A Search for Radio-Loud Supernovae

Elaine M. Sadler, Duncan Campbell--Wilson, PASA, 14 (2), in press.

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Title/Abstract Page: A Search for Radio-Loud
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A first estimate of the radio supernova rate

We found no new sources in any of the twelve galaxies during the pilot study. One galaxy (NGC 4945) was dominated by a very strong (tex2html_wrap_inline390 5Jy) unresolved nuclear source. `Spikes' and other artifacts from this source mean that the much weaker underlying extended emission is poorly mapped and a new source would probably need to be at least 150mJy to be recognised, so we excluded this galaxy from the statistical study described below.

In calculating supernova rates, we follow the method outlined for optical supernovae by van den Bergh et al. (1987) and Evans et al. (1989). The aim is to determine, for each galaxy observed, the `control time' during which we would have been able to detect a given event. Evans et al. also define the `surveillance time' as the control time (in years) divided by the galaxy's optical luminosity (in units of 10tex2html_wrap_inline392 Ltex2html_wrap_inline394). The number of detected supernovae divided by the surveillance time then gives the supernova rate per unit stellar luminosity. Since radio supernovae clearly cover a range in radio luminosity, we calculated the probability of detecting two well-observed radio-loud supernovae, SN1986J and the less luminous SN1978K.

The control time is calculated from model radio light curves (i.e. flux density as a function of time) for SN1978K and SN1986J scaled to the distance of each target galaxy. Figure 2 shows the model light curves adopted. For SN1986J, the light curve was calculated using the model parameters derived by Weiler et al. (1996; their Table 2) and shifted to the MOST observing frequency of 843MHz using the calculated radio spectral index tex2html_wrap_inline396. For SN1978K, the curve is from Ryder et al. (1993), fitted to the early 843 MHz observations and calculated as described in their Figure 4.

Figure 2: Model radio light curves for SN 1986J and SN 1978K at 843 MHz, assuming Htex2html_wrap_inline398 = 75 km stex2html_wrap_inline400 Mpctex2html_wrap_inline400.

The `surveillance time' is simply the control time scaled by the (blue) galaxy luminosity (galaxies very in size, so this lets us calculate the rate per fixed number of stars rather than per galaxy). As an example, we show the calculation of `control time' and `surveillance time' for NGC 1097:

The peak 843MHz flux density for SN1978K scaled to the distance of NGC1097 is predicted to be 9.5mJy. Thus a RSN like SN1978K will always lie below our 10mJy detection limit, and so the control time is zero no matter how long the galaxy is observed for.

The peak 843MHz flux density for SN1986J scaled to the distance of NGC1097 is predicted to be 46.4mJy. The model light curve implies that the flux density first rises above 10mJy on day 1450 (i.e. 4.0 years) after the SN explodes, and remains above 10mJy until day 14470 (i.e. 39.6 years after the explosion). In principle, therefore, a RSN like SN1986J should be detectable for a total of 35.6 years before fading below the detection limit.

An additional constraint, however, comes from our assumption that the RSN must vary in brightness by at least 20% between the two observations for it to be recognized as variable. The slow rate of decline at late times means that this becomes difficult unless there is a long time between the two epochs. For NGC1097, where the observations are separated by 4.2 years, we can detect a RSN as variable if it exploded no more than 15.5 years before the first-epoch observation (rather than the 39.6 years implied by the detection limit alone). Figure 3 shows the relation between the interval between observations (tex2html_wrap_inline404T) and the range of `time since explosion' (tex2html_wrap_inline406) for which a RSN can be detected.

Figure 3: Time span tex2html_wrap_inline404T needed to detect a RSN on the declining part of its light curve (assuming that the observed flux density must vary by 20% or more for the object to be recognized as variable), as a function of the elapsed time tex2html_wrap_inline406 between the supernova explosion and the first observation. Note the large gain if archival observations span a long interval -- each extra year added to tex2html_wrap_inline404T adds roughly 3.8 years to tex2html_wrap_inline406.

Note that the control time is independent of the value assumed for Htex2html_wrap_inline398, while the surveillance time, and hence the derived supernova rate, depends on Htex2html_wrap_inline398 only in the sense that the optical luminosity calculated for a galaxy (and hence the number of stars it is assumed to contain) depends on the precise distance adopted.

Table 1 lists the control time and surveillance time for galaxies in the pilot study. The total (blue) optical luminosity Ltex2html_wrap_inline420 is also listed for each galaxy, along with the time interval tex2html_wrap_inline404T between the two radio observations. Here, we adopt Htex2html_wrap_inline398 = 100h km stex2html_wrap_inline400 Mpctex2html_wrap_inline400.

Table 1: Comparison of optical and radio supernova rates

For objects like SN1978K, we have a total surveillance time of 62.4tex2html_wrap_inline474 years and have detected <1 RSN. Our detection rate for spiral galaxies (Sa-Sd) is therefore tex2html_wrap_inline478 objects/century/10tex2html_wrap_inline392 Ltex2html_wrap_inline394. For objects like SN1986J, we have a total surveillance time of 361.3tex2html_wrap_inline474 years, and have again detected <1 RSN. This gives a detection rate for spiral galaxies of tex2html_wrap_inline488 objects/century/10tex2html_wrap_inline392 Ltex2html_wrap_inline394.

Table 2 compares the radio supernova limits derived here with the optical supernova rates derived by Evans et al. (1989). For objects like SN1978K, our limits are not yet very restrictive -- we cannot rule out a picture in which almost all Type II and Type Ib supernovae behave like SN1978K. For more powerful RSNe like SN1986J, we can already say that they probably represent no more than 25% of all Type II supernovae (and no more than 18% of Types Ib and II combined), so they must be reasonably rare objects.

Table 2: Calculation of `surveillance time' for galaxies in the pilot study

It is interesting to compare the total surveillance time for radio and optical SNe in our study and that of Evans et al. (1989) respectively. Evans totals 3416tex2html_wrap_inline474 years/10tex2html_wrap_inline392Ltex2html_wrap_inline394 for Type II SNe (and a similar time for Type Ib SNe, which are also believed to come from massive stars) based on regular observations of 855 target galaxies over an eight-year period.

We have already reached a total of 361tex2html_wrap_inline474 years/10tex2html_wrap_inline392Ltex2html_wrap_inline394 for 1986J-like objects by observing only 11 targets twice each with an interval of 4-5 years between observations. Thus it should be possible to reach a total surveillance time which approaches or exceeds that of the Evans et al. optical search by making only a modest number of new radio observations. Since the objects we are seeking are presumably rarer than optical SNe, it is also clear that we need a total surveillance time at least this long to gather reasonable statistics.

Next Section: Optical supernovae in the
Title/Abstract Page: A Search for Radio-Loud
Previous Section: A radio supernova search
Contents Page: Volume 14, Number 2

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