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Euclid: Fast two-point correlation function covariance through linear construction

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arxiv 2205.11852 v1 pith:MWHHBG3R submitted 2022-05-24 astro-ph.CO

Euclid: Fast two-point correlation function covariance through linear construction

E. Keihanen , V. Lindholm , P. Monaco , L. Blot , C. Carbone , K. Kiiveri , A.G. S\'anchez , A. Viitanen
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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 G. Congedo L. Conversi Y. Copin L. Corcione M. Cropper A. Da Silva H. Degaudenzi M. Douspis F. Dubath C.A.J. Duncan X. Dupac S. Dusini A. Ealet S. Farrens S. Ferriol 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. K\"ummel S. Kermiche 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 L. Moscardini E. Munari S.M. Niemi C. Padilla S. Paltani F. Pasian K. Pedersen V. Pettorino S. Pires G. Polenta M. Poncet 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 P. Tallada-Cresp\'i 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 S. Andreon D. Maino S. de la Torre
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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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