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Supernovae Light Curves (II)

A professional perspective

Supernovae of both types reach maximum optical brightness 2 to 3 weeks after their explosions. At their peaks, type I SNe are brighter than type II by about one magnitude. The peak absolute magnitude depends on the extragalactic distance scale, which is known only to a factor of 2. On a "long-distance" scale corresponding to a Hubble Constant of 50 km/sec/Mpc, type I SNe reach an absolute magnitude of (~) -20 and have a peak luminosity of 2 x 1043 ergs/sec, 5 x 109 times the luminosity of the sun.

On a "short scale" corresponding to 100 km/sec/Mpc, the type I absolute magnitude is -18.5 and the luminosity is lower by a factor of 4. Observations made across the electromagnetic spectrum show that type I SNe emit almost all of their energy in the optical part of the spectrum while type II SNe emit a significant fracton at ultraviolet wavelengths. Consequently, type II SNe, although fainter optically, have nearly the same peak luminosity as type I. The total time-integrated emission of electromagnetic energy of both types is on the order of 1049 to 1050 ergs, much less than the kinetic energy of 1051 ergs. Thus the radiative efficiency of SN explosions is low.

The mean type I curve, which is well defined by observations, consisting of a initial rise and fall (the peak) lasting until 30 days after maximum light, and a subsequent, slowly fading tail. The tail appears to be nearly linear when magnitudes are plotted against time, but magnitude is a logarithmic measre of brightness and the tail actually corresponds to an exponential decay of brightness with time. The decay rate of the type I correspods to a half-life of 50 days.

Type II SNe are subdivided into II-P and II-L on the basis of their light curve shape. Two-thirds of the observed type II SNe are II-P, which interrupt the initial declines from their peaks to enter a plateau phase of nearly constant brightness until 80 days after maximum light. A type II-L shows nearly a linear decline from its peak for 80 days after maximum light. The able data on the later phases of type II light curves are not well defined, but both II-P and II-L do appear to have slowly fading, linear tails,with a decay rate corresponding to a half-life of 100 days.

Simulations of SN1987A and M1

At left, simulation of Sanduleak -69202, alias SN1987A explosion. At right, for comparison purpose, simulation of M1, the famous Crab nebula that exploded in 1054. Mpeg files of 2.1 MB and .Mov of 3.9 MB. Documents STSCI and Space Telescope

Characteristics of type Ia SN light and color curves

1. Light curves

In recent years a great deal of photometric data on type Is SNe has become available, giving the possibility of assembling a fairly large and homogeneous sample of light curves for this class of object....Due to the importance of the Ia SNe as possible distance indicators, it seems worthwhile to determine as accurately as possible the mean characteristics of these curves. 

We may reasonably infer the the SN Ia explosion is a well defined phenomenon occuring nearly on the same scale, which allow the fitting of all the best (well monitored) light curves,which are considered to be relatively representative in shape and absolute magnitude. 

The light curve also offers the possibility of finding some general properties of the Ia event from a photometric point of view (although observers in this program will be accomplishing this task in the visual). It allows also the determination of the epoch and brightness of the maximum for a SN which has not been well followed, simply by fitting its magnitudes to the average curve. 

The below table expresses the mean characteristics of most type I SNe :

Mean deviation at maximum  : +/- 0.15m

Duration of maximum  : 18-19 days (the point where the event rises and falls a half degree).

Number of days to rise of 3,2,1 magnitudes (to max.) :  (t-3) =15d, (t-2) =13d, (t-1) =10d.

Number of days to fall of 3,2,1 magnitudes (from max.) : (t-3) =55d, (t-2) =23d, (t-2) =14d.

Rate of decline (mag/day over the first 30 days from max.) : 0.087

Final rate of decline (mag per day from 50-300 days past max.) : 0.016

A peculiar feature of the type I SN is the Inflection point, about 30d past maximum light, and ~2.7 magnitudes below it, which is where the steep early decline ends and a slower final decline (linear) ensues. The change in the rate of decline at this point is rather sharp. In assembling the average light curve some difficulties have been encountered in obtaining a good fit for all the available models of light curves. 

In fact, some of the SNe showed peak maxima with large amplitude variations, while others have had broad and shallow maxima, these differances being apparently beyond the range of photometric errors. This leads to the possibility of a further subdivision of type Ia SNe in to two subclasses: "fast and slow", henceforward also called (in this paper reference) "a" and "b" (we will not get into the energetics that power these subdivisions at this time) characterized by different values of the following parameters :

                                                                                                               SN(a)      SN(b)

                                                                                                                (fast)    (slow)      

^T = width of the light curve two magnitudes below maximum light            32d          38d          

^m = amplitude from maximum light to the inflection point                         3.25m       2.50m       

  R = rate of decline from 30 days to 150 days past maximum light           0.016d      0.012d    

Ed. Note: Recent studies, after this article was written have been able to determine that there does exist different types of type I SNe; the type Ib, and Ic. We will not attempt to describe these events in detail here, but rather give a broad description of each due to the fact that there is still a lot of ongoing research being conducted (see below), although the importance of discovering SN events early in their apparition will enable professional astronomers to better define these events.

2. Color curves

"...Although our knowledge of the brightness, color, and spectra of SNe has grown substantially, investigators have therefore endeavored to reconstruct the light curves from elements that can readily be determined. These elements include the point at which the decline in brightness begins to slow down and the mean rate (B)[or Beta, which denotes a value of magnitude decline per 100 days] of decline in photographic brightness from maximum light to that point. Without question, maximum light represents one of the chief distinquishing points, although not the only one on the photographic light curve of a supernova...".

For all practical purposes the color index of a supernovae is represented by the differance in magnitude of the light curve of the photographic and the visual modes....thusly, a value of (-) would indicate that the SN event is diplaying more of a blue value, whilst the (+) value would be indicative of a more redder scenario.

Similiar in context to the color indices of many main sequence stars, ie. -0.31= a star of spectral type BO, while a value of +0.71 would be of a K5 star and so on...these differances occur within the explosive element of the doomed star and are usually synonymous with its spectral characteristics at a particular point in its evolution...  

The color index which some days before maximum light is negative (-0.30) steadily increases becoming zero about six days past maximum light and attaining its largest value, nearly +1.00 (or more), at phase (time) +30-35d. Later on the color index declines to nearly 0.6 at phase +80d, approaching zero about 150d past maximum. 

However, after phase +80d the color curve, even with the new data remains undefined, the dispersion points being fairly large. It is imperative that many accurate measures at that phase are necessary to reach certain conclusions.  It may be interesting to remark that, during the first 30 days from Max., the color curve and light curve of type I SNe show an opposite trend, B-V steadily increasing while the brightness declines. About 35d from max. just at the inflection point of the light curve, the color index reaches its maximum and then declines at a rate of ~0.01 mag/day, going roughly parellel to the corresponding light curve. The observed changes in the color curve at the end of the slow decline, are certainly related to spectral variations. 

However, besides the gradual increase in intensity the red relative to the blue-violet features, which begins 30-60d from maximum, and the general fading of all the emmisions, no other relative changes which may explain the peculiarities of the color curve are found in the spectra. It may be noted that the progressive red-shifting of some real physical changes in these stars seem to occur when the color curve turns down....(Note: For our studies, it is suggested that a color index of 0.00 in V will occur when the event is at maximum light in the visual).

Some curves recorded during the explosion of SN1987A. At left, the light curve, at center, the detection of neutrinos and at right the radio flux. Documents S.L.Shapiro/U.Illinois and al., Jaret Heise/U.Br.Columbia and U.Sidney/IoA.

Comments

The author has attempted a rise/decay time, magnitude chart utilizing data from Pg (photographic), V-band, and pv (photo visual) mean light curves (by eye). This will hopefully assist the observer in creating his/her own mean light curves. In this way their observations can be plotted against mean values of a type Ia SN, hopefully with enough data the observer could elliviate some degrees of his/her own personal equation. The Pg will relate to CCD imagers, whilst the V, and pv hopefully will assist the visual observer...the error here is: +/- 1.5d. For all practical purposes, the pv maximum is usually 2.5d later than V, and 0m.02 brighter.

Rise to Max :

                              Mag.           Pg                 V            pv (visual)    

               2.5m     ----     14.16d     17.33d

               2.0m    14.16d    12.91d     15.99d

               1.5m    12.91d    11.24d     14.33d

               1.0m    11.25d    10.00d     12.99d

               0.5m    08.75d    05.83d     09.66d

Maximum light :

Mag              Decay from Maximum

 0.5m        09.16d        14.16d          11.66d            

 1.0m        13.75d        24.58d          19.66d

 1.5m        17.91d        31.66d          28.33d

 2.0m        22.91d        42.49d          40.50d

 2.5m        28.74d        62.00d          59.50d

 3.0m        40.83d        81.66d          79.16d

 3.5m        70.00d        97.07d          99.16d

 4.0m        99.16d         ----                ---- 

Authors note: As one can see, the V band and pv decay times follow a rather close relationship, thusly when using charts, refer to the V band photometry, as more data is available on this value, than on pv values. A more detailed description of this utility is available in the program SNCURV.GIF, which can be accessed from the ISN (International Supernovae Network) home page.

Characteristics of type Ib SN

Based on optical spectroscopy the authors have initiated the following characteristcs for this subclass of SN...A SN is classified as Type Ib if it meets the following spectral properties.... There must be a general resemblence to the spectra of SNe1a during the first few months past maximum light (ed. note: The term used is that the SN is 'born old'). In particular, this includes an absence of hydrogen emission or absorption lines. Unlike SNe1a, the spectrum <25d after maximum light should display no 6150 absorption lines. Additionally, or alternatively, if the SN is observed long after maximum. 

The late-time spectrum must be dominated by strong emission lines of [OI] 6300, [Ca II] 7300, and other intermediate-mass metals. The spectrum must not show strong emission lines of hydrogen seen in late-time spectra of SNII... (ed. note: this paper was one of the first to reveal the appearance of the type Ib SN, the prototypes that satisfied all of the above criteria at the time were: SN 1983N, and SN 1984L).  

In another event, SN 1984I in the galaxy ESO 323-G99, the authors contend..."In spite of its red color and apparently low luminosity of SN 1984I might have been mistaken for a type Ia SN if the spectrum had not been obtained. This seems to emphasize the importance of spectroscopic observations in accurately sorting out Type Ia and Type Ib events..." Other additional information on these events..."The hypothesis we favor for the origin of SN Ib is that they are basically the same as SNII but have their hydrogen envelope removed...."

Characteristics of type Ic SN

This class of SNe is a relative "newcomer" on the scene, more events and analysis of same are required to place a more difinitive handle on this subclass. Here is a preliminary thought on the characteristics of this class. "....SNe Ic spectroscopically resemble SNe Ib, except that the He I lines are absent at early times. Thus, SNe Ic are sometimes called "helium-poor SNe Ib..."

Ed. Note: As studies continue on this subclass, it might be noted that there appears to be a subluminous nature [compared to the above classes/subclasses] associated with the type Ic SNe.

Characteristics of type II SN

1. Light curves

Barbon et. al has classified the light curves of type II SNe into two fairly homogeneous subclasses entitled "plateau" (SNe II-P), and "linear" (SNe II-L). Mean decay rates for SNe II, are considerably slower than their type I counterparts...."II-P"= 0.0075, and "II-L"= 0.012 mag per day. A phase of nearly constant brightness prior to day 80 is so distinctive, that it may be safe to classify SNe II-P on a light curve shape alone. Another interesting comparison is the similarity of the Type I SN, and SNe II-L, which exhibits almost a similiar linear decay posture, although it is noted that these events should not be classified by light curve shape alone. Spectoscopy is still the method of choice in determining various SN event characteristics.

2. Plateau

The physical characteristics attributed to plateau SNe (II-P) is the relative high amount of ejected mass (~10 Solar Masses). Because of the high ejected mass, the early pre-plateau light curve may be powered by internal energy that was deposited prompltly into the envelope by the explosion, and the early luminosity depends primarily on the radius of the progenitor star. Radioactivity cannot help to power the early luminosity because the time required for energy to diffuse from the deep interior to the surface is too long. Thus the wide range in the early luminosity is caused mainly by differances in progenitor radius e.g. SN 1987A was the explosion of a blue supergiant while SN 1983K was the explosion of a red one. 

During the plateau phase the light curve still can be powered by the diffuse release of internal energy if the progenitor radius was sufficiently large, but if it was small, as for SN 1987A, the initial internal energy is adiabatically degraded by expansion, and the plateau is powered only by the energy that is deposited slowly by 56Co decay. If the early luminosity was sufficiently low, the "plateau" will appear as a 'secondary peak'.

3. Linear

Why do the linears show a narrower range in peak luminosity than the plateau's? We suggest that because SN II-L's eject relatively little mass (otherwise,they would have plateaus) and have short diffusion times, their light curves are powered even at early times by radioactivity, just like SN Ia's and SN Ib's. When the diffusion time is short, the peak luminosity will depend primarily on the ejected mass of 56 Ni, unless the progenitor radius is very large. The role of radioactivity in powering the late tails of SN II light curves was suggested, and supported, and confirmed by SN 1987A. The first suggestion that radioactivity powers even the early light curves of linear SN II's was based on a resemblence between composite light curves of SN II-L's and SN I's.

A more specific comparison between the light curves of type II-L 1979C and the type Ia SN 1972E. These two light curves were practically indistinquishable during the dirst six magnitudes of decline. The close resemblance may be partially coincidental since 1979C was radiating strongly at Ha, while SN 1972E was not; nevertheless if SN 1972E was powered by radioactivity, so was SN 1979C. SN 1979C was significantly brighter than the other SN II-L's, the possibility of a large distance error for SN 1979C relative to all others is unlikely, because SN 1979C occured in M100, an apparent member of the Virgo cluster.

The most obvious possibility for the brightness differance is that SN 1979C was analogous to a type Ia explosion (inside some hydrogen), ejecting about 0.6 Solar masses of 56 Ni, while fainter linears were like SNe Ib, which eject only about 0.1 Solar Masses of 56 Ni. (ed note: As one can summize, the type II SNe do not display a difinitive continuity in either subtype, for example the absolute magnitude for these events can range from -14.1 (1987A) to -20.3 (1979C and 1978K).

Good luck !

This report has been published with the courtesy of the International Supernova Newtork, ISN.

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