ner_tags: O O O O O O O O O O O B-CelestialObject I-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Telescope O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength I-Wavelength O O O O O O O O O O O O O O O O O O O B-Wavelength I-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength I-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength I-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength I-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O
tokens: t b to be 23.0. Figure 3. Multi-band light-curve fitting of SN 2013dy using Equation ( 1 ) for estimating t 0 . The value of is fixed to be 1.90 and t b is fixed to be 23.0 during the fitting procedure. Diamond-shaped data points are included in the fitting, while cross-shaped ones are excluded. After applying the t 0 fit to each SN for each band, and for each case with different ( X varies from 0 to −7), we compare the estimated t 0 with the “known t 0 .” The result is shown in Figure 4 , where the upper panel shows the cases for each SN and each filter with different . For a certain , if there is more than one filter observed for an SN (as shown in Table 1 , except for the three Kepler SNe that were only observed with one broadband filter), a mean value of t 0 from all filters is also calculated. The bottom panel shows the histogram of the t 0 offsets compared with the “known t 0 ”; each filter is color-coded. Figure 4. Difference of first-light time t 0 estimated from Equation ( 1 ) fitting with the real t 0 . The upper panel shows the cases for each SN and each filter with different , arbitrarily shifted along the ordinate for clarity. The bottom panel shows the histogram of t 0 offsets for each filter, also arbitrarily shifted along the abscissa for clarity. In general, the smaller the X in (with earlier data), the smaller the offset. The B (or g ) band has the smallest offset, and appears to not change with X , with a 1 σ systematic error of ±0.7 days. Three important and clear conclusions can be drawn from Figure 4 . First, the offset between the fitting t 0 and the “known t 0 ” becomes smaller when earlier data are included—namely, the smaller the X value in , the smaller the offset. But once X reaches −3, then even earlier data do not help much for t 0 estimation. Second, B interestingly has the smallest offset, and no matter when starting with , the offset is always within ±1.5 days; we estimate a 1 σ systematic error of ±0.7 days by adopting only the B -band estimate of the t 0 offset. Third, the mean offset with multiple filters is similar to that of the B band; thus, for t 0 estimation, one should use either the mean value or the value estimated from B alone. Technically, it is not surprising to see why the B band gives the best estimate of t 0 ; in other bands, the peak is usually broader than that of B , making B better for estimating t 0 . Because of this, in the following we only adopt the t 0 estimate from B , even if the SN was observed with multiple filters. We will also add a systematic error of ±0.7 days for the t 0 estimated from B -band fitting. In addition, Figure 4 shows that the fixed value of is appropriate, giving a mean t 0 offset of 0.1 ± 0.7 days for the B -band, very close to 0 as expected. Furthermore, we performed two other sets of fitting with the value fixed to be 1.50 and 2.30 (respectively), and found t 0 offset by 1.2 ± 0.8 and −0.8 ± 0.7 for B , confirming that the fixed value of is appropriate. 2.4. A