Supernovae Type Ia A really good explosion.

SN 1998aq SN 1998dh SN 1998bu SN 1994D Type Ia supernovae are the biggest thermonuclear explosions in the universe. Twenty billion, billion, billion megatons. For several weeks their luminosity rivals that of a large galaxy. HST

SN 1994D Very bright, regular events, peak L ~ erg s -1 Associated with an old stellar population (found in ellipticals, no clear association with spiral arms) No hydrogen in spectra; strong lines of Si, Ca, Fe Not strong radio sources Total kinetic energy ~10 51 erg (no compact remnant) Higher speed, less frequent than Type II

Filippenko, (1996), Ann. Rev. Astron. Ap The Type Ia supernova spectrum at peak light is dominated by lines of singly ionized Si, Ca, S, Mg, Fe. The late time spectrum (not shown) has strong emission lines of singly and doubly ionized Co and Fe.

Possible Type Ia Supernovae in Our Galaxy SN D(kpc) m V Expected rate in the Milky Way Galaxy about 1 every 200 years, but dozens are found in other galaxies every year. About one SN Ia occurs per decade closer than 5 Mpc.

Spectra of three Type Ia supernovae near peak light – courtesy Alex Filippenko Spectra are similar from event to event

The B-band (blue) light curves of 22 Type Ia supernovae (Cadonau 1987). Broadly speaking they are quite similar.

The Phillips Relation (post 1993) Broader = Brighter Can be used to compensate for the variation in observed SN Ia light curves to give a “calibrated standard candle”. Note that this makes the supernova luminosity at peak a function of a single parameter – e.g., the width.

Some Critical Issues How do Type Ia supernovae explode. Can we understand the outcome from first principles? Yes, maybe someday Why is there a width-luminosity relation? It’s the opacity. Could there be “evolutionary” corrections that must be applied to the use of Type Ia supernovae as standard candles? Don’t know, but it is surprising that the light curves can be described to high accuracy as a single parameter family ( 56 Ni mass)

Leading Model Accretion and growth to the Chandrasekhar Mass (1.38 solar masses) Degenerate thermonuclear explosion. (Hoyle and Fowler, 1960). Explains: Lack of H in spectrum Association with old population Regularity Large production of 56 Ni and a light curve dominated by radioactivity.

In order for the white dwarf to grow and reach the Chandrasekhar Mass the accretion rate must be relatively high (to avoid the nova instability). This must be maintained for millions of years.

Progenitor Arnett (1968, 1969) Nomoto, Sugimoto, & Neo (1976) Ignition occurs as the highly screened carbon fusion reaction begins to generate energy faster than neutrino losses can carry it away. At a given temperature, the plasma neutrino losses first rise with density and then decline when

Neutrino Losses Itoh et al 1996, ApJS, 102, 411, see also Beaudet, Petrosian, & Salpeter 1967, ApJ, 147, 122 *

The ignition conditions depend weakly on the accretion rate. For lower accretion rates the ignition density is higher. Because of the difficulty with neutron-rich nucleosynthesis, lower ignition densities (high accretion rates) are favored. * Ignition when nuclear energy generation by (highly screened) carbon fusion balances cooling by neutrino emission.

Ignition Conditions Supernova preceded by 100 years of convection throughout most of its interior Last "good convective model" is when the central temperature has risen to 7 x 10 8 K Pressure scale height: 400 km Nuclear time scale: 10 2 s Convective time scale: 10 2 s Convective speed: 50 km s -1 Binding energy: 4 x erg Density: 2 x 10 9 g cm -3 Burning 0.05 solar masses can cause expansion by a factor of three

Conditions in a Chandrasekhar Mass white dwarf as its center runs away – following about a century of convection. Vertical bars denote convective regions

Convection for 100 years, then formation of a thin flame sheet. T radius 0 Note that at: 7 x 10 8 K the burning time and convection time become equal. Can’t maintain adiabatic gradient anymore 1.1 x 10 9 K, burning goes faster than sound could go a pressure scale height Burning becomes localized

Fuel Ash Diffusion Burning l Temperature This is the conductive - or sometimes “laminar” - flame speed.

Timmes and Woosley, (1992), ApJ, 396, 649 Laminar Flame Speed km/s cm nb. these speeds are slower than the convective speeds prior to runaway

Heat Capacity Nuclear burning to the iron group gives q nuc = 7 x erg/gm “ “ “ silicon group “ “ 5 x erg/gm Above about 10 7 gm cm -3 burning will go to nuclear statistical equilibrium and make only iron group elements

At 10 billion K burning always goes to completion and makes iron. Only below four billion K (few x 10 7 gm cm -3 ) does one begin to make Si, S, Ar, Ca, Mg, etc. Almost all the initial white dwarf is more dense than that. So, naive physics gives us a flame that burns the star slowly to iron, experiences a lot of electron capture, and barely unbinds the star – maybe after several pulses

A Successful Model Must: Produce approximately 0.6 solar masses of 56 Ni (0.1 to 1 M sun ) Produce at least 0.2 solar masses of SiSArCa Not make more than about 0.1 solar masses of 54 Fe and 58 Ni combined Allow for some diversity For the light For the spectrum For the nucleosynthesis (Starting from 1.38 solar masses of carbon and oxygen) Explode violently

These requirements are in conflict with the basic physics outlined so far Such a vastly subsonic speed will not give a powerful explosion or much 56 Ni Burning much fuel at 10 9 g cm -3 will result in copious electron capture and lots of 54 Fe and 58 Ni The flame will slow to almost a halt at the densities where SiSArCa might be made. The origin of diversity is not clear

It has been known empirically for some time that the way to get around these problems and agree with observations is with a flame that starts slowly, pre-expands the star (so as to avoid too much electron capture) then moves very rapidly when the density is around 10 7 – 10 8 gm cm -3. Unfortunately the laminar flame has just the opposite behavior and a prompt explosion (detonation) would turn the whole star to iron (in conflict with the spectrum).

Timmes and Woosley, (1992), ApJ, 396, 649 Laminar Flame Speed km/s cm

Thielemann, Nomoto, and Yokoi (1986), A&A, 158, 17 and (1984), ApJ, 286, 644 Model W7 1)0.0 s 2)0.60 s 3)0.79 s 4)1.03 s 5)1.12 s 6)1.18 s 7)1.24 s 8)3.22 s Note the long time spent at going slow near the center. The flame accelerates to nearly sound speed at the end Half of the time is spent burning the first 01 solar masses.

The fact that W7, an empirical parameterized model agrees so well with observations suggests that the correct SN Ia model should have similar properties.

Brachwitz et al. (2000) Nucleosynthesis compared to the Sun (normalized to 56 Fe = 1)

For over 25 years the search has been for the correct physics that would describe this solution, i.e., a little burning at high density and a lot of burning at low density. Rayleigh-Taylor Instability Turbulence Delayed Detonation Pulsational Detonation Off-center burning

Kercek, Hillebrandt, & Truran (1998)

Rogers, Glatzmaier, and Woosley (2002)

Combustion Rate In 1D for an undeformed flame: but in general in 3D: where r and l are the largest and smallest scales of the distortion and D is the fractal dimension (D = 2 for a plane, 3 for space filling of radius l). In the supernova D starts near 2 and grows as a consequence of instabilities. Bottom half is burning less fuel than top half

“Big whorls have little whorls that feed on their velocity....” L l One of the most effective ways of increasing surface area is turbulence.

The Gibson Length For a standard Kolmogorov picture of turbulence: l Gib is defined by: This is the smallest length scale that can be deformed by turbulence before burning first.

If use this for the smallest length scale and D=2.33 for Kolmogorov turbulence: The flame moves with an effective speed equal to that of the largest (local) turbulent eddy. This also turns out to be true for other for other representations of turbulence. e.g. Niemeyer and Kerstein, New Astron, (1997), 2, 239 for Bolgiano- Obukhov scaling.

Unlike the laminar flame speed which slows with time (density), the turbulent speeds and sizes of the largest eddies increase with time

"Sharp-Wheeler Model" g Model OK, but deficient in Si, S, Ar, Ca A simple toy model...

Speculation How many points and when and where each ignites may have dramatic consequences for the supernova (origin of diversity?)

Igniting the star at a single point off center gives very different results than igniting precisely at the center or in a spherical volume. This "single point ignition" model did not produce a supernova (pulsation would have ensued)

Ignition at 5 points did produce a successful supernova with 0.65 solar masses of burned material, 0.5 solar masses of which was 56 Ni. Note - this was a 2D calculation.

Reinecke et al. (2002)

Reinecke, Hillebrandt, Niemeyer, et al. (2002) MPA 0.4 solar masses “Fe” 4.5 x erg

slides from Martin Reinecke converged??

slide from Martin Reinecke

Light Curve After the white dwarf has expanded a few times its initial radius its internal energy (and entropy) will be chiefly due to radiation, that is - Before the radiation can diffuse out the supernova has expanded from 10 8 to cm. During that time, the internal energy goes down from ~10 51 erg to ~10 44 erg. The internal energy is totally inadequate to power the light curve.

Radioactivity q = 3.0 x erg/gm q = 6.4 x erg/gm 0.6 solar masses of radioactive Ni and Co can thus provide 1.1 x erg at late times after adiabatic expansion is essentially over.

t (days since peak) 56 Ni + 56 Co decay Optical light curve gamma-ray escape Qualitative Type Ia Supernova Light Curve Luminosity Diffusion and expansion time scales approximately equal

Why is there a Philipps Relation? Broader = Brighter Pinto & Eastman (2001) New Astronomy  at peak light Photons must diffuse through a forest of lines in a differentially expanding medium. Doppler shift causes a migration from line to line. The trapped radiation is mostly uv and the uv optical depth is very large. Photons escape chiefly by fluorescence.

Pinto and Eastman, (2000), ApJ, 530, 757 Blackbody peak near maximum light

More 56 Ni implies a larger luminosity at peak. (Arnett's rule) But more 56 Ni also implies higher temperature in the interior. This in turn implies that Fe, Co, Ni are more highly ionized (III rather than II) The more highly ionized Fe is less effective at "Photon Splitting" than less ionized Fe Hence hotter implies more optical opacity (actually less optical efficiency)

Pinto & Eastman, (2001), New Astron, Left – a single supernova model (energy, density structure, etc) in which only the mass of 56 Ni has been varied. Also shown are the standard template of light curves displaying the width-luminosity relation.

Light Curves What matters? The mass of 56 Ni -- contributes explosion energy, radioactive energy, and opacity. The mass of 54 Fe, 58 Ni, and other stable members of the iron group -- contribute opacity and explosion energy, but no radioactive energy. The mass of SiSArCa -- contribute to the explosion energy, but not the opacity or radioactive energy. The explosion energy -- depends on the ignition density (hence accretion rate) and C/O ratio as well as all the above masses. Mixing

An idealized model Assume a starting mass of 1.38 solar masses, a central density of 2 x 10 9 g cm -3 and a C/O ratio of 1::2 For a given starting density, the final composition (three variables, plus mixing) then defines the model.

The final velocity distribution is not very sensitive to how the energy is deposited (especially for the iron containing region).

Conclusions A first principles understanding of how Type Ia supernovae explode is still lacking, but progress is being made It may be that detonation plays no role in the explosion – though this issue is not conclusively resolved. SN Iae explode by a carbon deflagration in which instabilities and turbulence play a key role. The width-luminosity relation is a consequence of the atomic physics of the explosion, in particular a temperature- dependent escape probability. The most important parameter is the mass of 56 Ni. But there are four other parameters that ought to affect the light curve at some level. Evolutionary corrections could enter in this way.