IIA SUMMER PROGRAMME 2014

TITLE : Spectral Analysis of Supernova using SYNOW

Guide : Dr. Firoza Sutaria IIA, Bangalore

By: Sambit Kumar Panda M.Sc. Astrophysics, 2nd Year Pondicherry University

PLAN OF THE TALK:

1. Introduction to Supernovae and their classification.

2. Sobolev Approximation

3. Synthetic Spectrum code : SYNOW and ES

4. Output and Results

5. Conclusion

Supernovae:

●Result from the explosion of massive stars- one of the most violent events in the universe.

● Generate blinding flash of radiation and shock waves

● Energy released is of the order of 1051 ergs/sec.

● Leave behind Supernova Remnants-bounded by expanding shockwave, ejected material and the ISM it sweeps up.

● Typical temperature of the ISM ~ 10000 K.

● Synthesis of heavy elements is thought to happen in supernovae, thatbeing the only mechanism able to explain the present abundances.

TYPES OF SUPERNOVAE

1. Thermonuclear Supernovae: Type Ia

- Produced by White Dwarfs, when the mass accretion from its companion pushes its core over the Chandrasekhar Limit ( >1.4 M

⊙).

- When the temp at the core rises to (> 5×108 K), uncontrolled fusion of carbon and Oxygen results in a thermonuclear runaway process.

- Star explodes completely and no remnant is left behind.

- Do not show Hydrogen Lines in their spectrum.

- Their light curves exhibit sharp maxima and then die away smoothly and gradually.

- Type Ia supernovae occur in all kinds of galaxies.

2. Core Collapse Supernovae: Type Ib, Ic, II- Results from the violent explosion of a massive star(>8 M⊙) due to the rapid gravitational collapse under its own gravity.

- When the mass of the inert core exceeds the Chandrasekhar limit of about 1.4 solar masses, electron degeneracy alone is no longer sufficient to counter gravity

- The collapse is halted by neutron degeneracy, causing the implosion to rebound and bounce outward.

- Depending on initial size of the star, the remnants of the core form a neutron star or a black hole.

- They show Hydrogen in their early days spectra.

- Type II supernovae have less sharp peaks at maxima and peak at about 109 L⊙.- Type II supernovae are not observed to occur in elliptical galaxies, and are thought to occur in Population I type stars in the spiral arms of galaxies.

Sobolev Approximation :- A method allowing for a simplified solution to the → radiative transfer equation at frequencies of spectral lines in media moving with a high velocity gradient.

- This method assumes that the macroscopic velocity gradients are more important than local random variations of thermal line width: dv/dr > v

th/l

Where, 'dv/dr' is the velocity gradient 'V

th' is the thermal broadening of the line

and 'l' the length scale

- Only valid if the conditions of the gas do not change over the → Sobolev length.

ls = v

th/(dv/dr)

For coarse estimates: ls = R/(v/vth)

Where 'R' is the characteristic size occupied by the emitting gas and 'v' is the characteristic velocity of large-scale motion of the medium.

- In the case of supersonic motions we have ls << R, and the equation for the source

function is : S (r) = λ ∫v K (r,r ′) S (r′) dr′ + g(r)

in which K (r,r′) is the kernel determining the probability density of a transfer of radiative 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,and g represents the primary sources of excitation in the line under consideration

- Assuming S(r′) ≈ S(r) within the limits of vicinity and neglecting the influence of the Boundaries, assuming the medium fills and infinite volume of space,we get S(r) [1 − λ + λβ(r)] = g(r)⋅ ,

in which β is the probability of escape of a photon from the medium without scattering along the way: β(r) = 1 − ∫ K(r,r′) dr′ .

- In a stationary medium : ∫ K(r,r′)dr′ = 1

Line formation and Synthetic Spectrum Codes: SYNOW

Basic approximation: Homologous expansion(i) the radial velocity 'v' of a matter element is related to actual radial position by r = vt;(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; (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.

- Because SN ejection velocities ( 10, 000 km/s) are much larger than the random ∼thermal velocities( 10 km/s), a photon remains in resonance with an atomic transition ∼only within a small resonance region.

- Line optical depth :

τl=0.229 f λμ t dnl(1−glnμ /gμnl)

where f is the oscillator strength, λμ is the line wavelength in microns, td is thetime since explosion in days, and nl and nu are the populations of the lower andupper levels of the transition in cm−3 .

-The source function is : Sl=2hc /λ3[(gμnl/ glnμ)−1]

- All of the radial dependence of τl and Sl is in the level populations.

- The specific intensity that emerges from a resonance region is : I=Sl (1−e(−τ l))

Spectroscopic Evolution of Supernovae:

1. Photospheric phase: - when the SN is optically thick in the continuum below a photospheric velocity- line formation occurs above the photosphere- characterized by P Cygni lines superimposed on the photospheric continuum- demands a powerful radiative transfer technique

2. Nebular phase:- during which the whole SN is optically thin in the continuum- line formation occurs throughout the ejecta

SYNOW- A highly parameterized spectrum synthesis code used primarily for direct (empirical) analysis of SN spectra.- Input parameters :(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.(4) ea & eb - The lowest & highest wavelength to be considered respectively, in Angstroms.(5) nlam - Number of wavelength points where the spectrum is computed.(6) flambda - Make the output flambda vs lambda instead of fnu vs lambda if set to .true.(7) taumin - Minimum line optical depth to select.(8) grid - Grid resolution.(9) stspec - Place to start actually computing the spectrum. This should be lower than the value of ea(10)pwrlaw - Optical depth in all lines is deployed spatially according to this if set to “.true.”(according to pwrlwin), otherwise the density profile is exponential.(11) numref - The number of reference optical depths (ions) that will be specified 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 ionization, 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. Units are 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 Boltzmann Excitation.

- It uses the “Kurucz line list” as the reference file for atomic lines.

- Output is stored in “fort.11” file.

Data : sn2011dh- discovered on 31st May, 2011 in the “whirlpool” galaxy M51(~7.1 ± 1.2 Mpc)

UBVRI lightcurves of sn2011dh.The curves have been shifted by the amounts mentioned in theLegend (Bose, Sutaria et al.)

G. H. Marion et al. 2014 ApJ 781 69

Spectrum of sn2011dh after 36 days of explosion

Plotting spectra of sn2011dh, after 36 days of explosion, fitted with single and double hydrogenIons(2 different shells of H I with different velocities.)

Vphot = 10000 km/sVmax = 32000 km/sTbb = 7500 K

Single H I:Vmine = 30.0 kKm/sVmaxe= 38.0 kKm/sTau1 = 10.0

Double H I:Vmine= 12.0,31.0 kKm/sVmaxe=16.0,38.0 kKm/sTau1 = 3.0,15.0

Plotting spectra of sn2011dh, after 36 days of explosion, fitted with single and double HeliumIons(2 different shells of He I with different velocities.)

Vphot = 11000.0 Km/sVmax = 31000.0 Km/sTbb = 7500.0 K

Single He I :Vmine = 27.0 kKm/sVmaxe = 37.0 kKm/sTau1 = 10.0

Double He I :Vmine = 34.0,9.0 kKm/sVmaxe= 39.0,15.0 kKm/sTau1 = 8.0,10.0

Fig 1: H I, He I, Fe II, Na I with tbb=13000 KVphot = 12000.0 Km/s; vmax = 35000.0 Km/sTau1 = 15.0, 15.0, 15.0, 1.0, 4.0Vmine= 28.5, 30.0, 10.0, 6.0, 20.0 kKm/sVmaxe=36.0, 35.0, 20.0, 15.0, 30.0 kKm/s

Fig 2: H I, He I, Fe II, Na I, Si II with tbb=6000 K; vphot=12000 Km/s;vmax=35000 Km/s,Tau1=15.0,15.0,1.0,4.0,5.0Vmine=28.5,30.0,10.0,6.0,20.0,13.0 kKm/sVmaxe=36.0,35.0,20.0,10.0,30.0,30.0 kKm/s

ES : Elementary Supernova Spectrum SynthesisSYN++ : Consider this a rewrite of the original SYNOW [1]_ code in modern C++ with more Complete atomic data files.

SYNAPPS: with parallel run(mpirun) for fitting the spectra- automated SYN++

SYN++ vs SYNOW: 1. grid : bin_width -> opacity bin size in kkm/s v_size -> size of line-forming region grid v_outer_max -> fastest ejecta velocity in kkm/s

2.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 # parameterization ( exp or pwrlw) v_ref # reference velocity for parameterization log_tau_min : # opacity threshold3. source : mu_size : 10 # number of angles for source integration4. spectrum : p_size : 60 # number of phot. impact parameters for spectrum flatten : No # divide out continuum or not

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 (kkm/s) v_outer : 30.0 # outer velocity of line forming region (kkm/s) t_phot : 12.0 # blackbody photosphere temperature (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 (kkm/s) v_max : [ 30.0, 30.0, 30.0, 30.0 ] # upper cutoff (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. (kK)

The parameters "a0," "a1," and "a2" are the coefficients of a quadraticwarping function that can be multiplied by the synthetic spectrum onceit is computed.

A sample setup from the input file “syn++.yaml”. Multiple setups can be included withDifferent ion sets.

Vphot=10.0 kKm/sVout = 30.0 kKm/sTphot = 12.0 kK

Ions: H I, He I, Fe II, Na I, Si II, Mg II

Detached H I and He I lines With H more detached.

-without H also, the 6300 AngPeak falls on the same place

Reduced Tbb(tbb=6000 K) and adjusted velocities; with and without Na ISlightly detached H I and He I lines; Si II: vmine=4.0, vmaxe=6.0; log_tau=0.3Na I: vmine=8.0, vmaxe=25.0: log_tau=0.3

He I(5876)/Na I

Hα(6563)/He I(5875)/Si II(6347)

He I(6678)

Ca H & K

Fe II(5169)

Hβ

He I(7065)

49 days after the explosion

Output with and without oxygen lines. Na I lines are included. Rest ions are sameVphot= 8.0 kKm/s ; vout=28.0 kKm/s ; tphot = 4.0 kK

Ca H & K

Hβ

Fe II(5169)He I(5876)/Na I

Hα(6563)/He I(5875)/Si II(6347)

He I(7065)

He I(6678)

Results and Conclusions:

1. The supernova sn2011dh is of Type IIb which might have shown H in its early days spectra(as discussed in some papers) but later the H content is depleted.

2. The much debated 6300 Ang feature might be due to the line blending of He I and Si II ions and not due to H-alpha(which contributes to a very small extent)

3. The feature at ~5600 Ang is mainly due to the blending of He I(5876) and Na I Line.

4. Further study is needed and the work is far from complete. (Specially the fitting needs to be done with SYNAPPS) 5. Line identification also needs to be done properly.

Thank You