Lecture 4 - Interstellar Cloud Collapse

Lecture 4 - Interstellar Cloud Collapse • Topics to be covered: • The Interstellar Medium • Gravitational collapse • Virial Theorem • Jeans Instability PY4A01 Solar System Science

Interstellar Medium (ISM) • Interstellar space is not empty - there is gas and dust in the galaxy. • Chemical composition of gas is mostly hydrogen (~70%), some metals (~few %) and rest helium. • Clouds can be mainly • Neutral hydrogen (HI) • Ionized hydrogen (HII) • Molecular hydrogen (H2) • Because the ISM is diffuse, it does not radiate like a blackbody, so we don't see a continuous spectrum (like stars). PY4A01 Solar System Science

Interstellar Medium (ISM) - HI regions • Far from stars, no energy available to ionize/excite HI - therefore no optical emission lines. • Because electrons have charge and spin, have a magnetic dipole moment. Pauli Exclusion Principle: electron and proton “want” to be anti-aligned - this is their ground state. If aligned, have slightly more energy. If change spin can release energy difference as a photon. • Energy difference is small ~6x10-6eV, which is ~21 cm (radio waves). • From radio surveys of our galaxy find lots of HI gas: about 1 solar mass of gas for every 10 solar masses of stars. Radio IR PY4A01 Solar System Science

Interstellar Medium (ISM) - HII regions • HII regions are found near hot stars. • UV photons from nearby stars ionize H atoms. • When electrons and protons recombine, they generally emit Balmer lines. • Also observe lines from other atoms (e.g., oxygen, sulfur, silicon, carbon, …). • HII regions are associated with active star formation. PY4A01 Solar System Science

Interstellar Medium (ISM) - H2 regions • If density of gas is high, and temperature is low enough, H atoms can form H2. Unfortunately, no emission from H2 in the optical or radio bands. Therefore use, • Other molecules. For example, CO emits radiation at a wavelength of 2.6mm - microwaves. • Dust. Dust (and molecules) are often found together - dense, dark clouds (called Bok globules) are regions of very dense molecular gas. • Where there is lots of gas - in particular molecular and ionized gas => lots of stars formation … PY4A01 Solar System Science

The Virial Theorem • Applies to any system of particles with pair interactions for which the distribution of particles does not vary with time. • Theorem states that total energy of system E is related to gravitational potential energy U by: E = 1/2 U • But we know that total energy is sum of the kinetic and potential energy=> K + U = 1/ 2 U or 2K + U = 0 • Can be applied to a system of gravitationally interacting bodies such as stars forming a cloud, clusters of stars, clusters of galaxies, etc. • As K = 3/2 NkT and Eqn. 1 PY4A01 Solar System Science

Application of the Virial Theorem • VT can be used to estimate conditions for cloud collapse: • If 2K > U => gas pressure (energy) will exceed gravitational potential energy and expand. • If 2K < U => gravitational energy will exceed gas pressure and collapse. • The boundary between these two cases describes the critical condition for stability. • We know that  = Mc/Vc = Mc / (4/3Rc3) => and N = Mc/mHwhere  is the mean molecular weight and mHis the mass of a proton. Can we derive an expression for the critical mass? 2K U PY4A01 Solar System Science

Application of the Virial Theorem - The Jeans Mass • Substituting for R and N in Eqn. 1: • The Jeans Criterion is: Mc > MJ • If Mc > MJ=> cloud will collapse. • Rearranging Eqn. 2 gives: Eqn. 2 The Jeans Mass 2K U PY4A01 Solar System Science

Application of the Virial Theorem - The Jeans Radius • Is there a critical radius that corresponds to the critical mass? • We know Mc = 4/3  Rc3 . Equating this to the Jeans Mass gives: • If RC>RJ => stable. If RC <RJ => unstable and collapse. The Jeans Radius PY4A01 Solar System Science

Gravitational Collapse in the ISM • Properties of the ISM: • We know from the Jeans Criterionthat if Mc>MJcollapse occurs. • Substituting the values from the table into gives: • Diffuse HI cloud: MJ ~ 1500 MSun => stable as Mc<MJ. • Molecular cloud core: MJ ~ 15 Msun => unstable as Mc>MJ. • So deep inside molecular clouds the cores are collapsing to form stars. PY4A01 Solar System Science

Cloud Collapse and Star/Planet Formation • Jeans cloud collapse equations describe the conditions required for an ISM cloud to collapse. • As a cloud collapses, central temperature increases. • This is accompanied by spinning-up of the central star (to conserve AM). • Disk also flattens into an oblate spheroid. PY4A01 Solar System Science

Time-scale for collapse • The collapse time-scale tffwhen M >MJis given by the time a mass element at the cloud surface needs to reach the centre. • In free-fall, an mass element is subject to acceleration • The time to cover a distance R can therefore be estimated from: • By approximating R using R3 ~ M/ => tff ≈ (G )-1/2 • Higher density at cloud center = > faster collapse. • For typical molecular cloud, tff ~ 103 years (ie very short). PY4A01 Solar System Science

Nebular Collapse • Solar system was formed from a giant molecular cloud, known as the proto-solar or primordial nebula. • Similar to the Orion Nebula (right). • Nebula may have only contained only 10-20% more mass than present solar system. • Due to some disturbance, perhaps a nearby supernova, the gas was perturbed, causing ripples of increased density. • The denser material began to collapse under its own gravity… PY4A01 Solar System Science

Proto-star and Disk Formation • Nebula must have possessed some rotation. Due to the spin, the cloud collapsed faster along the ‘poles’ than the equator. • The result is that the cloud collapsed into a spinning disk. • Disk material cannot easily fall all the remaining way into the center because of its rotational motion, unless it can somehow lose some energy, e.g. by friction in the disk (collisions). • The initial collapse takes just a few 100,000 years. PY4A01 Solar System Science

Lecture 4 - Interstellar Cloud Collapse