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Subsections

4 Results

4.1 The optical light curve from the ground

The results of the ground based photometry are presented in Table 2, and shown in Fig. 3.


  \begin{figure}
\par\includegraphics[width=10cm,clip]{h3399.F3.ps}\end{figure} Figure 3: Ground-based B, V, R, and I photometry of SN 1998bw as obtained with the template subtraction method. The filter band light curves have been offset as indicated for clarity.

The light curves presented in Fig. 3 are all very smooth, with the exponential decay continuing all the way to the very last data points, some 540 days past explosion. The R and Icurves, for example, are perfectly well fit by a linear decline of 1.5-1.6 mag per 100 days. This is in contrast to the results published in S00 and P01, where the very late light curve appeared to flatten out. We interpret the difference as due to the complex background of SN 1998bw, and regard the new magnitudes achieved with template subtraction as more accurate. Having seen the very complex environment of the supernova in HST detail this may not be surprising. In fact, the total magnitude of the complex region surrounding the supernova amounts to $m_{{V}} \sim 21$. In measuring supernovae some 2 mag fainter than the background, even small errors in the PSF fitting will amount to substantial errors in the supernova magnitudes, an effect that will mimic a flattening of the late light curve. Core-collapse supernovae are known to explode in regions of star formation, and it is not unlikely that photometry of other supernovae at very late phases is hampered by similar effects (see Clocchiatti et al. 2001 for a similar discussion).

To investigate the total light emitted we should try to build a bolometric light curve. We begin by constructing the LBVRI light curve, containing the optical emission from 4400 to 7900 Å. We have done this in the following way.

All magnitudes were converted to a monochromatic flux using the conversions in Bessell (1979). To add the missing B-magnitudes, a linear fit to these magnitudes was used, where the day 141 mag from McKenzie & Schaefer (1999) was included to constrain the early evolution. The light curve slope in the B-band is then the same as in the other bands. The fluxes were corrected for an extinction of E(B-V)=0.06 mag (Schlegel et al. 1998; P01), and then the monochromatic fluxes were simply integrated from 4400 to 7900 Å. Finally we adopted a distance of 35 Mpc to convert to luminosity (z=0.0085, H0=73 km s-1 Mpc-1). To the resulting LBVRI points we will add a constant IR contribution in Sect. 4.4 to arrive at the light curve presented in Fig. 4.


  \begin{figure}
\par\includegraphics[width=10cm,clip]{h3399.F4.ps}\end{figure} Figure 4: The OIR light curve of SN 1998bw. The luminosities have been derived using the techniques described in the text. A constant IR contribution of 42%, as observed on day 370, has been added to all phases. The data up to 700 days are from ground based observations, and the later epochs are obtained with HST. The two error bars plotted indicate the uncertainty from 0.3 mag errors in the photometry. The arrows represent $3\sigma $ upper limits.

The slope of the late time decline is well fit by a linear decay in absolute magnitudes by 1.55 mag per 100 days from 140 to 538 days past explosion. This is certainly faster than the decay rate of the radioactive 56Co powering the supernova at this phase, again showing that most of the gamma-rays are slipping out of the ejecta at late phases (S00). We discuss this further in Sect. 5.

4.2 HST observations

The photometry from the HST observations is presented in Table 5. The CL magnitudes are the AB magnitudes measured by DAOPHOT on the template subtracted frames and with aperture corrections applied (CL $_{{\rm Sub}}$). The errors are simply the formal errors from DAOPHOT added to the standard deviations in the aperture corrections. This may be a bit optimistic, and from the artificial star test presented in Sect. 3.2 we regard an additional systematic error of 0.2 mag as a more reliable estimate of the errors. In Table 5 we have also included the magnitudes measured on the drizzled frames using DAOPHOT PSF-fitting (CL $_{{\rm PSF}}$). These clearly overestimate the flux of the supernova by including also light from the underlying structure, emphasizing the need of template subtraction even at the resolution achieved by HST.


 

 
Table 5: HST/STIS photometry of SN 1998bw.

Date
CL $_{{\rm PSF}}$ CL $_{{\rm Sub}}$

11 June 00
$25.33 \pm 0.06$ $25.90 \pm 0.05$
25 June 00 $25.45 \pm 0.05$ $26.03 \pm 0.04$
21 Nov. 00 $26.04 \pm 0.10$ $26.88 \pm 0.06$
28 Aug. 01 $\sim$ $27.4 \pm 0.1$ $\ga$28.5

AB-magnitudes from the STIS observations. The CLEAR-filter magnitudes
obtained by template subtraction are labelled CL $_{{\rm Sub}}$. The magnitudes estimated
directly from PSF-fitting (CL $_{{\rm PSF}}$) clearly overestimate the supernova luminosity.


The very first result to note is, of course, the clear detection of the supernova in the subtracted frames (Fig. 1). Fynbo et al. (2000) used VLT imaging (S00) to establish the position of the supernova in their STIS images. Based on this, they suggested that SN 1998bw was identical to the object positioned close to the middle of this messy region. Our analysis has demonstrated that this object is indeed fading. This strongly reinforces the supernova identification and allows us to follow the supernova to very late phases.

Secondly, from the magnitudes in Table 5, and from Fig. 3, we note that the supernova light curve seems to be levelling out at the very late phases. The reason for this will be discussed in Sect. 5.

In order to test if the supernova was still present in the 2001 Aug. 28 CL image we used DAOPHOT II/ ALLSTAR to fit a PSF to the light at the location of SN 1998bw. Since there was no template to subtract from this image, the PSF fit will be strongly biased by the underlying light at the location of the supernova. The aperture-corrected PSF magnitude is CL $_{{\rm PSF}} = 27.4 \pm
0.1$. However, an examination of the residuals after subtracting the PSF for the supernova suggests that the flux from the supernova is contaminated by light from the underlying structure and by the object $0\farcs056$ south of the supernova. To estimate an upper limit we again performed an artificial star test by injecting stars of different magnitudes onto regions of similar background as the supernova position. For input magnitudes fainter than $\sim$29-30, we found that the recovered PSF magnitudes were always close to 27.4, as measured for the supernova position. Using the standard deviation of the recovered magnitudes as a one sigma error, we find the $3\sigma $upper limit of about 28.5 for the supernova. This can be regarded as an upper limit on the emission from the supernova in the CL band 1221 days past explosion. This suggests that the supernova continued to fade well into 2001 at a rate similar to that observed between June and November 2000.

4.3 Combining the datasets

In measuring the ground based photometry, we made the implicit assumption that the supernova had completely disappeared in our last VLT template images. From the HST results we now know that the supernova was still there at this phase, although very faint. In fact, at a magnitude of $\sim$26.7 on day 907 the supernova will not affect any of the ground based measurements by more than 0.05 mag. We will make no correction for this effect.

However, our late VLT upper limit may indeed be significantly affected, by up to 0.25 mag. We have taken this into account in the combined upper limit on the luminosity presented in Fig. 4.

Better spatial resolution clearly allows more accurate subtractions and thus photometry. It is clear, however, that even with HST there may be unresolved substructures contributing to the PSF. At 35 Mpc each drizzled pixel corresponds to 4.3 parsecs on the sky. In Table 5 we have included the magnitudes obtained with PSF-fitting on the drizzled frames, and it is clear that such an approach overestimates the flux in the supernova. The effect increases at later phases and would again make the light curve flatten. This effect should, however, be correctly accounted for using the template subtraction. We therefore believe that the flattening of the late light curve as observed by HST is a robust result.

There is again the issue of contamination from remaining supernova flux in the HST template frame. Our estimate of the upper limit on the supernova CL magnitude in the 2001 August frame is $M^{{\it AB}}_{{\it CL}} \ga 28.5$. If the supernova was really at this magnitude in the template frame, the supernova would be brighter than estimated in June and November 2000. The effect could amount to 0.1 mag in June and some 0.2-0.3 mag in November. This is an uncertainty we can not overcome without further deep and very late imaging. Here we only note that such a contamination will not dramatically affect the late light curve slope. It would only flatten the late light curve between 778 and 940 days from a slope of 0.6 mag per 100 days to 0.5 mag per 100 days.

It is also non-trivial to compare directly the photometry obtained in the very broad CL filter with the ground based data. Established conversions as those presented in Rejkuba et al. (2000) are based on stars, and the late supernova spectrum differs from any stellar spectrum. Simply integrating a flat spectrum over the FWHM is a crude approach for such a wide filter. Nakamura et al. (2001a) assumed that ( MAB =) $M_{{V}} = M_{{\rm bol}}$ to put the photometry of Fynbo et al. (2000) onto their "bolometric'' light curve. Such an estimate differs by a factor 1.8 from the simple integration.

The correct approach would of course be to use the supernova spectra obtained at the same epochs for the corrections, but no such spectra are available. The latest spectrum from S00 is from 504 days past explosion. However, this spectrum is rather noisy and may be contaminated by the nearby objects revealed by HST.

We have taken the following approach to compare the different observations. From the broad band VLT photometry we do get a gross spectral energy distribution (SED) for the epochs up to 540 days past explosion. This distribution is seen to evolve fairly slowly with time and should not be influenced by the nearby objects. At all epochs, most of the energy ( ${\nu}F_{\nu}$) emerges in the R-band. From the late-time spectroscopy in S00 we know that this is mainly due to the strong [O I] $\lambda\lambda$ 6300, 6364 lines. We will assume that the same gross spectral distribution is appropriate at the late HST phases, with a fairly small contribution from the U-band (P01) and a continuation of the SED into the IR as observed on day 370.

We then used SYNPHOT to scale this SED to give the measured count rates for the CL filter function. The scaled SED can then be integrated, after a correction for extinction (Fitzpatrick 1999), and converted to luminosity as above. We noted that the count rate in the CL filter does not depend much on the assumed SED outside the LBVRI range. Assuming no flux outside 4000-8000 Å decreased the measured counts by only $\sim$14%, as both the SED and the CL filter curve peak in the middle of this interval. To avoid assumptions on the non-observed SED regimes we therefore integrated the SED only over the 4000-8000 Å range, to make it directly comparable to the ground based data.

4.4 The OIR light curve

An uncertainty in the bolometric light curve of P01 was the contribution of the IR emission. They assumed that the fraction of the UVOIR emission escaping in the IR was the same at late times as it was on day 65, the last day covered by their IR observations. Then the IR (JHK) contained $\sim$35% of the supernova emission, and this constant fraction was added to the optical light curve at all later phases (P01).

It is true that for the well observed SN 1987A, the fraction of the energy emerging from the supernova in the V, R, and I bands (LVRI) was virtually constant ($\sim$40%) up to 400 days after the plateau phase (Schmidt et al. 1993). However, the physics of a rapidly expanding, hydrogen-free ejecta will differ from the case of SN 1987A. As the radioactive heating decreases and the ejecta expand, the gas will cool down and a larger fraction of the emission may therefore be pushed into the IR. The assumption of constant IR contribution at late phases should therefore be checked.

To estimate the contribution in the IR we followed the same procedure as outlined above for LBVRI. The optical emission was interpolated on day 370 and integrated from B to I. The total emission was then calculated by including also the J and H-bands in the integral, where the conversions to flux from Wilson et al. (1972) were used. The result is that at this epoch 42% of the emission emerges in the near-IR. The same exercise for the data of day 65 gives a fraction of 31% (comparing LBVRI to LBVRIJH). At all epochs, most of the energy emerges in the R-band.

It is thus clear that the importance of the near-IR has increased with time, although the effect is not dramatic.

To complete our OIR (optical-infrared) light curve we have simply added the IR fraction observed at day 370 to all the dates on the light curve presented in Fig. 3. This assumes that the IR contribution does not evolve at the last HST phases.


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