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Gravitational Lensing of the Supernovae from the Supernova Legacy Survey (SNLS) Ayan Mitra

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Gravitational Lensing of the Supernovae from the Supernova Legacy Survey (SNLS) Ayan Mitra Gravitational Lensing of the supernovae from the Supernova Legacy Survey (SNLS) Ayan Mitra To cite this version: Ayan Mitra. Gravitational Lensing of the supernovae from the Supernova Legacy Survey (SNLS). Cosmology and Extra-Galactic Astrophysics [astro-ph.CO]. Sorbonne Universités, UPMC Univ Paris 06, CNRS, LIP6 UMR 7606, 4 place Jussieu 75005 Paris., 2016. English. tel-01797973 HAL Id: tel-01797973 https://tel.archives-ouvertes.fr/tel-01797973 Submitted on 23 May 2018 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. THÈSE DE DOCTORAT DE L’UNIVERSITÉ PIERRE ET MARIE CURIE Spécialité Astrophysique et Cosmologie Particules, Noyaux et Cosmos (ED 517) Présentée par M. Ayan MITRA En vue de l’obtention du grade de DOCTEUR de l’UNIVERSITÉ PIERRE et MARIE CURIE Gravitational lensing of the supernovae from the SuperNova Legacy Survey Date de la soutenance : le 30 septembre 2016 devant le jury composé de : M. Dominique FOUCHEZ Examinateur Mme Delphine HARDIN Directrice de thèse M. Michael JOYCE Examinateur Mme Simona MEI Rapporteur Mme Cécile RENAULT Rapporteur Mme Vanina RUHLMANN-KLEIDER Examinateur ii Contents 1 Cosmology 3 1.1 A homogeneous expanding universe . .3 1.2 The Friedman universe . .6 1.3 Hot Big Bang model and the thermal history of the universe . .8 1.4 Distances . .9 1.5 An inhomogeneous universe . 12 1.6 Cosmological Probes . 15 1.6.1 Cosmic Microwave Background . 15 1.6.2 Baryon Acoustic Oscillations . 18 1.6.3 Type Ia Supernovae . 19 1.6.4 Gravitational Lensing . 20 1.6.5 Galaxy Clusters . 21 1.6.6 The Cosmic concordance . 21 2 Type Ia supernovae and the Supernova Legacy Survey 23 2.1 Type Ia supernovae as standard candles . 23 2.1.1 Observations . 23 2.1.2 Theory . 24 2.1.3 The distance indicator . 25 2.1.4 K-correction . 26 2.1.5 A third relation . 27 2.1.6 Hubble diagram . 28 2.2 The Supernova Legacy Survey . 28 2.2.1 Experimental set-up . 28 2.2.2 SNLS Data Analysis . 32 2.2.3 Measuring the dark energy equation : JLA and SNLS5 . 37 3 Gravitational Lensing 41 3.1 Basics of gravitational lensing . 41 3.1.1 The deflection angle . 42 3.1.2 The lens equation . 42 3.1.3 The Einstein radius and the critical surface density . 45 3.1.4 Magnification . 45 3.1.5 Types of Lensing . 46 3.1.6 Multiple lens plane method . 48 3.2 Lens models . 49 3.2.1 Non-linear structure formation . 49 3.2.2 Halo Models . 51 3.2.3 Mass scaling relations . 56 3.3 Gravitational Lensing and Supernovae Ia . 60 iii CONTENTS 3.3.1 Lensing impact on the Hubble diagram . 60 3.3.2 Supernovae lensing signal detection . 61 4 Line-of-sight modeling and magnification computation 63 4.1 Galaxy catalogs building . 63 4.1.1 Image selection . 64 4.1.2 Image stacking . 64 4.1.3 Photometry . 64 4.1.4 Stars identification . 65 4.1.5 Catalog masking . 67 4.2 Photometric redshifts . 68 4.2.1 Spectral template sequence . 68 4.2.2 Spectral template sequence training . 70 4.2.3 Photometric redshift accuracy . 70 4.2.4 Galaxy classification . 70 4.3 The SNLS5 supernovae sample . 72 4.3.1 SN host galaxies identification . 72 4.3.2 Supernovae scoring for the lensing analysis . 74 4.3.3 Line-of-sight selection and masking . 74 4.4 Magnification computation . 77 4.4.1 Weak lensing approximation . 77 4.4.2 Galaxy halo models . 77 4.5 Magnification normalization . 81 5 The lensing signal detection 85 5.1 The lensing signal detection and prospects . 85 5.1.1 The lensing signal computation . 85 5.1.2 Detected signal significance . 86 5.1.3 Signal detection prospects . 86 5.2 SNLS5 lensing signal detection . 88 5.2.1 The SNLS3 sample . 88 5.2.2 The SNLS5 sample : a preliminary analysis . 90 5.2.3 Magnification computation method . 90 5.3 Conclusion and discussion . 94 A SNLS5 SNe Ia magnifications 97 References 116 iv List of Figures 1.1 Slice of the 3D map of the distribution of the galaxies in the universe from the Sloan Digital Sky Survey III. The earth is situated at the center and each point represents a galaxy. The radius of the circle is roughly 0.5 Gpc. Super-cluster and voids occur up to a few hundred Mpc, which is the scale on which the cosmological principle can be applied in the universe. The thinning out of the galaxies near the edges which are farthest from us represents the sparser sampling of these faint objects in the survey [Kee07]. More extensive mapping work will be done in future, for example by the Square Kilometre Array (SKA) [Sch04], [San15][Maa15]. .4 1.2 The abundances of light elements as predicted by the BBN as a function of the baryon-to-photon ratio η×1010. The bands show the 95% C.L. The narrow vertical 2 band indicates the measurement from CMB for ΩBh = 0.2230±0.00014 ([Ade14]) while the wider band indicates the BBN concordance region. The 4 boxes repre- sent Helium-4, Deuterium, Helium-3 and Lithium-7. The discrepancy between Lithium-7 and the otherwise agreeing abundances could simply reflect difficulty in determining the primordial lithium abundance. Image : [Fie14]...........8 1.3 The angular distance H0DA/c and the luminosity distance H0DL/c as a function of redshift. The solid line shows a FCDM model (Ωm = 1, ΩΛ = 0), the dotted line a solely baryonic matter model (Ωm = 0.05, ΩΛ = 0), and the dashed line a flat ΛCDM model (Ωm = 0.2, ΩΛ = 0.8) close to the concordance (Ωm = 0.3, ΩΛ = 0.7) model. Image: [Hog99].................................. 10 1.4 SDSS galaxies, CMB (WMAP), cluster, lensing and Ly-α forest constraints on the dimensionless power spectrum ∆(k) as a function of the structures scale 1/k. Credits: [Teg04]...................................... 13 1.5 Measurements of σ8 for different methods (Ωm is set to its concordance value Ωm = 0.3) : results from clusters are shown by circles (X-ray surveys), squares (optical surveys) or triangles (SZsurveys), while crosses show CMB constraints. The shaded, horizontal band corresponds to the 68.3 per cent confidence interval for the result (filled circle) obtained by the project “Weighting the Giants”. It is based on weak gravitational lensing measurements constraining the absolute mass scale of X-ray selected clusters detected in the ROSAT All-Sky Survey ([Man15]). 14 1.6 The CMB temperature power spectrum as measured by the Planck mission ([Ade15]). The position of the first peak, at l ∼ 220 (δθ ∼ 1◦) is related to the cosmological parameters describing the universe at the recombination epoch and the geometry and contents of the universe along the photons path towards us (curvature, dark energy). Superimposed is the best fit to the data, from which the cosmological parameters are inferred. The lower plot is the residual to the upper. The scatter at low l is due to the cosmic variance, that is the lack of possibility to average over sufficiently numerous cells of size δθ on the sky. Image: [Ade15]........... 16 v LIST OF FIGURES 1.7 Sky map temperature anisotropies as measured by the successive COBE (Cosmic Background Explorer, launched in 1989), WMAP (Wilkinson Microwave Anisotropy Probe, launched in 2001) and Planck mission (launched in 2009). 17 1.8 The distance DV as a function of redshift from BAO experiments : BOSS, on the CMASS and LOWZ SDSS galaxies sample, the 6dFGS survey ( [Jon09]) and the WiggleZ survey ([Bla11]). Superimposed is the flat ΛCDM model obtained using the CMB projects Planck and WMAP results ([Ade14]). There is a remarkable agreement between the different galaxy surveys and the Planck data. Image : [And14].......................................... 18 1.9 The original “discovery data”, the Hubble diagram of SNe Ia compiled from the High-z Supernova team and the Supernova Cosmology Project’s data. The bottom panel is the residual to the upper (distance modulus) corresponding to an open universe. The points can be seen to lie above the non-accelerating models (dashed and dotted lines). Image : [Fri08]........................... 19 1.10 Constraints on constant w dark energy models from the project Weighing the Gi- ants, which uses weak gravitational lensing measurements to improve the measure- ments of the galaxy cluster mass function and its evolution, using X-ray selected clusters detected in the ROSAT All-Sky Survey. This measurement is compared with constraints form the CMB (WMAP, ACT and SPT), supernova (from the Union sample including SNLS-1 year data) and BAO (SDSS/BOSS, 6dF galaxy survey) data, and their combination. Dark and light shading respectively indicate the 68.3 and 95.4 per cent confidence regions, accounting for systematic uncertain- ties. Image : [Man15].................................. 22 2.1 Supernovae categories . 23 2.2 Example of a supernovae Ia spectrum near it’s peak brightness. The clear dip in the spectra near the 6000Å indicates the presence of Si II which is the clear signature of a type Ia SN. Almost 3/4th of the emitted light is in the optical range (3800-7500 Å). Image : Daniel Kasen, LBL . 24 2.3 brighter-slower relation and the brighter-bluer relation : residual plots of µB − ? MB −mB (see eq.
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