ANALYSING THE SPECTROSCOPIC EVOLUTION OF SUPERNOVAE A Thesis submitted to Pondicherry University in partial fulﬁlment of the requirements for the award of the Degree of MASTER OF SCIENCE ASTROPHYSICS Submitted by SAMBIT KUMAR PANDA 13313007 Under the guidance of Dr. FIROZA SUTARIA IIA, BANGALORE DEPARTMENT OF ASTROPHYSICS PONDICHERRY UNIVERSITY PONDICHERRY 605 014 INDIA April 2014
Declared that the work presented in this dessertation is based on the original workdone by me under the guidance of Dr. FIROZA SUTARIA, Reader, IIA, Bangaloreand has not been included in any other thesis submitted previously for the award of anydegree.
Pondicherry [SAMBIT KUMAR PANDA]APRIL 2014
I extend my sincere thanks to Dr. Firoz Sutaria for being a constant support andguide to me throughout this M.Sc. thesis project. Without her motivation and guidanceI could never have completed this project. I would also like to thank the Board OfGraduate Studies, IIA and all the related members and officials for giving me thisopportunity to work under Dr. Firoza Sutaria and providing me with all the requiredresources and facilities for the smooth completion of the project. I would like to thankMr. Anish, System Admin at the Data Center, IIA for helping me install all therequired softwares and packages for my project and taking care of all the technical issuesrelated to the project. He was very patient in attending to all my doubts and problemsand was a real saviour at crucial times during the project work. Without his expertiseand guidance, I couldn’t have completed my work.
I would like to thank our respected Prof. K. Porsezian, Coordinator, Depart-ment of Astrophysics, Pondicherry University, for permitting me to do my projectat IIA, Bangalore and providing me with the best of the facilities and resources in the de-partment. I would also like to specially thank my Faculty Advisor, Dr. T. Pazhanivelfor his constant support and motivation through out the project work. I would like tothank Dr. G. Sakthivel for his un-flickering support and guidance though out thisproject work and for letting me miss occasional classes as and when required for theproject work. I would also like to thank all the faculty members for their support andmotivation in the project reviews and seminars. Their excellent suggestions and guidancehelped me shape my project in the best suitable manner. I would like to thank the Officeof Department of Astrophysics for providing me with best suitable environment andlab facilities required for the project work and helping me with the official proceedings.I would also like to thank my friends and classmates for their constant motivation andmoral support which kept me going in the darkest of hours.
Last, but not the least, I extend my sincere thanks and gratitude to God, for givingthe strength and intelligence to carry out this project work, and my parents, for theirblessings and prayers.
Supernovae are the most exotic and energetic events in the universe. For decades,people have tried to explain the occurence and evolution of such cataclysmic events re-sulting from the death of a star. Recently, a new and interesting field has emerged insupernova-research. Various SN research groups at different Institutes and Centers aretrying to develop supernova spectrum synthesis codes that would help us directly probethe supernova spectra. The spectra are often characterized by P-Cygni profiles, whichcontain both absorption and emission components of a line-excitation. This happens dueto the fast moving supernova ejecta, homologously expanding into the surrounding envi-ronment. Depending on the type of supernova, the evolution of the spectra differ fromone another.
In this project, I present the use of two such codes, called SYNOW and ES, devel-oped by D. Branch, A. Fisher and R.C. Thomas, which are 2-D simulations of SupernovaSpectrum using the Sobolev Aproximation. In section 2. Introduction to Supernovae, Iwill give a brief introduction to Supernovae, their types and mechanism through whichthey are formed, giving special emphasis on Core-Collapse Supernova. The section 3.Data describes about the data used in the project. In section 4. Line Formation andSynthetic Spectrum Codes: SYNOW and ES, I will describe about the underlying prin-ciples, Sobolev Approximation and the input files used in SYNOW and ES. I will alsodiscuss the results obtained from various runs from SYNOW and SYN++. Section 5.contains conclusions and future works to be carried out in this project.
This project is a mere understanding of a rather complex code which helps in under-standing the spectroscopic evolution of supernovae by directly probing the spectra usinguser-defined paramaters that contain the line formation under Sobolev Approximation.This can help in future Supernova research and 3-D simulation of supernovae explosions.
Supernovae are one of the most energetic explosive events known in the Universe. Theseoccur at the end of a star’s lifetime, when its nuclear fuel is exhausted and it is no longersupported by the release of nuclear energy. A star can go supernova in two ways: (i) byaccreting matter from a close companion evolved star which finally leads to thermonuclearrunaway and (ii) by gravitational collapse, if the stellar core is too massive(> 1.4M�).The supernovae are classified as thermonuclear runaway or core collapse on the basis ofthe above two processes respectively. Observationally, major difference between Type Isand Type IIs is the presence of Hydrogen(H) in the spectra of Type IIs but not in TypeIs. We present here the spectral study of two supernovae, SN 2011dh and SN 2013ej.While the former is of Type IIb, the later is of Type IIp whose light curve shows plateauin the later days after peak luminosity. The analysis is done using the famous supernovaspectrum synthesis codes SYNOW and SYN++. These codes interprete the supernovaspectra using models of radiation transfer in the moving supernova ejecta in terms of thesimple Sobolev approximation (Branch et al. 1997), assuming spherical symmetry andhomologous expansion.
2 Introduction to Supernovae
When a massive star explodes, it forms a supernova, releasing enormous amounts of en-ergy. Depending on the cause of explosion an formation, Supernovae are divided into twobasic physical types:
Type Ia: These result in some binary star systems in which a carbon-oxygen whitedwarf is accreting matter from a companion. In a popular scenario, so much mass pilesup on the white dwarf that its core reaches a critical density of 2 × 109 g/cm3. This isenough to result in an uncontrolled fusion of carbon and oxygen, thus detonating the starin a thermonuclear runaway process.
Type II: These supernovae occur at the end of a massive star’s lifetime, when it’s nuclearfuel is exhausted and it is no longer supported by the release of nuclear energy. If thestar’s iron core exceeds Chandrasekhar Mass, it will collapse and become a supernova.However, supernovae were originally classified based on the existence of hydrogen spectrallines: all Type I spectra do not show hydrogen lines, while Type II spectra do.
In general this observational classification agrees with the physical classification out-lined above, because massive stars have atmospheres that are made of mostly hydrogen,while white dwarf stars are bare. However, if the original star was so massive that it’sstrong stellar wind had already blown off the hydrogen from it’s atmosphere by the timeof the explosion, then it too will not show hydrogen spectral lines. These supernovae areoften called Type Ib supernovae, despite really being core collapse supernovae like otherType II class of super- novae. The above classification has been modified over the yearsand here is the modern 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
• Type II: Shows Hydrogen in the early spectra The further classification is based onlight curves and some spectral characteristics as follows:
# Type II-P/L: Only broad 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 magnitudeversus time).
# Type IIn: Lightcurve has a broad slowly decaying hump and the presence ofnarrow lines suggests that tere is a slow moving circumstellar medium surroundingit.
# Type IIb: Spectrum changes to become like Type Ib
Type II supernovae occur in regions with lots of bright, young stars, such as the spiralarms of galaxies, with massive star forming regions. They apparently do not occur inelliptical galaxies, which are dominated by old, low-mass stars. Since bright young starsare typically stars with masses greater than about 10 times the mass of the sun, this andother evidence led to the conclusion that Type II supernovae are produced by massivestars. Some Type I supernovae show many of the characteristics of Type II supernovas.These supernovae, called Type Ib and Type Ic, apparently differ from Type II becausethey lost their outer hydrogen envelope prior to the explosion. The hydrogen envelopecould have been lost by a vigorous outflow of matter prior to the explosion, or becauseit was pulled away by a companion star.
Core Collapse Supernovae: The general picture for Type II, Type Ib and Type Icsupernovas - also called core-collapse supernovae - goes something like this. When thenuclear power source at the center of core of a star is exhausted, the core collapses. Inless than a second, a neutron star (or a black hole, if the star is extremely massive) isformed. The formation of a neutron star releases an enormous amount of energy in theform of neutrinos and heat, which reverses the implosion. All but the central neutronstar is blown away at speeds in excess of 50 million kilometers per hour as a shock waveraces through the now expanding stellar debris, creating some heavier elements by rapidcapture of free neutrons and producing a brilliant visual outburst that can be as intenseas the light of several billion Suns.
Thermonuclear Supernovae: Type Ia supernovae, in contrast, are observed in allkinds of galaxies, and are produced by white dwarf stars, the condensed remnant of whatused to be sun-like stars. A white dwarf star, a dense ball primarily composed of carbonand oxygen atoms, is intrinsically the most stable of stars, as long as its mass remainsbelow the so-called Chandrasekhar limit of 1.4 M�. If, however, accretion of matter froma companion star or the merger with another white dwarf, pushes a white dwarf starover the Chandrasekhar limit of 1.4 M� , the temperature in the core of the white dwarfwill rise, triggering explosive nuclear fusion reactions that release an enormous amountof energy. The star explodes in about ten seconds, leaving no remnant. In both the corecollapse and thermonuclear runaway cases, radioactive nickel produced in the explosiondecays into cobalt and then iron.
2.1 Massive star core collapse sequence
Consider an evolved star, one which has evolved off the main sequence having mass M.At some point the pressure due to electron degeneracy becomes important(which actu-ally stops the gravitational contraction in case of white dwarfs). This is the pressurewhich results from electrons being forced to higher-energy states due to the Pauli ex-clusion principle, which applies to all fermions(spin = 1
2h particles) such as electrons or
neutrons. Now if M < 1.4M� , then the electron gas is non-relativistic, and the electronpressure 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 evolvedmass is < 1.44M� , then the electron gas is relativistic, the electron pressure is ∝ n
, and the star is in unstable equilibrium with the gravitational pressure. Eventually,an unstable equilibrium always moves towards a stable equilibrium with lower potentialenergy configuration. A massive, evolved star would eventually have a core temperature
of ∼ 5 × 109 K and a density of 3 × 1010 kg/m3 . The average thermal kinetic energyof nucleons is then ∼1 MeV and the Boltzmann distribution extends to sufficiently highenergy to allow fusion of nuclei up to nickel and iron. After iron, it is energetically un-favorable to go to higher atomic number, so the massive star develops an iron core withsilicon burning in the next sub-shell outward in radius. The silicon eventually ends upas iron, too, but after about one day this fuel is exhausted. Our massive star is nowin unstable mechanical equilibrium, supported only by the electron degeneracy pressure.The following describes what is thought to be a typical sequence of events for the collapseof a massive star, resulting in a supernova event:
1. After fusion processes fizzle out, there is some gravitational collapse which causesheating to T ∼ 1010 K. This is sufficient to trigger two processes:
(i) Photo-disintegration of iron and the subsequent photo-disintegration of the products,eventually leading to complete inverse fusion, with products p and n:
γ + Fe56 ←→ ...→ 13He4 + 4n; γ +He4 → 2p+ 2n (1)
(ii) Inverse beta decay. When electrons have K > 3.7 MeV then the following can 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 a density of 1012
Kg/m3 , so there are plenty of electrons which can trigger such inverse beta decays.
2. The processes above are endothermic, that is they remove kinetic energy (andhence fluid pressure) from the core. The unstable core now quickly collapses.
3. The iron core is now in free fall. The time of fall to a much smaller equilibriumradius is ∼ 100ms.
4. During collapse, the neutronization processes in Eqs. 1 and 2 proceed rapidly.Neutrinos result as well, and these mostly exit the star. This neutrino emission repre-sents about 1% to 10% of the total emission, the remainder resulting from subsequentsteps.
5. The collapse ends when the core reaches nuclear density. Actually, the densityexceeds 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 supernuclear den-sity. We can think of the protons and neutrons as bags of quarks bound together by verystrong springs (spring constant ∼ 10GeV/fm2 which are compressed by the collapse, butthen spring back to equilibrium, thus the bounce.
7. The bounce sends a shock wave outward at high velocity, blowing off the remainingstellar atmosphere in the process. One the shock reaches the outer atmosphere, the pho-tons emitted by recombination, powered by the shock itself and by subsequent nuclear
decays, become the visible supernova explosion.
8. The core will radiate away its huge energy content in neutrinos and the remnantcore will settle down into a neutron star. The radius is something like 15 km, dependingon initial core mass, but has a mass of 1.4 M� to about 3 M�.
9. The neutron-rich shocked ejecta, meanwhile, will induce creation of ele- mentsheavier than iron by neutron capture.
10. The shock continues into interstellar space at speeds of ∼ c/10. For example, thecrab neubula, resulting from the 1054 A.D. supernova is large and still expanding.
11. The neutron star may become visible in radio as a pulsar, depending on rotationand magnetic fields. The crabs neutron star is indeed a very loud pulsar, faithfully pro-ducing a radio burst once per revolution, every 33.3 ms.
The visible-light luminosity of a typical supernova is roughly 1042 J/s, with a peakpower of 1036 J/s. This is about a factor of 1010 greater than solar luminosity, which iscomparable to the entire galaxy. The visible light decays exponentially as unstable nucleidecay, so the supernova is visible for weeks, depending on its location.
Figure 1: Typical lightcurves of different types of supernovae. The peak of Type I is clearly higher than Type II. Notethe peculiar double peaks in the Type IIb supernovae with hydrogen in the early days which depleted as gradually withexpansion and the inner layers are revealed. The later part of the spectrum is mainly dominated by Helium
3 Spectrscopic Data Used in the project
Two different supernova data sets are used : one of Type IIb supernova SN 2011dhand the other one of Type IIp supernova SN 2013ej. The former was discovered in theWhirlpool galaxy M51(∼ 7.0Mpc). The lightcurves, taken from Marion et al. and Bose,Sutaria et al., are shown in the Figs  and . The spectrum was obtained from HCT,Hanle by Bose, Sutaria et al. The later is one of the brightest Type IIP supernova (SN) inthe nearby galaxy NGC 628 (distance ∼ 10 Mpc). The light curve is similar to a normalIIP SNe, but with a relatively shorter (∼ 85 day) and steeper (∼ 1.7 mag (100 d) 1 in V) plateau phase. The light curves (Fig ) and spectra are obtained by Bose, Sutaria etal using HCT, Hanle.
Figure 2: Lightcurves in different filters for SN 2011dh from Marion et al.2014 ApJ 781 69. Note the second peak inthe U band.
Figure 3: Lightcurves in different filters for SN 2011dh from Bose, Sutaria et al.
Figure 4: Lightcurves in different filters for SN 2013ej from Bose, Sutaria et al.
4 Line Formation and Synthetic Spectrum Codes:
SYNOW and ES
For the Raditaive energy transport through a medium, in perfect thermodynamic equi-librium, with both absorption and emission, the basic radiative transfer equation in theplane parallel case, is given by:
τλs= −Iλ +
= −Iλ + Sλ (4)
is called the source function. The above equation is easy to solve for stationary systems,but it becomes complicated in the case of supernovae in which there is a massive envelopeof ejected material along with the photosphere which is expanding homologously withtime with a huge velocity gradient. To make things simple, Sobolev came up with anapproximate asymptotic method, the accuracy of which is the higher, the larger thevelocity gradient in the medium. This method is therefore sometimes called the high-velocity approximation or supersonic approximation.
4.1 Sobolev Approximation
The essence of this approximation is that for large velocity gradients, as a result of theshift between the resonance frequencies of the emitting and absorbing atoms, the radiativeinteraction at each point −→r of the medium is determined mainly by its local vicinity. Thecharacteristic size
of this vicinity equals the distance from the given point at which the aforementionedshift in resonance frequencies equals the half-width of the profile of the coefficient ofabsorption, determined by the thermal or turbulent velocity υt . For coarse estimates,the velocity gradient in this expression is usually replaced by the ratio υ/R, where v isthe characteristic velocity of large-scale motion of the medium and R is the characteristicsize occupied by the emitting gas. As a result, we obtain the approximate relation
The parameter so , which was subsequently called the Sobolev length, is the main param-eter of the theory of radiative transfer in moving media, characterizing the size of thelocal vicinity of the point. In the case of supersonic motions we have so � R, and theequation for source fucntion is
in which K(−→r ,−→r ′) is the kernel determining the probability density of a transfer ofradiative excitation from the point −→r to the point −→r ′, λ is the probability of survival
of a photon in a single scattering, V is the volume of the space filled with atoms, andg represents the primary sources of excitation in the line under consideration, admitsof considerable simplifications. Assuming S(r′) ≈ S(r) within the limits of vicinity andneglecting the influence of the boundaries, considering the medium fills an infinite volumeof space, we get
S(−→r ).[1− λ+ λβ(−→r )] = g(−→r ) (9)
in which β is the probability of escape of a photon from the medium without scatteringalong the way:
β(−→r ) = 1−∫K(−→r ,−→r ′)d−→r ′ (10)
It should be noted that in a stationary medium the corresponding kernel function isalways 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 will be ab-sorbed in it sooner or later. As Sobolev showed, a fundamental difference in the processof radiative diffusion in a medium with a velocity gradient is that the normalization con-dition (11) is violated in this case and the integral of the kernel function over infinitespace turns out to always be less than unity. This means that because of clearing of themedium due to the Doppler effect, there is a nonzero probability of escape of a photonfrom a point of the medium lying formally at an infinite distance from its boundary:β(∞) > 0. This property of the process of radiative diffusion in moving media lies at thefoundation of Sobolevs method.
SYNOW is a highly parameterized spectrum synthesis code used primarily for direct(empirical) analysis of SN spectra. It was written by D. Branch and modified later byA. Fisher in early 1990s. The code considers Homologous Expansion for the ejecta, where:
(i) the radial velocity υ(r) of a matter element is a useful comoving coordinate withactual radial position of the element given by r = υ(r)t;
(ii) the density at any comoving point just scales as t3 ;
(iii) the photon redshift between matter elements separated by velocity ∆υ,∆λ = λ(∆υ/c), is time independent; and
(iv) the resonance surfaces for line emission at a single Doppler-shifted line frequencyare just planes perpendicular to the observers line of sight.
If continuous opacity in the line forming region is disregarded, the profile of an un-blended line can be calculated when the line optical depth τl(v) and source fucntion Sl(v)are specified. Because SN ejection velocities (∼ 10000 Km/s) are much larger than the
random thermal velocities (∼ 10 Km/s), a photon remains in resonance with an atomictransition only within a small resonance region. The Sobolev approximation, that thephysical conditions other than the velocity are uniform within the resonance region, usu-ally is a good one, and it allows the optical depth of a line to be simply expressed interms of the local number densities of atoms or ions in the lower and upper levels of thetransition:
where, f is the oscillator strength, λµ is the line wavelength in microns, td is the timesince explosion in days, and nl an nu are the populations of the lower and upper levels oftransition in cm3 . The term in brackets is the correction for stimulated emission. Thesource function is
All of the radial dependence of τλ and Sλ is in the level populations. The specific intensitythat emerges from a resonance region is
I = Sλ(1− e−τλ) (14)
Spectroscopic evolution can be divided into a photospheric phase when the SN is opticallythick in the continuum below a photospheric velocity, and a subsequent nebular phaseduring which the whole SN is optically thin in the continuum. In the photospheric phaseline formation occurs above the photo- sphere and in the nebular phase throughout theejecta. There is, of course, no sharp division between the two phases. However, spectralsynthesis modeling techniques in the photospheric and nebular limits can make use ofdifferent ap- proximations which are adequate for those limits. We will be focusing onthe photospheric phase in this project and will present the outputs of the code for thephotospheric phase.
During the photospheric phase a continuum radiation field is emitted by a photo-sphere which can be idealized as an infinitely thin layer. Above the photo- sphere theradiation interaction with continuous opacity is small. Line opacity on the other handcan be very large for the strongest lines. The large Doppler shifts spread line opacityover a large wavelength interval increasing the effect of strong lines compared to a staticatmosphere where such strong lines saturate and can only affect radiation in a narrowwavelength interval. The cumulative effect of many lines, strong and weak, can create aquasi-continuous opacity in the Eulerian frame. This effect has been called the expansionopacity;it dominates 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 characterized byP Cygni lines superimposed on the photospheric continuum. The P Cygni profile has anemission peak near the rest wavelength of the line and a blueshifted absorption feature.The peak may be formed in part by true emission or by line scattering into the line of sightof photons emitted by the photosphere. The emission peak would tend to be symmetricalabout the line center wavelength if not for the blueshifted absorption. The absorption is
formed by scattering out of the line of sight of photospheric photons emitted toward theobserver. Since this occurs in front of the photosphere, the absorption is blueshifted. Atearly times the ejecta density is high, the photosphere is at high velocity, and the lineopacity is strong out to still higher velocities. As expansion proceeds, the photosphereand the region of line formation recede deeper into the ejecta. The P Cygni line profilewidth thus decreases with time. The minimum of the absorption feature of weak linestends to form near the photospheric velocity, thus weak lines (e.g., weak Fe II lines)can be used to determine the photospheric velocitys time evolution. The recession of thepho- tosphere exposes the inner ejecta and permits its analysis. The source function of anunblended line can be given by Sλ(υ) = W (υ)Iphot where W (υ) is the usual geometricaldilution factor and Iphot is the continuum specific intensity (assumed angle-independent)radiated by the photosphere. Given the pure resonance scattering approximation for anunblended P Cygni line, the emission is formed just by scattering into the line of sightand the absorption just by scattering out of the line of sight.
Unfortunately, in general there is strong line blending. A photon that is scattered byone transition can redshift into resonance with another, so the influence of each transi-tion on others of longer wavelength must be taken into account. This multiple scatteringcorresponds to the observers line blending. It can be seen that the absorption peaks arestroinger than emission peaks. Thus absorption minima usually are more useful thanemission peaks for making line identifications during the photospheric phase.
A special case of a P Cygni line that has become of interest is a detached line: i.e, aline that has a significant optical depth only above some detachment velocity that exceedsthe velocity at the photosphere. A detached line consists of a flat inconspicuous emissionpeak and an absorption having a sharp red edge at the blueshift corresponding to thedetachment velocity.
4.2.1 Input file for SYNOW
The input file for SYNOW is given as in.dat with various paramaters which can be de-fined by the user. The linelist refered by the code is the Kurucz Line List. The importantinput 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 photosphereis characterized by this temperature.
(4) ea and eb - The lowest and highest wavelength to be considered respectively, inAngstroms.
(5) nlam - Number of wavelength points where the spectrum is computed.
(6) flambda - Makes the output flambda vs lambda instead of fnu vs lambdaif set to .true.
(7) taumin - Minimum line optical depth to select. The presence of a species in theenvelope is set by a nonzero optical depth in a reference line of the species(usually thestrongest optical line).
(8) grid - Grid resolution. This number controls the number of radial points used inthe calculation, and actually represents the radius of the photosphere in grid points.
(9) stspec - Place to start actually computing the spectrum. This should be lowerthan the value of ea.
(10) pwrlaw - Optical depth in all lines is deployed spatially according to this if setto ”.true.” (according to pwrlwin-the powerlaw index), otherwise the density profileis exponential.
(11) numref - The number of reference optical depths (ions) that will be specified atthe end of the file.
(12) an - Atomic numbers of species to include in the calculation.
(13) ai - Ionization stages of species included in the calculation ( 0 = neutral, 1 =first ionization, etc, up to ai = 5).
(14) tau1 - Optical depth in the reference line of the corresponding (an, ai) ionat 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. Units are in 1000s of km/s.
(16) vmaxe - Highest velocity in the envelope where the (an, ai) ion is present. Unitsare in 1000s of km/s.
(17) ve - efolding of the optical depths.
(18) temp - Excitation temp of the ion in 1000s of K. This temp is the temp used todetermine all lines relative to the reference line, assuming Boltzmann Excitation.
Output from synow is found (after each run) in the file fort.11, in the three columnsof lambda - relative flux - blackbody flux.
4.2.2 RESULTS FROM SYNOW
Here we discuss some of the analysis and results obtained from SY NOW for the dataset of SN 2011dh. It is always a good practice to study the line formation with just asingle ion in the input file. This gives you the expected positions for the various atomiclines throughout the spectrum. The relative strengths and doppler shifts can then be
accounted for by changing the tau1 and vmine and vmaxe respectively for the ions used.The output spectra may not be always upto the correct scale. So, we need to set thescales accordingly to overplot them with the data(usually done through GNUPLOT inthis project). We can also try putting the same ion species with two different velocitiesto account for certain features. This is a good practice for the study of early days spectrabut it may not be as fruitful for the later days spectra.
Fig  compares the output with single and double layers of He I ions moving atdifferent velocities. The detached lines can be identified by the flat emission edges whereas the undetcahed lines produce clear p-cygni profiles. Fig  and  show the spectra ofSN 2011dh after 36 days of explosion fitted with the SYNOW output with single ions. Thesynthetic spectra are not to the scales, but the emphasis was given to the line positionsand strengths.
Figure 5: Detached and undetached H I lines at with vphot = 10,000 km/s. The dotted lines are for Hydrogen layervelocities of 20,000 km/s(detached) and the solid lines for velocities of 10,000 km/s(undetached)
Figure 6: X-axis is wavelength in A and Y-axis is flux in ergs/sec. The SN 2011dh spectrum after 36 days ofexplosion(green) fitted with synthetic spectrum from SYNOW(red) with only H I ions detached at 30,000 km/s and vphot= 10,000 km/s. The tbb is set to 7500 K
Figure 7: X-axis is wavelength in A and Y-axis is flux in ergs/sec. The SN 2011dh spectrum after 36 days ofexplosion(green) fitted with synthetic spectrum from SYNOW with single and double layers of He I ions. Single(red) He Iis detached at 30,000 km/s. In case of the double layers(indigo), one is detached at vmine= 34,000 km/s and the other isundetached with vmine= 9000 km/s. vphot = 10,000 km/s and the tbb is set to 7500 K
Table 1: The various ions used and the related paramters for them used to get the spectra shown in fig . Thevelocities are in 1000s of km/s and the temp in 1000s of K
Fig  shows the best fit we got from SYNOW with H I, He I, Fe II, Ca II and Na I ions.Again the plots are not corrected for scales. The tbb used here is 13000 K. The interestingthing to note is the absorption feature at ∼ 6400 A. It is believed to be produced by Hαtransition as dicussed in various papers which dealt with early days spectra of sn2011dh.Some other papers refered it to be due to SI II ions. We tried to identify that featureand found that it could be produced with a blend of Hα, Si II and He I lines havingdifferent optical depths and moving at different velocities. This is better explained in thefuture sections related to ES results. Similar is the case of the feature at ∼ 5600 A whichis also a blend of He I and Na I ions. The detailed exlanation is given in the followingsections referrin to SYN++.
Figure 8: X-axis is wavelength in A and Y-axis is flux in ergs/sec. The SN 2011dh spectrum after 36 days ofexplosion(green) fitted with synthetic spectrum from 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. Theinput parameters are listed in Table .
4.3 ES: Elementary Supernova Spectrum Synthesis or ExtendedSYNOW
This is an extended version of SY NOW with two parts : SY N + + and SY NAPPS.SY N + + is a rewrite of the original SY NOW code in modern C++. It has a fewfurther enhancements, a new structured input control file format, and the atomic data fileshave been repackaged and are more complete than what SY NOW has. The other part,SY NAPPS, uses the same underlying library code used to build SYN++ to implementa spectrum synthesis calculation within the objective function of a parallel optimizationframework. So, SY NAPPS works like an automated SY N + + and does the fittingwork of the synthetic sectrum to the target spectrum. ES also uses atomic data lines(viz.Kurucz Line List). The syn++ executable requires one control file named as syn++.yamlas its arguement. It computes one or more synthetic spectra and writes them to standardoutput. If more than one spectrum is output, they are separated by a blank line. Theformat is multi-column ASCII, with the first two columns being wavelength and flux. Byconvention, all wavelength quantities in the SY N + + and SY NAPPS control files arein Angstroms, all temperatures are in 103 K, and all velocities are in 103 km/s.
4.3.1 Components of syn++.yaml
Following are the different components of control file for syn++. The values mentionedagainst some of the parameters are for examples. The output section controls the wave-length grid of the synthetic spec- trum::
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 function grids::
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-max can be setto a veru high value to impose an upper boundary to the ejecta. The next section is theopacity section::
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 the reference velocityfor all opacity profiles, they are scaled to the value of log-tau at this velocity (given byeach profile in each setup). Any ions having log-tau lower than log-tau-min are ignored.Next is spectrum which controls how the output spectrum is calculated::
p-size : 60 (number of phot. impact parameters for spectrum)
flatten : No (divide out continuum or not)
First is the number of impact parameter rays subtending the photosphere as viewed inprojection from infinity. The flatten option computes the spectrum without the underly-ing thermal continuum or any warping parameters. Each synthetic spectrum computationis governed by a setup. Multiple setups can be placed into a SYN++ YAML control file.They are simply expressed as YAML lists: Each setup is preceded on its first line by a -character. A sample setup is given below.
- 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)
The parameters a0, a1, and a2 are the coefficients of a quadratic warping function thatcan be multiplied by the synthetic spectrum once it is computed. These values werenever changed during the analysis. The rest of the parameters have the usual meaningas mentioned in the earlier section dealing with SYNOW.
4.3.2 Results from ES: SYN++
We present here the results from SYN++ runs for both the SN 2011dh and SN 2013ej datasets. The main aim while fitting the spectra was to get the line positions correct whichdepend on the log-tau values and the velocities for the different atomic layers present inthe supernova ejecta. Appropriate normalizations have been applied while plotting thespectra using GNUPLOT.
Analysis of SN 2011dh:Fig  shows the best fit for the spectra after 36 days of explosion. Ions used were H I,He I, Na I, Fe II, Sc I, O I, Ca II and Si II. As was evident from the previous SYNOWresults in section 4.2.2, the feature at ∼ 6300 A is a blend of Hα, He I(6560 A) and SiII(6347 A) lines . We tried to invetigate it further with SYN++ and found the results tobe consistent with that from SYNOW. Interestingly, use of double H I layers at differentoptical depths and velocities provide a better fit to the spectra. The double layers couldbe present in the supernova environment itself or in some circumstellar or interstellarmaterial. The double layers are separated in the velocity space by 2000 Km/s and havea difference of 0.5 in their log-tau values. Similarly, the feature at ∼ 5600 A is a blendof He I(5876 A) and Na I lines. The respective velocities of He I and Na I are 9.0 and10.1 kKm/s. The result can be verified by using He I and Na I ions alternatively andcomparing the results. The runs with the combination of both the layers give a betterfit to the concerned feature. The similar exercise can be worked out for the feature atfeature at ∼ 6300 A. O I lines, falling at ∼ 7600 A and moving at 10.0 kKm/s, blendtogether with He I(7065 A) to produce the feature at the stated region. Fe II (5169 A)are moving at 5.0 kKm/s with log − tau = 0.3. One important thing to notice is thatthe lines(absorption) are blue-shifted from their rest positions due to the fast movementof the ejecta towards the observer superimposed on the host galaxy motion relative toEarth. The width of the profiles can be controlled by the difference in v-min and v-maxvalues. The details of the input file can be found in Table .
Table 2: The various ions and the related paramters used for Fig . Note that double layers of H I are used. Thevelocities are in 1000s of km/s and the temp in 1000s of K. The ions are calculated as ion = Z * 100 + I, where I = 0 isneutral.
Figure 9: Best fit for 36d-analysis of sn2011dh from SYN++ with vphot = 10.0 kKm/s and tphot = 6.0 kK. The redline is the data after 36 days of explosion and the green line is the SYN++ model. Note that the features at ∼ 5600Aand ∼ 6300A are very well reproduced. The feature at the blue-end of the sectrum is due to Ca H&K. Although the linepositions are correct, still the emission flux is underestimated.
Fig  represents the best fit(so far) for the data set after 49 days of explosion fromSYN++ runs with vphot = 7.8 kKm/s and tphot = 5.0 kK. The ion-set is similar to theprevious one, except in the addition of another layer of He I and using Sc II in place ofSc I. The He I features are decently reproduced withn the use of double layers separatedby 1500 Km/s in the velocity space. It is again a blend of He I and Na I lines. TheO I features at about 7000 A are gain well reproduced here as before. Fe II ions aregiven a velocity of 4.5 kKm/s and log − tau = 0.90. The line positions are correct butthe flux values are underestimated at ∼ 4800 A. The Ca H&K lines are also at correctpositions, having the same velocities as before but with a slightly lower optical depth.This indicates the origin of the Calcium lines from the host galaxy or from some otherouter source, exterior to the supernova environment. The model overestimates the fluxin the region between 4200-4600 A, which we suspect, are produced by Sc II and Mg IIions. Corrections need to be done in the optical depths and probably more ions are tobe added. SYNAPPS runs could provide a better and more accurate fit to the spectra,which will be carried out in the future.
Table 3: The various ions and the related paramters used for Fig . Note that double layers of H I and He I are used.The velocities are in 1000s of Km/s and the temp in 1000s of K. The ions are calculated as ion = Z * 100 + I, where I =0 is neutral.
Figure 10: Best fit for 49d-analysis of sn2011dh from SYN++. The red line is the data after 49 days of explosionand the green line is the SYN++ model with vphot = 7.8 kKm/s and tphot = 5.0 kK. The profile at ∼ 5600A is wellreproduced. Although the profile similar to that at ∼ 6300A is produced by SYN++, but it is redhifted. Correct velocityshifts have to accounted for. The feature at the blue-end of the sectrum is due to Ca H&K. Although the line positionsare correct, but the profiles are broadened. The O I features are decently reproduced at the redder ends.
Analysis of SN 2013ej:This a type IIp supernova. So, as expected, it shows clear signs of H I lines in its spectraalong with other prominent atomic layers.
Fig  shows the SYN++ fits for the spectra obtained on 4th August, 2013. Thetphot and vphot are set to 28.0 kK and 8.75 kKm/s. Double layers of H I are usedalong with He I and Si II. The region between 6200-6500 A is a blend of Hα, He I andSi II lines. The profile is reproduced decently but the flux is underestimated. The Hβregion is well fitted. The two H I layers are moving with a difference of 3600 Km/s inthe velocity space. He I and Si II ions are both given a velocity of 6000 Km/s. He I linefluxes are overestimated at places. The difference could be reulting from some unknownions blanketing the He I features in the supernova environment.
Table 4: The various ions and the related paramters used for Fig . Note that double layers of H I are used. Thevelocities are in 1000s of Km/s and the temp in 1000s of K. The ions are calculated as ion = Z * 100 + I, where I = 0 isneutral.
Figure 11: Best fit for 4th-Aug data of sn2013ej from SYN++. The red line is the data and the green line is the SYN++model with vphot = 8.75 kKm/s and tphot = 28.0 kK. The profile at ∼ 4600A is well reproduced which corresponds toHβ. The profile between 6000-6500 A is a blend of Hα, Si II and He I ions. Although the line positions are mostly correct,but the flux estimates have to be adjusted properly. SYNAPPS would give a better result in this regard.
Fig  represents the best fit (so far) for the data obtained on 2nd October, 2013. Here,double layers of He I are used in the set-up. A number of other ions are also used,which include, Ca II, Fe II, Na I, O I and Sc I. The low-wavelength region is mostlydominated by Sc I, the blu-end being the Ca H&K feature. The position for Hβ iscorrectly reproduced, with a slight overestimation of the absorption. Again, the He I/NaI feature and O I features are very well reproduced. The blend of Hα, Si II and doublelayers of He I produce the feature at ∼ 6300 A. Although the absorption line is wellaccounted for by the model, yet the emission flux is underestimated. This mismatch hasto be accounted for in the future runs.
Table 5: The various ions and the related paramters used for Fig . Note that double layers of He I are used. Thevelocities are in 1000s of Km/s and the temp in 1000s of K. The ions are calculated as ion = Z * 100 + I, where I = 0 isneutral.
Figure 12: Best fit for 2nd-Aug data of SN 2013ej from SYN++. The red line is the data and the green line isthe SYN++ model with vphot = 6.30 kKm/s and tphot = 4.0 kK. The profile at ∼ 6300A is well reproduced, whichcorresponds to Hα, except that the emission flux is underestimated. Although the line positions are mostly correct, butthe flux estimates have to be adjusted properly. The feature at ∼ 5800 A is well fitted by He I and Na I blend. O I linesat ∼ 7600 A are well reproduced. The low-wavelength region is dominated by mostly Sc I and Mg I ions. SYNNAPS runsmight improve the accuracy.
5 Conclusion and Future works
SYN++ surpasses SYNOW in the accuracy and efficiency of fitting the spectra of boththe types of supernovae. The supernova SN 2011dh is of Type IIb which might haveshown H in its early days spectra (as discussed in some papers) but, later the H contenthas depleted. Most of the profiles present in the photospheric phase spectra are blendsof various ions, and in some cases, of multiple layers of same ion present at differentoptical depths and separated in the velocity space. The second spectra is of a Type IIpsupernova, which is also a core-collapse supernova as the former. Here, the initial spec-tra, being at a higher tphot on 4th August (28 kK), cools rather rapidly to 4 kK by 2nd
October, which is pretty rapid. The spectra is fitted with double layers of H I and He Iand shows signs of circumstellar interaction in the later stages. This has to be properlyprobed by analysing the later days spectra.
The parallel computing supernova spectrum syntheis code, SYNAPPS, provides directfitting to the spectra through various setups included in the input file specified by the user.We are currently configuring this package with the HYDRA cluster at IIA, Bangalore andrunning some test jobs on HYDRA. If the results are satisfactory, further fitting jobs willbe submitted on the cluster using SYNAPPS. We hope it will increase the accuracy andefficiency of the curve fitting and would provide better results than its serial-runningsibling SYN++.
1. G. H. Marion et al., 2014 ApJ 781 69: TYPE IIb SUPERNOVA SN 2011dh:SPECTRA AND PHOTOMETRY FROM THE ULTRAVIOLET TO THE NEAR-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 Supernovae withSYNOW.
4. David Branch, E. Baron et al. arxiv:astro-ph/011173v1 : Optical spectra of Super-novae
5. V. P. Grinin, Astrophysics, Vol. 44, No. 3, 2001: SOBOLEV’S APPROXIMATION