Contents
Homer L. Dodge Department of Physics and Astronomy, The University of Oklahoma
An invited review talk.
Updated 2007feb13 (but probably not for the last time).
Contents
A text version of this presentation will soon be posted at astro-ph with any luck at all.
Blanket permission is given for the noncommercial use with credit of any of DJJ's figures in this paper.
It's rather limp humor by modern standards---but it started a genre.
We won't cover so much ground.
But before we do that just a word on the visual aid for this talk.
It is one HTML FILE with embedded images.
Therefore, Nota Bene, the online text is a complete narrative---you CAN'T read everything and it is not intended that you should---just follow the speaker--moi that is---and look at key lines and images---unless, of course, you are actually reading this.
The talk is online, and so notes are not needed.
Now what we will cover in this talk is:
They are key distance indicators in cosmology and were used to discovering the ACCELERATING UNIVERSE (Schmidt et al. 1998; Perlmutter et al. 1999).
But we won't go into their cosmological importance: that story is told too often---often at the beginning of papers which are only remotely related to cosmology.
They are also vital in cosmic chemical evolution: they are a main---and perhaps the major--- producer of iron and also probably important for other elements or isotopes.
By focusing just one type of supernova, we avoid dissipating our time in endless ``on the other hands''.
For BOLOMETRIC LIGHT CURVES, we will just consider a HEURISTICALLY INTERESTING TOY MODEL.
For spectra, we will consider how spectrum modeling is done using the code SYNOW.
And we will illustrate how modeling with SYNOW together with other information allows us to make some progress in understanding SNe Ia.
They are ESSENTIAL since only they can DEFINITIVELY rule in or out EXPLOSION MODELS of supernovae.
But they CANNOT quite do that yet.
They still have approximations that VITIATE---your new word for the day---their conclusions.
Also the ADVANCED APPROACHES take a lot of computation.
So they don't give a QUICK ANSWER and don't allow QUICK EXPLORATION of PARAMETER SPACE.
Also the ADVANCED APPROACHES do NOT give you some of the physical insight that the SIMPLE-MINDED APPROACHES do.
The ADVANCED APPROACH used by the SUPERNOVA GROUP at the University of Oklahoma (OU) is the very advanced NLTE code PHOENIX (e.g., Hauschildt & Baron 1999) mainly developed by Peter Hauschildt (University of Hamburg) and Eddie Baron (OU).
Other workers with codes for SUPERNOVA WORK encorporating various kinds of ADVANCED APPROACHES are:
An extensive discussion of the ADVANCED APPROACHES is another talk---I thought of doing it, but it would be way too long.
But we will say a bit more about them in the Section Astrophysical Radiative Transfer and elsewhere as needed.
Almost everything we know empirically about extra-solar-system universe and great deal of what we know about the solar system comes from the electromagnetic radiation we receive from the GREAT BEYOND.
What we can see from our small platform
(postscript).
However, boring and mundane it seems to be---it does seem so often---feel free to yawn.
Usually there is NO direct inverse problem---you CAN'T derive the underlying structure from the spectrum or light curve (time-evolution of luminosity).
Rather there is an CYCLE of constructing physical models, calculating the radiative transfer through them, comparing to observation, adjusting the physical model, and so on.
The long CYCLE for solving astrophysical atmospheres
(postscript).
The CYCLE can go on for decades depending on the system of interest.
What's the big problem with RADIATIVE TRANSFER?
Usually the basic physics well understood---except maybe for some exotic systems like GRAVATARS (an alternate idea to black holes). So that's not it.
Several things are it:
Note in many cases we can't resolve the emitters---they are just point sources.
And they are often opaque---we can't see in to them.
Sometimes we can resolve and see in: e.g., gas clouds (nebulae).
But often that only shows how tough the thinking out the structure is.
Planetary nebula Cat's Eye from HST
postscript).
The Cat's Eye is about 3000 lyr away in constellation Draco. It is one of the most complex of planetary nebula and is estimated to be only about 1000 years old. The green color is due to green forbidden lines of O III (i.e., twice ionized oxygen).
Credit: NASA: Imagine the Universe.
Some systems like MAIN SEQUENCE STARS (ordinary hydrogen-burning stars) are well understood---until you look too closely---then even they have their complications: starspots and coronal mass ejections and the like.
a) 92 natural elements;
b) tens of ionization states for some elements like iron;
c) thousands atomic levels for some ions---like Fe II: PHOENIX currently uses a Fe II model with 617 energy levels ( Hauschildt et al. 1996).
The Grotrian diagram of Fe II
(postscript),
but this is just a subset of the awfulness.
Credit: Moore & Merrill (1968, p. 61). Copyright status uncertain. The image may be public domain: it's from a US government publication that is available online, but one author was not a US government employee. This image may fall in the-no-one-is-aggrieved category. If anyone considers the use here inappropriate, I will resolve the matter promptly.
Description of Grotrian diagram following Moore & Merrill (1968, p. 3).
d) then there are molecules: atoms promiscuously clumped together with their own arrays of energy levels.
e) then there is dust: silicates, carbon-containing, ices.
In some cases one can assume local thermodynamic equilibrium (LTE).
The radiation field emitted by the matter is Planckian.
But the local radiation field is determined non-locally and is generally not Planckian.
LTE usually holds at sufficiently high densities where electron collisions are sufficiently strong to drive the matter toward LTE
Assuming LTE is a vast simplification in astrophysical radiative transfer.
Sometimes it is valid or approximately valid---but often it is not.
Then you must solve the RATE EQUATIONS for the thermal state: i.e., solve immense MATRIX PROBLEMS: in the worst cases with thousands of equations.
One one needs is copious accurate atomic data.
In the past the data was often not available: e.g., electron collision strengths.
Nowadays there is more and more data---of course, that's means were drowning in it.
But there is still NOT as much as one needs at the accuracy one needs it.
This can often be an immense non-linear problem.
The most straightforward approach is an ALTERNATING ITERATION: an iteration with a cycle consisting of a thermal state calculation and then a radiative transfer calculation---and so on until OCCUPATION NUMBERS and TEMPERATURE converge.
Actually, I'm hopeful that the ALTERNATING ITERATION will become widely used when used with MONTE CARLO RADIATIVE TRANSFER where it seems to work very well (e.g., Lucy 1999a; Kasen et al. 2006).
But the simple ALTERNATING ITERATION has been intolerably slow in difference equation approaches (where it is called the LAMBDA ITERATION) and can show FALSE CONVERGENCE where the solutions arn't changing much per iteration, but are far from converge (e.g., Mihalas 1978, p. 147--150; Olson & Kunasz 1987).
Thus, methods that couple to some degree the radiative transfer and thermal state calculations have had a strong vogue: mainly the ACCELERATING LAMBDA ITERATION in one form or another.
The alternating iteration or sometimes the Lambda iteration
(postscript).
In works well enough in optically thin cases: i.e., where the whole atmosphere is only a few photon mean-free-paths thick.
But in optically thick cases, information about changing conditions propagates too slowly---about one photon mean-free-path per iteration.
Assuming the physical structure model is a given, what is the main problem with the radiative transfer?
Getting a solution by NUMERICAL METHODS on the COMPUTER.
There are analytic results for highly simplified atmospheres: e.g., the GREY ATMOSPHERE (e.g., Mihalas 1978, p. 53--76). They are very important for insight and as test cases for numerical methods.
But almost no real atmosphere can be treated with quantitative accuracy by analytic solutions.
So much of the main problem of RADIATIVE TRANSFER is one of developing numerical methods.
There are many radiative transfer formalisms.
Many of these are only useful in special cases.
For example, the SOBOLEV METHOD which is used by SYNOW (see Section Spectrum Modeling with SYNOW).
Many of these formalism are obsolete or nearly obsolete. They have just been back-numbered by better formalisms. I've done my share of creating obsolete formalisms.
The RADIATIVE TRANSFER PROBLEM can be formulated by a differential equation: the equation of radiative transfer (e.g., Mihalas 1978, p. 30--34, 499--502)---which is sort of the Boltzmann equation for photons.
Solving the RADIATIVE TRANSFER EQUATION together with boundary conditions (one of which is photon escape to infinity---i.e., to us) in most advanced treatments is done by DIFFERENCE EQUATIONS.
Very powerful DIFFERENCE EQUATION CODES have been developed like PHOENIX.
But such codes have been largely restricted to PLANE PARALLEL SYMMETRY or SPHERICAL SYMMETRY.
They can be generalized to 3 dimensions, but only with difficulty and usually only with various simplifications or limitations. PHOENIX is being so generalized, but is only so far able to do static atmospheres in 3 dimensions (Hauschildt & Baron 2006).
And at some level all astro-bodies are 3-DIMENSIONAL or asymmetric.
Many, of course, are not symmetric at all: e.g., clouds of gas.
Is there a technique that generalizes easily to 3 dimensions---and in many other respects?
Yes, MONTE CARLO RADIATIVE TRANSFER which is made use, of example, by Dan Kasen's code SEDONA (Kasen et al. 2006).
Because of its infinite parallelizability and the great physical realism one can implement with it, I have great hopes that MONTE CARLO RADIATIVE TRANSFER will become an even more important technique than it now is.
It's also relatively easy to develop codes for MONTE CARLO RADIATIVE TRANSFER.
The STANDARD---AND SINGULAR---MODEL for SNe Ia is a carbon-oxygen (CO) white dwarf (WD) is grows to near the Chandrasekhar mass limit (i.e., 1.38 M_sun (e.g., Jeffery et al. 2006a, Appendix A)) by accretion from a close binary companion which is probably some sort of post-main-sequence star.
The exact nature of the progenitor binary system is NOT known though there are many possibilities (e.g., Parthasarathy et al. 2007).
Another scenario is the double-degenerate (DD) scenario in which the companion is another WD. The two WDs are supposed to merge and initiate an explosion possibly with a super-Chandrasekhar mass.
The DD scenario has had moments of being in favor and still has supporters (e.g., Piersanti et al. 2003), but others contend that mergers (which must happen sometimes) lead to conversion to O-Ne-Mg WDs and eventual collapse (e.g., Saio & Nomoto 2004).
Observational evidence for potential progenitors suggests that most or all SNe Ia follow the SD scenario (e.g., Parthasarathy et al. 2007).
They are not bright systems and they are remote.
Also the evolution to explosion is complex.
The progenitor WDs certainly explode because of unstable CARBON BURNING just before reaching the Chandrasekhar mass limit. The progenitor is completely disrupted: no remnant is left.
The STANDARD MODEL has 3 main GOOD THINGS (plus many other lesser ones) about it:
Except for some probable SNe Ia with circumstellar hydrogen emission (e.g., SN 2002ic (Hamuy et al. 2003; Deng et al. 2004); SN 2005gj (Aldering et al. 2006)), NO SN Ia has shown any definite trace of hydrogen or helium.
SNe Ia intrinsically seem to have an ALL-METAL COMPOSITION.
The actual explosion of CO WD takes about a second and no remnant is left.
The EJECTA fly off into space and within tens of seconds ???? are virtually force-free: virtually no pressure forces or gravity forces act: the velocity of any matter element is a constant.
The initial radius of a matter element of velocity v is quickly negligible and its radial position is just
r = v t , where t is the time since explosion.
In the force-free condition, the EJECTA is in HOMOLOGOUS EXPANSION, where all structures scale up with time and velocity is a good COMOVING FRAME COORDINATE: i.e., on uses v rather r to locate structures.
Inhomogeneous and clumpy SN Ia ejecta in homologous expansion
(postscript).
The CLUMPINESS of the EJECTA in the cartoon is suggested by the promising 3-dimensional explosion models of, e.g., the PULSATING REVERSE DETONATION MODELS of Bravo & Garcia-Senz (2007) and the DELAYED DETONATION MODEL of Roepke & Niemeyer (2007).
The whole of the EJECTA can be the supernova ATMOSPHERE in the jargon I use.
However, in much RADIATIVE TRANSFER MODELING, one often defines an inner opaque region whose surface serves as an inner boundary for the ATMOSPHERE.
There are problems with the STANDARD MODEL of SNe Ia.
Most critically how the NUCLEAR BURNING progresses to explosive, hydrodynamic nuclear burning and how hydrodynamic nuclear burning explodes the star are not exactly understood.
The EXPLOSION is not a pure, SUPERSONIC DETONATION igniting NUCLEAR BURNING as first hypothesized---that would burn almost all the EJECTA to IRON-PEAK ELEMENTS (IPEs)---and spectroscopically we know that typically only about the inner half of the ejecta are mainly IRON-PEAK ELEMENTS (IPEs) and the outer half are mainly or at least significantly newly synthesized INTERMEDIATE-MASS ELEMENTS (IMEs).
Spectroscopically it is clear that only a little CO material remains and perhaps only in some cases (e.g., SN 2006D (Thomas et al. 2007)).
A long-standing model for the hydrodynamic burning is DEFLAGRATION in which the burning propagates by SUBSONIC TURBULENT FLOW.
They improved on the pure CO core detonation model of Arnett (1969) in that they didn't lead to the implication that almost all the CO matter became IPEs.
But these papers dealt with the degenerate carbon cores of intermediate mass stars (in the range about 4--8 M_Sun) as SN Ia models not with the CO WDs of the STANDARD MODEL.
But most 1-dimensional DEFLAGRATION MODELS were no good: they had only thin layers of IMEs sandwiched between an IPE CORE and an outer layer of unburnt CO.
One DEFLAGRATION MODEL what was rigged to give spectroscopically plausible ejecta is what has come to be regarded as the basic reference model W7 (Nomoto et al. 1984; Thielemann et al. 1986).
W7 is probably NOT the right model for any SN Ia----but it clearly is not too far from being right in some respects from a normal SN Ia.
Rather we see a continuum of behaviors radiating outward from the CORE NORMALS in the directions of the SHALLOW SILICONS, the COOLS, and the BROAD LINES.
There are some very PECULIAR SNe Ia that do NOT fit into our subtypes.
We havn't convinced everyone else to use our subtypes---but the malcontents will be dealt with eventually.
The density profile of W7 and an exponential fit
(postscript).
The approximately exponential density profile is typical of SN Ia explosion models.
Long ago Pierre Pizzochero pointed out that core-collapse supernova explosion models often had approximately piecewise exponential density profiles Pizzochero (1990, Fig. 4 and 5).
I believe Pierre pointed this out to me at a conference in Elba in 1990 and then I think I was the first to introduce the idea of exponential density profiles for SN Ia work.
Analytic formulae for the exponential density profile model for supernovae are given several papers (Jeffery et al. 1992; Jeffery et al. 1999; Jeffery et al. 2006a; Woosley et al. 2006).
Recall the speed of light is c = 2.99792458*10**5 km/s
= approx 3*10**5 km/s .
Typically, the highest speed parameter beta that one needs to consider for ordinary supernovae
is of order 0.1 to 0.13.
And recall most RELATIVISTIC EFFECTS go as beta**2. Thus RELATIVISTIC EFFECTS in SNe Ia are very small in general.
Actually, W7's profile cuts off at too low a speed probably due to poor outer discretization of the calculation.
When using W7 in RADIATIVE TRANSFER MODELING, one must extend it's profile to greater than 30,000 km/s.
Just for reference here is the exterior mass fraction and kinetic energy fraction of the exponential density profile supernova model.
The exterior mass fraction and kinetic energy
fraction of the exponential density profile supernova model.
(postscript).
The time zero composition structure of W7 is given below. The net yields by nuclide of W7 at time zero and time infinity are given in w7_abund.dat.
W7 had a detailed nucleosynthesis which is one of the reasons it has remained a basic reference model.
The composition structure of W7 at time zero (not counting the minute explosion phase)
(postscript).
The pre-explosion W7 composition by mass fraction is 0.4875 C-12, 0.4875 O-16, and 0.025 Ne-22 (Thielemann et al. 1986.
This is the composition of the unburnt outer layer above about 14,500 km/s.
The dash of Ne-22 is just to give right neutron/proton ratio.
For good realism in RADIATIVE TRANSFER MODELING, one must add a scaled metallicity (in solar composition units) for all neglected elements more massive than C in the unburnt outer layer.
The middle layer of W7 is the IME LAYER.
The region below about 10,000 km/s, is the IPE CORE.
One sees that much of the IPE CORE is RADIOACTIVE Ni-56.
The Ni-56-->Co-56-->Fe-56 decay chain
(postscript).
For nuclear data see
Firestone & Ekstroem (2004)
How pure Ni-56 changes into Co-56 and Fe-56 with time
(postscript).
Adiabatic cooling removes all that initial internal energy.
SNe Ia would be very dim in the ULTRAVIOLET-OPTICAL-INFRARED (UVOIR) without reheating by the Ni-56-->Co-56-->Fe-56 decay chain (e.g., Nomoto et al. 1994, p. 219; Harkness 1991).
Typically 0.6 M_Sun of Ni-56 is produced.
But there is considerable variation with a continuum of Ni-56 masses from about 0.05 to 0.85 M_Sun (Howell 2006) and with perhaps some extreme outliers such as the recent probable super-Chandrasekhar mass SN Ia SN 2003fg (Howell et al. 2006; Jeffery et al. 2006) which may have a Ni-56 mass of about 1.3 M_Sun.
There are a lot of flavors of DELAYED DETONATION MODELS.
The 1-dimensional ones are best known and studied by ATMOSPHERE MODELING.
In these 1-DIMENSIONAL DELAYED DETONATION MODELS, there is NO prompt detonation which was ruled out in 1970s as noted above.
The EXPLOSION starts as a DEFLAGRATION and this expands the exploding CO WD.
Then somehow----which has not yet been been completely understood---a detonation begins.
The density of the expanded CO WD is lower than initially and this STOPS the burning from turning all the ejecta into IPEs.
Typical 1-DIMENSIONAL DELAYED DETONATION MODELS have composition structure much like W7, except that the newly synthesized IMEs extend nearly to the the surface and very little unburnt CO is left.
Here is the DENSITY PROFILE and COMPOSITION of
M36,
an older and well-regarded 1-DIMENSIONAL DELAYED DETONATION MODEL
(Hoeflich 1995;
Hoeflich & Khokhlov 1996).
The density profile of M36 at 1 day after explosion
(postscript).
Note that the density profile of M36 is even more exponential than that of W7.
The composition structure of M36 at time zero (not counting the minute explosion phase)
(postscript).
Hoeflich (1995) found that M36 gave good good fits to the light curves and spectra of CORE NORMAL SN Ia SN 1994D.
It is similar to W7, but the burnt layers extend to the surface.
There is only a trace of carbon, except right at the surface.
The initial composition was mainly carbon-oxygen as for W7.
The gamma-rays and POSITRON KINETIC ENERGY from the Ni-56-->Co-56-->Fe-56 decay chain (hereafter usually Ni-56/Co-56 decay chain) power the UVOIR LIGHT CURVES out to maybe of order DAY 1000.
They do this by being DEGRADED into internal energy in the matter and photons which are mainly UVOIR (ultraviolet-optical-infrared) photons.
This CASCADE can also drive extreme NLTE ionization and excitation as the EJECTA DENSITY falls with expansion: high density tends to drive matter to LTE.
The UVOIR photons from the heated matter leak out of the EJECTA and provide almost the whole luminous display of SNe Ia.
We return to this point below.
Scaled SN Ia light curves at early times
(postscript).
The TOTAL RADIOACTIVE DECAY ENERGY EMISSION RATE strictly decreases from time zero.
But initially the UVOIR photons are strongly trapped in the OPTICALLY THICK EJECTA.
It takes time for them to leak out.
Thus, the UVOIR LIGHT CURVES of SNe Ia RISE from near time zero.
As the EJECTA expands, the OPTICAL DEPTH through the ejecta falls and UVOIR photons escape more readily and this cuts off the rising of the UVOIR LIGHT CURVES.
The UVOIR LIGHT CURVES and the UVOIR BOLOMETRIC LIGHT CURVE reach their respective MAXIMUM LIGHTS at about day 20 past explosion.
The B BAND LIGHT CURVE is a good proxy in shape for the UVOIR BOLOMETRIC LIGHT CURVE and the old Doggett & Branch (1985) fiducial SN Ia B light curve is still good for illustrating the behavior of the B BAND LIGHT CURVE.
B MAXIMUM on average is about day 19.5 past explosion it seems (Conley 2006).
The analytic UVOIR BOLOMETRIC MAXIMUM LIGHT SOLUTIONS of Arnett (1979) and Arnett (1982) give what is often called ARNETT'S RULE:
L_bol-max = alpha * M_NI-56* R_radioactive-decay(t_max) , where
L_bol-max is the maximum UVOIR bolometric luminosity,
alpha = 1,
M_Ni-56 is the mass of newly synthesized radioactive Ni-56,
R_radioactive-decay(t_max) is the radioactive decay energy emission rate
(not counting neutrinos, of course,
since they mostly freely stream away and are never
noticed again by anything) which
is almost entirely just the
Ni-56-->Co-56-->Fe-56 DECAY CHAIN EMISSION RATE near
maximum light,
and
t_max is the time since explosion to UVOIR BOLOMETRIC MAXIMUM LIGHT.
In real cases, ALPHA can only be a factor of order 1
(Branch 1992;
Hoeflich & Khokhlov 1996) because of
many complexities of EJECTA (especially those of opacity) not incorporated in
ARNETT'S RULE.
The SCALED-LIGHT-CURVE FIGURE illustrates the IDEAL ARNETT'S RULE CASE where alpha = 1.
Scaled SN Ia light curves at early times
(postscript).
There comes a time at about day 75 past explosion when the UVOIR photons are no longer trapped for long time periods and stream out rather freely.
This DAY 75 TRANSITION can be used as one definition---but not the only one--- of the transition from PHOTOSPHERIC PHASE to NEBULAR PHASE
Lines tend to be P-CYGNI LINES. See Section Spectrum Modeling with SYNOW below.
The UV and STRONG LINES will be optically thick much longer than the PHOTOSPHERIC PHASE.
NEBULAR PHASE: From when the OPTICAL-IR CONTINUUM PHOTOSPHERE virtually vanishes until quasi-eternity.
Lines tend to be EMISSION LINES. See Section Spectrum Modeling with SYNOW below.
There is, of course, no real sharp transition between PHOTOSPHERIC PHASE and NEBULAR PHASE.
Scaled SN Ia light curves for long times
(postscript).
But as both scaled-light-curve figures show the QUASI-EXPONENTIAL DECLINE is well below and steeper than the Ni-56/Co DECAY CHAIN EMISSION RATE.
This is because the gamma-rays from shortly near GENERIC MAXIMUM LIGHT begin to leak out directly without depositing their energy in the matter.
The result is that actual light curves fall well below the Ni-56/Co-56 DECAY CHAIN EMISSION RATE.
In fact, the actual light curves are tending to asymptotically approach the Ni-56/Co-56 DECAY CHAIN EMISSION RATE just for the POSITRON KINETIC ENERGY (plus a smidgen from ATOMIC ELECTRONS: i.e., internal conversion electrons and Auger electrons) which is about 3.5 % of the total emission rate (not counting neutrinos as noted above).
The positrons are much more strongly trapped than gamma-rays and deposit almost all their KINETIC ENERGY before PAIR ANNIHILATION with some UNLUCKY ELECTRONS.
The POSITRON KINETIC ENERGY is vital to maintaining the SN Ia LIGHT CURVES to late times.
The POSITRON KINETIC ENERGY and the kinetic energy of ATOMIC ELECTRONS of other radioactive decay chains probably are the main contributors to the intrinsic light curves out to very late times: see below.
Extrinsic sources like circumstellar emission and light echoes, we will not consider for simplicity and lack of expertise of yours truly.
It's NOT a model from which one can learn a lot more about SNe Ia than we do now.
It really isn't useful to fit it to data since its parameters (free and many unfree) are only approximately related to EJECTA QUANTITIES and are mostly integrals or products of EJECTA QUANTITIES of basic interest.
But the ONE-FREE-PARAMETER SN Ia UVOIR BOLOMETRIC LIGHT CURVE MODEL does show that at a QUALITATIVE level we do understand the evolution of the UVOIR BOLOMETRIC LIGHT CURVE of SNe Ia.
The ONE FREE PARAMETER of the ONE-FREE-PARAMETER SN Ia UVOIR BOLOMETRIC LIGHT CURVE MODEL is the RISE TIME to UVOIR MAXIMUM LIGHT.
Since the B BAND LIGHT CURVE is a good proxy for the UVOIR BOLOMETRIC LIGHT CURVE, I have set this rise time to that for the B MAXIMUM: i.e., 19.5 days (Conley 2006).
The SN Ia BOLOMETRIC LIGHT CURVE MODEL again.
Scaled SN Ia light curves for long times
(postscript).
One can see that the agreement is NOT GOOD anywhere with the Doggett & Branch (1985) fiducial SN Ia B light curve---but it's NOT BAD either.
The MAXIMUM LIGHT is qualitatively well reproduced.
There seems to be qualitative difference in the QUASI-EXPONENTIAL TAIL.
But the Doggett & Branch (1985) fiducial SN Ia B light curve may not be that good at about day 300 and also the B BAND LIGHT CURVE is not a perfect roxy for the UVOIR bolometric luminosity at any time.
ONE-FREE-PARAMETER SN Ia UVOIR BOLOMETRIC LIGHT CURVE MODEL has been extended to very late times by including the Co-57, Fe-55, Ti-44, and Si-32 decay chains.
For the model, we set the time-zero masses of radionuclides to their time-zero values in W7.
It is the POSITRON KINETIC ENERGY and the kinetic energy of ATOMIC ELECTRONS these decay chains that we assume is deposited in the ejecta to power the UVOIR bolometric light curve.
Note the following.
W7 at time zero gives 0.627 M_Sun of Ni-56 and negligible Co-56 (i.e., 6.26*10**(-5) M_Sun) (w7_abund.dat).
Since SNe Ia may be the dominant or co-dominant source of Fe-56 and other IPEs in the UNIVERSE, we expect other IPEs from SNe Ia to have of order their solar ratio with respect to Fe-56.
W7 at time zero gives 0.0216 M_Sun of Ni-57 and 0.000903 M_Sun of Co-57 (w7_abund.dat).
Because Ni-57 and Co-57 are trace isotopes, their production in W7 is not very certain.
The mass ratio of Fe-57/Fe-56 from W7 1.5 times the solar ratio (Thielemann et al. 1986).
Thus, the amount of radioactive Co-57 to help power the UVOIR light curves may be close to the maximum allowed by cosmic abundances.
The Ni-57 per se makes a negligible contribution to the light curves because of its short half-life, and so we refer to this decay chain as the Co-57 decay chain.
The long Co-57 half-life makes it the dominant source of UVOIR light curve energy in the ONE-FREE-PARAMETER SN Ia UVOIR BOLOMETRIC LIGHT CURVE MODEL from of order day 1000 to day 2000 even though not much Ni-57 and Co-57 are produced in W7
Co-57 produces no positrons, but about 11 % of its decay energy is in the kinetic energy of ATOMIC ELECTRONS emitted by Auger electron emission and/or internal conversion electron emission (Browne & Firestone (1986, p. 57-2)).
The kinetic energy of the emitted ATOMIC ELECTRONS ranges up to 5.7 KeV.
Because the Co-57 gamma-rays are about as free-escaping as the C-56 ones, the kinetic energy of the emitted ATOMIC ELECTRONS is probably the dominant contribution of Co-57 to the UVOIR light curves.
W7 at time zero gives 0.00459 M_Sun of Co-55 and 0.00155 M_Sun of Fe-55 (w7_abund.dat).
Because Co-55 and Fe-55 are trace isotopes, their production in W7 is not very certain.
The mass ratio of Mn-55/Fe-56 from W7 0.97 times the solar ratio (Thielemann et al. 1986).
Thus, the amount of radioactive Fe-55 to help power the UVOIR light curves may be close to the maximum allowed by cosmic abundances.
The Co-55 per se makes a negligible contribution to the light curves because of its short half-life, and so we refer to this decay chain as the Fe-55 decay chain.
The long Fe-55 half-life makes it the dominant source of UVOIR light curve energy in the ONE-FREE-PARAMETER SN Ia UVOIR BOLOMETRIC LIGHT CURVE MODEL from of order day 2500 to day 5000 even though not much Co-55 and Fe-55 are produced in W7
Fe-55 produces no positrons, but about 69 % of its decay energy is in the kinetic energy of ATOMIC ELECTRONS emitted by Auger electron emission and/or internal conversion electron emission (Browne & Firestone (1986, p. 57-2)).
The kinetic energy of the emitted ATOMIC ELECTRONS ranges up to 2.5 KeV.
Because the Fe-55 gamma-rays are about as free-escaping as the C-56 ones, the kinetic energy of the emitted ATOMIC ELECTRONS is probably the dominant contribution of Fe-55 to the UVOIR light curves.
W7 at time zero gives 1.81*10**(-5) M_Sun of Ti-44 at and negligible Sc-44 (i.e., 1.78*10**(-9) M_Sun) (w7_abund.dat).
Because Ti-44 and Sc-44 are trace isotopes, their production in W7 is not very certain.
The mass ratio of Ca-44/Fe-56 from W7 0.023 times the solar ratio (Thielemann et al. 1986).
Thus, the amount of radioactive Ti-44 to help power the light curves is only about 2 % of the maximum allowed by cosmic abundances.
Maybe real SN Ia have a lot more time zero Ti-44, Sc-44 (which would not affect the light curve much), or Ca-44 than in W7.
Ti-44 emits no positrons and relatively little kinetic energy in ATOMIC ELECTRONS: only about 0.0109 MeV per decay.
But its nearly nearly instantly decaying daughter Sc-44 emits positrons (with 0.5972 MeV per decay) and these will provide the dominant ``Ti-44'' energy to the UVOIR light curves.
The Ti-44 and Si-32 (see below) decay chains power the ONE-FREE-PARAMETER SN Ia UVOIR BOLOMETRIC LIGHT CURVE MODEL from about day 5000 on.
Because of its long half-life, Ti-44 and Si-32 (see just below) are almost constant sources of energy for some years after explosion.
W7 at time zero gives 1.19*10**(-5) M_Sun of Si-32 at and negligible P-32 (i.e., 2.31*10**(-7) M_Sun) (w7_abund.dat).
Because Si-32 and P-32 are trace isotopes, their production in W7 is not very certain.
The mass ratio of S-32/Fe-56 from W7 0.4 times the solar ratio (Thielemann et al. 1986).
Thus, the amount of radioactive Si-55 to help power the UVOIR light curves may be close to the maximum allowed by cosmic abundances.
Both Si-32 and P-32 emit positrons; the respective mean kinetic energies per decay are 0.0691 MeV and 0.6963 MeV.
Since P-32 decays almost instantly compared to Si-32, and therefore, sets the time-scale, one says that ``Si-32'' energy powers the UVOIR light curves.
The ones we have noted are:
Cu-59-->Ni-59-->Co-59 with half-lives 81.5 (5) s and 7.6*10**4 (5) years (Firestone & Ekstroem 2004).
Fe-60-->Co-60-->Ni-60 with half-lives 1.5*10**6 (3) years and 5.2714 (5) years (Firestone & Ekstroem 2004) with uncertainties in trailing digits indicated in the brackets.
Fe-53-->Mn-53-->Cr-53 with half-lives 8.51 (2) minutes and 3.74*10**6 (4) years (Firestone & Ekstroem 2004).
We have not included these in the ONE-FREE-PARAMETER SN Ia UVOIR BOLOMETRIC LIGHT CURVE MODEL since extending the model to hundreds of years is pushing it well beyond where it is warranted---and since the extension is more work than we want to do right now.
Circumstellar interaction must become an important energy source at some point.
Scaled SN Ia light curves for long times
(postscript).
Note we are making the IN SITU ASSUMPTION for LEPTON KINETIC ENERGY DEPOSITION: i.e., the kinetic energy of the positrons and ATOMIC ELECTRONS goes virtually instantaneously into UVOIR luminosity.
This assumption may NOT be very good particularly for positrons which can take considerable time to slow down before PAIR ANNIHILATION (e.g., Milne et al. 1999).
This delay in PAIR ANNIHILATION of the positrons would tend to store decay energy from early times and release it and release at later times flattening the bolometric light curve in comparison to the ONE-FREE-PARAMETER SN Ia UVOIR BOLOMETRIC LIGHT CURVE MODEL on the time scale of the first 1000 days past explosion (Milne et al. 1999).
There may also be significant POSITRON ESCAPE from the EJECTA which would depress tend to depress the real SN Ia UVOIR BOLOMETRIC LIGHT CURVE below the ONE-FREE-PARAMETER SN Ia UVOIR BOLOMETRIC LIGHT CURVE MODEL.
The positrons have of order MeV ENERGY, and so are quite relativistic with relativistic speed parameters (beta) in the range 0.4---0.97.
The positrons can outrun the EJECTA if they can move fairly freely.
Whether positrons escape or not depends on the MAGNETIC FIELD in the EJECTA.
If it is radial, there can be significant POSITRON ESCAPE; if it is tangled, probably not (e.g., Milne et al. 1999).
Which is the case is not yet determined (Lair et al. 2006).
The Co-57 ATOMIC ELECTRONS are NOT USUALLY so relativistic as the positrons.
Typically, they often have of order a few KeV ENERGY, but ranging up to MeV ENERGY.
They should be much more strongly trapped than the positrons.
The ONE-FREE-PARAMETER SN Ia UVOIR BOLOMETRIC LIGHT CURVE MODEL only provides a BENCH MARK for the SN Ia bolometric light curve.
At early times it only crudely incorporates PHOTON TRAPPING.
At late times, one expects strong deviations from it because of the complexities of POSITRON AND FAST ELECTRON ESCAPE and DELAYED DEPOSITION AND EMISSION.
The theoretical prediction of UVOIR bolometric and multi-color light curves for SN Ia are quite UNCERTAIN even with advanced procedures.
There uncertainties in the INPUT ATOMIC DATA and in modeling TIME-DEPENDENT EFFECTS.
At late times, there is the aforementioned difficulties of POSITRON ESCAPE and DELAYED DEPOSITION AND EMISSION.
Observations are NOT as helpful as we would like.
For early times, the observations in multiple bands are for some SN Ia are quite good.
But they never have as much accuracy, time coverage, or wavelength coverage as one would like.
At late times, the observations are much scarcer.
The number of SNe Ia with light curves extending to day 500 is small---though growing (e.g., Cappellaro et al. 1997; Lair et al. 2006).
And most unfortunately most of the data is for optical and near-IR bands and much of the luminosity could be farther in the IR.
Thus, we do NOT have empirical BOLOMETRIC LIGHT CURVES for SNe Ia that extend well into the phase when the deposition of Co-56 positrons dominates the BOLOMETRIC LIGHT CURVE.
There is still lots to be done for both EARLY SN Ia LIGHT CURVES and LATE SN Ia LIGHT CURVES.
Assumptions and features of SYNOW are as follows.
The PHOTOSPHERE is the only original source for photons in the calculation.
Any photons that hit the PHOTOSPHERE are assumed absorbed there, and thus leave the calculation.
The SYNOW atmosphere
(postscript).
The settings at DETACHMENT VELOCITIES are used to give HIGH VELOCITY FEATURES (see below).
A good fit to a spectrum does not mean that the fitted parameters necessarily correspond well to the actual underlying structure of the supernova.
But despite its limitations, the spectrum modeling with SYNOW has NOT gone OUT OF DATE.
SYNOW MODELING has many useful qualities.
One useful source of such insight is the paper of Hatano et al. (1999b).
There reference plots of SOBOLEV LINE OPTICAL DEPTHS as a function of temperature for the REFERENCE LINES of ions important in supernovae are given along with single-ion spectra for characteristic conditions.
Those approaches take long computations times and are NOT suitable for just playing around.
PHOENIX standing on the shoulders of giants (A.K.A. SYNOW)
(postscript).
Unlike many downloadable codes SYNOW really is EASY to set-up and run.
Many people now use it and it has become a sort of standard code.
The origins of SYNOW go back to circa 1980 (Branch 1980; Branch et al. 1981).
A detailed reference for how SYNOW 1.0 (as we now call it) is given by Fisher (2000).
A briefer reference is Branch et al. (2005).
SYNOW 2.0 is now/soon available and is briefly described by Branch et al. (2007).
For the simple application of the SOBOLEV METHOD to supernovae (which are homologously expanding atmospheres), probably most useful are the papers of Bartunov & Mozgovoi (1987), Jeffery & Branch (1990), Jeffery (1993), and Jeffery (1995a).
In ATMOSPHERES with large velocities gradients---LARGE-VELOCITY-GRADIENT ATMOSPHERES---photons continually Doppler shift.
And thus, the photons will propagate through LINES FREQUENCY BANDS or, more briefly, through LINES.
The propagation of photons in comoving frequency space as they propagate
in space space in a LARGE-VELOCITY-GRADIENT ATMOSPHERE
(postscript).
The CHARACTERISTIC LINE FREQUENCY WIDTH of a LINE is set by thermal Doppler broadening of the LINE and for stronger lines by natural or collisional broadening.
In the LARGE-VELOCITY-GRADIENT ATMOSPHERES, the CHARACTERISTIC LINE FREQUENCY WIDTH gives rise to a CHARACTERISTIC LINE SPATIAL WIDTH which is the size scale of the RESONANCE REGION: i.e., the spatial region where the photons interact strongly with the LINE.
The RESONANCE POINT is the spatial point where the photons are at the (REST-FRAME) LINE CENTER FREQUENCY.
If all thermal state conditions are constant across the RESONANCE REGION, except VELOCITY, LINE EMISSIVITY (Mihalas 1978, p. 25), and LINE OPACITY (Mihalas 1978, p. 23), then the equation of radiative transfer is vastly simplified and ANALYTIC SOLUTION is obtained.
One only has complex radiative transfer in the RESONANCE REGIONS.
The SOBOLEV METHOD is in fact, exact in such an Sobolev-ideal atmosphere and in a sense it is for such an atmosphere that the derivation follows.
But Sobolev-ideal atmospheres are not realistic---although the expanding universe is something like except for the local inhomogeneities.
The SOBOLEV METHOD method works because real moving atmospheres approximate Sobolev-ideal atmospheres over sufficiently large regions.
These surfaces are often called the COMMON DIRECTION OR COMMON POINT VELOCITY SURFACES since they have a common velocity in some direction or toward some point.
The COMMON DIRECTION VELOCITY SURFACES are used for calculating line emission toward an observer.
The COMMON POINT VELOCITY SURFACES for calculating the line emission directed at a point (which is the COMMON POINT itself) where some radiation-field dependent quantity is to be calculated.
In HOMOLOGOUS EXPANSION, the photons are continually REDSHIFTING in the COMOVING FRAME, and thus REDSHIFTING through LINES and VELOCITY SURFACES.
In HOMOLOGOUS EXPANSION, the COMMON DIRECTION VELOCITY SURFACES are very simple.
They are just PLANES perpendicular to the LINE-OF-SIGHT.
This makes the formation of both P-CYGNI LINES and EMISSION LINES easy to understand.
P-CYGNI LINE FORMATION in a photospheric homologously expanding,
pure-scattering atmosphere such as is used by the code
SYNOW
(postscript).
For pure-scattering P-CYGNI LINES, photons from PHOTOSPHERE the scattering on COMMON DIRECTION VELOCITY SURFACES.
Some of the those photons heading directly to the observer from the PHOTOSPHERE are scattered OUT of the LINE-OF-SIGHT by COMMON DIRECTION VELOCITY SURFACES that are moving toward the observer, and these photons are blueward of in the OBSERVER-FRAME LINE CENTER FREQUENCY because they have to be REDSHIFTED into the REST-FRAME LINE CENTER FREQUENCY to be scattered.
On the other hand, photons both blueward and redward of the REST-FRAME LINE CENTER FREQUENCY can be scattered INTO the LINE-OF-SIGHT on the COMMON DIRECTION VELOCITY SURFACES.
This into-the-line-of-sight scattering would be strongly symmetrically about the the REST-FRAME LINE CENTER FREQUENCY, except that photons scattered into the LINE-OF-SIGHT from behind the PHOTOSPHERE hit the PHOTOSPHERE and are absorbed there in the simple approach of SYNOW.
This, of course, is because of the SPHERICAL SYMMETRY of the EJECTA and approximate symmetry of the Doppler shift for equal speeds moving away and toward the observer.
EMISSION LINE FORMATION in a nebular homologously expanding atmosphere.
(postscript).
The blue wing of an EMISSION LINE just comes from the COMMON DIRECTION VELOCITY SURFACES moving toward the observer and the red wing by COMMON DIRECTION VELOCITY SURFACES moving away from the observer.
Note EMISSION LINES require non-scattering emissivity which is not currently built into SYNOW.
The COMMON POINT VELOCITY SURFACES are just spheres centered on the COMMON POINT in HOMOLOGOUS EXPANSION.
The photons from the line for which a COMMON POINT VELOCITY SURFACE is specified arrives at the COMMON POINT from the COMMON POINT VELOCITY SURFACE with the same frequency, and so can scattering in a second line blueward of the first line at the COMMON POINT.
At the level of SYNOW, COMMON POINT VELOCITY SURFACE are only used for evaluating SCATTERING LINE SOURCE FUNCTIONS.
The simple picture sketched is complicated by LINE BLENDING.
The photons in a HOMOLOGOUSLY EXPANDING ATMOSPHERE can be redshifted through and therefore scatter in many lines.
This is true everywhere in the SPECTRUM, but particularly in the BLUE OPTICAL and UV where LINES are dense in frequency space.
For PURE SCATTERING LINES, the ABSORPTIONS of the P-CYGNI LINES lines tend to dominate the EMISSION FEATURES.
An ABSORPTION of one line overlapping the EMISSION FEATURE of an equally strong second line, tends to result in an overall ABSORPTION where the first line's ABSORPTION would have been.
LOCALLY NORMALIZATION flattens spectra by dividing the observed spectrum by smoothed version of itself where the smoothing length is large (i.e., 30 % of the current wavelength in our implementation).
The LOCALLY NORMALIZED SPECTRA are largely independent of the original spectrum continuum.
This means that they are independent of reddening and overall calibration error.
This is one of their virtues.
The other is that SYNOW does not model continuum adequately in general.
Thus eliminating the continuum largely removes a distracting continuum mismatch between observed and synthetic spectra that always needs an apology.
SYNOW synthetic spectrum fitted to an observed SN 1994D Ia spectrum
(postscript).
SN 1991D is CORE NORMAL SN Ia in the subtype terminology we use in Oklahoma.
Perhaps SN 1991D is even the CORIEST NORMALEST of them all.
The spectrum is from day -1 relative to B MAXIMUM. The fit was done by my co-boss David Branch who inventing analysis with SYNOW.
You can see that the fit is overall pretty good. In fact, this degree of fit is about the best one can expect with SYNOW.
The IDENTIFICATIONS have to be made on the basis of physical insight not just what is in the SYNOW spectrum.
The line chosen to fit a LINE PROFILE may not be the only choice.
This particularly true of weak and strongly blended lines.
The IDENTIFICATIONS of the strong lines in the spectrum follow not only from this fit but from decades of analysis using many techniques and are very certain.
If a supernova has a strong absorption in the vicinity of 6150 A, it is nearly always SN Ia.
In some SNe Ia the Si II \lambda6355 line is absent or very weak in the PRE-MAXIMUM PHASE and weak compared to other SNe Ia in the POST-MAXIMUM PHASE.
Recall in the subtype terminology we use in Oklahoma, these SNe Ia are the SHALLOW SILICONS.
The Si II Grotrian diagram
(postscript).
Credit: Moore & Merrill (1968, p. 22). Copyright status uncertain. The image may be public domain: it's from a US government publication that is available online, but one author was not a US government employee. This image may fall in the-no-one-is-aggrieved category. If anyone considers the use here inappropriate, I will resolve the matter promptly.
It never seems to appear in any other type of supernova.
The SULFUR W is a result of a blend of lines of S II.
S II Grotrian diagram
(postscript).
Credit: Moore & Merrill (1968, p. 30). Copyright status uncertain. The image may be public domain: it's from a US government publication that is available online, but one author was not a US government employee. This image may fall in the-no-one-is-aggrieved category. If anyone considers the use here inappropriate, I will resolve the matter promptly.
These two lines of Ca II show one of the limitations of the SYNOW approach.
SYNOW assumes pure scattering, but these lines share a common upper level.
The Ca II H&K are often very strong lines since they arises from the ground level of Ca II and photons are often strongly TRAPPED in them.
By TRAPPED we mean that photons that REDSHIFT into the Ca II H&K are scattered many times while attempting to escape the line RESONANCE REGIONS.
Frequently, then the instead of a H&K line absorption being followed by an H&K line emission, the upper levels of the Ca II H&K lines decay by emission in the Ca II \lambda8579 IR triplet which is a usually weaker (and so less-trapping) multiplet since its lower term is not the ground term although it is a METASTABLE TERM.
Ca II ions in the lower term of the Ca II \lambda8579 IR triplet can be changed to the ground term by electron collisions or by FORBIDDEN LINE EMISSION by the forbidden [Ca II] \lambda\lambda7291,7324 multiple (e.g., Wiese et al. 1969, p. 255; Moore & Merrill (1968, p. 12))
The latter process can become obvious in the NEBULAR PHASE when electron collisions become weak.
Actually, emission from [Ca II] \lambda\lambda7291,7324 multiple is usually weak or absent in nebular SNe Ia, but it is seen in the subtype COOLS.
For example, it is seen in nebular spectra of SN 1991bg Turatto et al. 1996).
The process by which absorbed line photon energy is emerges as photons of redder lines is, of course, fluorescence (e.g., Mihalas 1978, p. 22).
The Grotrian diagram of Ca II
(postscript).
Credit: Moore & Merrill (1968, p. 12). Copyright status uncertain. The image may be public domain: it's from a US government publication that is available online, but one author was not a US government employee. This image may fall in the-no-one-is-aggrieved category. If anyone considers the use here inappropriate, I will resolve the matter promptly.
It may be that there is non-monotonicity in density profile or in composition.
It seems most likely that the HV FEATURES are caused by some high-velocity component in the EJECTA.
HV FEATURES were first identified for lines of
Ca II and
Fe II
by Hatano et al. (1999a)
Since then the identification of HV FEATURES of
Ca II and
Fe II
in SNe Ia
have become a common result of
analyses with SYNOW
(e.g., Branch et al. 2007b).
HV FEATURES for the
Si II \lambda6355 line
have also been identified
(e.g., Mazzali 2001;
Wang et al. 2003;
Mazzali et al. 2005;
Branch et al. (2007b)).
SN 2005cf offer the
strongest evidence for HV FEATURES and a two-component in
Si II \lambda6355 line
(Garavini et al. 2007).
The typical velocity of the HV FEATURES is around 20,000 km/s
which is usually well above the PHOTOSPHERIC VELOCITY
(Branch et al. (2007b)).
Actually, we---me most of all---missed the boat on HV FEATURES of the
Si II \lambda6355 line.
The earliest spectra of SN 1990N
showed the evolution of the
Si II \lambda6355 line and the
2-component structure is strongly suggested.
Unfortunately, the spectrum from day -12.5 relative to B MAXIMUM was overlooked and
never published by the observers Massimo Turatto and Stephano Benetti
(Turatto 1995).
It was a very noisy spectrum and they did not consider it useful.
But smoothed, the day -12.5 spectrum shows the transition from the early spectrum with the broad
Si II \lambda6355 line absorption
to the latter narrower
Si II \lambda6355 line absorption.
There seems to be two distinct components in the day -12.5 spectrum.
The evolution of the
Si II \lambda6355 line in
SN 1990N actually looks much like
that in SN 2005cf
(Garavini et al. 2007, Fig. 7).
I've had the day -12.5 spectrum of SN 1990N
since before 1995, and thought about a 2-component nature for the
Si II \lambda6355 line---but never
got around to publishing the spectrum and my opinion---of course, Massimo and Stephano really
missed the boat.
What is the cause of the HV FEATURES?
It is possible that they are caused by CLUMPS of varied composition and density
in the outer EJECTA.
Strong polarization (about 0.7 %) is seen with a HV FEATURE of the
Ca II \lambda8579 IR triplet line
of SN 2001el
at day -7 relative to B MAXIMUM
(Wang et al. 2003).
This polarization position angle (PA) differed from that of the average of the EJECTA.
Polarization shows that symmetry of the EJECTA is broken and the different
PA of the HV FEATURE suggests the asymmetry that causes the HV FEATURE polarization
is different from that of the bulk of the EJECTA.
So perhaps a CLUMP or CLUMPS caused the HV FEATURE of the
Ca II \lambda8579 IR triplet line.
Leonard et al. (2005b) from an admittedly
small sample of 4
SNe Ia and from
an number of perspectives also
conclude that somewhat random CLUMPS are the most likely origin of
the polarization of SNe Ia.
A simple organized bulk asymmetry causing the polarization seems to be ruled out
in most cases.
Perhaps CLUMPS in density and/or composition are the general cause of
HV FEATURES.
CLUMPINESS is expected from the modern 3-dimensional explosion models such
as the promising PULSATING REVERSE DETONATION MODELS of
Bravo & Garcia-Senz (2007)
and the DELAYED DETONATION MODEL of
Roepke & Niemeyer (2007).
To illustrate how progress---very slow progress it seems---emerges from
spectrum modeling at the level of SYNOW
in interaction
with many other kinds of work let's take up the story of FAST Ni-56/Co-56/Fe-56
in SNe Ia.
By FAST, we mean well above 10,000 km/s in COMOVING VELOCITY COORDINATES.
Everyone pretty much agrees now that
W7
is about right in that there is IMP CORE mainly of
Ni-56 at time zero.
The IMP CORE boundary is at about 10,000 km/s
in W7
where Ni-56 and SILICON have about equal abundance
This is probably generally about right.
Above the IMP CORE
SNe Ia
must have composition with significant IMEs.
But is there any or significant or dominant
FAST Ni-56/Co-56/Fe-56.
The IMP CORE boundary (using equal mass fractions of Ni-56 and silicon
as the marker) is at about 11000 km/s.
IUE UV spectra of CORE NORMAL
SNe Ia
analyzed by SYNOW MODELING
(Branch 1985;
Branch & Venkatakrishna 1986)
suggested that Co II could fit a minimum at about 3250 A.
Branch & Venkatakrishna (1986)
found this Co II was at velocity of order 12,000 km/s near
maximum light about day 20 past explosion.
The 3250 A feature was not fit by a single line, but by complex blend of lines.
This is necessarily true in the UV of
SNe Ia
where the whole spectrum is just complex blend of lines blanketing the whole UV region.
SYNOW MODELING
CANNOT definitively say
if COBALT is needed and cannot say whether more than of
order solar abundance COBALT existing from before the explosion is needed.
This makes it very hard and not only at the level the
SYNOW to
be decisive about elemental abundances.
NLTE approaches have difficulty too because of their approximations and their
adjustable parameters.
For example, for a weak line is there very little of the element or only very little of the ionization
stage giving rise to the line?
For another example, for a strong line is there a lot of the element or only a relatively large
amount of the ionization stage giving rise to the line or a very high excitation of the line lower
level or does the line have a very
large CROSS SECTION (which in radiative transfer given in the dimensionless form of
an OSCILLATOR STRENGTH (Mihalas 1978, p. 84)).
Alas lines tend to be TRIPLY removed from ABUNDANCES by wildly varying
IONIZATION, EXCITATION, and OSCILLATOR STRENGTH.
Note that ionization fractions are very sensitive temperature, density, ordinary NLTE EFFECTS, and
radioactive decay energy NLTE EFFECTS.
Because of limited observational data and the UNDEFINITIVENESS of
SYNOW MODELING
the idea of
FAST Ni-56/Co-56/Fe-56 was NOT immediately followed up either
in spectral analysis or explosion modeling.
But it wasn't forgotten.
In 1991, a new SUBTYPE of
SNe Ia
that in the jargon of OKLAHOMA we call SHALLOW SILICON SNe Ia
(Branch et al. (2006b))
was discovered with the PROTOTYPE being
SN 1991T.
SN 1991T did NOT show the characterizing strong
Si II \lambda6355 line
in the PREMAXIMUM PHASE.
Credit:
Moore & Merrill (1968, p. 22).
Copyright status uncertain. The image may be public domain: it's from a US government
publication that is available online, but one author was not a US government employee.
This image may fall in the-no-one-is-aggrieved category.
If anyone considers the use here inappropriate, I will resolve the matter promptly.
A Si II \lambda6355 line absorption
did appear weakly near MAXIMUM LIGHT---and thus eventually led to the name
SHALLOW SILICON for the SUBTYPE.
Early workers
(Filippenko et al. 1992;
Ruiz-Lapuente et al. 1992;
Jeffery et al. (1992))
identified the strongest absorption features at about
4200 A and 4900 A as due to the multiplets
Fe III \lambda 4404
Fe III \lambda 5129.
NLTE calculations---but at a level below the
PHOENIX approach---not all
NLTE calculations are equal---came to the conclusion that
newly-synthesized Ni-56 and decay products dominated the composition
beyond about 13,000 km/s
(Ruiz-Lapuente et al. 1992;
Mazzali et al. 1995).
A highly parameterized radiative transfer calculation at about the
level of SYNOW, but
with some difference partially agreed
Jeffery et al. 1992).
It made the newly-synthesized Ni-56 and decay products important, but
not dominant above about 10,000 km/s.
The idea of outer IPE-dominated layer and then an intermediate layer centered
at about 10,000 km/s with the well-established inner IPE CORE below about 10,000 km/s
has been called the ``sandwich composition''
Ruiz-Lapuente et al. 1992).
But here, as mentioned above, we just call abundant, but not necessarily dominant,
newly-synthesized Ni-56 and decay products in the outer layers well
above 10,000 km/s FAST Ni-56/Co-56/Fe-56.
One class, were helium detonations on
WDs
that produced EJECTA that were largely Ni-56 and He-4 in some mixture and
did not disrupt the whole WDs
in all cases
(Nomoto 1982;
Woosley et al. 1986)
These are not plausible models for
SNe Ia since
little IMEs were produced.
Later versions helium detonations of sub-Chandrasekhar mass
WDs
were interesting for several reasons among others that it seemed plausible that
such objects could occur
(Livne \& Glasner 1990;
Livne \& Glasner 1991;
Woosley \& Weaver 1994b;
Livne \& Arnett 1995).
These models, a priori, also seem spectroscopically implausible because
the IMEs were confined to velocities that seemed too low.
Synthetic spectrum analysis with
PHOENIX
ruled them out for for SNe Ia
One is left wondering why they don't happen it seems.
Another class can be retrospectively be recognized as
precursos of the DELAYED DETONATION MODEL.
One of these was MODEL C8 of
Nomoto et al. (1984)
which was Ni-56 dominated in the outermost layers
(Nomoto (1991)
in a private communication to
Ruiz-Lapuente et al. (1992)).
The other was model 3 of
Woosley & Weaver (1986b).
Calculations using PHOENIX
(an older version compared to today, but still more advanced in some respects than the then codes
of Ruiz-Lapuente et al. (1992) and
Mazzali et al. (1995)) found that
just using a higher luminosity and thus a higher atmosphere temperature on average
and a composition of from
above 8000 km/s homogeously mixed from
W7
gave a synthetic spectrum that was a fair match to the
spectrum of
SN 1991T
from day -3.5
(Nugent et al. 1995).
BUT Nugent et al. (1995)
conceded that the IME LINES were a bit too strong in their
synthetic spectrum.
So perhaps using more FAST Ni-56/Co-56/Fe-56, but perhaps NOT
dominant in the outer EJECTA would improve the fits with
PHOENIX.
This is being looked into.
Direct signatures of COBALT in the OPTICAL are unfortunately rather
ABSENT.
Just about the only noted one, is the FORBIDDEN [Co III] \lambda\lambda5888.5,5906.8 resonance lines
(NIST 2007).
This appears in the NEBULAR PHASE from perhaps about day 50 to about day 300 at least
relative to B maximum
(Axelrod 1980;
Kuchner et al. 1994).
Unfortunately---for the purposes of identification---the FORBIDDEN [Co III] \lambda\lambda5888.5,5906.8 resonance lines
are approximately coincident with strongest optical lines of He I and Na I: the
He \lambda5876 line
(e.g., Wiese et al. 1966, p. 14;
Moore & Merrill 1968, p. 6)
and
Na I \lambda\lambda5890,5896 RESONANCE DOUBLET
(e.g., Wiese et al. 1969, p. 2).
They modeled the emission taking into account the declining of abundance of
Co-56 due to the radioactive decay of the Ni-56-->Co-56-->Fe-56 decay chain.
However, there usually seems to be an absorption feature at with minimum blueshifted by
by about 9000 km/s or a bit more from 5900 A in POST-MAXIMUM
SNe Ia
from maybe of order day +7 to day of order +300 (relative to
B maximum) judging from the spectra of
SN 1994D
using SYNOW MODELING
(Branch et al. 2005).
Recall SN 1994D is
a CORE NORMAL
A reconciliation of these results is that the emission is indeed
from the FORBIDDEN [Co III] \lambda\lambda5888.5,5906.8 resonance lines
which have vanishing optical depth in the POST-MAXIMUM PHASE,
but the absorption is caused by the Na I \lambda\lambda5890,5896 RESONANCE DOUBLET.
In the POST-MAXIMUM PHASE the ejecta above the IPE CORE becomes
low enough in ionization that Na I becomes abundant enough for
the Na I \lambda\lambda5890,5896 RESONANCE DOUBLET to become strong.
SODIUM is a trace element in the ejecta, but its resonance lines are very strong.
The absorption of the Na I \lambda\lambda5890,5896 RESONANCE DOUBLET
probably cannot recede into the IPE CORE because probably no SODIUM was
created there or survived the burning to IPEs there.
Thus, the absorption probably becomes locked at a blueshift of about 9,000 km/s.
Solar mass fraction for SODIUM is about 3*10**(-5)
Asplund et al. 2005:
see also Solar Composition).
In W7, SODIUM
should be set to solar abundance above the burned layer which ends at
about 14,800 km/s.
In the range, 11,500--14,800 km/s, SODIUM mass fraction rises from about 10**(-9)
to about 10**(-4)
(W7).
But this is only suggestive since probably trace abundances are hard to realistically
assess from particular models of SNe Ia.
But if we said that SODIUM mass fraction was of order 10**(-7) or larger at about 10,000 km/s
and Na I was the dominant ionization stage of SODIUM, then SOBOLEV OPTICAL DEPTH of the
Na I \lambda\lambda5890,5896 RESONANCE DOUBLET would be greater than 1 out to about day 300
past explosion.
Perhaps the SODIUM is in a kind of layer detached somewhat the IPE CORE.
If this so we would expect it give rise to low flat-topped emission profile
if it was acting principally as a scattering line.
So the emission feature that we see could be
the FORBIDDEN [Co III] \lambda\lambda5888.5,5906.8 resonance lines as aforesaid.
This picture reconciles the analyses of
Kuchner et al. (1994)
and
Branch et al. (2005) .
The PHOTOSPHERIC VELOCITY of the model is 10,000 km/s, and so all the lines
are formed outside of the IPE CORE.
Consider the FORBIDDEN [Co III] \lambda\lambda5888.5,5906.8 resonance lines
acting as an explanation for the peak in the figure near 5900 A.
If the matter is mostly COBALT above the PHOTOSPHERE at this phase of and the overwhelmingly
dominant ionization is Co III, then a simple calculation show that the
SOBOLEV OPTICAL DEPTH of this resonance doublet is of order 1/2.
This would give rise to a weak P-CYGNI line that would be noticeable in
a spectrum where all the lines in the vicinity are rather weak as is the case here.
The radioactive Co-56 is actually about most abundant at MAXIMUM LIGHT near
day 20 after explosion.
Recall the following figure.
On the other hand, maybe the peak is caused by
the FORBIDDEN [Co III] \lambda\lambda5888.5,5906.8 resonance lines acting
as emission lines even at this early phase
as mentioned by
Jeffery et al. 1992
If either the interpretation of the 5900 peak as P-CYGNI emission or
pure emission of
FORBIDDEN [Co III] \lambda\lambda5888.5,5906.8 resonance lines is correct,
then that there probably must be
significant super-solar COBALT above the IPE CORE.
The spectrum we have analyzed only as a PHOTOSPHERIC VELOCITY of
10,000 km/s which puts it just at about where the
IPE CORE is thought to start.
But the 5900 A peak appears in all earlier spectra going back to day -12.5 before
B maximum when the PHOTOSPHERIC VELOCITY was
13,000 km/s or greater
(Ruiz-Lapuente et al. 1992;
Jeffery et al. (1992);
Mazzali et al. 1995).
On the other hand, the 5900 A feature may be allowed lines of Co III
in which case some further analysis is needed to say whether that requires
super-solar COBALT above the IPE CORE.
If a large amount of Ni-56 is synthesized
in exploding WDs,
then it is possible under some conditions to get mass fraction of order
10**(-1) of He-4
as shown for instance
by the LATE DETONATION MODELS
(Yamaoka et al. 1992)
and the PULSATING REVERSE MODELS
(Bravo & Garcia-Senz 2007).
I have, in fact, used He I LINES in my fit to the day -6.3
spectrum of SN 1991T.
[Co III] and Co III were discussed above.
My colleagues assure me that Na I is very unlikely in the PRE-MAXIMUM
when SODIUM is probably too highly ionized to give rise to a strong
Na I \lambda\lambda5890,5896 RESONANCE DOUBLET LINE.
We will discuss the Na I identification no further.
The He I LINES which make obvious P-CYGNI LINES in the
SYNTHETIC SPECTRUM are
He \lambda5876 line,
He \lambda6678 line,
and, in the NEAR-INFRARED (NIR),
He \lambda10830 line
(e.g., Wiese et al. 1966, p. 12--14;
Moore & Merrill 1968, p. 6).
In the
SYNTHETIC SPECTRUM FIT, the He \lambda5876 line helps,
He \lambda6678 line is too blue,
and the
He \lambda10830 line
has no observational counterpart.
Credit:
Moore & Merrill (1968, p. 6).
Copyright status uncertain. The image may be public domain: it's from a US government
publication that is available online, but one author was not a US government employee.
This image may fall in the-no-one-is-aggrieved category.
If anyone considers the use here inappropriate, I will resolve the matter promptly.
One can see that these optical/NIR He I LINES are from levels that
are very highly excited.
Actually, one would not expect to see them in the thermal conditions of
supernovae.
But they do appear in
Type Ib supernovae
because of non-thermal excitation ultimately owing to
gamma-rays from
the Ni-56-->Co-56-->Fe-56 DECAY CHAIN where the the newly synthesized
Ni-56 has been mixed out into He-rich envelope
(Lucy 1991).
But the situation in
SNe Ia
is different in that instead of a He-rich envelope at most one can expect
a few percent of He by mass.
On the other hand this He (if it exists at all) is produced thoroughly
mixed with the Ni-56.
So the idea of He I LINES in
SNe Ia
has continued to tantalize.
But brave are the men (and women), who claim to have even tentatively
identified He I LINES
(Meikle et al. 1992).
??????????????
This diagram alas omits the multiplet Mg II \lambda10926
(e.g., Wiese et al. 1969, p. 30)
that connects 3d to 4p levels.
Credit:
Moore & Merrill (1968, p. 10).
Copyright status uncertain. The image may be public domain: it's from a US government
publication that is available online, but one author was not a US government employee.
This image may fall in the-no-one-is-aggrieved category.
If anyone considers the use here inappropriate, I will resolve the matter promptly.
On the other hand.
-HV fe and si
To illustrate how progress---very slow progress it seems---emerges from
SYNOW MODELING
in interaction
with many other kinds of work let's take up the story of FAST Ni-56/Co-56/Fe-56
and CLUMPS (of varying composition)
in SNe Ia.
By FAST, we mean well above 10,000 km/s in COMOVING VELOCITY COORDINATES.
Everyone pretty much agrees now that
W7
is about right in that there is IMP CORE mainly of
Ni-56 at time zero.
The IMP CORE boundary is at about 10,000 km/s
in W7
where Ni-56 and SILICON have about equal abundance
This is probably generally about right.
Above the IMP CORE
SNe Ia
must have composition with significant IMEs.
But is there any or significant or dominant
FAST Ni-56/Co-56/Fe-56 and is the composition clumpy?
ONE-DIMENSIONAL EXPLOSION MODELS must give a stratified compositions
of course (e.g., W7).
As for FAST Ni-56/Co-56/Fe-56, ONE-DIMENSIONAL EXPLOSION MODELS
are all parameterized in some way and the parameters can be adjusted to give:
The IMP CORE boundary (using equal mass fractions of Ni-56 and silicon
as the marker) is at about 11000 km/s.
What of CLUMPS in the composition above the IPE CORE?
ONE-DIMENSIONAL EXPLOSION MODELS must give a stratified compositions
of course (e.g., W7)
and so cannot address this issue.
-brute's no clumps,
-polarization's clumps
-C II line sporadically.
Thomas et al. (2007)
give the most convincing evidence for the identification of the C II \lambda6580
in SNe Ia
(i.e., SN 2006D).
The line C II \lambda6580 (e.g.,
Wiese et al. 1966, p. 38;
Moore & Merrill 1968, p. 20).
is usually the strongest C II line in the optical in LTE
(e.g., Hatano et al. 1999b).
Credit:
Moore & Merrill (1968, p. 20).
Copyright status uncertain. The image may be public domain: it's from a US government
publication that is available online, but one author was not a US government employee.
This image may fall in the-no-one-is-aggrieved category.
If anyone considers the use here inappropriate, I will resolve the matter promptly.
And when we see the possible/probable
C II \lambda6580 line absorption,
it is blueshifted by less than about 15,000 km/s
Branch et al. (2007b).
If it was blueshifted more, it would be lost in the
Si II \lambda6355 line absorption.
The
-Marion's IR
-Bravo & Garcia-Senz model.
-contradiction or split the difference.
The SIMPLE-MINDED APPROACHES can NEVER be definitive.
But they give first-order results and give one an understanding of what
is happening.
The ADVANCED APPROACHES using codes like
PHOENIX
(e.g., Hauschildt & Baron 1999)
and SEDONA
(Kasen et al. 2006) are
needed for DEFINITIVE conclusions about explosion models.
But they havn't delivered the goods yet.
In regard to SNe Ia
from SIMPLE-MINDED APPROACHES and more ADVANCED APPROACHES
both tell us that
W7 is NOT
an adequate model for SNe Ia.
W7 has some of the right features,
of course---or it would not have been a basic reference model all these years.
Three dimensional explosion models such
as the PULSATING REVERSE MODELS
Bravo & Garcia-Senz (2007)
and the DELAYED DETONATION MODEL of
Roepke & Niemeyer (2007) are promising.
We in Oklahoma and others elsewhere are keen to
explore their
radiative-transfer behavior
with a variety of approaches.
SYNOW synthetic spectrum fitted to an observed SN 1994D Ia spectrum.
The evolution of the absorption of Si II \lambda6355 line
in earliest spectra of SN 1990N.
The phases are relative to B MAXIMUM
(postscript).
Inhomogeneous and clumpy SN Ia ejecta in homologous expansion
(postscript).
(NOT COMPLETED.)
The composition structure of W7 at time zero (not counting the minute explosion phase)
(postscript).
ONE-DIMENSIONAL EXPLOSION MODELS must give a stratified compositions
of course (e.g., W7).
As for FAST Ni-56/Co-56/Fe-56, ONE-DIMENSIONAL EXPLOSION MODELS
are all parameterized in some way and the parameters can be adjusted to give:
So ONE-DIMENSIONAL EXPLOSION MODELS alone simply cannot say if they is
abundant FAST Ni-56/Co-56/Fe-56 or not.
Let us consider the evidence for abundant FAST Ni-56/Co-56/Fe-56.
We should point out that observed lines are often the result of
low-abundance ionization stages of elements and lines from excited states.
If the COBALT in question was newly from synthesized Ni-56 and abundant,
it was perhaps well above where
W7 allowed Ni-56 and
somehow co-existing with
newly synthesized IMEs which give rise to
the IME lines in the optical spectra.
The Si II Grotrian diagram
(postscript).
An observed pre-maximum SN 1991T Ia spectra.
Actually, the first suggestions for FAST Ni-56/Co-56/Fe-56
in SN 1991T
were supported by reference to older 1-dimensional explosion models.
Now the case for dominant FAST Ni-56/Co-56/Fe-56
was not definitively established by the NLTE CALCULATIONS
Ruiz-Lapuente et al. (1992) and
Mazzali et al. (1995).
It seems clear from Kuchner et al. (1994)
that the emission centered at about 5900 A is
the FORBIDDEN [Co III] \lambda\lambda5888.5,5906.8 resonance lines in emission.
For this talk I tried my own hand at a fit to the day -6.3 (relative to
B maximum) spectrum of
SN 1991T
in which there is POSSIBLE EMISSION FEATURE and a
weak P CYGNI absorption and emission (at about 5900 A)
which it may be caused by any---or none of---or
some mixture of
the FORBIDDEN [Co III] \lambda\lambda5888.5,5906.8 resonance lines,
He \lambda5876 line
and
Na I \lambda\lambda5890,5896 RESONANCE DOUBLET.
Flat-topped emission for P-CYGNI LINES from detached scattering layers
is discussed by, e.g., Jeffery & Branch (1990, p. 190).
Thus Na I \lambda\lambda5890,5896 RESONANCE DOUBLET would NOT give rise to
much of an emission feature.
Observed and synthetic SN 1991T Ia spectra for day -6.3.
A few other forbidden [Co III] lines might have SOBOLEV OPTICAL DEPTH might
have optical depths of order 0.1 or so.
Even though we do not usually think that FORBIDDEN LINES can affect the photospheric
spectrum as scattering lines---they are too weak---the
[Co III] \lambda\lambda5888.5,5906.8 resonance lines may do so if
indeed the outer atmosphere is dominated by COBALT at maximum light.
How pure Ni-56 changes into Co-56 and Fe-56 with time
(postscript).
An observed pre-maximum SN 1991T Ia spectra.
Another on the other hand, is that the 5900 A peak may be the emission
feature of
He \lambda5876 line.
[Co III], Co III, and Na I as possible line identifications
but they were not included in the synthetic spectrum.
Observed and synthetic SN 1991T Ia spectra for day -6.3.
The He I Grotrian diagram
(postscript).
The Mg II Grotrian diagram
(postscript).
(NOT COMPLETED.)
The composition structure of W7 at time zero (not counting the minute explosion phase)
(postscript).
And one-dimensional explosion models alone simply cannot say if they is
abundant FAST Ni-56/Co-56/Fe-56 or not.
The Grotrian diagram of C II
(postscript).
The line C II \lambda6580 has been more tentatively identified in earlier work:
As Thomas et al. (2007) put it,
carbon only gives a signature sporadically.
The earliest SN 1990N spectrum from day -14.3 relative to B maximum.
Note the possible weak possible/probable
C II \lambda6580 line absorption
at about 6300 A.
We have given a brief overview of the SUPERNOVA ATMOSPHERE MODELING using
radiative transfer
with
an emphasis on the SIMPLE-MINDED APPROACHES and
using SNe Ia as
the illustrative objects of analysis.