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

Keihanen, E.; Lindholm, V.; Monaco, P.; Blot, L.; Carbone, C.; Kiiveri, K.; Sanchez, A. G.; Viitanen, A.; Valiviita, J.; Amara, A.; Auricchio, N.; Baldi, M.; Bonino, D.; Branchini, E.; Brescia, M.; Brinchmann, J.; Camera, S.; Capobianco, V.; Carretero, J.; Castellano, M.; Cavuoti, S.; Cimatti, A.; Cledassou, R.; Congedo, G.; Conversi, L.; Copin, Y.; Corcione, L.; Cropper, M.; Da Silva, A.; Degaudenzi, H.; Douspis, M.; Dubath, F.; Duncan, C. A. J.; Dupac, X.; Dusini, S.; Ealet, A.; Farrens, S.; Ferriol, S.; Frailis, M.; Franceschi, E.; Fumana, M.; Gillis, B.; Giocoli, C.; Grazian, A.; Grupp, F.; Guzzo, L.; Haugan, S. V. H.; Hoekstra, H.; Holmes, W.; Hormuth, F.; Jahnke, K.; Kummel, M.; Kermiche, S.; Kiessling, A.; Kitching, T.; Kunz, M.; Kurki-Suonio, H.; Ligori, S.; Lilje, P. B.; Lloro, I.; Maiorano, E.; Mansutti, O.; Marggraf, O.; Marulli, F.; Massey, R.; Melchior, M.; Meneghetti, M.; Meylan, G.; Moresco, M.; Morin, B.; Moscardini, L.; Munari, E.; Niemi, S. M.; Padilla, C.; Paltani, S.; Pasian, F.; Pedersen, K.; Pettorino, V.; Pires, S.; Polenta, G.; Poncet, M.; Popa, L.; Raison, F.; Renzi, A.; Rhodes, J.; Romelli, E.; Saglia, R.; Sartoris, B.; Schneider, P.; Schrabback, T.; Secroun, A.; Seidel, G.; Sirignano, C.; Sirri, G.; Stanco, L.; Surace, C.; Tallada-Crespi, P.; Tavagnacco, D.; Taylor, A. N.; Tereno, I.; Toledo-Moreo, R.; Torradeflot, F.; Valentijn, E. A.; Valenziano, L.; Vassallo, T.; Wang, Y.; Weller, J.; Zamorani, G.; Zoubian, J.; Andreon, S.; Maino, D.; De La Torre, S.

doi:10.1051/0004-6361/202244065

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 (random-to-data 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 with a size of M = 1 and M = 2, and the covariance for arbitrary M is constructed as a linear combination of the two. We show that the LC covariance estimate is unbiased. We validated the method with PINOCCHIO simulations in the range r = 20-200 h-1 Mpc. With M = 50 and with 2 h-1 Mpc bins, the theoretical speedup of the method is a factor of 14. We discuss the impact on the precision matrix and parameter estimation, and present a formula for the covariance of covariance.

Euclid: Fast two-point correlation function covariance through linear construction / Keihanen, E.; Lindholm, V.; Monaco, P.; Blot, L.; Carbone, C.; Kiiveri, K.; Sanchez, A. G.; Viitanen, A.; Valiviita, J.; Amara, A.; Auricchio, N.; Baldi, M.; Bonino, D.; Branchini, E.; Brescia, M.; Brinchmann, J.; Camera, S.; Capobianco, V.; Carretero, J.; Castellano, M.; Cavuoti, S.; Cimatti, A.; Cledassou, R.; Congedo, G.; Conversi, L.; Copin, Y.; Corcione, L.; Cropper, M.; Da Silva, A.; Degaudenzi, H.; Douspis, M.; Dubath, F.; Duncan, C. A. J.; Dupac, X.; Dusini, S.; Ealet, A.; Farrens, S.; Ferriol, S.; Frailis, M.; Franceschi, E.; Fumana, M.; Gillis, B.; Giocoli, C.; Grazian, A.; Grupp, F.; Guzzo, L.; Haugan, S. V. H.; Hoekstra, H.; Holmes, W.; Hormuth, F.; Jahnke, K.; Kummel, M.; Kermiche, S.; Kiessling, A.; Kitching, T.; Kunz, M.; Kurki-Suonio, H.; Ligori, S.; Lilje, P. B.; Lloro, I.; Maiorano, E.; Mansutti, O.; Marggraf, O.; Marulli, F.; Massey, R.; Melchior, M.; Meneghetti, M.; Meylan, G.; Moresco, M.; Morin, B.; Moscardini, L.; Munari, E.; Niemi, S. M.; Padilla, C.; Paltani, S.; Pasian, F.; Pedersen, K.; Pettorino, V.; Pires, S.; Polenta, G.; Poncet, M.; Popa, L.; Raison, F.; Renzi, A.; Rhodes, J.; Romelli, E.; Saglia, R.; Sartoris, B.; Schneider, P.; Schrabback, T.; Secroun, A.; Seidel, G.; Sirignano, C.; Sirri, G.; Stanco, L.; Surace, C.; Tallada-Crespi, P.; Tavagnacco, D.; Taylor, A. N.; Tereno, I.; Toledo-Moreo, R.; Torradeflot, F.; Valentijn, E. A.; Valenziano, L.; Vassallo, T.; Wang, Y.; Weller, J.; Zamorani, G.; Zoubian, J.; Andreon, S.; Maino, D.; De La Torre, S.. - In: ASTRONOMY & ASTROPHYSICS. - ISSN 0004-6361. - 666/2022:(2022), pp. A129."-"-A129."-". [10.1051/0004-6361/202244065]