
System Diagram
m(v)
BT (u!
,v)
AT (!, !!)FT (!!,u!)
AT (u,u
!)
![Page 31: MW A LFD Epoch of R eionization P ow er Spectr um Obser vations · 2007-09-18 · MW A !LFD Epoch of R eionization P ow er Spectr um Obser vations Miguel F . M orales for the MW A](https://reader030.vdocuments.site/reader030/viewer/2022040807/5e49ca1ece1de5111971eb01/html5/thumbnails/31.jpg)
Correlator
Receiver
Node
Correlator Boards
Realtime Computer
Visibility Binner
Calibrate &
Integrate
Visibilities to
2-8 sec. in
baseline rings
(2 Gvis, 8 Gops)
Bin subset of
baselines at full
freq. & time
resolution to 2°
FOV (100 M u,v,f,p
cells, 250 Mops)
Combine vis.
in freq. to 32
kHz resolution
(500 Mvis, 1/2
Gops)
125 Mvis/s 0.5 GB/s
50 MB/s
EOR Realtime
System –
integrates to 10
min. and adds to
database
Sort into per
antenna sets [500]
& beamform each
in direction of 100
calibrators (25
Gops)
Mapper
Ionospheric
Calibration
ASM v1
Survey
Instrumental
Calibration
Faraday Rotation
Solar Imaging,
2° FOV, 32 kHz
every 8 sec.
(75 Mops)
1 GB/sec.
1.7
GB
/s~
1/2
Gvis
/s
125 M
vis
/s
Oversampled
map of primary
FOV, every 8
sec. (4 pol., 32
kHz, 3.6 Gcells
3.5 Gops)
Map to RA Dec
at array res.
(96 kHz, I pol.,
every 8 sec.,
0.5 Gops)
Map to RA Dec
at array res.
(32 kHz, 4 pol.,
every ~100
sec. 0.5 Gops)
GSM
Prediction
EOR Imaging
EOR Power
Spectrum
SurveyPostage
stamps towards
calibrators (4
pol. 32 kHz, <<
1 Mops)
Solar Imaging
Legend
Software Block
Hardware Block
Parallel Software
Block
Output Broadcast
IPS Power
Detection
Pulsar
Interface
16 GB/s – 2 Gvis every 1/2 sec.
Voltage
Beamformer
16 voltage beams, 2 pol., 1 GB/s
Monitor &
Control
Antenna
Beamformer
Bin to primary
beam FOV & 32
kHz channels
(1.8 G u,v,f,p cells,
~10 Gops)
Bin towards 100
calibrators, image
postage stamps, 1
pol. (outside
primary FOV) 25
Gops
Clock
IPS
Pulsars
Data Transport Layer
32 GB/s
Faraday Rotation
Solar Imaging
Realt
ime S
cie
nce
P
ack
ag
es
Offl
ine S
cie
nc
e
Pa
ck
ag
es
MWA-LFD Dataflow Diagram
Realtime Common Data Processing
Shadow indicates
workpackage
GPS
GSM
v2
System Diagram
m(v)
BT (u!
,v)
AT (!, !!)FT (!!,u!)
AT (u,u
!)
!
OTN
!1O
"
!1
![Page 32: MW A LFD Epoch of R eionization P ow er Spectr um Obser vations · 2007-09-18 · MW A !LFD Epoch of R eionization P ow er Spectr um Obser vations Miguel F . M orales for the MW A](https://reader030.vdocuments.site/reader030/viewer/2022040807/5e49ca1ece1de5111971eb01/html5/thumbnails/32.jpg)
Correlator
Receiver
Node
Correlator Boards
Realtime Computer
Visibility Binner
Calibrate &
Integrate
Visibilities to
2-8 sec. in
baseline rings
(2 Gvis, 8 Gops)
Bin subset of
baselines at full
freq. & time
resolution to 2°
FOV (100 M u,v,f,p
cells, 250 Mops)
Combine vis.
in freq. to 32
kHz resolution
(500 Mvis, 1/2
Gops)
125 Mvis/s 0.5 GB/s
50 MB/s
EOR Realtime
System –
integrates to 10
min. and adds to
database
Sort into per
antenna sets [500]
& beamform each
in direction of 100
calibrators (25
Gops)
Mapper
Ionospheric
Calibration
ASM v1
Survey
Instrumental
Calibration
Faraday Rotation
Solar Imaging,
2° FOV, 32 kHz
every 8 sec.
(75 Mops)
1 GB/sec.
1.7
GB
/s~
1/2
Gvis
/s
125 M
vis
/s
Oversampled
map of primary
FOV, every 8
sec. (4 pol., 32
kHz, 3.6 Gcells
3.5 Gops)
Map to RA Dec
at array res.
(96 kHz, I pol.,
every 8 sec.,
0.5 Gops)
Map to RA Dec
at array res.
(32 kHz, 4 pol.,
every ~100
sec. 0.5 Gops)
GSM
Prediction
EOR Imaging
EOR Power
Spectrum
SurveyPostage
stamps towards
calibrators (4
pol. 32 kHz, <<
1 Mops)
Solar Imaging
Legend
Software Block
Hardware Block
Parallel Software
Block
Output Broadcast
IPS Power
Detection
Pulsar
Interface
16 GB/s – 2 Gvis every 1/2 sec.
Voltage
Beamformer
16 voltage beams, 2 pol., 1 GB/s
Monitor &
Control
Antenna
Beamformer
Bin to primary
beam FOV & 32
kHz channels
(1.8 G u,v,f,p cells,
~10 Gops)
Bin towards 100
calibrators, image
postage stamps, 1
pol. (outside
primary FOV) 25
Gops
Clock
IPS
Pulsars
Data Transport Layer
32 GB/s
Faraday Rotation
Solar Imaging
Realt
ime S
cie
nce
P
ack
ag
es
Offl
ine S
cie
nc
e
Pa
ck
ag
es
MWA-LFD Dataflow Diagram
Realtime Common Data Processing
Shadow indicates
workpackage
GPS
GSM
v2
System Diagram
m(v)
BT (u!
,v)
AT (!, !!)FT (!!,u!)
AT (u,u
!)
!
OTN
!1O
"
!1
Calibration
![Page 33: MW A LFD Epoch of R eionization P ow er Spectr um Obser vations · 2007-09-18 · MW A !LFD Epoch of R eionization P ow er Spectr um Obser vations Miguel F . M orales for the MW A](https://reader030.vdocuments.site/reader030/viewer/2022040807/5e49ca1ece1de5111971eb01/html5/thumbnails/33.jpg)
Instrumental calibration
Instrument:
Gain from one antenna to rest of array, simultaneously for all antennas & 100 sources
![Page 34: MW A LFD Epoch of R eionization P ow er Spectr um Obser vations · 2007-09-18 · MW A !LFD Epoch of R eionization P ow er Spectr um Obser vations Miguel F . M orales for the MW A](https://reader030.vdocuments.site/reader030/viewer/2022040807/5e49ca1ece1de5111971eb01/html5/thumbnails/34.jpg)
Ionospheric calibration
Up to 1500 sources with known location, fit every 8 seconds ➙ rubber sheet
(Doeleman, Ting)
![Page 35: MW A LFD Epoch of R eionization P ow er Spectr um Obser vations · 2007-09-18 · MW A !LFD Epoch of R eionization P ow er Spectr um Obser vations Miguel F . M orales for the MW A](https://reader030.vdocuments.site/reader030/viewer/2022040807/5e49ca1ece1de5111971eb01/html5/thumbnails/35.jpg)
Ionospheric calibration
Up to 1500 sources with known location, fit every 8 seconds ➙ rubber sheet
(Doeleman, Ting)
![Page 36: MW A LFD Epoch of R eionization P ow er Spectr um Obser vations · 2007-09-18 · MW A !LFD Epoch of R eionization P ow er Spectr um Obser vations Miguel F . M orales for the MW A](https://reader030.vdocuments.site/reader030/viewer/2022040807/5e49ca1ece1de5111971eb01/html5/thumbnails/36.jpg)
1995MNRAS.274..324G
EOR foreground subtraction
![Page 37: MW A LFD Epoch of R eionization P ow er Spectr um Obser vations · 2007-09-18 · MW A !LFD Epoch of R eionization P ow er Spectr um Obser vations Miguel F . M orales for the MW A](https://reader030.vdocuments.site/reader030/viewer/2022040807/5e49ca1ece1de5111971eb01/html5/thumbnails/37.jpg)
EOR collaboration
J. Hewitt, M. Morales, R. Webster, F. Briggs, C. Carilli, S. Furlanetto, L. Greenhill,
L. Hernquist, A. Loeb, C. Lonsdale, A. de Oliveira-Costa, M. Tegmark, S. Wyithe, M. Zaldarriaga
![Page 38: MW A LFD Epoch of R eionization P ow er Spectr um Obser vations · 2007-09-18 · MW A !LFD Epoch of R eionization P ow er Spectr um Obser vations Miguel F . M orales for the MW A](https://reader030.vdocuments.site/reader030/viewer/2022040807/5e49ca1ece1de5111971eb01/html5/thumbnails/38.jpg)
Stages of astrophysical foreground subtraction
• Bright source & RFI subtraction
• Spectral fitting
• Parameter estimation, using power spectrum templates
![Page 39: MW A LFD Epoch of R eionization P ow er Spectr um Obser vations · 2007-09-18 · MW A !LFD Epoch of R eionization P ow er Spectr um Obser vations Miguel F . M orales for the MW A](https://reader030.vdocuments.site/reader030/viewer/2022040807/5e49ca1ece1de5111971eb01/html5/thumbnails/39.jpg)
Spectral fitting
Morales, Bowman & Hewitt (2006)
![Page 40: MW A LFD Epoch of R eionization P ow er Spectr um Obser vations · 2007-09-18 · MW A !LFD Epoch of R eionization P ow er Spectr um Obser vations Miguel F . M orales for the MW A](https://reader030.vdocuments.site/reader030/viewer/2022040807/5e49ca1ece1de5111971eb01/html5/thumbnails/40.jpg)
Spectral foreground errors
!Ps(!)" = 2!d"B2
!
"2a
#2!4+
"2
b
#2!2+ "2
c!$k(!)
"
!S(f) = !a df2 + !b df + !c
![Page 41: MW A LFD Epoch of R eionization P ow er Spectr um Obser vations · 2007-09-18 · MW A !LFD Epoch of R eionization P ow er Spectr um Obser vations Miguel F . M orales for the MW A](https://reader030.vdocuments.site/reader030/viewer/2022040807/5e49ca1ece1de5111971eb01/html5/thumbnails/41.jpg)
Parameter fitting
v
u
h
v
u
h
• Use templates to separate EOR signal from residual foreground subtraction errors
• Fit both local parameters & their ensemble errors
Morales, Bowman & Hewitt (2006)
![Page 42: MW A LFD Epoch of R eionization P ow er Spectr um Obser vations · 2007-09-18 · MW A !LFD Epoch of R eionization P ow er Spectr um Obser vations Miguel F . M orales for the MW A](https://reader030.vdocuments.site/reader030/viewer/2022040807/5e49ca1ece1de5111971eb01/html5/thumbnails/42.jpg)
MWA-LFD power
spectrum sensitivity
Bowman, Morales & Hewitt (2005)
z = 8, 360 hours of integration
0
1
2
3
4
5
6
7
8x 108
P [J
y2 Hz2 ]
0
1
2
3
4
5
6
7
8x 108
10-3 10-2 10-1 100 10110-1
100
101
102
103
k [Mpc-1 ]
(k3 P
/ 2π
t2 )1/2 [M
pc-3
/2 J
y Hz
]
10-3 10-2 10-1 100 10110-1
100
101
102
103
![Page 43: MW A LFD Epoch of R eionization P ow er Spectr um Obser vations · 2007-09-18 · MW A !LFD Epoch of R eionization P ow er Spectr um Obser vations Miguel F . M orales for the MW A](https://reader030.vdocuments.site/reader030/viewer/2022040807/5e49ca1ece1de5111971eb01/html5/thumbnails/43.jpg)
MWA-LFD sensitivity vs. redshift
!
"
#!
#"$%#!
&
'%()*+%,-+.
!
"
#!
#"$%#!
&
-%/%0
#!!+
#!!
#!!#
#!!
#!#
#!+
1%(234!#.
516%'%7%+!+8#7+%(234!67+%)*%,-.
#!!6
#!!+
#!!#
#!!
#!!#
#!!
#!#
#!+
!
#
+
6
9
"
0
:
&$%#!
&
!
#
+
6
9
"
0
:
&$%#!
&
-%/%&
#!!+
#!!
#!!#
#!!
#!#
#!+
1%(234!#.
#!!6
#!!+
#!!#
#!!
#!!#
#!!
#!#
#!+
!
!;"
#
#;"
+
+;"
6$%#!
&
!
!;"
#
#;"
+
+;"
6$%#!
&
-%/%#!
#!!+
#!!
#!!#
#!!
#!#
#!+
1%(234!#.
#!!6
#!!+
#!!#
#!!
#!!#
#!!
#!#
#!+
!
"
#!
#"$%#!
:
!
"
#!
#"$%#!
:
-%/%#+
#!!+
#!!
#!!#
#!!
#!#
#!+
1%(234!#.
#!!6
#!!+
#!!#
#!!
#!!#
#!!
#!#
#!+
Bowman, Morales & Hewitt (2005)
![Page 44: MW A LFD Epoch of R eionization P ow er Spectr um Obser vations · 2007-09-18 · MW A !LFD Epoch of R eionization P ow er Spectr um Obser vations Miguel F . M orales for the MW A](https://reader030.vdocuments.site/reader030/viewer/2022040807/5e49ca1ece1de5111971eb01/html5/thumbnails/44.jpg)
MWA-LFD vs. MWA+,,,
0
1
2
3
4
5
6
7
8x 108
P [J
y2 Hz2 ]
0
1
2
3
4
5
6
7
8x 108
10-3 10-2 10-1 100 10110-1
100
101
102
103
k [Mpc-1 ]
(k3 P
/ 2π
2 )1/2 [M
pc-3
/2 J
y Hz
]
10-3 10-2 10-1 100 10110-1
100
101
102
103
angu
lar o
nly
![Page 45: MW A LFD Epoch of R eionization P ow er Spectr um Obser vations · 2007-09-18 · MW A !LFD Epoch of R eionization P ow er Spectr um Obser vations Miguel F . M orales for the MW A](https://reader030.vdocuments.site/reader030/viewer/2022040807/5e49ca1ece1de5111971eb01/html5/thumbnails/45.jpg)
MWA-LFD
http://web.haystack.mit.edu/arrays/MWA/index.html
• ~$., million instrument, funded
• Data taking starting in late /,,0
• Premier EOR instrument• Strict attention to systematic errors