Measuring Polarization	Modeling Geometries	Resolving Spectra

When Lifan Wang and his colleagues trained a telescope on SN 2001el, they became the first to observe net polarization in a "normal" Type Ia supernova -- the first to find unambiguous evidence that the most common of these thermonuclear blasts were not, after all, perfectly symmetric events.

But there was more. Not only was SN 2001el polarized, its otherwise normal spectrum showed an unusual feature -- a feature that opened a new window on the explosion processes of Type Ia supernovae and what their progenitors might have been like before they blew up.

A stand-out feature

"We got interested because 2001el showed a high-velocity calcium feature in its spectrum," says Peter Nugent, an astrophysicist with Berkeley Lab's Computational Research Division. "There were two separate sets of calcium II lines, one indicating a velocity that was normal for a Type Ia photosphere but the other showing a very high velocity."

The photosphere (visible surface) of a Type Ia explosion typically expands outward at a velocity of about 10,000 kilometers per second, over 22 million miles per hour. This velocity is calculated by determining how far typical absorption lines in the spectrum, like that of doubly ionized calcium (calcium II), have been shifted. A blueshift indicates material speeding toward the observer, a redshift material speeding away. But SN 2001el exhibited an additional calcium II feature blueshifted farther than normal, indicating material coming at the observer roughly twice as fast as the expanding photosphere.

The spectrum of SN 2001el shows two calcium II features. One is shifted farther toward the blue end of the spectrum, indicating material moving away from the photosphere at higher velocity, and is much more strongly polarized.

"Then Lifan showed us the spectropolarimetry," Nugent says. "The high-velocity calcium line had a very different polarization than the supernova as a whole." It was not only more strongly polarized but polarized at a different angle as well.

"This is a rare observation, a supernova in which components with different velocities are apparently oriented in different directions," says Daniel Kasen, who works with Nugent to build computer models of supernova explosions.

The combined data on polarization and flux (the brightness of the supernova's light in various parts of its spectrum) presented an exciting opportunity for computer modeling. Whereas the net polarization of SN 2001el could be interpreted as an ellipsoidal explosion, one "flattened" by about 10 percent, the different polarization of the high-velocity calcium II line suggested a more complex geometry -- one that could not be explained by previous attempts to model Type Ia supernovae.

The candidates for complexity are many. If a Type Ia supernova begins as a white dwarf star orbiting a companion from which it accretes matter, the spin of the white dwarf, the companion star, the accretion disk, and their interaction -- whether taken individually or together -- would all contribute to asymmetry.

"The only way to decide what geometries might account for the observations is to try different explosion models, use them to generate synthetic spectra, and see which comes closest to reproducing the observations," says Nugent. "Very few people are doing such complex 3-D models. It's a nasty task. It takes months just to run the codes."

A typical run for just one of the several models devised by Kasen and Nugent takes 20,000 processing hours on the IBM SP supercomputer at the National Energy Research Scientific Computing Center (NERSC) -- equivalent to 27 months on a single-processor machine.

Nugent and Kasen concentrated on a stage of the evolving explosion when the asymmetry was most evident, about a week before the supernova reached its maximum brightness. Armed with a Department of Energy "Big Splash" award -- a grant of supercomputer time to computationally intensive scientific investigations -- they modeled four different likely geometries, each with two components.

Sophisticated computer models of supernovae have previously concentrated on a limited number of parameters, for example the 3-D models of radiative transfer of Wang's University of Texas colleague Peter Hoeflich. The Berkeley Lab models were less complicated but capable of exploring a larger set of parameters. For simplicity, they assumed the main explosion (the photosphere) of SN 2001el formed a simple ellipsoid; they concentrated their efforts on finding an explanation for the differently polarized, high-velocity material.

The "winning" model would be able to produce a synthetic spectrum closely matching the actual observations of SN 2001el -- both the spectral features of the flux and the amount and orientation of their polarization.

Models of a cosmic bomb

One model assumed the ellipsoidal photosphere was surrounded by a spherical shell of high-velocity material. Another model assumed that the shell too was ellipsoidal, but rotated at an angle to the photosphere. A third assumed a spherical shell containing dense blobs or clumps of matter. The last assumed an offset donut-shaped (toroidal) structure around the photosphere.

A toroid of high-velocity material would reproduce the spectral features of SN 2001el if viewed edge-on, but the degree of polarization would be too great.

Says Nugent, "Each of these models could explain the observations, but only from some favored point of view" -- that is, only if the supernova had a peculiar history or were oriented toward observers on Earth in a very special way. Considered more generally, all had weaknesses.

The spherical-shell model nicely reproduced the degree of polarization in the high-velocity material but was unable to account for the polarization angle.

The rotated elliptical shell could explain the polarization angle, but failed to match a feature in the supernova's flux that suggested an uneven absorption of light from the photosphere. The configuration itself would have required a peculiar history, a rapidly spinning white dwarf that exploded off center.

The model most resembling a star system with an accretion disk was the toroid, and Nugent admits he favored it for that reason: "I tried to force the toroid idea on Dan, but he didn't go for it." Calculations showed that the flux features were nicely reproduced, provided the toroid was observed edge-on -- but the polarization was much too strong.

The best fit in terms of both flux and polarization -- if still far from perfect -- was the so-called clumped shell. Physically, the picture is of a blob of calcium blowing away from the photosphere. Blob-like features could also result if a shell of high-velocity material were to become unstable and fall apart.

A clump of high-velocity material comes closest to reproducing both flux and polarization features observed in SN 2001el.

"The clumped shell model has a nice way of explaining the absorption feature, and the polarization doesn't get incredibly strong," Nugent says. Moreover, by rotating the model and looking at it from various angles, other clumpy scenarios are possible, all of them physically reasonable.

Still starved for data

While SN 2001el provided much more information about the explosion of a Type Ia supernova than had been available before, trying to generate computer models from it underscored just how limited the data still is. The geometry of SN 2001el may be consistent or even common among Type Ia supernovae, but many more observations -- viewing the explosions from many different lines of sight -- will be needed to pin that geometry down.

Better observations of flux are needed too. "If we could see other trace elements, maybe we'd learn more about the geometry and physics of explosions," Nugent says. "Most observations aren't set up to look closely at the wavelengths where these interesting features occur -- blue-shifted calcium is often overlooked, for example. I suspect high-velocity calcium may occur often, but you have to catch it early -- it goes away fast."

Kasen adds that "this clump has other stuff in it. We'd like to measure silicon and iron, but those are much weaker signals. And we need to look at the whole spectrum, all the way out, before the supernova reaches maximum brightness."

If the clump is really there, it may come from nuclear burning inside the exploding white dwarf, or it may come from the companion star. Says Kasen, "People tend to forget about this, but in a binary system an explosion is going to run into the companion in just a few minutes."

The Visualization Group in Berkeley Lab's Computational Research Division runs a multidimensional model of a supernova interacting with a companion star.

What effect would this have on the polarization of a Type Ia supernova? "The 2-D models that have been done suggest the companion carves out a cone in the explosion," Kasen says. "We would expect a low-density hole."

Nugent says, "Many people seeing asymmetry say, 'Let's call it an ellipsoid.' But here" -- in the effect of the companion on the shape of the explosion -- "is a model that already fits the total observed asymmetry. From some lines of sight, it would look even weirder!"

Nugent cites SN 1991T, a hot blue supernova with very weak spectral features, of which the International Astronomical Union Circular remarks, "The spectrum is highly unusual but is certainly not that of a classic type-II or type-Ia supernova near maximum." Were the observers looking down into a big hole in the explosion?

These are the kinds of questions that can't be answered without finding a lot more Type Ia supernovae, near enough and therefore bright enough -- as was SN 2001el -- to yield copious details about both flux and polarization.

The Shapes of Exploding Stars, part 3

Additional information

• "Analysis of the flux and polarization spectra of the Type Ia supernova SN 2001el: exploring the geometry of the high-velocity ejecta," by Daniel Kasen, Peter Nugent, Lifan Wang, D. A. Howell, J. Craig Wheeler, Peter Hoeflich, Dietrich Baade, E. Baron, and P. H. Hauschildt, appeared in the Astrophysical Journal, 2003, vol 593, p 788.