2008

A star seen in three colours

Round: Theory
Points: Not given
Level: Silver
Taught in: Section 4.7

Adapted from IOAA 2008 (Bandung), theory problem L2. We have restated it in our own words and kept the original data. The solution was last checked on 20 October 2026.

A star is measured in the U, B and V filters as $U = 8.15$ , $B = 8.50$ and $V = 8.14$ . Its spectrum shows that its intrinsic colour is $(U - B)_{0} = - 0.45$ . The star has radius $2.3 R_{⊙}$ , absolute bolometric magnitude −0.25 and bolometric correction −0.15. Take $R_{V} = 3.2$ , and use the relation $E (U - B) = 0.72 E (B - V)$ between the two colour excesses. Find:

(a) the magnitudes $U_{0}$ , $B_{0}$ and $V_{0}$ the star would have without dust,

(b) its effective temperature,

I solved it without the solution

AnswerWithout dust the star would have $U_{0} = 7.47$ , $B_{0} = 7.92$ and $V_{0} = 7.70$ . Its effective temperature is about 12 000 K and it is about 360 pc away.

This problem also appears among the olympiad problems of Section 4.7, Colour, temperature and bolometric correction, which teaches the ideas it uses. Equation and figure numbers refer to the course.