Jeans Length - When does Gravity win? β€’ 𝑡 molecules of mass π’Ž in a box of size 𝑳 (do not confuse with the luminosity) at temperature 𝑻 β€’ Gravitational Energy: 𝐸 𝐺 ~ βˆ’ 𝐺 𝑀2 𝐿 β€’ Thermal Energy: 𝐸 𝑇 ~ 𝑁 π‘˜ 𝑇 β€’ Total mass: 𝑀 = 𝑁 π‘š ~ 𝐿3 𝜌 β€’ Ratio: 𝐸 𝐺 𝐸 𝑇 ~ 𝐺 𝑀2 𝐿 𝑁 π‘˜ 𝑇 ~ 𝐺 𝜌 𝐿3 π‘š 𝐿 π‘˜ 𝑇 = 𝐿 𝐿 𝐽 2 β€’ Jeans Length: 𝐿𝐽 ~ π‘˜ 𝑇 𝐺 𝜌 π‘š β€’ Gravity wins when 𝐿 > 𝐿𝐽 Jeans Mass β€’ Jeans Length: 𝐿𝐽 ~ π‘˜ 𝑇 𝐺 𝜌 π‘š β€’ Jeans Mass: 𝑀𝐽 = 𝐿𝐽 3 𝜌 = 𝜌 π‘˜ 𝑇 𝐺 𝜌 π‘š Ξ€3 2 ∝ 𝑇 Ξ€3 2 𝜌 Ξ€βˆ’1 2 β€’ Lowest Jeans Mass for cool and dense clouds Star formation Gravitation β€žwinsβ€œ Magnetic field, Shock wave Protostar FREE GAS NO FREE GAS Star formation β€’ The detection of free Gas in a Star Cluster is an excellent indicator for the time scale of continuous stellar formation Hartmann et al., 2001, ApJ, 562, 852 Star formation lasts 3 to 4 Myrs and is continuous This is also the β€œintrinsic” error of an age determination Numerical simulation of star formation in Giant Molecular Clouds β€’ Hypothesis: the formation of all members of a star cluster is continuous for 3 to 4 Myrs within one GMCs β€’ Is this a realistic approach? β€’ Is it possible to simulation the formation of star clusters and compare the results with observational data within the solar vicinity? Numerical simulation of star formation in Giant Molecular Clouds β€’ Detailed paper by Bate & Bonnell, 2005, MNRAS, 356, 1201 β€’ Basis: Orion Nebula and Taurus star forming region β€’ β€œComplete” astrophysical numerical simulation including Shock Waves, dynamical parameters and 3D-Hydrodynamics, Jeans Mass < 1 M(sun) β€’ The numerical simulations are astonishing close to the observations Numerical simulation of star formation in Giant Molecular Clouds Input parameter: 1. Mass (GMC) = 50 M(sun), limited by CPU time 2. Diameter = 0.375 pc, limited by CPU time 3. Time for the gravitational collapse: 19000 years 4. Random turbulence field with a 3D Gaussian distribution β€žStarsβ€œ: Mass > 0.084 M(sun) Brown Dwarfs: Mass < 0.084 M(sun), no Hydrogen burning More low mass stars formed due to the IMF For star clusters it is essential to know the internal velocity distribution because of their evolution (see later) Continuous star formation in time The formation of Binary systems Binaries are connected with a line The rms velocity dispersion of the simulations is 4.3 km s-1 Such observational data for d > 500 pc are still not available => Gaia satellite mission Magnetic field – star formation β€’ Price & Bate, 2009, MNRAS, 398, 33 β€’ Effects of magnetic pressure on fragmentation Increasing magnetic field strength Increasingmagneticfieldstrength Evolution of Star Clusters β€’ Star Clusters form with the following characteristics 1. Total Mass: IMF 2. Metallicity 3. Kinematics of the Cluster center: location within the Galaxy 4. Internal velocity dispersion β€’ How does a Star Cluster evolve with these starting parameters? β€’ Each member (= star) evolve β€œas an individual”, some important topics 1. Binary Evolution 2. Mass Loss (hot stars) 3. AGB Evolution 4. Planetary Nebula (cool stars) 5. Supernovae explosions β€’ In Star Clusters, collisions are very uncommon (see later), almost no new multiple (binary) systems form during the later evolution β€’ Star Clusters, normally, follow Galactic Rotation