2019

Nova Delphini 2013

Round: Data analysis
Points: 45
Level: Silver
Taught in: Section 8.6

Adapted from IOAA 2019 (Keszthely), data-analysis problem 1. We have restated it in our own words and kept the original data. The original asked for readings from a light curve and a set of spectra, and for a graph. We give the readings of the official solution instead and leave out those parts, so the points add up to 45 of the original 60. The solution was last checked on 21 October 2026.

The nova V339 Delphini was discovered on MJD 56518.584, where MJD is the Julian date minus 2 400 000.5. Its light curve peaked at visual magnitude $4.50 \pm 0.05$ and it took $t_{2} = 11 \pm 1$ days to fade by 2 magnitudes and $t_{3} = 23 \pm 1$ days to fade by 3. Three fits give its peak absolute magnitude.

$M_{0} = - 7.92 - 0.81 \arctan [(1.32 - \log t_{2}) / 0.23]$ , by Della Valle and Livio (1995).
$M_{0} = - 11.32 + 2.55 \log t_{2}$ , by Downes and Duerbeck (2000).
$M_{0} = - 11.99 + 2.54 \log t_{3}$ , by the same authors.

The colour excess towards the nova is $E (B - V) = 0.184 \pm 0.035$ . Six spectra near the peak show the Hα line, of rest wavelength 6562.82 Å, with a P Cygni profile, an emission peak and a blueshifted absorption made in the outer part of a spherical shell moving towards us. The absorption lies at these wavelengths.

MJD	56518.986	56519.813	56520.843	56521.835	56522.829	56523.827
Wavelength (Å)	6527	6531	6534	6537	6542	6544

(a) Find $M_{0}$ from each fit, their mean, and their standard deviation as its uncertainty. [5 points]

(b) Find the extinction $A_{V}$ and its uncertainty, with $R_{V} = 3.1$ . [4 points]

(d) Find the radial velocity of the shell from each spectrum. [14 points]

(e) Assuming that the shell was negligibly small at the first spectrum, find its radius at the last, in astronomical units. [7 points]

(f) Find the angular diameter of the shell at the last spectrum, about 5 days after discovery. [4 points]

I solved it without the solution

Answer(a) $M_{0} = - 8.61 \pm 0.07$ . (b) $A_{V} = 0.57 \pm 0.11$ . (c) $d = 3.2 \pm 0.3$ kpc. (d) From $- 1636$ km/s on the first night to $- 860$ km/s on the last. (e) About 3.4 au. (f) About 2.1 milliarcseconds. The official solution takes the mean of only the first and last speeds, 1248 km/s, and gets 3.5 au and 2.2 milliarcseconds, which are as good within the accuracy of the readings.

This problem also appears among the olympiad problems of Section 8.6, Interacting binaries and novae, which teaches the ideas it uses. Equation and figure numbers refer to the course.