An excellent website relating to all areas of physics is to be found at a Georgia State University. To read some basics about different kinds of supernovae, find the word "supernova" in their index after first clicking here .

Two web archives that contain supernova spectra are the Online Supernova Spectrum Archive and the Harvard-Smithsonian Center for Astrophysics .

Information on the Carnegie Supernova Project can be obtained by clicking here .

Here are some spectra of Type Ia supernovae at the time of B-band maximum (taken from a paper on SN 1999aa, astro-ph/0404393, by Garavini et al.):

In short, Type II supernovae (SNe) show strong hydrogen emission lines in their spectra. Type Ia supernovae do not show hydrogen lines; their spectral signature is singly ionized silicon (blue shifted to a wavelength of about 615 nm). Note that the basic differentiation between these two types of exploding stars does not say anything (yet) about the nature of the stars that exploded. Type II SNe are explosions (due to core collapse) of single stars more massive than 8 solar masses.

What are the progenitors of Type Ia SNe? Suffice it to say that that Type Ia SNe are regarded to be exploding carbon-oxygen (CO) white dwarf stars which have reached a critical mass of 1.4 solar masses (the Chandrasekhar limit) owing to mass transfer from a companion star (most likely a giant star). A good review of some of the early successes in the modelling of Type Ia SNe is the article by Nomoto, Iwamoto, & Kishimoto (1997). The interested reader can search the more recent literature for articles by Peter Hoeflich, Phil Pinto, Paolo Mazzali and others. Mario Livio wrote an excellent review in 2000. It can be obtained by clicking here .

It should be said, however, that it is not yet really proven that Type Ia SNe are indeed all expolosions of CO white dwarfs. This idea has just become part of the "common knowledge" of the past few years. Why? On the plus side, consider the analogy of making a fire in the fireplace. If you always burn three oak logs of the same total mass, you will get essentially the same energy output from your fire. If you blew up a sequence of white dwarf stars of 1.4 solar masses, producing the same amount of radioactive Nickel-56, you should get just about the same energy output from the explosion. However, consider this other analogy. If you explode a bomb next to a table full of watermelons, you would expect to see watermelon material flying around. If you blew up a bomb next to a dead whale, you would see whale meat flying around. If you blow up a white dwarf star next to a giant star (which would have hydrogen gas in its outer atmosphere), why don't we see hydrogen lines in the spectrum of the explosion if the hydrogen is nearby? There is only one example I know of which shows this, SN 2002ic (Hamuy et al. 2003). In that paper we assert that the SN explosion was plowing into the circumstellar gas once part of the white dwarf star or its much larger (and less evolved) companion.

It is possible that some Type Ia SNe are mergers of two white dwarf stars. If the sum of the masses exceeds 1.4 times that of the Sun, then such a merger will explode. With no hydrogen nearby, that would explain the lack of hydrogen in the spectra.

Let us consider the optical and infrared light curves of Type Ia SNe.

Mark Phillips discovered in 1993 that there is relationship between the the absolute magnitudes at maximum light of Type Ia supernovae and the rate of decline of the light curves (Phillips 1993). He introduced the decline rate paramter Delta m_15(B), which is the number of magnitudes that a Type Ia SN declines in its B-band light curve in the first 15 days after maximum light.

There are three basic methods of analyzing and describing the decline rate relation. In addition to the dm15 method (Phillips et al. 1999), there is the Multi-color Light Curve Shape (MLCS) method of Riess, Press, & Kirshner (1996), and the "stretch method" of Perlmutter et al. (1997; see also Goldhaber et al. 2001). For the B-band and V-band light curves, the Type Ia SNe which are intrinsically brighter at maximum light have wider light curves. Here we show a pair of graphs from the Perlmutter group (Supernova Cosmology Project, or SCP). The top graph shows that the narrower V-band light curves correspond to fainter objects. To construct the bottom graph the light curves of a number of objects are stretched in the time domain, then laid on top of each other to produce a V-band template, which can be stretched to fit the light curves of other Type Ia SNe.

In the graph below, made by Mark Phillips for a paper by Krisciunas et al. (2003), we see the "decline rate relations" for Type Ia SNe in the B-, V-, I, and near infrared H-bands, which are plots of the absolute magnitudes vs. the decline rate parameter Delta m_15(B). Note that the slope of the points in the left-most two-thirds of the diagram is steepest in the B-band, and gets less and less steep as we proceed to longer wavelengths. By the time we consider the H-band magnitudes (10 days after the time of B-band maximum), the slope may be statistically zero. What this means is that at optical wavelengths Type Ia SNe are standardizable candles (i.e. they can be reduced to the analog of 100 Watt light bulbs at a particular value of the decline rate parameter), but at near-IR wavelengths, they may be standard candles , meaning that all objects have the same intrinsic brightness within the errors. The idea that most Type Ia SNe may be standard candles in the near-IR was first suggested by Elias et al. (1985) and further substantiated by Meikle (2000) using Cepheid-based distances to the host galaxies of 8 Type Ia SNe. We have more to say on this subject towards the end of this web document.

Here is one of the best optical and infrared light curves we have, of SN 2001el (Krisciunas et al. 2003). Note the post-maximum "shoulder" in the R-band light curve and the secondary maxima in the IJHK light curves. (The J-, H-, and K-bands are at 1.25, 1.65, and 2.2 microns in the near infrared (IR).)

Using data from the Calan/Tololo supernova search, Hamuy et al. (1996) first noticed that the slowly declining Type Ia SNe had stronger I-band secondary maxima. This aspect of the morphology of the I-band light curves is built into the MLCS method (Riess et al. 1996). More recently, Krisciunas et al (2001) parameterized the strength of the I-band secondary maxima by converting two dozen I-band light curves from magnitudes to flux units (with respect to the I-band maxima) and integrating the light curves from 20 to 40 days after the time of B-band maximum. An example is shown below:

If we plot the decline rate parameter Delta m_15(B) vs. the relative strength of the secondary maximum, we find that that more than 90 percent of the examples fall along a particular curve. Note that there are exceptions to the trend. SNe 1994M and 1992bc have I-band secondary maxima with "anomalous" strengths. Thus, while it generally true that a strong I-band secondary maximum is indicative of a bright Type Ia SN, for a single given object one cannot automatically predict the decline rate (and, hence, the intrinsic brightness) with great accuracy.

The "stretch method" of Perlmutter et al. (1997) does not work for the R- and I-band light curves. What I mean by this is that there are no R- and I-band templates which can be stretched in the time domain to fit the R- and I-band light curves over their whole range from 10 days before maximum light to 60 or 90 days after maximum. As we have accumulated more and more near-IR data this fact had limited our ability to find templates for the near-IR light curves. We simply did not have enough well-sampled objects like SN 2001el seen above.

In July of 2003 Mark Phillips had a bright idea. It went something like this. We know that there are Perlmutter-type stretch parameters for the B- and V-band light curves. These stretch factors correlate with another measure of the intrinsic brightness of Type Ia SNe at maximum -- the decline rate parameter Delta m_15(B). Let's see what happens if we take Perlmutter-type stretch factors and apply them to the infrared light curves of our best sampled objects at maximum . Never mind what happens at the time of the secondary maximum.

We did not have the Perlmutter B- and V-band templates and the code to compute the stretch factors directly from the B- and V-band light curves. But, we did have the means to calculate the decline rate parameter Delta m_15(B).

From p. 182 of Saurabh Jha's Ph. D. Dissertation (Jha 2002), we find the following regression lines:

Delta m_15(B) = -2.04 (s_B) + 3.06 ;

Delta m_15(B) = -2.13 (s_V) + 3.21 .

So, for any given value of Delta m_15(B) we have an estimate of the the B-band stretch factor s_B and the V-band stretch factor s_V. Recall that the stretch factor is a factor used to scale the template light curve to fit a light curve of some individual supernova. Since we are trying to make a template from light curves we actually want the reciprocals of the stretch factors. So, for example, if Delta m_15(B) = 1.1 (a very typical value), s_B = 0.961 and s_V = 0.991 (approximately). The reciprocals are 1.041 and 1.009. The average of those is 1.025. To try to build up an IR template we scale the "time since B-band maximum" of the IR light curves of an object with Delta m_15(B) by 1.025. We did this for a sample of eight objects: SNe 1980N, 1986G, 1998bu, 1999aw, 1999ee, 2000ca, 2001ba, and 2001el, whose decline rates range from Delta m_15(B) = 0.81 to 1.73. Our JHK templates (from Krisciunas et al. 2004a and 2004b) are shown below:

In the graph shown above we have coded the points by color and shape for each of the eight template objects. The root-mean-square errors of the fits are +/- 0.062 mag in J, +/- 0.080 mag in H, and +/- 0.075 mag in K. What these mean is that if we have an accurate time of B-band maximum, an accurate value of Delta m_15(B) from the optical light curves, and just one night of IR data in the time window of -12 to +10 (stretched) days with respect to the time of B-band maximum, we can determine the IR maxima. Admittedly, the scatter of the points is not exactly equal along the three curves shown above. In particular, in the H-band the light curves exhibit more scatter at 10 days after T(B_max). But until we have many light curves as well sampled as SN 2001el, this is the best we can do in order to study a sufficiently large sample of Type Ia SNe at maximum.

The next thing one would want to do is to plot the extinction-corrected apparent magnitudes at maximum vs. the redshift (or logarithm of the redshift). These are known as Hubble diagrams. Not long ago one saw Hubble diagrams in the literature which contained a great deal of scatter. However, I'm sure you'll agree that the Hubble diagrams shown below have data which are just likes beads on a string. The red triangles and blue dots are data from Krisciunas et al. (2004a). The red triangles correspond to objects whose host galaxies have directly measured distances, either from Cepheids or surface brightness fluctuations (SBFs). The blue dots are objects with redshifts > 0.01. These are considered far enough away that they lie in the smooth Hubble flow. We have added five more objects from Krisciunas et al. (2005). They are SN 2002bo (the yellow triangles) and four objects out in the smooth Hubble flow (represented by green squares).

I should mention one of our prime motivations for making observations in the infrared. Below we see a figure from an often-reference article by Cardelli, Clayton, & Mathis (1989).

Infrared extinction by dust is considerably lower in the near-IR compared to optical wavelengths. If an object had a V-band extinction of 1.0 mag, then its J-band extinction would be about 0.28 mag, its H-band extinction would be about 0.19 mag, and its K-band extinction would be about 0.13 mag. Many Type Ia SNe have host extinctions of A_V = 0.5 mag or less, so the JHK extinctions would be correspondingly smaller. If we observe in the infrared, the uncertainties in the extinction corrections are often on the order of the uncertainties in the IR photometry. Thus, while extinction by dust can be a serious constraint for optical determinations of the distances to Type Ia supernovae, by observing in the IR we essentially eliminate a potentially serious source of systematic error. This even holds true if the dust in some galaxy has very unusual properties compared to dust in our galaxy. For what is the significance of the difference of an H-band extinction correction of 0.08 vs. 0.05 mag if the uncertainties of the photometry are +/- 0.04 mag themselves?

One could say that the Hubble diagrams shown above only tell us that the universe is expanding. After all, it is hard to see just how good the fits are in detail. It could be that deviations from the lines are correlated with some other observables. So the next thing to do is to calculate the absolute magnitudes using either Hubble's Law (and some assumed value of the Hubble constant, such as H_0 = 72 km/sec/Mpc from Freedman et al. 2001) for objects out in the smooth Hubble flow, or using directly determined distances such via Cepheids or Surface Brightness Fluctuations for the more nearby objects. Krisciunas et al. (2004a) did this for a sample of 16 objects. To that we can add 5 more objects from Krisciunas et al. (2005) and also the fast decliner SN 1999by (Garnavich et al. 2004). In the figure below we plot the absolute magnitudes at maximum vs. the Phillips parameter Delta m_15(B). SN 1999by is represented buy the grey right-pointing triangles.

What this shows is something we alluded to above. Most Type Ia SNe are IR standard candles. There are no signifanct decline rate relations over the range of 0.8 < Delta m_15(B) < 1.74. We have one semi-outlier and one outlier: SN 2000bk in the H-band, and the fast decliner SN 1999by (which has Delta m_15(B) = 1.90). The 2000bk data are rather ragged, and we only had two points in the window of time -12 to +10 days after T(B_max). SN 1999by is the only really fast decliner we have reduced data for so far. However, since last July we acquired very nicely sampled optical and IR light curves of SN 2003gs, which has Delta m_15(B) = 1.84. It could be that the fast decliners have statistically significantly fainter absolute magnitudes at maximum compared to the rest of Type Ia SNe. We just don't know yet for certain. But just as Meikle (2000) suggested, and Elias et al. (1985) before him, most Type Ia SNe are excellent standard candles in the IR. For the objects with Delta m_15(B) < 1.74 we find an rms scatter of their absolute magnitudes of about +/- 0.14 mag. This means that we can determine the distance to the an individual object to +/- 7 percent.

For information on using optical and infrared data of Type Ia supernovae to determine their intrinsic colors and the extinction along the line of sight, click here .

References:

Cardelli, J. A., Clayton, G. C., & Mathis, J. S. 1989, "The Relationship between Infrared, Optical, and Ultraviolet Extinction," Astrophysical Journal , 345 , 245

Elias, J. H., Matthews, K., Neugebauer, G., & Persson, S. E. 1985, "Type I Supernovae in the Infrared and Their Use as Distance Indicators," Astrophysical Journal , 296 ,379

Freedman, W., Madore, B. F., Gibson, B. K., et al. 2001, "Final Results from the Hubble Space Telescope Key Project to Measure the Hubble Constant," Astrophysical Journal , 553 , 47

Garnavich, P., Bonanos, A. Z., Krisciunas, K., et al. 2004, "The Luminosity of SN 1999by in NGC 2841 and the Nature of 'Peculiar' Type Ia Supernovae, Astrophysical Journal , in press (The original version of this article can be found on the astrophysics preprint server as astro-ph/0105490. It is finally being re-submitted in April, 2004, and contains infrared data from the Fred L. Whipple Observatory 1.2-m telescope.)

Goldhaber, G., Groom, D. E., Kim, A., et al. 2001, "Timescale Stretch Parameterization of Type Ia Supernova B-band Light Curves," Astrophysical Journal , 558 , 359

Hamuy, M., Phillips, M. M., Suntzeff, N. B., et al. 1996, "The Morphology of Type Ia Supernova Light Curves," Astronomical Journal , 112 , 2438

Hamuy, M., et al. 2003, "An asymptotic-giant-branch star in the progenitor system of a type Ia supernova," Nature , 424 , 651

Jha, S. 2002, Exploding Stars, Near and Far , Ph. D. Dissertation, Harvard University

Krisciunas, K., Phillips, M. M., Stubbs, C., et al. 2001, "Optical and Infrared Photometry of the Type Ia Supernovae 1999da, 1999dk, 1999gp, 2000bk, and 2000ce," Astronomical Journal , 122 , 1616

Krisciunas, K., Suntzeff, N. B., Candia, P., et al. 2003, "Optical and Infrared Photometry of the Type Ia Supernova 2001el," Astronomical Journal , 125 , 166

Krisciunas, K., Suntzeff, N. B., & Phillips, M. M. 2004a, "Hubble Diagrams of Type Ia Supernovae in the Near-Infrared," Astrophysical Journal , 602 , L81

Krisciunas, K., Suntzeff, N. B., Phillips, M. M., et al. 2004b, "Optical and Infrared Photometry of the Nearby Type Ia Supernovae 1999ee, 2000bh, 2000ca and 2001ba," Astronomical Journal , 127 , 1664

Krisciunas, K., Suntzeff, N. B., Candia, P., et al. 2005, "Optical and Infrared Photometry of the Nearby Type Ia Supernovae 1999ek, 2001bt, 2001cn, 2001cz, and 2002bo," in preparation

Meikle, P. 2000, "The Absolute Infrared Magnitudes of Type Ia Supernovae," Monthly Notices of the Royal Astronomical Society , 314 , 782

Nomoto, K., Iwamoto, K., & Kishimoto, N. 1997, "Type Ia Supernovae: Their Origin and Possible Applications in Cosmology," Science , 276 , 1378

Perlmutter, S., Gabi, S., Goldhaber, G., et al. 1997, "Measurements of the Cosmological Parameters Omega and Lambda from the First Seven Supernovae at z > 0.35," Astrophysical Journal , 483 , 565

Phillips, M. M. 1993, "The Absolute Magnitudes of Type Ia Supernovae," Astrophysical Journal , 413 , L105

Phillips, M. M., Lira, P., Suntzeff, N. B., Schommer, R. A., Hamuy, M., & Maza, J. 1999, "The Reddening-Free Decline Rate Versus Luminosity Relationship for Type Ia Supernovae," Astronomical Journal , 118 , 1766

Riess, A. G., Press, W. H., & Kirshner, R. P. 1996, "A Precise Distance Indicator: Type Ia Supernova Multicolor Light-Curve Shapes," Astrophysical Journal , 473 , 88

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