Date | November 2019 | Marks available | 3 | Reference code | 19N.3.SL.TZ0.10 |
Level | Standard level | Paper | Paper 3 | Time zone | 0 - no time zone |
Command term | Determine | Question number | 10 | Adapted from | N/A |
Question
Eta Cassiopeiae A and B is a binary star system located in the constellation Cassiopeia.
The following data are available.
Apparent brightness of Eta Cassiopeiae A = 1.1 × 10–9 Wm–2
Apparent brightness of Eta Cassiopeiae B = 5.4 × 10–11 Wm–2
Luminosity of the Sun, L⊙L⊙ = 3.8 × 1026 W
A Hertzsprung–Russell (HR) diagram is shown.
Distinguish between a constellation and a stellar cluster.
The peak wavelength of radiation from Eta Cassiopeiae A is 490 nm. Show that the surface temperature of Eta Cassiopeiae A is about 6000 K.
The surface temperature of Eta Cassiopeiae B is 4100 K. Determine the ratio radius of the Eta Cassiopeiae Aradius of the Eta Cassiopeiae Bradius of the Eta Cassiopeiae Aradius of the Eta Cassiopeiae B.
The distance of the Eta Cassiopeiae system from the Earth is 1.8 × 1017 m. Calculate, in terms of L⊙L⊙, the luminosity of Eta Cassiopeiae A.
On the HR diagram, draw the present position of Eta Cassiopeiae A.
State the star type of Eta Cassiopeiae A.
Calculate the ratio mass of Eta Cassiopeiae Amass of the Sunmass of Eta Cassiopeiae Amass of the Sun.
Deduce the final evolutionary state of Eta Cassiopeiae A.
Markscheme
stars in a cluster are gravitationally bound OR in constellation are not ✔
stars in a cluster are the same/similar age OR in constellation are not ✔
stars in a cluster are close in space/the same distance away OR in constellation are not ✔
stars in a cluster originate from same gas cloud OR 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.
«T=2.9×10-3490×10-9T=2.9×10−3490×10−9»
5900 K ✔
NOTE: Answer 6000 K is given in the question.
Answer must be to at least 2 s.f. OR correct working.
«from b∝ L∝ R2 T4»
realization that R2∝bT4R2∝bT4 «for binary stars which are same distance away» ✔
RARB=√(1.1×10-95.4×10-11)(59004100)4RARB= ⎷(1.1×10−95.4×10−11)(59004100)4 ✔
RARB=2.2RARB=2.2 ✔
NOTE: Award [2] for answer 0.46 from inverted ratio.
«use of L=4πd2bL=4πd2b»
L=4π×(1.8×1017)2×1.1×10-9 «=4.48×1026 W»✔
L=1.2 L⊙ ✔
approximately correct position on the main sequence as shown, within highlighted region ✔
main sequence star
OR
type F or G star ✔
MM⊙=1.213.5=1.05 ✔
mass of the «remnant» star <1.4M⊙ OR Chandrasekhar limit
OR
mass OR luminosity similar to the Sun ✔
the final stage is white dwarf ✔