Is supernova iPTF15dtg powered by a magnetar?

Stockholm University

Department of Astronomy

Bachelor of Science Thesis

Is supernova iPTF15dtg powered by a magnetar?

Author:

Stuart West

Supervisor:

Jesper Sollerman

June 15, 2017

Abstract

iPTF15dtg is a supernova (SN) Type Ic (lacking hydrogen and helium in its spectrum) with a light curve indicating that it is the result of a massive star explosion. Taddia et al.(2016) sug- gested that the progenitor star was a Wolf-Rayet (WR) star that previously suffered strong mass loss. More recent observations show that the SN light curve did not decline as expected, indicat- ing the existence of an additional power source. One possibility is a magnetar, a hyper-magnetic neutron star capable of injecting its rotational energy into the light curve during relevant time scales. This bachelor thesis adds previously unpublished data to the iPTF15dtg light curve and compares simple semi-analytical models to rule out a radioactive scenario and discuss the possi- bility of a magnetar as the primary source of luminosity.

Contents

1 Introduction 2

1.1 Supernovae . . . . 2

1.2 Supernova light curves . . . . 5

1.3 Previous study of iPTF15dtg . . . . 7

1.4 Data collection . . . . 8

1.4.1 Pseudo-bolometric light curve . . . . 9

2 Models 11 2.1 Nadyozhin (1994) model . . . . 11

2.2 Arnett model . . . . 13

2.2.1 SN 2007gr with Arnett. . . . 14

2.2.2 iPTF15dtg with Arnett . . . . 14

2.3 Magnetar model . . . . 16

3 Spectral analysis 18

4 Alternative power source: ⁵⁷Co 21

5 Discussion 22

6 Conclusions 23

7 Acknowledgments 24

Bibliography 24

List of Tables 26

List of Figures 26

Appendices 27

1 Introduction

This bachelor thesis has been prepared between early April and early June 2017. The author’s contribution includes collecting previously unpublished photometric data from the intermediate Palomar Transient Factory (iPTF) collaboration and spectroscopic data from the Keck I tele- scope, together with previous data and results from Taddia et al. (2016) regarding supernova (SN) iPTF15dtg, and to analyze the findings. Several Python-based programs were written to produce light curve data, model fit-algorithms and create subsequent plots.

iPTF15dtg is a SN Type Ic (lacking hydrogen and helium in its spectrum). The initial study byTaddia et al. (2016) indicated that the post maximum light curve was declining as expected, given that the main source of power was the radioactive decay of ⁵⁶Ni →⁵⁶Co →⁵⁶Fe. More recent observations, however, show that the late time SN light curve did not decline as expected, indicating the possible existence of an alternative power source. This thesis discusses whether that alternative source might be a rapidly spinning, highly magnetized neutron star, i.e. a mag- netar.

1.1 Supernovae

A supernova is the explosion of a star that has a luminosity rivaling that of an entire galaxy.

Supernovae (SNe) are classified according to their their early spectra, light curves and spectral evolutions into two main types (I and II). Type I SNe are identified by their lack of hydrogen lines, while Type II SNe have hydrogen Balmer lines such as Hα λ6563 and Hβ λ4861 as can be seen in the spectrum labelled (b) in Fig.1 fromFilippenko(1997).

Figure 1: Spectra of SNe, showing early-time distinctions between the four major types and subtypes (Filippenko,1997).

Type Ia SNe are believed to be thermonuclear SNe. A typical spectrum is shown at the top of Fig. 1. If the progenitor star, a white dwarf, can accrete mass so that the Chandrasekhar limit (≈ 1.4 M) is exceeded, the star becomes unstable and a runaway thermonuclear process is initiated resulting in a supernova Type Ia explosion. At early times, within a few weeks of maximum brightness, SN Ia spectra are characterized by a deep absorption trough around 6150 Å produced by blueshifted Si II at wavelength ∼6355 Å (Filippenko,2004). The fact that SNe Type Ia explode with similar masses leads to the consequence that they have similar peak luminosities,

greatly simplifying distance estimates.

Figure 2 shows a flow-chart diagram indicating how SN classification is accomplished. The green color indicates thermonuclear SNe. Yellow is for stripped-envelope, core-collapse Type I SNe. Red is for Type II core-collapse SNe.

Figure 2: The most common SN types, as classified based on spectroscopic and photometric signatures. Noted references suggest the first use of the given classification (Nyholm,2017).

All SNe, except Type Ia, are core-collapse (CC) SNe, including Type I stripped-envelope SNe and Type II SNe. Current theory suggests that all zero age main sequence mass (MZAM S) stars of at least 8 solar masses (M) will end their existence in a CC SN explosion (Poelarends et al., 2008). These massive stars undergo a series of different nuclear burning processes, beginning with the fusion of four hydrogen (H) atoms into one helium (He) primarily via the CNO cycle and resulting in energy production. When core H is depleted, the CNO process stops, causing a core contraction that results in central densities and temperatures sufficient to ignite He-burning.

This process is called "Triple Alpha", which fuses three He atoms into one carbon (C) atom and energy. Oxygen (O), and more energy production, is formed if an additional He atom fuses with a C atom. H continues to fuse in a layer around the He core. As each successive core is depleted a new layer (or "onion skin") is formed within the star. Each new process requires higher pressures and temperatures and occurs on shorter and shorter time scales. The succession ends with the formation of an iron (Fe) core, as any further fusion process would be endothermic and thereby not able to create energy to counteract the inward pressure created by the gravitational force be- tween the core and the surrounding layers of Silicon (Si), O, Ne, C, He and H (e.g. Taddia,2014).

Massive stars with MZAM Sbetween 8 and 20 Mwill end their lives as red supergiants (RSG) with mass-loss rates on the order of ∼ 10⁻⁸to 10⁻⁶ M yr⁻¹. Stars with MZAM S& 25 Mwill end their lives as Wolf-Rayet (WR) stars, stripped of their H envelope and possibly even their He envelope. WR stars have typical mass-loss rates ∼ 10⁻⁵ M yr⁻¹ (Nugis and Lamers,2000).

Eventually, the iron core of a massive star reaches the Chandrasekhar limit (e.g. for MZAM S= 25 M, Mch= 1.79 M (Taddia,2014)) and begins to collapse. Neutrino emission, electron cap-

ture and photo-disintegration of Fe nuclei into He nuclei all accelerate the collapse. Gravitational potential energy is thereby converted into mechanical motion and heat. Fremling(2016) writes that the collapsing Fe bounces off a highly dense proto-neutron star, which is formed within the Fe core during the collapse, creating a strong outward-moving shock wave. This shock wave then propagates outwards through the stellar structure until it is predicted to stall due to energy loss via photo-disintegration. However, neutrino capture by densely packed protons and neutrons is predicted to inject the necessary additional energy to complete the explosive destruction of the star (Janka, 2012). Shock propagation then synthesizes various isotopes of Fe, Nickel (Ni), Titanium (Ti) etc., especially⁵⁶Ni. It has been shown by e.g. Cano et al.(2017) that the gamma photons produced by the subsequent radioactive decay of ⁵⁶Ni →⁵⁶Cobolt (Co), with a halflife of 6.1 days, followed by its decay to ⁵⁶Fe, with a halflife of 77.3 days, can well explain ensuing SN light curves. The gamma photons initially find themselves inside an expanding SN-ejecta and begin a complicated diffusion process involving, inter alia, Compton scattering off free electrons until resulting visible photons are able to escape into space. By 100 days post explosion, the bolometric light curve will normally decline according to the ⁵⁶Co → ⁵⁶Fe decay process until gamma rays are no longer completely trapped and thermalized within the ejecta. It is there- fore possible to use simple analytical models (e.g. Arnett,1982) to estimate parameters such as ejecta mass (Mej), initial mass of ⁵⁶Ni and kinetic energy of the explosion. More sophisticated hydrodynamical models (e.g. Blinnikov et al.,2000) are able to estimate additional parameters.

It is also known that SNe can interact with their circumstellar media (CSM), producing char- acteristic spectral signatures in the form of a narrow (small full width at half maximum (FWHM)) Hα emission lines due to the lower velocities of the CSM.Taddia(2014) writes that, due to the need to use a different set of physical principles to describe the shock physics involved, "CSM- interacting SNe can therefore sustain high luminosity for several years" (Taddia,2014).

Referring back to the flow chart in Fig. 2, one finds a great variety of SN classes. Figure3 shows a pie chart indicating the relative fractions of CC SNe from observations in a volume-limited sample (Shivvers et al.,2017).

Figure 3: Relative fractions of different CC SN types. 99 SNe were charac- terized as CC SNe (total database includes 180 SNe) (Shivvers et al.,2017).

The total fraction of stripped-envelope SNe is given as 30 ± 5 percent (Shivvers et al., 2017, p.21), while SN Ic is calculated to be only 8.5 ± 0.4 percent of all CC SNe.

As evidenced by its early spectrum, iPTF15dtg’s progenitor star lacked both H and He in its envelope prior to exploding. The origins of these so called "stripped-envelope" SNe are suggested

to be twofold. The first is a single massive "Wolf-Rayet" (WR) star, with MZAM S & 25 M and temperatures T& 30, 000 Kelvin (K), which has completely lost its H envelope. The second possible origin is a lower mass progenitor with MZAM S > 11 M (Taddia,2014, p.51), with its envelope stripped by a compact binary companion. Analysis of the stellar Initial Mass Function (IMF) suggests that a significant number of stripped-envelope SN progenitors should be massive stars in binary systems.

One interesting subclass of SN Ic is called "broad-line SNe Ic" (Ic-BL). These so called "hyper- novae" are classified by their fast expanding ejecta (vph& 20, 000 km s⁻¹) and can sometimes be associated with a long gamma-ray burst (GRB) or an X-ray flash (Taddia,2014). For instance, SN 1998bw (Ic-BL) was discovered at the same location and time as GRB 980425 (Galama et al., 1998).

Interesting stripped-envelope SN-characteristics are revealed by plotting SN-luminosity versus time in days (light curve). For instance, the number of days to reach peak has been shown to be lower in He-poor (Ic) than in He-rich CC SNe (Taddia et al., 2015). Spectral analysis can estimate the photospheric velocity of the ejecta as well as the metallicity. With a good estimate of Mej, one can then infer the form of the progenitor star using, inter alia, Fig.4.

Figure 4: Probability density functions of stripped-envelope SN types for Mej (Lyman et al.,2016).

Notice the three gray bands at the top of Fig. 4, which imply that most SN-progenitors are binaries and that single high mass progenitors tend to have ejecta masses (Mej)& 5 M.

So, in summary, we know that SNe Type Ic, like iPTF15dtg, are a rare type of CC SN representing only about 8.5 percent of the total. We also know that if the SN-progenitor is a single high mass star then it will have ejecta mass& 5 M.

1.2 Supernova light curves

Parameters that affect the shape of a stripped-envelope CC SN light curve are the ejecta mass (Mej), the mass of⁵⁶Ni, and the expansion velocity of the ejecta photospere (vph). Note, it is

common in other articles to use ejecta mass (Mej) and ejecta kinetic energy (Eej = ₁₀³× Mej× v²_ph) as the parameters. Increasing the ejecta mass should directly increase the diffusion time by making it more difficult for photons to scatter their way through the ejecta. Increasing the initial ⁵⁶Ni mass should increase the availability of the main source of power to the light curve, thereby increasing the curve’s total energy output (including the maximum value). Increasing the expansion velocity of the ejecta (v_ph) should directly decrease the diffusion time by reducing the ejecta density and thereby the number of scatters within the ejecta. Figure5 is a plot showing what happens when these parameters are adjusted one at a time.

Figure 5: Light curves generated with the Arnett model (see Sec. 2.2) with 3 variations of parameter shifts from the blue reference curve.

To conceptually understand the luminosity of a SN over time, one begins with a few assump- tions. First, if it is assumed that the main power source to the SN is the radioactive decay of

56Ni and that all of the gamma photons are trapped within the ejecta before escaping as visible wavelength photons. It is then expected that, if the amount of ⁵⁶Ni is halved, the entire light curve should be shifted down equivalently. Note how the green line is lower than the blue line in Fig.5.

Second, if it is assumed that a known mass of ejecta is homologous and symmetrical while expanding with a known photospheric velocity, and that the ⁵⁶Ni is located near the core of the ejecta, then it becomes possible to calculate the "effective diffusion time scale" (τm) for the power input from the⁵⁶Ni to diffuse its way through the expanding ejecta by using the following relationship (Cano et al.,2017).

τm≈ κ βc

¹₂ M_ej vph

¹₂

, (1)

where κ (opacity), β and c are constants and vph is the photospheric velocity. If the diffusion

phase of the light curve is approximated by a Gaussian (normal) distribution, then τm can be estimated by the FWHM of the light curve. Spectroscopic measurements of the photospheric velocity, together with a calculated value of the light curve FWHM, can then be used to estimate the ejecta mass using Eq. 1.

Note how a decrease in the photospheric velocity (purple line) widens the light curve FWHM, while a decrease in the ejecta mass (red line) makes the light curve FWHM more narrow in Fig.5.

It is therefore clear that the light curve is a useful tool in characterizing a SN.

1.3 Previous study of iPTF15dtg

Taddia et al.(2016) published an article titled, "iPTF15dtg: a double-peaked Type Ic Supernova from a massive progenitor". They collected optical photometry up to about 130 days post explo- sion date (t_explo = JD 2457333.448 ± 0.483). Ten spectra were taken with five different telescopes between +3 and +123 days. These data were analyzed using analytical and numerical models to determine that iPTF15dtg was a SN Type Ic that was spectroscopically normal, but had an early optical excess followed by a long (approx. 30 days) rise to maximum luminosity.

The host of the SN is an anonymous galaxy located in the constellation Triangulum at right ascension (RA) = 02^h:30^m:20.05^s and declination (DEC) = +37^◦:14’:06.7". Figure 6 shows clearly that the SN is not situated close to the galaxy center, obviating the possibility that other transient objects (e.g. "tidal disruptive events" (TDE) or "active galactic nuclei"(AGN)) are involved.

10" / 11.25 kpc

N

E

Figure 6: SN iPTF15dtg (marked by two lines at center) and its host galaxy taken with the Nordic Optical Telescope in g-band with the ALFOSC camera on day 64 post explosion (Taddia et al.,2016).

Taddia et al.(2016) used both an Arnett model (Arnett,1982) (to be described in Sec. 2.2) and a more complex hydrodynamical model, with initial parameters based on the Arnett results.

Pseudo-bolometric data were well fit with both models, yielding similar parameter values. The sole exception was the small difference in ⁵⁶Ni mass as noted in Table 1 below. This difference

arises because the hydrodynamical model allows for Ni-mixing, which is not possible in the sim- pler Arnett model.

A magnetar model was also invoked to fit the data points. However, the conclusion was that, since the SN was not superluminous, and since its spectra was typical for a SN Type Ic, the magnetar scenario was not favored.

Table 1 shows a compilation of important data and calculated parameters describing iPTF15dtg, which can be found inTaddia et al.(2016). The particular results used in modelling code for this project include, inter alia, the distance modulus µ = 36.83 mag. and the photospheric velocity of 6000 km s⁻¹.

Table 1: Results fromTaddia et al.(2016).

What? Value Units Comments

redshift (z) 0.0524 ± 0.0002 -

luminosity distance (DL) 232.0 Mpc

distance modulus (µ) 36.83 mag assumed: H₀=70.5 km s⁻¹ Mpc⁻¹, Ω_M=0.27, Ω_Λ=0.73

host extinction none mag no Na I D adsorption lines in SN spec.

MW extinction r-band 0.148 mag

MW extinction g-band 0.214 mag

metallicity [12+log(O/H)] 8.22 ± 0.20 galaxy at SN location

galaxy metallicity (Z/Z) 0.34 34 percent of solar metallicity light curve broadness ∆m15 0.34, 0.16, 0.11 mag g-, r-, i-band

max. Mr -18.3 mag

ejecta kinetic energy EK 2.2 ± 0.1 × 10⁵¹ erg

Mej 10.3 ± 0.6 M

M(⁵⁶Ni) 0.62; 0.42 ± 0.01 M hydrodynamical; Arnett models

M(⁵⁶Ni)/Mej ca. 0.04 - similar to other normal SNe Ic

Mf inal 12.1 M

MZAM S 35 M

56Ni mixing 97.5%

photospheric velocity (v_ph) 6000 km s⁻¹ from Fe II λ5169 P-Cygni min.

Taddia et al.(2016) concluded that, given the massive ejecta and the lack of H and He lines in its spectrum, the progenitor of iPTF15dtg was a massive (M_{ZAM S}& 35 M) WR star which over time lost about 23 Mvia stellar wind or transfer to an eventual binary compact companion, and exploded with a mass of about 12 M. The explosion then ejected about 10 M, leaving a remnant of about 2 M. These conclusions imply the simple stellar evolution shown in Table 2.

Table 2: The evolution of iPTF15dtg’s progenitor star (Taddia et al.,2016)

35 M = MZAM S 23 M lost via stellar wind or transfer to ev. binary companion 12 M = Mexplosion 10 M was then ejected in the SN-explosion

2 M = Mremnant likely a neutron star (pulsar or magnetar)

1.4 Data collection

SN iPTF15dtg was discovered on 2015-11-07 (JD 2457333.931) using the 48-inch Samuel Oschin telescope (P48) at the Palomar Observatory, located in north San Diego County, California. Sit- uated atop Mount Palomar (elevation 1,816 meters), the Palomar Observatory is operated by the California Institute of Technology (Caltech). P48 was used by the intermediate Palomar Tran- sient Factory (iPTF) project to scan the sky to identify, inter alia, potential SN candidates for

further study. iPTF is a scientific collaboration between Caltech; Los Alamos National Labora- tory; the University of Wisconsin, Milwaukee; the Oskar Klein Centre in Sweden; the Weizmann Institute of Science in Israel; the TANGO Program of the University System of Taiwan; and the Kavli Institute for the Physics and Mathematics of the Universe in Japan. The Palomar Observatory also employs a 60-inch telescope (P60) and a 200-inch telescope (Hale).¹

Absolute magnitudes used in this thesis were obtained using data collected with the P48 and the P60 telescopes. Point spread function (PSF) photometry and template subtractions were done using two different pipelines. The P48 data were prepared using the Palomar Transient Factory Image Differencing and Extraction (PTFIDE) pipeline with P48 reference images to subtract out the host galaxy light contribution Masci et al. (2017). The P60 data were prepared using the FPipe pipeline fromFremling et al.(2016) with Panoramic Survey Telescope and Rapid Response System (pan-STARRS) [Haleakala Mountain in Maui, Hawaii] reference images to subtract out the host galaxy light contribution. The g- and r-band photometry were used in this project. The resulting luminosity data, in the form of absolute magnitudes, error estimations, and days post explosion (Julian date minus texplo), are shown in Fig.7.

Figure 7: Absolute magnitudes for r- and g-bands, including error bars, as collected with the P48 and P60 telescopes.

P48 r-band measurements were not taken in the initial 130 days. Measurements were not taken between day 130 and day 279 after explosion due to solar conjunction. Given the good agreement between the P48 and the P60 data, the availability of P60 measurements in both bands for the majority of the SN-lifespan, and considering the larger aperture of the P60 telescope, only the P60 data were subsequently used in this project.

1.4.1 Pseudo-bolometric light curve

Lyman et al.(2014) shows that, by creating spectral energy distributions (SEDs), one can trans- form optical light curves to full bolometric light curves by using corrections based on optical

1www.ptf.caltech.edu/page/abouton 2017-05-09

colors (e.g. g − r). A bolometric correction (BC) is added to the absolute magnitudes from the selected base band measurements to arrive at the so called "pseudo-bolometric" absolute magni- tudes for each epoch. The main assumption is that flux emitted in regimes outside measurement windows must conform to the data set used to create the relevant correction relationship. It is also assumed that the fraction of light emitted outside of measurement windows is constant with time, even though g − r is time dependent. It is also important to note that the corrections are based on data limited to a maximum of 120 days past peak luminosity (Lyman et al.,2014).

Python code was written to perform the transformation. The first step was to make adjust- ments to the absolute magnitudes to account for Milky Way (MW) dust extinction. The r-band adjustment is +0.148 magnitudes, and the g-band adjustment is +0.214 magnitudes. These val- ues are found in Table 1 above, and can be derived using data sets available from the NASA/IPAC Infrared Science Archive.² Schlegel et al.(1998) andSchlafly and Finkbeiner(2011) describe how the MW dust extinctions were collected. The second step was to adjust the time frame of the data to the "rest frame" by multiplying each time in days by 1/(1 + z), where z is the redshift of the host galaxy. This small adjustment was done to put the data points into the same frame of reference (rest frame) with regard to the expansion of the universe, so that it is possible to make comparisons with other SNe. The third step was to create interpolated data points for the r-band that exactly match the measurement epochs for the g-band, followed by a calculation of g − r for each epoch. The g − r values were then used in the following formula as indicated by Lyman et al.(2014) in their eq. 6.

BCg= 0.054 − 0.195 × (g − r) − 0.719 × (g − r)² (2) Finally, the bolometric corrections, BCg, were added to the g-band values to arrive at the bolometric magnitudes. Error bars were then propagated. The resulting values are plotted together with the r- and g-band magnitudes in Fig.8.

Figure 8: Pseudo-bolometric absolute magnitudes and the BCgs used based on Eq. 2 are shown in blue.

2http://irsa.ipac.caltech.edu/applications/DUST/

Note that the late time BCgs are within the same range of values as the early time BCgs.

In order to perform model fits, it was necessary to transform the absolute magnitudes for the pseudo-bolometric light curve into luminosities (erg s⁻¹). This was accomplished using the following equation.

L_?= L₀× 10^{−0.4∗Mbol} (3)

Mbol is the star’s bolometric absolute magnitude, L? is the star’s luminosity, and L0 is the zero-point luminosity, which is 3.0128 × 10³⁵ ergs s⁻¹. The zero-point value was set by the International Astronomical Union (IAU) so that the Sun’s luminosity of 3.828 × 10³³ ergs⁻¹ corresponds to the commonly used value of 4.74 in absolute bolometric magnitude. Figure9is a scatter-plot of the resulting bolometric light curve.

Figure 9: Pseudo-bolometric light curve including error bars in erg s⁻¹

2 Models

Three different models were used to analyze the pseudo-bolometric light curve. TheNadyozhin (1994) model studies only the energy input by⁵⁶Ni radioactive decay. TheArnett(1982) model considers the effects of light diffusion through the ejecta from the⁵⁶Ni decay energy source. Fi- nally, a magnetar model as described byInserra et al.(2013) considers the effects of light diffusion through the ejecta from magnetic dipole spin-down energy deposition by a magnetar.

2.1 Nadyozhin (1994) model

The initial⁵⁶Ni that is naturally created in a SN explosion radioactively decays according to⁵⁶Ni

→⁵⁶Co →⁵⁶Fe and is typically found to power its post peak SN light curve. This mechanism is also implemented in the Arnett model (see Sec. 2.2). Python code was written according to equations 11 and 12 inNadyozhin (1994). These equations represent only the radioactive power

input with no consideration to the diffusion process of the gamma photons through the ejecta mass.

NCo= NN i(0)

 τCo

τCo− τN i



e^−(t/τCo)− e^{−(t/τN i)}

(4) N_{F e}= N_{N i(0)}



1 + τ_{N i} τCo− τN i

e^{−(t/τN i)}− τ_Co τCo− τN i

e^−(t/τCo)



(5) N stands for the total number of isotope nuclei. τ_{N i}(= 8.77 days) and τ_Co(= 111.3 days) are the radioactive lifetimes for ⁵⁶Ni and⁵⁶Co. The energy release for each decay process is estimated to be _{N i}= 3.90 × 10¹⁰erg s⁻¹ g⁻¹ and _Co= 6.78 × 10⁹ erg s⁻¹ g⁻¹ (Sutherland and Wheeler, 1984). Putting these values into Eqs. 4 and 5 makes it possible to plot the expected decay based on the initial⁵⁶Ni mass as shown in Figs.10and11.

Notice in Figs.10 and11, that up until about 15 days, the slope of the line is equivalent to the negative inverse of the ⁵⁶Ni lifetime while the ⁵⁶Ni to ⁵⁶Co process is dominant; and after about 20 days the slope is equivalent to the negative inverse of the⁵⁶Co lifetime since the⁵⁶Co to ⁵⁶Fe process is then dominant.

The initial mass of ⁵⁶Ni determines the vertical location of the decaying light curves as ex- pected. Mass estimates of the initial ⁵⁶Ni can therefore be selected to coincide with data from different epochs as can be seen in Figs.10and11.

Figure 10: Initial ⁵⁶Ni mass that fits maximum and 100 day luminosities

Figure 11: Initial⁵⁶Ni mass that fits post 300 day luminosities

Additional runs of the model in Fig. 10show that values in a range between 0.24 and 0.35 M were able to give reasonable fits to the early data (4 to 110 days).

Additional runs of the model in Fig.11show that values in a range between 0.9 and 1.5 M

were able to give reasonable fits to the late data (314 to 388 days).

Assuming that the above ranges each span out one standard deviation of normally distributed parameter values, it can be concluded that the early data and the late data are not explained simultaneously by the same set of parameters (p-value = 0.0017). Approximately four times the amount of initial⁵⁶Ni would be required to explain the late data.

2.2 Arnett model

In order to model the main peak of a SN,Arnett(1982) introduced an analytical model wherein SNe are powered solely by the radioactive decay of⁵⁶Ni →⁵⁶Co →⁵⁶Fe, and wherein the resulting gamma photons must scatter and diffuse through an expanding ejecta before being able to escape as visible wavelength photons. The exact formulation of the Arnett model used in this project can be found inCano et al.(2017) and is as follows. First, the model makes the following simplifying assumptions:

1. The expansion of the ejecta is homologous.

2. The ejecta is spherically symmetric.

3. The⁵⁶Ni is located at the center of the SN and does not mix.

4. Radiation pressure dominates.

5. The pre-explosion stellar radius is small (R0→ 0).

6. The diffusion approximation of photons is applicable.

The modelled luminosity, as a function of time, is then defined by the following set of equations (Cano et al., 2017).

L(t) = MN ie^−x2



(N i− Co) Z x

0

A(z)dz + Co

Z x 0

B(z)dz



1 − e^−Ct−2

(6)

A(z) = 2ze^−2zy+z2 (7)

B(z) = 2ze^{−2zy+szs+z2}, (8)

where

x ≡ t

τ_m, y ≡ τm

(2τ_{N i}), s ≡ τm(τCo− τN i)/(2τCoτN i). (9) τmis called the effective diffusion time as it determines the overall width of the light curve. τm

is estimated with the following equation:

τm≈ κ βc

¹₂ M_ej vph

¹₂

(10)

The final term, (1 − e^−Ct−2), is replaced in this model by the equivalent term from Sollerman et al. (1998):

(1 − 0.965e^{−(t/τ )−2}), (11)

where τ is the time when the gamma ray optical depth is equal to one, i.e. when leakage of the gamma rays begins to become important. Once the gamma rays are able to escape directly into space without interacting with the SN ejecta, the visual measurements of the SN luminosity should thereafter decrease according to this term.

The constants in Eqs. (6) through (10) are explained as follows. N i, Co, τN i and τCo have the same values as used in the Nadyozhin model. β ≈ 13.8 is a unitless integration constant.

κ = 0.07 cm²g⁻¹ is the opacity. c = 2.998 cm s⁻¹ is the speed of light in vacuum.

Of particular interest is the use of constant opacity (κ) in the Arnett model. Dessart et al.

(2016) dispute the use of constant opacity by arguing that opacity has complicated time and spa- cial dependencies, which may compromise the light curve rise time and width. However, Cano et al.(2017) refer toChugai(2000), who calculated that the sum of the Thomson and Rosseland opacities for free-free and bound-free transitions varies only slightly with radius. The opacity is therefore assumed here to be constant, allowing for faster computation (Chugai, 2000). The choice of κ = 0.07 is widely used (e.g. Cano et al., 2017) for SNe Ib/c since electron scattering is assumed to be the dominant source of opacity.

2.2.1 SN 2007gr with Arnett

The Arnett model has been used with relative success in other papers (e.g. Cano et al., 2017).

However, it would be of benefit to first check the method and code written for this project with data from a well-studied SN Type Ic, e.g. SN 2007gr (z=0.001728). As it exploded closer to Earth, more accurate luminosity measurements were available. Data (B- and I-band) were taken from the appendix from Hunter et al. (2009). The pseudo-bolometric light curve was created with equation 3 from Lyman et al. (2014). Python code written for this thesis then compared the bolometric data points within a selected range of ejecta mass and initial⁵⁶Ni mass, together with the photospheric velocity (10000 km s⁻¹) suggested byHunter et al.(2009), and chose the best fit by minimizing the least squares of the model versus actual photometry results. The red line in Fig. 12is the resulting plot.

As can be seen in Fig.12, the code written for the Arnett model is capable of matching data from both early and late epochs. Note that there is a small luminosity excess for a few days post peak and that the data set does not cover the extended number of days as seen with iPTF15dtg.

However, the results do point out the general accuracy of the model, even when data with smaller error bars are being compared.

Figure 12: Arnett model best fit for SN 2007gr.

2.2.2 iPTF15dtg with Arnett

The same Arnett model code was then used with the iPTF15dtg pseudo-bolometric data as shown in Fig.13. The code compared the bolometric data points within a selected range of ejecta mass and initial⁵⁶Ni mass, together with a fixed photospheric velocity (6000 km s⁻¹) as determined by Taddia et al.(2016), and chose the best fit results. The plot of the best fit model is indicated by the red line. The lmfit.minimize function calculated a one standard deviation parameter range which is then plotted using black lines. Finally, additional code was written to search through the above parameter space to choose parameters based on their resulting chi-square calculations. The parameters that resulted in reduced chi-squared values less than 1.7 have the following ranges:

8.0M  < Mej < 12.0 M and 0.25 M < M⁵⁶N i < 0.35 M. The chi-square limit of 1.7 was chosen to create models that span the error bars from data near maximum luminosity. These parameter models are plotted using grey lines. Figure13shows all these lines and the bolometric luminosities in one scatter-plot.

Figure 13: Bolometric data points together with best fit Arnett model results, where the model results from a one standard deviation range of parameter values are indicated by the black lines and the results from a chi-square <1.7 range are indicated by the grey lines.

The value of τ from Eq. (11) was set at the arbitrarily high value of 2,000 days, rendering Eq.

(11) = 1. Lower values of τ turn the late time model line downwards and thereby worsen the chi-square result. This indicates that, within the Arnett model, the eventual effects of gamma ray leakage were not recognized.

Notice also that the best fit result of⁵⁶Ni ' 0.28 M is equivalent to what was obtained in the Nadyozhin model fit. This is as expected since the two calculations both use the same atomic physics relationships and the effects of diffusion are substantially reduced by the time of peak luminosity in the Arnett model.

Additional runs of the model showed that values in a range between 0.25 and 0.35 M were able to give reasonable fits to the early data (< 100 days). Note that this range of initial M56N i

values is quite similar to the range found by the Arnett model above (0.24 and 0.35 M).

Recall also the results from the Nadyozhin model in Sec. 2.1, where four times the amount of initial⁵⁶Ni used to fit the early data were required to fit the late time data. The same relationship was confirmed by rerunning the Arnett model with a fixed value of 1.2 Mof initial⁵⁶Ni as shown in Fig. 14. Note that the subsequent best fit parameter of M_ej = 12 M only reproduces the actual light curve for the late time (> 300 days) and is a poor fit for the light curve as a whole.

Figure 14: Arnett model with initial⁵⁶Ni mass of 1.2 M

Clearly, the Arnett model is not able to fit the early and the late time iPTF15dtg bolometric light curve with the same set of parameters. The conclusion here is that radioactivity alone does not explain the iPTF15dtg light curve. One possible alternative explanation is a magnetar remnant, which is discussed in Sec. 2.3.

2.3 Magnetar model

Neutron stars are remnants of core collapse SN explosions with typical radii Rns ∼ 12 km and masses Mns ∼ 1.5 M, and are suggested to be primarily composed of degenerate neutrons at densities exceeding the nuclear matter saturation density of ρ0= 2.5 × 10¹⁴g cm⁻³(Staff et al., 2012). Rotational periods have been measured into the millisecond time scale, as well as up into the 10s of seconds range. Staff et al. (2012) discuss the relationship between the neutron star’s magnetic field strength and the two main spindown mechanisms, r-mode gravitational wave emis- sion and magnetic braking. Staff et al.(2012) point out that r-mode gravitational waves begin to be an important component in the overall braking rate as B drops below 10¹³ Gauss (G).

Essentially, if the neutron star magnetic field is above 10¹³ G, then magnetic braking will be the primary neutron star braking mechanism.

One popular measure of magnetic braking is called the "spindown rate" in units of periodic time decrease divided by time unit, i.e. unitless. Another way of describing the same mechanism is the "spindown timescale" in units of time (e.g. days), assuming a power law description of the braking (as used in Eq. 16 below).

Magnetars are a form of neutron star theorized to have magnetic field strengths of up to 10¹⁷ G, but are normally expected to be in the range of 10¹⁴ to 10¹⁵ G while rotating initially with millisecond timescale periods (Kouveliotou et al.,2003). However, well-characterized magnetars are commonly found to have rotational periods of 5 seconds or more (Kouveliotou et al., 2003), indicating that large amounts of rotational energy are dissipated during the early lifetime of a magnetar. Kasen and Bildsten (2010) used simple estimates of magnetar heating to conclude

that magnetars with magnetic fields in the range of B14= 1 − 10 (10¹⁴G) and initial spins in the range of Pi= 2 − 20 (ms) can power SNe with Lpeak∼ 10⁴³− 10⁴⁵erg s⁻¹(Kasen and Bildsten, 2010). These potential peak luminosity estimates are more than enough to match iPTF15dtg’s peak luminosity of L_peak= 3.8 ± 0.4 × 10⁴²erg s⁻¹.

For the sake of comparison, pulsars are another more common form of neutron star that are found to have significantly shorter rotational periods (from milliseconds to seconds) and signifi- cantly weaker magnetic fields.

Kasen et al. (2016) offers a possible explanation for magnetar energy dissipation. A long- lived, rapidly rotating and highly magnetized neutron star, denoted a "millisecond magnetar", continuously injects energy into a seemingly ordinary SN explosion (Kasen et al.,2016).

Inserra et al.(2013) proposes a set of equations based on four parameters (SN ejecta mass and its photospheric velocity, as well as the magnetar’s rotational period and magnetic field strength), which is incorporated into Python code that can produce theoretical light curves based on spin- down energy deposition into the SN ejecta by a magnetar.

Here is a summary of the magnetar model equations used by Inserra et al. (2013). The luminosity L(t) of a homologously expanding ejecta that is subjected to an absorbed power P(t) is derived with the same diffusion equations as used byArnett(1982) as well as other physically motivated relationships to be the following:

L(t) = e^−(t/τm)2 Z t/τ_m

0

P (t⁰)2(t⁰/τm)e^(t0/τm)2d(t⁰/τm) erg s⁻¹, (12) where:

τm= 1.05

 κ (βc)

1/2

M_ej^3/4E_k^−1/4 seconds (13) is the diffusion time-scale parameter, and where:

Ek= 3

10Mejv_ph² ergs (14)

is the kinetic energy of the expanding ejecta with uniform density, and where:

P (t) = 4.9 × 10⁴⁶B₁₄²P_ms⁻⁴ 1

(1 + t/τp)² erg s⁻¹, (15) and where B14is the magnetic field strength in 10¹⁴ G, and where Pms is the initial spin period in milliseconds, and where:

τp= 4.7 × B⁻²₁₄P_ms² days (16)

is the spindown timescale. The constants β, c and κ all have the same values as in the Arnett model in Sec. 2.2. Figure 15shows the plot of the magnetar model as per the above equations.

Figure 15: Best fit magnetar parameters give the red line. The two grey lines use the one sigma upper and lower bounds on the parameters.

As in the Arnett model, the lmfit.minimize function within the Python code calculates the one standard deviation ranges for each of the parameters. After an initial run of the program, the extreme parameter values were used to create model lines (in grey) to indicate the resulting one sigma spread of the model light curves.

Figure15shows clearly that there is good agreement between the best magnetar model results and the iPTF15dtg pseudo-bolometric light curve data.

3 Spectral analysis

As pointed out by Filippenko (1997), spectral analysis of a SN can be used to determine its classification. To create a spectrum, an observational slit is oriented across the grism in a way to minimize background interference. The signal along the slit is extracted by subtracting the galaxy background and the Earth’s sky lines from the measured flux per wavelength.

Taddia et al.(2016) analyzed ten different optical spectra from iPTF15dtg between day 3.2 and day 123.3 post explosion and concluded that the SN is a normal Type Ic. Figure 16is the spectral development of the SN over this time frame.

Figure 16: Spectral sequence of iPTF15dtg. Days post explosion are noted on the right. Important lines are noted with red markers. Spectra are de- redshifted but not corrected for extinction. The area subject to telluric water vapor interference is marked by a grey vertical ribbon (Taddia et al.,2016, fig.5).

A new spectrum of iPTF15dtg was taken with the Keck I telescope on 2016-10-31 (day 359.6 post explosion) and is shown in Fig.17with the spectrum from SN iPTF13bvn, a normal stripped- envelope SN (Type Ib), at day 346 taken with the Very Large Telescope (VLT) and the FORS2 (FOcal Reducer and Spectrograph) (Fremling et al.,2016).

Figure 17: Late time spectrum of iPTF15dtg taken with the Keck I telescope at Keck Observatory (Mauna Kea, Hawaii) compared to late time spectrum of iPTF13bvn taken with the VLT at Paranal Observatory (Cerro Paranal, Chile). Both spectra are normalized and de-redshifted.

Both spectra have pronounced broad emission lines from [O I] at λ6300 and [Ca II] at λ7291 and λ7324 indicating that iPTF15dtg’s spectrum is as expected at later days.

Figure 18: Typical late time spectra for different SN types (Filippenko,1997).

Notice in Fig.17that the iPTF15dtg narrow emission lines at 5006, 5985, 6043 & 6562 Å are not evident in the 13bvn spectrum. The 5006 line is likely from [O III] λλ 4959, 5007, which is

also evident at 123.3 days in Fig.16. The 6562 Å line is likely from H I λ 6562.85, which is most likely to originate from the host galaxy for three reasons: there is no H in a Type Ic SN; the line can also be seen in almost every epoch in iPTF15dtg (see Fig. 16); and the line is also seen in the typical late time Type Ic (or Ib) SN in Fig.18. The 5985 and 6043 Å lines are likely to be artefacts caused by cosmic ray interference.

Hypothetically, a SNe could interact with a hollow circumstellar media (CSM), causing an eventual late time light curve excess. The expectation would be that a narrow (small FWHM) H I emission line should emerge in the spectral sequence. No such increase in the H I narrow emission line is observed in the late time spectra shown in Fig.17. Furthermore, the late time development of the narrow [O III] line near 5006 Å is not considered to be a clear indication of CSM interaction.

The two conclusions here are:

1. The overall form of the late time iPTF15dtg spectrum is typical for a normal Type Ic SN.

2. There is no clear CSM interaction detected in the late time spectrum.

4 Alternative power source: ⁵⁷Co

For the purpose of completeness, one other radioactive decay power source was considered. Diehl and Timmes(1998) discusses SN 1987A, where⁵⁷Co was shown to become an important power source after about 1,200 days, as shown in Fig.19.

Figure 19: Late time light curve for SN 1987A (Diehl and Timmes,1998).

The Nadyozhin model used in Sec. 2.1, was modified to add the effect of ⁵⁷Co (lifetime = 391.2 days and released energy = 6.89 erg s⁻¹ g⁻¹Kozma and Fransson,1998) to determine the combination of initial masses, M(⁵⁷Co) and M(⁵⁶Ni) that would best fit the iPTF15dtg pseudo- bolometric light curve. Figure20shows the best fit result.

Figure 20: Nadyozhin model fit including⁵⁷Co and⁵⁶Ni as initial radioactive power sources.

Since the observed excess in iPTF15dtg was observed much earlier than when ⁵⁷Co became important for SN 1987A, and since the required initial mass of ⁵⁷Co (11 M) is more than the entire ejecta mass of SN iPTF15dtg, it is not possible for ⁵⁷Co decay to explain the iPTF15dtg late time light curve excess.

5 Discussion

Taddia et al.(2016) categorized iPTF15dtg as a CC SN Type Ic with a massive WR star progen- itor. Its light curve was considered to be broader than other SNe and had an interesting feature in the first days before reaching maximum, which was therein discussed at length. Otherwise, the light curve was behaving as expected. However, later luminosity measurements using the P48 telescope with the PTFIDE pipeline, as well as the P60 telescope with the FPipe pipeline, resulted in a late time light curve that remained at levels higher than expected. To create the pseudo-bolometric light curve, P60 r- and g-band absolute magnitude measurements were used in an approximation by Lyman et al. (2014), which was developed statistically based on light curves from similar SNe with luminosities up to about 123 days post maximum (Lyman et al., 2014, fig.1). Note that the bolometric corrections were created by extrapolating theLyman et al.

(2014) relationship out to almost 400 days. This extrapolation is reasonable since the blackbody temperature was shown byTaddia et al.(2016, fig.8) to have already stabilized near 6,000 K (with a maximum blackbody luminosity in the visible range) starting from 40 days post explosion and the computed bolometric corrections at late times were all well within the range of early time bolometric corrections, where the Lyman bolometric approximation is well-motivated.

This thesis project has thereafter employed two well known models to explore possible expla- nations for the unexpected measurements. The first one is a semi-analytical model introduced byArnett(1982), which is clearly described byCano et al.(2017), from where code was written utilizing two parameters: ejecta mass (Mej) and initial⁵⁶Ni mass. The photospheric velocity is a third parameter that was measured directly. Fits were produced based on a set of simplifying assumptions that allow for more robust numerical parameter scanning by simplifying the involved calculations.