Gravitational lensing of the SNLS supernovae Taia Kronborg To cite this version: Taia Kronborg. Gravitational lensing of the SNLS supernovae. Cosmology and Extra-Galactic Astro- physics [astro-ph.CO]. Université Pierre et Marie Curie - Paris VI, 2009. English. tel-00562370 HAL Id: tel-00562370 https://tel.archives-ouvertes.fr/tel-00562370 Submitted on 3 Feb 2011 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Gravitational lensing of the SNLS supernovae Taia Kronborg February 3, 2011 1 Acknowledgements This is it!!!! I finally finished my thesis and I still cannot believe it. It is a great moment to savor which marks the end of a long, sometimes difficult, but most of all exciting journey. First of all, I would like to thank both the supernova group at the LPNHE in Paris and the people at DARK in Copenhagen for having accepted me as their Phd student. I am sincerely grateful for having had this opportunity. These three years have been absolutely extraordinary. Even though I have been commuting between Tours and Paris by train for two years (1h and 45 minutes to work) and lived in Copenhagen without my husband with the charge of my 3 children for one year, it has all been worth it! I gratefully thank Marek Kowalski and James Bartlett for accepting to be members of the reading committee and providing me with interesting and constructive comments on this thesis. I also thank the rest of the jury for taking the time to come. I would like to thank my 3 fantastic advisors, Julien Guy, Reynald Pain and Kristian Pedersen from the bottom of my heart. It has been a great pleasure working with you. You have all been supportive, and without your help, this work would not have been possible. A special thanks goes to Delphine Hardin and Pierre Astier for helping out with the analysis and the drafting. Thank you Nicolas and Nicolas for being such nice office-mates and thank you to the rest of the super- nova team in Paris, you are a great team. To Pierre, I love it when you laugh, it simply makes my day... 2 Abstract Type Ia supernovae have become an essential tool of modern observational cosmology. By studying the distance-redshift relation of a large number of supernovae, the nature of dark energy can be unveiled. Distances to Type Ia SNe are however affected by gravitational lensing which can induce systematic effects in the measurement of cosmology. The majority of the supernovae is slightly demagnified whereas a small fraction is significantly magnified due to the mass distribution along the line of sight. This causes naturally an additional dispersion in the observed magnitudes. There are two different ways to estimate the magnification of a supernova. A first method consists in comparing the supernova lu- minosity, which is measured to about 15% precision, to the mean SN luminosity at the same redshift. Another estimate can be obtained from predicting the magnification induced by the foreground matter density modeled from the measurements of the luminosity of the galaxies with an initial prior on the mass-luminosity relation of the galaxies. A correlation between these 2 estimates will make it possible to tune the initially used mass-luminosity relation resulting in an independent measurement of the dark matter clustering based on the luminosity of SNe Ia. Evidently, this measurement depends crucially on the detection of this correlation also referred to as the lensing signal. This thesis is dedicated to the measurement of the lensing signal in the SNLS 3-year sample. Les supernovae de Type Ia sont devenues un outil essentiel dans la cosmologie observationnelle moderne. En etudiant´ la relation distance-redshift d’un grand nombre de supernovae, la nature de l’energie´ noire peut etreˆ contrainte. Les distances au SNe de Type Ia sont neanmoins´ affectees´ par l’effet de lentilles gravitationnelles qui pourrait induire des effets systematiques´ dans les mesures de cosmologie. La plupart des supernovae sont faiblement demagnifiees´ et une petite fraction sont mag- nifiees´ de maniere` importante du fait de la distribution de masse dans la ligne de visee.´ Ceci induit na- turellement une dispersion supplementaire dans les magnitudes observees.´ Il existe 2 fac¸ons d’estimer l’amplification des SNe Ia. Une premiere` methode´ consiste a` comparer la luminosite´ de la supernova, qui est mesure´ avec une precision´ typique de 15% , a` la moyenne des luminosites´ de SNe au memeˆ redshift. Une autre estimation peut etreˆ obtenue en predisant´ l’amplification induit par la densite´ de matiere` en avant-plan modelee´ en se basant sur les mesures de la luminosite´ des galaxies avec un a` pri- ori initial sur la relation de masse-luminosite´ des galaxies. La correlation´ entre ces 2 estimateurs permet d’accorder la relation de masse-luminosite´ utilisee´ initialement pour obtenir une mesure independante´ fondee´ sur la luminosite´ des SNe Ia. Bien evidemment,´ cette mesure necessite´ dans un premier temps la detection´ de cette correlation´ et cette these` a et´ e´ dedi´ ee´ a` la mesure de la correlation´ dans l’echantillon´ de SNLS 3 ans. 3 4 Contents Introduction 1 1 Cosmology 3 1.1 Homogeneity and isotropy . 4 1.2 Friedmann’s equations . 5 1.3 Definition of redshift . 6 1.4 The cosmological parameters . 6 1.5 The present universe . 7 1.6 Distance measurements . 9 1.7 The magnitude system . 10 1.8 Cosmological probes . 10 1.8.1 CMB (Cosmic Microwave Background radiation) . 10 1.8.2 Baryonic Acoustic Oscillations . 13 1.8.3 Cosmic shear . 16 1.8.4 Type Ia Supernovae . 17 1.9 Current state and the future . 18 2 Type Ia Supernovae 23 2.1 Observational facts . 23 2.2 Theoretical model . 27 2.3 Estimation of distances with SNe Ia . 30 2.3.1 Distance modulus . 30 2.3.2 Light curve fitting . 31 2.4 Hubble diagram . 32 2.5 Systematic uncertainties . 32 2.5.1 Calibration systematics . 34 2.5.2 Selection bias . 35 2.5.3 Possible supernova evolution . 35 2.5.4 Color parameterization . 36 2.5.5 Gravitational lensing . 37 3 Gravitational lensing 38 3.1 Some historical events . 38 3.2 Theory and the thin screen approximation . 39 3.2.1 The lens equation . 40 i 3.2.2 Magnification . 41 3.3 Spherical symmetric lenses . 41 3.3.1 A particularly simple model - The Singular Isothermal Sphere (SIS) . 42 3.4 Multiple lens-plane method . 43 4 Gravitational magnification of Type Ia SNe: a new probe for Dark Matter clustering 46 4.1 The effect of gravitational lensing on the SNeIa Hubble diagram . 46 4.2 Signal detectability . 47 4.2.1 Previous results . 47 4.2.2 Prospects for the SNLS survey . 48 4.3 Mass-luminosity relations. 51 4.3.1 Weak galaxy-galaxy lensing . 51 4.3.2 Faber-Jackson (FJ) and Tully-Fisher (TF) relations . 57 4.3.3 Comparison . 62 5 Measuring the SNLS supernovae magnification 67 5.1 SNLS 3 year dataset . 67 5.1.1 The survey . 67 5.1.2 Detection and identification of Type Ia Supernovae . 70 5.1.3 Photometry of the supernovae . 71 5.1.4 Calibration . 72 5.1.5 Third year SN sample . 75 5.2 Summary of the analysis chain . 77 5.3 The galaxy catalogs . 78 5.3.1 Stacking, photometry and extraction . 78 5.3.2 Classification of stars and SN host galaxies . 80 5.3.3 Masking areas in the catalogs . 82 5.3.4 Classification of spiral and elliptical galaxies based on colors . 83 5.4 Photometric redshifts . 87 5.4.1 The spectral template sequence . 88 5.4.2 The training of the spectral template sequence . 88 5.4.3 The photometric redshift fit . 89 5.4.4 The resolution of the photo-z . 92 5.4.5 High resolution photometric and spectroscopic redshifts . 93 5.5 Selection of galaxies along the line of sight . 93 5.6 Normalization of the magnification distribution . 96 5.7 Uncertainties on the magnification of the SNe . 97 6 Results and prospects 99 6.1 Expectations for a signal detection . 99 6.1.1 Simulations of the SNLS supernova magnification distributions . 99 6.1.2 Detection criterion - Weighted correlation coefficient . 100 6.1.3 Signal expectations for the 3-year SNLS sample . 101 6.2 Magnification of the SNLS 3-year SNe . 103 ii 6.3 The supernova lensing signal for the SNLS 3-year sample . 105 6.4 Prospects . 114 6.4.1 The SNLS 5-year sample . 114 6.4.2 Optimization of the detection of the lensing signal . 114 6.4.3 Future surveys . 115 7 Conclusion 116 iii Introduction In science, the most important revolutions are often initiated by small disagreements. Copernicus suggested in the 16th century that the earth is not the center of the universe. This was based on variations in the movements of the planets which was at that time considered negligible. In 1919, Arthur Eddington went on an important solar eclipse expedition to provide the first proof in favor of the theory of General Relativity by Einstein. He measured the very small deflection of light induced by the sun’s gravitational field and found it to be twice the expected value from a newtonian point of vue.