Light Curve Powering Mechanisms of Superluminous Supernovae

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A dissertation presented to

the faculty of

the College of Arts and Science of Ohio University

In partial fulﬁllment

of the requirements for the degree

Doctor of Philosophy

Kornpob Bhirombhakdi

May 2019

This dissertation titled

Light Curve Powering Mechanisms of Superluminous Supernovae

KORNPOB BHIROMBHAKDI

has been approved for

the Department of Physics and Astronomy

and the College of Arts and Science by

Ryan Chornock

Assistant Professor of Physics and Astronomy

Joseph Shields

Interim Dean, College of Arts and Science 3 Abstract

BHIROMBHAKDI, KORNPOB, Ph.D., May 2019, Physics

Light Curve Powering Mechanisms of Superluminous Supernovae (111 pp.)

Director of Dissertation: Ryan Chornock

The power sources of some superluminous supernovae (SLSNe), which are at peak 10–

100 times brighter than typical SNe, are still unknown. While some hydrogen-rich SLSNe that show narrow Hα emission (SLSNe-IIn) might be explained by strong circumstellar

interaction (CSI) similar to typical SNe IIn, there are some hydrogen-rich events without

the narrow Hα features (SLSNe-II) and hydrogen-poor ones (SLSNe-I) that strong CSI has

diﬃculties to explain. In this dissertation, I investigate the power sources of these two

SLSN classes. SN 2015bn (SLSN-I) and SN 2008es (SLSN-II) are the targets in this study.

I perform late-time multi-wavelength observations on these objects to determine their power

sources. Evidence supports that SN 2008es was powered by strong CSI, while the late-time

X-ray non-detection we observed neither supports nor denies magnetar spindown as the

most preferred power origin of SN 2015bn. Interestingly, we identify the missing energy

problem for SN 2015bn: >97 % of the total spindown luminosity must be in other forms besides the UV/optical/infrared and 0.3–10 keV X-rays. This dissertation also contains a preliminary study of the UV/optical photometric properties of CSI motivated by SN 2008es.

In future studies, I aim to understand the UV excess phase of CSI SNe, and hope to be able to develop a better way to describe the spectral energy distribution (SED) and its evolution.

Preliminary systematic study of 15 SNe IIn reveals interesting features, and shows promising results that would lead to interesting implications such as a better description for the SED of CSI SNe during the UV excess. 4 Dedication

To everyone who dares to stand up against all odds,

and does what is right. 5 Acknowledgments

I would like to thank my advisor, Prof. Ryan Chornock, for his great mentorship, expertise, and collaboration. I thank all individuals who supported me through the graduate program, and whom I worked with. Orangi, Silver, Ronald Abram, and Gregory Janson, I thank for your great emotional support. 6 Table of Contents

Page

Abstract...... 3

Dedication...... 4

Acknowledgments...... 5

List of Tables...... 8

List of Figures...... 9

List of Acronyms...... 12

1 INTRODUCTION...... 13

2 REVIEW...... 17 2.1 Supernovae...... 17 2.2 Superluminous Supernovae...... 19 2.3 Power Sources of Superluminous Supernovae...... 20 2.3.1 General Picture of SLSN Light Curves...... 20 2.3.2 Radioactive 56Ni...... 22 2.3.3 Circumstellar Interaction...... 23 2.3.4 Magnetar Spindown...... 26 2.4 Light Curve Fitting Software...... 28 2.4.1 TigerFit...... 28 2.4.2 MOSFiT...... 29 2.5 Mechanisms of Infrared Emission...... 32 2.5.1 Dust Emission...... 32 2.5.2 Echo...... 33 2.6 SN 2008es...... 35 2.7 SN 2015bn...... 37

3 SN 2008ES: STRONG CIRCUMSTELLAR INTERACTION WITHOUT NARROW FEATURES...... 39 3.1 Data...... 40 3.2 Analysis and Discussion...... 44 3.2.1 Spectroscopy: Strong CSI and CDS Dust Condensation...... 44 3.2.1.1 Hα Emission and Strong CSI...... 45 3.2.1.2 Blueshifted Hα and CDS Dust Condensation...... 46 3.2.2 NIR Excess: CDS Dust Emission...... 47 3.2.3 Powering Mechanisms...... 50 3.2.3.1 Evolution of the Light Curve of SN 2008es...... 50 3.2.3.2 CSI...... 52 7

3.2.3.3 Magnetar Spindown...... 58 3.3 Conclusion...... 60

4 MAGNETAR SPINDOWN & MISSING ENERGY PROBLEM in SLSNE-I: A CASE STUDY OF SN 2015BN...... 63 4.1 Data...... 63 4.2 Analysis and Discussion...... 65 4.2.1 Constraining Magnetar Spindown...... 65 4.2.1.1 Light Curve in Magnetar Spindown Scenario...... 66 4.2.1.2 X-ray Ionization Breakout...... 68 4.2.1.3 X-ray Ionization Breakout in the Future?...... 71 4.2.2 Constraining Ejecta-Medium Interaction...... 71 4.2.3 Oﬀ-Axis GRB...... 74 4.2.4 Black Hole as a Central Engine...... 75 4.3 Conclusion...... 75

5 MODELLING UV EXCESS OF STRONGLY INTERACTING SUPERNOVAE. 78 5.1 Scope and Goals...... 81 5.2 Preliminary Results...... 82 5.2.1 Data...... 82 5.2.2 Analysis...... 84 5.2.2.1 The Photosphere Temperature...... 84 5.2.2.2 The UV Excess...... 87 5.2.2.3 Color Evolution...... 89 5.2.2.4 Single Band Evolution...... 94 5.3 Conclusion and Future Prospects...... 95

6 CONCLUSION...... 99

References...... 102 8 List of Tables

Table Page

3.1 Late-time photometry of SN 2008es...... 40 3.2 Host emission of SN 2008es (no extinction correction)...... 41 3.3 Bolometric luminosity of the NIR component...... 48 3.4 Bolometric luminosity of late-time optical component...... 50 3.5 Fit results from CSMRAD model from TigerFit...... 53 3.6 Fit results from magnetar modela ...... 58

4.1 Expected luminosity in various scenarios...... 66

5.1 Number of data points of each event (post processing)...... 83 5.2 Linear cooling rates of BVRI photosphere temperatures...... 86 9 List of Figures

Figure Page

3.1 Photometry of SN 2008es in apparent magnitude. Filled symbols are the late-time data presented in this paper, while open symbols are the early-time data from [84, 145]. Dotted horizontal line = modelled host-galaxy emission. The figure shows that the emission in gV R converges to the host-galaxy light, while IHK0 is significantly brighter because of the strong Hα emission in the I band and the NIR excess in the HK’ bands...... 41 3.2 SN 2008es spectra, centered at Hα, at 89 (purple) and 288 (black) days after explosion in the rest frame. A linear continuum has been subtracted from each spectrum to isolate the line emission. Both spectra are normalized to unity for comparison purposes. We note that the spikes bluewards on the late-time spectrum are noise...... 45 3.3 NIR excess. Data points are gV RIK0 (black, diamond) at 254–255 days, and HK0 (purple, square) at 301 days. Solid grey line = 288-day spectrum scaled to the R band, showing Hα contamination in the I band. Solid black line = 5000 K blackbody, optical component, fit to the R data at 255 days. Dashed black line = 1485 K blackbody, NIR component, scaled to the K0 data at 254 days. Dotted purple line = 1485 K blackbody, NIR component, fit to the HK0 data at 301 days. Downward black arrow = 3σ upper limit of the gV bands at 255 days...... 47 3.4 Bolometric luminosity of SN 2008es compared with SN 2013hx. Circle (black) = optical component, diamond (red) = NIR component, square (green) = optical + NIR component, downward arrow = 3σ upper limit, upward arrow = 3σ lower limit, solid line (purple) = bolometric luminosity of SN 2013hx [102]... 51 3.5 Bolometric luminosity of SN 2008es with models of CSI and 56Ni powering. Circle (black) = optical component, diamond (red) = NIR component, square (green) = optical + NIR component, solid line with hourglass (orange) = 56Co decay, dotted line (purple) = CSMRAD1, solid line (black) = CSMRAD2, dashed line (grey) = CSMRAD3, dot-dot-dot-dash line (blue) = CSMRAD4.. 54 3.6 Bolometric luminosity of SN 2008es with magnetar spin-down model. Circle (black) = optical component, diamond (red) = NIR component, square (green) = optical + NIR component, solid line (black) = MAG1 and MAG2 (the lines overlap and cannot be distinguished), dot-dash line (purple) = fully-trapped magnetar spin-down fit from Chatzopoulos et al. [30] implemented by TigerFit. 59

4.1 EPIC-pn image of SN 2015bn (1000 red circle) in 0.3–10 keV X-rays at 805 days. Black = high counts. North is up and east is to the left. The red scale bar is 10 in length...... 64 10

4.2 Light curve of SN 2015bn. Dark green dots = UVOIR data (<801 days from [158, 159] and at 801 days from [163]. Black arrows = 3-sigma upper limits from 0.3–10 keV X-ray observations from XMM -Newton [129]. Gray diamond = gri luminosity at 801 days [163]. Black dotted line = magnetar spin-down model with leakage effects without including the 801-day data [161]. Purple dashed line = magnetar spin-down model without leakage effects and including the 801-day data [163]. Gray solid line = predicted X-ray luminosity from the ionization breakout. Blue dot-dashed line = magnetar spin-down model with leakage effects and including the 801-day data [163]. Red solid line = the difference in luminosity between the models with and without leakage, representing the missing energy. These observations identify a missing energy problem in SLSNe-I...... 66 4.3 Allowed parameter space, assuming that X-ray ionization breakout will occur 5 after 805 d and that Te = 10 K. The area to the right of the line is feasible. The rectangular area with the contours approximately corresponds to the posterior distribution estimated from the UVOIR data by [161] and is entirely feasible. 69 4.4 X-ray luminosity (0.3–10 keV) with predicted lines from the ejecta-medium interaction models. Black arrow = 3σ upper limits of X-ray data of SN 2015bn from XMM -Newton, assuming zero intrinsic absorption and 20 keV thermal bremsstrahlung model. Lines = predicted luminosity from the reverse shock 3 −1 −1 in the interaction model [73], assuming vw = 10 km s , and M˙ = 10 (red −2 −1 dotted), 10 (black solid) M yr with the intrinsic column density of neutral hydrogen of 1020, 1021, 1022, 1023, 1024 cm−2 (from top to bottom). X-ray data for some SNe IIn are presented, including SN 1995N (brown leftwards triangle [27]), SN 1998S (blue rightwards triangle [172]), SN 2006jd (dark green circle [28]), and SN 2010jl (magenta diamond [166])...... 72

5.1 SEDs of SN 2009ip. BVRI fits are assumed blackbodies with BVRI bands. The excess is calculated by subtracting the blackbody from the observations. Linear UV excess fits with the excess from the three UV bands: UVW2,UVM2,UVW1, then connects to zero at U band. The sum line simply adds the optical blackbody with the linear UV excess. Phase is relative to the optical peak in rest frame...... 79 5.2 SN 2009ip with the CSI fit to U and B bands from MOSFiT, including MJD 56200 (slightly before peak) – 56290 and shell-like density profile. The plot showed that MOSFiT can find a CSI solution with a subset of the full multi-band SED. The solution tends to fit well in B band but deviates in others, implying the problem of assuming a blackbody SED. Moreover, UV excess is noticeable in U and UVM2 bands...... 80 5.3 Temperature evolution of the BVRI photospheres...... 84 5.4 UVW2 excess. Dot = detection. Triangle = upper limit...... 89 5.5 UVM2 excess. Dot = detection. Triangle = upper limit...... 89 5.6 UVW1 excess. Dot = detection. Triangle = upper limit...... 90 5.7 U excess. Dot = detection. Triangle = upper limit...... 90 11

5.8 Pseudobolometric UV excess relative to λFλ peak V band. Triangle = upper limit. Other symbols are detections. Excess upper limit model comes from the SVM classifiers in each band integrated...... 91 5.9 UVW2 /UVM2 flux ratio...... 93 5.10 UVM2 /V flux ratio...... 93 5.11 B/V flux ratio...... 94 5.12 UVM2/V flux ratio with clustering: fast and slow evolution. The slow evolving cluster shows flat UV-optical change at some phases, while the fast evolving cluster does not...... 95 5.13 Single band V evolution, training set. Horizontal bar = range of each bin.... 96 5.14 Single band UVM2 evolution, training set. Horizontal bar = range of each bin. 97 12 List of Acronyms

BH black hole MOS Metal Oxide Semi-conductor

CC core collapse NIR near infrared

CCSN core-collapse supernova OSC The Open Supernova Catalog

CDS cool dense shell PI pair instability

CSI circumstellar interaction PISN pair-instability supernova

CSM circumstellar material PWN pulsar wind nebula

EPIC European Photon Imaging Camera RS reverse shock

ESA European Space Agency SAS Science Analysis System

FS forward shock SED spectral energy distribution

GRB γ-ray burst SLSN superluminous supernova

GTI Good Time Interval SN supernova

IC inverse Compton UT Universal Time

IR infrared UVOIR UV/optical/IR

LAT Large Area Telescope WD white dwarf

MJD modiﬁed Julian date ZAMS zero-age main sequence 13 1 INTRODUCTION

A supernova (SN) is an explosion marking the death of a star, giving bright light that can travel more than 10 billion years, and yet still can be observed on earth [23, 51, 89, 182].

Because of the long journey, along its passage the light contains useful information for studying, e.g., stellar evolution, stellar population, properties of circumstellar material

(CSM), and cosmology. Moreover, some SNe like Type Ia also serve as standard candles that help us measuring distance. A SN also ejects heavy elements (i.e., heavier then helium) which the star spent its whole life time fusing from hydrogen to iron. Also, during the explosion, heavier elements than iron can be produced. Especially, in a core-collapse supernova (CCSN) that happens with a massive star with zero-age main sequence (ZAMS) mass >8 M , r-process elements are produced, as well as neutrinos and a gravitational wave. A SN also aﬀects its host galaxy in various aspects including metallicity, star formation, and dust.

After centuries of SN studies, humans are again challenged by new SN-like events, which cannot be explained by the existing understanding of SNe. These events are 10-100 times brighter, and more energetic, than typical SNe [78, 79, 152]. They are called superluminous supernova (SLSN) due to their extreme brightness. For over a decade, SLSNe have been actively studied, but yet still far from being understood.

Among many unusual characteristics that we do not understand, what powers a SLSN is one of the questions that needs immediate attention. This dissertation addresses this question. Given a SLSN light curve (which represents the time evolution of the brightness) reaching its peak, brighter than -20 mag, in a timescale of weeks to months, resulting in the total radiated energy ∼1051–1052 erg. This amount of radiated energy is unusually energetic compared to a canonical CCSN. An alternative explanation is that a SLSN is a pair-instability supernova (PISN), instead of being a CCSN. However, several evidence, such as light curve timescale and spectral proﬁle, has been inconsistent with the PISN, but supported being a CCSN [103, 159]. 14

CCSNe are very diverse. They are basically classified as hydrogen-poor (Type I) or hydrogen-rich (Type II) events with further sub-classification regarding to some unique characteristics [23]. SLSNe are classified similarly. Currently, SLSNe-I do not have sub- classification scheme, while SLSNe-II are sub-classified into SLSNe-IIn for showing strong narrow Hα emission during the peaks (similar to typical SNe IIn [186]), and simply SLSNe-

II for showing only broad Hα features but not the narrow ones. The prototypes of these events are SN 2015bn (SLSN-I [158]), SN 2006gy (SLSN-IIn [165]), and SN 2008es (SLSN-II

[84, 145]).

Since the classiﬁcation scheme groups events with simiar characteristics, it also helps us to associate each group to its potential power origin. For SLSNe-IIn, since they show narrow Hα emission similar to SNe IIn [186] which are well known to be powered by strong circumstellar interaction (CSI)[53, 242], that converts kinetic energy into radiation from the interaction between ejecta and CSM, this mechanism is also likely to power

SLSNe-IIn with the narrow features as the signatures of the mechanism. Recent literature

[41, 195, 198] also supports this argument, and shows that with a certain conﬁguration of

CSM, the mechanism can explain SLSNe-IIn. Precisely, the configuration requires massive and optically thick CSM effectively locating ∼1015 cm away from the explosion site to support efficient conversion of the kinetic energy from the core collapse (CC) explosion.

The strong CSI has diﬃculties to explain SLSNe-I and SLSNe-II, mainly due to the absence of the narrow Hα features. Many solutions had been proposed including some exotic scenarios like quark-nova transition [114, 169], and fallback accretion [57]. However, the current situation favors a more natural scenario as having a central engine as a newly born millisecond-period neutron star with a strong magnetic ﬁeld (i.e., a magnetar [58]). The magnetar loses its rotational energy (i.e., spindown) into radiation via magnetic braking, and this mechanism is called “magnetar spindown” [106, 234].

The magnetar spindown model ﬁts well to both SLSN-I and SLSN-II light curves

[31, 99, 102, 229]. Moreover, spectral evidence from SLSNe-I is also consistent with the 15 scenario [104, 157, 162]. However, there has been no deﬁnitive proof to conﬁrm about this scenario.

One definitive proof to confirm the scenario, as a smoking gun, is the hard photon X/γ- ray leakage at late times due to the activity of a central engine [139, 159, 229]. This idea is consistent with the observed increasing discrepancy with ages between the predicted total spindown luminosity and the observed UV/optical/IR (UVOIR) luminosity. The model incorporating the leakage effects fits well to the UVOIR observations. Also, the leakage timescale about a few years after an explosion, predicted by the X-ray ionization breakout model [127, 139] as the driving mechanism of the leakage, is also consistent with the observed discrepancy. There were many X-ray observations from various SLSNe-I (see [129] for the compilation and references therein), and only a very bright X-ray source was detected from SCP06F6 [120]. However, other non-detections are still consistent with the magnetar scenario, and continuing the search for the X-ray leakage was recommended. Besides X- rays, the search for γ-ray leakage was also non-detections [180]. Besides the hard photon leakage, there were other proposed definitive proof for the magnetar spindown including radio emission [49, 168] and UVOIR light curve evolution [163]. However, none of these proposals has yet confirmed the magnetar spindown.

In this dissertation, I continue investigating the power sources of SLSNe-I and SLSNe-

II. To determine this, I followed multi-wavelength emission behaviour of SN 2015bn and

SN 2008es, as the prototypes of each class. Additionally, motivated by the results of SN

2008es supporting strong CSI as the power origin, I preliminarily investigate the UV/optical photometric properties of CSI SNe. 15 CSI SNe IIn are systematically studied with my focus on developing better understanding of the spectral energy distribution (SED) of CSI

SNe during the UV excess phase, and developing a better way to describe and predict the behaviour.

The rest of the dissertation is structured as follows. I review relevant topics in Chapter

2. Chapter 3, I discuss the power source of SN 2008es. The results of SN 2015bn are discussed in Chapter 4. Chapter 5 presents the preliminary analysis on the UV/optical 16 photometric properties of CSI SNe. Last, I conclude. I note that the results of SN 2008es were originally published as a pre-printed version in arXiv: 1807.07859 and is under review at Monthly Notices of the Royal Astronomical Society (MNRAS), and SN 2015bn were published in Bhirombhakdi et al. 2018, Astrophysical Journal Letters, 868, L32. 17 2 REVIEW

In this chapter, we review relevant topics to the powering mechanisms of SLSNe. We

start by discussing general concepts of typical SNe (Section 2.1) and SLSNe (Section 2.2).

Then, we review some candidate power sources (Section 2.3). Software, applied for the light

curve ﬁtting in order to determine the power sources, is discussed in Section 2.4. We also

review mechanisms related to infrared emission (Section 2.5) separately because this topic

will be crucial in the case of SN 2008es. Last, we review SN 2008es (Section 2.6) and SN

2015bn (Section 2.7) which are the two targets in our studies.

2.1 Supernovae

ASN marks the death of a star from losing balance between gravitational pull and

radiative push. SNe can be classiﬁed into Type I for hydrogen-poor and Type II for

hydrogen-rich according to the presence of hydrogen features in spectra around the peaks

of their light curves. Moreover, Type I can be further sub-classiﬁed according to other

spectral features: Type Ia for strong silicon features, Type Ib for strong helium features,

and Type Ic for having neither silicon nor helium features. On the other hand, Type II can

be sub-classiﬁed by the post-peak behavior of the light curve: Type II-L for linear decay

in magnitude, and Type II-P for having the post-peak plateau. Additionally, there is Type

IIn for a hydrogen-rich event showing strong narrow absorption/emission features in its

spectra. Some objects can deviate from this prototypical classiﬁcation scheme, mainly at

the sub-classiﬁcation level.

This classiﬁcation scheme has been proven to relate to the underlying physics ofSNe.

For example, all Type Is are powered by the radioactivity of 56Ni, while most of the Type

IIs are powered by hydrogen recombination or CSI. While the rest are CCSNe, only Type

Ia is a thermonuclear explosion. The thermonuclear explosion is an explosion of a white

dwarf (WD) in binary interaction, i.e., accretion or merger. The perturbation from binary

interaction makes a stableWD gain more mass beyond the Chandrasekhar limit, i.e., ∼1.4

M , then it explodes. The explosion disrupts the entire WD, and leaves no compact object. 18

While on the opposite, some explosions leave compact objects, e.g., neutron stars or black holes. These areCC explosions. The explosion happens naturally without requiring any perturbation in the evolution of a star with ZAMS mass >8 M , while a WD is formed for a star with ZAMS mass less than this amount.1

For either explosion mechanism, the observed light of a SN is so bright that we can observe the event out to a distance more than 10 Gly (redshift z = 2) [51, 89, 182]. A SN

10 (especially Type Ia and IIn) has its peak luminosity ∼10 L . Because of the long journey, along its passage the light contains useful information

for studying, e.g., stellar evolution, stellar population, properties of CSM, and cosmology.

Moreover, aSN also serves as a standard candle that helps us to measure distance. Besides

the light, aSN also ejects heavy elements (i.e., heavier then helium) which the star spent

its whole life time producing. These elements evolve the host galaxy in various aspects

including metallicity, star formation, and dust. Speciﬁcally for a CCSN, the explosion

produces r-process elements, neutrinos, and a gravitational waves that are another subjects

of interests in physics and astronomy.

In summary, a SN is an explosion of a star. Each SN event looks diﬀerent because of

several reasons. Classiﬁcation helps us to group SNe by their similarity into hydrogen-rich

Type II or hydrogen-poor Type I. A sub-classiﬁcation scheme is applied to further break

down the similarity into Type Ia, Ib, Ic, II-P, II-L, and IIn. This classiﬁcation scheme

also relates to underlying physics of their power origins. For example, Type Is are powered

by radioactivity of 56Ni, while Type IIs are powering by hydrogen recombination or CSI.

Additionally, only SNe Ia are thermonuclear explosions ofWDs in binary interactions, while

the rest are CC explosions of massive stars. SNe yield many implications and applications

across various ﬁelds including, but not limited to, stellar evolution, galaxy evolution, and

cosmology.

1Besides the ZAMS mass, other factors (e.g., composition and rotation) also play roles in determining

the evolution of a star. 19

2.2 Superluminous Supernovae

A SLSN is a CCSN which is 10-100 times brighter than typical SNe [78]. SLSNe have their peaks of the light curves reach 1044–1045 erg s−1, which makes them be observable from a farther distance than redshift z > 4 [16, 48, 178].2 SLSNe are estimated to happen at the rate 10−5–10−4 event per a CCSN [137]. The host galaxies of SLSNe are usually low in metallicity and faint [8, 123, 188].

Analogous to the classiﬁcation scheme for SNe, SLSNe can be classiﬁed into Type

II for hydrogen-rich events and Type I otherwise. SLSNe-I typically have strong oxygen features in their spectra, and also look similar to typical SNe Ic, i.e., hydrogen, helium, and silicon poor. SLSNe-I include, for example, SN 2015bn [104, 158, 159], SN 2005ap [177],

SN 2010gx [178], and SN SCP06F6 [15].3 While most hydrogen-rich SLSNe show narrow absorption/emission features (mainly Hα emission; SLSNe-IIn) similar to SNe IIn, some rare events do not show the narrow features and we simply call them SLSNe-II. Examples of SLSNe-IIn include SN 2006gy as the prototype [176], and SN 2006tf [200]. SLSNe-II include SN 2008es as the prototype [84, 145], SN 2013hx, and PS15br [102].

There is a lot that we do not understand about SLSNe (e.g., light curve undulations

[158], a light curve with a pointy peak [233], and dust production [124]). One of these problems at the forefront is the power source of a SLSN. Given SLSNe radiating totally

∼1051–1052 erg [78], this amount of energy is unusually high for a CCSN because a CCSN releases the gravitational energy ∼1053 erg of which only 1 percent can contribute to the radiation, while the rest of the energy is carried out by neutrino emission.

Currently, the candidate power source of SLSNe is either strong CSI with dense and massive CSM eﬀectively lying at ∼1015 cm from the explosion site to support eﬃcient

2Some objects can be fainter than this criteria, but they are more suitable to be categorized as SLSNe because they are inconsistent with the typical explanation of SNe. PS15br is an example [102]. 3We note that some SLSNe Type I can show hydrogen features at the later time such as iPTF13ehe

[238, 239]. 20 conversion of the kinetic energy into radiation [41, 78, 148, 149, 195], or a magnetar spindown central engine [106, 234]. We review these powering mechanisms in the following sections.

2.3 Power Sources of Superluminous Supernovae

SLSNe are very energetic. They radiate ∼1051–1052 erg in total with UVOIR peaks

44 −1 reaching &10 erg s and light curve timescales from weeks to months [78, 79, 152]. Because of their very energetic nature, we think they are powered by strong CSI similar to SNe IIn.

However, besides SLSNe-IIn, we are still uncertain what power SLSNe-I and SLSNe-II.

In this section, we discuss three candidate power sources: radioactive 56Ni (Section

2.3.2), strong CSI (Section 2.3.3), and magnetar spindown (Section 2.3.4). First, we start by brieﬂy discussing the general picture of SLSN light curves.

2.3.1 General Picture of SLSN Light Curves

After losing its stability, the progenitor star explodes, giving the bright event known as a supernova. The explosion (or shock) energy is released from unbinding the system.

Then, the system starts its expansion phase [13, 232]. In this phase, the explosion energy is partitioned into kinetic and thermal energies, with equipartition held if radiation dominates

(which is true especially for the early time after the explosion). The kinetic energy is used for the expansion, while the thermal energy is converted to energy for adiabatic expansion

(a.k.a. PdV work) and for radiation. The adiabatic loss is bigger if the initial eﬀective size of the system is smaller, and leaving less thermal energy for radiation. The radiation cannot emerge out of the system directly because the opacity of the system is high at the early

1 time. In other words, the photon mean free path, i.e., l ∼ κρ where κ is the opacity and ρ is the density, is short compared to the size of the system. Hence, the radiation slowly

and thermally diﬀuses out. The important parameter associated with the diﬀusion process

is the diﬀusion timescale td deﬁned as [11, 12]

κM t = (2.1) d βcR 21 where κ is the opacity, M is the diﬀusive mass, β ≈ 13.8 is the characteristic constant which

is approximately good for various density profiles, R is the effective diffusion radius, and c

is the speed of light. This expression implies that the diﬀusion of the radiation is slow, and

takes long time to emerge, for a massive and small system.

Since the expansion increases the size of the system, the diﬀusion timescale decreases

with time causing the thermal radiation to emerge and increase in its brightness. The

brightness reaches its peak when the diﬀusion timescale is comparable to the expansion (or

dynamical) timescale, ts, which is deﬁned as R ts = (2.2) vsc

where vsc is the scale velocity of the system, for which the expansion velocity v is normally

applied as a proxy, i.e., vsc ≈ v. The expansion timescale increases with time because of both increasing the size of the system due to the expansion, and slowing down of the velocity

due to losing kinetic energy from some interaction. Recall that the diﬀusion timescale is

long at the early time after the explosion, it implies that the expansion dominates the

diﬀusion during this expansion phase.

The expansion phase ends when the light curve reaches its peak, then the system starts

the cooling phase. This phase contributes to the post-peak light curve which, typically,

decreases monotonically with time. By assuming isotropy, spherical symmetry, adiabatic

expansion, homologous expansion, radiation pressure domination, constant gray opacity,

and centralized energy source, the light curve in the cooling phase is described as [11, 12, 30]

2 2 t 2R0t Lout(t) = exp − 2 + 2 × (2.3) tLC tLC vtLC Z t 2 τ 2R0τ R0 τ exp 2 + 2 + Lin(τ)dτ + 0 tLC vtLC vtLC tLC 2 Eth t 2R0t exp − 2 + 2 td tLC vtLC

where Lout is the emerging luminosity, Lin is input luminosity from any energy source, t is √ the time after explosion, tLC = 2tdts is the eﬀective timescale of the light curve, R0 is the inner radius of the expanding diﬀusive envelope at time t = 0, v is the homologous expansion 22 speed, and Eth is the initial thermal energy from the explosion. We note that, because of the assumption, this model is approximately good during early times after the peak, but

may not be at later times because, for example, the opacity is actually time dependent.

However, at the later time, the shape of the light curve should behave according to the

energy source with very little modiﬁcation by diﬀusion since the system turns optically

thin.

Equation 2.3 shows that the post-peak light curve has a Gaussian tail (a.k.a. ﬁreball)

if there is no additional energy source rather than the shock energy. However, all SNe and

SLSNe have additional energy sources, hence their light curves do not show Gaussian tails.

In the following section, we discuss in details of three candidate energy sources: radioactive

56Ni, strong CSI, and magnetar spindown.

In summary, the shock energy from the explosion is partitioned into kinetic energy for the physical expansion of the system, adiabatic expansion, and radiation. The small initial effective size of the system causes large adiabatic loss, hence smaller energy in radiation is expected. The radiation during the early period after the explosion thermally diffuses out because the system is optically thick. The system becomes more optically thin with time, and the radiation becomes brighter. The brightest radiation emerges when the system expands enough so that the diffusion timescale is comparable to the expansion timescale.

At this point, the light curve reaches its peak. After that, the system starts cooling down, which causes the light curve to decrease in its brightness. The Gaussian tail is expected if there is no additional energy source. However, all SNe and SLSNe do not show the Gaussian tails, implying that they have additional energy sources.

2.3.2 Radioactive 56Ni

The cascade breakdown of 56Ni→ 56Co→ 56Fe is the main power source of typical SNe

I during the ﬁrst couple of years because of the short half life [12]. The half lives of 56Ni

and 56Co are 6 and 77 days respectively, while other radioactive species like 44Ti with 60

years of half life play roles at later times [90, 217]. 23

The 56Ni breakdown process releases γ-rays, positrons, and neutrinos. Neutrinos are insigniﬁcant for the radiation, while the rest contribute to radiation as [155] L (t) M t t in,RAD = Ni,0 6.45 × exp − + 1.45 × exp − (2.4) 43 −1 10 erg s M 8.8 111.3 56 where t is days after explosion in rest frame, and MNi,0 is initial Ni mass. We note that this assumes fully trapped energy (a.k.a. no leakage), which is good when the system is

optically thick, i.e., during the early time after the explosion. The expression implies that 1

56 44 −1 M of Ni can power ∼10 erg s , which means ∼1–10 M required for powering SLSNe at peak. Note also that, according to Equation 2.3, the amount of 56Ni directly inferred

from Equation 2.4 is a lower limit because the diﬀusion process smears the light curve.

56 For typical CCSNe, .0.1 M of Ni is produced [94]. Thermonuclear explosions, 56 56 i.e., SNe Ia, produce ∼0.1–1 M of Ni [44]. In SLSNe, ∼1–10 M of Ni is achievable only in the pair instability (PI) explosion [80, 111, 235, 237]. However, several evidence,

such as light curve timescale and spectral proﬁle, has been inconsistent with the PISN, but

supported being a CCSN [56, 103, 159].

2.3.3 Circumstellar Interaction

Circumstellar interaction (CSI) is an important powering mechanism of some hydrogen-

rich SNe, especially SNe IIn and SLSNe-IIn [40, 78, 186, 198], although some hydrogen-poor

events might show unusual characteristics which are explicable by CSI such as a pointy light

curve in SN 2017egm [233] and frequently observed late-time Hα features [130, 143, 238, 239].

CSI converts kinetic energy of ejecta into radiation. The light curve output is complicated

because of various reasons such as eﬀects of instabilities, multiple structures, i.e., forward

shock (FS), reverse shock (RS), and cool dense shell (CDS) with internal interactions like

re-processing of radiation from one region by another, and both thermal and non-thermal

radiation playing signiﬁcant roles. While 3D hydrodynamic simulations are the standard

way to understand the process [14, 17, 22, 43, 55, 107, 175, 223, 236, 241], the analytical

models exist in the form of power law (a.k.a. self-similar solution) [30, 34, 38, 40, 42, 73, 154].

The validity of the models is still questionable. For example, while the model typically 24 assumes spherical symmetry, there is evidence supporting that some systems had CSM in disk/torus shapes and possibly clumpy in distribution [4–6, 45, 46, 74, 203].

The typical picture of CSI is as following. The explosion accelerates ejecta to high velocity, which typically is in homologous expansion with characteristic velocity ∼104 km s−1. The high-velocity ejecta interact with CSM creating a double-shock structure:

FS andRS. In mass coordinates, theFS propagates outwards andRS inwards.

The characteristic electron temperature of theFS is ∼109 K, while for theRS is ∼107–

8 10 K. Because of this, the thermal radiation from the FS is harder (i.e., &10 keV) than from the RS. However, since the RS is denser, it is more likely to be radiative and be the main contributor to the total radiation than the FS, which turns to be adiabatic soon after the shock breakout. Also note that since the FS moves with a higher velocity into a less dense region compared to the RS, the ion-electron collision is ineﬀective and the ion and electron temperatures are not in equilibrium, with the electron temperature much less than the ion one. Some plasma instabilities might heat electrons collisionlessly and reduce this temperature gap.

Besides the thermal emission, the shocks can accelerate electrons to be relativistic and non-thermal processes, including both synchrotron and inverse Compton (IC) radiation, are important. Since IC is the process in which relativistic electrons up-scatter low-energy photons to higher-energy ones [184], this process is signiﬁcant during the early times after explosion when the photon density is high [129]. Mainly, by up-scattering optical photons from the SN photosphere, the results are UV, X-ray to low γ-ray photons. For synchrotron radiation in which the relativistic electrons are spiralling under the inﬂuence of a magnetic

ﬁeld, the peak radiation can range from X-ray photons to radio depending on the the size of the system. A larger system (i.e., later times after explosion) emits synchrotron radiation that peaks at longer wavelength. However, due to synchrotron self-absorption, the synchrotron emission is typically observed at very late times in radio [172].

In addition to the shocked regions, the CDS which is located between the shocks is also important for the radiative cooling process [73]. This region is formed by thermal 25 instabilities during the early times after explosion (i.e., .500 days). It has a characteristic 4 temperature .10 K and is so dense that it thermally emits at optical/UV wavelengths. It also re-processes hard photons from the shocked regions to lower energy. With the mixing of metals from the inner ejecta through, e.g., Rayleigh-Taylor instabilities, the cooling might be further enhanced. Dust might also be condensed in this region at the early times, which is typically observed in SNe IIn [71].

Analytically, the solution of CSI exists in the form of a self-similar solution, i.e., power law [33]. The solution involves parameters including the explosion properties (i.e., energy, velocity, and ejecta mass), density profiles of ejecta and CSM, and some initial conditions like the initial progenitor radius. Note that some of these parameters, such as the density profiles, are unknown but sensitive in the model. We refer to [40] for the review and references therein for detailed discussion about the self-similar solution. Also, we note that another version of CSI model which incorporated the diffusion approximation and turn-off timescales from shock termination (i.e., running through all the available material) was discussed in [30].

Observationally, strong CSI is practically inferred by the presence of strong and narrow lined emission, mainly Hα, like what we observe in SNe IIn and SLSNe-IIn [186]. However, we note that some strong CSI SNe might not show the narrow features [3, 41, 148, 192, 206], which was also the case for SN 2008es shown in our study (Chapter 3). Non-thermal emission fromIC and synchrotron radiation is also another possible observed signal typically inferred from X-ray and radio emission [128]. For UVOIR observations, strong CSI typically shows very bright UV that fades away quickly afterwards compared to optical and IR [53, 174, 242].

The UV-bright properties of CSI SNe normally exhibit as an excess emission relative to the underlying SN photosphere [128]. We address more details of the UV excess in Chapter

5. The near infrared (NIR) excess is also commonly developed during the early-time post peak due to thermal dust emission either in the CDS or in the CSM as the echo ([71]; we discuss more details about the NIR thermal dust emission in Section 2.5). 26

The UVOIR light curve of CSI is expected to be more complex than other single- component power sources such as 56Ni and magnetar spindown [30, 233]. Its SED also deviates signiﬁcantly from a single blackbody approximation. However, the typical light curve is composed of the rise to peak due to the shock breakout, following by a brief ﬁreball phase which fades quickly, then the post-peak slow decline, which is normally slower than

56Ni and 56Co rates and might look similar to the plateau, and a sharp drop that might exhibit a pointy turn on the light curve possibly due to the shock termination. After that, the light curve normally connects to the 56Co tail.

In summary, CSI is the main powering mechanism of SNe IIn and SLSNe-IIn typically inferred from the narrow Hα features, although some CSI SNe might not show the features. CSI is complicated because of the emission from multiple components and various unknown internal effects. Hydrodynamic simulation is the standard way to understand the mechanism, but is computationally expensive. The analytic solution of CSI exists in the form of a self-similar solution with a recent extension that introduces more physics into it. Observationally, CSI manifests its characteristics at multiple wavelengths, including radio and X-rays from non-thermal emission. At different timescales, which also affected by parameters that we normally lack of prior knowledge about, different emission mechanisms dominate and we expect the signals to come out at different wavelengths with different behaviour. The lack of understanding how CSI SNe evolve due mainly to the lack of well-sampled observations in multiple filters contemporaneously is the biggest challenge.

Therefore, multi-wavelength studies at diﬀerent epochs are the best way to understand the mechanism.

2.3.4 Magnetar Spindown

A magnetar is a strongly magnetized (i.e., >1013 G for the surface dipole ﬁeld) neutron star [58]. By extrapolating the periods of known pulsars (which are old, rotating, and strongly magnetized neutron stars that periodically beam light to observers), we believe that a magnetar is born from a CCSN with very fast rotational period ∼1–10 27 ms. Then, it loses its rotational energy (i.e., spindown) by experiencing magnetic braking

[106, 234]. Magnetar spindown is believed to power most SLSNe-I with increasing amounts of supporting evidence such as light curves ﬁtting well to the model, spectral similarities to some SNe Ic-BL harboring GRBs, and late-time light curve decay slower than 56Co rate

[31, 122, 162, 163, 229, 231].

By assuming a dipole magnetic ﬁeld, no relativistic jet, and a typical neutron star (i.e.,

mass 1.4 M and radius 10 km) the spin energy Ep is [106, 234]

I Ω2 P −2 E = NS = (2 × 1050 erg) (2.5) p 2 10 ms

45 2 2π where INS ≈ 10 g cm is the moment of inertia of a neutron star [113], and Ω = P is the angular frequency given the spin period P . And the spindown timescale is

6I c3 B −2 P 2 t = NS = (1.3 yr) (2.6) p 2 6 2 14 B RNS Ω 10 G 10 ms

where B is the surface equatorial dipole ﬁeld, RNS ≈ 10 km is the radius of the magnetar, and c is the speed of light. We note that in the literature there are slightly diﬀerent

deﬁnitions of calculating the spindown timescale regarding to diﬀerent assumptions, we

follow the deﬁnition in [106].4 Given ∼1 ms period at birth, the expression implies the total

spindown energy ∼1052 erg, which is an order of magnitude more energetic than the kinetic

energy from a CCSN. With the spindown timescale from weeks to months [31, 125, 161, 229],

45 −1 the spindown luminosity can comfortably reach .10 erg s as observed in SLSNe. The

spindown luminosity Lin,MAG is −2 Ep t Lin,MAG(t) = 1 + ; t > tp. (2.7) tp tp

Even though evidence including light curve timescales and spectral features supports

that SLSNe-I, and possibly also some SLSNe-II, are powered by magnetar spindown engines

[52, 102, 125, 161–163], we cannot conﬁrm due to lacking of a smoking gun. One proposed

smoking gun is the leakage of hard photons at late times due to the activity of a central

4Different derived spindown timescale also affects the derived magnetic field. The conversion factors of

the derived magnetic ﬁeld across diﬀerent assumptions are discussed in [161]. 28 engine [139]. This idea is consistent with the increasing discrepancy with time between the predicted total spindown luminosity and the observed UVOIR luminosity [31, 159, 161, 229].

Also, the timescale of the discrepancy starting months after the explosion seems consistent with the prediction of the ionization breakout which might be the driving mechanism for the leakage [127, 139]. Many attempts were made to detect the leakage in many SLSNe-I at various ages mainly in X-rays (see [129] for the compilation), but only one detection of very bright X-rays came from SCP06F6 [120]. However, these non-detections are consistent with the predictions, and continuing the search is the recommendation.

2.4 Light Curve Fitting Software

We briefly review in this section two packages for the light curve fitting software developed for SLSN studies. The first one is TigerFit which will be used mainly in Chapter

3. The second one is MOSFiT that will relate to our analysis in Chapter4 and5.

2.4.1 TigerFit

TigerFit was developed by Prof. Manos Chatzopoulos.5 The corresponding papers of

the code were presented in [30, 31], and references therein. In fact, most of the SLSN light

curve codes currently follow the expression presented in [30], including MOSFiT. Besides

our work in Chapter3, TigerFit was also applied in the analysis of SN 2017egm [233] of

which the developer was one of the authors.

TigerFit is available for Python 2.7/3.x. The code takes input three columns: days

after explosion in the rest frame, bolometric luminosity (erg s−1), and the errors of the

luminosity (erg s−1). The code ﬁts the light curve given a selected model. The choices for

the model include radioactivity, magnetar spindown, CSI with steady wind proﬁle (s = 2),

CSI with uniform density proﬁle (s = 0), fallback accretion, and the combination of CSI,

radioactivity, and magnetar spindown. The models also include corresponding versions with

an assumption of a small initial radius. The diﬀusion approximation (see Section 2.3.1) is

5https://github.com/manolis07gr/TigerFit 29 applied for every model in the code. We note that TigerFit does not incorporate the leakage eﬀects [31, 229] for the magnetar spindown. See more discussion in Chapter 2.3.4 about the hard photon leakage in magnetar spindown.

Chi-squared minimization is the objective for the optimization problem. The search algorithm is implemented by scipy.optimize.curve ﬁt given the errors of the luminosity as

the weights.6 Users can opt out the errors, and the code would assume equal weight to each

data point. Upper and lower boundaries of the search space are set by default internally.

Outputs from the code include the best ﬁt parameters, a plot of the observation against the

best ﬁt model, and data points of luminosity from the model.

As we can see, TigerFit is simple, easy to use, and inexpensive computationally.

It applies the frequentist approach, which takes no prior knowledge of the parameter

distribution unlike the Bayesian approach, and tries to minimize the objective function

given the power source model and the input data as luminosity. However, this is a trade-

oﬀ between the simplicity and the loss of information. To be precise, since normally

we observe in speciﬁc ﬁlters at each epoch, not the bolometric luminosity, we have to

transform the observed SED to the bolometric luminosity, which makes us signiﬁcantly lose

information. Also, because an assumption or approximation of the SED must be made in

the transformation such as assuming a blackbody SED, the validity of the assumption is

typically uncertain. MOSFiT can be considered as an extension of TigerFit that improves

these issues. Last, it is important to note that TigerFit does not incorporate the leakage

eﬀects in the magnetar spindown, which would generally cause over-prediction of the light

curve at late times. MOSFiT also takes care of this issue.

2.4.2 MOSFiT

MOSFiT (The Modular Open Source Fitter for Transients) was published by Dr.

Guillochon and his team [93].7 The code provides various choices of transient power

sources, not only for SLSNe, but also for typical SNe Ia, Ic, kilonova, tidal disruption

6https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.curve ﬁt.html 7https://mosﬁt.readthedocs.io/en/latest/ 30 events, and some others. Many published papers have applied MOSFiT (for example, see

[151, 161, 163, 225, 226]), including our analysis in Chapter4 and5.

MOSFiT is available for Python 2.7/3.x, and can be installed with the Anaconda

Distribution. It is integrated to work by default with the transient databases in the

Astrocats: Open Astronomy Catalogs.8 The code can load data of specified objects directly from the databases using an internet connection. Users can use their own data files with the support of the code to transform the data into the defined schema that the code can further understand. In brief, the data must be saved in the JSON format (i.e., {key: value}).9

The format is equivalent to dictionary type in Python. However, since the code reads pre-speciﬁed keys, converting user data must be done carefully.

Users execute the code with a command line specifying arguments and values. The arguments mainly include the object name matched with the name in the database, or the

file name, and the power source model. Other arguments extend the capabilities of the code by providing a lot of flexibility to users such as specifying data inclusion/exclusion criteria, specifying model parameters, fine-tuning parameters, and requesting extra outputs that the code has in the computing environment but would not return by default such as luminosity and temperature.

After the call, the code processes through the defined list of modules, which process different tasks. Each module takes inputs mainly saved as global variables, and returns outputs that will be used in the following modules. These modules include, for example, transforming observations from different facilities to the same standard, extinction correction, power source models, and SED.

A Bayesian approach with an ensemble of Markov Chain Monte Carlo is the framework applied in MOSFiT (see [93] and references therein). The objective function is a Gaussian

Process Likelihood with a speciﬁed kernel by default. The Watanabe-Akaike information

8https://github.com/astrocatalogs/astrocats 9https://www.json.org/ 31 criterion (WAIC) is applied to calculate the total objective scores from the ensemble, and the potential scale reduction factor (PSRF) is applied as the convergence score.

The output from the analysis is saved in a JSON ﬁle containing the original observation,

WAIC and PSRF scores, ﬁnal realization of the model parameters from each member in the ensemble, and the prediction of each data point corresponding to the epoch and bandpass of the original data. The JSON output can further be passed into a pre-made Python Notebook

ﬁle (which is an interactive Python environment10) to visualize the results including the light curve plot, and the posterior distribution of the model parameters as a corner plot. If users specify extra outputs in the command line, the extra output will be saved in another JSON

ﬁle containing only the requested variables. The extra output will not be visualized by the

Notebook.

Unlike TigerFit that fits a bolometric light curve, MOSFiT tries to fit the light curves in each individual photometric band. However, because the power source models are still expressed as a bolometric light curve, MOSFiT relies heavily on the assumed SED to decompose the luminosity at each epoch into fluxes at each bandpass. A single blackbody

SED is applied in most models, besides “slsn” model that applied a modiﬁed blackbody

SED, which incorporates the UV line blanketing eﬀects observed to be signiﬁcant in most

SLSNe-I [161]. Moreover, MOSFiT adds the leakage eﬀects into the magnetar spindown.

We note that our analysis in Chapter4 with SN 2015bn (SLSN-I), the “slsn” model is applied. While in Chapter5 the “csm” model (i.e., circumstellar interaction model) with a normal blackbody SED is applied.

In summary, MOSFiT is a large and complex light curve fitting tool that also provides a lot of flexibility for modifications. It also applies ensemble-MCMC Bayesian which is more suitable to solve scientific problems with some prior knowledge, errors of measurement, and possibly an ill-behaved objective function. MOSFiT has been shown to be very successful in fitting SLSNe-I with the “slsn” model, which incorporates both UV line blanketing and leakage effects resulting in better fit to the observations. However, it shows some issues

10https://jupyter.org/ 32 when applied to CSI SNe using the “csm” model or its variants. As will be shown in

Chapter5, this issue comes from the assumed blackbody SED. Moreover, MOSFiT is very computationally expensive, so that one has to be careful when using because the program might crash during a long run without any save point in between.

2.5 Mechanisms of Infrared Emission

In this section, we discuss the mechanisms involving the observed infrared (IR) emission at late times, which will be important in our analysis of SN 2008es (Chapter 3). The IR emission can come from the cooling-down SNe. However, we sometimes observe an IR excess, implying that there are additional IR-emitting components, rather than the cooling- down SNe. The mechanisms of the IR excess emission include line emission, synchrotron radiation, dust emission, and echo. Since our scope of interests is to study late-time emission of SLSNe during the timescales which the line emission and synchrotron radiation are insigniﬁcant (i.e., less than 5 years after the explosion), we focus on discussing more on the dust emission and echo.

2.5.1 Dust Emission

Dust emission is a thermal process in which the dust re-processes the input heat and emits into IR wavelengths as an excess component. The frequently mentioned heat sources include mainly CSI and radioactivity. Given a heat source, the IR light curve of the thermal dust emission evolves accordingly to the behavior of the heat source. For example, if the heat source is 56Co which decays ∼0.01 mag day−1, the IR light curve decays at the same rate. We note that an IR echo, which will be discussed in more detail in the next section, is also a thermal process but its light curve does not evolve accordingly to the heat source.

Dust emission is common, especially with hydrogen-rich events [4–6, 18, 54, 60–62, 69–

71, 75, 81, 98, 98, 110, 132–134, 170, 173, 199, 215, 218]; this commonality supports the belief that SNe are the dust producers. Besides studying the thermal properties of the dust, distinguishing which dust component is responsible for the observed emission is also 33 a subject of interest. The dust component can be either in the pre-existing CSM or newly formed in the ejecta. If a CDS exists, the dust component can be formed in this region as well. To distinguish the dust component, diﬀerent lines of evidence (e.g., the blackbody temperature, the blackbody radius, the radius of the forward shock, spectral features, and spectral energy distribution) are required to be consistent. The presence of newly formed dust is frequently inferred from progressive red-wing attenuation.11 The presence of CDS

dust is inferred from the sign of strong CSI and the early onset of observing dust formation,

i.e., earlier than about 500 days after the explosion [6]. We also note that the presence of

one dust component does not rule out the presence of other types.

2.5.2 Echo

In SNe, a light echo happens when the incident light is scattered by CSM dust lying

beyond the dust-free cavity, which is created by the peak UV/optical output. The scattered

light travels back to the line of sight, and is bright because of the accumulation of light

from diﬀerent angles.

There are two types of echo: scattered and thermal [35, 60, 61, 71, 85, 86, 146, 201].

The scattered echo is the scenario where the incident light scattered by CSM dust without

being re-processed. The same spectral features as of the incident light are expected on those

of the scattered light. Additionally, the scattered light is expected to be bluer because of

the wavelength dependence of the dust scattering cross-section, i.e., Q ∝ λ−n; n > 0.

11It is believed that the newly formed dust can obscure more of the emission from the further end,

which is the red-wing side, relative to an observer, causing the attenuation. However, this must be

distinguished from the “Bochum event”, which can looks similar to the red-wing attenuation, implying

asymmetry of the ejecta [47, 63, 95, 138]. It evolves by starting with an undisturbed P Cygni proﬁle, and

blue-shifted peak. Then, the peak moves toward lower velocity with the development of an additional

peak on the red-shifted side. A multiple-peak proﬁle usually has developed by the late-time observation.

This evolution is diﬀerent than that of dust condensation in which the blue-shifted peak progressively

moves to higher velocity. Both scenarios can be present together, e.g., in SN 2004dj. 34

The thermal echo is also called an IR echo because the CSM dust thermally re-processes the incident light, and re-emits at IR wavelengths. The IR echo requires an optically thin system, and CSM dust beyond the dust-free cavity. Observationally, the optical depth can be estimated by

E τ = IR (2.8) EIR + EOPT

where τ is the optical depth, EIR is the observed radiation in IR component (i.e., thermal

dust), and EOPT is the observed radiation in optical component (i.e., cooling down SN). The expression assumes that the total radiative energy is distributed into the IR and optical

components, and implies that the optically thin system, of which τ < 1, partially re-

processes the energy of the optical component and emits into the IR component. For the

−1 size of the dust-free cavity, given the grain emissivity Qν ∝ λ , it is estimated by 0.5 Q¯ν(Lpeak/L ) Revap = (23 pc) 5 (2.9) (λd/µm)Tevap

where Q¯ν is the mean grain emissivity, Lpeak is the peak luminosity, λd = 2πa where a is

the radius of dust grain, and Tevap is the dust evaporation temperature. The expression implies that the size of the dust-free cavity depends on the peak UV/optical output and

11 properties of the dust grains. For typical SLSNe with an UV/optical peak ∼10 L and typical graphite grains with a = 0.1 µm and Tevap = 1900 K, the size of the dust-free cavity is ∼1017 cm. We note that this size is a lower limit since other species of dust grains, such

as silicates, have lower evaporation temperatures.

The signature of the light curve of IR echo is that IR component reaches its peak

luminosity at a later time than the UV/optical peak. Then, the IR luminosity slowly

declines as a plateau, called an echo plateau. The duration of the plateau is determined

by the size of the dust-free cavity (Equation 2.9). After the plateau, the IR luminosity

plummets.

The IR peak luminosity Lecho can be estimated from conservation of energy as

tSN Lecho ≈ τ( )Lpeak (2.10) techo 35 where Lpeak is the peak UV/optical output of the SN, tSN is the e-folding time of the h i post-peak UV/optical light curve, i.e., L(t) = L exp − t , and t is the duration peak tSN echo of the IR echo plateau. The expression shows that the IR peak luminosity depends on the

UV/optical peak of the SN, the SN e-folding time, and the duration of the echo plateau,

which is estimated by 2R t = evap (2.11) echo c where c is speed of light. The expressions – Equation 2.9 to Equation 2.11 – imply that the brighter the SN, the bigger the size of the dust-free cavity, the longer the IR echo plateau, and the fainter the IR peak luminosity is. For typical SLSNe with graphite grains,

17 10 techo ∼ 100 days is a lower limit because Revap & 10 cm, and Lecho ∼ 10 L , given τ = 1 and tSN = 20 days, which tends to be an upper limit. Instead of the IR echo in the traditional sense which is caused by the peak UV/optical output, the post-peak X-ray/UV output from CSM interaction can also cause the IR echo.

This is called a circumstellar shock echo [83]. The physics underlying this mechanism is similar to the traditional one. [71] provides good discussion and a model for the analysis.

The paper also shows that the circumstellar shock echo seems to be more common than the traditional one.

Last, we note that the light curve of an IR echo is sensitive to the geometry of the

CSM dust. The discussion here assumes spherical symmetry, which is approximately good enough and has been used in literature. Any interested readers can refer to [64] for details of the IR echo with aspherical symmetry of CSM dust.

2.6 SN 2008es

SN 2008es is one of the rare cases of a SLSN-II without narrow features [84, 145].

Other SLSNe-II lacking narrow features inclue SN 2013hx and PS15br [102]. The object in this class have only broad (∼10,000 km s−1)Hα emission, without a narrow component.

The early-time (up to ∼100 days) photometric data of SN 2008es ﬁt well to both CSI and magnetar spindown models [31, 102]. Even though the strong CSI is the preferred power 36 origin of SN 2008es and other SLSNe-II, we did not understand why the narrow Hα emission

was absent.

SN 2008es is located at 11h 56m 49.13s +54d 27m 25.7s (J2000.0) at the distance of

−1 redshift z = 0.205. The host of SLSN 2008es is a dwarf galaxy with 0.007 M yr of star

6 formation rate, 6 × 10 M of total stellar mass, 154 million years old in age, and low metallicity [8, 188].

The early-time observation was done until ∼100 days after explosion. Its photometry

included X-ray, UV, optical, and NIR wavelengths. The 0.3–10 keV X-ray was non-detection

with <1042 erg s−1 as the 3σ upper limit. UVOIR data ﬁt well with blackbody, with UV

excess. The event took ∼23 days of rise, and linearly decayed with ∼25 days of e-folding timescale, which is comparable to SN 2005ap (Type I) [177]. Its peak reached 3 × 1044 erg s−1, implying the total radiated energy ∼1051 erg, comparable to other SLSNe [78].

Its early-time spectra showed strong blue continuum but featureless. Only HeIIλ4686 emission was detected. Starting about 20 days, broad Hα emission without absorption

component and Hβ with both emission and absorption components showed up. The emission

without absorption was similar to what commonly observed in SNe II-L [67, 187]. The Hα

emission showed ∼10000 km s−1, corresponding to the expansion velocity of the ejecta, with

ﬂuxes ∼1041 erg s−1, corresponding to equivalent width 22 A.˚ The expansion velocity was

constant until the last available spectrum at about 100 days. The Hβ emission showed

the velocity increasing from 6000–8700 km s−1 during 40–90 days. This was uncommon,

but also observed in SN 2005bf (Ib/peculiar), SN 1979C (II-L), and SN 1980K (II-L)

[24, 147, 171, 222]. SN 1979C spectra were similar to SN 2008es the most.

Blackbody temperature was 14000 K with radius 3 × 1015 cm at peak. By 100 days,

it was 6400 K with radius 5 × 1015 cm, which implied that the photosphere expanded

consistently with the expanding ejecta. The temperature tended to converge to ∼5000–

6000 K after the end of the early-time observation, implying hydrogen recombination.

Strong CSI seemed to be the natural power origin of SN 2008es. With the condition that

the dense and massive CSM lying ∼1015 cm away from the explosion site, the mechanism 37 can convert the kinetic energy into radiation eﬃciently and can reach the observed peak of the event. Although the lack of narrow Hα features might be inconsistent with the mechanism, recent studies showed that strong CSI without narrow features is possible

[3, 41, 148, 192, 206]. CSM mass of 3 M was estimated [31, 102], which is lighter than SN

2006gy (SLSN-IIn) with 10 M [198] and SN 2006tf (SLSN-IIn) with 18 M [200]. The power origin of SN 2008es was still under debate. The strong CSI was the most preferred explanation, but the lack of narrow features challenged this scenario. Other alternatives in recent literature included the magnetar spindown [31, 102], and fallback accretion [57] which is less likely because of requiring ﬁne tuning.

2.7 SN 2015bn

SN 2015bn (a.k.a. PS15ae, CSS141223-113342+004332, MLS150211-113342+004333)

is one of the closest and best-studied SLSNe-I [49, 100, 104, 119, 129, 158, 159, 163, 180],

providing the opportunity to perform detailed multi-wavelength studies at late times.

Currently, SN 2017egm [160] and SN 2018bsz [2] are closer than SN 2015bn. SN 2015bn is

located at 11h 33m 41.55s +00d 43m 33.4s (J2000.0) with redshift z = 0.1136. Its host is a faint dwarf galaxy with low metallicity, similar to other SLSNe-I [8, 188].

SN 2015bn had 92 days of rise, reaching peak at ∼2×1044 erg s−1 with ∼12000 K from its UVOIR light curve. Total radiated energy >1051 erg s−1 was estimated until 250 days after peak. The temperature converged to ∼7000 K at 70 days after peak, and remained approximately constant until the end of the early-time observation around 400 days after peak. Its ejecta expanded with small deceleration, and remained constant since 100 days after peak at 7500 km s−1, which was slower than other SLSNe-I expanding at 10000 km s−1 on average [99, 157, 240]. Later-time optical emission was observed and the UVOIR light curve was estimated to about 1000 days [163]. The light curve was still bright and evolved as t−4 which was more consistent with the magnetar spindown scenario rather than others.

SN 2015bn was observed frequently in radio, X-rays, and γ-rays as well. The radio observations extended to about 900 days were all non-detections [163], as well as soft (<10 38 keV) X-rays (extended to about 300 days [129]) and γ-rays (<600 GeV extended to about 6

months [180]). These non-detections constrained and ruled out a large space of parameters

in various powering mechanisms, but were still consistent with the magnetar scenario.

We observed some interesting features in SN 2015bn that we believe they are common

for SLSNe-I that we had not observed before due to lacking of well-sampling studies. One

interesting feature is the multiple undulations, both pre- and post-peak [158]. The pre-peak

undulation was observed before in some events [118, 157, 207], as well as the post-peak one

[80, 156]. Although we are still uncertain about what caused these undulations, many

explanations were proposed including recombination, ionization breakout, sudden change

in opacity or CSM structure, multiple-shell shock, binary interaction, and magnetar-driven

shock breakout [76, 108, 131, 139, 158].

The magnetar spindown was the most preferred explanation for SN 2015bn, and for

SLSNe-I in general. With the oxygen-dominated spectra, nearly constant expansion velocity,

and t−4 late-time light curve evolution, these features are consistent with the magnetar

scenario [139, 163]. However, we cannot conﬁrm due to lacking of a deﬁnitive proof. The

late-time t−4 light curve evolution was proposed to be the smoking gun [163], but more

samples are required to be studied. Observing hard photon emission in X/γ-rays at late

times is one of the deﬁnitive proof due to the activity of a central engine that many attempts

had done but detected none in many SLSNe-I [129, 180]. Radio emission was another

proposed proof but none was detected [49, 163, 168]. However, these non-detections were

actually consistent with the magnetar scenario [127, 139], and continuing the search was

recommended. 39 3 SN 2008ES: STRONG CIRCUMSTELLAR

INTERACTION WITHOUT NARROW FEATURES

The data and analysis in this chapter was submitted, and are under review at Monthly

Notices of the Royal Astronomical Society (MNRAS). The pre-print version can be found at arXiv:1807.07859.

Strong CSI is well known for powering some bright hydrogen-rich SNe of which spectral features around their peaks show strong and narrow-lined features, mainly Hα emission, as the signatures of this mechanism. Because of this, we term them SNe IIn or SLSNe-IIn, “n” for narrow [186]. However, there is a very rare hydrogen-rich subclass among SLSNe-II that did not show the narrow features. These events include SN 2008es, as the ﬁrst discovered event in this subclass [84, 145], SN 2013hx, and PS15br [102]. To distinguish this rare subclass from the more common SLSNe-IIn, we will refer them as SLSNe-II. Because of not showing narrow features, even though the strong CSI is the preferred power origin, we did not understand why the features were absent. Alternative power sources were proposed, and the magnetar spindown is one of them [31, 102].

In this study, we investigated the power origin of SN 2008es as the prototype of SLSNe-

II. We investigated its multi-wavelength signatures at age &100 days, and determined its power source. We reviewed the event at young age in Section 2.6. Also, we recommend

Section 2.5 that directly relates to our discussion in this chapter.

We discussed the observations in Section 3.1. Then, we analyze the data to determine its power source in Section 3.2, and conclude in Section 3.3. Throughout, unless speciﬁed otherwise, all dates are Universal Time (UT), all SN phases are days after explosion in the rest frame, the assumed explosion date is modiﬁed Julian date (MJD) = 54574 and the peak of the light curve is MJD = 54602 [84], all magnitudes are on the AB system, the

Galactic extinction is assumed to be E(B − V ) = 0.011 mag [185], and the cosmology is

−1 −1 H0 = 70 km s Mpc ,ΩM = 0.3, ΩΛ = 0.7, Ωk = 0. 40 Table 3.1: Late-time photometry of SN 2008es

Observation Date Phase Filter Mag (observed) Mag (corrected)a SN Detection? Telescope/ Exp. time

(UT) (days) Instrument (s)

2008-12-05 192.12 i 21.718 (0.068) 21.800 (0.069) Y P200/COSMIC 1530

2009-02-18 254.36 K0 23.494 (0.046) 23.558 (0.049) Y Gemini/NIRI 3120

2009-02-19 255.19 V (24.449) (24.417) N Keck I/LRIS 300

2009-02-19 255.19 g (25.776) (25.737) N Keck I/LRIS 420

2009-02-19 255.19 R 24.863 (0.298) 25.270 (0.446) Y Keck I/LRIS 390

2009-02-19 255.19 I 23.810 (0.192) 23.928 (0.218) Y Keck I/LRIS 300

2009-04-16 301.66 H 24.543 (0.189) 24.768 (0.234) Y Gemini/NIRI 3150

2009-04-16 301.66 K0 23.734 (0.118) 23.816 (0.128) Y Gemini/NIRI 1800

2009-06-25 359.75 R (25.092) (25.066) N Keck I/LRIS 1050

2009-06-25 359.75 I 24.439 (0.073) 24.678 (0.095) Y Keck I/LRIS 360

2009-06-27 361.41 g 26.436 (0.120) (27.365) N Keck I/LRIS 570

2010-01-08 523.24 g (25.570) (25.531) N Keck I/LRIS 1500

2010-01-08 523.24 R 25.123 (0.202) 25.685 (0.352) Y Keck I/LRIS 720

2010-01-08 523.24 I 24.765 (0.156) 25.110 (0.220) Y Keck I/LRIS 480

2010-02-15 554.77 R 25.698 (0.142) 27.016 (0.527) Y Keck II/DEIMOS 1020

2010-02-15 554.77 I (25.113) (25.095) N Keck II/DEIMOS 960

2011-03-01 871.78 g 26.565 (0.198) (27.304) N Keck I/LRIS 1930

2011-03-01 871.78 R (25.379) (25.353) N Keck I/LRIS 1180

aAfter extinction correction and host-galaxy subtraction.

3.1 Data

SN 2008es is located at α = 11h56m49.13s, δ = +54◦27025.700 (J2000.0) at redshift z = 0.205 [84]. Our late-time observations include one epoch of Hα spectroscopy, as shown in Figure 3.2, and several epochs of optical and NIR photometry, as shown in Table 3.1.

Aperture photometry from IRAF/DAOPHOT [210] was applied. Our late-time photometry covers 2008 December 5 (192 days) to 2010 February 15 (554 days), including one epoch from the Palomar 200-inch Hale telescope (P200) with the Carnegie Observatories Spectroscopic

Multislit and Imaging Camera (COSMIC) in the i band,12 several epochs of gV RI imaging obtained with the Low Resolution Imaging Spectrometer (LRIS) on the Keck I 10 m

12http://www.astro.caltech.edu/palomar/observer/200inchResources/cosmicspecs.html 41 Table 3.2: Host emission of SN 2008es (no extinction correction)

Filter Mag (measured)a Mag (modelled)b

B 26.96 (0.25) 26.75 (0.08)

g 26.44 (0.27) 26.45 (0.08)

V - 26.05 (0.08)

R 25.96 (0.20) 26.07 (0.08)

I - 26.13 (0.08)

F 160W/H 26.85 (0.40) 26.34 (0.08)

K0 - 26.53 (0.08) aFrom [8, 188]. bUncertainties come only from the estimate of the normalisation constant.

18 25.5 20 26.0 g 22 24 i/I 26.5 26 18 18 20 20 22 V 22 H 24 24 26 26

(observed) 18 23 20 R 24 22 25 K’ Apparent magnitude 24 26 26 27 0 200 400 600 800 1000 0 200 400 600 800 1000 Days after explosion in rest frame

Figure 3.1: Photometry of SN 2008es in apparent magnitude. Filled symbols are the late-time data presented in this paper, while open symbols are the early-time data from [84, 145]. Dotted horizontal line = modelled host-galaxy emission. The ﬁgure shows that the emission in gV R converges to the host-galaxy light, while IHK0 is signiﬁcantly brighter because of the strong Hα emission in the I band and the NIR excess in the HK’ bands. 42 telescope [167, 181] and with the DEep Imaging Multi-Object Spectrograph (DEIMOS) on Keck II [65], and two epochs of HK0 from the Near InfraRed Imager and spectrograph

(NIRI) on Gemini [96]. Additionally, we acquire gR photometry from the public Keck

Observatory Archive (KOA), extending the coverage to 2011 March 1 (871 days).

We obtained a single 2000 s spectroscopic exposure using the Gemini Multi-Object

Spectrograph (GMOS) [97] on the 8 m Gemini-North telescope on 2009 March 31.5 (288 days). Our instrumental setup used the R400 grating and a 100. 0 wide slit to cover the

observed spectral range of 5500–9750 A˚ at a resolution of 7 A.˚ We used standard IRAF13

tasks to perform two-dimensional image processing and spectral extraction, as well as

custom IDL routines to apply a relative ﬂux calibration using an archival standard star. At

the position of the transient, a very faint trace is barely detected in the continuum. However,

a single broad emission feature is present between 7650–7950 A,˚ which we identify as Hα

emission from the SN.

For photometric data, images of SN 2008es were reduced by following the standard

procedures (bias, dark, ﬂat, and photometric calibration) in IRAF. The data on 2011 March

1 were stacked from two diﬀerent epochs to increase the signal-to-noise ratio (S/N): 2011

February 1 and 2011 March 26. Up to nine standard stars were identiﬁed in the ﬁeld of

images from the SDSS DR8 catalog for optical bands (ugriz), which were transformed to

UBVRI by following [21]. We calibrated the LRIS g-band images to SDSS g (the two

bands diﬀer slightly). For NIR bands, the standard star FS 21 observed on 2009 April

16 was taken as the standard for calibrating HK0 at the same epoch, while K0 on 2009

February 18 was calibrated by creating a catalog from the stars in the ﬁeld observed on

2009 April 16. The quality of the created catalog was veriﬁed with a few stars presented

in the ﬁeld of view and presented in the 2MASS catalog. For AB conversion, we followed

[21, 25, 219]. For consistency with the other observations of SN 2008es, we transformed

13IRAF is distributed by the National Optical Astronomy Observatory, which is operated by the

Association of Universities for Research in Astronomy (AURA), Inc., under cooperative agreement with

the National Science Foundation (NSF). 43 the i-band data from 2008 December 5 to the I band using I(AB) = i(AB) −0.518, found

by assuming constant colour from 2009 February 19 with transformation equations from

[21]. This was a reasonable assumption since SN 2008es converged to a temperature of

T = 5000–6000 K by the end of the early-time observations [84, 145].

Table 3.1 shows the observed AB magnitudes for the source at the position of the

SN, including contamination from the host galaxy and the Galactic extinction. Some data are marked non-detection because their ﬂuxes are less than 3σ above zero; these data are

reported as 3σ upper limits (in parentheses). Figure 3.1 plots the late-time data, including

the earlier-time data from [84, 145].

Next, a faint (MR ≈ 26 mag) host galaxy has been previously reported [8]. The late-time data tend to converge to constants, corresponding to the host emission. Host

subtraction was performed numerically owing to the lack of template images in several

ﬁlters and the low signiﬁcance of several of the detections, including those of the host only.

A Galactic extinction correction was applied. Host-galaxy extinction was assumed to be

negligible because the host of SN 2008es is blue and has low metallicity [8, 188], and then

host subtraction was performed via adopting a host-galaxy model from Starburst99[115–

117, 224]. These templates are simulated for an instantaneous burst of star formation given

the initial mass function with power-law index 2.35 over the range 1–100 M , and nebular emission included. The templates include metallicity 0.001–0.04 and age 1–900 Myr. The

best galaxy model was selected by ﬁtting the measured BgR/F 160W emission of the host

of SN 2008es from [8] and [188], as shown in Table 3.2. We note that the host images

in the bands BR and F 160W , which is equivalent to the H band, were taken at phase

∼ 1700 days, much later than the last H data presented in Figure 3.1. We assume that

there is no SN contamination at ∼ 1700 days. The best-ﬁt galaxy, determined by the lowest

summed squared residuals, has metallicity 0.001 and an age of 200 million years, which is

consistent with the results of [188]. Then, the host emission estimated from the best-ﬁt

galaxy model was estimated for each band, as shown in Table 3.2; Figure 3.1 also shows

the modelled host emission. We note that the estimated uncertainties of the modelled 44 emission are unrealistically low. This is because only the statistical error from estimating the normalisation factor is included. However, as we will see, our analysis is insensitive to this.

Then, we apply the modelled host emission to perform the host subtraction. Table 3.1 shows corrected AB magnitudes of the late-time data after extinction correction and host subtraction. We also note that in this column the i data are also transformed into the I

band. Some data, which are detections before the correction, are marked as nondetections

because the corrected ﬂuxes are less than 1σ above zero; therefore, these data are reported

as 3σ upper limits (in parentheses). For some data which are marked as non-detection before

the subtraction, only the extinction correction is applied, and the data are reported as 3σ

upper limits. For a quick summary, Table 3.1 provides the column determining whether the

data after the correction are considered as a SN detection.

3.2 Analysis and Discussion

In this section, we analyse the data of SN 2008es and discuss the implications. First,

we look at the Hα emission, which exhibits a sign of dust condensation in the cool dense

shell (CDS) and strong CSI but still shows no sign of narrow absorption/emission features.

Then, we show that there exists a NIR excess corresponding to the thermal dust emission

in the CDS. Last, we verify that CSI is the preferred powering mechanism, which is still

the dominant mechanism during the late-time epochs.

3.2.1 Spectroscopy: Strong CSI and CDS Dust Condensation

It is common in SNe II that the strong CSI leads to the formation of a CDS, and

dust condensation in this region at early times (i.e., .500 days, which is earlier than the expectation of dust forming in the inner ejecta) [4,6, 71, 81, 82, 173, 199, 200, 203, 205, 211].

We discussed about the CDS in Section 2.3.3, and signals fromt the dust emission in Section

2.5. In this following sections 3.2.1.1 and 3.2.1.2, we investigate our observed late-time Hα 45

1.0

0.5

0.0

−0.5 89d

Normalized specific flux 288d −1.0 −2•104 −1•104 0 1•104 2•104 Velocity (km/s) in rest frame

Figure 3.2: SN 2008es spectra, centered at Hα, at 89 (purple) and 288 (black) days after explosion in the rest frame. A linear continuum has been subtracted from each spectrum to isolate the line emission. Both spectra are normalized to unity for comparison purposes. We note that the spikes bluewards on the late-time spectrum are noise.

emission,shown in Figure 3.2, that supports the strong CSI as the power source of this

event.

3.2.1.1 Hα Emission and Strong CSI

From the photometry, Figure 3.1, we note the excess ﬂux in the I band. Figure 3.3

shows the excess relative to the assumed continuum of a 5000 K blackbody scaled to R band.

We assume the continuum blackbody temperature of 5000 K because there is evidence from the early-time analysis [84, 145] that the temperature was converging to this value, which corresponds to the temperature of hydrogen recombination.

The excess I-band ﬂux comes from strong line emission, as presented in Figure 3.2.

The ﬁgure shows spectra from the bandpass equivalent to the I band. We clearly see the strong Hα line emission.

The strong Hα emission implies strong CSI. We can quantitatively show this by estimating the luminosity of Hα emission and its equivalent width (EW). For the luminosity 46 of Hα, since we cannot estimate directly from the spectra owing to the lack of an absolute

calibration, we apply photometric data at 255 days instead. The I-band data have contributions from both the Hα emission and the continuum, so we subtract the assumed continuum of a 5000-K blackbody scaled to the R band, as presented in Figure 3.3. The estimate yields ∼ 5 × 1040 erg s−1 of Hα emission at 255 days; at a similar epoch, this is comparable to some SNe IIn (e.g., SN 1988Z [220], SN 1998S [135]) and to SLSN-II with narrow features (e.g., SN 2006gy [204]).

We can estimate the EW of the Hα emission directly from the spectra. The estimate

is 807 A˚ at 288 days, and 161 A˚ at 89 days. We note that, relative to the continuum

estimated from the vicinity around the emission, Hα emission at 288 days is signiﬁcantly

stronger than that of 89 days. At similar epoch, the 288-day EW is comparable to those of

SN 1988Z (Type IIn) [209, 220] and SLSN 2006tf (SLSN II with narrow features) [200], and

signiﬁcantly stronger than that of SLSN 2006gy [204]. The increasing trend of EWs of Hα

emission is also common in SNe IIn, which are powered by CSI, even though SLSN 2006gy

does not show such a trend [200, 203, 204].

3.2.1.2 Blueshifted Hα and CDS Dust Condensation

Red-wing attenuation of spectral features is expected, but not always, if dust is formed

in the CDS [4,6, 71, 81]. Observationally, the red-wing attenuated spectra show blueshifted

peaks, and asymmetry by having the red-side emission weaker than that of the blue side,

because dust in the CDS obscures more of the emission from the far side than from the

near side. Progressively stronger attenuation with time is also expected because more dust

is formed.

Figure 3.2 compares the shape of the 89-day and 288-day spectra of Hα emission. The

blueshifted peak in the 288-day spectrum is evident, while the maximal velocity of the blue

wing at ∼ 10, 000 km s−1 is similar to that of the 89-day one. This evidence, together

with strong CSI and the early onset (i.e., as early as less than 288 days), supports the

interpretation of dust condensation in the CDS. 47

Last, we note two other possible scenarios causing the observed blueshifted peak. First is the asymmetry of the ejecta with a higher concentration of the radioactive material

(i.e., 56Co during these epochs) toward the near side along the line of sight yielding more excitation and, therefore, more emission from the blue wing [63, 81, 95]. However, this is unlikely because 56Co is not signiﬁcantly powering the light curve (see Section 3.2.3).

Second is asymmetry of CSM, with a higher concentration of CSM toward the near side of the ejecta enhancing the blue-wing emission [7, 190]. This scenario cannot be ruled out but is less favoured, compared to the interpretation of CDS dust, because the scenario does not explain the observed NIR excess. We show the evidence of a NIR excess and discuss its implication in the next section.

3.2.2 NIR Excess: CDS Dust Emission

Observed wavelength in Angstrom 5.0•103 1.0•104 1.5•104 2.0•104 10−18 gVRIK’ 254−255d HK’ 301d 288d spectrum BB 5000 K, 255d BB 1485 K, 254d BB 1485 K, 301d

10−19 Specific flux in erg/cm^2/s/A

10−20 5.0•103 1.0•104 1.5•104 Rest−frame wavelength in Angstrom

Figure 3.3: NIR excess. Data points are gV RIK0 (black, diamond) at 254–255 days, and HK0 (purple, square) at 301 days. Solid grey line = 288-day spectrum scaled to the R band, showing Hα contamination in the I band. Solid black line = 5000 K blackbody, optical component, ﬁt to the R data at 255 days. Dashed black line = 1485 K blackbody, NIR component, scaled to the K0 data at 254 days. Dotted purple line = 1485 K blackbody, NIR component, ﬁt to the HK0 data at 301 days. Downward black arrow = 3σ upper limit of the gV bands at 255 days. 48 Table 3.3: Bolometric luminosity of the NIR component

Phase log10[L] Temperature Radius (days) (erg s−1) (K) (cm)

254.36 41.59 (0.45) 1485a 1.06 × 1016

301.66 41.49 (0.45) 1485 (218) 9.41 × 1015 aAssumed 1485 K from 301 days.

In this section, we continue verifying the existence of the CDS dust by exploring the photometry. We discuss the evidence of a NIR excess, which is consistent with the interpretation of CDS dust condensation. Figure 3.3 gives us a clue of the NIR excess by having emission in the K0 band brighter than if the emission came from the same continuum as the optical bands.

To be more speciﬁc, we present gV RIK0 data at 254–255 days and HK0 data at 301

days in Figure 3.3. We note that gV data are nondetections and the 301-day HK0 data are

not contemporaneous with the optical gV RIK0 data – about 50 days diﬀerence. To show

the NIR excess, we ﬁt the gV RIK0 data at 254–255 days with two blackbody components:

optical and NIR. The optical gV RI component is assumed to have T = 5000 K, implied

by the temperature evolution shown in the early-time analysis being consistent with the

temperature of hydrogen recombination [84, 145], and scaled to the R band (because gV

are nondetections and I is contaminated by Hα emission). For the NIR K0 component, since

we cannot ﬁt the blackbody function nor the temperature, we approximate by ﬁtting the

component from the HK0 data at 301 days, and assume the same temperature in the range

254–301 days. We note that the contribution of the optical component at 301 days to the

NIR component at the same epoch seems to be insigniﬁcant; we verify this by estimating

the optical component at 301 days from assuming the same 5000 K blackbody temperature

scaled to R at 301 days estimated by the linear interpolation of the R data between 255

and 523 days. The NIR component has a blackbody temperature of 1485 K. 49

As shown in Figure 3.3, the NIR excess component is evident. The NIR excess about a year after the explosion supports the existence of thermal dust emission [71, 81].

Next, we provide supporting evidence that the dust emitting this NIR excess is the

CDS dust by showing that, ﬁrst, the photospheric radius of the NIR component is located around the CDS region, and second, the radius is inconsistent with alternative explanations associated with CSM dust.

With the 1485 K temperature, we estimate the bolometric luminosity of the NIR component, shown in Table 3.3, by simply integrating the blackbody function. The implied photospheric radius is ∼ 1016 cm. The radius corresponds to the location of the forward shock, assuming an expansion velocity of 10,000 km s−1 as implied by the spectra. The correspondence of the location of the forward shock and the NIR component strongly supports the hypothesis that the CDS dust is responsible for emitting the observed thermal

NIR excess; this is similar to the NIR-emitting CDS dust observed in some events such as

SN 2005ip (Type IIn) [69, 85]. Moreover, the ∼ 1500 K temperature of the NIR component is reasonable for the dust-condensation temperature.

The observed NIR excess is inconsistent with other explanations involving CSM dust emission (e.g., collision of ejecta [86], IR echo [60]) because the blackbody radius of ∼ 1016

cm is signiﬁcantly smaller than the size of the dust-free cavity, at ∼ 1017 cm for typical

parameters of SLSNe. The size of the dust-free cavity is estimated by Equation 2.9.

Our analysis is sensitive to only the warm dust that emits at NIR wavelengths; colder

dust, which lies farther away (for example, in the CSM) might exist and emits at longer

wavelengths via mechanisms such as an IR echo, which is observed in SN 2006gy at epochs

similar to those of our late-time observations [72, 146]. However, the emission from cold

dust, if it exists, does not aﬀect our interpretation of the warm dust. Also, we note that

the spectral energy distribution is assumed to be a blackbody in our analysis. 50

3.2.3 Powering Mechanisms

In this section, we discuss possible powering mechanisms of SN 2008es, speciﬁcally CSI and magnetar spindown (see Section 2.3 for the review). Both candidates ﬁt well with the early-time data, and can be constrained better by our later-time data. We start by discussing the evolution of the light curve in general. Then, we show that CSI is more preferred, and yields implications consistent with other observed evidence. However, we also show that magnetar spin-down cannot be ruled out (but is less favoured).

3.2.3.1 Evolution of the Light Curve of SN 2008es

Table 3.4: Bolometric luminosity of late-time optical component

a Phase log10[L] Temperature Radius (days) (erg s−1) (K) (1014 cm)

192.12 42.28–42.63b 5000 20.7–31.0

255.19 41.43 (0.18) 5000 7.76

359.75 <41.51 5000 <8.52 aAssumed to be 5000 K. bSee text for the estimation of lower and upper limits.

The evolution of the light curve of SN 2008es is shown in Figure 3.1 for each ﬁlter

(which is discussed in the previous section), and in Figure 3.4 for the bolometric luminosity including the early-time data from [84, 145] as well as our later-time data shown in Table 3.3 and Table 3.4. When determining the bolometric luminosity, we estimate separately the

NIR excess component from the SN component, so that we can investigate the contribution from each component. The bolometric luminosity of the SN component, which we refer to as the optical component, is estimated by simply integrating the 5000 K blackbody. At day 192, our only observation is in the i band, which is potentially contaminated by Hα

emission. We set an upper limit by scaling the blackbody to the I band, which is equivalent 51

45 SN/optical component 44 NIR component optical+NIR component SLSN 2013hx 43

41 log[Luminosity in erg/s] 40 −100 0 100 200 300 400 Days after peak in rest frame

Figure 3.4: Bolometric luminosity of SN 2008es compared with SN 2013hx. Circle (black) = optical component, diamond (red) = NIR component, square (green) = optical + NIR component, downward arrow = 3σ upper limit, upward arrow = 3σ lower limit, solid line (purple) = bolometric luminosity of SN 2013hx [102].

to assuming negligible Hα contamination. The lower limit is estimated by assuming constant

R − I index from 255 days; this is set as a lower limit since the colour at 192 days can be bluer, hence brighter, than assumed if the EW of Hα emission is increasing with time. At

359 days, the upper limit is estimated from the 3σ upper limit in the R band. For the rising

part, the data from ROTSE-IIIb in [84] are transformed into equivalent R-band points by

using the data near peak; then, we assume constant temperature during the rise to the

peak to estimate the bolometric luminosity. For the NIR excess component, we integrate

the 1485 K blackbody function for the bolometric luminosity.

The light curve has a peak ∼ 3×1044 erg s−1, and the estimated explosion is at about 23

days [84]. (Note that Figure 3.4 shows days after peak brightness). Then, it linearly decays

(in magnitude) until the end of the early-time data. At later times, the NIR component

shows a slow decay rate of 0.005 ± 0.003 mag day−1estimated from the two K0 epochs. If the 56Co was powering the NIR component, this would set the upper limit of the initial

56 56 Ni mass to . 0.4 M by scaling the luminosity from Co decay to the NIR components. 52

We note that the evolution of the optical component depends on whether the constraints from a single band (i) at 192 days are correct.

In addition, Figure 3.4 shows the bolometric light curve of SN 2013hx [102], which is

also a SN II without narrow features. Although the light curves are strikingly similar, the

spectral evolutions of the two objects diﬀer, leading to diﬀerent interpretations. While our

spectra of SN 2008es show red-wing attenuation implying the existence of dust formation,

the spectra of SN 2013hx exhibit Hα emission with multiple peaks and multiple velocity

components, implying the interaction with asymmetric CSM [102]. This similarity in the

light curves may imply similar powering mechanisms. At ∼ 300 days after peak brightness,

SN 2013hx shows brighter emission in the K band relative to optical bands [102], hinting the possible NIR excess. However, there is not enough information to verify this, and whether dust emission exists in SN 2013hx is an interesting question deserving of future investigation. Besides SN 2013hx, other SLSNe II lacking narrow features include PS15br

[102]. Their light curves diﬀer from that of SN 2008es, thus implying possibly diﬀerent powering mechanisms.

3.2.3.2 CSI

Eﬃcient conversion of shock energy to radiation by CSI seems to be a natural explanation for the powering mechanism in SLSNe II with narrow features, such as SN

2006gy [165, 198]. Although SN 2008es lacks narrow features, the CSI model ﬁts well with its bolometric light curve at early times. Here, we include our later-time data in a similar analysis for a better constraint on the mechanism.

We apply a semi-analytical model of CSI by using the CSMRAD routine in the TigerFit package14. Similar to [30, 31, 233], this model implements CSI with a diﬀusion process, including forward/reverse shock interaction, and radioactive (i.e., 56Ni and 56Co) heating.

56 Parameters in the model include the initial Ni mass MNi, explosion energy ESN, progenitor

radius Rp (which is equivalent to the inner radius of the CSM in this model), ejecta mass

14https://github.com/manolis07gr/TigerFit 53 Table 3.5: Fit results from CSMRAD model from TigerFit

Parameters CSMRAD1 CSMRAD2 CSMRAD3 CSMRAD4

dataa early early + late early early + late

s 0 0 2 2

MNi (M ) 0.012 0.001 0.000 0.039

51 ESN (10 erg) 5.856 5.800 5.155 5.427

14 Rp (10 cm) 5.072 4.617 1.761 1.707

Mej (M ) 11.591 11.271 16.308 15.473

2 −1 κej (cm g ) 0.30 0.30 0.36 0.34 d 2 2 2 2

n 12 11 12 12

MCSM (M ) 2.668 2.349 2.647 2.491

14 RCSM (10 cm) 12.759 11.672 15.574 13.417

−13 −3 ρCSM (10 g cm ) 6.544 7.519 98.249 116.138 Reduced χ2 3.643 3.267 3.669 4.851 aFit with early-time data, or including late-time data at 192 and 255 days.

Mej, ejecta opacity κej, power-law index of the density profile of the inner ejecta d and of the outer ejecta n, power-law index of the density profile of the CSM s, CSM mass MCSM, mass-loss rate M˙ , and CSM wind velocity vw. We note that, because of the large parameter set and nonlinearity of the model, the model tends to have high degeneracy which yields nonunique solutions with some uncertainty. Therefore, determining the best fit requires careful inspection.

Table 3.5 shows four selected best-ﬁt results. CSMRAD1 and CSMRAD3 are fed with only the early-time data, while the others also have the 192-day and 255-day (only optical component) data in the ﬁt; we include the 192-day data by using the average and dispersion of the lower and upper limits. CSMRAD1 and CSMRAD2 assume a uniform 54

45 Co−56 CSMRAD1 44 CSMRAD2 CSMRAD3 CSMRAD4 43

41 log[Luminosity in erg/s] 40 0 100 200 300 400 Days after explosion in rest frame

Figure 3.5: Bolometric luminosity of SN 2008es with models of CSI and 56Ni powering. Circle (black) = optical component, diamond (red) = NIR component, square (green) = optical + NIR component, solid line with hourglass (orange) = 56Co decay, dotted line (purple) = CSMRAD1, solid line (black) = CSMRAD2, dashed line (grey) = CSMRAD3, dot-dot-dot-dash line (blue) = CSMRAD4.

density distribution (s = 0), while the others assume a steady wind (s = 2). To be comparable with the results of [31, 102], all models assume a power-law index of 2 (d = 2) for the density proﬁle of the inner ejecta. We note that the solutions are insigniﬁcantly changed when applying d = 0, which is another common value used in the literature

[233]. Also, we note that, in the table, we present the outer radius of the CSM RCSM and the CSM density ρCSM instead of the mass-loss rate and the wind velocity by applying ˙ 2 s 3−s 1/3 ρCSM = M/(4πvwRp) and RCSM = [3MCSM/(4πρCSMRp) + Rp ] (see [30] and also the code in TigerFit). Figure 3.5 plots these models, showing that they are degenerate at early times but are distinguishable at later times. According to our coverage, we still cannot determine with certainty the best model among the four. It is interesting to note that, with only the early-time data, the solutions (CSMRAD1 and CSMRAD3) also ﬁt well the later-time data, supporting the continuation of CSI dominating the light curve during the observational epochs. 55

The result of uniform-density models ﬁtting with only the early-time data (CSMRAD1) is comparable to previous estimates [31, 102, 145]. For all models, the results show similar properties of the progenitor and CSM. The estimate indicates a low mass of 56Ni, implying that it is not the dominant source of energy during our observational epochs. The explosion

51 energy is ∼ 5×10 erg with ejecta mass ∼ 10–20 M . The eﬀective CSM mass is ∼ 2–3 M , which is comparable to that of SN 2006tf (superluminous SN II with narrow features [200]), but less than that of SN 2006gy having ∼ 10 M [146]. Comparing to typical SNe IIn, which have CSM mass ∼ 0.1–10 M [23], the estimated CSM mass of SN 2008es is greater than that of SN 2005ip having ∼ 0.1 M [203], comparable to that of SN 2010jl [5], but less than that of SN 1988Z having ∼ 10 M [10]. The eﬀective outer radius of the CSM is ∼ 1015 cm, comparable to the photospheric radius at peak brightness and supporting the

−1 CSI mechanism. For the steady-wind models, the mass-loss rate is ∼ 0.1–1 M yr given a wind velocity of ∼ 100 km s−1, and for the uniform-density models the CSM density is

∼ 10−12–10−13 g cm−3.

We investigate the potential radio emission properties of this CSI given the large derived

−1 51 mass loss rate of 0.1–1 M yr and the explosion energy ∼ 5 × 10 erg estimated in the steady wind models following [36, 39, 208] as synthesized by [49] and assuming similar microphysical parameters. The synchrotron radio emission is heavily self absorbed at all early times when the shock is located within RCSM derived above, but if the wind extends to a large radius we estimate the 5 GHz synchrotron radio emission to reach its peak at ∼1 mJy

(i.e., ∼1030 erg s−1 Hz−1) at an age of 6–20 years, corresponding to an interaction region at a radius of ∼1017 cm from the explosion site. However, it is unphysical for a steady wind with such a high mass loss rate to extend to this large radius without truncation because the total mass in the wind becomes very large, and so the true peak radio ﬂux will lie below this estimate. Therefore, any prediction is uncertain because it depends on the CSM density at larger radii than those probed by the optical light curve presented in this work.

We note that the estimated mass-loss rate of SN 2008es is very high compared to

−3 −1 −1 known massive stellar winds, at most . 10 M yr with vw ≈ 10 km s for extreme 56 red supergiants (RSGs) [191, 192, 227]. The mechanism for this extreme mass loss a few years before the explosion is still unknown, but is believed to be either by binary interaction

−1 −1 −1 (. 10 M yr with vw ≈ 10–100 km s ) or a luminous blue variable (LBV)-like giant −1 −1 eruption (. 10 M yr with vw ≈ 100–1000 km s ) such as those observed in η Carinae or P Cygni [37, 191, 192, 194, 196, 197]. The mass-loss rates of most of strong CSI events

(such as SLSNe 2006gy and 2006tf, and SN IIn 2010jl), are consistent with those of giant

eruptions, while the mass-loss rates of some SNe IIn (such as SNe 1988Z and 1998S) are

consistent with those of binary interaction [192]. For SN 2008es, the estimated mass-

loss rate is consistent with that of a giant eruption. Other proposed extreme mass-loss

mechanisms include hydrodynamic instabilities [193], gravity-wave-driven mass loss [189],

or centrifugal-driven mass loss of spun-up Wolf-Rayet stars [1], which might be more related

to the hydrogen-poor events rather than to the hydrogen-rich ones.

Regardless of what exact mechanism causing the extreme mass loss, the CSM structure

is unlikely to have a steady-wind proﬁle, but is more likely approximated by a dense

shell of uniform density [30]. Therefore, the CSI with wind models (i.e., CSMRAD3 and

CSMRAD4) are less favourable, compared to the uniform-density ones. Also, the estimates

assume spherical symmetry, yet it is likely that the CSM structure is actually complex.

With bipolar/disc/torus shapes, multiple shells, or clumpy structure [4,6, 190, 191, 202],

the mass-loss rate can be lower than that of spherical symmetry.

Our ﬁt results strongly support CSI as the powering mechanism of SN 2008es.

Moreover, the interpretation of CSI powering both the early-time and later-time emission is

consistent with the high EW of Hα and the existence of CDS dust, discussed in the previous section.

Finally, we note that lacking narrow features, SN 2008es was argued to be inconsistent with the CSI powering scenario [84]. However, recent literature [3, 41, 148, 195, 206, 237] discusses how CSI powering SLSNe II without narrow features is possible with some CSM conﬁgurations that the CSM is shocked and accelerated to high velocities before the shock breaking out. Therefore, a luminous SN without narrow features can be powered by the 57 strong CSI. Similar objects of this nature are termed “transitional IIn” subclass [192] in which its members include, e.g., iPTF14hls which is an interacting hydrogen-rich SNe hiding its narrow features until about three years after discovery [3], and PTF11iqb which had been discovered with Hα narrow feature that was weakened quickly afterwards [206]. Without performing a hydrodynamic simulation, we cannot precisely discuss whether SN 2008es is an object in this case. However, we support our claim by following the analysis presented in [41] for the steady-wind case, and [148] for the uniform-density case in following of this section.

In [41], by assuming a steady-wind CSM, conditions determining whether a shock breaking outside or inside the optically thick CSM were formulated. For the case of shock breaking outside, the CSM is shocked and accelerated before the shock breaking out, leaving insigniﬁcant amount of unshocked CSM that the SN shows no sign of narrow features. It happens when the outer CSM radius Rw is smaller than the diﬀusive radius (or breakout radius) Rd. In this case, the timescale since when photons can emerge from the optically

2 thick CSM to its peak (i.e., the rising time tr) is Rw/(vRd), where v is the shock velocity.

Rd 2 −1 This directly implies tr < v ≈ 6kD∗ day where k = κ/0.34 cm g , κ is the opacity, −2 −1 M/˙ 10 M yr and D∗ = −1 is the density parameter. From the ﬁt models with steady wind, vw/10 km s

D∗ ≈ 8. With k = 1 for typical opacity in hydrogen-rich SNe and the rise timescale of 23 days observed in SN 2008es, the condition is satisﬁed. We note that we cannot rule out the other case, shock breaking inside the CSM, because the outer CSM radius is not constrained.

From [148], CSI powering SLSNe II without narrow features is possible with uniform density configuration (see Figure 1 in the article), which is consistent with our fit results of SN 2008es. In this scenario, the condition vtLC/Rw ≥ 1, where tLC is the effective light-

15 curve timescale, is implied. Given typical characteristic shock velocity and Rw & 10 cm, the rise timescale of 23 days, which is typically assumed to be a proxy for the light-curve timescale, satisﬁes the condition. 58

Last, we note that further thorough investigations of how a strong interacting SN can hide the narrow features are necessary. Since asymmetry might play important roles in this scenario, 2D or 3D hydrodynamic simulations are required.

3.2.3.3 Magnetar Spindown

Table 3.6: Fit results from magnetar modela

Parameters MAG1 MAG2

Trapb OI

tLC (days) 19.47 (4.66) 18.94 (2.40)

tp (days) 23.88 (19.96) 23.92 (8.67)

51 Ep (10 erg) 2.41 (1.42) 2.34 (0.58) A (days2) 5424 (4576) 5173 (1854)

P (ms) 2.88 2.92

B (1014 G) 1.28 1.30

Mej (M ) 0.53 0.50 L(t = 255) (erg s−1) 1.2 × 1042 1.2 × 1042

L(t = 302) (erg s−1) 7.1 × 1041 6.9 × 1041

L(t = 360) (erg s−1) 4.0 × 1041 3.9 × 1041

Reduced χ2 5.54 4.48 aUncertainties in parentheses. bImplementation of trapping function (O = outside integral, I = inside).

In this section, we ﬁt the magnetar spin-down model to the light curve of SN 2008es.

The model is reviewed at Equation 2.3 and Equation 2.7. Additionally, we apply the trapping (or leakage) function T = (1 − exp[−At−2]), where A is the trapping coeﬃcient

and A → ∞ for fully trapped energy [30, 31, 50, 229, 230]. There are two diﬀerent

implementations for the trapping function, which we call case “O” for being outside the

integral and case “I” for being inside the integral. Physically, case “O” assumes that the bulk 59

45 MAG1/MAG2 Fully−trapped 44 magnetar (C12)

41 log[Luminosity in erg/s] 40 0 100 200 300 400 Days after explosion in rest frame

Figure 3.6: Bolometric luminosity of SN 2008es with magnetar spin-down model. Circle (black) = optical component, diamond (red) = NIR component, square (green) = optical + NIR component, solid line (black) = MAG1 and MAG2 (the lines overlap and cannot be distinguished), dot-dash line (purple) = fully-trapped magnetar spin-down ﬁt from Chatzopoulos et al. [30] implemented by TigerFit.

input luminosity is fully trapped during the diﬀusion process but the observed luminosity is not, while case “I” assumes that the diﬀusion process cannot fully trap the input luminosity.

Table 3.6 and Figure 3.6 present the best-ﬁt results where tLC is the light curve

timescale, tp is the initial spindown timescale, Ep is the spindown energy, P is the spin period, and B is the strength of magnetic dipole. We note also that the results were fed

only the early-time post-peak data; because of the condition t > tp, we omit the pre-peak data, and because of the uncertainty of the later-time conditions (e.g., changes in opacity and hard photon leakage) which are invalid for the model assumptions, we also omit the later-time data. Additionally, we plot the solution from [31] as the case of fully trapped energy for comparison purposes. This solution greatly overpredicts the late-time brightness.

The solutions MAG1/MAG2, which differ by the implementation of the trapping function but yield insignificantly different results, have the effective light-curve timescale

∼ 19 days comparable to the spin-down timescale ∼ 24 days, and have initial rotational 60 energy ∼ 1051 erg. By applying Equations (1) and (2) of [106] and Equation (10) of

[31], the typical solution implies the magnetar with initial spin period P ≈ 3 ms, ﬁeld

14 15 strength B ≈ 10 G, and ejecta mass Mej ≈ 0.5 M . This solution is consistent with the SLSN magnetar described by [140], and it is also consistent with results from other studies

[31, 102, 106]. The solution ﬁts the early-time data well, but predicts a brighter later-time

light curve than what is observed; at 255 days, the discrepancy between the prediction of

the typical solution and the observation is ∼ 5×1041 erg s−1, given that both the optical and

NIR components are summed together. The discrepancy at late times is a common issue

of ﬁtting SLSNe with the magnetar model [31, 102, 106, 229]. X-ray leakage or ionisation

breakout is hypothesised to explain the discrepancy; however, besides SCP06F6 (SLSN

I) showing very bright X-ray emission at early times [120] and weak X-ray emission from

SN 2006gy [198], there have been no other detections from the X-ray observations (especially

in SLSNe I; Margutti et al. 129).

Thus, we do not favour the magnetar model because the ﬁt to the late-time observations

is poorer compared to the CSI models, and the magnetar scenario is likely incompatible

with the observation of CDS dust, since the hot bubble produced by the magnetar is hostile

to dust condensation [139]. However, we note that the magnetar scenario currently cannot

be ruled out.

3.3 Conclusion

We present and analyse late-time data (192–554 days after explosion in the rest frame)

for SN 2008es, including optical/NIR photometry and spectroscopy of Hα. The spectra show

strong and broad (without detected very narrow) Hα emission with red-wing attenuation

as early as 288 days, implying strong CSI and dust formation in the CDS. The blue-wing

side of the emission extends to about 10,000 km s−1, implying the ejecta expansion velocity

15We note that in the literature, there are slightly diﬀerent deﬁnitions for calculating the spin-down

timescale with different specifications. We follow the definition of [106]. See [161] for a discussion of

diﬀerent speciﬁcations. 61 being constant since the earlier-time data. The late-time photometry is consistent with a cooling SN photosphere and a NIR-excess component at T ≈ 1500 K, implying thermal dust emission. The distance argument supports newly formed CDS dust being responsible for emitting the NIR excess, possibly heated by CSI.

The analysis of the light curve supports CSI as the main powering mechanism from early times until the observed later-time epochs. The ﬁt to the CSI model yields ∼ 10–20

M of ejecta and ∼ 2–3 M of CSM with either a uniform or steady-wind distribution. For the uniform-distribution model, the density is ∼ 10−13–10−12 g cm−3, while for the steady-

−1 −1 wind model the mass-loss rate is ∼ 0.1–1 M yr given a wind velocity of ∼ 100 km s , consistent with that of an LBV-like great eruption. A uniform-density CSM shell is more

likely than a stellar-wind structure. The eﬀective CSM radius is ∼ 1015 cm, supporting the eﬃcient conversion of shock energy to radiation by CSI. A low amount of of 56Ni is estimated, . 0.4 M (if excluding CSI) or 0.04 M (if including CSI). The CSI powering scenario also provides a consistent explanation for the CDS dust condensation and strong

Hα emission. The magnetar spin-down powering mechanism cannot be ruled out, but it is less favourable because of the large brightness discrepancy at late times. Moreover, it is not consistent with other evidence at late times such as the NIR excess and strong CSI.

We note some limitations in our analysis. (1) The assumption of spherical symmetry of the CSM might not be valid, given the growing evidence supporting asymmetric or clumpy

CSM [4–6, 47, 69–71, 109, 218]. If this is the case, the interpretation of the condensation of the CDS dust will need to be reconsidered. However, this should not affect our other interpretations including the CDS dust condensation, which is still supported by the NIR excess and additional arguments. (2) The NIR observation is sensitive to warm dust, which corresponds to the CDS dust in our case. Colder dust located beyond the CDS could exist, and its emission might contaminate the NIR observation. If this is the case, we overestimate the NIR contribution to the energy budget. However, this should not affect our interpretation of CDS dust. (3) The assumption of a blackbody might be invalid, especially at late times when line emission dominates in the nebular phase. This limitation can affect 62 significantly the estimation of luminosity and temperature. (4) The diffusion approximation in both CSI and magnetar spin-down assumes spherical symmetry, homologous expansion, a centrally-concentrated energy source, and constant opacity. Whether these assumptions hold for the analysis at late times is still unknown.

This work reveals, to some extent, the nature of SLSNe II lacking narrow features, a very rare class of which SN 2008es was the ﬁrst object. We note two important aspects of the class that need to be studied: the powering mechanism and dust production. The powering mechanism tends to be explainable by eﬃcient CSI better than by magnetar spindown. However, whether SN 2008es is a good representative of the class or is a unique case is still unknown. More objects of a similar nature are required. Besides SN 2008es,

SLSNe II without narrow features besides include (for example) SN 2013hx, and PS15br

[102]. Investigating the late-time behaviour of these objects might shed some light on the subject, although this will be challenging since they are distant. X-ray and radio observations are recommended probes for the CSI, as observed in some SNe IIn (e.g.,

SN 1998S [172], SN 2010jl [29]), and superluminous SN 2006gy [198]. To explore dust production, NIR to mid-IR observations are recommended probes for future objects, and should be attempted with the James Webb Space Telescope. 63 4 MAGNETAR SPINDOWN & MISSING ENERGY

PROBLEM in SLSNE-I: A CASE STUDY OF SN 2015BN

The data and analysis in this chapter were published by Bhirombhakdi et al. 2018,

Astrophysical Journal Letters, 868, L32 . This study based on observations obtained with

XMM-Newton, an ESA science mission with instruments and contributions directly funded by ESA Member States and NASA.

In this chapter, we investigate the power origins of hydrogen-poor SLSNe-I by applying

SN 2015bn as our case study. Typically for SLSNe-I, the magnetar spindown scenario is the most preferred explanation for the power source of this class [31, 99, 106, 140, 156, 161, 229,

231, 234]. However, whether SLSNe-I are powered by magnetar spindown central engines was inconclusive mainly due to lacking of a smoking gun. One of the proposed smoking gun is the hard photon leakage at late times [31, 229] driven by the ionization breakout [139].

In this study, we observed X-ray emission by XMM -Newton at the age of about 800 days as suggested by the X-ray ionization breakout model [129, 140].

Following in this chapter, the observation is discussed in Section 4.1. In Section 4.2, we constrain various X-ray emission scenarios, and conclude in Section 4.3. Throughout, we adopt the redshift z = 0.1136, luminosity distance 513 Mpc, and explosion MJD 57013

[129]. Any calendar date refers to Universal Time, and theSN phases (or ages) are measured since the explosion in the rest frame, unless speciﬁed otherwise.

4.1 Data

Our observation includes one epoch of X-ray images from the European Photon Imaging

Camera (EPIC) of the European Space Agency (ESA)’s X-ray Multi-Mirror Mission (XMM -

Newton16). The images were taken in all EPICs including Metal Oxide Semi-conductor

(MOS) 1 and 2, and pn cameras [212, 221]. The observation started on 2017 June 5 (MJD

57909) and ended on 2017 June 6 (MJD 57910), at phase ∼805 days (ID: 0802860201; PI:

Chornock). The most constraining image was from EPIC-pn with the thin ﬁlter and 37.7

16https://www.cosmos.esa.int/web/xmm-newton 64

Figure 4.1: EPIC-pn image of SN 2015bn (1000 red circle) in 0.3–10 keV X-rays at 805 days. Black = high counts. North is up and east is to the left. The red scale bar is 10 in length.

ks of exposure, therefore all subsequent analyses are performed regarding to this image. By

applying the Science Analysis System (SAS)17, version 20170719 1539-16.1.0, and following the standard procedure for image reduction, the data has a Good Time Interval (GTI) of

35.7 ks.

As shown in Figure 4.1, no X-ray source was detected at the location of the SN. The

3σ upper limit is estimated to be 1.57 × 10−3 count s−1 in the 0.3–10 keV bandpass. By

applying WebPIMMS18, and a Galactic neutral hydrogen column density in the direction of

20 −2 the transient of NHMW = 2.4×10 cm [105], and assuming zero intrinsic column density of neutral hydrogen, the upper limit on the unabsorbed ﬂux (0.3–10 keV) is 3.6 × 10−15

−1 −2 41 −1 erg s cm (LX . 1.1 × 10 erg s ) assuming a power-law spectrum with photon index −15 −1 −2 41 −1 Γ = 2, or 5.3 × 10 erg s cm (LX . 1.7 × 10 erg s ) assuming a 20 keV thermal 17https://www.cosmos.esa.int/web/xmm-newton/sas-news 18https://heasarc.gsfc.nasa.gov/Tools/multimissiontools.html 65 bremsstrahlung model (this ﬂux conversion is insensitive to the precise temperature as long as it is above the XMM bandpass).

4.2 Analysis and Discussion

Independent of the UVOIR data, the X-ray non-detections of SLSN can provide

constraints on the properties of the explosion and the environment (see [129] for examples).

In this section, four X-ray emission scenarios are considered: magnetar spindown (section

4.2.1), ejecta-medium interaction (section 4.2.2), oﬀ-axis γ-ray burst (GRB) afterglows

(section 4.2.3), and black hole (BH) fallback accretion (section 4.2.4).

4.2.1 Constraining Magnetar Spindown

Magnetar spindown [106, 234] is the most favored explanation for SLSNe-I currently.

The magnetar, which is a neutron star with the surface dipole magnetic strength >1013

G, releases its rotational energy from magnetic braking [58], creating a pulsar wind nebula

(PWN) which is composed of energetic electron/positron pairs [77]. The particles cool down

by synchrotron or inverse Compton emission, which in turn creates more pairs if the energy

allows, resulting in the pair cascade [121, 213, 228]. X-ray photons are emitted but may

not emerge from the ejecta due to photoelectric absorption. A recent example of this may

be SN 2012au, whose 6-year optical spectrum showed evidence for ionization of oxygen by

a PWN, but X-ray observations resulted in a non-detection, which was interpreted as being

due to high ejecta opacity [144]. Reprocessing of this absorbed emission by the ejecta is

responsible for powering the optical/UV light [139].

In this section, we compare the observed energy to the predicted input (Section 4.2.1.1),

then constrain the parameter space of magnetar spindown under the X-ray ionization

breakout scenario (Section 4.2.1.2), and last discuss the possibility of observing the breakout

in the future (Section 4.2.1.3). 66

46 ] 10 Leak−801d −1 45 No leak+801d 10 Leak+801d Missing 1044 X−ray gri UVOIR 1043 XBO 1042

[Luminosity in erg s 41

10 10

log 1040 0 200 400 600 800 1000 Days after explosion in rest frame

Figure 4.2: Light curve of SN 2015bn. Dark green dots = UVOIR data (<801 days from [158, 159] and at 801 days from [163]. Black arrows = 3-sigma upper limits from 0.3–10 keV X-ray observations from XMM -Newton [129]. Gray diamond = gri luminosity at 801 days [163]. Black dotted line = magnetar spin-down model with leakage effects without including the 801-day data [161]. Purple dashed line = magnetar spin-down model without leakage effects and including the 801-day data [163]. Gray solid line = predicted X-ray luminosity from the ionization breakout. Blue dot-dashed line = magnetar spindown model with leakage effects and including the 801-day data [163]. Red solid line = the difference in luminosity between the models with and without leakage, representing the missing energy. These observations identify a missing energy problem in SLSNe-I.

Table 4.1: Expected luminosity in various scenarios

Case Model (M) or Include Bandpass Luminosity (1042 erg s−1)

observation (O)? leakage eﬀects? 145 days 325 days 805 days

No leak+801d M N Total 125.17 35.34 7.22

Leak+801d M Y Total 63.52 51% 5.03 14% 0.18 2.5%

UVOIR data O - UVOIR 60.67 48% 7.44 21% 0.17 2.4%

X-ray data O - 0.3–10 keV <0.31 <0.2% <0.17 <0.5% <0.11 <1.5%

4.2.1.1 Light Curve in Magnetar Spindown Scenario

Figure 4.2 shows the light curve of SN 2015bn, along with ﬁts to the magnetar model.

The latest optical gri luminosity observed on 2017 June 1 (MJD 57905), corresponding to 67

41 −1 phase 801 days, is from [163], with LUVOIR ≈ 1.7 × 10 erg s . The ﬁt lines are the total bolometric luminosity from the “slsn” model, which is the modiﬁed magnetar spindown model [161] of MOSFiT19 [93]. We note that the “Leak-801d” model was presented by

[161], and was downloaded from The Open Supernova Catalog (OSC;[92])20. Moreover, the “No leak+801d” model is estimated by applying the same parameters from the fit of the “Leak+801d” but changing the leakage coefficient (see [31, 161, 229] about the leakage effect) so that the leakage effect is negligible. The “Missing” line shows the difference between the models with and without leakage.

As presented in the figure, adding the 801-day UVOIR data into the fit does not significantly change the fit parameters: initial spindown period 2.16 ms, magnetic field

13 strength 3 × 10 G, and ejecta mass 11.7 M for the median values [161]. We note that there are other magnetar spindown results in literature [158, 159] which have similar parameters, but we include only the ones from MOSFiT for consistency. Moreover, the modiﬁed magnetar spindown in MOSFiT, “slsn,” has more parameters than mentioned here (see [161]), but those extra parameters are irrelevant to the discussion.

For the case without the leakage eﬀect, which represents the eﬃcient conversion of the total spin-down luminosity into radiation [31, 229], the discrepancy with the UVOIR observations has started since about 100 days, corresponding to its spectrum starting to show some noticeable changes [158]. Then, the gap tends to increase with age while the

SN evolved into the nebular phase. Table 4.1 numerically shows the discrepancy at the three epochs corresponding to the deep XMM -Newton observations. The percentage of the luminosity relative to that of the non-leakage case is also calculated.

The models imply that the leakage continuously increases relative to the total luminosity (i.e., ∼50% at 145 days to ∼97% at 805 days). The X-ray non-detections mean that radiation in the 0.3–10 keV bandpass cannot account for the total leakage. We have three possibilities: non-radiative losses (e.g., adiabatic expansion and accelerating ejecta

19https://mosﬁt.readthedocs.io/en/latest/ 20https://sne.space/ 68 due to the expanding hot bubble from the PWN’s activity, or simply losing non-interacting particles created from the PWN’s activity), radiative losses outside our observational bands, or that the magnetar model is not correct.

Because the magnetar injects relativistic particles and high-energy photons (i.e., X- ray and γ-ray) into the PWN, the energy has to be converted to the UVOIR and soft

X-ray photons that we observe. If this energy can escape the ejecta at other wavelengths

(such as the γ-rays), the observed bandpasses might not provide a complete account of

the bolometric luminosity. Also, the MOSFiT model assumes a blackbody SED in the

optical/infrared bandpass, which might not be accurate during the nebular phase due to

strong line emission. Furthermore, it is also possible that the magnetar ﬁt to the peak

of the light curve might not apply at late times if, for instance, the spindown parameters

change due to accretion [141], or if the magnetar collapses to a black hole [150]. However,

it is unlikely that the central engine completely shut oﬀ because the late-time optical light

curve up to ∼1,100 days has a decay rate L ∝ t−4, which is also slower than the 56Co rate, and requires ongoing energy input from an engine [163]. If the magnetar ceased to exist by becoming a black hole, we would require fallback accretion to power the optical light curve, for which the shape is predicted to be L ∝ t−5/3 [151].

Last, we also note that the analysis is sensitive to assumptions implicitly included in the leakage term (e.g., homologous expansion and constant leakage coeﬃcient). The assumption of spherical symmetry is vital and might not be accurate in some scenarios such as having clumps or jets. Moreover, the analysis assumes no emission is contributed via other mechanisms such as radioactivity, circumstellar interaction, or a light echo (such as that observed in the SLSN-I iPTF16eh [124]). However, the late time optical observations of SN 2015bn strongly constrain these mechanisms [163].

4.2.1.2 X-ray Ionization Breakout

We constrain the parameter space of the magnetar spindown in this section by applying the model of the X-ray ionization breakout [139]. Because of the frequent X-ray observations 69

Figure 4.3: Allowed parameter space, assuming that X-ray ionization breakout will 5 occur after 805 d and that Te = 10 K. The area to the right of the line is feasible. The rectangular area with the contours approximately corresponds to the posterior distribution estimated from the UVOIR data by [161] and is entirely feasible.

during early times (see [129] for the compilation), X-ray ionization breakout is unlikely to have happened in the past. If the breakout occurred between ∼300–800 days and the model is correct, the X-ray luminosity would have reached the predicted values, as shown in Figure 4.2, and would have been detected at 805 days. The breakout light curve is insensitive to ﬁt parameters presented in [161]. Any X-ray event behaving like SCP06F6, which had a subsequent non-detection faster than the model’s prediction [139], cannot be excluded, although it might not be an ionization breakout. These non-detections through

805 days are consistent with the predictions that the breakout timescales are ∼1–100 years

[101, 129]. In the following analysis, we assume that X-ray ionization breakout will take place in the future, and that the model remains valid to these late times. (We discuss possible caveats in the following Section 4.2.1.3.)

The timescale for the X-ray ionization breakout is estimated by following the model in [139] (see also [129], equations 2, 4, and 5). Since SN 2015bn is oxygen dominated, we are interested in the breakout of oxygen (Z = 8). We assume the mass fraction of oxygen 70

4 −1 in the ejecta XO = 0.7 [104, 159], the characteristic ejecta velocity vej = 10 km s , and

5 the electron temperature Te = 10 K corresponding to the temperature for ionizing oxygen

[129, 139]. We constructed a grid of ejecta mass (Mej) and magnetic ﬁeld strength (B) in

13 14 3 the ranges 5–20 M and 10 –10 G. The inferred breakout timescales range over ∼1–10 years. Then, we identify “feasible” grids if the timescale is >805 days. Figure 4.3 shows the result with the contour of the posterior distribution (in the rectangular area) presented by

[161], which is estimated from the UVOIR data. The X-ray non-detections, independently of the UVOIR data, rule out the parameter space of the magnetar spindown with low ejecta

13 mass (.8 M ) and low magnetic strength (.2 × 10 G). The feasible space is consistent with, but less constrained than, that of the UVOIR data.

In summary, we demonstrate how even non-detections in the X-rays can constrain magnetar spin-down independently of the UVOIR data. For SN 2015bn, the X-ray non- detections until 805 days can rule out a portion of the parameter space of the magnetar spindown with low ejecta mass and low magnetic strength. Later epochs of X-ray observation, if still non-detections, will shift the feasible line to the right, possibly ruling out some overlapping space with the results from the ﬁts to the UVOIR data.

We note that the electron temperature is uncertain and can significantly affect the analysis. Although the characteristic temperature in the PWN is ∼107 K[139], the temperature of gas in the ionized layers of the ejecta, Te, is significantly less than this.

5 Here we have assumed a gas temperature Te = 10 K[139], but the actual temperature could be lower than this at very late times [127]. Since the ionization breakout timescale

−n obeys tion ∝ Te for n = {0.3, 0.8} depending on some conditions [139], this can increase the breakout time, implying a large shift of the allowed parameter space comapared to that shown in Figure 4.3. Indeed, [127] found that X-ray ionization breakout is unlikely to occur at late times in SLSNe, due in part to the decreasing ejecta temperature (increasing recombination rate) as the ejecta expands. 71

4.2.1.3 X-ray Ionization Breakout in the Future?

In the magnetar-powered PWN, energetic electron/positron pairs cool, creating gamma-ray photons, which can further annihilate and create lower energetic pairs, which then can Compton upscatter the nebular radiation [139]. This process, which repeats multiple times, is known as a “pair cascade” [213]. If the system is suﬃciently “compact”

(suﬃciently high energy density), the process becomes “saturated” after many cycles,

−β resulting in ﬂat photon SED, with Fν ∝ ν and β ∼ 1. Otherwise, the SED from synchrotron or Inverse Compton emission is likely to be harder, β . 1, and therefore the X-ray emission will be fainter than predicted by the model [139].

The ionization breakout process requires a large density of UV/X-ray photons and thus

favors a relatively soft nebula spectra (high compactness). In the magnetar scenario, as the

ejecta expands, the nebula compactness drops. For SN 2015bn, we estimate the compactness

at 805 days to be ∼10−3 (see equation 13 in [139] and 4 in [129] with parameters in [161]),

given the albedo 0.5 and the diﬀusive timescale ∼80 days (approximately the rising time

of the UVOIR light curve [11, 12, 30]). Such low compactness means that in principle

high energy gamma-rays could escape from the nebula (without creating pairs) and thus

leaving few UV/X-ray photons to ionize the ejecta. Future studies of ionization break-out,

analogous to those of [127] should account self-consistently for the predicted hardening in

the ionizing spectrum at late times.

4.2.2 Constraining Ejecta-Medium Interaction

X-ray emission in the ejecta-medium interaction is well studied in many events,

especially SNe IIn like SN 1998S [172], SN 2006jd [28], and SN 2010jl [29], and SNe Ib/c [39].

In this scenario, the X-ray emission constrains the medium density at the location of the

shock, in our case ∼1017 cm from the explosion site at 805 days after explosion, given 104

km s−1 for the typical shock velocity (see [129] for the constraints on the medium density

at earlier epochs). Even though there has been no clear sign of circumstellar interaction

during the earlier phases [158, 159], the medium at the late phases might have diﬀerent 72

1043 ) −1 1042

1041

1040 -2 10 MO •/yr 2006jd 39 -1 10 10 MO •/yr 2010jl 1995N 2015bn

X−ray Luminosity (erg s 1998S 1038 100 1000 Phase (days)

Figure 4.4: X-ray luminosity (0.3–10 keV) with predicted lines from the ejecta-medium interaction models. Black arrow = 3σ upper limits of X-ray data of SN 2015bn from XMM -Newton, assuming zero intrinsic absorption and 20 keV thermal bremsstrahlung model. Lines = predicted luminosity from the reverse shock in the interaction model [73], 3 −1 −1 −2 −1 assuming vw = 10 km s , and M˙ = 10 (red dotted), 10 (black solid) M yr with the intrinsic column density of neutral hydrogen of 1020, 1021, 1022, 1023, 1024 cm−2 (from top to bottom). X-ray data for some SNe IIn are presented, including SN 1995N (brown leftwards triangle [27]), SN 1998S (blue rightwards triangle [172]), SN 2006jd (dark green circle [28]), and SN 2010jl (magenta diamond [166]).

properties. There has been growing evidence for hydrogen-poor SNe showing hydrogen features from the interaction in their late-time spectra [32, 112, 136, 143, 238, 239], and there is the recent evidence of the light echo from iPTF16eh [124] implying a signiﬁcant amount of hydrogen-poor circumstellar medium in a SLSN-I at ∼1017 cm. Moreover, the

early-time undulations seen in the optical light curve of SN 2015bn [158, 159] might imply

inhomogeneities in the circumstellar medium. Therefore, estimating the medium properties

at various phases can help constrain the presence of interaction.

In the absence of more detailed simulations, we do not know what the main emission

mechanism for the X-ray photons from the ejecta-medium interaction would be at this

epoch. At earlier epochs, inverse Compton scattering dominates the emission [129]. At

late times, synchrotron radiation dominates the non-thermal X-ray emission unless the 73 medium is suﬃciently dense, in which case the emission is thermal bremsstrahlung [40].

The estimates here assume the latter scenario, and also assume that the soft 0.3–10 keV X- ray emission is dominated by the reverse shock according to its characteristic temperature

[40, 73], as expected in a medium with the density proﬁle of a wind. Since we also cannot tell whether the X-ray photons can escape the dense reverse shock from its absorption, our estimation here presents a conservative upper limit.

We apply the model from [73] (see also equation 16 in [40]). Since, under this assumption, the emission is likely to be thermal, in this section we estimate the emission by assuming a 20 keV thermal bremsstrahlung model, representative of detections of previous strongly interacting SNe (e.g., [29, 130]). All of the calibration was estimated using

WebPIMMS. Figure 4.4 presents the absorbed luminosity of the three XMM -Newton X-ray

data points, only correcting for the Galactic (NHgal) column density of neutral hydrogen of

20 −2 2.37 × 10 cm . We note that the assumed zero intrinsic absorption (NHint) gives us the conventional lower limit of the luminosity, since more intrinsic absorption shifts the limit to higher luminosity (given a ﬁxed count rate). We also assume a steady wind environment.

The absorbed luminosity (L) depends on the mass loss rate (M˙ ), steady wind velocity

(vw), the ejecta velocity (vej), the power-law index of the density of the outer part of the

ejecta (n), the absorption parameters (i.e., NHgal, and NHint), and the reference day for scaling (i.e., L ∝ t−3/(n−2)). We use n = 10 as the typical value for a stripped-envelope SN

3 −1 4 −1 20 −2 [40], vw = 10 km s , vej = 10 km s , NHgal = 2.37×10 cm , and the scaling relative

−2 −1 −1 to 805 days. Figure 4.4 shows the models with M˙ = 10 , and 10 M yr . Each model

20 21 22 23 24 −2 is estimated with NHint = 10 , 10 , 10 , 10 , 10 cm (from top to bottom). Since ˙ 3 ˙ −2 −1 4 L ∝ Mvej, the X-ray data are consistent with the model M < 10 M yr , vej < 10 −1 km s , and any NHint. For a larger mass loss rate, the data might be consistent with the predictions if the intrinsic absorption is large. This result is also consistent with the radio

limits at late times [163].

Figure 4.4 also shows some SNe IIn (see [59] and references therein) with soft X-ray

(0.3–10 keV) detections at comparable ages to SN 2015bn. The data demonstrate that the 74

X-ray luminosity in some strongly interacting SNe IIn (e.g., SN 2006jd [28]) can be brighter than the upper limits for SN 2015bn.

4.2.3 Oﬀ-Axis GRB

Some SNe with features similar to SLSNe might also harbor jets, like the luminous SN

2011kl associated with GRB 111209A [91, 126]. X-ray to radio emission can be observed

at late times after the explosion from the jet interaction with the circumburst medium

[26, 164, 183]. Depending mainly on the injected energy, the medium properties, the energy

conversion factors, the jet opening angle, and the angle between the line of sight and the

jet axis, the afterglows vary in the timescale and the SED [87, 88].

For SN 2015bn, the earlier X-ray and radio non-detections rule out portions of the

parameter space [49, 129, 158]. Here, we apply the same BOXFIT [243] simulated 0.3–10

keV X-ray light curves in the scenario of oﬀ-axis GRB jets, as presented by [129], with

our latest X-ray non-detection. The data further rule out only a very small additional

portion of parameter space, including most cases of jets with unrealistically high isotropic

equivalent kinetic energy >1055 erg, the circumburst medium with >10−3 cm−3 uniform

density proﬁle, the jet opening angle <15◦, and the line of sight angle <30◦ with respect

to the jet axis, given the ﬁducial values of the energy conversion factors: B = 0.01 and

e = 0.1. If a jet exists, the missing energy might be directly carried away by it. However, we

require most spindown energy input near peak to be trapped and power the luminous optical

peak. The jet energy would then have to escape at later times, e.g., after the ejecta expand

suﬃciently. It is not clear how to reconcile a choked jet at early times with an escaping jet

at later times. For the total missing energy ∼1051 erg over ∼800 days, it is possible to be

carried away by a weak jet with isotropic equivalent kinetic energy <1052 erg that cannot

be ruled out by any X-ray/radio non-detections [49, 129, 158]. 75

4.2.4 Black Hole as a Central Engine

Instead of forming a neutron star, a SLSN-I might form a BH, in which case the UVOIR peak would be powered by the fallback accretion of slow ejecta at the inner boundary [57].

Although this is unlikely to be the case for SN 2015bn due to the large accreted mass required to power the main UVOIR peak [151], a BH could also form at late times from a magnetar accreting enough fallback material [150]. In either case, X-rays could be emitted as the result of the central engine’s activity. Our late-time X-ray limit constrains such a scenario. The combined UVOIR and X-ray data at ∼800 days imply that the bolometric luminosity is .100 times the Eddington value for a central BH with mass 10 M , although the fraction of the accretion luminosity to escape would depend on the ionization state and amount of soft X-ray absorption in the ejecta, as discussed above in a magnetar scenario.

4.3 Conclusion

We present the latest deep X-ray observation from XMM -Newton of SN 2015bn, one of the closest SLSNe-I. The observation corresponding to the phase 805 days shows a 0.3–

41 −1 10 keV X-ray non-detection, with a 3-sigma upper limit of LX . 10 erg s , with the implication that we still cannot distinguish models for the power source of the event. In the

magnetar spindown scenario, the best-ﬁt model predicts ∼97% of the total energy input

leaks outside of the UVOIR bandpass, and the UVOIR data up to ∼800 days follow the prediction. Our X-ray upper limit is <1.5% of the total, strongly constraining the leakage, unless non-radiative loss is important.

Independent of the UVOIR data, the X-ray upper limits rule out the possibility of having an ionization breakout earlier than 805 days, and rule out magnetar spindown with

13 low ejecta mass (.8 M ) and low magnetic strength (.2 × 10 G), consistent with the results from the UVOIR data in recent literature [104, 161]. In the future, however, the breakout is unlikely to happen due to the compactness problem. This issue is generally true for any old-age SNe. In the ejecta-medium interaction scenario, we constrain the 76

17 −2 −1 3 −1 environment at ∼10 cm to be .10 M yr for a 10 km s steady wind. In the oﬀ-axis GRB and BH fallback scenarios, our observations only rule out extreme models.

We note that the analysis here is sensitive to some assumptions. For example, the SED estimated in the ionization breakout model, which assumes the pair-cascade saturation that seems true at young ages, might not be valid in the low-compactness regime at old ages. In this regime, we note that the SEDs are expected to be harder than assumed in the ionization breakout model [139], and therefore X-ray emission should be fainter than predicted and observing the emission will be challenging. The feasible line presented in Figure 4.3 is also sensitive to the electron temperature at the ionizing layers. The magnetar spin-down model, which assumes some parameters to be constants since early times and includes the leakage eﬀects with a constant coeﬃcient, might not be accurate at old ages. The estimated density of the ambient medium in the interaction scenario assumes the X-ray emission is dominated by the reverse shock. All models assume spherical symmetry, which might not hold [100, 119].

The search for the smoking gun of a central engine is still ongoing. [163] suggests that the late-time ﬂattening of the optical light curve of SN 2015bn after ∼500 days with a decline rate slower than that of 56Co decay is evidence for the continuous input of energy from a central engine, although conﬁrmation requires more examples. In addition, the energetic

SN Ib-pec 2012au, which might be a lower-luminosity counterpart of some SLSNe-I [142], including SN 2015bn [159], had an optical spectrum at an age of 6 yr that was recently interpreted as photoionized oxygen-rich gas shocked by a high pressure PWN [144]. For the

X-ray signal, we still encourage the early-time observations, despite many non-detections in the past, because there is a chance of observing the signal similar to what was observed in SCP06F6 [120]. Asphericity might play a signiﬁcant role in the observed signal, which yields an additional opportunity to study the geometric distribution of the explosion.

According to [127], the early-time ionization breakout timescale is less than the spindown timescale, typically <1 year. Therefore, this might be the golden period to observe such the scenario. After the ﬁrst year, the chance of observing ionization breakout 77 is low, but still possible. We also suggest observations in MeV–GeV γ-rays to constrain the

high energy emission, as might be the case for direct leakage from the PWN in the low-

compactness regime. We note that recent Fermi-Large Area Telescope (LAT) observations

44 −1 of SN 2015bn set a limit on the >600 MeV γ-ray luminosity of Lγ . 10 erg s during the ﬁrst six months after its UVOIR peak [180]. However, these limits are not constraining

on the expected leakage of the nebula energy in gamma-rays. At old ages, if the central

engine exists, the X-ray signal will eventually emerge out due to the dilution eﬀects, rather

than the ionization breakout [127]. Therefore, despite the predicted timescale >100 years,

continued monitoring is essential. Besides the X-ray signal, we note that the radio signal is

also a potential smoking gun [153, 168]. Theoretical models or simulations to predict SEDs

in various scenarios are necessary to distinguish the observed signals. The best candidates

for future observations are the increasing number of very nearby events. 78 5 MODELLING UV EXCESS OF STRONGLY

INTERACTING SUPERNOVAE

Motivated by the case of SN 2008es in Chapter3, strong CSI can play signiﬁcant roles in powering many hydrogen-rich SLSNe, regardless of the presence of the narrow Hα emission. The signiﬁcance of CSI might also extend to some hydrogen-poor events like SN

2017egm [233]. However, because of its complexity (see Section 2.3.3 for more discussion), the current understanding of CSI is limited. Therefore, developing better understanding of

CSI is the aim of this chapter.

Among various aspects of CSI that we have not yet fully understood, we focus our interest at the UV excess properties commonly observed during the peak of an interacting

SN [23, 40, 128]. The UV excess is likely to come from the re-processing of hard photons from the shock regions by a colder region like the CDS, which is a unique product from strong CSI [23, 40]. Therefore, understanding the properties of UV excess would lead us to better understanding of CSI. The excess should also be able to constrain the CSI parameters, which relate to the evolution of progenitor at its advanced stage such as its mass loss rate. Moreover, since we know that CSI SEDs cannot be well described by a single blackbody, which is normally adopted as the ﬁrst-order approximation, incorporating a UV excess component as a correction to the single blackbody would bring better description to the CSI SEDs.

UV excess is defined by having stronger UV fluxes than predicted by a blackbody fit to the optical SED, as shown in Figure 5.1. The plots show the SEDs of SN 2009ip, a well-known strongly interacting SN IIn [128]. Four phases, relative to phase 0 day at its optical peak in the rest frame, are presented to convey the general idea of how CSI SED evolves. It is commonly evident that the UV excess develops before the optical peak. Then, the strength of the excess decreases until the SED shows a UV deficit, defined by having

UV ﬂuxes less than predicted by the optical blackbody. While a UV deﬁcit at late times is 79

. 1e 1.0 0−0 − 0 0.8 -5.79E-17 x + 1.65E-13 -3.61E-17 x + 9.45E-14 Sum Sum 0 -5 days 0.6 0 days

0 0.4 Å 0 0.2

00 0.0

1e 1e 1.75 3.0 − − 1.50 2.5 -2.30E-17 x + 6.06E-14 -4.09E-18 x + 1.02E-14 Sum 1.25 Sum 2.0

Specific flux in erg s erg in flux Specific 10 days 13 days 1.00 1.5 0.75

1.0 0.50

0.5 0.25

0.0 0.00 2000 3000 4000 5000 6000 7000 8000 2000 3000 4000 5000 6000 7000 8000

Observed wavelength in Å

Figure 5.1: SEDs of SN 2009ip. BVRI ﬁts are assumed blackbodies with BVRI bands. The excess is calculated by subtracting the blackbody from the observations. Linear UV excess ﬁts with the excess from the three UV bands: UVW2,UVM2,UVW1, then connects to zero at U band. The sum line simply adds the optical blackbody with the linear UV excess. Phase is relative to the optical peak in rest frame.

common across various classes of CCSNe due to line blanketing [174], UV excess tends to

be a unique feature for CSI.

Similar to Figure 5.1, Figure 5.2 also shows the UV excess and how the blackbody SED

is an inappropriate assumption for CSI SED. In this ﬁgure, we tried to ﬁt SN 2009ip with its

full light curve from UV to IR by including data from slightly before the optical peak to less

than about a hundred days after by MOSFiT (see Section 2.4 for a brief review of MOSFiT).

By including UV to IR data, the software cannot converge to a solution after running a

very long chain of Markov-Chain Monte Carlo. Several combinations of parameters (such 80

12 12 SN 2009ip, U 14 14 16 16 18

20 18 22 20

Apparent magnitude 24 Apparent magnitude

26 SN 2009ip, UVM2 22 160 180 200 220 240 260 280 160 180 200 220 240 260 280 MJD - 56000 MJD - 56000

14 14

16 16

18 18

20 20 Apparent magnitude Apparent magnitude 22 SN 2009ip, B 22 SN 2009ip, V

160 180 200 220 240 260 280 160 180 200 220 240 260 280 MJD - 56000 MJD - 56000

Figure 5.2: SN 2009ip with the CSI fit to U and B bands from MOSFiT, including MJD 56200 (slightly before peak) – 56290 and shell-like density profile. The plot showed that MOSFiT can find a CSI solution with a subset of the full multi-band SED. The solution tends to fit well in B band but deviates in others, implying the problem of assuming a blackbody SED. Moreover, UV excess is noticeable in U and UVM2 bands.

as shell and wind density proﬁles, or ﬁxing the explosion date parameter) and data coverage

were tried, but none can converge to a solution. Then, since we suspected that the source

of the problem came from the blackbody SED assumed by the software, we tried ﬁtting

with a small subset of bands such as only B and U/B bands. Figure 5.2 demonstrates in

the case of ﬁtting only U/B bands that the software can ﬁnd a solution. In other words,

the blackbody constraint was a part of the problem, while the other part might be due to

the CSI model itself. Even though a solution is found, we notice the poorer ﬁts to other 81 bands besides B and the presence of UV excess, implying again invalidity of blackbody SED assumption.

Some recent studies addressed the UV properties in interacting SNe. UV properties across various classes in CCSNe had been compared [174]. [242] focused directly on 10

SNe IIn and their UV excess properties. [53] simulated CSI light curves with various

CSI parameters to see how the parameters aﬀect the light curves and tried to apply this understanding to explain the diversity of CCSNe with some detailed discussion on SN

2009ip and SN 2011ht (both are IIn). In summary, these studies analyzed data from

Swift/UVOT which included UVW2,UVM2,UVW1,U,B,V ﬁlters. These studies showed that UV properties of SNe IIn are diverse with linear decay (in magnitude space). The

UV decay rates are faster than optical, with variations possibly due to the CSM properties.

Normalization was attempted. The biggest challenges were the lack of constraints on the peak epochs, and well-sampling data, i.e., including both pre- and post-peak epochs in

UV and optical contemporaneously. However, some degree of uniformity was remarkable including the peak UV brightness and the color evolution.

In this study, we continue exploring the UV properties of interacting SNe. We discuss the scope and goals of this study in Section 5.1. The preliminary results are discussed in

Section 5.2. Last, we conclude and discuss the future prospects.

5.1 Scope and Goals

The goals of this study are to model the UV excess from interacting SNe in order to extend the SED model for a better accuracy. Also, we might learn about the properties of

CSI from this study. This study focuses on UV and optical photometry of SNe IIn similar to previous literature [53, 174, 242], but extends in several aspects including the sample, bandpass coverage including R/I bands, and applying diﬀerent approaches.

The scope of this preliminary study is to investigate just general properties to gauge the prospects of extensive future studies. SNe IIn are included. Photometric observations from UVW2 to I bands are included. The analysis will make an assumption that each event 82 governed by the same physics of CSI with diﬀerent parameters. Despite this simplicity, we will see interesting results that the data show some degrees of uniformity.

5.2 Preliminary Results

5.2.1 Data

We acquired the data of SNe IIn photometry from The Open Supernova Catalog (OSC), which is an open source online databases for SN events [92]. We ﬁltered the data by sorting on Type IIn events, descending by the number of photometric data available in the database.

Then, we manually inspected each event to determine whether to include into the study.

The inclusion criteria were centered around whether i) UV and optical data were available, ii) data included both pre- and post-peak, and iii) quality of data was acceptable. We note that the data available in the database were not of perfect quality for several reasons, and some subjective calls were made based on the criteria without measurable quantities.

For future improvement, we plan to get the data directly from the primary sources with quantitatively measurable inclusion criteria. However, for a preliminary study, our current criteria should be suﬃcient.

We inspected about 200 SNe IIn, and 15 events were included for having both UV and optical data. We note that most of the objects were excluded because they lacked the UV data, or data were of poor quality. Table 5.1 shows the number of data points of each event included in this study after the cleaning process.

For the cleaning procedure, we manually inspected each event for the consistency of the data in order to convert all photometric data into the same standard. The sources of inconsistency found included mixing of Vega and AB magnitude systems, and duplication of data with diﬀerent ﬁlter labels (e.g., r, r0, and R) that actually are the same data points.

We note that these inconsistencies were found mainly by manual inspection, and there was not enough explicit information guiding us. Following the basic standard stated by the database, we treated all uppercase ﬁlters (e.g., U, R, I) originally in the Vega system, while the lowercase ones (e.g., r, r0) in AB system. Some data might not comply to the 83 Table 5.1: Number of data points of each event (post processing)

Event Starta Enda Peakb z UVW2 UVM2 UVW1 U B V R I

SN2007pk -8 49 54423 0.0167 9 9 10 25 51 51 20 9

SN2008iy -4 37 54940 0.0410 2 1 1 2 7 7 5 4

SN2009ip -15 50 56206 0.0059 103 75 72 107 139 158 100 113

SN2009kr -2 47 55147 0.0065 7 7 11 14 31 31 12 12

SN2010al -8 48 55284 0.0171 9 9 10 10 26 27 17 19

SN2010jl -9 50 55487 0.0107 22 18 22 9 42 49 10 10

SN2010jp -1 20 55519 0.0092 3 3 9 10 12 5 0 0

SN2011ht -15 47 55888 0.0036 11 11 11 11 22 22 11 11

SN2011hw -4 44 55891 0.0230 5 5 5 5 12 5 8 6

SN2011iw 0 19 55906 0.0230 1 2 2 3 5 5 0 0

SN2013fs -6 39 56577 0.0119 40 37 42 57 59 55 83 19

SN2014G -7 18 56680 0.0045 15 12 13 14 12 12 8 0

SN2015bh -8 24 57166 0.0064 14 14 13 15 33 36 24 19

PTF11iqb -14 49 55779 0.0125 11 11 10 0 3 3 162 27

PS15cww -3 44 57361 0.0630 5 5 6 6 1 0 4 0 aPhase in days relative to the peak optical in the rest frame bIn MJD standard, which we worked around each case separately. All data were converted into the

AB system with Galactic de-reddening rules from [68]. Generic Vega-to-AB conversions and effective wavelengths were adopted [21, 25]. Then, we re-assigned all the filters into their uppercase equivalence without further correction such as the k-correction, which should be approximately justified due to the redshift range, i.e., 0.003 ≤ z ≤ 0.063, of the sample.

However, PS15cww with redshift 0.063 would not appear in most of the analysis because the lack of contemporaneous data in multiple bands. The SN phase deﬁned throughout this chapter was relative to the brightest optical data (mostly in V band) in the rest frames,

found directly from the data. We note that the brightest assigned epoch of some events 84 might not imply the real peak. Then, we ﬁltered only phase [-15,50] days in the analysis, that will represent slightly before the peak, UV excess phase, and early UV deﬁcit phase.

In some of the analysis, we required multiple-wavelength observations at the contemporaneous epochs. We adopted the values and error of measurement from “nearest” interpolation. We did this to avoid making assumption about the light curve behavior. From inspection, the interpolation also resulted in slightly smoothing the light curves, which was a desirable eﬀect.

5.2.2 Analysis

5.2.2.1 The Photosphere Temperature

y = -5.35E+02 x + 1.12E+04 BVRI Blackbody Temperature 20000 y = -1.50E+02 x + 1.03E+04 y = -3.36E+01 x + 7.93E+03 18000 SN2010al SN2014G 16000 SN2010jl SN2007pk 14000 SN2013fs SN2009ip 12000 SN2011ht SN2015bh 10000 SN2009kr SN2010jp 8000 SN2008iy SN2011hw SN2011iw Temperature in K, rest frame 6000 bin mean 4000 10 0 10 20 30 40 50 Phase in days

Figure 5.3: Temperature evolution of the BVRI photospheres.

We ﬁrst start by looking at the photosphere temperature. This is a good starting point because we have quite a good idea of how the photosphere should behave [242]. We expect the temperature of the photosphere to rise, reaching its peak when the shock breaks out, then decline as it cools down. 85

We model the photosphere with a single blackbody, as commonly applied in literature

(see [128] for an example). Since our observations might be contaminated by the UV excess, we apply optical bands BVRI to ﬁt the model. Figure 5.3 shows the results. In general, we notice the temperature increases to the peak around phase 0d or before, then decreases. The temperature tends to converge at a temperature ﬂoor &6,000 K approximately equivalent to the hydrogen recombination temperature that dominates the emission at late times typically for SNe II [9, 66]. We note that PTF11iqb and PS15cww were excluded in the analysis due to being an outlier and lacking of data, respectively.

To get a meaningful statistics, we perform bootstrapping. Unless specify otherwise, any bootstrapping will be performed for 10,000 iterations with a sample size of each iteration equal to the original sample size in that analysis.

For each iteration, we accumulate at least 5 data points in a phase bin, and calculate mean temperatures and phases of each bin, which is then rounded to the closest integer.

Then, we construct the inferences of the mean temperatures in each bin. We note that the distributions are approximately normal starting since phase −4 days, while multi- modal distributions are shown for earlier phases possibly due to the lack of data. The bin mean temperatures are shown in Figure 5.3. They behave similarly to what we discussed previously.

It is evident from the bin mean temperatures that the cooling rate of the photosphere from the peak temperature is non-linear with a signiﬁcantly faster rate during the early- time post peak compared to later times [242]. It has been shown in some literature [128] that a piecewise linear can be applied to estimate the non-linear cooling rate. In the ﬁgure, we estimate the cooling rate into three pieces: very fast after peak [-7,0] days, fast [0,20] days, and slow [20,50] days. We approximate the cooling rate with a linear model which yields the rates 535, 150, and 33.6 K/day, respectively.

Since the cooling rates are actually diverse among SNe IIn as we see from the plot, it would be more informative to understand the distribution of the cooling rates, and their other characteristics. Therefore, we estimate the cooling rates of each event as presented in 86 Table 5.2: Linear cooling rates of BVRI photosphere temperatures

Event Slow Fast Very fast Note

K/day K/day K/day

SN2007pk 98.0 539.4 2276.7

SN2008iy 26.2 577.5 Large gap [0,25] days

SN2009ip 117.3 223.6 Increasing temperature to phase 0d

SN2009kr 58.2 362.2 Converged

SN2010al 30.4 396.3 Converged

SN2010jl 2.4 Converged, cover [20,50] days

SN2010jp 160.3 1886.9 Converged

SN2011ht 100.0 100.0 100.0

SN2011hw Irregular

SN2011iw 369.0

SN2013fs 115.2 115.2 2092.4

SN2014G 105.2 868.6

SN2015bh 87.0 173.6 173.6 Converged

Mean 70.4 253.6 1136.9

SD 13.3 45.5 322.6

Table 5.2. We also perform the bootstrapping for the means and standard deviations (SD) of each cooling rate.

There are several interesting characteristics from each individual cooling rate. In general, the very fast, fast, and slow cooling rates are approximately at the orders of 1,000,

100, and 10 K/day, respectively. The slow cooling rate is a typical sign for the convergence to ∼6,000 K as discussed previously. We note that SN 2011ht, SN 2013fs, and SN 2011hw

show unusual behaviour. SN 2011ht shows on approximately constant cooling rate extending

from [-15,50] days without a sign of very fast rate, while SN 2013fs shows from [0,40] days

with a quick transitioning to a very fast rate. For SN 2011hw, it shows irregular cooling 87 behaviour with increasing temperature during [0,5] and [30,40] days. Investigating these unusual behaviours would be an interesting exercise in a future study.

In summary, the BVRI photosphere temperatures tend to show some degree of uniformity. However, when considering each individual object, the evolution tracks of photosphere temperature show diversity. We are able to identify three possible cooling regimes: slow ∼10 K/day at late times, fast ∼100 K/day at earlier times, and very fast

∼1000 K/day possibly right after the shock breakout. The slow cooling rate tends to be uniform across events because of the convergence to hydrogen recombination temperature.

Compared to the slow cooling rate, the fast and very fast ones show more variation which might relate to the CSI properties. How the cooling rates relate to the properties of CSI and UV excess would be an interesting investigation in a future study. We note that the results in this section can be applied to estimate photosphere temperature depending on what information is currently present. For example, if we have enough information to verify that the observed event is post optical peak and before the convergence to hydrogen recombination, we might adopt the fast cooling rate of ∼250 K/day to perform

any estimation. Since the cooling rate tend to be faster at earlier phases, we can also

backwardly extrapolate using the fast cooling rate to set lower temperature limits.

5.2.2.2 The UV Excess

We continue assuming the blackbody photosphere to estimate the UV excess observed.

As shown in the previous section, we can decompose the emission into the photosphere

dominating the emission in BVRI and the UV component. Therefore, we can estimate the UV excess by simply subtracting the emission from the modelled photosphere from the observations. Figure 5.1 showed an example with SN 2009ip. Four epochs are selected in the example to show the general expectation for the UV excess evolution that the excess would decrease over times, and the SED typically transitions from showing UV excess to

UV deﬁcit, i.e., fainter than the blackbody photosphere, due mainly to the line blanketing at late times [128, 174, 242]. 88

Figure 5.4 to Figure 5.7 show the UV excess from our sample. An upper limit is set when the data point shows UV deﬁcit. The limit is set to be the observed value. We also normalize the excess with the ﬂuxes of peak V band. The plots show declining trends of the UV excess over times as expected.

For a rough estimation, we can estimate a boundary to separate the detections and upper limits. As an example, we separate the space into detections versus upper limits with the Support Vector Machine (SVM) Classifier with the linear kernel from scikit-learn library in python. We choose to work with the (phase,log10[normalized flux]) space because of the observed linear decay of UV magnitudes [174, 242]. With the default setting, the solution is found by iteratively excluding events and adjusting the detection:limit relative weight. The final results presented in Figure 5.4 to Figure 5.7 exclude SN 2009ip and

SN 2010jl because of their unusually strong UV excess especially at late times, and 10:1 for the detection:limit relative weight for setting a strong limit model that can almost

100% correctly classify detections. We note that, interestingly, X-ray sources [29, 128] were detected from SN 2009ip and SN 2010jl approximately corresponding to phases that UV excess over the boundary, which might explain their unusual UV excess behaviours.

We can trapezoidally integrate the UV excess from UVW2 to U bands for the pseudobolometric excess. Zero ﬂux outside the bandpass is assumed. Figure 5.8 shows the result. The values are relative to λFλ at peak in V band. These plots provide useful information to set an upper limit of the UV excess, especially if we only observe optical bands. For example, since SN 2005kd which emitted peak V band at ∼3×1039 erg s−1 A˚−1, Figure 5.8 suggests that the excess pseudobolometric luminosity at phase 0d from UVW2 to U is <1×1043 erg s−1. Then, we can set a lower limit by applying the optical photosphere blackbody. In another scenario, if some UV bands are observed, instead of using Figure 5.8, the upper limit boundaries estimated in Figure 5.4 to

Figure 5.7 can be applied to set the upper limits of missing bands in a similar fashion. We note that the excess limit drops below 10 % and 1 % by phase 10 and 28 days, respectively. 89

UVW2 101

1.19E 01x + 7.34E 01

d y = 10 0 n 10 Weight limit:detect = 1:10 a b SN2010al V

k SN2014G a 1 e 10 SN2010jl p

o SN2007pk

e SN2013fs x 2 u

l 10 SN2009ip f Excess normalized to SN2011ht SN2015bh 10 3 10 0 10 20 30 40 50 Phase in days

Figure 5.4: UVW2 excess. Dot = detection. Triangle = upper limit.

UVM2 101

1.08E 01x + 4.14E 01

d y = 10 0 n 10 Weight limit:detect = 1:10 a b SN2010al V

k SN2014G a 1 e 10 SN2010jl p

o SN2007pk

e SN2013fs x 2 u

l 10 SN2009ip f Excess normalized to SN2011ht SN2015bh 10 3 10 0 10 20 30 40 50 Phase in days

Figure 5.5: UVM2 excess. Dot = detection. Triangle = upper limit.

5.2.2.3 Color Evolution

In previous sections, our analysis relied heavily on the blackbody assumption. In a complicated scenario like CSI where the emission comes from multiple regions and from both 90

UVW1 101

7.38E 02x + 2.11E 01

d y = 10 0 n 10 Weight limit:detect = 1:10 a b SN2010al V

k SN2014G a 1 e 10 SN2010jl p

o SN2007pk

e SN2013fs x 2 u

l 10 SN2009ip f Excess normalized to SN2011ht SN2015bh 10 3 10 0 10 20 30 40 50 Phase in days

Figure 5.6: UVW1 excess. Dot = detection. Triangle = upper limit.

U 101

3.89E 02x + 1.01E 02

d y = 10 0 n 10 Weight limit:detect = 1:10 a b SN2010al V

k SN2014G a 1 e 10 SN2010jl p

o SN2007pk

e SN2013fs x 2 u

l 10 SN2009ip f Excess normalized to SN2011ht SN2015bh 10 3 10 0 10 20 30 40 50 Phase in days

Figure 5.7: U excess. Dot = detection. Triangle = upper limit.

thermal/non-thermal mechanisms, the validity of the assumption is uncertain. Without assuming a blackbody, we analyze the data by looking at the color indices instead.

Figure 5.9– Figure 5.11 show some selected color indices. Despite the diﬀerence in deﬁning phase 0d and events in the sample, the color evolution generally agrees with [242] that the UV-optical indices (e.g., UVM2-V ) evolving faster than UV-UV (e.g., UVW2- 91

Pseudobolometric UV Excess

100

10 1

SN2010jl SN2009ip 10 2 Detection Upper limit Pseudobolometric UV excess relative to peak V band fluxes Excess upper limit model 10 3 10 0 10 20 30 40 50 Phase in days

Figure 5.8: Pseudobolometric UV excess relative to λFλ peak V band. Triangle = upper limit. Other symbols are detections. Excess upper limit model comes from the SVM classiﬁers in each band integrated.

UVM2 ) or optical-optical (e.g., B-V ) ones. Moreover, UV-UV and optical-optical indices show less dispersion compared to UV-optical ones. This evidence might support that there are separate entities involved with the evolution of UV and optical emission.

We perform bootstrapping and fit the bin mean indices. For the UV-UV and optical- optical indices, they show approximately linear evolution with flat slopes of the flux ratios.

As shown in Figure 5.9 and Figure 5.11, the slopes are ∼0.001 and ∼0.01 per day. For

UV-optical indices, as shown in Figure 5.10, they have signiﬁcantly faster evolution during early-time post optical peaks at phase [0,20] days, equivalent to the UV excess phase. The evolution during the pre peak and beyond phase ∼20 days tends to be ﬂat. However, the

ﬂat evolution is inconclusive due to small sample size. We then ﬁt the fast evolution part with an exponential function indicated by the linear decay in magnitudes [174, 242]. The

ﬁt result is shown in the ﬁgure.

Moreover, we notice the significant variation in the UV-optical indices. Especially, some events (e.g., SN 2009ip and SN 2010jl) show almost flat evolution at some phases, while others (e.g., SN 2007pk and SN 2011hw) do not show the behaviour. Therefore, we cluster 92 the events into two groups: a slow cluster which shows flat UV-optical evolution at some phases, and a fast cluster which does not. Figure 5.12 shows the result. We note that some events in the slow cluster like SN 2009ip [128] and SN 2010jl [29] were detected bright X-ray sources corresponding to the flat phase. Whether the turning on of the X-ray emission in

CSI would relate to the ﬂat UV-optical evolution would require futher investigation.

We also investigate whether there is any correlation between the cooling rate of the optical photosphere and the presence of the ﬂat UV-optical evolution. By comparing the fast cooling regime of photosphere, the UV-optical evolution tends to be uncorrelated with the cooling rate. For example, SN 2007pk shows both fast UV-optical evolution and cooling rate

(∼500 K/day), while SN 2013fs shows fast UV-optical evolution but slow cooling rate (∼100

K/day). Also, SN 2009ip shows approximately ﬂat UV-optical evolution during [−10, 10]

days but its cooling rate was ∼200 K/day during [0,10] days, which is faster than SN 2013fs.

The uncorrelated UV-optical evolution and photosphere cooling rate also supports that UV

and optical components evolve separately.

In other words, the color evolution gives us some clues about the diﬀerent relative

cooling behaviour between the optical and UV components. We see evidence supporting

that these two components evolve separately. Understanding the relative evolution of UV

and optical components might be the key to understand CSI and its UV excess. Moreover, it

is evident that the ﬂat UV-optical evolution might correlate with the periods when the X-ray

emission is turned on in CSI, which would be interesting for a more detailed investigation

in the future.

We note that the results can be applied to estimate the UV or optical emission in

a missing band. For example, given an UVM2 observation, we can estimate UVW2 by

assuming the linear evolution as shown in Figure 5.9. Also, since the UV-optical evolution

tends to have a uniform shape across events (i.e., an almost constant ﬂux ratio during the

ﬂat phase, or an exponential evolution with constant rate otherwise), we might be able to

estimate the V band to some confidence if we can verify which phase the observed epoch 93 should be in. Or, we might simply apply both flat and non-flat evolution to set limits for the V band.

SN2010al PS15cww UVW2-UVM2 SN2014G SN2010jl 2.0 SN2007pk SN2013fs 1.8

2 PTF11iqb F

/ 1.6 SN2009ip 1

F SN2011ht 1.4 o i

t SN2015bh a

r 1.2 SN2009kr x u l 1.0 SN2010jp F SN2011hw 0.8 y = -4.06E-03 x + 1.10E+00 0.6 bin mean

10 0 10 20 30 40 50 Phase in days

Figure 5.9: UVW2 /UVM2 ﬂux ratio.

SN2010al SN2014G UVM2-V SN2010jl SN2007pk SN2013fs 101 PTF11iqb SN2009ip 2 F

/ SN2011ht 1

F SN2015bh 100 o i SN2009kr t a r

SN2010jp x

u SN2011hw l F SN2011iw 10 1 y = 3.04E+00 e 1.13E 01x bin mean

10 0 10 20 30 40 50 Phase in days

Figure 5.10: UVM2 /V ﬂux ratio. 94

SN2010al SN2014G SN2010jl B-V SN2007pk 2.25 SN2013fs PTF11iqb 2.00 SN2009ip

2 1.75 SN2011ht F

/ SN2015bh 1 1.50

F SN2009kr

i 1.25

t SN2010jp a r 1.00 SN2008iy x u

l SN2011hw F 0.75 SN2011iw 0.50 y = -1.63E-02 x + 1.60E+00 bin mean 0.25 10 0 10 20 30 40 50 Phase in days

Figure 5.11: B/V ﬂux ratio.

5.2.2.4 Single Band Evolution

Here, we investigate whether the light curve evolution of a single band can inform us

something about how SNe IIn evolve. Figure 5.13 and Figure 5.14 show the results for the

V and UVM2 bands with their bin means from bootstrapping. The data are normalized so

that for each band of each object the brightest epoch is at 0d and zero magnitude. We also

ﬁt the bin means starting from phase 0d with linear models, which show that UV emission

generally fades faster than optical one [174, 242]. Since the results from this analysis can

be interpreted as an increment of magnitude, we can apply them to extra/interpolate the

observations. For example, the increment of V band is approximately 0.03 mag per day.

However, we note that some events might have signiﬁcantly diﬀerent evolution, which makes this approximation is invalid. 95

UVM2-V SN2009ip SN2010jl 101 SN2011ht SN2011hw

2 SN2015bh F

/ PTF11iqb 1 F 100 o SN2007pk i t

a SN2009kr r SN2010al x u

l SN2010jp F SN2011iw 10 1 SN2013fs SN2014G

10 0 10 20 30 40 50 Phase in days

Figure 5.12: UVM2/V ﬂux ratio with clustering: fast and slow evolution. The slow evolving cluster shows ﬂat UV-optical change at some phases, while the fast evolving cluster does not.

5.3 Conclusion and Future Prospects

The results show promising and interesting implications we would achieve for continuing the investigation on the UV/optical properties of CSI SNe IIn. Despite the diverse behavior we see, there seems to be underlying uniformity to some degree such as the evolution of the blackbody temperature and the color evolution. These results might be able to extend the current SED model in the light curve ﬁtting software like MOSFiT.

Since our study focuses on understanding the UV excess phase, which is commonly observed during the optical peak of CSI SNe II, the present analysis supports that we might be able to understand the UV excess by treating it as a separate entity from the underlying

SN photosphere. In this study, we model the photosphere to dominate emission in optical

BVRI with a blackbody function. Despite some outliers, sensitivity to data calibration, and individuality, the mean values of photosphere blackbody temperature can explain overall data to some extent. The photosphere cooling rate of each object shows uniformity at phase 96

SN2010al SN2014G SN2010jl

V SN2007pk

0.0 SN2013fs PTF11iqb 0.2 SN2009ip 0.4 SN2011ht SN2015bh 0.6 SN2009kr 0.8 SN2010jp

1.0 SN2008iy SN2011hw 1.2 SN2011iw

1.4 y = 3.23E-02 x + 5.29E-02 bin mean 1.6

5 0 5 10 15 20

Figure 5.13: Single band V evolution, training set. Horizontal bar = range of each bin.

older than ∼10 days with ∼10 K/day as we refer as slow cooling rate. At earlier phases

from the slow cooling rate regime, most objects show faster cooling rate with ∼100 K/day,

and possibly even faster with ∼1000 K/day right after the shock breakout. Only a few

objects show the slow cooling regime extending from phase 0d to later times. We further

develop from the assumed blackbody photosphere to estimate the UV excess ﬂux density

in each band, and compute the pseudobolometric UV excess. By standardizing with the

ﬂuxes at the peak V band, the estimation can be practical applied in the future since we

are likely to constrain the peak optical value better than relying on, e.g., the explosion or

shock breakout date.

We have also analyzed by relaxing the blackbody assumption, and investigated the

light curve evolution in both color index and single band evolution. The color index shows

interesting implications when computing UV-optical indices. While UV-UV and optical-

optical evolutions show very slow evolution with small dispersion, UV-optical evolution is

more diverse and faster. This evidence supports that UV and optical ﬂuxes come from 97

SN2010al PS15cww SN2014G SN2010jl

UVM2 SN2007pk

0 SN2013fs PTF11iqb SN2009ip 1 SN2011ht SN2015bh

2 SN2009kr SN2010jp SN2008iy 3 SN2011hw SN2011iw 4 y = 1.82E-01 x + 2.76E-02 bin mean

5 0 5 10 15 20

Figure 5.14: Single band UVM2 evolution, training set. Horizontal bar = range of each bin.

diﬀerent components. Moreover, we identify two clusters, i.e., fast and slow evolving, from

the UV-optical indices. The rate of UV-optical evolution seems uncorrelated with the

cooling rate of photosphere temperature, being consistent with the separate UV and optical

components. Moreover, the almost ﬂat evolution of UV-optical indices observed in the slow

cluster might be correlated with the turning on of the X-ray emission from the interaction.

Overall, the evidence convinces that the key to understand CSI is by understanding both

the cooling rate of photosphere temperature and the rate of UV-optical color evolution.

We have a lot of information that is practically useful for estimating the UV excess.

We lay out some examples of how to use the information in each section. For extending the

SED model in the software like MOSFiT, we can deﬁne a photosphere blackbody SED for

BVRI bands and a diﬀerent description of UV SED evolving independently, but connecting

through the ﬂuxes at peak optical. If we are in the UV excess regime, that might last about

10 days after the optical peak or might be associated with the photosphere temperature 98 hotter than 10,000 K as suggested in literature [174, 242], estimating the UV ﬂuxes from the blackbody photosphere yields a lower limit, while our model provides an upper limit. To be more accurate about the estimation, it is possible to be done by including other constraints highlighted in this analysis. However, this would not be a simple modiﬁcation for MOSFiT.

At least, two important aspects would improve the analysis: the nature of being time- series events, and state parameters. We see the time-series effects during our estimation of the temperature cooling rates. Understanding the time-series properties would provide a better way to handle the problem, rather than using the pool statistics like mean. For the state parameters, they will connect us to a deeper level of the time-series properties, as they will determine how the time-series evolve rather treating the time-series as a stochastic process with trends. Moreover, the state parameters should be more associated with the physical parameters in CSI like the density profiles, that will provide us a better understanding of the underlying physics. Moreover, calibrating the data to remove effects like the extinction, and trying different ways to standardized each event might yield a more unified result. Since multiple pieces of information can be drawn independently, we should also develop a statistical framework that can account for all the constraints simultaneously.

A Bayesian approach, and machine algorithms like Recurrent Neural Network might be better frameworks to deal with this task.

We note that the analysis here assumes known redshift and the epoch at optical peak. Moreover, the analysis and models in this study are based mainly on empirical evidence, which provides us information regardless of underlying theories. These results would be useful inputs for theoretical development. Working together between theoretical and empirical studies is the challenge of future studies. 99 6 CONCLUSION

In this dissertation, I have tried to identify the power sources of SLSNe-I and SLSNe-

II. SN 2015bn and SN 2008es are my case studies of each class, respectively. The strong

CSI, like in SLSNe-IIn and SNe IIn, has diﬃculties matching observational evidence, mainly due to the lack of narrow Hα features in these classes. Therefore, alternatives have been proposed with magnetar spindown as the most preferred one. By following their late-time multi-wavelength emission behaviour, I acquired more evidence that helps to constrain the power sources.

For SN 2008es, multiple lines of evidence support CSI as the origin of power. The evidence includes a good ﬁt to the CSI model, strong emission of broad Hα, and evidence supporting dust formation in the CDS, which includes NIR excess with consistent blackbody properties expected for the scenario, and red-wing attenuated Hα proﬁle at relatively early times (<500 days). As the CDS is a product of strong shock interaction and is typically observed in SNe IIn, and also dust formation in the CDS is commonly observed in the events as well, my interpretation further supports CSI as the power source of SN 2008es despite the lack of narrow Hα emission. By following arguments in recent literature, I am able to show that the properties of SN 2008es are consistent with the scenario where its narrow Hα features were absent as the slow-moving CSM was shocked and accelerated to high velocity by the time of shock breakout. Despite the success in identifying strong CSI as the power origin of SN 2008es, it is still too early to conclude that this power origin is common across SLSNe-II, and our analysis cannot rule out if a central engine exists inside the massive hydrogen shell. More samples are required.

For SN 2015bn, previous evidence from the literature pointed out that the event, as well as other SLSNe-I, should have a central engine in the form of a spinning down magnetar.

However, this speculation cannot be confirmed due to the lack of direct evidence. One proposed smoking gun is the leakage of hard photons in X/γ-rays at late times, which I aimed to observe here. Without direct evidence to confirm, the expectation of the leakage 100 tends to be consistent with the observed increasing discrepancy with time between the expected total spindown luminosity and the observed UVOIR one. A magnetar spindown model with the leakage effects also fit very well to the data. I observed X-ray emission in SN 2015bn at ∼2 years as suggested by the X-ray ionization breakout model, which is believed to be the driving mechanism of the leakage at this timescale. The observation showed a non-detection with a deep limit of 0.3–10 keV X-rays that can constrain various

X-ray emission scenarios. For the magnetar scenario, together with my collaborative work that observed optical emission of the event at a similar epoch, I can constrain the observed emission in UVOIR plus 0.3–10 keV X-rays to be .3 % of the total spindown luminosity.

This result implies the missing energy problem that &97 % of the total spindown luminosity must be somewhere else besides the UVOIR and 0.3–10 keV X-ray emission. The analysis shows a consistent picture that at the observed epoch, the system had already evolved to the next stage where the leakage shifts to harder photons. I note that the conclusion here still cannot generalize to the population of SLSNe-I, and more samples are required at similar phases. Also, a multi-wavelength program that includes observing MeV–GeV photons simultaneously is advised for a future study.

Besides studying these two objects, I am motivated by SN 2008es, which was powered by CSI without the presence of narrow Hα emission. Therefore, I further investigated the UV/optical photometric properties in the strong CSI SNe. With various unknown properties, I focused on studying the UV excess phase which is typically observed in CSI

SNe around their optical peaks. The goals are to develop better understanding of the CSI mechanism, and model the SED during this UV excess phase in order to extend the current model for a more accurate description. I present our preliminary study on a subset of 15 SNe

IIn for their unquestionable power origins from the CSI. By decomposing the UV excess phase emission into a photosphere dominating optical BVRI range and UV component dominating UV range, I revealed underlying structures that are promising to pursue in the future. I performed various analyses using different sets of information and assumptions that provided useful constraints on the UV excess properties in various scenarios. I propose 101 how to extend the SED description in the software SED fitting tool like MOSFiT for a better approximation of the UV emission during the UV excess phase. Moreover, I find the key to understand the underlying CSI lies in the relative evolution between UV and optical emission, instead of each individual evolution.

In summary, this dissertation contributed to the existing body of knowledge about the power sources of SLSNe. SLSNe would also be particularly important objects in the future because they would serve us as beacons from the distant universe, thanks to their very brightness at peaks. SLSNe-II and SLSNe-IIn which are strongly interacting SNe would be the best beacons because of their very bright UV at peaks that would be observed in optical bands due to the cosmological redshift. With coming technologies like LSST, JWST, and WFIRST, more than hundreds to thousands of SLSNe are expected to be discovery annually [179, 214, 216, 226]. 102 References

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