D.4a Jeans criterion and main-sequence fusion

NASA / Public domain

THE IB SAYS

Understandings: The Jeans criterion; Nuclear fusion

Applications and skills: Applying the Jeans criterion to star formation; Applying the mass–luminosity relation to compare lifetimes on the main sequence relative to that of our Sun

Guidance: Only an elementary application of the Jeans criterion is required, ie collapse of an interstellar cloud may begin if M > Mj

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Jeans criterion

Stars are formed from a cloud of interstellar gas and dust collapsing. This collapse is prompted by the self-gravity of the cloud, but resisted by the thermal kinetic energy of the particles of the cloud. The Jeans criterion states that for gravity to win, the gravitational potential energy of the cloud must be greater than the thermal kinetic energy. This means that a collapsing, or collapsible, cloud will tend to be cold and dense relative to other clouds.

Main-sequence nuclear fusion

Main sequence stars are defined by the burning of hydrogen to helium as their source of nuclear fusion. There are two main methods for doing this. The proton-proton chain dominates in lower mass stars ( <1.3 solar masses) while the CNO cycle is more efficient in higher mass stars.

Main-sequence lifetime

Larger stars have more fuel, however they are also significantly more luminous, as described by the mass-luminosity relationship (the luminosity increases with mass to the power 3.5!). This means that despite their increase fuel reserves the have significantly shorter lifetimes. Additionally very low mass stars (small red dwarfs) are able to use all of the fuel in the stars envelope thanks to the whole-star convection cells, while any larger star is restricted to that hydrogen available in the core.

Resources from textbooks

Oxford Physics: pages 666 - 672

Hamper HL (2014): pages 548 - 551

Relevant questions from Dot Point Physics (E Astrophysics)

Page 229 has something on the initial conditions for star formation. Otherwise see the textbooks.