Supernovae seen through gravitational telescopes Tanja Petrushevska Academic dissertation for the Degree of Doctor of Philosophy in Physics at Stockholm University to be publicly defended on Monday 29 May 2017 at 10.15 in sal FB42, AlbaNova universitetscentrum, Roslagstullsbacken 21.

Abstract Galaxies, and clusters of galaxies, can act as gravitational lenses and magnify the light of objects behind them. The effect enables observations of very distant supernovae, that otherwise would be too faint to be detected by existing telescopes, and allows studies of the frequency and properties of these rare phenomena when the universe was young. Under the right circumstances, multiple images of the lensed supernovae can be observed, and due to the variable nature of the objects, the difference between the arrival times of the images can be measured. Since the images have taken different paths through space before reaching us, the time-differences are sensitive to the expansion rate of the universe. One class of supernovae, Type Ia, are of particular interest to detect. Their well known brightness can be used to determine the magnification, which can be used to understand the lensing systems. In this thesis, galaxy clusters are used as gravitational telescopes to search for lensed supernovae at high redshift. Ground- based, near-infrared and optical search campaigns are described of the massive clusters Abell 1689 and 370, which are among the most powerful gravitational telescopes known. The search resulted in the discovery of five photometrically classified, core-collapse supernovae at redshifts of 0.671supernova rates for 0.4 ≤ z < 2.9 were calculated, and found to be in good agreement with previous estimates and predictions from cosmic star formation history. During the survey, two Type Ia supernovae in A1689 cluster members were also discovered, which allowed the Type Ia explosion rate in galaxy clusters to be estimated. Furthermore, the expectations of finding lensed supernovae at high redshift in simulated search campaigns that can be conducted with upcoming ground- and space-based telescopes, are discussed. Magnification from a galaxy lens also allows for detailed studies of the supernova properties at high redshift that otherwise would not be possible. Spectroscopic observations of lensed high-redshift supernovae Type Ia are of special interest since they can be used to test for evolution of the standard candle nature of these objects. If systematic redshift- dependent properties are found, their utility for future surveys could be challenged. In the thesis it is shown that the strongly lensed and very distant supernova Type Ia PS1-10afx at z=1.4, does not deviate from the well-studied nearby and intermediate populations of normal supernovae Type Ia. In a different study, the discovery of the first resolved multiply-imaged gravitationally lensed supernova Type Ia is also reported.

Keywords: supernovae, strong gravitational lensing, star formation history, supernova rates.

Stockholm 2017 http://urn.kb.se/resolve?urn=urn:nbn:se:su:diva-141633

ISBN 978-91-7649-797-5 ISBN 978-91-7649-798-2

Department of Physics

Stockholm University, 106 91 Stockholm SUPERNOVAE SEEN THROUGH GRAVITATIONAL TELESCOPES

Tanja Petrushevska

Supernovae seen through gravitational telescopes

Tanja Petrushevska ©Tanja Petrushevska, Stockholm University 2017

ISBN print 978-91-7649-797-5 ISBN PDF 978-91-7649-798-2

Printed in Sweden by US-AB, Stockholm 2017 Distributor: Department of Physics, Stockhom University

Cover image: Artist's interpretation of a supernova discovery with a gravitational telescope. Courtesy of Maedeh Mohammadpour Mir. Abstract

Gravitational lenses such as galaxies and galaxy clusters, can magnify the flux of background galaxies. These galaxies at high redshift can host supernovae (SNe) which, thanks to the magnification boost due to lensing, can be observed, otherwise too faint to be detected by current telescopes. Under the right circumstances, the background galaxies may also have multiple images due to the strong lensing. Of particular interest is to detect lensed supernovae of type Ia (SNe Ia), because of their standard brightness. They could help improve lensing models and, if multiple images are observed, the Hubble constant can be measured independently. In this thesis, we use galaxy clusters as gravitational telescopes to search for lensed SNe at high redshift. We performed ground-based, near-infrared and optical search campaigns towards the massive clusters Abell 1689 and 370, which are among the most powerful gravitational telescopes known. Our search resulted in the discovery of five photometrically classified, core- collapse SNe at redshifts of 0.671 < z < 1.703 with significant magnification from the cluster. Owing to the power of the lensing cluster, we calculated the volumetric core-collapse SN rates for 0.4 z < 2.9,andfindgoodagreement  with previous estimates and predictions from cosmic star formation history. During our survey, we also discovered two SNe Ia in A1689 cluster members, which allowed us to determine the cluster Ia rate. Furthermore, we discuss the expectations of finding lensed SNe at high redshift in simulated search campaigns that can be conducted with upcoming ground- and space-based telescopes. Magnification from a galaxy lens also allows for detailed studies of the SN properties at high redshift that otherwise would not be possible. Spec- troscopic observations of lensed high-redshift SNe Ia are of particular interest since they can be used to test for evolution of the standard candle nature of these objects. However, if systematic redshift-dependent properties are found, their utility for future surveys could be challenged. We investigate whether the properties of the strongly lensed and very distant SN Ia PS1- 10afx at z = 1.4,deviatesfromthewell-studiednearbyandintermediate populations of normal SNe Ia. In other study, we report the discovery of the first resolved multiply-imaged gravitationally lensed SN Ia.

List of Accompanying Papers

The following papers, referred to in the text by their Roman numerals, are included in this thesis.

PAPER I: High-redshift supernova rates measured with the gravi- tational telescope A1689 T. Petrushevska, R. Amanullah, A. Goobar, S. Fabbro, J. Jo- hansson, T. Kjellsson, C. Lidman, K. Paech, J. Richard, H. Dahle, H. Dahle, R. Ferretti, J. P. Kneib, M. Limousin, J. Nordin and V. Stanishev , A&A, Vol. 594,A54(2016). DOI: 10.1051/0004-6361/201628925

PAPER II: iPTF16geu: A multiply-imaged gravitationally lensed Type Ia supernova A. Goobar, R. Amanullah, S. R. Kulkarni, P. E. Nugent, J. Johansson, C. Steidel, D. Law, E. Mörtsell, R. Quimby, N. Blagorodnova, A. Brandeker, Y. Cao, A. Cooray, R. Ferretti, C. Fremling, L. Hangard, M. Kasliwal, T. Kupfer, R. Lunnan, F. Masci, A. A.Miller, H. Nayyeri, J. D. Neill, E. O. Ofek, S. Papadogiannakis, T. Petrushevska, V. Ravi, J. Sollerman, M. Sullivan, F. Taddia, R. Walters, D. Wilson, L. Yan and O. Yaron, Science, Vol. 356,6335,291-295(2017). DOI: 10.1126/science.aal2729

PAPER III: Testing for redshift evolution of Type Ia supernovae us- ing the strongly lensed PS1-10afx at z = 1.4 T. Petrushevska, R. Amanullah, M. Bulla, M. Kromer, R. Fer- retti, A. Goobar and S. Papadogiannakis, submitted in A&A, (2017).

PAPER IV: Searching for supernovae in the multiply-imaged galax- ies behind the gravitational telescope A370 T. Petrushevska, D. J. Lagattuta, R. Amanullah, A. Goobar, L. Hangard, S. Fabbro, C. Lidman, K. Paech, J. Richard, and J. P. Kneib to be submitted in A&A.

Reprints were made with permission from the publishers. Other publications

The following papers, referred to in the text by their letters, are not included in this thesis.

PAPER A: Search for Lensed Supernovae by Massive Galaxy Clus- ters with the 2.5m Nordic Optical Telescope T. Petrushevska. Publications of the Astronomical Observatory of Belgrade, 92, 85-86,(2013).

PAPER B: The Rise of SN 2014J in the Nearby Galaxy M82 A. Goobar, 33 additional authors including T. Petrushevska. ApJL, 784, 12,(2014). DOI: 10.1088/2041-8205/784/1/L12

PAPER C: The Peculiar Extinction Law of SN 2014J Measured with the Hubble Space Telescope R. Amanullah, 12 additional authors including T. Petrushevska. ApJL, 788, 21,(2014). DOI: 10.1088/2041-8205/788/2/L21

PAPER D: Diversity in extinction laws of Type Ia supernovae mea- sured between 0.2 and 2 µm R. Amanullah, 36 additional authors including T. Petrushevska. MNRAS, 453, 3,(2015). DOI: 10.1093/mnras/stv1505

PAPER E: Supernova spectra below strong circum-stellar interaction G. Leloudas, 11 additional authors including T. Petrushevska. A&A, 574, A61,(2015). DOI: 10.1051/0004-6361/201322035

PAPER F: Time-varying sodium absorption in the Type Ia supernova 2013gh R. Ferretti, 20 additional authors including T. Petrushevska. A&A, 592, A40,(2016). DOI: 10.1051/0004-6361/201628351

PAPER G: Color Me Intrigued: The Discovery of iPTF16fnm, a Su- pernova 2002cx-Like Object A. A. Miller, 15 additional authors including T. Petrushevska. submitted to ApJ,(2017). Author’s contribution

The main focus of this thesis is the study of supernova properties through gravitational telescopes, and the thesis is accompanied by four papers which are relevant to the main theme. I led the projects presented in Papers I, III and IV, and done most of the work, including the preparation of the text and figures in the papers. In Paper II, I had more modest contribution. I contributed to the proposals that were written to obtain ground- and space- based observations and I investigated the spectroscopic properties of the supernova, the host and lensing galaxy. Not all the work during my PhD is enclosed in these four papers. Some of the contribution to the analysis done for the papers which are not attached in the thesis, is discussed in this thesis (Papers B, D). There are other not-so- glamorous, yet important tasks that I have contributed as an observational astrophysicist, such as processing imaging data (Papers D,F). In this thesis, I also discuss briefly the pilot study I proposed at the Nordic Optical Telescope, which gave me the opportunity to experience the process from having an idea to its realization, which meant writing of a proposal, planning of a telescopic survey and performing observations at the telescope. From 2013 until recently, the intermediate Palomar Transient Factory was running and I was part of it. In Papers B, II and G, some of the results of the joint effort are reported. For me, that effort mostly meant searching for candidates as probable supernovae in the data, processing spectroscopic data in order to classify the candidates and writing astronomical telegrams to notify the community about these discoveries. I have authored and co- authored more than 60 of these telegrams.

Contents

Abstract i

List of Accompanying Papers iii

Other publications v

Author’s contribution vii

Abbreviations xi

List of Figures xiii

List of Tables xvii

1 Introduction 19

2 Gravitational telescopes 23 2.1 Gravitational lensing ...... 23 2.2 The lens equation ...... 24 2.3 Galaxy clusters as gravitational telescopes ...... 26 2.4 Galaxy clusters Abell 1689 and 370 ...... 27

3 Supernovae 31 3.1 Properties of supernovae ...... 31 3.2 Discovering supernovae ...... 35 3.2.1 Intermediate Palomar Transient Factory ...... 36 3.2.2 Discovering high-redshift supernovae with gravitational telescopes ...... 37

4 Cosmology with supernovae Type Ia 41 4.1 The standard cosmological model ...... 41 4.1.1 The energy content of the Universe ...... 43 4.2 Mapping the expansion history of the Universe ...... 44 4.2.1 Luminosity distance ...... 44 4.2.2 Standardizable candles ...... 45 4.3 Supernovae Ia and their host galaxy environment ...... 47 4.3.1 Local metallicity ...... 48 4.4 Searching for possible redshift evolution in intrinsic properties of distant supernovae Ia ...... 49

5 Supernova rates 51 5.1 Introduction ...... 51 5.2 Volumentric supernova rates ...... 52 5.2.1 Systematic errors in supernova rates estimates . . . . 52 5.2.2 Core-collapse supernova rates and star formation history 54 5.2.3 Supernova Ia rates in galaxy clusters ...... 55

6 Strongly lensed supernovae 57 6.1 Introduction ...... 57 6.2 iPTF16geu: A multiply-imaged gravitationally lensed Type Ia supernova ...... 58 6.3 Supernovae in the resolved strongly lensed multiply-imaged galaxies behind A1689 and A370 ...... 60

7 Summary and outlook 63 7.1 Summary ...... 63 7.2 Outlook ...... 63

Sammanfattning lxvii

Acknowledgements lxix

References lxxi Abbreviations

A1689 Galaxy cluster Abell 1689

A370 Galaxy cluster Abell 370

ACS Advanced Camera for Surveys

AGN Active galactic nucleus

ALFOSC Andalucia Faint Object Spectrograph and Camera

CANDELS Cosmic Assembly Near-infrared Deep Extragalactic Legacy Sur- vey

CC SN Core-collapse supernova

CLASH Cluster Lensing and Supernova survey with Hubble

CMB Cosmic microwave background

DD Double degenerate

DTD Delay time distribution

GALEX Galaxy Evolution Explorer

GOODS Great Observatories Origins Deep Survey

HAWK-I High Acuity Wide field K-band Imager

HST Hubble Space Telescope

IMF Initial mass function

JWST James Webb Space Telescope

LSST Large Synoptic Survey Telescope

LOSS Lick Observatory Supernova Search

MUSE Multi-Unit Spectroscopic Explorer NIR Near infrared

NOT Nordic Optical Telescope iPTF Intermediate Palomar Transient Factory

SD Single degenerate

SDSS Sloan Digital Sky Survey

SFH Cosmic star formation history

SFR Star formation rate

SN Supernova

SN Ia Type Ia Supernova

SNLS Supernova Legacy Survey

UV Ultraviolet

VLT Very Large Telescope

WD White dwarf

WFIRST Wide Field Infrared Survey Telescope

ZTF Zwicky Transient Facility List of Figures

2.1 Simplified scheme of the setup of a gravitational lens. The light from the background source is being bent by the cur- vature of the massive object acting as a lens. If certain con- ditions are satisfied, the observer sees multiple images of the same source...... 24 2.2 Geometry of gravitational lensing in the thin lens approximation. 25 2.3 In the upper panel, ACS/HST image of the galaxy cluster A1689 (z = 0.18), one of the most massive and best studied. It actually consists of two clusters which are merging with one another. In the lower panel, ACS/HST image of the galaxy cluster A370 at z = 0.37,withits"GiantLuminous Arc" at z = 0.735,whichwasthefirstfeatureofstronglens- ing from galaxy clusters discovered in 1987. The effects of strong lensing are visible in the image through the presence of distorted and arc-like galaxies. Credit: ESA/NASA. . . . . 28 2.4 A1689 with the iso-magnification contours for a background source at z = 1.5.Theredcontoursindicatemagnifications of 6.5, 4.0, 2.5 and 2.0 times, from inside to outside. The magnification map is produced from the A1689 mass model from Limousin et al. (2007)...... 29

3.1 On the left, light curve comparison between different super- nova types. The supernova light curves are shown in their absolute magnitudes in V band with the shaded areas repre- sent their 1s uncertainty. On the right, supernova taxonomy according to their spectroscopic signatures. Credit: Kasen D. 32 3.2 On the left, a cartoon of the single degenerate scenario is portrayed, while on the right for the double degenerate case. Credit:Cosmos – A Spacetime Odyssey/Maedeh Mohammad- pourMir...... 35 3.3 The usual tecnique used in finding SNe: subtract the new image from the reference image which have been previously aligned and their point spread functions (PSF) matched. The PSF describes how point sources, such as the light from a star does not land on a single pixel, and is instead spread over several pixels. The distribution is typically described by aMoffatprofilewhichresemblesagaussian,exceptforthe wings. The PSF is affected by atmospheric conditions and determines the resolution for ground observations. These patches are from SN 2014J presented in Paper B...... 36

3.4 Filter response functions for commonly used filters in the optical wavelengths: g, r, i and z,inthenear-infraredJ and H. Spectral template of supernova Ia [51] at maximum is also shown, which flux has been normalized and redshifted to z = 2.0...... 38

3.5 Redshift distribution of core-collapse supernova discoveries expected from the A1689 surveys with a rate model [75]. The redshift of the core-collapse supernovae discovered with our surveys are indicated with dashed line. The total expected number of core-collapse supernovae is also shown...... 38

4.1 Recent SN Ia Hubble diagram. SNe Ia from ground-based discoveries are shown as diamonds, HST-discovered SNe Ia are shown as filled symbols. Overplotted is the best fit for a flat cosmology: WM = 0.27 and WL = 0.73. Inset: Residual Hubble diagram and models after subtracting empty universe model. Credit: A. Riess...... 46

4.2 (a) Absolute magnitude, an inverse logarithmic measure of intrinsic brightness, is plotted against time before and after peak brightness. The brightest SNe have broader light curves than the faintest. (b) The SN Ia light curves after stretching the time scales, and then scaling the brightness by an amount determined by the required time stretch. Credit: S. Perlmutter. 46

4.3 Patches of the seven supernovae Ia studied in Paper D from the spaced-based telescope GALEX in the near-UV filter. UV emission in galaxies is mostly due to hot and young massive stars, thus indicating the ongoing star formation. Arbitrary scale for presentation purpose...... 49 5.1 Volumetric core-collapse supernova rates from the literature and those measured in Paper I (marked with red). Error bars are statistical with total errors (statistical and system- atic added in quadrature) as a transparent/faded extra error bar for all surveys. The various lines represent cosmic star formation histories from several authors scaled with factor k50 = 0.007.Thebest-fittedvaluetotheratesdataofthe scale factor k = 0.00930 0.00096 is also shown...... 53 CC ± 5.2 The history of cosmic star formation as measured from UV and IR rest-frame SFR tracers. From Madau & Dickinson 2014...... 55 2 12 1 1 5.3 Cluster SN Ia rates in units SNuM h , where SNuM 10 SNeM yr . ⌘ The line shows the best-fit power-law DTD from Barbary et al. (2012) [5]. The DTD is the hypothetical SN rate versus time that would follow a brief burst of star formation that here is assumed to have happened when the Universe was 3 Gyrs old...... 56 ⇠ 6.1 Left panel: The first strongly lensed core-collapse super- nova with multiple images at z = 1.49, SN Refsdal (indicated with arrows), behind galaxy cluster MACS J1149.6+2223 at z = 0.54. The four images of SN Refsdal lensed by the el- liptical galaxy are visible in an Einstein cross. The observed re-appearance of SN Refsdal as predicted is shown in the right lower panel. Credit: Adapted from NASA/ESA. . . . . 58 6.2 Image of iPTF16geu showing the spatial resolution of the ground based instruments presented in Paper II. In panel A, the discovery image in R-band at P48. The improved spatial resolution using a Natural star Guide System AO (NGSAO, panel B, and further using the Laser Star aided AO System (LGSAO, panel C) is shown...... 59 6.3 High spatial resolution images from the Hubble Space Tele- scope and the Keck Observatory used to resolve the positions of the SN images, the partial Einstein ring of the host galaxy and the intervening lensing galaxy. The images reveal four point sources, except for F475W where SN images 3 and 4 are too faint. All four SN images are clearly seen in J-band (panel D). For the H and Ks images, both the lensing galaxy at the center of the system and the lensed partial Einstein ring of the host galaxy are visible...... 60 6.4 Upper panel: The locations of the multiply-imaged galaxies with a time delay of less than five years shown on a NIR HAWK-I image. The multiply galaxies are noted with the same number. From Paper I. Lower panel: Cropped HAWK-I image in J band overplotted with the 21 background galaxies with 67 multiple images. The predicted magnifications for these galaxies from the lensing model are of order of 1 2 ⇠ magnitudes and are presented Paper IV...... 62

7.1 Observer frame light curves for a SN Ia (upper panels), SN IIn (middle panel) and SN IIP (lower panels) in the HAWK-I J , HST F125W and WFIRST H bands, respectively. The horizontal dashed lines indicate the depths assumed in the calculation, 24.5 for the J band and 26.15 for F125W.In the H band the three depths represent the three main survey modes planned for WFIRST [118]. The yellow band denotes the average magnification from the galaxy cluster A1689 at the same redshifts in the central region with 2.7 3.3 .... 65 0 ⇥ 0 List of Tables

7.1 Expected supernova discoveries in the multiply-imaged galax- ies behind A1689 for future surveys...... 65

1. Introduction

Supernovae are very rare phenomena in the Universe and their transient nature made them difficult to find for a long time. So, it is not surprising that the discovery rate was around two supernovae per month 30 years ago. Today, we are able to find supernovae daily, but most of these are all relatively nearby, since the surveys are not sensitive to the very distant ones. Supernova rates, or the measurement of the frequency of supernova explosions per unit volume, are important for several reasons. For example, core-collapse supernovae originate from the deaths of massive and short lived stars, and their rate can be used to trace the history of star formation in galaxies. Also, supernovae are the one of the major producers of heavy elements in the Universe, so measuring supernova rates informs us about the chemical enrichment of galaxies over time. Measuring the supernova rate in the distant Universe, where it is poorly

19 known, is difficult. Even though supernovae are one of the brightest explo- sions that exist, at distances bigger than four billion light years they are hard to find simply because they become too faint. This has been especially prob- lematic for the study of the rate of core-collapse explosions since they are on average the faintest objects in the supernova family and often embedded in dusty environments. Furthermore, due to the expansion of the Universe, the visual light from all distant objects is shifted to longer wavelengths. From the ground, near-infrared observations are particularly challenging due to the brightness of and variability of the atmosphere at these wavelengths. Instead of waiting for more powerful telescopes to come online, we used the existing facilities and the magnification power of galaxy clusters as grav- itational telescopes to take a peek at the supernovae in the early Universe. Galaxy clusters are the most massive gravitationally bound objects in the Universe, serving as a gravitational lenses. Gravitational lensing magnifies the flux of background objects, thereby increasing the depth of the survey. In this way, the ability to find very distant supernovae is enhanced. It was Fritz Zwicky who suggested the use of gravitational telescopes nearly 80 years ago, but it is only recently that systematic supernova searches have been performed in background galaxies behind clusters. The supernova group here in Stockholm, has been leading this type of search using ground-based facilities since 2003. As a continuation of this effort, during 2008-2014, we surveyed the galaxy cluster Abell 1689 and A370, which are one of the most powerful gravita- tional telescopes that Nature provides. We used a near-infrared instrument on the Very Large Telescope in Chile, with obtaining supporting optical data from the Nordic Optical Telescope at La Palma. Our search resulted in the discovery of five very distant and magnified supernovae. Notably, we discovered a supernova located nearly 10 billion light years away that was magnified four times by the galaxy cluster, which makes it among the most distant core-collapse supernovae observed at the time. Using these discover- ies, we measured the supernova rates up to the time when the Universe was only two billion years old, without requiring expensive space-based follow-up facilities. Type Ia supernovae have proven to be very useful tool as distance indi- cators, mapping the accelerated expansion of the Universe. Spectroscopic observations of lensed supernovae Ia at high distances are particularly in- teresting. These can be used to test the evolution in their intrinsic proper- ties. We have investigated the strongly lensed and very distant supernova Ia PS1-10afx, if it deviates from the well-studied nearby sample of normal supernovae Ia. Strong lensing, not only magnifies, but can also give multiple images of the background objects. We witnessed the discovery of the first

20 resolved strongly lensed supernova Ia, iPTF16geu. With the help of high resolution images, we were able to observe four multiple images of the same supernova. This thesis contains seven chapters and is organized as follows. Chap- ter 1 is an overview of the work presented in the attached publications, and introduces my research in a larger scientific context. Chapter 2 describes the basic concepts of gravitational lensing and gravitational telescopes. Chapter 3 focuses on the properties of supernovae, and the methods of systematic searches for their discovery. It shortly presents the surveys dedicated at finding lensed supernovae behind galaxy clusters Abell 1689 and 370. The intermediate Palomar Transient factory, in which I have been involved and led to the discovery of iPTF16geu is also mentioned. Chapter 4 gives an introductory overview of the modern cosmology with the emphasis on the role of distant supernovae Type Ia. The work with PS1-10afx is men- tioned. Chapter 5 concerns measuring supernova rates including our results presented in the attached publications. In Chapter 6 we discuss strongly lensed supernovae with multiple images. The concluding Chapter 7 con- sists of summary and outlook. The expectations for future surveys are also discussed.

21 22 2. Gravitational telescopes

This Chapter aims in introducing the concept of gravitational telescopes which is used throughout this thesis work. In order to do that, it is necessary to mention few crucial concepts from gravitational lensing. For a thorough introduction to gravitational lensing, the reader can turn to numerous text books and reviews, such as Lectures on gravitational lensing by Narayan & Bartelmann, 2008. We shortly present galaxy clusters Abell 1689 and 370, the gravitational telescopes that were used in our search campaigns.

2.1 Gravitational lensing

Gravitational lensing is the astrophysical phenomenon where the propagation of light is affected by the massive objects in the Universe. The path of the photons in the Universe is perturbed by the gravitational effects of mass concentrations with respect to one they would have followed in a perfectly homogeneous universe (see Figure 2.1). Gravitational lensing results from the ability of matter to curve spacetime and is one of the predictions of the general theory of relativity. General relativity predicts a deflection angle aˆ of a light passing at a distance r from an object with mass M as

4GM 1 aˆ = (2.1) c2 r where there is an additional factor of two, compared to the value obtained with classical physics. This factor stems from the spatial curvature which is missed if photons are just treated as particles. According to this prediction, alightraysthatpassesclosetothesolarlimbwouldbedeflectedbyan angle of 1.7400,andinfactthatanglewasobservedbyEddingtonduringthe notorious Sun eclipse in 1919.1 There are two regimes of lensing: strong and weak. Strong lensing, the one important for this thesis work, is when there are strong image distortions

1 The concept of gravitational lens goes back to Newton, but the first written account of the deflections of light was given by a German geodesist Johann Soldner in 1804. By using classical physics, he calculated that a light rays that passes close to the Solar limb would be deflected by a smaller angle 0.8400.

23 Figure 2.1: Simplified scheme of the setup of a gravitational lens. The light from the background source is being bent by the curvature of the massive object acting as a lens. If certain conditions are satisfied, the observer sees multiple images of the same source.

such as the formation of arcs and multiple images of the background objects (noticeable in Figure 2.3). This can be observed when the lens is very massive and the geometrical alignment between the source, the lens and the observer is favorable. The strong lensing regime occurs in the line-of-sight of galaxies and massive galaxy clusters. This was not confirmed until 1979 when the first pair of gravitationally lensed quasars were found [130], followed by many other similar discoveries. The short-lived durations of supernovae has made it much more difficult to find this special configuration for supernova explosions. Lensed Type Ia supernovae are particularly interesting sources due to their "standard candle" nature, which makes them excellent distance indicators in cosmology, as discussed in the Chapter 4 and 6. The weak lensing is when the distortions of background sources are much smaller and can only be detected by statistically analyzing large numbers of sources.

2.2 The lens equation

The simple way to understand how the gravitational lensing mechanism is to consider a point mass as in Figure 2.2. In this configuration, the deflection angle is given as 4GM 1 aˆ = . (2.2) c2 x

24 Image

Source

Observer Lens Dds Dd

Ds

Figure 2.2: Geometry of gravitational lensing in the thin lens approximation.

Without the lensing, we would see the object with an angle b,thedeflection angle is a,thedistancetothesourceisDs,thedistancetothelensisDd and the lens-source distance is Dds.Theradiusx is much smaller than the distance D ,sothedeflectionangleissmall,a 1.Typicaldeflection d ⌧ angles are of order of arcminutes when the lens is a galaxy cluster, while for galaxies is of order of arcseconds. From Figure 2.2, the following relations hold:

qDs = bDs + aˆ Dds (2.3)

Dds a(q)= aˆ (q) (2.4) Ds b = q a(q) (2.5) where the last is the is the lens equation. Combining equation 2.2 and 2.4 and the fact that x = qDd,thelensequationcanbewritten

Dds 4GM b(q)=q (2.6) DdDs q In the case of a point mass lens aligned with a background point source (b = 0), a ring-like image can be formed. The radius of this ring is called the Einstein radius qE : 2 4GM Dds qE = 2 . (2.7) c DdDs The Einstein radius is not given only by the mass of the lens, but also from the geometry of the observer, lens and source. The sources which are at angular distances of few q to the optic axis, are strongly lensed ⇠ E 25 i.e. experience significant magnification. Furthermore, roughly within the Einstein ring, is where the multiple images are expected. If the lens equation is rewritten as: q 2 b = q E (2.8) q which gives two solutions for q: 1 q = (b b 2 + 4q 2) (2.9) ± 2 ± E q which means that, in the special case of a point mass lens, the sources are imaged twice, separated by q and q+.Themagnificationµ of an image is defined as the ratio between the solid angles of the image and the source: q dq µ = (2.10) b db

From the lens equation we can relate the magnification to the Einstein radius:

1 4 qE µ = 1 (2.11) q  ± ! thus, great magnification is expected near the Einstein radius qE . Here, we have described the simplest case of a point mass lens, where there is the possibility to observe two images. In a more general case, when the lens is not a point mass, there is a possibility of more than two multiple images, like the Einstein cross. Moreover, realistic astrophysical gravitational lenses, such as galaxies and galaxy clusters, suffer from many aberrations and the focusing is not perfect. However, since the geometry of the light paths is independent of wavelength, it does not suffer from chromatic aberration.

2.3 Galaxy clusters as gravitational telescopes

Strong gravitational lensing can be very useful because it can increase the ap- parent brightness of astrophysical objects behind galaxy clusters that would otherwise be too faint to detect. However, as for any lens, conservation of flux ensures that the area of the source plane is shrunk, which results in a smaller field of view. Galaxy clusters are the most massive gravitationally bounded objects in the Universe. A typical galaxy cluster mass is 1014 1015 M ,madeof hundreds of galaxies, gas in the intracluster medium, but most of it, 90%, ⇠ is dark matter. The total mass of clusters can be inferred from several

26 independent techniques, such as by measuring the velocity dispersion of the galaxies along the line of sight and by measuring the X-ray emission of the hot intracluster gas. In order to carefully model the mass distribution of galaxy clusters, the most important information comes from the observations of the multiply-imaged galaxies. This is because the model is required to produce the configuration of the image positions and brightnesses of the background sources. In fact, models of the mass distribution of galaxy clusters have improved significantly from the observations with the Advanced Camera for Surveys (ACS) aboard Hubble Space Telescope (HST). ACS observations have lead to many discoveries of tens of multiple images behind lensing clusters Abell 1689 and 370 [15, 96].

2.4 Galaxy clusters Abell 1689 and 370

Abell 1689 (A1689) is one of the best studied massive galaxy clusters to date. Its total mass is M = 1.77 1015M and it can be found at z=0.187 ⇥ (670 Mpc) [15, 68]. This galaxy cluster has a very extended Einstein radius of q 50 for a source redshift at z = 2 [15] which makes it particularly E ⇡ 00 interesting as a gravitational telescope. With the help of the magnifying power, the discovery of one of the most distant galaxies at z 7.6 [13, 131] ⇡ was made possible. In Figure 2.4, the typical magnifications in the few arc minutes field of view are shown for a background object at redshift z = 1.5. Abell 370 (A370) at redshift z = 0.375 is another massive (Mtotal = 2.3 1015M )andwell-studiedcluster.Ithashistoricalsignificancefor ⇥ the gravitational lensing effect, since the background galaxy arcs were the first ones detected (in 1987), visible in lower panel of Figure 2.3 [115]. The Einstein radius for this cluster is somewhat smaller than the one for A1689, q 40 for a source redshift at z = 2. E ⇡ 00 In Papers I and IV, we used these two galaxy clusters, shown in Figure 2.3, as gravitational telescopes to search for supernovae in the galaxies behind them. This will be further discussed in Chapter 6.

27 Figure 2.3: In the upper panel, ACS/HST image of the galaxy cluster A1689 (z = 0.18), one of the most massive and best studied. It actually consists of two clusters which are merging with one another. In the lower panel, ACS/HST image of the galaxy cluster A370 at z = 0.37, with its "Giant Luminous Arc" at z = 0.735, which was the first feature of strong lensing from galaxy clusters discovered in 1987. The effects of strong lensing are visible in the image through the presence of distorted and arc-like galaxies. Credit: ESA/NASA.

28 Figure 2.4: A1689 with the iso-magnification contours for a background source at z = 1.5. The red contours indicate magnifications of 6.5, 4.0, 2.5 and 2.0 times, from inside to outside. The magnification map is produced from the A1689 mass model from Limousin et al. (2007).

29 30 3. Supernovae

The focus of this Chapter are the properties of supernovae, divided into thermonuclear and core-collapse explosions. The methods of discovering supernovae, which are used in the work presented in Papers I, II and IV, are also superficially discussed.

3.1 Properties of supernovae

Most stars are like our Sun, they will live long until they finish their ther- monuclear fuel and cool down to become a white dwarf. Very few stars will end their life with a spectacular explosion called supernova (SN). SNe are among the most energetic phenomena in the Universe, when they explode they almost outshine their host galaxies. Several SN varieties exists and are classified by distinct spectral charac- teristics. The first SN taxonomy was made in the early 1940’s based on the presence or the absence of emission lines of hydrogen (Ha ). Type I show no hydrogen lines in their spectra, while the opposite is true for the type II SNe. There are further subclasses: SNe Type Ia (SNe Ia) are distinguished by the lack of hydrogen and helium features and the presence of other features, especially Si ii at of 6150 Å. The Si ii line has actually a rest wavelength of 6355 Å, so typically the outflow moves with velocities of 10000 km/s. ⇠ The subclass Ib show a non-ionized helium (He I) line, while Ic does not (see right panel of Figure 3.1). SN maximum light is usually reached 15 20 days after the explo- ⇠ sion (see left panel of Figure 3.1). The light curves of the SNe, i.e. the measurements of their magnitudes1 (or flux) over times can be explained as energy release of the radioactive nickel chain decay [20], rather than heat which is gone due to the fast expansion of the ejecta. The 56Ni that was synthesized during the explosion decays into 56Co and finally into 56Fe.The gamma rays produced in this decay are thermalized when they interact with

1The relationship between apparent magnitude, m,andflux, f ,ism = 2.5log ( f )+ 10 const. The absolute magnitude, M, or the magnitude of the object at 10 parsecs in empty space is: m = 2.5log f + M. Parsec is the distance at which one astronomical 10 f (10pc) unit subtends an angle of one arcsecond, corresponding to 3.26 light-years. ⇠

31 Figure 3.1: On the left, light curve comparison between different supernova types. The supernova light curves are shown in their absolute magnitudes in V band with the shaded areas represent their 1s uncertainty. On the right, supernova taxonomy according to their spectroscopic signatures. Credit: Kasen D.

32 the surroundings. These gamma rays have been observed for the first time with the INTEGRAL space observatory when a SN Ia exploded in the nearby galaxy M82 [28]. It is possible to estimate the quantity of 56Ni needed to reproduce the light curve of the SN [3], for example for a SN Ia, 0.6M is ⇡ needed, while for type II 0.1M . Thus, is expected that SNe (especially ⇡ type Ia) are the major iron contributors in galaxies. Based on their progenitor star that gives birth to the explosion, SNe can be divided into two distinct categories: core-collapse and thermonu- clear. Type II, Ib and Ic SNe are believed to be core-collapse explosions that originate from the end of a massive star1 of more than 8 10 M .After iron synthesis, fusion in the core ceases and pressure support is lost, which leads to a gravitational collapse. On average, these are fainter than SNe Ia and they present greater dispersion in their luminosity. These are found in regions of stellar formations (for example in the ionized hydrogen regions of the spiral or irregular galaxies) which suggests that their progenitors must be short-lived massive star. Type Ia SNe are found in all types of galax- ies: elliptical, spiral and irregular, which supports the idea that there must be at least one low mass star involved. In order to explain the fact that some SN Ia occur in old stellar populations and lack hydrogen, Hoyle and Fowler in 1960 [50] proposed that they were the observational signature of the thermonuclear disruption of a degenerate star, presumably in a binary system. Currently, a great effort is dedicated to pinpoint which type of stars give rise to the different type of core-collapse explosions. Thanks to large amount of archival data with high resolution such as the HST, it is possible to search for the progenitor at the SN location before the explosion. For example, SN IIn 2009ip was found to be arising from blue supergiant star [114].

IIP and IIL The spectra of this subtype of core collapse SNe contain strong hydrogen lines, so it is thought that they originate in a star which has hydrogen left in its envelope as it explodes. In the most recent review of observational constraints on the progenitors of core-collapse SNe [113], SNe IIP come from red supergiants for which the lowest mass estimated is 8M and the highest mass progenitor is 18M .Given ⇠ ⇠ that the spectra of these two subtypes look very similar, the slope of the linear light-curve decay after maximum light has historically been used to distinguish between plateau (SN IIP) and linear (SN IIL). IIP represent the most common in the local Universe, with about 52% of all the core-collapse SN subtypes [66].

1Some of these are due to binary systems.

33 IIn SNe IIn are distinguished by the narrow lines in the spectra which are probably the result of interaction of the SN ejecta with dense circum- stellar material. This SN class consists of objects that show the largest dispersion in peak magnitudes and can be bright as M = 22.3 [97]. R Ib and Ic As these SNe do not show hydrogen in their spectra, it is thought that these explosions originate from massive Wolf-Rayet stars above M & 18 20 M that have lost their outer layers of hydrogen and/or helium, so they are also called stripped core-collapse SNe.

Contrary to the case for core-collapse SNe, the progenitor of a SN Ia has never been directly observed. However, there is a indirect evidence such as the composition of their ejecta and the energy released in the explosion. All this indicates that SNe Ia form a special group, thought to be caused by thermonuclear explosions of a white dwarf (WD) accreting material from acompanionstar.Thematterthatistransferredfromthecompanionis enough to push the mass close to the Chandrasekhar limit, the largest pos- sible mass that can be sustained by the electron degeneracy pressure. The degenerate WD ignites thermonuclear fusion that destroys most of the WD star, pushing ejecta at high velocity. There is a debate whether the companion is a red giant or main-sequence phase star (the so called single degenerate scenario [133], [83] or a white dwarf (the double degenerate scenario [53] (see Figure 3.2). There are sev- eral classes of hydrodynamical explosion models, where, after the ignition, the flame is transfered by heat conduction (subsonic deflagration) or by shock wave (supersonic detonation). To obtain the observables, such as light curves and spectra in a chosen filter band, radiate transfer calculations starting from the products of the explosion models are necessary. It is prob- lematic that rather different explosion models are able to reproduce to same extent the observables (spectra and light curves) of normal SNe Ia, which makes it difficult to rule out the invalid models [48]. For a summary of the proposed models for SNe Ia progenitors, see the review by Hillebrandt et al. (2013). Pre-explosion data at the location of nearby SNe Ia, could give observa- tional clues to this dilemma. In the case of SN 2014J, the closest SN Ia in decades, we searched for potential signatures of a SD progenitor system in pre-explosion images from HST (Paper B). Given the uncertainty from the dusty environment in the location of SN 2014J, we could not draw any firm conclusions. Later studies, e.g. by using spectra at late epochs, authors have searched for Ha and Pab emission to constrain any interaction with hydrogen rich material [70, 109]. As they did not find any trace of the aforementioned emission, it is likely that SN 2014J belongs to the DD scenario. However,

34 Figure 3.2: On the left, a cartoon of the single degenerate scenario is por- trayed, while on the right for the double degenerate case. Credit:Cosmos – A Spacetime Odyssey/Maedeh Mohammadpour Mir.

given that these studies rely on models with large uncertainties, the nature of the SN 2014J progenitor has not been confirmed and it is still debatable.

3.2 Discovering supernovae

Only a few SNe have been recorded in our Milky Way over the past millen- nium. SNe are very rare and their transient nature made them difficult to find for a long time. In the 1980’s, increasing computer power and the introduc- tion of the wide-field surveys with CCD detectors replacing the photographic plates made this task much easier. SN discoveries became more frequent with the so-called rolling searches, where pre-defined fields were observed repeatedly. Also, reliable image subtraction methods were necessary for the fast search of transients. However, despite this progress, as shown later in Chapter 5, most of these surveys focused mainly on discovering SNe Ia for their cosmological application. Today, there are only 30 SNe Ia at z > 1, ⇠ which most of these have been discovered with HST [100, 105, 107, 125]. The usual modern technique is to subtract a reference image from an new image, which is not trivial given that images will be taken under differ- ent atmospheric conditions (see Figure 3.3). After the image differencing, an automated SN detection algorithm is run on the subtracted images. Dif- ferent requirements can be applied in order for something to be classified as a SN candidate. For example, one can impose minimum signal-to-noise ratio and/or that the candidate has to be detected on at least two consec- utive epochs. After that, the candidates can be visually examined by eye. This includes examining the image and subtraction stamps, the light curves from photometry on previous archival data and inspecting the photomet-

35 ric/spectroscopic redshift of the presumable host galaxy in order to estimate the absolute magnitude of the candidate. In the case of the surveys towards galaxy clusters, which will mentioned in the next Section, the lensing mag- nification should also taken into account [55, 68]. As mentioned before, the image subtraction is not perfect, so most of the candidates are subtraction residuals. Some of these are easily revealed by their low increase in bright- ness at the core of bright galaxies. Moreover, point source-like candidates with high signal-to-noise ratio close to the center of galaxies could arise from active galactic nuclei (AGN). To exclude AGNs, one can cross-match the position to an existing AGN and X-ray point course catalog, given that AGNs are expected to emit in these range of frequencies, while SNe are not.

Figure 3.3: The usual tecnique used in finding SNe: subtract the new image from the reference image which have been previously aligned and their point spread functions (PSF) matched. The PSF describes how point sources, such as the light from a star does not land on a single pixel, and is instead spread over several pixels. The distribution is typically described by a Moffat profile which resembles a gaussian, except for the wings. The PSF is affected by atmospheric conditions and determines the resolution for ground observations. These patches are from SN 2014J presented in Paper B.

3.2.1 Intermediate Palomar Transient Factory As a perfect example of a wide-field rolling search survey efficient in discov- ering nearby transients, it is worth mentioning the intermediate Palomar1 Transient Factory (iPTF, [63]), in which our SN group in Stockholm has been involved. Replacing its predecessor Palomar Transient Factory (PTF, [64]), iPTF started in February 2013 and ended this March 2017. iPTF used a fully-robotized 48-inch (P48) telescope at the Palomar Ob- servatory with a 7.3 square degree camera with 11 active CCDs. Each night,

1The history of systematic searches starts with Zwicky with a 0.46 m telescope at Palomar, which was the unique provider of SNe for many years.

36 it imaged a portion of the sky at least twice. After SN detection algorithm was ran on the subtracted images, machine-learning classifier selected real from bogus SN candidates. This preliminary selection between real and bo- gus is crucial, given the avalanche of candidates of which the majority are artifacts. iPTF automated machinery enabled to deliver transient candi- dates within ten minutes of images being taken at the Palomar Observatory [16]. The SN candidates detected twice during night in California, were in the meantime examined by humans in Stockholm or Israel while it was daytime. These so-called human scanners could pick the interesting tran- sients, so that they can be followed (photometrically and spectroscopically) with bigger telescopes. The iPTF setup allowed SNe and other transient phenomena to be detected and classified within a day of explosion. This is helpful, as the initial stages of explosion contain important information about the progenitor system and its environment. The telescopes available for follow-up observations were the 60 inch (P60, automated) and 200 inch (P200) telescopes, which are also at the Palomar Observatory. Other telescope time was also used for this follow-up, in particular for spectroscopic data, for example with the 8-meter Gemini and 10-meter Keck telescopes. Moving forward, iPTF will transform into the Zwicky Transient Facility (ZTF; [9]) in October 2017 and it will last for at least three years. It will ⇠ use the same P48 telescope, but with a bigger camera that will fill the entire focal plane of 42 square degrees.

3.2.2 Discovering high-redshift supernovae with gravitational tele- scopes

The bulk of SN light at maximum is emitted in the optical and UV rest frame wavelengths. This is why the optical bands have been used for finding nearby SNe. At high redshifts, z & 1, the peak SN luminosity is shifted from the optical to the near-infrared (NIR) wavelengths (see Figure 3.4). It necessary to conduct the SN surveys in the NIR in order to maximize our sensitivity to high-z SNe . From the ground, NIR surveys are difficult to carry out because of the bright and variable atmospheric foreground. There are still somewhat stable parts of the NIR transmissive windows of the atmosphere where the commonly used filters J, H and Ks are centred (see Figure 3.4). The night sky in these bands is very bright1,andsorequiresshortindividualexposure times on the order of a minute, in order to monitor background variability and avoid saturation.

1for example in B-band is 22.7 mag/arcsec2, while in J-band is 16 mag/arcsec2

37 Figure 3.4: Filter response functions for commonly used filters in the optical wavelengths: g, r, i and z, in the near-infrared J and H. Spectral template of supernova Ia [51] at maximum is also shown, which flux has been normalized and redshifted to z = 2.0.

Figure 3.5: Redshift distribution of core-collapse supernova discoveries ex- pected from the A1689 surveys with a rate model [75]. The redshift of the core-collapse supernovae discovered with our surveys are indicated with dashed line. The total expected number of core-collapse supernovae is also shown.

38 In Paper I, we presented a dedicated ground-based NIR rolling search, accompanied with an optical program, which was aimed at discovering high- redshift lensed SNe behind the galaxy cluster Abell 1689. The NIR data were obtained with the HAWK-I instrument [90] mounted on the Very Large Telescope (VLT). HAWK-I has four chips that cover total field of view of 7.5 7.5 . The optical survey was conducted with the ALFOSC camera at 0 ⇥ 0 the Nordic Optical Telescope (NOT). The NOT is a 2.56 m telescope at the Observatorio del Roque de los Muchachos at La Palma at the Canary Islands. The field of view of ALFOSC is 6.4 6.4 .During2008–2014, 0 ⇥ 0 we obtained a total of 29 and 19 epochs in the J and i bands, respectively, and discovered five core-collapse SNe behind the cluster and two SNe Ia associated with A1689. Notably, one of the most distant core-collapse SN ever discovered was found at z = 1.703 [1] with significant magnification factor of 4.3 0.3. In Figure 3.5, the redshift distribution of our discovered ± SNe is shown together with the expected one from simulations. In Paper IV, we presented a similar NIR search towards A370. The data were taken with HAWK-I/VLT in J band over 15 separate nights in 2012 and 2013. This search did not result in discovering SNe.

39 40 4. Cosmology with supernovae Type Ia

In this Chapter, cosmology will be briefly covered, in which the utility of supernovae Type Ia is introduced. In the near future, planned surveys such as the LSST and WFIRST will provide numerous SN Ia light curves to be used for cosmological studies. It is possible that the evolution of SNe Ia properties over redshift will represent important systematics for the high- redshift sample. In this context, the analysis of the supernova PS1-10afx at redshift z = 1.4,asamemberoftheveryhigh-redshiftpopulationis presented (Paper III). Moreover, the pilot study at the NOT regarding the metallicity of the SN Ia environments is mentioned.

4.1 The standard cosmological model

Just over hundred years ago, humans had a very different image of the Universe. Today, we have a model that can describe the evolution of the Universe that begins 14 billions years ago in a very hot, dense state from ⇠ which it expanded and cooled. This so-called Big Bang cosmological model is based on three main observational evidences: the expansion of the Uni- verse, the abundance of light elements and the cosmic microwave background (CMB). The beginnings can be put in the early 1900’s when a set of ob- servations revealed that the majority of objects outside the Milky Way were moving away from us. Vesto Slipher in 1917 was the first one to measure this, followed by Carl Wilhelm Wirtz and Knut Lundmark in 1924. At the Mount Wilson Observatory in southern California, Edwin Hubble working with Milton Humason1 plotted the distances for 46 galaxies against their recession velocities (v)andfoundalinearrelationship.Thisrelationshipis what became known as the Hubble law [52]:

v = H d (4.1) 0 · where H0 is the Hubble constant.

1Milton Humason dropped out of high school and worked as an assistant at the observatory. Later he was awarded with an honorary doctorate at the University of Lund.

41 Because of the huge spread due to the additional peculiar velocities of the galaxies, it was not easy to see the linear relationship between distance and velocity. Once they repeated these measurements in 1930 towards galaxies with higher distances where the peculiar velocities become negligible, the relation became clear and the conclusion was that the Universe was indeed expanding. Even though it is written in many popular texts and books, E. Hubble was not responsible for the discovery of the expanding Universe in 1929 [6, 132]. This was done by the Belgian astronomer and priest G.Lemaître who first to gathered theoretical and observational arguments to support this claim. This cosmological revolution would not have been possible if the path was not paved by the contribution of the Einstein’s general theory of relativity in 19161.Ifweapplygeneralrelativity(asthebestavailabletheorytodescribe the motion of objects responding to the distribution of matter) to the study of the Universe, we expect that, in general, the geometry of the space- time is not static, but varies in time. Einstein introduced the cosmological constant L into the field equation to obtain a solution for a static universe which was the common belief at that time. However, the view of the static universe was soon dismantled by observational evidence (the Hubble law) and the development brought a new dynamic view on the Universe. The cosmological constant was abandoned by Einstein, but as we will see later, reintroduced to account for the enigmatic dark energy. At scales beyond 100 Mpc, the Universe appears homogeneous and isotropic2.TheisotropyoftheUniverseisevidentintheCMBradiation (fingerprint of the early stages) where the anisotropies appear only at a 5 10 level. Homogeneity is implied by requiring isotropy around any posi- tion in space, since in non-homogenous space it will not be possible to have isotropy everywhere. Without the two theoretical pillars of modern cosmol- ogy, general relativity and isotropy, all the predictions on the dynamics of the Universe from the standard model may be wrong. In a homogeneous and isotropic Universe, one can choose a spacetime coordinate system so that the metric takes a simple form. Isotropic and homogeneous space-time is described by the Robertson-Walker metric [103]:

dr2 c2dt2 = c2dt2 + a(t)2 + r2(dq 2 + sin2 qdf 2) (4.2) 1 kr2 ✓ ◆ 1and of course amongst the other theories like the development of non-Euclidean geometries from the beginning of the 1800’s from mathematicians like Gauss, Bolyai, Lobachevski, Klein and Riemann. 2That is the First Cosmological principle: At certain epoch, the Universe seems equal in any point, except for the local irregularities.

42 where r, q, f and t are the time-independent co-moving space-time coordi- nates and c is the speed of light. The curvature of the space is represented by k and the scale factor a(t) is introduced as a function of time that represents the relative expansion of the Universe. It is useful to define here an observable quantity, the cosmological redshift z,whichhasbeenusedthroughouttheentirethesis.Thisredshiftiscaused by the expansion and it can be defined in terms of the ratio between observed wavelength and wavelength at emission:

lobs 1 + z (4.3) ⌘ lem

a(tobs) which can be shown to become 1 + z = in the Robertson-Walker a(tem) metric and z = 0 corresponds to present time t = 0. Starting from the Robertson-Walker metric and applying the Einstein field equations to the Universe, the evolution of the cosmological scale factor a(t) is obtained from the Friedmann equations [35]:

a˙ 2 8pGr kc2 Lc2 H2 = = + (4.4) a 3 a2 3 ✓ ◆ where L is the cosmological constant, G is the Newtonian gravitational con- stant and r is the total energy density of the Universe. Here the Hubble a˙(t) parameter at any time is defined as: H(t) ,whereH ,theHubblecon- ⌘ a(t) 0 stant, is the value at present time. Following Hubble’s footsteps, the Hubble constant was determined first by measuring the redshift and the distance to galaxies [110]. Later, different methodologies were used to measure the Hubble constant such as observations of Sunyaev-Zel’dovich effect1 towards galaxy clusters [12] and CMB radiation missions [10, 78, 91].

4.1.1 The energy content of the Universe The energy density scales in time according to r a 3(1+w),withw being ⇠ the equation of state parameter w = p/rc2 (both dark and ordinary). On cosmological scales matter can be approximated as pressureless w 0. ⇡ The critical density is the value where the Universe has enough density to stop expanding forever and not collapse back on itself either. It is expressed 3H2 from the Friedmann equations by assuming L and k equal to zero r . cr ⌘ 8pG 1Sunyaev-Zel’dovich effect is when high energy electrons distort the CMB radiation through inverse Compton scattering.

43 The density parameters are often normalized with the critical density to r 8pGr obtain dimensionless quantity W = 2 . ⌘ rcr 3H CMB observations suggest that the geometry of the space is Euclidean, thus k = 0 [71]. From this point on, we assume that W = 0.Only 5% k ⇡ of this density consists of ordinary (baryonic) matter (W 0.05). Inferred b ⇡ from its gravitational effect and structure formation in the early Universe, 25% is most probably dark matter (W 0.25). Finally, 70% is dark ⇡ M ⇡ ⇡ energy (W 0.7), inferred from the accelerated expansion at low redshift L ⇡ where it is dominant. If dark energy has an equation of state w = 1,it corresponds to Einstein’s cosmological constant, L,identifiedwiththezero- point vacuum energy of all quantum fields. The most recent constraint of w = 1.018 0.057 (stat+sys) for a Universe with a zero curvature and ± assuming that w does not evolve with time [11]. However, the cosmological constant is a very problematic solution for dark energy, since the standard model of particle physics predict a vacuum energy that is 10120 times ⇠ greater than the one from astrophysical data.

4.2 Mapping the expansion history of the Universe

The expansion history of the Universe can be mapped by measuring distances and redshifts to objects that are distant enough for peculiar motions of the sources to be subdominant. This is typically valid for z & 0.01 and those objects are said to be in the Hubble flow.Luminousvariablestarscalled Cepheids are reliable distance indicators (or standard candles), but they only work for our Galaxy or very nearby galaxies. Indeed it was the discovery of the Cepheids in the Magellanic Clouds and the Cepheid period-luminosity relation by Henrietta Leavitt [65] that allowed E. Hubble to measure the distance to Andromeda Galaxy and understand that it was an extragalactic object. However, intrinsically brighter objects were required to reach further away. Pioneer work by Baade and Zwicky in the 1930’s suggested that SNe Ia can be used as distant standard candles. They realized that SNe Ia have quite uniform peak brightness, and that their large intrinsic brightness allows them to be observed at very large distances.

4.2.1 Luminosity distance In order to understand how standard candles are used for measuring distances we need to introduce the luminosity distance. The bolometric flux f (erg/s/cm2)thatwemeasurefromthesource at redshift z can be written as the luminosity L (erg/s) irradiated at the

44 distance r from the object and us: L f = 2 2 2 (4.5) 4pr a (t0)(1 + z) Compared to the usual formula for Euclidean geometry, there is an extra 2 2 term a (t0)(1 + z) which comes from the expansion time-dilation and the energy dissipation due to the redshift. The luminosity distance dL is defined as: L 1/2 d a(t )r(1 + z)= (4.6) L ⌘ 0 4p f ✓ ◆ and it depends on the redshift and the cosmological parameters WM and WL [41]. It is common to use the logarithmic distance modulus, µ,given as the difference between the apparent magnitude m filter and the absolute magnitude Mfilter,inacertainfilter:

µ m M = 5logd (z;W ,W )+25 (4.7) ⌘ filter filter L M L The SN Ia Hubble diagram is often plotted as the distance modulus versus the redshift, similar to what shown in Figure 4.1. In the 1990’s two independent teams, the High-Z Supernova Search Team and the Supernova Cosmology Project, were making the SN Ia Hubble diagram [87, 99]. The cosmological model that provided the best fit to the data was the one that, at present epoch, WM > 0, WL > 0 and that WL > WM.Thus,theyfoundoutthat,at present epoch, the expansion of the Universe is accelerating 1.Theleaders of these teams Saul Perlmutter, Brian P. Schmidt and Adam G. Riess were awarded the Nobel prize in physics in 2011 for this result.

4.2.2 Standardizable candles SNe Ia present remarkably homogeneous sample with absolute magnitude at peak M 19.5,intheB band, which is centered at 4450 Å. The B ⇡ ⇠ measured dispersion in the B band is around 0.35 mag. To standardize the ⇠ light curve, two main corrections are taken into account. The first correction comes from the so-called Phillips relationship [89] between the light curve shape and the brightness: bright SNe have broader light curves. The second relationship is between the brightness and the color: redder SNe are fainter corr and vice-versa [129]. After these corrections, the dispersion of MB reduces to 0.15 0.18 magnitudes (see Figure 4.2). It is important to note that ⇠ here the assumption that SN properties does not evolve with cosmic history is made. 1opposite what is shown in Star Trek Deep Space 9 where the it is shown that the Universe will end with a Big Crunch in sixty trillion years.

45 Figure 4.1: Recent SN Ia Hubble diagram. SNe Ia from ground-based dis- coveries are shown as diamonds, HST-discovered SNe Ia are shown as filled symbols. Overplotted is the best fit for a flat cosmology: WM = 0.27 and WL = 0.73. Inset: Residual Hubble diagram and models after subtracting empty universe model. Credit: A. Riess.

Figure 4.2: (a) Absolute magnitude, an inverse logarithmic measure of intrin- sic brightness, is plotted against time before and after peak brightness. The brightest SNe have broader light curves than the faintest. (b) The SN Ia light curves after stretching the time scales, and then scaling the brightness by an amount determined by the required time stretch. Credit: S. Perlmutter.

46 Despite being an extremely homogeneous sample, there are some outliers. For example, there are at least two subclasses named after their prototypes [32]: 1991T-like, over-luminous SNe Ia with slow declining light curves, found predominately in spiral galaxies and 1991bg-like, sub-luminous SNe Ia with fast declining light curves found in elliptical and lenticular galaxies. However, these subclasses represent only a minority: as an example the Lick Observatory Supernova Search (LOSS) discovered more than 300 SNe, from which 70% of these were normal type Ia, while 9% of these were 1991T-like, 18% were 1991bg-like, and the rest 3% other peculiar types [66].

4.3 Supernovae Ia and their host galaxy environment

The precision of distance indicators depends on the ability to calibrate them through the established empirical relations between their absolute magni- tude and light curve shape [89, 129]. With the wealth of host galaxy data from wide field surveys targeting nearby SNe Ia, extensive ongoing research is looking for correlations between SNe Ia properties and their host galaxy environment [2, 18, 47, 57, 85, 92, 124, 134]. Common measurable quanti- ties for the host galaxies are their total stellar mass, the star formation rate, and the metallicity1. This is an active field of research since it could possibly provide cir- cumstantial evidence of the elusive SN Ia progenitor. Apparent dichotomy in the emerging picture of these studies: on one side old, massive galax- ies with low specific star formation rate hosting preferentially the fainter, steep-declining (including the sub-luminous 1991bg-like SNe Ia) SNe Ia; on the other side, galaxies that have higher star formation activity host brighter SNe Ia (including the over-luminous 1991T-like SNe Ia), on average [18, 101, 102, 121, 134]. Another reason why this research field is so active is because of the con- cern that there could be a so-called host bias when extracting cosmological parameters from SN Ia light curves. It was suggested that host galaxy mass should be introduced as a third parameter when calibrating SN Ia light curves for cosmology. This is based on the 3.3s indication that SNe Ia with similar light-curve shape and color are, on average, 0.08 mag brighter in massive host galaxies [121]. In another study, by using 114 SNe, it was found that SNe Ia that have locally star-forming environments are dimmer than SNe Ia having locally

1 In astronomy, metals are called all the elements heavier than hydrogen and helium. After hydrogen and helium, the most abundant elements in the Universe are carbon, oxygen and nitrogen, produced by nucleosynthesis in stars. Oxygen is generally used as a proxy for total metal content, since it is the most abundant gas-phase metal in a galaxy.

47 passive environments [102]. They used Ha emission as a tracer for ongoing star formation. Later, they confirmed the same result by using UV data from the Galaxy Evolution Explorer (GALEX) [56, 101]. The UV luminosity is thought to be a tracer of the star formation activity of a galaxy. The bulk of the UV luminosity in a galaxy is thought to be produced by the massive and short-lived stars, thus indicating the instantaneous star formation. A simple relation between the UV luminosity LNUV to the ongoing star formation rate (SFR) of a galaxy:

L = c SFR (4.8) NUV NUV · where cNUV is the conversion factor and the luminosity LNUV has already been corrected for extinction [22]. The value of this factor is dependent on the assumption of the initial mass function (IMF). The IMF is the empirical function that describes the mass distribution of the population of stars at birth1 The most commonly used IMF are the Salpeter power-law function [108] or the Kroupa broken power law [61]. In Paper D, we measured the star formation rate at the position of a small sample of SNe Ia (see Figure 4.3), by performing NUV photometry on GALEX archival images. However, given the limited size of our sample, we did not find the same correlation.

4.3.1 Local metallicity A commonly used method to estimate the metallicity at the SN explosion site, is to use projected radial gradients which suffer from large uncertainties. In 2015, we proposed a pilot study at the NOT to measure the metallicities immediately surrounding the explosion sites of 16 well-measured SNe Ia (P.I. Petrushevska). We also intended to use the data to test and train sophisti- cated chemical evolution models that could allow us to predict the metallicity gradients in a galaxy given its global properties. Unfortunately, the weather did not cooperate in the four observing nights, which left us with only four successfully observed galaxy spectra. In 2016, by using the 4.2 m William Herschel Telescope, another group measured the local metallicity of 28 SN Ia sites, and claimed that metal-rich galaxies host fainter SNe Ia than those observed in metal-poor galaxies [81]. Studies of local host environment will improve with the Integral Field spectroscopy2 surveys, such as the CALIFA

1It is often given as a probability distribution function for the mass at which a star enters the main sequence. 2Integral Field spectrographs are instruments that allow spectra of the sky to be ob- tained over a two-dimensional field-of-view. This technique is ideal for exploring spatially extended sources such as galaxies.

48 Figure 4.3: Patches of the seven supernovae Ia studied in Paper D from the spaced-based telescope GALEX in the near-UV filter. UV emission in galaxies is mostly due to hot and young massive stars, thus indicating the ongoing star formation. Arbitrary scale for presentation purpose. survey [37]. However, it is difficult to interpret the studies of SN Ia host metallicity. It has been argued that current local metallicity of the galaxy does not necessarily represent the metallicity of the progenitor, due to the unknown time between the progenitor birth and SN Ia explosion in which the galaxy metallicity might evolve significantly [14].

4.4 Searching for possible redshift evolution in intrinsic prop- erties of distant supernovae Ia

In the future, Wide Field Infrared Survey Telescope (WFIRST; [118]) will detect 2700 SNe Ia up to z 1.7 and will be limited by systematic errors ⇠ ⇡ [117]. One important systematic effect is the possibility of evolution of the mean SN properties with redshift in a way that cannot be corrected for with the current standardization techniques [21, 31, 33, 34, 49, 73, 123]. Properties of galaxies such as mass, age, dust and metallicity change with cosmic time, and this may also affect the SNe that they host. For instance, the star formation rate density should peak at z 1.9 and then ⇡ decline exponentially [72]. This means that at higher redshifts, larger fraction of SNe Ia will originate from star forming galaxies. However, this will not

49 necessarily create problems for cosmology, as long as the empirical relations hold for their calibration. It is also expected that the host metallicity increases over time, as heav- ier elements are synthesized and accumulated. Some authors have argued that the host mass bias is a proxy for the underlying metallicity relation. For instance, some theoretical studies from modeling SN explosions [127], sug- gested that high metallicity progenitors produce less 56Ni,thuslessluminous SNe Ia. However, several studies based on large SN Ia datasets, have found only modest correlation (1 2s)betweenmetallicityandHubbleresiduals [17, 85, 134]. At present, the signal-to-noise and the resolution of the modest sample of spectra at high redshift [100], z > 1.2,isnotgoodenoughforadetailed study of spectroscopic properties of high redshift SNe Ia. Thus, even in- dividual high signal-to-noise events at high redshift could be of interest if they show discrepancies from what has been observed in the large low-z samples. This unique opportunity arose with the the strongly lensed SN Ia PS1-10afx, which we studied in Paper III. PS1-10afx was discovered in 2010 with the Pan-STARSS1 Medium Deep Survey and follow-up spectroscopy revealed a redshift of z = 1.3883 [19]. At this distance, the transient was brighter than any previously observed SN. Later, PS1-10afx was classified as a SN Ia magnified 30 times by an foreground galaxy [93, 94]. ⇠ In Paper III, we compared PS1-10afx to mean spectra from nearby and intermediate-redshift, spectroscopically normal SNe Ia from the literature at phases similar to the one of PS1-10afx. We did not find significant signs of spectral evolution in PS1-10afx and the near-UV spectra of PS1-10afx are consistent with spectra of normal SNe Ia at low and intermediate redshifts.

50 5. Supernova rates

Supernova rates, in particular those of core-collapse supernovae that trace directly the cosmic star formation history, are discussed in this Chapter. Supernova rates in galaxy clusters are also presented.

5.1 Introduction

The frequency of SN explosions in the Universe was first estimated in 1938 when Zwicky started a systematic SN search with a 0.46 m telescope at Palomar Observatory [135]. Few years later, he found that the rate is one SN per galaxy per 359 years in the local Universe [136].

The measurements of SN rates are important for answering several as- trophysical questions. SNe are providers of iron, so their rate dictates the chemical enrichment of their environment [79, 84]. Given that the progeni- tors of core-collapse SNe are short-lived stars, they trace ongoing SFR. Thus, the measurement of the volumetric core-collapse SN rate with redshift can trace the cosmic star formation history (SFH) [23, 24]. The cosmic SFH has also received a great attention in modern cosmology, as it is important in understanding how structure in the Universe forms and evolves. Thermonu- clear SNe have long-lived progenitors, so their rate does not reflect directly the cosmic SFH, instead there is unknown time delay between formation and explosion of the progenitors. If their rate is compared to the cosmic SFH, the delay-time distribution (DTD), in principle, can be inferred. The measurement of the DTD has been proposed as a method for distinguishing among progenitor models discussed in Section 3.1 [43, 77], because the DTD is sensitive to the lifetimes of the SN Ia progenitors and physical timescales that lead to their explosion.

51 5.2 Volumentric supernova rates

j 3 1 3 1 The volumetric SN rate, rV , for a SN type j,inunitsMpc yr h , is given by Nj(z) r j (z)= (1 + z), (5.1) V T (z) V (z) j · C where Tj(z) is the visibility time (often called the survey control time), which indicates the amount of time the survey is sensitive to detecting a SN can- didate [135]. The value Nj is the number of SNe and VC is the co-moving volume. The factor (1 + z) corrects for the cosmological time dilation. The monitoring time above the detection threshold for a SN of type j, Tj,isa function of the SN light curve, absolute intrinsic SN brightness, M,detec- tion efficiency, e,extinctionbydust,Dmext,andthelensingmagnification, Dmlens. The volumetric SN Ia rate at z < 1 has been well constrained. The Sloan Digital Sky Survey (SDSS; [36]), measured SN rate to z 0.12 [29] and to ⇠ z < 0.3 [30]. At higher redshift the Supernova Legacy Survey (SNLS;[4]) dataset to z 0.5 [82] and 0.1 < z < 1.1 [88]. Beyond z > 1, HST col- ⇡ laborations, Great Observatories Origins Deep Survey (GOODS), Cosmic Assembly Near-infrared Deep Extragalactic Legacy Survey (CANDELS) and Cluster Lensing and Supernova survey with Hubble (CLASH), have measured the volumetric SN Ia rates up to z < 2.5 [25, 44, 106]. Unlike SNe Ia which have received a great deal of attention due to their cosmological applications, core-collapse SN rates have been measured poorly for a long time for several reasons. Most importantly, core-collapse SNe are on average intrinsically fainter than SNe Ia (see Figure 3.1) and they explode often in dusty environments [80]. A few ground-based SN Ia surveys such as SDSS-II and SNLS, collected core-collapse SNe in their samples and measured their rates [7], [126], but only at low redshifts. Recently, a joined effort of large HST programs, GOODS+CLASH+CANDELS, made possible to extend the redshift range up to z 2.5 [120]. In Figure 5.1, the ⇡ core-collapse SNe rate measurements from the literature are shown, which includes our results presented in Paper I.

5.2.1 Systematic errors in supernova rates estimates Stating the statistical uncertainties, or the precision, is not enough by itself, but there it is necessary to show the systematic errors, or the accuracy of the measurement. In Paper I, we discussed in detail the sources of system- atic errors in measuring core-collapse SN rates. We highlighted the need for

1 1 1 h is the Hubble parameter in units of 70 km s Mpc

52 Figure 5.1: Volumetric core-collapse supernova rates from the literature and those measured in Paper I (marked with red). Error bars are statistical with total errors (statistical and systematic added in quadrature) as a transpar- ent/faded extra error bar for all surveys. The various lines represent cosmic star formation histories from several authors scaled with factor k50 = 0.007.The best-fitted value to the rates data of the scale factor k = 0.00930 0.00096 CC ± is also shown.

53 better understanding of the core-collapse SN properties, such as the subtype fractions and peak magnitudes, which affect the systematics budget signif- icantly. Furthermore, making an appropriate correction for the host galaxy extinction is very important and this correction represents one of the most uncertain assumptions. As the number of core-collapse SNe discovered in the survey presented in Paper I was low, our error budget was dominated by the Poisson un- certainties. However, the impact of systematic uncertainties will become increasingly important for upcoming wide-field surveys such as the the Large Synoptic Survey Telescope (LSST; [69]) which are expected to discover a large number of SNe [67].

5.2.2 Core-collapse supernova rates and star formation history The cosmic SFH describes the star formation of the Universe as a whole, as a global average at a given time or redshift. The estimate of the SFH is based on several star formation tracers1. SFR tracers can probe the direct stellar light emerging from galaxies (such as the SFR indicators in the UV mentioned in Sec. 4.3) or probe the stellar light reprocessed by dust. In spite of SFR calibrations have existed for decades, they all suffer own uncertainty. For example, dust attenuation corrections have to be applied, and these are uncertain, as previously mentioned. However, with the arrival of large amount of multi-wavelength data and by combining the range of complementary techniques, Madau & Dickinson (2014) have presented a consistent picture of the SFH, which peaks at z 1.9 and then declines ⇡ exponentially [72] (see Figure 5.2). CC The core-collapse SN rates, rV (z),areexpectedtoreflectthecosmic SFH, y(z),withasimplerelation,

rCC(z)=k y(z), (5.2) V CC · 3 12 where the units of y(z) are M Mpc yr and the scale factor kCC is the number of stars per unit mass that explode as SNe. This factor is obtained as the ratio of two integrals over the IMF,

Mmax ( ) Mmin f M dM kCC = 125M . (5.3) 0R.1M Mf(M)dM R 1For more thorough discussion regarding SFR indicators, the reader can turn to several reviews on this subject, such as Star formation rate indicators by Calzetti, 2013 and Star Formation in the Milky Way and Nearby Galaxies by Kennicutt & Evans, 2012 2 CC 3 since rV scales as h , this needs to be taken into account when comparing to SFHs.

54 Figure 5.2: The history of cosmic star formation as measured from UV and IR rest-frame SFR tracers. From Madau & Dickinson 2014.

We assumed that kCC does not evolve with redshift. Similar to previous high- z CC SN rate studies, we used a Salpeter IMF [108] and Mmin = 8M and Mmax = 50 M as range of stellar masses that explode as core collapse SNe. 50 +0.0019 1 With these assumptions, the scale factor is k8 = 0.0070 0.0022 M .The uncertainty comes from the assumed IMF and the extremes of integration i.e. the stellar mass ranges that end up as core collapse SNe. In Figure 5.1, we plotted several cosmic SFHs and found good agreement between the Madau & Dickinson SFH and the core-collapse SN rates. In the previous calculation, we used kCC which we obtained from equation 5.3. Conversely, by comparing to a given cosmic SFH, the measurement of the core-collapse SN rate can, in principle, constrain the kCC,thustheMmin 1 and Mmax,assuminganIMF .Weusedourandliteraturedatatoobtainthe average core-collapse SN rates in five redshift bins from 0 < z < 2.5 and the latest SFH parametrization [72]. We obtained a k = 0.00930 0.00096, CC ± which is within 1s of k50.Inconclusion,accurateconstraintsonthefactor ⇠ 8 kCC from the comparison of the core-collapse rate to SFH remain difficult at the present, with the available data.

5.2.3 Supernova Ia rates in galaxy clusters Surveying galaxy clusters offers the opportunity to detect SNe that originate from cluster members. These are mostly thermonuclear SNe, since clusters

1It is custom to assume that there is one cosmic (universal) IMF. Of course this might not hold as the IMF could evolve with time.

55 are dominated by elliptical galaxies with old stellar populations where star formation has ceased. Cluster SN Ia rates have been proposed as a superior tool for inferring the DTD, rather than the field SN Ia rates. The reason for this is that galaxy clusters are dominated by almost dust-free elliptical galaxies where the star formation happened presumably in one single burst, so in principle, it is easier to estimate the DTD [5, 30, 42, 76, 77, 112]. Moreover, cluster SN Ia rates are essential in understanding several astro- physical processes such as the iron abundance in the intracluster medium [30].

Figure 5.3: Cluster SN Ia rates in units SNuM h2,whereSNuM 12 1 1 ⌘ 10 SNeM yr . The line shows the best-fit power-law DTD from Barbary et al. (2012) [5]. The DTD is the hypothetical SN rate versus time that would follow a brief burst of star formation that here is assumed to have happened when the Universe was 3 Gyrs old. ⇠ In Paper I, we used the SNe Ia detected in galaxies in A1689 to measure the SN rate in the galaxy cluster. Cluster SN rates are usually normalized with the cluster total stellar luminosity in one specific band. Alternatively, they are normalized by the stellar mass of the galaxy cluster, since the lu- minosity changes with the stellar population age [5]. In Figure 5.3 we plot our result together with literature values of the SN Ia cluster rates per stel- lar mass unit (SNuM). As most of the measurements from the literature, cluster SN Ia rates have large statistical uncertainty, because they are based on small number on SNe Ia. In Figure 5.3, we also show the best-fit power- law DTD from the literature [5]. Pinpointing the DTD from cluster SN Ia remain difficult at the present, with the available data with large statistical uncertainties [5].

56 6. Strongly lensed supernovae

This Chapter is dedicated to supernovae which are strongly lensed by galaxies and galaxy clusters. We discuss iPTF16geu, the first strongly lensed super- nova Type Ia with resolved multiple images. We present the expectations for supernovae in the multiply-imaged galaxies behind A1689 and A370 for our near-infrared surveys.

6.1 Introduction

Sjur Refsdal in 1964 showed that strong gravitational lensing can be used for constraining cosmological parameters [95]. In particular, he suggested the idea that by comparing the time delay Dt of multiply imaged background SNe, it is possible to obtain an independent measurement of the cosmological parameters such as the Hubble constant H0 (discussed in Chapter 4). As the light from the multiple images travels on different paths, there is time delay of the arrival of the images. The dependence of the arrival time of the multiple images can be separated into geometrical and gravitational components. The time arrival depends on the geometry between the lens, source and the observer, so it depends to first approximation of the way the Dd Ds 1 Universe is expanding, µ H ,andtolesserextenttoothercosmological Dds 0 parameters Wm and WL [98]. After the discovery of the first arc-like structures in some galaxy clusters in the mid-1980s [116], the idea to look for type Ia SNe in the arcs of the background galaxies was suggested [60]. However, systematic searches were only initiated after the feasibility studies by Sullivan et al. (2000) and Gunnarsson & Goobar (2003) [46, 122]. The ground-based search for lensed SNe behind galaxy clusters was pioneered here in Stockholm [119]. Their search targeted three galaxy clusters with a NIR instrument ISAAC at VLT and discovered one highly magnified SN IIP at z = 0.6 [40]. The work presented in this thesis (Papers I and IV), is a continuation of that effort. Very large HST programs with more than thousand orbits [44, 86, 104, 106, 128] have been targeting galaxy clusters, to improve cluster lensing models and search for SNe. Most notably, in 2015 they reported the discovery of the first core-collapse SN with multiple images behind the galaxy cluster

57 November/December 2014

Figure 6.1: Left panel: The first strongly lensed core-collapse supernova with multiple images at z = 1.49, SN Refsdal (indicated with arrows), behind galaxy cluster MACS J1149.6+2223 at z = 0.54.ThefourimagesofSN Refsdal lensed by the elliptical galaxy are visible in an Einstein cross. The observed re-appearance of SN Refsdal as predicted is shown in the right lower panel. Credit: Adapted from NASA/ESA.

MACS J1149.6+2223 (dubbed "SN Refsdal") [58]. It was at z = 1.49 with four images arranged around the elliptical galaxy at z = 0.54 in an Einstein cross, shown in Figure 6.1. Even though the main lens was a galaxy, further contribution in the lensing came from the galaxy cluster. Several authors were able to model independently the detailed gravitational potential and predicted that SN Refsdal would re-appear almost a year later. The re- appearance of SN Refsdal was observed close to the predicted position and time (see Figure 6.1, [26, 45, 54, 59]).

6.2 iPTF16geu: A multiply-imaged gravitationally lensed Type Ia supernova

Observing strongly lensed SNe Type Ia, are particularly interesting given their standard luminosities. The measurement of the lensing magnification is independent of any assumptions on cosmology, e.g., the value of the Hubble constant or other cosmological parameters. The lensing magnification is also independent of a lens model, which is the only way to determine the magnification for almost all other strong lensing systems, e.g. multiply- imaged quasars. Before the discovery of iPTF16geu, only one other strongly lensed SN Ia was known. That was PS1-10afx which we discussed in Section 4.4. It

58 Figure 6.2: Image of iPTF16geu showing the spatial resolution of the ground based instruments presented in Paper II. In panel A, the discovery image in R-band at P48. The improved spatial resolution using a Natural star Guide System AO (NGSAO, panel B, and further using the Laser Star aided AO System (LGSAO, panel C) is shown. was discovered in 2010, but only few years later it was realized that it was a SN Ia magnified 30 times by the foreground galaxy. PS1-10afx most ⇠ probably had multiple images, which could not be resolved with the available data [93]. iPTF16geu was discovered withing the SN search of iPTF in September 2016. Soon after, spectroscopic identification was carried out with P60, P200 and the NOT, so iPTF16geu was found to be spectroscopically con- sistent with a normal SN Ia at z = 0.409. At the position of iPTF16geu, there is a known foreground elliptical galaxy at z = 0.216,whichactedas the gravitational lens. After fitting the photometry of iPTF16geu to SN light curve templates which further confirm the consistency with a SN Ia at z = 0.409, the absolute magnitude of iPTF16geu was found. This allowed to estimate the lensing amplification to be µ 52. ⇠ As in the case of PS1-10afx, the discovery data of iPTF16geu did not have the resolution to observe the multiple images of the SN (see Fig- ure 6.2). Timely observations obtained with ground-based adaptive optics instruments1 at the Keck and the HST, revealed four SN images (see Fig- ure 6.3). iPTF16geu was found by chance and given its remarkable magnification, it is extremely rare. However, a simple technique has been proposed to find more strongly lensed SNe Ia in upcoming wide-field SN surveys such as LSST and ZTF [39]. The idea is to look for SN Ia that appear to be hosted by known elliptical galaxies, but that have absolute magnitudes that are far brighter than the absolute magnitudes of normal SNe Ia. The reason to look at elliptical galaxies is because these mostly host SNe Ia, as discussed

1Adaptive optics are used at ground-based telescopes to obtain high-resolution imag- ing which is usually limited by the atmospheric turbulence

59 Figure 6.3: High spatial resolution images from the Hubble Space Telescope and the Keck Observatory used to resolve the positions of the SN images, the partial Einstein ring of the host galaxy and the intervening lensing galaxy. The images reveal four point sources, except for F475W where SN images 3 and 4 are too faint. All four SN images are clearly seen in J-band (panel D). For the H and Ks images, both the lensing galaxy at the center of the system and the lensed partial Einstein ring of the host galaxy are visible. in Chapter 3 and 4. The absolute magnitude of the SNe can be estimated from existing catalog of the hosts’ photometric redshifts. They estimated that with this method, up to 10 strongly lensed SNe Ia can be found with ⇠ ZTF. However, as in the case of iPTF, ZTF will not be able to resolve the multiple images of the system and promptly high-resolution observation will be required.

6.3 Supernovae in the resolved strongly lensed multiply- imaged galaxies behind A1689 and A370

Deep HST images and ground-based spectroscopy of A1689, have revealed more than 114 multiply images from 34 individual background galaxies with redshifts from z 1 to z 5 (see Figure 6.4) [15, 26, 68]. Moreover, by using ⇠ ⇠ HST imaging and Multi-Unit Spectroscopic Explorer (MUSE) spectroscopy, there are now 21 systems with 67 images known behind A370 at redshift 1 . z . 6 (see Figure 6.4) [27, 62, 96]. Using the recently published model of A370 [62], in Paper IV we present for the first time the magnifications and the time delays of the arrivals of the multiple images. This information is helpful when estimating the power of the galaxy cluster as a gravitational telescope for discovering strongly lensed SNe.

60 In Papers I and IV, we did not detect SNe in these galaxies with mul- tiple images. However, we computed the expected number of SNe in these galaxies in our NIR surveys. To estimate the SN rate in each galaxy, we used deep multi-band HST photometry of these galaxies from the literature. 1 The expected core-collapse SN rate for each galaxy in units yr was then calculated from: R = k50 SFR. (6.1) CC 8 · The SN Ia rates were obtained from the simple and commonly used two- component model [111]:

RIa = A SFR + B M , (6.2) · · ⇤ where there is a component proportional to the stellar mass M of the indi- ⇤ vidual galaxies, obtained from the rest-frame B band luminosity, and another to the current SFR. The total expected number of SNe over all the systems are then simply summed. For the A1689 survey, the result was N 0.23 CC ⇠ and N 0.14 for CC SNe and SNe Ia , respectively. For the A370 survey, Ia ⇠ the result was N 0.19 and N 0.02. CC ⇠ Ia ⇠

61 Figure 6.4: Upper panel: The locations of the multiply-imaged galaxies with a time delay of less than five years shown on a NIR HAWK-I image. The multiply galaxies are noted with the same number. From Paper I. Lower panel: Cropped HAWK-I image in J band overplotted with the 21 background galaxies with 67 multiple images. The predicted magnifications for these galaxies from the lensing model are of order of 1 2 magnitudes and are presented Paper IV. ⇠

62 7. Summary and outlook

7.1 Summary

In this thesis, I have presented the utility of observing SNe with gravitational telescopes. The light from distant SNe can be magnified through gravita- tional lensing if a foreground galaxy or a galaxy cluster is located along the line of sight. This line-up allows for detailed studies of SNe at high redshift that otherwise would remain undetected. In Paper I and IV it was presented ground-based, near-infrared search for lensed SNe behind the massive clusters A1689 and A370. Our A1689 search resulted in the discovery of five core-collapse SNe with high redshifts of 0.671 < z < 1.703 and significant magnifications. Owing to the power of the lensing cluster, the survey had the sensitivity to detect SNe up to very high redshifts, z 3,albeitforalimitedregionofspace.Wewereabletomeasure ⇠ the core-collapse SN rates for 0.4 z < 2.9,andfoundgoodagreement  with previous estimates and predictions from star formation history. We also discovered two SNe Ia in A1689 cluster members, which allowed us to determine the cluster Ia rate. In Paper III we used the spectroscopic data of strongly lensed high- redshift PS1-10afx to test for evolution of SN Ia intrinsic properties. We did not find signs of spectral evolution in PS1-10afx. The observed deviation between PS1-10afx and the median templates, are within what is expected for any SNe observed at low and intermediate redshift. In Paper II we reported one of the highlights of wide field SN survey, iPTF. That was the discovery of the first strongly lensed SN Ia with resolved images from ground- and space-based facilities.

7.2 Outlook

It is interesting to explore the feasibility of finding SNe at z & 2,wherethe SN rates are poorly constrained, using current facilities. At these very high redshifts, it is particularly interesting to compare core-collapse rates with those expected from the SFH. In Figure 7.1 from Paper I, we simulated typical light curves of SNe Ia,

63 IIn, and IIP in observers frame at redshifts 2.0,2.5,3.0,3.5,and4.0.We used three NIR bands, HAWK-I-like J , HST F125W and H (similar to HST F160W). We found that it would be challenging to construct a realistic survey with the existing ground- and space-facilities that would significantly improve the measurement of SN rates at z > 2.0,evenwiththehelpof h i agravitationaltelescope.Thiswillmostlikelynotbepossiblebeforethe forthcoming next generation facilities, such as the space-based WFIRST, are in operation. In the rightmost panel of Figure 7.1, the depths of the three main survey modes planned for WFIRST in H band [118] are shown. The WFIRST will be able to detect SNe to very high-z in the H band. Without considering the contribution from gravitational lensing, we estimated the expected number of core-collapse SNe to be discovered with WFIRST. During its planned six-years duration, it will dedicate six months spread over two years for a SN search, focusing mainly on SNe Ia to study the possible evolution of the dark energy equation of state parameter [118]. However, even a larger number of core-collapse SNe can be expected. For instance, we calculated that their planned survey could discover 300 core-collapse SNe at z 2 ⇠ ⇡ and 60 at z 2.5. ⇠ ⇡ The James Webb Space Telescope (JWST; [38]), planned for launch in 2018, with a 6.5 m aperture, it will have an unmatched resolution and sensitivity reaching up to 31 magnitude from the optical to the mid-IR. ⇠ With this depth, the aid of gravitational telescopes are not necessarily needed to discover SNe at z . 4. We can also consider the expectations of discovering SNe exploding in the multiply-imaged galaxies behind A1689 and A370 for future surveys. Instead of using the volumetric SN rate, we adopt the SN rate in the resolved galaxies for which we use the predictions derived from the SFR. In Paper I and IV, we simulated the expectations for several upcoming transient surveys: ZTF, LSST, WFIRST and JWST. The results of the expected SN discoveries in the multiply-imaged galaxies behind A1689 are shown in Table 7.1. The shallowness makes ZTF not useful for discovering SNe in multiply- imaged galaxies behind clusters. The situation is different for LSST with its improved depth, more suitable filters, and considering the length of the survey. The LSST will be a ground-based survey with 8.4 m telescope aimed to continuously scan the sky in several filters from u to i in search for transients. The LSST goal is to revisit the same field 164 and 180 ⇠ ⇠ times in the z and i bands, respectively, over ten years, so close epochs can be combined for a better image depth. Around 70 galaxy clusters with Einstein radii larger than qE > 2000 are estimated to be visible to LSST, which would amount to 1000 strongly lensed multiply-imaged galaxies that are ⇠ 64 Figure 7.1: Observer frame light curves for a SN Ia (upper panels), SN IIn (middle panel) and SN IIP (lower panels) in the HAWK-I J , HST F125W and WFIRST H bands, respectively. The horizontal dashed lines indicate the depths assumed in the calculation, 24.5 for the J band and 26.15 for F125W. In the H band the three depths represent the three main survey modes planned for WFIRST [118]. The yellow band denotes the average magnification from the galaxy cluster A1689 at the same redshifts in the central region with 2.7 3.3 . 0 ⇥ 0

Table 7.1: Expected supernova discoveries in the multiply-imaged galaxies behind A1689 for future surveys.

a a Survey/ Depth Duration Epochs Cadence NCC NSN Ia Filter (mag) (yrs) (/yr) (days) ZTF/R 22.5b 3 7150.017 0.007 0.04 0.03 ± ± ZTF/i 22.5b 3 7150.03 0.01 0.06 0.05 ± ± LSST/i 24.0c 10 7300.18 0.09 0.21 0.17 ± ± LSST/i 25.0b 10 7300.38 0.18 0.26 0.20 ± ± LSST/z 22.76c 10 7301.14 0.61 0.68 0.40 ± ± WFIRST/H 28.01d 2 3301.74 0.82 0.17 0.08 ± ± JWST/F115W 27.5e 5 4302.5 1.20.5 0.2 ± ± JWST/F150W 27.5e 5 4305.4 2.60.6 0.3 ± ± JWST/F115W 27.5e 5 12 30 4.4 2.10.7 0.4 ± ± JWST/F150W 27.5e 5 12 30 7.7 3.60.7 0.4 ± ± The errors in the NCC and NSN Ia originate from the propagated uncertainty in the SFR. a The number of expected SNe in the background galaxies with resolved multiply images. b Limiting 5s image depth of a co-add of several images. c Limiting 5s image depth for a single visit with 2x15s exposure [69]. d Limiting 5s image depth for the WFIRST Deep Supernova Survey [118]. e Limiting 5s image depth for a 1 hour exposure [8].

65 detectable with the LSST [69]. Thus, extrapolating from our expectation result from A1689 with 17 systems, we may expect roughly 40 strongly ⇠ lensed SNe Ia with the possibility of measuring the time delay between the multiply images. The WFIRST all-sky survey will also be excellent for this task, since it will offer even more suitable filters for higher-z SNe . In Paper IV, we simulated realistic monitoring surveys targeting A1689 and A370, by using the NIR filters F115W and F150W aboard the JWST. The designed duration of JWST will be five years (possibly extended to ten), so we set the duration of the survey to five years. The observable number of SNe exploding in the multiply-imaged galaxies behind A370 will be lower, compared to A1689. For example, we can expect 0.5 SN Ia ⇠ behind A1689, while only 0.04 SN Ia behind A370, by assuming 4 visits ⇠ per year. The reason for is that A370 has fewer multiple-image galaxy pairs with a time delay of less than five years (19 compared to 48). Furthermore, the median magnification at the positions of the multiply-lensed galaxies, are 1.9 mag, while for A1689 is a one magnitude greater, 2.9.Byincreasing ⇠ ⇠ the epochs per year from 4 to 12, we found that the number of expected SNe does not increase significantly. Therefore, the strategy to spread the time over several clusters, is more productive than investing more epochs targeting single galaxy cluster. As more detailed lensing models of galaxy clusters are being published, as an example that of Abell 2744 [74], these simulations can be extended on more clusters. This type of studies will be useful when deciding which clusters will be targeted with JWST for a dedicated multi-year search with its relatively small field of view of 2.2 2.2 . 0 ⇥ 0

66 Sammanfattning

Supernovor är mycket sällsynta företeelser i universum och deras övergående natur har gjort dem svåra att hitta under lång tid. Så det är inte förvånande att omkring två supernovor per månad upptäcktes för 30 år sedan. Idag kan vi hitta supernovor dagligen, men de flesta av dessa är alla relativt närliggande, eftersom dagens teleskop inte är känsliga för de mer avlägsna. Supernova rates, eller mätningen av frekvensen av supernovaexplosioner per volymenhet, är viktigt av flera skäl. De kan till exempel användas för att spåra historien om stjärnbildning i galaxerna. Genom att mäta frekvensen av kärn-kollaps supernovor vilket är kollapsen av massiva och kortlivade stjär- nor per volumenhet. Supernovor är en av de största tillverkarna av tunga grundämnen i universum, så mätning av supernova rates informerar oss om kemisk anrikning av galaxer över tid. Mätning av supernova rates i det avlägsna universum är svårt att upp- skatta. Även om supernovor är en av de ljusstarkaste explosionerna som finns, på avstånd större än fyra miljarder ljusår, är de svåra att hitta ef- tersom de blir för ljussvaga. Detta har varit särskilt problematiskt vid studier av kärn-kollaps explosioner eftersom de i genomsnitt är de ljussvagaste ob- jekten i supernova familjen och ofta inbäddade i stoftrika miljöer. Dessutom, på grund av universums expansion, är det synliga ljuset från alla avlägsna objekt skiftade till längre våglängder. Från marken, är dock nära-infraröda observationer särskilt utmanande på grund av ljusstyrkan och variabilitet av atmosfären vid dessa våglängder. I stället för att vänta på mer kraftfulla teleskop för att komma online, använde vi befintliga anläggningar och förstoringskraften i galaxhopar som gravitationsteleskop för att studera supernovor i det tidiga universum. Ga- laxhopar är de mest massiva gravitationsbundna objekt i universum, som fungerar som gravitationslinser. Gravitationslinser förstorar ljuset av bak- grundsobjekt, och kan därigenom öka djupet för undersökningen, dvs hur långt borta vi kan se supernovor. På detta sätt ökar förmågan att hitta myc- ket avlägsna supernovor. Det var Fritz Zwicky som föreslog användningen av gravitations teleskop för nästan 80 år sedan, men det är först nyligen som systematiska supernova sökningar har utförts i bakgrunden av galaxer bakom kluster. Supernova gruppen i Stockholm har lett den här typen av sökning från markbaserade anläggningar sedan 2003. Som en fortsättning på detta arbete under 2008-2014, undersökte vi galaxhoparna Abell 1689 och A370, som är ett av de mest kraftfulla gra- vitationsteleskop som naturen erbjuder. Vi använde det nära infraröda in- strument på Very Large Telescope i Chile, med medföljande optiska data från Nordic Optical Telescope på La Palma. Vår undersökning resulterade i upptäckten av fem mycket avlägsna och förstorade supernovor. I synnerhet upptäckte vi en supernova som ligger nästan 10 miljarder ljusår bort och som förstorats fyra gånger av en galaxhop, vilket gör det bland den mest avlägsna kärnakollaps-supernova som observerats vid den tidpunkten. Med hjälp av dessa upptäckter, mätte vi supernova rates upp till den tid då uni- versum bara var två miljarder år gammal, utan att det krävdes kostsamma rymdbaserade uppföljningar. Supernovor typ Ia har visat sig vara ett mycket användbart verktyg som avståndsindikatorer, som kan kartlägga den accelererande expansionen av universum. Spektroskopiska observationer av linsade supernovor Ia vid stora avstånd är särskilt intressanta. Dessa kan användas för att testa utvecklingen i sina egna inneboende egenskaper. Vi har undersökt den starkt linsade och mycket avlägsna typ Ia supernovan PS1-10afx, för att se om den avviker från välstuderade närliggande normala typ Ia supernovor. Kan de supernovor typ Ia ha varit annorlunda i det avlägsna förflutna? Våra spektral jämförelser avslöjade ingen skillnad mellan egenskaper av supernovor i vår närhet och den mycket avlägsna supernova PS1-10afx. Starka gravitationslinser förstorar inte bara, men kan också ge flera bilder av bakgrundsobjektet. Vi upptäckte den första upplösta starkt linsade super- novan Ia, iPTF16geu. Med hjälp av högupplösta bilder kunde vi samtidigt observera fyra bilder av samma supernova. Acknowledgements

In previous theses, I always avoided having an acknowledgment section as Ifeltthatsomethingsarehardtoexpresswithwrittenwords.Thisis probably my last thesis, so I will give it a try. Firstly, I would like to thank my supervisors Rahman Amanullah and Ariel Goobar without whom this thesis would not have been possible. Besides being a perfect example of a great scientist, Rahman has been very patient in teaching me how to do research and how to present it. I would like to acknowledge Ariel who has transmitted to me his contagious enthusiasm for the search of strongly lensed supernovae. Also for organizing all kinds of social activities such as dinners with Nobel laureates, julbord, coffee machines, and very importantly, fruit baskets. I thank all the current and past SNOVA members for all the work, stress and free time we shared together. Moreover, I thank Joel Johansson for passing to me his immense supernova and youtube knowledge and orga- nizing wonderful Midsommar in Knarsta; Semeli Papadogiannakis (toughest ninja I know) for organizing impulsive aurora chasing trip and discovering Storsjödjuret, Raphael Ferretti for being great statistics study buddy and always available to discuss all kinds of animals; Tor Kjelsson with whom I worked together in the very beginning and became a great friend; Mattia Bulla with whom I worked at the end and sang together in the Sankta Lucia choir. I thank Francesco Taddia for all the knowledge he has shared with me about spectroscopy at the Nordic Optical Telescope. I thank Markus Kromer and David J. Lagattuta, with whom it has been a rewarding experi- ence collaborating. I thank all the members of the CoPS and OKC for the creating a great working environment. In particular I am grateful to the circle of friends here, Brandon, Timur, Angnis, Raphael, Manuel, Knut and few more. Midsom- mar, archipelago, forest mushrooms trips are some of the great experiences we shared together. I thank Katarina Bendtz and Ingrid Byng Strøm for be- ing part of my life in Stockholm, being great and supportive friends. I thank all my colleagues from the Fysikshow with whom we had great adventures and distracted me from my research. I had a lot of fun during our Fysikshow tours in Dalarna and Göteborg. I thank Nils Elander and Jan Conrad for being my mentors and sharing their wisdom with me. Perhaps, I would not have been here if some events did not align the way they did. The idea to become an astrophysicist in Macedonia could be something against all odds, as there is very little scientific research, no observatory or a astronomy department. It all started when I discovered the Skopje Astronomy Association in 1999, which was a small paradise for me. I thank my friends from the Skopje Astronomy Association that have encouraged me to pursue science when I was young. I thank that person in the Italian embassy that granted me the visa to study in Italy, despite the fact I did not fulfill the requirements because my parents were unemployed at the time. He later told he made that decision after seeing me at the Skopje square, showing the Mars opposition to the public with a telescope in August 2003. IthankmylifetimefriendsfromBologna;Maedeh,Cinzia,Gabriele, Elena, Francesco and Linda. I remember with great pleasure our times studying together and our travels (Solar eclipse in Turkey, Lisbon, Byurakan Observatory...). Special thanks to Maedeh who created the cover image and some more artist’s impressions for this thesis. Ithankmyparentsfortheirsupport,givingmecompletefreedomand independence, and teaching me to question almost everything. Thanks to my twin sister Maja for always encouraging me. IthankVlatkoforhisinfinitelove,patienceandbelieveinme. References

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