Spectral Analysis of Supernove using SYNOW

Mr. Sambit Kumar PandaM.Sc Astrophysics, Pondicherry University

IAS0108Guide: Dr. Firoza Sutaria

IIA, Bangalore

11th July, 2014

Contents

0.1 Introduction to Supernovae . . . . . . . . . . . . . . . . . . . . . 10.1.1 Types of Supernovae . . . . . . . . . . . . . . . . . . . . . 10.1.2 Massive star core collapse sequence . . . . . . . . . . . . . 3

0.2 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50.3 Line Formation and Synthetic Spectrum Codes: SYNOW and ES 6

0.3.1 Sobolev Approximation . . . . . . . . . . . . . . . . . . . 70.3.2 SYNOW . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80.3.3 ES: Elementary Supernova Spectrum Synthesis or Ex-

tended SYNOW . . . . . . . . . . . . . . . . . . . . . . . 130.4 Conclusion and Discussion . . . . . . . . . . . . . . . . . . . . . . 190.5 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

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Certificate

This is to certify that Mr. Sambit Kumar Panda(M.Sc. Astro-physics, 2nd year, Pondicherry University) did this project: “SpectralAnalysis of Supernovae using SYNOW” as a part of the IIASummer Programme-2014 at IIA, Bangalore under the guidance ofDr. Firoza Sutaria(IIA, Bangalore).

BGS: Guide:

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Acknowledgement

I extend my sincere thanks to Dr. Firoz Sutaria for being a constant supportand guide to me throughout this Summer Programme. Without her motivationand guidance I could never have completed this project. I would also like tothank the Board Of Graduate Studies, IIA and all the related members andofficials who helped organise this Summer Programme-2014 at IIA, Bangalore.It was really enlightening and fruitful for all the participants including me. Last,but not the least, I would like to thank Mr. Anish, Head at the Data Center,IIA and the all the support staff at Data center for helping me install all therequired softwares and packages for my project and taking care of all the techicalissues of all the participants of the summer programme.

Sambit Kumar Panda(IAS0108)M.Sc Astrophysics, 2nd Year,Pondicherry University

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Abstract

Supernovae are one of the most energetic explosive events known in the Universe.These occur at the end of a star’s lifetime, when its nuclear fuel is exhausted andit is no longer supported by the release of nuclear energy. A star can go super-nova in two ways: (i) by accreting matter from a close companion evolved starwhich finally leads to thermonuclear runaway and (ii) by gravitational collapse,if the stellar core is too massive(> 1.4M�). The supernovae are classified asthermonuclear runaway or core collapse on the basis of the above two processesrespectively. Observationally, major difference between Type Is and Type IIsis the presence of Hydrogen(H) in the spectra of Type IIs but not in Type Is.We present here the spectral study of a type IIb supernova SN 2011dh whichwas discovered near the ’Whirlpool’ galaxy M51 (D≈ 8.5 Mpc) using a softwarecalled SYNOW. I will discuss the direct analysis of this spectra using mod-els of radiation transfer in the moving supernova ejecta in terms of the simpleSobolev approximation (Branch et al. 1997), assuming spherical symmetry andhomologous expansion.

0.1 Introduction to Supernovae

Supernovae result from the explosion of massive stars(> 8M�). These are one ofthe most violent events in the universe, and the force of the explosion generatesa blinding flash of radiation, as well as shock waves analogous to sonic booms.The energy released during the process is of the order of 1×1051 ergs/sec. Theseexplosions often leave behind structures which are called Supernova Remnants.These remnants are bounded by an expanding shockwave, and consists of ejectedmaterial expanding from the explosion, and the ISM it sweeps up.The typicalISM temperatures are of the order of 10,000 K. The synthesis of the heavyelements is thought to occur in supernovae, that being the only mechanismwhich presents itself to explain the observed abundances of heavy elements.

0.1.1 Types of Supernovae

Supernovae are divided into two basic physical types:Type Ia: These result in some binary star systems in which a carbon-oxygen

white dwarf is accreting matter from a companion. In a popular scenario, somuch mass piles up on the white dwarf that its core reaches a critical densityof 2 × 109 g/cm3. This is enough to result in an uncontrolled fusion of carbonand oxygen, thus detonating the star in a thermonuclear runaway process.

Type II: These supernovae occur at the end of a massive star’s lifetime,when its nuclear fuel is exhausted and it is no longer supported by the releaseof nuclear energy. If the star’s iron core exceeds Chandrasekhar Mass, it willcollapse and become a supernova.

However, supernovae were originally classified based on the existence of hy-drogen spectral lines: all Type I spectra do not show hydrogen lines, while TypeII spectra do.

In general this observational classification agrees with the physical classifi-cation outlined above, because massive stars have atmospheres that are made ofmostly hydrogen, while white dwarf stars are bare. However, if the original starwas so massive that its strong stellar wind had already blown off the hydrogenfrom its atmosphere by the time of the explosion, then it too will not showhydrogen spectral lines. These supernovae are often called Type Ib supernovae,despite really being core collapse supernovae like other Type II class of super-novae. The above classification has been modified over the years and here is themodern Supernovae Taxonomy:

• Type I : No Hydrogen

– Type Ia: Presents a singly ionized silicon (Si II) line at 615.0 nm(nanometers), near peak light

– Type Ib/c: Weak or no silicon absorption feature

∗ Type Ib: Shows a non-ionized helium (He I) line at 587.6 nm

∗ Type Ic: Weak or no helium

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• Type II: Shows Hydrogen in the early spectra The further classification isbased on light curves and some spectral characteristics as follows:

– Type II-P/L/N/: Type II spectrum throughout

∗ Type II-P/L: Only braod features and clear p-cygni profiles· Type II-P: Reaches a ”plateau” in its light curve· Type II-L: Displays a ”linear” decrease in its light curve (lin-

ear in magnitude versus time).

∗ Type IIn: Lightcurve has a broad slowly decaying hump andthe presence of narrow lines suggests that tere is a slow movingcircumstellar medium surrounding it.

– Type IIb: Spectrum changes to become like Type Ib

Type II supernovas occur in regions with lots of bright, young stars, such asthe spiral arms of galaxies, with massive star forming regions. They apparentlydo not occur in elliptical galaxies, which are dominated by old, low-mass stars.Since bright young stars are typically stars with masses greater than about 10times the mass of the sun, this and other evidence led to the conclusion thatType II supernovae are produced by massive stars.

Some Type I supernovas show many of the characteristics of Type II super-novas. These supernovas, called Type Ib and Type Ic, apparently differ fromType II because they lost their outer hydrogen envelope prior to the explosion.The hydrogen envelope could have been lost by a vigorous outflow of matterprior to the explosion, or because it was pulled away by a companion star.

Core-Collapse Supernovae The general picture for Type II, Type Iband Type Ic supernovas - also called core-collapse supernovae - goes somethinglike this. When the nuclear power source at the center of core of a star isexhausted, the core collapses. In less than a second, a neutron star (or a blackhole, if the star is extremely massive) is formed. The formation of a neutron starreleases an enormous amount of energy in the form of neutrinos and heat, whichreverses the implosion. All but the central neutron star is blown away at speedsin excess of 50 million kilometers per hour as a shock wave races through thenow expanding stellar debris, creating some heavier elements by rapid captureof free neutrons and producing a brilliant visual outburst that can be as intenseas the light of several billion Suns.

Thermonuclear Supernovas Type Ia supernovas, in contrast, are ob-served in all kinds of galaxies, and are produced by white dwarf stars, the con-densed remnant of what used to be sun-like stars. A white dwarf star, a denseball primarily composed of carbon and oxygen atoms, is intrinsically the moststable of stars, as long as its mass remains below the so-called Chandrasekharlimit of 1.4 M�.

If, however, accretion of matter from a companion star or the merger withanother white dwarf, push a white dwarf star over the Chandrasekhar limitof 1.4 M�, the temperature in the core of the white dwarf will rise, triggeringexplosive nuclear fusion reactions that release an enormous amount of energy.The star explodes in about ten seconds, leaving no remnant. In both the core

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collapse and thermonuclear runaway cases, radioactive nickel produced in theexplosion decays into cobalt and then iron.

0.1.2 Massive star core collapse sequence

Consider an “evolved” star, one which has evolved off the main sequence havingmass M.At some point the pressure due to electron degeneracy becomes impor-tant(which actually stops the gravitational contraction in case of white dwarfs).This is the pressure which results from electrons being forced to higher-energystates due to the Pauli exclusion principle, which applies to all fermions(spin= 1

2 h particles) such as electrons or neutrons. Now if M < 1.4M�, then theelectron gas is non-relativistic, and the electron pressure is ∝ n

53 , where n is

the electron number density, and the star is stable under gravitational collapse.The fate of such a star is a white dwarf. However, if the evolved mass is < 1.4M�, then the electron gas is relativistic, the electron pressure is ∝ n 4

3 , and thestar is in unstable equilibrium with the gravitational pressure. Eventually, anunstable equilibrium always moves toward a stable equilibrium at with lowerpotential energy configuration. A massive, evolved star would eventually havea core temperature of ∼ 5 × 109 K and a density of 3 × 1010kg/m3. Theaverage thermal kinetic energy of nucleons is then ∼1 MeV and the Boltzmanndistribution extends to sufficiently high energy to allow fusion of nuclei up tonickel and iron. After iron, it is energetically unfavorable to go to higher atomicnumber, so the massive star develops an iron core with silicon burning in thenext sub-shell outward in radius. The silicon eventually ends up as iron, too, butafter about one day this fuel is exhausted. Our massive star is now in unstablemechanical equilibrium, supported only by the electron degeneracy pressure.

The following describes what is thought to be a typical sequence of eventsfor the collapse of a massive star, resulting in a supernova event:

1. After fusion processes fizzle out, there is some gravitational collapsewhich causes heating to T ∼ 1010K. This is sufficient to trigger two processes:(i) Photo-disintegration of iron and the subsequent photo-disintegration of theproducts, eventually leading to complete “inverse fusion,” with products p andn:

γ + Fe56 ←→ · · · → 13He4 + 4n; γ +He4 → 2p+ 2n (1)

(ii) Inverse beta decay. When electrons have K > 3.7 MeV then the followingcan occur:

e− + Fe56 →Mn56 + νe (2)

and by the time we get down to nucleons

e− + p→ n+ νe (3)

Note that the Fermi energy of the degenerate electron gas is ≈ 4 Mev at adensity of 1012kg/m3, so there are plenty of electrons which can trigger suchinverse beta decays.

2. The processes above are endothermic, that is they remove kinetic en-ergy (and hence fluid pressure) from the core. The unstable core now quicklycollapses.

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3. The iron core is now in free fall. The time of fall to a much smallerequilibrium radius is ∼ 100ms.

4. During collapse, the neutronization processes in Eqs. 1 and 2 proceedrapidly. Neutrinos result as well, and these mostly exit the star. This neu-trino emission represents about 1% to 10% of the total emission, the remainderresulting from subsequent steps.

5. The collapse ends when the core reaches nuclear density. Actually, thedensity exceeds nuclear briefly by what is estimated to be a factor of 2 to 3.

6. The core now strongly bounces back to nuclear density from the super-nuclear density. We can think of the protons and neutrons as bags of quarksbound together by very strong springs (spring constant ∼ 10GeV/fm2 whichare compressed by the collapse, but then spring back to equilibrium, thus thebounce.

7. The bounce sends a shock wave outward at high velocity, blowing off theremaining stellar atmosphere in the process. One the shock reaches the outeratmosphere, the photons emitted by recombination, powered by the shock itselfand by subsequent nuclear decays, become the visible supernova explosion.

8.The core will radiate away its huge energy content in neutrinos and theremnant core will settle down into a neutron star. The radius is something like15 km, depending on initial core mass, but has a mass of 1.4 M� to about 3M�.

9. The neutron-rich shocked ejecta, meanwhile, will induce creation of ele-ments heavier than iron by neutron capture.

10. The shock continues into interstellar space at speeds of ∼ c/10. Forexample, the crab neubula, resulting from the 1054 A.D. supernova is large andstill expanding.

11. The neutron star may become visible in radio as a pulsar, depending onrotation and magnetic fields. The crab’s neutron star is indeed a very “loud”pulsar, faithfully producing a radio burst once per revolution, every 33.3 ms.

The visible-light luminosity of a typical supernova is roughly 1042J/s, witha peak power of 1036J/s. This is about a factor of 1010 greater than solarluminosity, which is comparable to the entire galaxy. The visible light decaysexponentially as unstable nuclei decay, so the supernova is visible for weeks,depending on its location.

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Figure 1: Typical lightcurves of different types of supernovae. The peak of Type I is clearly higherthan Type II. Note the peculiar double peaks in the Type IIb supernovae which hydrogen in theearly days which depleted as gradually with expansion and the inner layers are revealed. The laterpart spectrum is mainly dominated by Helium

0.2 Data

The data used here is the spectrum of the Type IIb Supernova SN 2011dh whichwas discovered in the “Whirlpool” galaxy M51(∼ 7.0Mpc). The lightcurves aretaken from Marion et al. and Bose, Sutaria et al. are shown in the Figs [2]AND [3]. The spectrum was obtained from HCT by Dr. Sutaria et al.

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Figure 2: Lightcurves in different filters for SN 2011dh from Marion et al.2014 ApJ 781 69. Notethe second peak in the U band.

Figure 3: Lightcurves in different filters for SN 2011dh from Bose, Sutaria et al.

0.3 Line Formation and Synthetic Spectrum Codes:SYNOW and ES

For the Raditaive energy transport through a medium, in perfect thermody-namic equilibrium, with both absorption and emission, the basic radiative trans-fer equation in the plane parallel case, is given by:

dIλkλds

=dI

τλs

= −Iλ +ελκλ

= −Iλ + Sλ (4)

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where

Sλ =ελκλ

(5)

is called the source function. The above equation is easy to solve for stationarysystems, but the it becomes complicated in the case of supernovae in whichthere is a huge envelope of ejected material along with the photosphere whichis expanding homologously with time with a huge velocity gradient. To makethings simple, Sobolev came up with an approximate asymptotic method, theaccuracy of which is the higher, the larger the velocity gradient in the medium.his method is therefore sometimes called the high-velocity approximation orsupersonic approximation.

0.3.1 Sobolev Approximation

The essence of this approximation is that for large velocity gradients, as a resultof the shift between the resonance frequencies of the emitting and absorbingatoms, the radiative interaction at each point −→r of the medium is determinedmainly by its local vicinity. The characteristic size

so =vt

dv/ds(6)

of this vicinity equals the distance from the given point at which the aforemen-tioned shift in resonance frequencies equals the half-width of the profile of thecoefficient of absorption, determined by the thermal or turbulent velocity vt.For coarse estimates, the velocity gradient in this expression is usually replacedby the ratio v/R, where v is the characteristic velocity of large-scale motion ofthe medium and R is the characteristic size occupied by the emitting gas. As aresult, we obtain the approximate relation

so ≈R

(v/vt)(7)

The parameter so, which was subsequently called the Sobolev length, is the mainparameter of the theory of radiative transfer in moving media, characterizingthe size of the local vicinity of the point. In the case of supersonic motions wehave so � R, and the equation for source fucntion is

S(−→r ) = λ

∫v

K(−→r ,−→r ′)S(−→r ′)d−→r ′ + g(−→r ) (8)

in which K(−→r ,−→r ′) is the kernel determining the probability density of a transferof radiative excitation from the point −→r to the point −→r ′, λ is the probabilityof survival of a photon in a single scattering, V is the volume of the spacefilled with atoms, and g represents the primary sources of excitation in the lineunder consideration, admits of considerable simplifications. Assuming S(r′) ≈S(r) within the limits of vicinity and neglecting the influence of the boundaries,considering the medium fills an infinite volume of space,we get

S(r).[1− λ+ λβ(r)] = g(−→r ) (9)

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in which β is the probability of escape of a photon from the medium withoutscattering along the way:

β(−→r ) = 1−∫K(−→r ,−→r ′)d−→r ′ (10)

It should be noted that in a stationary medium the corresponding kernel func-tion is always normalized so that we have∫

K(−→r ,−→r ′)d−→r ′ = 1 (11)

This reflects the obvious fact that a photon emitted in an infinite medium willbe absorbed in it sooner or later.

As Sobolev showed, a fundamental difference in the process of radiative dif-fusion in a medium with a velocity gradient is that the normalization condition(11) is violated in this case and the integral of the kernel function over infi-nite space turns out to always be less than unity. This means that because ofclearing of the medium due to the Doppler effect, there is a nonzero probabilityof escape of a photon from a point of the medium lying formally at an infinitedistance from its boundary: β(∞) > 0. This property of the process of radiativediffusion in moving media lies at the foundation of Sobolev’s method.

0.3.2 SYNOW

SYNOW is a highly parameterized spectrum synthesis code used primarily fordirect (empirical) analysis of SN spectra. It was written by D. Branch andmodified later by A. Fisher in early 1990s. The code considers HomologousExpansion for the ejecta, where :

(i) the radial velocity v(r) of a matter element is a useful comoving coordinatewith actual radial position of the element given by r = v(r)t;

(ii) the density at any comoving point just scales as t−3;(iii) the photon redshift between matter elements separated by velocity ∆v,

∆λ = λ(∆v/c), is time independent; and(iv) the resonance surfaces for line emission at a single Doppler-shifted line

frequency are just planes perpendicular to the observer’s line of sight.If continuous opacity in the line forming region is disregarded, the profile of

an unblended line can be calculated when the line optical depth τl(v) and sourcefucntion Sl(v) are specified. Because SN ejection velocities (∼ 10000Km/s) aremuch larger than the random thermal velocities (∼ 10Km/s), a photon remainsin resonance with an atomic transition only within a small resonance region. TheSobolev approximation, that the physical conditions other than the velocity areuniform within the resonance region, usually is a good one, and it allows theoptical depth of a line to be simply expressed in terms of the local numberdensities of atoms or ions in the lower and upper levels of the transition:

τl =πe2

mecfλtnl

(1− glnu

gunl

)= 0.229fλµtdnl

(1− glnu

gunl

), (12)

where f is the oscillator strength, λµ is the line wavelength in microns, td is thetime since explosion in days, and nl an nu are the populations of the lower and

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upper levels of transition in cm−3. The term in brackets is the correction forstimulated emission. The source function is

Sl =2hcλ3

(gunlglnu

− 1)−1

(13)

All of the radial dependence of τl and Sl is in the level populations. The specificintensity that emerges from a resonance region is

I = Sl(1− e−τl) (14)

Spectroscopic evolution can be divided into a photospheric phase when theSN is optically thick in the continuum below a photospheric velocity, and asubsequent nebular phase during which the whole SN is optically thin in thecontinuum. In the photospheric phase line formation occurs above the photo-sphere and in the nebular phase throughout the ejecta. There is, of course, nosharp division between the two phases. However, spectral synthesis modelingtechniques in the photospheric and nebular limits can make use of different ap-proximations which are adequate for those limits. We will be focusing on thephotospheric phase in this project and will present the outputs of the code forthe photospheric phase.

During the photospheric phase a continuum radiation field is emitted by aphotosphere which can be idealized as an infinitely thin layer. Above the photo-sphere the radiation interaction with continuous opacity is small. Line opacityon the other hand can be very large for the strongest lines. The large Dopplershifts spread line opacity over a large wavelength interval increasing the effectof strong lines compared to a static atmosphere where such strong lines saturateand can only affect radiation in a narrow wavelength interval. The cumulativeeffect of many lines, strong and weak, can create a quasi-continuous opacityin the Eulerian frame. This effect has been called the “expansion opacity”;itdominates in the ultraviolet, where it effectively pushes the photosphere out toa larger radius than in the optical.

In the optical, which is our chief focus of analysis, the spectrum is charac-terized by P Cygni lines superimposed on the photospheric continuum. TheP Cygni profile has an emission peak near the rest wavelength of the line anda blueshifted absorption feature. The peak may be formed in part by trueemission or by line scattering into the line of sight of photons emitted by thephotosphere. The emission peak would tend to be symmetrical about the linecenter wavelength if not for the blueshifted absorption. The absorption is formedby scattering out of the line of sight of photospheric photons emitted towardthe observer. Since this occurs in front of the photosphere, the absorption isblueshifted. At early times the ejecta density is high, the photosphere is athigh velocity, and the line opacity is strong out to still higher velocities. Asexpansion proceeds, the photosphere and the region of line formation recededeeper into the ejecta. The P Cygni line profile width thus decreases with time.The minimum of the absorption feature of weak lines tends to form near thephotospheric velocity, thus weak lines (e.g., weak Fe II lines) can be used todetermine the photospheric velocity’s time evolution. The recession of the pho-tosphere exposes the inner ejecta and permits its analysis. The source functionof an unblended line can be given by Sl(v) = W (v)Iphot where W (υ) is theusual geometrical dilution factor and Iphot is the continuum specific intensity

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(assumed angle-independent) radiated by the photosphere. Given the pure res-onance scattering approximation for an unblended P Cygni line, the emissionis formed just by scattering into the line of sight and the absorption just byscattering out of the line of sight.

Unfortunately, in general there is strong line blending. A photon that isscattered by one transition can redshift into resonance with another, so theinfluence of each transition on others of longer wavelength must be taken intoaccount. This multiple scattering corresponds to the observer’s line blending. Itcan be seen that the absorption peaks are stroinger than emission peaks. Thusabsorption minima usually are more useful than emission peaks for making lineidentifications during the photospheric phase.

A special case of a P Cygni line that has become of interest is a “detached”line: i.e, a line that has a significant optical depth only above some detachmentvelocity that exceeds the velocity at the photosphere. A detached line consistsof a flat inconspicuous emission peak and an absorption having a sharp red edgeat the blueshift corresponding to the detachment velocity.

Figure 4: Detached and undetached H I lines at with vphot = 10,000 km/s. The dotted lines arefor Hydrogen layer velocities of 20,000 km/s(detached) and the solid lines for velocities of 10,000km/s(undetached)

Input file for SYNOW

The input file for SYNOW is given as “in.dat“ with various paramaters whichcan be defined by the user. The linelist refered by the code is the Kurucz LineList. The important input paramaters are as follows :

(1) vphot - Velocity at photosphere in km/s.(2) vmax - An artificially imposed upper boundary on the envelope in km/s(3) tbb - Blackbody temperature in K. The continuum emitted from the

photosphere is characterized by this temperature.

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(4) ea and eb - The lowest and highest wavelength to be considered respec-tively, in Angstroms.

(5) nlam - Number of wavelength points where the spectrum is computed.(6) flambda - Makes the output flambda vs lambda instead of fnu vs lambda

if set to .true.(7) taumin - Minimum line optical depth to select. The presence of a species

in the envelope is set by a nonzero optical depth in a reference line of the species(usually the strongest optical line).

(8) grid - Grid resolution. This number controls the number of radial pointsused in the calculation, and actually represents the radius of the photospherein grid points.

(9) stspec - Place to start actually computing the spectrum. This should belower than the value of ea

(10) pwrlaw - Optical depth in all lines is deployed spatially according tothis if set to “.true.”(according to pwrlwin-the powerlaw index), otherwise thedensity profile is exponential.

(11) numref - The number of reference optical depths (ions) that will bespecified at the end of the file.

(12) an - Atomic numbers of species to include in the calculation.(13) ai - Ionization stages of species included ( 0 = neutral, 1 = first ioniza-

tion, etc, up to ai = 5).(14) tau1 - Optical depth in the reference line of the corresponding (an, ai)

ion at vphot.(15) vmine - Lowest velocity in the envelope where the (an, ai) ion is present.

If vmine > vphot, we say the ion is “detached” from the photosphere. Unitsare in 1000’s of km/s.

(16) vmaxe - Highest velocity in the envelope where the (an, ai) ion is present.Units are in 1000’s of km/s.

(17) ve - efolding of the optical depths(18) temp - Excitation temp of the ion in 1000’s of K. This temp is the temp

used to determine all lines relative to the reference line, assuming BoltzmannExcitation.

Output from synow is found (after each run) in the file “fort.11”, in thethree columns of lambda - relative flux - blackbody flux.

RESULTS FROM SYNOW

Here we discuss some of the analysis and results obtained from SYNOW. It isalways a good practice to study the line formation with just a single ion in theinput file. This gives you the expected positions for the various atomic linesthroughout the spectrum. The relative strengths and doppler shifts can thenbe accounted for by changing the tau1 and vmine & vmaxe respectively for theions used. The output spectra may not be always upto the correct scale. So,we need to set the scales accordingly to overplot them with the data(usuallydone through GNUPLOT in this project). We can also try putting the sameion species with two different velocities to account for certain features. This isa good practice for the study of early days spectra but it may not be as fruitfulfor the later days spectra.

Fig [5] and [6] show the spectra of SN 2011dh after 36 days of explosion fittedwith the SYNOW output with single ions. Fig [4] compares the output with

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single and double layers of He I ions moving at different velocities. The detachedlines can be identified by the flat emission edges where as the undetcahed linesproduce clear p-cygni profiles. The synthetic spectra are not to the scales, butthe emphasis was given to the line positions and strengths.

Figure 5: The SN 2011dh spectrum after 36 days of explosion(green) fitted with synthetic spectrumfrom SYNOW(red) with only H I ions detached at 30,000 km/s and vphot = 10,000 km/s. The tbbis set to 7500 K

Figure 6: The SN 2011dh spectrum after 36 days of explosion(green) fitted with synthetic spectrumfrom SYNOW with single and double layers of He I ions. Single(red) He I is detached at 30,000km/s. In case of the double layers(indigo), one is detached at vmine= 34,000 km/s and the otheris undetached with vmine= 9000 km/s. vphot = 10,000 km/s and the tbb is set to 7500 K

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an 1 2 20 26 11ai 0 0 1 1 0tau1 15.0 15.0 15.0 1.0 4.0vmine 28.5 30.0 10.0 6.0 20.0vmaxe 36.0 35.0 20.0 15.0 30.0ve 4.0 4.0 3.0 3.0 3.0temp 13.0 13.0 10.0 10.0 15.0

Table 1: The various ions used and the related paramters for them used to get the spectra shownin fig [7]. The velocities are in 1000’s of km/s and the temp in 1000’s of K

Fig [7] shows the best fit we got from SYNOW with H I, He I, Fe II, Ca IIand Na I ions. Again the plots are not corrected for scales. The tbb used hereis 13000 K. The interesting to note is the absorption feature at ∼ 6400 A. It isbelieved to be produced by Hα transition as dicussed in various papers whichdealt with early days spectra of sn2011dh. Some other papers refered it to bedue to SI II ions. We tried to identify that feature and found that it may notbe due to the Hα. The arguement behind it is that when we tried to fit thatparticular feature with the combination of different ions, it was seen that theprofile was relatively independent of the presence of the H I ions. This is betterexplained in the future sections related to ES.

Figure 7: The SN 2011dh spectrum after 36 days of explosion(green) fitted with synthetic spectrumfrom SYNOW(red) using H I, He I, Fe II, Ca II and Na I ions. vphot = 12,000 km/s and vmax =35,000 km/s. The tbb is set to 13000 K. The scales used are mentioned in the legends. The inputparameters are listed in Table [1].

0.3.3 ES: Elementary Supernova Spectrum Synthesis orExtended SYNOW

This is an extended version of SYNOW with two parts : SYN++ and SYNAPPS.SYN++ is a rewrite of the original SYNOW code in modern C++. It has a few

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further enhancements, a new structured input control file format, and the atomicdata files have been repackaged and are more complete than what SYNOW has.The other part, SYNAPPS, uses the same underlying library code used to buildSYN++ to implement a spectrum synthesis calculation within the objectivefunction of a parallel optimization framework. So, SYNAPPS works like anautomated SYN++ and does the fitting work of the synthetic sectrum to thetarget spectrum. ES also uses atomic data lines(viz. Kurucz Line List).

The “syn++” executable requires one control file named as “syn++.yaml”as its arguement. It computes one or more synthetic spectra and writes them tostandard output. If more than one spectrum is output, they are separated by ablank line. The format is multi-column ASCII, with the first two columns beingwavelength and flux. By convention, all wavelength quantities in the SYN++and SYNAPPS control files are in Angstroms, all temperatures are in 103 K,and all velocities are in 103 km/s.

Components of “syn++.yaml”

Following are the different components of control file for syn++. The valuesmentioned against some of the parameters are for examples.

The “output” section controls the wavelength grid of the synthetic spec-trum::

output :min-wl : 2500.0 (minimum wavelength in A)max-wl : 10000.0 (maximum wavelength in A)wl-step : 5.0 (wavelength spacing in A)

The “grid” section controls the velocity, line opacity, and line source functiongrids::

grid :bin-width : 0.3 (opacity bin size in kkm/s)v-size : 100 (size of line-forming region grid)v-outer-max : 30.0 (fastest ejecta velocity in kkm/s)

These values were kept constant throughout our analysis. The v-outer-maxcan be set to a veru high value to impose an upper boundary to the ejecta.

The next section is the “opacity” section::opacity :

line-dir : /usr/local/share/es/lines (path to atomic line data)ref-file : /usr/local/share/es/refs.dat (path to ref. line data)form : exp (parameterization (exp or pwrlw))v-ref : 10.0 (reference velocity for parameterization)log-tau-min : -2.0 (opacity threshold)

The line-dir is the line-list path for reference. The value of ”v-ref” is thereference velocity for all opacity profiles, they are scaled to the value of ”log-tau”at this velocity (given by each profile in each setup). Any ions having log-taulower than log-tau-min are ignored.

Next is “spectrum” which controls how the output spectrum is calculated::spectrum :

p-size : 60 (number of phot. impact parameters for spectrum)flatten : No (divide out continuum or not)

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First is the number of impact parameter rays subtending the photosphere asviewed in projection from infinity. The “flatten” option computes the spectrumwithout the underlying thermal continuum or any warping parameters.

Each synthetic spectrum computation is governed by a “setup”. Multiplesetups can be placed into a SYN++ YAML control file. They are simply ex-pressed as YAML lists: Each setup is preceded on its first line by a “-” character.A sample setup is given below.

setups :- a0 : 1.0 (constant term)

a1 : 0.0 (linear warp term)a2 : 0.0 (quadratic warp term)v-phot : 8.0 (velocity at photosphere in kkm/s)v-outer : 30.0 (outer velocity of line forming region in kkm/s)t-phot : 12.0 (blackbody photosphere temperature in kK)ions : [ 1601, 2201, 2401, 2601 ] (ions :100*Z+I, I=0 is neutral)active : [ Yes, Yes, Yes, Yes ] (actually use the ion or not)log-tau : [ 0.1, 1.0, 1.0, 1.0 ] (ref. line opacity at v-ref)v-min : [ 10.0, 10.0, 10.0, 10.0 ] (lower cutoff in kkm/s)v-max : [ 30.0, 30.0, 30.0, 30.0 ] (upper cutoff in kkm/s)aux : [ 1.0, 10.0, 10.0, 10.0 ] (e-folding for exp form)temp : [ 10.0, 10.0, 10.0, 10.0 ] (Boltzmann exc. temp. in kK)

The parameters “a0”, “a1”, and “a2” are the coefficients of a quadraticwarping function that can be multiplied by the synthetic spectrum once it iscomputed. These values were never changed during the analysis. The rest of theparameters have the usual meaning as mentioned in the earlier section dealingwith SYNOW.

Results from ES

The similar initial procedures, as in SYNOW, were followed with ES also forthe line identification using single ions in the input file. As mentioned before,the interesting to note was the the two absorption features near ∼ 6300A and∼ 5600A. The first one was found out to be independent of the Hα transition,in contrast to the popular beliefs in many of the papers. This was confirmedby first obtaining the best fit for the profile near the region of 6300 A andthen testing the presence of Hydrogen by setting the H I ions on and off in twodifferent runs. By doing so, it was found that the feature is mostly a result ofline blending between Si II(6347 A) and He I(6560 A ) lines with a very minutecontribution from Hα which can be considered negligible. The disagreementwith the previous papers can be explained as follows: since it is a Type IIbsupernova, it might have shown Hα signatures in the early days sectra. Butsince our data is of 36-days after explosion, so we believe that by this time theHydrogen layer might have become very optically thin and thus the inner layersof He and Si are now exposed to the observer. Hence, the line blending of theseions would have resulted the observed absorption feature. The result is shownin Fig [8].

The second prominent feature observed is at ∼ 5600A. This feature can notbe explained by only He I(5876 A) transition. When we introduce Na I ionsinto the input ions list, the result is much better and the synthetic spectra gives

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a very good fit for the observed feature at 5600 A. This is depicted by the Fig[9].

Figure 8: The SN 2011dh spectrum after 36 days of explosion(green) fitted with synthetic spectrumfrom ES(red and blue) using H I, He I, Fe II, Ca II, Mg II and Si II ions. The red line is with Hand blue line is without H. It is clear that presence of hydrogen doesn’t affect the profile of theabsorption feature at 6300 A. Here, v-phot = 10,000 km/s and v-outer = 30,000 km/s. The t-photis set to 12,000 K. The scales used are mentioned in the legends. The input parameters are listedin Table [2].

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ions 100 200 2001 2601 1201 1401log-tau 1.0 -0.698 1.6 0.0 1.0 1.0v-min 30.0 20.0 10.0 10.0 10.0 10.0v-max 35.0 30.0 30.0 30.0 30.0 30.0aux 3.0 3.0 3.0 3.0 3.0 3.0temp 13.0 13.0 13.0 13.0 13.0 13.0

Table 2: Input ions and the related parameters for Fig [8]. v-phot = 10.0 kkm/s; v-outer = 30.0kkm/s; t-phot = 12.0 kK. The Hydrogen ion was simply set off in the next run keeping all otherparameters constant to check the absorption feature.

ions 100 200 2001 2601 1201 1401 1101log-tau 1.0 0.50 1.6 0.0 0.30 0.30 0.30v-min 10.0 11.0 10.0 10.0 10.0 4.0 8.0v-max 30.0 20.0 30.0 15.0 20.0 10.0 28.0aux 3.0 3.0 3.0 3.0 3.0 3.0 3.0temp 13.0 13.0 13.0 13.0 13.0 13.0 13.0

Table 3: Input ions and the related parameters for Fig [9] with sodium ions which gives the bestfit. v-phot = 10.0 kkm/s; v-outer = 30.0 kkm/s; t-phot = 6.0 kK. The Na I ion was simply set offin the next run keeping all other parameters constant to check the presence of Na in the absorptionfeature.

Figure 9: The SN 2011dh spectrum after 36 days of explosion(green) fitted with synthetic spectrumfrom ES(red and blue) using H I, He I, Fe II, Ca II, Mg II, Si II and Na I ions. The red line iswithout Na I and blue line is with Na I. It is clear that Na I gives a better fit to the feature at5600 A. Here, v-phot = 10,000 km/s and v-outer = 30,000 km/s. Settiing t-phot to 6,000 K givesa much better fit than fig [8]. The scales used are mentioned in the legends. The input parametersare listed in Table [3].

The other prominent features are at ∼ 3700A, due to the Ca II H & K lines,and at ∼ 5000A due to the Fe II(5169 A). Other Helium features(6678 and 7065A) can also be seen in the spectrum which are blueshifted to lower wavelengths.

Next we present the results of the synthetic spectra produced by ES to fitthe spectrum of 49 days after explosion. Here also we try all the ions as we used

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ions 100 200 2001 2601 1201 1401 1101 800log-tau 0.80 0.70 1.0 -0.20 0.30 0.30 0.70 0.50v-min 10.50 10.0 8.0 5.0 7.0 2.0 7.0 6.0v-max 30.0 27.0 28.0 15.0 27.0 6.0 24.0 26.0aux 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0temp 13.0 13.0 13.0 13.0 13.0 13.0 13.0 15.0

Table 4: Input ions and the related parameters for Fig [10] with Oxygen ions(O II) which gives thebest fit. v-phot = 8.0 kkm/s; v-outer = 28.0 kkm/s; t-phot = 4.0 kK. The O II ion was simply setoff in the next run keeping all other parameters constant to check the presence of O in the profileat 6000 A.

in the previous analysis but with lower values of t-phot, v-phot and v-outer.The ion velocities and optical depths are set accordingly so as to get the bestfit. We have tried to fit the spectrum with and without Oxygen, and it wasobserved that Oxygen gives a better fit for the feature seen at 6000 A. Theresult is shown in Fig [10] and the input parameters are listed in Table [4].

Figure 10: The SN 2011dh spectrum after 49 days of explosion(green) fitted with synthetic spectrumfrom ES(red and blue) using H I, He I, Fe II, Ca II, Mg II and Si II ions. The red line is with Oxygenand blue line is without Oxygen(O II). It is clear that presence of Oxygen improves the profile at6000 A. Here, v-phot = 8,000 km/s and v-outer = 28,000 km/s. The t-phot is set to 4,000 K. Thescales used are mentioned in the legends. The input parameters are listed in Table [4].

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0.4 Conclusion and Discussion

1. The supernova SN 2011dh is of Type IIb which might have shown H in itsearly days spectra(as discussed in some papers) but later the H content hasdepleted. This is evident from the Fig [6] where it is seen that the feature at∼ 6300A is most probably due to the lines blending of He I and Si II with veryweak contribution from H I which might have decreased as time passed.

2. The feature at ∼ 5600A is not just due to the He I(5876) line but due toits blending with Na I Line.

3. Using Fe II instead of Fe I gives better results in terms of describing thefeatures near 5000 A.

4. Due to some technical problems, we couldn’t use SYNAPPS for thefitting purpose. But we are currently working on it. We strongly believe thatthe results from SYNAPPS run would give a much better fit to the observedspectra.

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0.5 References

[1] G. H. Marion et al. 2014 ApJ 781 69: TYPE IIb SUPERNOVA SN 2011dh:SPECTRA AND PHOTOMETRY FROM THE ULTRAVIOLET TO THENEAR-INFRARED (for the lightcurve and SYNOW analysis).

[2] Bose, Sutaria et al.:(for the lightcurve).[3] David Branch, Jerod Parrent et al.: Probing the Nature of Type I Su-

pernovae with SYNOW.[4] David Branch, E. Baron et al. arxiv:astro-ph/011173v1 : Optical spectra

of Supernovae[5] Supernovae and Nucleosynthesis: David Arnett[6] Wikipedia websources on Supernovae

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