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Jishnu Suresh
Efficient methods to probe
With Ground-based DetectorsStochastic Gravitational Wave Background Anisotropy
!1ICRR seminar, March 11,2019
Jishnu Suresh
http://mwmw.gsfc.nasa.gov/mmw_allsky.html
To Map the GW Sky
????
????
LISA ~0.001 Hz DECIGO
??
~0.1 Hz LIGO/VIRGO/KAGRA
??
~100 Hz
slide: Sanjit Mitra
!2ICRR seminar, March 11,2019
5
FIG. 2. We present a simulated time series of duration 104
seconds illustrating the character of the BBH and BNS signalsin the time domain. In red we show a simulated BNS back-ground corresponding to the median rate as shown in Figure 1,and in green we display the median BBH background. We donot show any detector noise, and do not remove some loudand close events that would be detected individually. The re-gion in the black box, from 1800 – 2600 seconds, is shown ingreater detail in the inset. The BNS time series is continuousas it consists of a superposition of overlapping signals. On theother hand the BBH background (in green) is popcorn-like,and the signals do not overlap. Remarkably, even though thebackgrounds have very di↵erent structure in the time domain,the energy in both backgrounds are comparable below 100 Hz,as seen in Figure 1.
dation (NSF) for the construction and operation of the342
LIGO Laboratory and Advanced LIGO as well as the343
Science and Technology Facilities Council (STFC) of the344
United Kingdom, the Max-Planck-Society (MPS), and345
the State of Niedersachsen/Germany for support of the346
construction of Advanced LIGO and construction and347
operation of the GEO600 detector. Additional support348
for Advanced LIGO was provided by the Australian Re-349
search Council. The authors gratefully acknowledge the350
Italian Istituto Nazionale di Fisica Nucleare (INFN),351
the French Centre National de la Recherche Scientifique352
(CNRS) and the Foundation for Fundamental Research353
on Matter supported by the Netherlands Organisation354
for Scientific Research, for the construction and oper-355
ation of the Virgo detector and the creation and sup-356
port of the EGO consortium. The authors also grate-357
fully acknowledge research support from these agencies358
as well as by the Council of Scientific and Industrial Re-359
search of India, the Department of Science and Technol-360
ogy, India, the Science & Engineering Research Board361
(SERB), India, the Ministry of Human Resource Devel-362
opment, India, the Spanish Agencia Estatal de Inves-363
tigacion, the Vicepresidencia i Conselleria d’Innovacio,364
Recerca i Turisme and the Conselleria d’Educacio i Uni-365
versitat del Govern de les Illes Balears, the Conselleria366
d’Educacio, Investigacio, Cultura i Esport de la General-367
itat Valenciana, the National Science Centre of Poland,368
the Swiss National Science Foundation (SNSF), the Rus-369
sian Foundation for Basic Research, the Russian Science370
Foundation, the European Commission, the European371
Regional Development Funds (ERDF), the Royal Soci-372
ety, the Scottish Funding Council, the Scottish Universi-373
ties Physics Alliance, the Hungarian Scientific Research374
Fund (OTKA), the Lyon Institute of Origins (LIO), the375
National Research, Development and Innovation O�ce376
Hungary (NKFI), the National Research Foundation of377
Korea, Industry Canada and the Province of Ontario378
through the Ministry of Economic Development and In-379
novation, the Natural Science and Engineering Research380
Council Canada, the Canadian Institute for Advanced381
Research, the Brazilian Ministry of Science, Technol-382
ogy, Innovations, and Communications, the International383
Center for Theoretical Physics South American Insti-384
tute for Fundamental Research (ICTP-SAIFR), the Re-385
search Grants Council of Hong Kong, the National Natu-386
ral Science Foundation of China (NSFC), the Leverhulme387
Trust, the Research Corporation, the Ministry of Science388
and Technology (MOST), Taiwan and the Kavli Foun-389
dation. The authors gratefully acknowledge the support390
of the NSF, STFC, MPS, INFN, CNRS and the State of391
Niedersachsen/Germany for provision of computational392
resources.393
This article has been assigned the document number394
LIGO-P1700272.395
[1] J. Aasi et al. (LIGO Scientific Collaboration), Classical396
and Quantum Gravity 32, 074001 (2015).397
[2] F. Acernese et al., Classical and Quantum Gravity 32,398
024001 (2015).399
[3] B. P. Abbott et al. (LIGO Scientific Collaboration400
and Virgo Collaboration), Phys. Rev. Lett. 119 (2017),401
10.1103/PhysRevLett.119.161101.402
[4] B. P. Abbott et al., Phys. Rev. Lett. 116, 061102 (2016).403
[5] B. P. Abbott et al., Phys. Rev. Lett. 116, 241103 (2016).404
[6] B. P. Abbott et al., Phys. Rev. X 6, 041015 (2016).405
[7] B. P. Abbott et al., Phys. Rev. Lett. 118, 221101 (2017).406
[8] B. P. Abbott et al. (LIGO Scientific Collaboration and407
Virgo Collaboration), Phys. Rev. Lett. 119, 141101408
(2017).409
[9] B. Allen and J. D. Romano, Phys. Rev. D 59, 102001410
(1999).411
[10] N. Christensen, Phys. Rev. D 46, 5250 (1992).412
[11] T. Regimbau, Res. Astron. Astrophys. 11, 369 (2011).413
[12] X.-J. Zhu, E. Howell, T. Regimbau, D. Blair, and Z.-H.414
Zhu, ApJ 739, 86 (2011).415
[13] P. A. Rosado, Phys. Rev. D 84, 084004 (2011).416
[14] S. Marassi et al., Phys. Rev. D 84, 124037 (2011).417
[15] C. Wu, V. Mandic, and T. Regimbau, Phys. Rev. D 85,418
104024 (2012).419
[16] X.-J. Zhu, E. J. Howell, D. G. Blair, and Z.-H. Zhu,420
(~3 hr)
(no noise)
(PRL 120, 091101, 2018)
Jishnu Suresh!3
• individually undetectable (subthreshold)
• but detectable as a collectivity via their common influence on multiple detectors
• combined signal described statistically—stochastic gravitational-wave background
ICRR seminar, March 11,2019
Stochastic Gravitational Wave Background (SGWB)
Jishnu Suresh
Stochastic Gravitational Wave Background (SGWB)
Characterizing the stochastic background
⇢c =3c2H2
0
8⇡GN= 7.8⇥ 10�9erg/cm3
Many models give power law spectra in our band
Critical energy density to close the universe
⌦GW(f) = ⌦↵
✓f
fref
◆↵
↵ = 0
↵ = 2/3
Flat (inflation, cosmic strings in our band…)
Binary inspiral (BBH, BNS)
!4
•Unresolved astrophysical or cosmological sources
• popcorn or continuous
•Carry information not accessible in electro-magnetic astronomy
• astrophysical sources - information on the anisotropic local universe
• primordial cosmological background (CGWB) - direct probe of inflation
•Persistent unknown isotropic or anisotropic sources
ICRR seminar, March 11,2019
Jishnu Suresh
4
FIG. 1. The left panel shows the predicted median background for the BNS (red) and BBH (green) models described in thetext, the total (combined) background (blue), and the Poisson error bars (grey shaded region) for the total background. We alsoshow expected PI curves for observing runs O2, O3, and design sensitivity (see the main text for details about the assumptionsmade for these observing runs). Virgo is included in O3 and beyond. The PI curves for O3 and beyond cross the Poisson errorregion, indicating the possibility of detecting this background or placing interesting upper limits on the evolution of the binarymerger rates with redshift. In the right panel, we plot the signal-to-noise ratio as a function of observing time for the mediantotal background (blue curve) and associated uncertainty (shaded region). The median of the predicted total background canbe detected with SNR = 3 after 40 monthsof observation time, with LIGO-Virgo operating at design sensitivity (2022 – 2024).The markers indicate the transition between observing runs. We only show 12 months of the Design phase here, although forthe calculation of the PI curves it is assumed to be 24 months long (see [45]).
The BBH background is di↵erent in nature even286
though the resulting energy density spectrum is simi-287
lar. BBH events create a highly non-stationary and non-288
Gaussian background (sometimes referred to as a pop-289
corn background in the literature), i.e. individual events290
are well separated in time, on top of the continuous back-291
ground from contributed BNS inspirals. The duration of292
the waveform is much smaller for these massive sources293
(14 s on average in the band above 10 Hz, considering294
both the power law mass distribution and the distribu-295
tion in redshift [46]) and much less than the time interval296
between events (223+352
�115s on average) resulting in rare297
overlaps.298
Table I shows the estimated energy density at 25 Hz299
for each of the BNS, BBH and Total backgrounds. We300
also show the average time between events ⌧ for each301
of these backgrounds as well as the average number of302
overlapping sources at any time �, and the associated303
Poisson error bounds. The inverse of ⌧ gives the rate of304
events in Universe in s�1.305
Conclusion — The first gravitational wave detection of306
a binary neutron star system implies a significant contri-307
bution to the stochastic gravitational wave background308
from BNS mergers. Assuming the median merger rates,309
the background may be detected with SNR = 3 after 40310
monthsof accumulated observation time, during the De-311
sign phase (2022+)[45]. In the most optimistic case, an312
astrophysical background may be observed at a level of313
3� after only 18 monthsof observation, during O3, the314
next observing run.315
There are additional factors which may lead to an316
even earlier detection. First, the presence of additional317
sources, for example black hole-neutron star systems, will318
further add to the total background. Even small contri-319
butions to the background can decrease the time to detec-320
tion significantly. Second, the analysis we have presented321
here assumes the standard cross-correlation search. Spe-322
cialized non-Gaussian searches may be more sensitive,323
particularly to the BBH background [47, 48]. Unlike a324
standard matched filter search, non-Gaussian pipelines325
do not attempt to find individual events, but rather to326
measure the rate of sub-threshold events independently327
of their distribution.328
A detection of the astrophysical background allows for329
a rich set of follow-up studies to fully understand its com-330
position. The di↵erence in the time-domain structure of331
the BBH and BNS signals may allow the BNS and BBH332
backgrounds to be measured independently. After de-333
tecting the background, stochastic analyses can address334
whether the background is isotropic [49–51], unpolarized335
[52], and consistent with general relativity [53]. Finally,336
understanding the astrophysical background is crucial to337
subtract it and enable searches for a background of cos-338
mological origin [46].339
Acknowledgments — The authors gratefully acknowledge340
the support of the United States National Science Foun-341
(PRL 120, 091101, 2018)
Potentially detectable with advanced LIGO/Virgo
!5ICRR seminar, March 11,2019
(ArXiv:1903.02886)
Jishnu Suresh
(like cosmic microwave background)
(statistically) isotropic anisotropic
(galactic plane in equatorial coords)
Types of Stochastic Gravitational Wave Background
(i) Stochastic backgrounds can differ in spatial distribution
Joe’s lectures;Les Houches Summer School 2018
!6ICRR seminar, March 11,2019
Jishnu Suresh
(yr)10
(ii) differ in temporal distribution and amplitude
Stationary Gaussian Non-stationary (non-gaussian)
(e.g., from galactic white dwarf binaries;
modulated by LISA’s orbital motion)
Foreground
Joe’s lectures;Les Houches Summer School 2018
!7ICRR seminar, March 11,2019
Jishnu Suresh
(iii) differ in power spectra depending on source
white noiseσ = 1
histograms
2Δt σ2
f-7/3
BNS chirp
Joe’s lectures;Les Houches Summer School 2018
!8ICRR seminar, March 11,2019
Example: Rate estimates and signal durations imply BNS “confusion” & BBH “popcorn” for LIGO / Virgo
BBH “popcorn” histograBBH (m1=m2=10 Msolar)
BNS “confusion” histogramBNS (m1=m2=1.4 Msolar)
Jishnu SureshICRR seminar, March 11,2019
!9
Joe’s lectures;Les Houches Summer School 2018
Example: Rate estimates and signal durations imply BNS “confusion” & BBH “popcorn” for LIGO / Virgo
Jishnu SureshICRR seminar, March 11,2019
!10
Joe’s lectures;Les Houches Summer School 2018
5
FIG. 2. We present a simulated time series of duration 104
seconds illustrating the character of the BBH and BNS signalsin the time domain. In red we show a simulated BNS back-ground corresponding to the median rate as shown in Figure 1,and in green we display the median BBH background. We donot show any detector noise, and do not remove some loudand close events that would be detected individually. The re-gion in the black box, from 1800 – 2600 seconds, is shown ingreater detail in the inset. The BNS time series is continuousas it consists of a superposition of overlapping signals. On theother hand the BBH background (in green) is popcorn-like,and the signals do not overlap. Remarkably, even though thebackgrounds have very di↵erent structure in the time domain,the energy in both backgrounds are comparable below 100 Hz,as seen in Figure 1.
dation (NSF) for the construction and operation of the342
LIGO Laboratory and Advanced LIGO as well as the343
Science and Technology Facilities Council (STFC) of the344
United Kingdom, the Max-Planck-Society (MPS), and345
the State of Niedersachsen/Germany for support of the346
construction of Advanced LIGO and construction and347
operation of the GEO600 detector. Additional support348
for Advanced LIGO was provided by the Australian Re-349
search Council. The authors gratefully acknowledge the350
Italian Istituto Nazionale di Fisica Nucleare (INFN),351
the French Centre National de la Recherche Scientifique352
(CNRS) and the Foundation for Fundamental Research353
on Matter supported by the Netherlands Organisation354
for Scientific Research, for the construction and oper-355
ation of the Virgo detector and the creation and sup-356
port of the EGO consortium. The authors also grate-357
fully acknowledge research support from these agencies358
as well as by the Council of Scientific and Industrial Re-359
search of India, the Department of Science and Technol-360
ogy, India, the Science & Engineering Research Board361
(SERB), India, the Ministry of Human Resource Devel-362
opment, India, the Spanish Agencia Estatal de Inves-363
tigacion, the Vicepresidencia i Conselleria d’Innovacio,364
Recerca i Turisme and the Conselleria d’Educacio i Uni-365
versitat del Govern de les Illes Balears, the Conselleria366
d’Educacio, Investigacio, Cultura i Esport de la General-367
itat Valenciana, the National Science Centre of Poland,368
the Swiss National Science Foundation (SNSF), the Rus-369
sian Foundation for Basic Research, the Russian Science370
Foundation, the European Commission, the European371
Regional Development Funds (ERDF), the Royal Soci-372
ety, the Scottish Funding Council, the Scottish Universi-373
ties Physics Alliance, the Hungarian Scientific Research374
Fund (OTKA), the Lyon Institute of Origins (LIO), the375
National Research, Development and Innovation O�ce376
Hungary (NKFI), the National Research Foundation of377
Korea, Industry Canada and the Province of Ontario378
through the Ministry of Economic Development and In-379
novation, the Natural Science and Engineering Research380
Council Canada, the Canadian Institute for Advanced381
Research, the Brazilian Ministry of Science, Technol-382
ogy, Innovations, and Communications, the International383
Center for Theoretical Physics South American Insti-384
tute for Fundamental Research (ICTP-SAIFR), the Re-385
search Grants Council of Hong Kong, the National Natu-386
ral Science Foundation of China (NSFC), the Leverhulme387
Trust, the Research Corporation, the Ministry of Science388
and Technology (MOST), Taiwan and the Kavli Foun-389
dation. The authors gratefully acknowledge the support390
of the NSF, STFC, MPS, INFN, CNRS and the State of391
Niedersachsen/Germany for provision of computational392
resources.393
This article has been assigned the document number394
LIGO-P1700272.395
[1] J. Aasi et al. (LIGO Scientific Collaboration), Classical396
and Quantum Gravity 32, 074001 (2015).397
[2] F. Acernese et al., Classical and Quantum Gravity 32,398
024001 (2015).399
[3] B. P. Abbott et al. (LIGO Scientific Collaboration400
and Virgo Collaboration), Phys. Rev. Lett. 119 (2017),401
10.1103/PhysRevLett.119.161101.402
[4] B. P. Abbott et al., Phys. Rev. Lett. 116, 061102 (2016).403
[5] B. P. Abbott et al., Phys. Rev. Lett. 116, 241103 (2016).404
[6] B. P. Abbott et al., Phys. Rev. X 6, 041015 (2016).405
[7] B. P. Abbott et al., Phys. Rev. Lett. 118, 221101 (2017).406
[8] B. P. Abbott et al. (LIGO Scientific Collaboration and407
Virgo Collaboration), Phys. Rev. Lett. 119, 141101408
(2017).409
[9] B. Allen and J. D. Romano, Phys. Rev. D 59, 102001410
(1999).411
[10] N. Christensen, Phys. Rev. D 46, 5250 (1992).412
[11] T. Regimbau, Res. Astron. Astrophys. 11, 369 (2011).413
[12] X.-J. Zhu, E. Howell, T. Regimbau, D. Blair, and Z.-H.414
Zhu, ApJ 739, 86 (2011).415
[13] P. A. Rosado, Phys. Rev. D 84, 084004 (2011).416
[14] S. Marassi et al., Phys. Rev. D 84, 124037 (2011).417
[15] C. Wu, V. Mandic, and T. Regimbau, Phys. Rev. D 85,418
104024 (2012).419
[16] X.-J. Zhu, E. J. Howell, D. G. Blair, and Z.-H. Zhu,420
Jishnu Suresh
Cross-Correlation SearchAllen & Romano (2001)
h1 = n1 + sh2 = n2 + s
signal
signal and noise are uncorrelated
noise at H1 and L1 is uncorrelated
!11
• Detector output = true signal + noise
• Normally detector noise are uncorrelated for far away detectors and times:
• Cross-correlation (CC) statistic is the best choice for unmodeled sources
- one detector’s signal is the filter for other detector’s data
ICRR seminar, March 11,2019
Jishnu Suresh
cross-correlation is essentially a one dimensional map of the sky
There are three sources of different strength (strong, medium and weak) marked in red.
!12ICRR seminar, March 11,2019
Jishnu Suresh
Stochastic search
⌦GW(f) = ⌦↵
✓f
fref
◆↵
Overlap reduction function for H1/L1
For a power law background…
We can write an optimal estimator for theenergy density
Accounts for separation and orientation of detectorsNote we are most sensitive below 100 Hz
Allen and Romano, Phys.Rev. D59 (1999) 102001
de-weight correlation when noise is large or overlap is small
⟨h1( f )h*2 ( f′�)⟩ =12
δ( f − f′�)Γ12( f )Sh( f )
Q( f ) ∝Γ12( f )H( f )P1( f )P2( f )
Choose Q to maximize SNR for fixed spectral shape:
expected signal spectrum
!13ICRR seminar, March 11,2019
Jishnu Suresh
Radiometer Algorithm
.
x_
Δ x_
Ω−
Ω−
Ω−
Detector 1 Detector 2
(t)
(t)
Δ
Zdt
Zdt0 s1(t) s2(t
0) q(t, t0) ⌘Z
df es⇤1(t, f) es2(t, f) eq(t, f)
Lazzarini & Weiss (2004)Ballmer (2006)Mitra et al (2007)
!14
• Essentially Earth Rotation Synthesis Imaging
- Cross-correlate detector outputs in short time segments
-map making: use time dependent phase delay
• Use spectral filters
- to enhance signal power
- to reduce noise power
ICRR seminar, March 11,2019
Jishnu Suresh
Terrestrial Network
H L
I V K
H
L
V K I
(credit: N. Cornish)
Sky coverage of individual detectors
!15ICRR seminar, March 11,2019
Jishnu Suresh
H
L
V K
Terrestrial Network
I
(credit: N. Cornish)
!16ICRR seminar, March 11,2019
Jishnu Suresh
H
L
V K
Terrestrial Network
I
(credit: N. Cornish)
!17ICRR seminar, March 11,2019
Jishnu Suresh
H
L
V K
Terrestrial Network
I
(credit: N. Cornish)
!18ICRR seminar, March 11,2019
Jishnu Suresh
H
L
V K
Terrestrial Network
I
I
(credit: N. Cornish)
19
!19ICRR seminar, March 11,2019
Jishnu Suresh
H
L
V K
Terrestrial Network
K
I
(credit: N. Cornish)
!20ICRR seminar, March 11,2019
Jishnu Suresh
Radiometric Search for SGWB
CI � CIft := �s�I1
(t; f) �sI2(t; f)
nI � nIft := �n�
I1(t; f) �nI2(t; f)
N � Cov(CIft, C
I�
f �t�) ⇥(�T )2
4�II� �tt� �ff � PI1(t; f) PI2(t; f)
!21
• Observed data := Cross Spectral Density := product of SFT’s
• Noise (in the small signal limit):
• Covariance matrix:
ICRR seminar, March 11,2019
Jishnu Suresh
CSD Observed from an Anisotropic Background
P(�) :=�
�
P� e�(�); P � P�
CIft :=
�
�
KIft,�P� + nI
ft
�I�(f, t) :=
�
A=+,⇥
⇥
S2d�FA
I1(�, t) FA
I2(�, t) e2⇥if⇥·�x(t)/c e�(�)
KI � KIft,� := �T H(f) �I
�(f, t)
Low signal limit
!22
• Anisotropic SGWB in some basis:
• Observed CSD = convolution of anisotropic background with additive noise
- the “kernel” or “beam”:
✴ generalized overlap reduction function
ICRR seminar, March 11,2019
Jishnu Suresh
ML Estimation of SGWB Anisotropy
P� ⇥ P = � · X
X := K† · N�1 · C ⇥ X� =4
�T
�
I,ft
H(f) �I⇥ft,�
PI1(t; f)PI2(t; f)⇥s⇥I1
(t; f) ⇥sI2(t; f)
��1 := K† · N�1 · K ⇥ [��1]��� = 4�
I,ft
H2(f)PI1(t; f) PI2(t; f)
�I⇥� (f, t) �I
��(f, t)
P(�) :=�
�
P� e�(�); P � P�
!23
• ML estimate of SGWB anisotropy in any basis with a network of detectors:
- “Dirty” map (essentially filtered output):
- Fisher information matrix:
ICRR seminar, March 11,2019
Jishnu Suresh
Base Line Sidereal Rotation
The white circles indicate positions in the sky map which will have equal time/phase delay when the signal from that part of the sky arrive in the LIGO Livingston and
Hanford detectors
!24ICRR seminar, March 11,2019
Jishnu Suresh!25ICRR seminar, March 11,2019
SGWB point source pre-processing
Jishnu Suresh!26ICRR seminar, March 11,2019
Jishnu Suresh
SGWB point source processing
!27ICRR seminar, March 11,2019
Jishnu Suresh
SGWB point source post-processing
!28ICRR seminar, March 11,2019
Jishnu Suresh
SGWB extended source pre-processing
!29ICRR seminar, March 11,2019
Jishnu Suresh
SGWB extended source processing
!30ICRR seminar, March 11,2019
Jishnu Suresh
SGWB extended source post-processing
!31ICRR seminar, March 11,2019
Jishnu Suresh
Folding stochastic data to one sidereal day
0
1
2
3
Sid
ere
al D
ay
Sidereal Time
Time
Ain, Dalvi & Mitra, PRD 92, 022003 (2015)
Folded full LIGO O2 CSD (abs)
!32
• No approximation, based on a mathematical symmetry
• Incorporates all the dirty stuff (quality cuts, overlapping window correction)
Folding stochastic data to one sidereal day
ICRR seminar, March 11,2019
Jishnu Suresh!33ICRR seminar, March 11,2019
Folding Data
• The estimator (“dirty map”)
X↵ =X
Ift
KI⇤↵,ft
��2Ift C
Ift � 1
2"It�1
n��2Ift + ��2
If(t�1)
oCI
f(t�1)
� 1
2"It+1
n��2Ift + ��2
If(t+1)
oCI
f(t+1)
�
� 1
2"Iiday+tsid�1
n��2If(iday+tsid)
+ ��2If(iday+tsid�1)
oCI
f(iday+tsid�1)
=X
Iftsid
KI⇤↵,ftsid
X
iday
h��2If(iday+tsid)
CIf(iday+tsid)
� 1
2"Iiday+tsid+1
n��2If(iday+tsid)
+ ��2If(iday+tsid+1)
oCI
f(tsid+tsid+1)
�
Jishnu Suresh!34ICRR seminar, March 11,2019
• The Fisher information matrix (three data streams)
�↵↵0 =X
Ift
KI⇤↵,ft
��2Ift K
Ift,↵0 � 1
2"It�1
n��2Ift + ��2
If(t�1)
oKI
f(t�1),↵0
� 1
2"It+1
n��2Ift + ��2
If(t+1)
oKI
f(t+1),↵0
�
=X
Iftsid
KI⇤↵,ftsid K
Iftsid,↵0
X
iday
��2If(iday+tsid)
�X
Iftsid
KI⇤↵,ftsid K
If(tsid�1),↵0
X
iday
1
2"Iiday+tsid�1
n��2If(iday+tsid)
+ ��2If(iday+tsid�1)
o
�X
Iftsid
KI⇤↵,ftsid K
If(tsid+1),↵0
X
iday
1
2"Iiday+tsid+1
n��2If(iday+tsid)
+ ��2If(iday+tsid+1)
o
Jishnu Suresh
(HV baseline) (LV baseline)
• No data quality cuts has been incorporated to these SIDs
• One can incorporate either in folding code or SID code
!35ICRR seminar, March 11,2019
Jishnu Suresh
Validation of Folded Data
RMS Differences = RMS (folded - unfolded) / RMS (unfolded)
Real parts of FSID Fisher matrix = 4.51e-03Imaginary parts of FSID Fisher matrix = 4.92e-03
Dirty SpH = 2.38e-02Clean SpH = 2.44e-02Dirty map = 2.05e-02Clean map = 2.25e-02
Variance map = 2.12e-03SNR map = 2.08e-02
!36ICRR seminar, March 11,2019
Jishnu Suresh
(previous) Stochastic Pipelines
537 higher than the noise PSD. We calculated the CSD for538 these injected sources and added them to the CSD data.539 After running the code, the injected sources were properly540 recovered. The results from applying this injection on541 simulated data are shown in Fig. 5. This figure also includes542 a map in the bottom right which is obtained by deconvo-543 lution of the dirty map with a Fisher matrix. This was a544 check to see if the source strength and location in the clean545 map match the injected map. In this case, the point sources546 in the clean map appears at the same location as the injected547 map, thus validating the deconvolution method. Moreover,548 the point sources in the clean map are more localized than549 in the dirty map.
550 V. CONCLUSIONS
551 The primary advantage of PyStoch is the speed up and552 convenience. It makes the map calculation few hundred553 times faster3 Table I shows the scale of speed up by folding554 and PyStoch. It also gets rid of the requirement for555 storage to save intermediate results. With folding and556 PyStoch SGWB searches with LIGO data can be done557 on a laptop, in place of parallel computing on few hundred558 processors, which is very convenient.559 Another advantage is that PyStoch produces results560 regarding narrowband maps. In the older pipeline one had561 to specify the expected SGWB spectrum HðfÞ before562 running the pipeline. But PyStoch does not require the563 spectrum. From Eq. (28), the set of narrowband maps, the564 spectrum-specific result can be produced using the follow-565 ing equation,
Xp ¼X
If
HðfÞXf;p ð29Þ
566567568The above summation of narrowband maps can be done569in one matrix multiplication. Also, PyStoch is a directed570search for all directions in the sky, which means that if one571wants to search a particular direction of the sky, e.g., Sco572X-1 or Virgo cluster, it is straightforward. We only have to573see which pixel(s) include the source and we can just add574the pixels (since HEALPix pixels corresponds to the equal575area in the sky one does not even have to worry about pixel576weights). Similarly, PyStoch search results can be con-577tracted into the result of isotropic search just by adding578all the pixel values. All data quality cuts, removing bad
F5:1 FIG. 5. The top left map is broadband dirty map from simulatedF5:2 data, the top right map shows the injected sources. The bottomF5:3 left map is the dirty map made from simulated data including theF5:4 injections. The bottom right map is the clean map obtained byF5:5 deconvolution of the (bottom left) dirty map including injections.
TABLE I. This table shows the estimated calculation time (on asingle node of IUCAA computational facility) and storagerequired to calculate the narrowband maps using three pipelines:the standard pipeline, the standard pipeline with folded data, andPyStoch with folded data.
Conventionalpipeline
Foldingpipeline
Folding andPyStoch
Intermediatedata
450 GB 1.5 GB 1.5 GB
Processingtime
10 CPUyears
10 CPUdays
40 CPUminutes
Intermediateresults
800 TB 2.5 TB Not required
Final results 500 MB 500 MB 500 MB
F6:1FIG. 6. Flowchart for a pipeline including folding andF6:2PyStoch. The interferometer data are cross-correlated in theF6:3first step preproc (short for pre-processing), turning the data intoF6:4SID. The SID is then folded into FSID by the folding module.F6:5PyStoch takes the FSID and calculates the narrowband maps.F6:6Directional or spectrum specific searches can be performed onF6:7those narrowband maps. Corrections for bad frequencies (notchF6:8list), segment overlaps, data qualities can be applied at manyF6:9points in this pipeline (solid arrows indicate where we applied it,
F6:10dotted arrows indicate other modules where it can be applied).
3Tens of times faster on a single thread, hundred times fasterwhen used with multithreading.
ANIRBAN AIN, JISHNU SURESH, and SANJIT MITRA PHYS. REV. D XX, 000000 (XXXX)
8
!37ICRR seminar, March 11,2019
Jishnu Suresh
PyStoch - fast HEALPix based SGWB mapmakingAin, Suresh & Mitra, PRD 98 024001 (2018)
!38
• Folding + PyStoch = Few thousand times speed up
- perform the whole analysis on a laptop in few minutes!
• Produces the narrowband maps as intermediate result
- so separate search for different frequency spectra becomes redundant
PyStoch - fast HEALPix based SGWB mapmaking
ICRR seminar, March 11,2019
Jishnu Suresh
Breaking Down the ORF
3314 pairs of seed maps (for one sidereal day) produced in a laptop in 20 seconds.
GPS Time1126615273
�Ift,↵ :=
X
A
Z
S2
d⌦FAI1(⌦, t)FA
I2(⌦, t)e2⇡if
⌦·�xI (t)c e↵(⌦)
Efficient Overlap Reduction Function Computation
!39ICRR seminar, March 11,2019
Jishnu Suresh
GPS Time1126615273
ORF from ORF seed maps
!40ICRR seminar, March 11,2019
Jishnu Suresh
Time Series Data
from Hanford & Livingston
Stochastic Intermediate Data (SID)
Dirty Maps & Fisher Matrices
for each job
Job File
(Each line is a job list of GPS tag stat & end)
Parameter File
(for SID)
Pre-Processing
(produces CC spectra)
Cache Files (named by job number)
Frame locations Gps tag start
Processing
(produces dirty map
and Fisher matrices)
Post-Processing
Sph search
Combined dirty map
and Fisher matrix
Mapping program
Parameter File
(for sph search)
Sky Maps
Dirty MapVariance Map
(inv fisher matrix)SNR Map Clean Map
Data
Pipeline
Task
Input
Parameters
Information
Required for
processing
Folding
Parameter File
(for folding)
Cache Files (named by job number)
Frame locations Gps tag start
Folded Stochastic
Intermediate Data (FSID)
SID Meta Data
(GPS tag & locations)
Stochastic pipeline
Stochastic pipeline - PyStoch
!41ICRR seminar, March 11,2019
Jishnu Suresh
537 higher than the noise PSD. We calculated the CSD for538 these injected sources and added them to the CSD data.539 After running the code, the injected sources were properly540 recovered. The results from applying this injection on541 simulated data are shown in Fig. 5. This figure also includes542 a map in the bottom right which is obtained by deconvo-543 lution of the dirty map with a Fisher matrix. This was a544 check to see if the source strength and location in the clean545 map match the injected map. In this case, the point sources546 in the clean map appears at the same location as the injected547 map, thus validating the deconvolution method. Moreover,548 the point sources in the clean map are more localized than549 in the dirty map.
550 V. CONCLUSIONS
551 The primary advantage of PyStoch is the speed up and552 convenience. It makes the map calculation few hundred553 times faster3 Table I shows the scale of speed up by folding554 and PyStoch. It also gets rid of the requirement for555 storage to save intermediate results. With folding and556 PyStoch SGWB searches with LIGO data can be done557 on a laptop, in place of parallel computing on few hundred558 processors, which is very convenient.559 Another advantage is that PyStoch produces results560 regarding narrowband maps. In the older pipeline one had561 to specify the expected SGWB spectrum HðfÞ before562 running the pipeline. But PyStoch does not require the563 spectrum. From Eq. (28), the set of narrowband maps, the564 spectrum-specific result can be produced using the follow-565 ing equation,
Xp ¼X
If
HðfÞXf;p ð29Þ
566567568The above summation of narrowband maps can be done569in one matrix multiplication. Also, PyStoch is a directed570search for all directions in the sky, which means that if one571wants to search a particular direction of the sky, e.g., Sco572X-1 or Virgo cluster, it is straightforward. We only have to573see which pixel(s) include the source and we can just add574the pixels (since HEALPix pixels corresponds to the equal575area in the sky one does not even have to worry about pixel576weights). Similarly, PyStoch search results can be con-577tracted into the result of isotropic search just by adding578all the pixel values. All data quality cuts, removing bad
F5:1 FIG. 5. The top left map is broadband dirty map from simulatedF5:2 data, the top right map shows the injected sources. The bottomF5:3 left map is the dirty map made from simulated data including theF5:4 injections. The bottom right map is the clean map obtained byF5:5 deconvolution of the (bottom left) dirty map including injections.
TABLE I. This table shows the estimated calculation time (on asingle node of IUCAA computational facility) and storagerequired to calculate the narrowband maps using three pipelines:the standard pipeline, the standard pipeline with folded data, andPyStoch with folded data.
Conventionalpipeline
Foldingpipeline
Folding andPyStoch
Intermediatedata
450 GB 1.5 GB 1.5 GB
Processingtime
10 CPUyears
10 CPUdays
40 CPUminutes
Intermediateresults
800 TB 2.5 TB Not required
Final results 500 MB 500 MB 500 MB
F6:1FIG. 6. Flowchart for a pipeline including folding andF6:2PyStoch. The interferometer data are cross-correlated in theF6:3first step preproc (short for pre-processing), turning the data intoF6:4SID. The SID is then folded into FSID by the folding module.F6:5PyStoch takes the FSID and calculates the narrowband maps.F6:6Directional or spectrum specific searches can be performed onF6:7those narrowband maps. Corrections for bad frequencies (notchF6:8list), segment overlaps, data qualities can be applied at manyF6:9points in this pipeline (solid arrows indicate where we applied it,
F6:10dotted arrows indicate other modules where it can be applied).
3Tens of times faster on a single thread, hundred times fasterwhen used with multithreading.
ANIRBAN AIN, JISHNU SURESH, and SANJIT MITRA PHYS. REV. D XX, 000000 (XXXX)
8
(New) Stochastic Pipeline - PyStoch
Ain, Suresh & Mitra, PRD 98 024001 (2018)
!42ICRR seminar, March 11,2019
Jishnu Suresh
Narrowband Maps1920 Narrowband maps (20 Hz to 500 Hz, 0.25 Hz bins) produced in a laptop in
less than 10 minutes.
!43ICRR seminar, March 11,2019
Jishnu Suresh
injected source
clean_map_HL
clean_mapdetector network
Multi-baseline studies
How the stochastic analysis is going to improve with KAGRA coming online ?
Multi baseline improvements :
• Sensitivity improvement • Sky coverage• Parameter accuracy• Quality of the sky maps
Phys. Rev. D 83, 063002, 2011
!44ICRR seminar, March 11,2019
Jishnu Suresh
Multi-baseline Maps : Broad Source
!45ICRR seminar, March 11,2019
Jishnu Suresh
Multi-baseline Maps : Clean Maps
!46ICRR seminar, March 11,2019
• The GW radiometer algorithm is optimal to search for backgrounds
- folding+PyStoch has made the algorithm few thousand times faster
- PyStoch is handy to study multi baseline efficiency for stochastic searches
- can also search for persistent unknown sources
- can rapidly follow up the outliers
Jishnu Suresh!47ICRR seminar, March 11,2019
Jishnu Suresh!48ICRR seminar, March 11,2019
…and we expect many more weaker signals…Stay tuned for..
thank you
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