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MWA–LFD Epoch of Reionization
Power Spectrum Observations
Miguel F. Morales for the MWA–LFD EOR power spectrum collaboration
December 16, 2006 @ Melbourne University
Overview
• EOR power spectrum signal
• Building an EOR machine: MWA–LFD
• Foreground subtraction
0 (now)~6CMBBigBang
EOR
redshift
EOR power spectrum signal
0 (now)~6CMBBigBang
EOR
redshift
H& during EOR
100
200
300
400
500
7
7.58
8.59
Mpc/h
z
sv_z8_zeta10_ME.fts_0
Oliver Zahn
Statistical EOR detection
f
iy
ImageCube
ix
v
f
Visibilities
u
v
h
FourierRepresentation
u
FT SkyCoordinates
FTFrequency
Morales & Hewitt (2004)
Spherical symmetry
v
u
h
Morales & Hewitt (2004)
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)
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)
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)
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)
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)
Building an EOR machine: the MWA–LFD
Challenges 1: Foregrounds• Faint point sources
• Smooth galactic emission
• Galactic radio recombination lines
• RFI
• Others!
Challenges 2: Ionosphere & Polarization
325 MHz polarized flux, 6° x 6°,4’ beam, 5 K peaks (de Bruyn)
Lonsdale (2004)
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)
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
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:
Laying down the math
m(v) = B(v,u!)F(u!, !!)A(!!, !)I(!) + n(v)
Observation:
(Tegmark, Zaldarriaga, Morales)
Laying down the math
m(v) = B(v,u!)F(u!, !!)A(!!, !)I(!) + n(v)
Observation:
true sky
(Tegmark, Zaldarriaga, Morales)
Laying down the math
m(v) = B(v,u!)F(u!, !!)A(!!, !)I(!) + n(v)
Observation:
true skyionosphericdistortion
(Tegmark, Zaldarriaga, Morales)
Laying down the math
m(v) = B(v,u!)F(u!, !!)A(!!, !)I(!) + n(v)
Observation:
true skyionosphericdistortion
Fouriertransform
(Tegmark, Zaldarriaga, Morales)
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)
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)
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
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.)
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
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)
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)
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!)
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
!)
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
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
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nce
P
ack
ag
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Offl
ine S
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nc
e
Pa
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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
Instrumental calibration
Instrument:
Gain from one antenna to rest of array, simultaneously for all antennas & 100 sources
Ionospheric calibration
Up to 1500 sources with known location, fit every 8 seconds ➙ rubber sheet
(Doeleman, Ting)
Ionospheric calibration
Up to 1500 sources with known location, fit every 8 seconds ➙ rubber sheet
(Doeleman, Ting)
1995MNRAS.274..324G
EOR foreground subtraction
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
Stages of astrophysical foreground subtraction
• Bright source & RFI subtraction
• Spectral fitting
• Parameter estimation, using power spectrum templates
Spectral fitting
Morales, Bowman & Hewitt (2006)
Spectral foreground errors
!Ps(!)" = 2!d"B2
!
"2a
#2!4+
"2
b
#2!2+ "2
c!$k(!)
"
!S(f) = !a df2 + !b df + !c
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)
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
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)
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
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
Recommended