Euclid: Fast two-point correlation function covariance through linear construction
E. Keihanen
,
V. Lindholm
,
P. Monaco
,
L. Blot
,
C. Carbone
,
K. Kiiveri
,
A.G. Sánchez
,
A. Viitanen
,
J. Valiviita
,
A. Amara
,
N. Auricchio
,
M. Baldi
,
D. Bonino
,
E. Branchini
,
M. Brescia
,
J. Brinchmann
,
S. Camera
,
V. Capobianco
,
J. Carretero
,
M. Castellano
,
S. Cavuoti
,
A. Cimatti
,
R. Cledassou
(1, 2)
,
G. Congedo
,
L. Conversi
,
Y. Copin
(3)
,
L. Corcione
,
M. Cropper
,
A. Da Silva
,
H. Degaudenzi
,
M. Douspis
(4)
,
F. Dubath
,
C.A. J. Duncan
,
X. Dupac
,
S. Dusini
,
A. Ealet
(3)
,
S. Farrens
(5)
,
S. Ferriol
(3)
,
M. Frailis
,
E. Franceschi
,
M. Fumana
,
B. Gillis
,
C. Giocoli
,
A. Grazian
,
F. Grupp
,
L. Guzzo
,
S.V. H. Haugan
,
H. Hoekstra
,
W. Holmes
,
F. Hormuth
,
K. Jahnke
,
M. Kümmel
,
S. Kermiche
(6)
,
A. Kiessling
,
T. Kitching
,
M. Kunz
,
H. Kurki-Suonio
,
S. Ligori
,
P.B. Lilje
,
I. Lloro
,
E. Maiorano
,
O. Mansutti
,
O. Marggraf
,
F. Marulli
,
R. Massey
,
M. Melchior
,
M. Meneghetti
,
G. Meylan
,
M. Moresco
,
B. Morin
(5)
,
L. Moscardini
,
E. Munari
,
S.M. Niemi
,
C. Padilla
,
S. Paltani
,
F. Pasian
,
K. Pedersen
,
V. Pettorino
(5)
,
S. Pires
(5)
,
G. Polenta
,
M. Poncet
(1)
,
L. Popa
,
F. Raison
,
A. Renzi
,
J. Rhodes
,
E. Romelli
,
R. Saglia
,
B. Sartoris
,
P. Schneider
,
T. Schrabback
,
A. Secroun
,
G. Seidel
,
C. Sirignano
,
G. Sirri
,
L. Stanco
,
C. Surace
(7)
,
P. Tallada-Crespí
,
D. Tavagnacco
,
A.N. Taylor
,
I. Tereno
,
R. Toledo-Moreo
,
F. Torradeflot
,
E.A. Valentijn
,
L. Valenziano
,
T. Vassallo
,
Y. Wang
,
J. Weller
,
G. Zamorani
,
J. Zoubian
(6)
,
S. Andreon
,
D. Maino
,
S. de la Torre
(7)
1
CNES -
Centre National d'Études Spatiales [Toulouse]
2 IN2P3 - Institut National de Physique Nucléaire et de Physique des Particules du CNRS
3 IP2I Lyon - Institut de Physique des 2 Infinis de Lyon
4 IAS - Institut d'astrophysique spatiale
5 AIM (UMR7158 / UMR_E_9005 / UM_112) - Astrophysique Interprétation Modélisation
6 CPPM - Centre de Physique des Particules de Marseille
7 LAM - Laboratoire d'Astrophysique de Marseille
2 IN2P3 - Institut National de Physique Nucléaire et de Physique des Particules du CNRS
3 IP2I Lyon - Institut de Physique des 2 Infinis de Lyon
4 IAS - Institut d'astrophysique spatiale
5 AIM (UMR7158 / UMR_E_9005 / UM_112) - Astrophysique Interprétation Modélisation
6 CPPM - Centre de Physique des Particules de Marseille
7 LAM - Laboratoire d'Astrophysique de Marseille
E. Keihanen
- Function : Author
V. Lindholm
- Function : Author
P. Monaco
- Function : Author
L. Blot
- Function : Author
C. Carbone
- Function : Author
K. Kiiveri
- Function : Author
A.G. Sánchez
- Function : Author
A. Viitanen
- Function : Author
J. Valiviita
- Function : Author
A. Amara
- Function : Author
N. Auricchio
- Function : Author
M. Baldi
- Function : Author
- PersonId : 759882
- ORCID : 0000-0003-4145-1943
D. Bonino
- Function : Author
E. Branchini
- Function : Author
- PersonId : 759617
- ORCID : 0000-0002-0808-6908
M. Brescia
- Function : Author
J. Brinchmann
- Function : Author
- PersonId : 755781
- ORCID : 0000-0003-4359-8797
- IdRef : 224540513
S. Camera
- Function : Author
- PersonId : 766641
- ORCID : 0000-0003-3399-3574
V. Capobianco
- Function : Author
J. Carretero
- Function : Author
M. Castellano
- Function : Author
- PersonId : 755152
- ORCID : 0000-0001-9875-8263
S. Cavuoti
- Function : Author
A. Cimatti
- Function : Author
- PersonId : 786030
- ORCID : 0000-0002-4409-5633
G. Congedo
- Function : Author
- PersonId : 766465
- ORCID : 0000-0003-2508-0046
L. Conversi
- Function : Author
Y. Copin
- Function : Author
- PersonId : 48
- IdHAL : yannick-copin
- ORCID : 0000-0002-5317-7518
- IdRef : 15009728X
L. Corcione
- Function : Author
M. Cropper
- Function : Author
A. Da Silva
- Function : Author
H. Degaudenzi
- Function : Author
F. Dubath
- Function : Author
C.A. J. Duncan
- Function : Author
X. Dupac
- Function : Author
S. Dusini
- Function : Author
S. Farrens
- Function : Author
- PersonId : 791647
- ORCID : 0000-0002-9594-9387
M. Frailis
- Function : Author
E. Franceschi
- Function : Author
M. Fumana
- Function : Author
B. Gillis
- Function : Author
C. Giocoli
- Function : Author
- PersonId : 766463
- ORCID : 0000-0002-9590-7961
A. Grazian
- Function : Author
F. Grupp
- Function : Author
L. Guzzo
- Function : Author
S.V. H. Haugan
- Function : Author
H. Hoekstra
- Function : Author
- PersonId : 759828
- ORCID : 0000-0002-0641-3231
W. Holmes
- Function : Author
F. Hormuth
- Function : Author
K. Jahnke
- Function : Author
- PersonId : 755700
- ORCID : 0000-0003-3804-2137
M. Kümmel
- Function : Author
A. Kiessling
- Function : Author
T. Kitching
- Function : Author
M. Kunz
- Function : Author
H. Kurki-Suonio
- Function : Author
S. Ligori
- Function : Author
P.B. Lilje
- Function : Author
I. Lloro
- Function : Author
E. Maiorano
- Function : Author
O. Mansutti
- Function : Author
O. Marggraf
- Function : Author
F. Marulli
- Function : Author
- PersonId : 766464
- ORCID : 0000-0002-8850-0303
R. Massey
- Function : Author
M. Melchior
- Function : Author
M. Meneghetti
- Function : Author
- PersonId : 759266
- ORCID : 0000-0003-1225-7084
- IdRef : 235928291
G. Meylan
- Function : Author
M. Moresco
- Function : Author
- PersonId : 761800
- ORCID : 0000-0002-7616-7136
L. Moscardini
- Function : Author
E. Munari
- Function : Author
S.M. Niemi
- Function : Author
C. Padilla
- Function : Author
- PersonId : 791235
- ORCID : 0000-0001-7951-0166
S. Paltani
- Function : Author
- PersonId : 755532
- ORCID : 0000-0002-8108-9179
F. Pasian
- Function : Author
K. Pedersen
- Function : Author
G. Polenta
- Function : Author
L. Popa
- Function : Author
F. Raison
- Function : Author
A. Renzi
- Function : Author
J. Rhodes
- Function : Author
- PersonId : 755435
- ORCID : 0000-0002-4485-8549
E. Romelli
- Function : Author
R. Saglia
- Function : Author
- PersonId : 759894
- ORCID : 0000-0003-0378-7032
B. Sartoris
- Function : Author
P. Schneider
- Function : Author
- PersonId : 755611
- ORCID : 0000-0002-5094-2245
T. Schrabback
- Function : Author
A. Secroun
- Function : Author
G. Seidel
- Function : Author
C. Sirignano
- Function : Author
G. Sirri
- Function : Author
L. Stanco
- Function : Author
P. Tallada-Crespí
- Function : Author
D. Tavagnacco
- Function : Author
A.N. Taylor
- Function : Author
I. Tereno
- Function : Author
R. Toledo-Moreo
- Function : Author
F. Torradeflot
- Function : Author
E.A. Valentijn
- Function : Author
L. Valenziano
- Function : Author
T. Vassallo
- Function : Author
Y. Wang
- Function : Author
J. Weller
- Function : Author
G. Zamorani
- Function : Author
- PersonId : 755662
- ORCID : 0000-0002-2318-301X
- IdRef : 190956429
S. Andreon
- Function : Author
D. Maino
- Function : Author
Abstract
We present a method for fast evaluation of the covariance matrix for a two-point galaxy correlation function (2PCF) measured with the Landy-Szalay estimator. The standard way of evaluating the covariance matrix consists in running the estimator on a large number of mock catalogs, and evaluating their sample covariance. With large random catalog sizes (data-to-random objects ratio M>>1) the computational cost of the standard method is dominated by that of counting the data-random and random-random pairs, while the uncertainty of the estimate is dominated by that of data-data pairs. We present a method called Linear Construction (LC), where the covariance is estimated for small random catalogs of size M = 1 and M = 2, and the covariance for arbitrary M is constructed as a linear combination of these. We validate the method with PINOCCHIO simulations in range r = 20-200 Mpc/h, and show that the covariance estimate is unbiased. With M = 50 and with 2 Mpc/h bins, the theoretical speed-up of the method is a factor of 14. We discuss the impact on the precision matrix and parameter estimation, and derive a formula for the covariance of covariance.
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