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Date May 2014 Marks available 2 Reference code 14M.3.HL.TZ2.4
Level Higher level Paper Paper 3 Time zone Time zone 2
Command term Outline Question number 4 Adapted from N/A

Question

This question is about stellar evolution.

Achernar may evolve to become a neutron star.

Achernar is a main sequence star with a mass that is eight times the mass of the Sun. Deduce that Achernar has a greater temperature than the Sun.

[2]
a.

Outline why Achernar will spend less time on the main sequence than the Sun.

[2]
b.

(i)     State the condition relating to mass that must be satisfied for Achernar to become a neutron star.

(ii)     Some neutron stars rotate about their axes and have strong magnetic fields. State how these stars may be detected.

[3]
c.

Markscheme

from the mass–luminosity relation, Achernar has a higher luminosity; { (reference to mass–luminosity is essential)

so it is above/to the left of the Sun on the main sequence / temperature increases with luminosity in the main sequence;

Ignore irrelevant statements that \(L = \sigma A{T^4}\).

Allow second marking point even if only mass is discussed.

a.

Achernar has greater luminosity/temperature and so fuses hydrogen at a (disproportionately) higher rate than the Sun / OWTTE;

so it will run out of hydrogen/move to red giant region in less time than the Sun / OWTTE;

b.

(i)     the remnant mass/the mass of its core/the mass after the supernova stage; { (do not allow “mass” bald)

must be between the Chandrasekhar and Oppenheimer limits / \(1.4{M_\square } < {M_{{\text{core}}}} < 3{M_\square }\); { (allow answer in words or numerical values)

Allow 2.5 \({M_\square }\) to 3 \({M_\square }\) as O–V limit.

(ii)     detection of EM radiation from pulsars/stars that pulsate / stars whose intensity varies rapidly / OWTTE;

Accept answers that refer to any regions of the electromagnetic spectrum.

c.

Examiners report

In (a) most candidates correctly referred to the mass-luminosity equation, but then asserted that luminosity was proportional to temperature without consideration of a star’s surface area.

a.

(b) was answered well by most.

b.

In (c)(i) the Chandrasekhar and Oppenheimer-Volkoff limits (or their values) were both expected but not often provided. Also it was common to refer to a star's 'mass' rather than 'remnant mass' or 'mass of the core'. Many candidates realised that a pulsar was being described in (c)(ii).

c.

Syllabus sections

Option D: Astrophysics » Option D: Astrophysics (Core topics) » D.2 – Stellar characteristics and stellar evolution
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