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 Incoming links: Bolometric magnitude

Past exam of the short options paper shared by Prelims and Parts A and B of the physics course of the University of Oxford / 2015 / S2 / 2 / 2 / Solution 2026-10-25

The parallax gives

d = 1/0.00763 ≃ 131 pc

. Ignoring extinction, the distance modulus gives

M_{bol} = m_{bol} - 5 lo g_{10} (d /10 pc) ≃ - 6.29.

The bolometric magnitude relation then yields

L / L_{⊙} = 1 0^{0.4 (4.72 - M_{bol})} ≃ 2.53 \times 1 0^{4}

. With

T_{⊙} ≃ 5772 K

,

\frac{R}{R _{⊙}} = \frac{L}{L _{⊙}} (\frac{T _{⊙}}{3500 K})^{2} ≃ 4.3 \times 1 0^{2} .

A star this cool and luminous belongs to the red-supergiant region of the Hertzsprung-Russell diagram. Extinction and the adopted effective temperature are important systematic inputs; this calculation uses the supplied temperature to infer the radius.

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