Introduction

We applied data from [1] to reproduce the result of the SN 2008es’s light curve around 100 days after discovery. We took the data from Table 5 in the article and reproduced Fig. 4 of the article. Necessary constants are defined as following [1]:

  1. Z = 0.213, E(B-V) = 0.011
  2. H0 = 70, OmegaM = 0.3, OmegaLambda = 0.7

The analysis was done in RStudio.

Procedure and Results

[Note: SI unit was used in the analysis]

  1. Define constants.
  2. Input data from Table 5 of [1] which was prepared in .csv file.
  3. Convert date of discovery (2008 Apr 26.23 UT) to Julian date and compare with the t_obs in data to get date observed after discovery.
  4. Transform date observed after discovery into rest frame: t_rest = t_non_rest / (1+z)
  5. Correct galactic extinction to the magnitue: mag_correct = mag - R_x * E(B-V). We used data of galactic extinction from [2]’s Table 14 at 10000K BB. Also, we assumed no host extinction and E(B-V) = 0.011 as [1].
  6. Map filter with wavelength profile. We used [3] for the wavelength profile.

  7. Convert magnitude to flux (in microJy): mag = -2.5 * log10(flux/3631)

  8. For each filter, we selected 10 periods.

  9. For each period, to get temperature, we applied chi-squared minization to fit single-component blackbody model.

[Note: Optimization problem chose (temperature,norm). Local minimum is possible to be a solution in this process. To fix this, try random initialization]

  1. Convert to surface temperature: temp_eart = temp_surface / (1+z)

  2. For each period, apply trapezoid integration to get bolometric flux.

  3. Convert bolometric flux to bolometric luminosity by using luminosity distance: flux = luminosity / (4 * pi * lumi_distance^2)

[Note: luminosity distance was calculated from [4]]

  1. Apply Stefan-Boltzmann equation to get radius.

  2. Plot.

[Note: there were two periods which optimization gave bad result. We excluded the periods from the plots.]

[Note: L_Bol BB fit was calculated by applying temperature to BB model to get flux. Then, we followed the previous process to obtain L_Bol.]

  1. Calculate percentage difference of log(L_Bol) from direct integration and BB fit.
# percentage diff
abs( (log_lumi_bol - log_fit_lumi_bol) * 100./ (log_lumi_bol) )
##  [1]  1.140257 58.516577  1.339214  2.001152  1.518167  1.873966  1.857826
##  [8]  2.487345  1.714177  2.598441

References:

1: Miller et al., 2008, “The Exceptionally Luminous Type II-Linear Supernove 2008ES”

2: Brown et al., 2010, “The Absolute Magnitudes of Type Ia Supernovae in the Ultraviolet”

3: Poole et al., 2007, “Photometric Calibration of the Swift Ultraviolet/Optical Telescope”

4: http://www.astro.ucla.edu/~wright/CosmoCalc.html (accessed 8/17/2015)