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Subsections

4 Photometry

   
4.1 R-band light-curve of the OT

In comparison with GRB 000301C (Jensen et al. 2001) GRB 000926 was found to be hosted by a relatively luminous host galaxy (see Sect. 6). When measuring the magnitude of the OT directly on the images with Point Spread Function (PSF) photometry there will be a contribution from the underlying host galaxy. The relative strength of this contribution depends on the seeing and is therefore a source of systematic errors if not corrected for. We therefore subtracted an aligned and scaled image of the host galaxy from each of the individual R-band images from the NOT listed in Table 2. This image of the host galaxy was obtained about 30 days after the burst when the magnitude of the OT, based on an extrapolation of the light-curve, as well as a possible underlying supernova would be negligible (see Sect. 6). We then measured the magnitude of the OT using DAOPHOT-II (Stetson 1987, 1997). The OT was last detected in the image obtained on October 2. The photometry was transformed to the standard system using photometric observations of the four secondary reference stars A-D marked in Fig. 1 obtained at the U.S. Naval Observatory Flagstaff Station. The calibrated UBVRI magnitudes of the stars A-D are given in Table 1.

We first fitted a broken power-law

 \begin{displaymath}f_{\nu}(t) = \left \{
\begin{array}{lll}
f_{\nu}(t_{\rm b})...
... \mathrm{if} & t \ge t_{\rm b},
\end{array} \right.
\nonumber
\end{displaymath}   (1)

to the data, which provided a very good fit. The parameters of the fit are given in Table 3. We then followed Beuermann et al. (1999) and fitted an empirical function of the form

\begin{displaymath}f_{\nu}(t) = (f_1(t)^{-n} + f_2(t)^{-n})^{-1/n},\end{displaymath}

where $f_i(t) = k_i~t^{-\alpha_i}$ and t is the time since the GRB measured in days. For large values of n this function approaches the broken power-law. We performed this fit both keeping n fixed at 1 similar to Stanek et al. (1999) and with n as a free parameter. The results of these fits are also given in Table 3.

The $\chi^2$ per degree of freedom is smallest for the broken power-law fit. The data favor a very large value of n as the $\chi^2$ is monotonically decreasing as n is increased even for n > 100. The 2$\sigma $ lower limit on n is 7 in the sense that the difference between $\chi^2$ for a fit with n = 7 and the broken power-law is 2. This indicates that the break in the light-curve is very abrupt (within a few hours).

In conclusion, the data are best fit by a sharp break around $t=2.12 \pm 0.09$ days after the burst. In Fig. 2 we show the R-band light-curve of the OT together with the three fits and the residuals around the fits.


  \begin{figure}
\par\includegraphics[width=8.2cm,clip]{lightcurve.eps}\end{figure} Figure 2: The R-band light-curve of the OT. The upper panel show the R-band measurements together with the three light-curve fits. The three lower panels shows the deviations around the fits for, from top to bottom, the broken power-law, the n fixed and the n free fits.


 

 
Table 3: Results of fits to the R-band light-curve. There were 24 degrees of freedom in the fits.
Fit $\alpha_1$ $\alpha_2$ other $\chi^2$/d.o.f.
b. p.-l. $1.69 \pm 0.02$ $2.39 \pm 0.09$ $t_{\rm b}=2.12\pm0.09$ 1.000
n=1 $1.40 \pm 0.13$ $3.36 \pm 0.41$ n=1 (fixed) 1.263
n free $1.69 \pm 0.02$ $2.39 \pm 0.09$ n>7 (2$\sigma $) 1.084


4.2 Other optical bands

The OT was also imaged in the U,B,V and I bands during the first four nights after the detection at the NOT and CA.

To precisely determine the broad band colours of the OT we used the UBV and I band observations obtained at NOT and INT. The CA points were excluded since Johnson R and I filters are significantly different from Bessel, Cousins and Harris. We determined the colours as the offset of the broken power-law fit to the R-band light-curve that minimized the $\chi^2$ of the fit. Due to the lower error bars the magnitudes obtained on Sep. 27 have the largest weight in the fits. Therefore we do not expect a large systematic uncertainty due to emission from the underlying host galaxy. In order to minimize the effect of the host galaxy only points obtained earlier than and including September 29 were used in the fits. The 1$\sigma $ errors on the colours were determined as the colours that increased the value of $\chi^2$ by 1, but the true uncertainty including calibration and systematic errors is most likely somewhat larger ($\sim$5%). For all filters U,B,V and I the fits were consistent with the (offset) broken power-law fit, which shows that the data within the errors (few percent) are consistent with an achromatic optical afterglow. The results are given in Table 4.


 

 
Table 4: Colours of the OT of GRB 000926 and GRB 000301C. The colours of the OT of GRB 000301C are from Jensen et al. (2001).
Colour GRB 000926 $\chi^2$/d.o.f.   GRB 000301C
U-R $0.96 \pm 0.04$ 0.59   $0.40 \pm 0.05$
B-R $1.06 \pm 0.03$ 0.53   $0.91 \pm 0.03$
V-R $0.50 \pm 0.01$ 0.34   $0.44 \pm 0.05$
R-I $0.48 \pm 0.01$ 0.48   $0.49 \pm 0.04$
R-K $3.35 \pm 0.07$ 1.87   $2.98 \pm 0.08$


4.3 Infrared photometry

The afterglow was observed in the K'-band on September 29, 2000 with the IRCS instrument on the 8.2-m Subaru telescope in a seeing of about 0.7 arcsec and a total integration time of 1800 s. No standard star observations were obtained on the same night, but fortunately there is a bright, unsaturated 2MASS source in the field which we could use for calibration. We measured the magnitude of the OT and of the 2MASS source in a 2 arcsec circular aperture. The formal photometric error-bar is less than a percent, but we estimate conservatively that the uncertainty in the colour-transformation for the IRCS instrument amounts to 0.10 mag.

The afterglow was also observed in the J, H and K bands with the UFTI imager on UKIRT on September 30. The final frames were accumulated in 26, 24 and 9 dithered exposures of 60s duration for J, H and K respectively resulting in a total on-source integration time of 1.56 ks, 1.44 ks and 540s, all in photometric conditions. Employing standard procedures these frames were reduced, combined and calibrated using observations of UKIRT faint standards bracketing the science exposures. The final frames have only a (for this instrument) modest seeing of 0.55-0.60'' FWHM due to the relatively high airmass of the observations, 1.5-2, but clearly detect the OT in all three passbands. The magnitude of the OT was again measured using aperture photometry. The results of the IR photometry is presented in Table 5.

Using the standard star calibrated UKIRT K-band observations we confirmed from faint objects visible in both the UKIRT and SUBARU images that the calibration of the SUBARU images is consistent with that of the UKIRT K-band observations.


 

 
Table 5: Log of IR observations.
UT (Sep) filter/Obs. mag Seeing Exp. time
      (arcsec) (sec)
30.276 J/UKIRT $20.83 \pm 0.15$ 0.6 1560
30.250 H/UKIRT $19.46 \pm 0.10$ 0.6 1440
29.24 K'/SUBARU $17.86 \pm 0.10$ 0.7 1800
30.301 K/UKIRT $18.66 \pm 0.11$ 0.6 540



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