4 star formation

1. 4 star formation Stellar Structure: TCD 2006: 4.1

2. massive interstellar clouds • The galactic interstellar medium (ISM) consists of a roughly uniform gas with n~105 atoms/m3. • At current epoch, star formation takes place in massive interstellar clouds. • Clouds have dimensions: R~10 pc, n~5 109 atoms/m3, T~10 K. • Galaxy is pervaded by a magnetic field with field lines approximately parallel to the galactic plane. Field strongly tied to the ionized plasma in the ISM. Small local perturbations in the field lead to local potential wells. ISM condenses in these wells, increasing their strength as it pulls the magnetic field with it  Rayleigh-Taylor instability. • Provides initial mechanism for the formation of dark clouds of interstellar matter. • What causes these clouds to collapse to the point of forming stars? Stellar Structure: TCD 2006: 4.2

3. Jeans’ criterion for gravitational collapse Stellar Structure: TCD 2006: 4.3

4. contraction, fragmentation and formation Stellar Structure: TCD 2006: 4.4

5. contraction, fragmentation and formation (2) Stellar Structure: TCD 2006: 4.5

6. approach to hydrostatic equilibrium • After ionisation is complete (all H  H+), temperature and pressure rise, contraction slows down  hydrostatic equilibrium. <T> can be estimated using the Virial theorem. • Thermal kinetic energy is • Ekin~(M/mH)(3kT/2) = M/mH. 3kT. • Gravitational energy at end of collapse is • Egrav~-GM2/R2~-M/mH(D/2+I). • But 2Ekin+Egrav=0, so protostar approaches equilibrium at <T> given by • k<T>~(D+2I)/12~2.6eV 4.5 • Hence T~30,000 K, independent of M ! Stellar Structure: TCD 2006: 4.6

7. thermal contraction • Subsequent contraction governed by opacity. • Opacity controls the loss of radiation from the surface, and hence the release of gravitational energy on a thermal timescale (tkin­ ~107 –108 years). • Virial theorem can again be used because the star remains close to hydrostatic equilibrium. Stellar Structure: TCD 2006: 4.7

8. minimum mass for nuclear reactions Stellar Structure: TCD 2006: 4.8

9. stellar luminosity • We know Sun has been in hydrostatic equilibrium for 4.5 billion years, implies Virial theorem useful. For example: <P>~1014 Pa (104 atm), <>~103 kg m-3 (cf. water) <TI>~6.106 K. • We also know L=4R2 Teff4 (Stefan’s law: Eq. 1.4) • But Teff~6000 K ~ <TI>/1000. • Why are TI and Teff different ? • If star in equilibrium at temperature TI, it radiates as a blackbody with L = 4R2 TI4 ~ 1012 L, 4.8and photons would have mean energies kT~0.5 kEV (X-ray). • Fortunately, X-rays are trapped (absorbed and re-emitted) by ions, a temperature gradient is established and radiant energy diffuses towards the surface (Section 2). Stellar Structure: TCD 2006: 4.9

10. stellar luminosity Stellar Structure: TCD 2006: 4.10

11. 4 star formation - review • Stars form from interstellar clouds, providing Jeans criterion for gravitational collapse is satisfied. • Virial theorem used to determine radius after contraction to point where opacity increases, timescale from earlier, and average temperature. • Minimum electron separation used to estimate minimum mass for nuclear ignition. • Photon mean free path used to estimate stellar luminosity. Stellar Structure: TCD 2006: 4.11