Astronomers Walter Baade (1893 – 1960) Bart Bok (1906 – 1983) James Jeans (1877 – 1946) Ejnar Hertzsprung (1873 – 1967) Henry Russell (1877 – 1957) Luminosity versus radius and temperature R = 2 R T = T R = R T = T Which star is more luminous? 1 2 Luminosity versus radius and temperature • Each cm2 of each surface emits the same amount of radiation. • The larger star emits more radiation because it has a larger surface. It emits 4 times as much radiation. 1 2 R = 2 R T = T R = R T = T Luminosity versus radius and temperature 1 21 Which star is more luminous? R = R T = T R = R T = 2 T Luminosity versus radius and temperature 1 21 Which star is more luminous? The hotter star is more luminous. Luminosity varies as 𝑇4 (Stefan-Boltzmann Law) R = 2 R T = T R = R T = 2 T Luminosity Law 1 2 L  R2 T4 Luminosity  surface area  (Radius)2 Luminosity  (Temperature)4 If star A is 2 times as hot as star B, and the same radius, then it will be 24 = 16 times as luminous. Where do stars form? • Bok globules for low mass stars Rosette Nebula Characteristics of the Globules: r < 1 pc M < 1000 M T ≈ 10 K Where do stars form? • Giant Molecular Clouds (GMC) Characteristics of GMCs: 10 < r < 100 pc M up to a few 106 M T ≈ 10 K Jeans Length - When does Gravity win? • 𝑵 molecules of mass 𝒎 in a box of size 𝑳 (do not confuse with the luminosity) at temperature 𝑻 • Gravitational Energy: 𝐸 𝐺 ~ − 𝐺 𝑀2 𝐿 • Thermal Energy: 𝐸 𝑇 ~ 𝑁 𝑘 𝑇 • Total mass: 𝑀 = 𝑁 𝑚 ~ 𝐿3 𝜌 • Ratio: 𝐸 𝐺 𝐸 𝑇 ~ 𝐺 𝑀2 𝐿 𝑁 𝑘 𝑇 ~ 𝐺 𝜌 𝐿3 𝑚 𝐿 𝑘 𝑇 = 𝐿 𝐿 𝐽 2 • Jeans Length: 𝐿𝐽 ~ 𝑘 𝑇 𝐺 𝜌 𝑚 • Gravity wins when 𝐿 > 𝐿𝐽 Jeans Mass • Jeans Length: 𝐿𝐽 ~ 𝑘 𝑇 𝐺 𝜌 𝑚 • Jeans Mass: 𝑀𝐽 = 𝐿𝐽 3 𝜌 = 𝜌 𝑘 𝑇 𝐺 𝜌 𝑚 Τ3 2 ∝ 𝑇 Τ3 2 𝜌 Τ−1 2 • Lowest Jeans Mass for cool and dense clouds The first stage • Gravity tries to pull material in < = > Pressure tries to push it out • Time to collapse = free fall time 𝑡 𝐺 • Gravitational acceleration: 𝑔 ~ 𝐺 𝑀 𝐿2 ~ 𝐿 𝑡 𝐺 2 • Time to collapse: 𝑡 𝐺 ~ 𝐿 𝑔 ~ 𝐿3 𝐺 𝑀 ~ 1 𝐺 𝜌 • Note: – Denser regions collapse faster – Independent of the size The first stage • Pressure waves travel at the sound speed 𝑐𝑆 • For ideal gas: 𝑐𝑆 ~ 𝑃 𝜌 ~ 𝑘 𝑇 𝑚 • Sound crossing time: 𝑡 𝑆 ~ 𝐿 𝑐 𝑆 ~ 𝐿 𝑚 𝑘 𝑇 • Note: faster for smaller and hotter regions The first stage • Ratio of time scales: 𝑡 𝑆 𝑡 𝐺 ~ 𝐿 𝐺 𝜌 𝑐 𝑆 ~ 𝐿 𝐺 𝜌 𝑚 𝑘 𝑇 ~ 𝐿 𝐿 𝐽 • Jeans Length: 𝐿𝐽 ~ 𝑐 𝑆 𝐺 𝜌 • Larger clouds are more likely to collapse No collapse Condensation of in-falling molecular gas Hydrostatic low-luminosity proto-stellar object Protostar still enshrouded by optically thick material. Emission from thermal winds/jets ionized by neutral winds impacting the ambient medium Optical emission starts to come out along with an outflow and wind The star approaches the main sequence. Accretion substantially halted, protoplanetary disks may be present. Protostars evolve into main-sequence stars Protostars evolve into main-sequence stars Protostars evolve into main-sequence stars Protostars evolve into main-sequence stars