☰ Contents · Astronomy

Variable stars and stellar evolution

Lessons 54–55 · 2 lessons · M. Mamadazimov. Astronomy Grade 11, 1st edition. DAVR NASHRIYOTI, Tashkent, 2018
55

Stellar evolution. Neutron stars and black holes

Textbook: pp. 118–120
GoalExplain the stages of stellar evolution and the formation of white dwarfs, neutron stars and black holes, and calculate the Schwarzschild radius.
New words
protostar · protoyulduzneutron star · neytron yulduzblack hole · qora tuynukSchwarzschild radius · Shvartsshild radiusi
Explanation

A star is born when a cloud of gas and dust contracts: a protostar forms, and then hydrogen burning starts in the core – the main sequence. When the hydrogen is gone the star becomes a red giant. A star of mass ≲ 8 M☉ (the Sun included) sheds its outer layers as a planetary nebula and becomes a white dwarf (mass ≤ 1.4 M☉ – the Chandrasekhar limit). A more massive star explodes as a supernova; if the remnant core is ≈ 1.4–2.2 M☉ it becomes a neutron star (radius ≈ 10–12 km, density ≈ 10¹⁷ kg/m³; a spinning one is a pulsar – discovered by Jocelyn Bell in 1967), and if more massive, a black hole – with gravity so strong that not even light can escape. The black hole’s boundary is the event horizon, whose radius is R_s = 2GM / c² ≈ 3 km · (M / M☉). Merging black holes make gravitational waves (first detected on 14 September 2015); at the centre of our Galaxy lies a black hole of ≈ 4 million M☉ (Sgr A*). In about 5 billion years the Sun will become a red giant and then a white dwarf.

Worked examples
If the Sun were a black hole, R_s ≈ 3 km; for a 10 M☉ hole, R_s ≈ 3 · 10 = 30 km.
Sgr A* has ≈ 4,000,000 M☉: R_s ≈ 3 · 4,000,000 = 12,000,000 km – about 17 times the Sun’s radius (≈ 0.7 million km).
Class activity

An indirect model: put a heavy weight on a stretched cloth (or rubber sheet) – the cloth sags and light balls roll towards it, an analogy of gravity (not a perfect one). Be careful if the balls are heavy.

Practice
1
How will the Sun end its life?
2
For a 20 M☉ black hole, how many km is R_s ≈ 3 km · 20?
3
Why is a neutron star so dense?
4
If a black hole cannot be seen directly, how do we know it exists?