9 SN1998bw and GRB 980425

The time and position of the peculiar gamma ray burst 980425 (Soffita et al. 1998) coincided with supernova SN1999bw (Tinney et al. 1998) in the spiral galaxy ESO 184-G82, at a nearby z=0.0085 (Tinney et al. 1998; Sadler et al. 1998; Galama et al. 1998c; Lidman et al. 1998; Iwamoto et al. 1998). Iwamoto et al. (1998) estimated the the core collapse of SN1998bw to have happened within -2 to +7 days of GRB 980425. The BeppoSAX Narrow Field Instrument (NFI) located 10h after burst an X-ray source coincident in position with SN1999bw that declined slowly with time between April and November 1998 (Pian et al. 2000). A posteriori statistics indicate a very low chance probability ($\leq$10^-4) of a GRB being so nearly coincident in position. But despite how close - if it was associated with SN1999bw - the progenitor of GRB 980425 was to us (38 Mpc for $H=65\, \rm km\,Mpc^{-1}\, s^{-1}$), the $\gamma$-ray fluence indicated only $7\times 10^{48}$ erg equivalent spherical energy release in $\gamma$ rays, much smaller than $\sim$ $3\times 10^{53}$ erg, the mean value for the score of other GRBs with known - cosmological - redshifts.

9.1 SN1998bw: The accepted lore

Like its accompanying GRB, SN1998bw was also claimed to be a very peculiar radio supernova (e.g. Kulkarni et al. 1998). Over the past twenty years approximately two dozen SNe have been detected in the radio: 2 Type Ib, 5 Type Ic, and the rest Type II. A much larger list of more than 100 additional SNe have low radio upper limits (for a review see, e.g., Weiler et al. 2000 and references therein). Type Ib/c SNe are fairly homogeneous in their radio properties, but SN1998bw had a peak 6-cm radio luminosity of $\sim$ $\rm 8\times 10^{28}\, erg s^{-1} \, Hz^{-1}$, that is 20 to 40 times brighter than other radio Type Ib/c SNe, which fall typically in the range $\rm 1.4{-}2.6\, \times 10^{28}\, erg s^{-1} \, Hz^{-1}$. SN1998bw also reached a high radio luminosity earlier than any known SN. Simple arguments based on the brightness temperature of its radio luminosity (e.g., Readhead 1994) required the radiosphere of SN1998bw to have expanded surprisingly fast, at $\geq$ $\rm 200\,000\, km\, s^{-1}$, at least during the first few days. Its unusually high optical and radio luminosities and its extraordinarily large initial speed of expansion led many authors to conclude that SN1999bw was a hypernova (Paczynski 1998) rather than a peculiar supernova (e.g., Iwamoto et al. 1998).

9.2 The pair SN1998bw/GRB 980425 in the CB model

In Dar & De Rújula (2000a) we argued that the only peculiarity of SN1998bw was that it was viewed very near its axis. The peculiarity of GRB 980425 was its nearness, that allowed for its detection at an angle, $\theta\sim 8/\gamma(0)$ unusually large relative to the other GRBs of known redshift, for which $\theta\sim 1/\gamma_0$. These facts conspired to produce a ``normal'' GRB fluence, and resulted in an optical AG dominated by the SN. In DDD 2001, we demonstrated that the X-ray AG of this GRB was also ``normal'': it has precisely the light curve (in shape and normalization) expected in the CB model if the X rays are produced by the CBs and not, as the observers assume (Pian et al. 2000), by the supernova.

In the CB model (Dar & De Rújula 2000a), the gamma-ray fluence of GRBs at large viewing angle ( $\gamma_0^2\, \theta^2\gg 1$) is $\propto \delta_0^3\propto \theta^{-6}$. The radio AG spectral energy density is proportional to $\gamma^{1/2}\, \delta^{7/2}$, as implied by Eqs. (4), (6), (8), the dependence $\rm\nu_b\propto \gamma^3$ and the relation $\rm\nu_{obs}\propto\nu_{_{CB}}\,\delta$. As a function of time, the AG peaks when $\gamma\, \theta\sim 1$, so that $\gamma\simeq\delta\simeq 1/\theta$ and the peak value is proportional to $\theta^{-4}$. Because its proximity and large viewing angle ``conspired'' to make GRB 980425 appear ``normal'' in gamma rays, its peak radio intensity should have been enhanced by a factor $\sim$ $\rm (\theta/mrad)^2$ relative to that of ordinary GRBs. Thus, for $\theta\sim 8.3$mrad, as estimated for GRB 980425 in Dar & De Rújula (2001), its expected peak radio intensity is $\sim$60 times larger than that of ordinary GRBs. Observationally, it is 50 to 100 times larger.

In Figs. 51 to 55 we show our CB model fits to the temporal and spectral behaviour of the radio afterglow of GRB 980425. The fit parameters (in particular the large observation angle $\theta$) are quite close to the ones that explain its GRB fluence (Dar & De Rújula 2000a), and its X-ray afterglow (DDD 2001). These figures show how, in the CB model, the radio AG of GRB 980425 also has a ``normal'' magnitude and shape. That is, once more, if the radio AG is produced by the CBs and not by the SN, unlike, once again, it is generally assumed (e.g., Kulkarni et al. 1998; Li & Chevalier; Weiler et al. 2000).

In the case of GRB 980425 the relatively large viewing angle and the subsequently small Doppler factor imply that, at late times, even the radio frequencies are above the injection bend. The large $\nu$ behaviour in Figs. 53 to 55 is $\nu^{-p/2}\sim\nu^{-1.1}$. Also, the late time trend of the radio light curves in Figs. 51 and 52 approaches the asymptotic $t^{2(p+1)/3}\sim t^{-2.1}$.

For GRB 980425 the radio data are overwhelmingly more abundant and precise than the X-ray data, and it is interesting to check what the prediction for the X-ray light curve is, if the input parameters are those determined in the radio fits. This is done in Fig. 56 for two values of the electron spectral index p. For our fixed choice, p=2.2, the prediction misses the data by a factor $\sim$20. There are two excuses for that. First, since GRB 980425 is seen much more ``sideways'' than other GRBs, and its Doppler factor $\delta$ is much smaller than usual, the cumulation, illumination and limb-darkening factors play a bigger role than usual. These factors involve many simplifying assumptions (such as spherical symmetry) and significantly affect the normalization of the radio AG, but not that of the X-rays. Second, the extrapolation from radio to X-rays is over some 10 orders of magnitude in frequency, and a small change in the spectral photon's slope, (p - 1)/2, entails a very large change in relative magnitude, as can be seen in Fig. 56 by comparing the p=2.2 and p=2curves.

Figure 56: The X-ray afterglow of GRB 980425.

The X-ray light-curve of GRB 980245 is essentially flat in the time-interval of the first four observed points (Pian et al. 2000), while the corresponding data for all other GRBs fall with time much faster. The last observational point in Fig. 56, a preliminary result from XXM Newton (Pian 2002) and Chandra (Kouveliotou 2002), falls precisely in the expected subsequent fast decline (predicted in DDD 2001) and definitely not in a naive power-law extrapolation. The peculiar light curve is a consequence of the large observing angle (Dar & De Rújula 2000a). For the reasons stated in this paragraph and the preceding one, we consider the prediction of the X-ray fluence completely satisfactory.

In DDD 2001, on the basis of the very meager X-ray data, we argued that the last optically-measured point of the SN1998bw/GRB 980425 pair, at day 778 (Fynbo et al. 2000), was due to the CB's AG and not to the supernova. Redoing the analysis with the input of the abundant radio data, we must now revise this conclusion. In Fig. 55 we show the result, with inclusion of the late optical measurement. This point lies more than two orders of magnitude above the predicted CB's AG: it must be due to the SN. We do not have an explanation - specific to the CB-model - of the fact that this point also lies somewhat above the expectation based on $\rm ^{56}Co$ decay (Sollerman et al. 2000).

We are claiming that long duration GRBs are associated with a good fraction of core-collapse SNe. Yet, SN1998bw was one of the brightest in its class. The apparent contradiction may be dispelled by the increasing evidence that SN explosions are fairly asymmetric. It is quite conceivable that, viewed very close to their ``CB axis'' SNe appear to be brighter than when observed from other directions.

The conclusion is twofold. GRB 980425 is, in every respect, normal (z and $\theta$ being chance variables). And, deprived of very abnormal X-ray and radio outputs - which are not due to the supernova, but to its ancillary GRB - SN1998bw loses most of its ``peculiarity''.

9.3 Superluminal motion in SN1998bw/GRB 980425

The transverse projected velocity in the sky of a CB relative to its parent SN is, for large $\gamma$ and small $\theta$:

$$V_{_{\rm CB}}(t)\simeq {\gamma(t)\, \delta(t)\, \theta\over (1+z)}\; c\, ,$$ (30)

which, for typical parameters, is extremely superluminal. The resulting angular separation at time $\rm t$ is:

$$\Delta \alpha(t)={1\over D_A}\int_0^t\,V_{_{\rm CB}}(t')\;{\rm d}t',$$ (31)

where $D_A=(1+z)^2\, D_{\rm L}$ is the angular distance to the SN/CB system. In Fig. 57 we show $\Delta(t)$ for SN1998bw/GRB 980425 with our parameters fit to the corresponding radio data (for our adopted H₀, $D_{\rm L}\simeq D_A\simeq 38$ Mpc). In Dar & De Rújula (2000a) we argued that this separation was sufficient to justify a dedicated effort to search for a ``binary'' source. It is interesting to discuss what the situation is with the data currently available.

Figure 57: The predicted angular separation of SN1998bw and GRB 980425, in milliarcseconds, as a function of time.

The most accurate determination of the position in the sky of the SN1998bw/GRB 980425 system is based on the radio observations made with the Australian Telescope Compact Array (ATCA, Wieringa et al. 1998). Recall that in the CB model the radio coordinates are those of the CB (GRB 980425 was a single-pulse GRB, that is, it had a single dominant CB). In days 3, 4 and 10 the source is reported to be at (RA 19:35:03.31, Dec -52:50:44.7). In the subsequent 33 observations, ranging from day 12 to day 790, the position is (RA 19:35:03.32, Dec -52:50:44.8), some $0\hbox{$.\!\!^{\prime\prime}$ }18$away from the original determination, but not inconsistent with the observational uncertainty of $0\hbox{$.\!\!^{\prime\prime}$ }1$. In the penultimate observation at day 320 the source has faded to the point that it is not observable in 2 out of 6 frequencies, and in the last observation at date 790 there is no clear sighting at any frequency. The predicted values of $\Delta \alpha$from Eq. (30) at some relevant dates are 12, 158, 183 and 292 mas at days 12, 249, 320 and 790, respectively. These results, the observational error, and the fact that the ATCA observers were not trying to follow the source's motion imply that their results are insufficient to claim either that the early change of position was significant, or that a motion of the CB comparable to the predicted one is excluded.

Observations of the vicinity of the source of GRB 980425 were made with the Hubble Space Telescope (HST) at day 778 (Fynbo et al. 2000), with a tiny astrometric uncertainty of $0\hbox{$.\!\!^{\prime\prime}$ }018$, and pointing at ATCA's first reported coordinates. The observations are compatible with SN1998bw lying at that point, and reveal six other objects in a ( $1\hbox{$.\!\!^{\prime\prime}$ }0\times 1\hbox{$.\!\!^{\prime\prime}$ }0$) field centered there. As a result of our CB model fit to the radio data, as we have explained, we expect the optical observations to correspond to SN1998bw, and there it is, at the field's center. We also expect, as in Fig. 55, the CB to be more than two orders of magnitude fainter: not observable. It would be nice if this conclusion was wrong, that is, if the large ``naive'' extrapolation from radio to optical frequencies in Fig. 55 was an underestimate by a considerable factor, which is the case for the larger extrapolation from optical to X-ray frequencies in Fig. 56 (the ``naive'' prediction there is the one labelled p=2.2). In that case, it may be that a subsequent observation of the same field reveals that one of the closer-by extra sources has faded away! Three of these sources are $\sim$ $0\hbox{$.\!\!^{\prime\prime}$ }5$away from the SN, if one of them is the CB, and it is dimming, we would not excessively mind that this is $\sim$60% more distant than the prediction in Fig. 57, based on a constant-density approximation for the ISM.