Euclid preparation. LIX. Angular power spectra from discrete observations
Abstract
We present the framework for measuring angular power spectra in the Euclid mission. The observables in galaxy surveys, such as galaxy clustering and cosmic shear, are not continuous fields, but discrete sets of data, obtained only at the positions of galaxies. We show how to compute the angular power spectra of such discrete data sets, without treating observations as maps of an underlying continuous field that is overlaid with a noise component. This formalism allows us to compute exact theoretical expectations for our measured spectra, under a number of assumptions that we track explicitly. In particular, we obtain exact expressions for the additive biases ("shot noise") in angular galaxy clustering and cosmic shear. For efficient practical computations, we introduce a spin-weighted spherical convolution with a well-defined convolution theorem, which allows us to apply exact theoretical predictions to finite-resolution maps, including HEALPix. When validating our methodology, we find that our measurements are biased by less than 1% of their statistical uncertainty in simulations of Euclid's first data release.
Cite
@article{arxiv.2408.16903,
title = {Euclid preparation. LIX. Angular power spectra from discrete observations},
author = {Euclid Collaboration and N. Tessore and B. Joachimi and A. Loureiro and A. Hall and G. Cañas-Herrera and I. Tutusaus and N. Jeffrey and K. Naidoo and J. D. McEwen and A. Amara and S. Andreon and N. Auricchio and C. Baccigalupi and M. Baldi and S. Bardelli and F. Bernardeau and D. Bonino and E. Branchini and M. Brescia and J. Brinchmann and A. Caillat and S. Camera and V. Capobianco and C. Carbone and V. F. Cardone and J. Carretero and S. Casas and M. Castellano and G. Castignani and S. Cavuoti and A. Cimatti and C. Colodro-Conde and G. Congedo and C. J. Conselice and L. Conversi and Y. Copin and F. Courbin and H. M. Courtois and M. Cropper and A. Da Silva and H. Degaudenzi and G. De Lucia and J. Dinis and F. Dubath and C. A. J. Duncan and X. Dupac and S. Dusini and M. Farina and S. Farrens and F. Faustini and S. Ferriol and M. Frailis and E. Franceschi and M. Fumana and S. Galeotta and W. Gillard and B. Gillis and C. Giocoli and P. Gómez-Alvarez and A. Grazian and F. Grupp and L. Guzzo and S. V. H. Haugan and H. Hoekstra and W. Holmes and F. Hormuth and A. Hornstrup and P. Hudelot and K. Jahnke and M. Jhabvala and E. Keihänen and S. Kermiche and A. Kiessling and B. Kubik and M. Kümmel and M. Kunz and H. Kurki-Suonio and S. Ligori and P. B. Lilje and V. Lindholm and I. Lloro and G. Mainetti and E. Maiorano and O. Mansutti and O. Marggraf and M. Martinelli and N. Martinet and F. Marulli and R. Massey and E. Medinaceli and S. Mei and M. Melchior and Y. Mellier and M. Meneghetti and E. Merlin and G. Meylan and J. J. Mohr and M. Moresco and B. Morin and L. Moscardini and E. Munari and R. Nakajima and S. -M. Niemi and C. Padilla and S. Paltani and F. Pasian and K. Pedersen and W. J. Percival and V. Pettorino and S. Pires and G. Polenta and M. Poncet and L. A. Popa and F. Raison and A. Renzi and J. Rhodes and G. Riccio and E. Romelli and M. Roncarelli and E. Rossetti and R. Saglia and Z. Sakr and A. G. Sánchez and D. Sapone and B. Sartoris and M. Schirmer and P. Schneider and T. Schrabback and A. Secroun and G. Seidel and M. Seiffert and S. Serrano and C. Sirignano and G. Sirri and L. Stanco and J. Steinwagner and P. Tallada-Crespí and A. N. Taylor and I. Tereno and R. Toledo-Moreo and F. Torradeflot and L. Valenziano and T. Vassallo and Y. Wang and J. Weller and G. Zamorani and E. Zucca and A. Biviano and M. Bolzonella and A. Boucaud and E. Bozzo and C. Burigana and M. Calabrese and D. Di Ferdinando and J. A. Escartin Vigo and F. Finelli and J. Gracia-Carpio and S. Matthew and N. Mauri and A. Pezzotta and M. Pöntinen and V. Scottez and A. Spurio Mancini and M. Tenti and M. Viel and M. Wiesmann and Y. Akrami and S. Anselmi and M. Archidiacono and F. Atrio-Barandela and A. Balaguera-Antolinez and M. Ballardini and D. Benielli and A. Blanchard and L. Blot and H. Böhringer and S. Borgani and S. Bruton and R. Cabanac and A. Calabro and B. Camacho Quevedo and A. Cappi and F. Caro and C. S. Carvalho and T. Castro and K. C. Chambers and A. R. Cooray and S. de la Torre and G. Desprez and A. Díaz-Sánchez and S. Di Domizio and H. Dole and S. Escoffier and A. G. Ferrari and P. G. Ferreira and I. Ferrero and A. Finoguenov and A. Fontana and F. Fornari and L. Gabarra and K. Ganga and J. García-Bellido and T. Gasparetto and E. Gaztanaga and F. Giacomini and F. Gianotti and G. Gozaliasl and C. M. Gutierrez and W. G. Hartley and H. Hildebrandt and J. Hjorth and A. Jimenez Muñoz and S. Joudaki and J. J. E. Kajava and V. Kansal and D. Karagiannis and C. C. Kirkpatrick and S. Kruk and F. Lacasa and M. Lattanzi and A. M. C. Le Brun and J. Le Graet and L. Legrand and J. Lesgourgues and T. I. Liaudat and J. Macias-Perez and M. Magliocchetti and F. Mannucci and R. Maoli and J. Martín-Fleitas and C. J. A. P. Martins and L. Maurin and R. B. Metcalf and M. Miluzio and P. Monaco and A. Montoro and C. Moretti and G. Morgante and C. Murray and S. Nadathur and Nicholas A. Walton and L. Patrizii and V. Popa and D. Potter and P. Reimberg and I. Risso and P. -F. Rocci and R. P. Rollins and M. Sahlén and E. Sarpa and A. Schneider and M. Sereno and P. Simon and K. Tanidis and C. Tao and G. Testera and R. Teyssier and S. Toft and S. Tosi and A. Troja and M. Tucci and C. Valieri and J. Valiviita and D. Vergani and G. Verza and P. Vielzeuf and M. L. Brown and E. Sellentin},
journal= {arXiv preprint arXiv:2408.16903},
year = {2025}
}
Comments
27 pages, 12 figures. Code available at https://github.com/heracles-ec/heracles. v2: Author Accepted Manuscript