IB DP Physics Option D: Astrophysics (Core topics) : D. 1 – Stellar quantities SL Paper 3

Ans:

a. stars in a cluster are gravitationally bound $O R$ in constellation are not
stars in a cluster are the same/similar age $O R$ in constellation are not
stars in a cluster are close in space/the same distance away $O R$ in constellation are not
stars in a cluster originate from same gas cloud $O R$ in constellation do not
stars in a cluster appear much closer in night sky than in a constellation
Notes: Take care to reward only 1 comment from a given marking point for MP1 to MP5.
$
\begin{gathered}
\mathrm{b}(\mathrm{i}) \lll T=\frac{2.9 \times 10^{-3}}{490 \times 10^{-9}} » \\
5900 \mathrm{~K} \checkmark
\end{gathered}
$
NOTE: Answer $6000 \mathrm{~K}$ is given in the question.
Answer must be to at least 2 s.f. OR correct working.
$\mathrm{b}\left(\mathrm{iii}\right.$ s from $b \propto L \propto R^2 T^4$ »
realization that $R^2 \propto \frac{b}{T^4}$ «for binary stars which are same distance away» $\checkmark$
$
\frac{R_{\mathrm{A}}}{R_{\mathrm{B}}}=\sqrt{\frac{\left(\frac{1.1 \times 10^{-9}}{5.4 \times 10^{-11}}\right)}{\left(\frac{5900}{4100}\right)^4}}
$
$
\frac{R_{\mathrm{A}}}{R_{\mathrm{B}}}=2.2
$

NOTE: Award [2] for answer 0.46 from inverted ratio.
$\mathrm{b}$ (iiik)use of $L=4 \pi d^2 b »$
$
\begin{aligned}
& L=4 \pi \times\left(1.8 \times 10^{17}\right)^2 \times 1.1 \times 10^{-9} \ll=4.48 \times 10^{26} \mathrm{~W} \gg \checkmark \\
& L=1.2 L_{\odot} \checkmark
\end{aligned}
$

approximately correct position on the main sequence as shown, within highlighted region

c(ii)main sequence star
OR
type F or G star
$\mathrm{c}\left(\mathrm{iii} \frac{M}{M_{\odot}}=1.2 \frac{1}{3.5}=1.05\right.$
c(iv)hass of the «remnant» star $<1.4 M_{\odot}$ OR Chandrasekhar limit
OR
mass OR luminosity similar to the Sun
the final stage is white dwarf