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ASTROPHYSICS Mr. P.R.S. Tissera Department of Physical Sciences and Technology Faculty of Applied Sciences Sabaragamuwa University of Sri Lanka 1 PHYSICAL PARAMETERS OF A STAR Overview Interstellar Gas Molecular Clouds...

ASTROPHYSICS Mr. P.R.S. Tissera Department of Physical Sciences and Technology Faculty of Applied Sciences Sabaragamuwa University of Sri Lanka 1 PHYSICAL PARAMETERS OF A STAR Overview Interstellar Gas Molecular Clouds Gravitational Collapse : The Jeans Criterion Free Fall Collapse Homologous and Adiabatic Collapse Young Stars and Its Evolution 2 INTERSTELLAR MEDIUM (ISM) Galactic disk has significant dust and gas between stars Stars are born in molecular clouds The gas is composed of 90% Hydrogen and 9% Helium The composition of interstellar dust, is mostly unknown, but is believed to be heavier elements and “dirty” ices The most of the gas in ISM and the rest of the cosmos is Hydrogen which can be either Atomic or Molecule 3 4 MOLECULAR CLOUDS ▪ Stars form inside relatively dense concentrations of interstellar gas and dust known as molecular clouds ▪ These regions are extremely cold (temperature about 10 to 20 K, just above absolute zero) ▪ At these high temperatures, gases become molecular meaning that atoms bind together ▪ CO and Hydrogen are the most common molecules in interstellar gas clouds 5 TYPES OF MOLECULAR CLOUDS ▪ Giant Molecular Type ▪ Translucent Molecular cloud ✓ More than 106 solar masses and ✓ More than 3-100 solar temperature ~20 K masses ✓ Temperature ~15-50 K ▪ Small molecular clouds ✓ Small, denser almost spherical ✓ Low temperature ~10 K ✓ Low mass 1-1000 solar masses 6 NEBULA Nebula another name for gathering dust and gas cloud Types of nebula Reflection nebula Emission nebula Absorption nebula 7 DUST IN ISM ▪ Dust (1%) consists of minute grains of silicates and ices ▪ Ices : frozen water, methane ( CH4 ), ammonia ( NH3 ), Carbon dioxide (CO2 ) 8 WHAT IS THE ROLE OF DUST PARTICLES? ▪ The grains act as a catalyst in the formation of molecules. In the conditions present in molecular clouds, it’s quite rare that two colliding hydrogen atoms would stick to form a molecule ▪ The dust helps reduce the ionization of the cloud ▪ The dust acts as a thermostat, helping keep the cloud cool 9 GRAVITATIONAL COLLAPSE AND THE JEANS CRITERION ▪ Jeans proposed that there are two competing processes in the gravitational collapse of a molecular cloud. ▪ The gravitational contraction increases the internal pressure of the cloud which tends to expand the cloud, gravity acts on the cloud and tends to further contract it. ▪ Which of these two processes will dominate is determined by the mass of the cloud. ▪ If the internal pressure is more than the gravitational force, the cloud will break up. A clump of cloud must have a minimum mass to continue collapsing and give birth to a star. ▪ This minimum mass is called the Jeans mass. 10 ▪ To obtain an expression for the Jeans mass, we make the following simplifying assumptions: i) the cloud is uniform and non-rotating ii) the cloud is non-magnetic iii) the gas and dust is confined to a certain region of space by the gravitational force and is in hydrostatic equilibrium. 11  3 GMc 2 ▪ The self-gravitating cloud in equilibrium has a potential energy , U=− 3 5 Rc and total energy, K = NkT 2 ▪ N is the total number of particles and μ is mean-molecular mass, then, Mc N= μmH 3 Mc kT ▪ So, K= 2 μmH ▪ Note: 2K + U = 0 Equilibrium 2K + U > 0 Cloud expands 2K + U < 0 Cloud collapses 12 JEAN’S CRITERION ▪ The necessary conditions for cloud to collapse is given by the Jeans criterion 2K < U 3Mc kT 3 GMc 2 < μmH 5 Rc 1Τ3 3Mc ▪ Replacing R c = , we can take, 4𝜋𝜌0 1Τ3 3Mc kT 3GMc 2 4𝜋𝜌0 < μmH 5 3Mc 13  3Τ2 1Τ2 5kT 3 Mc > GμmH 4𝜋𝜌0 ▪ Jeans Mass : The minimum mass necessary to collapse a cloud of density 𝜌0 3Τ2 1Τ2 5kT 3 ≈ MJ GμmH 4𝜋𝜌0 Mc > MJ ▪ Jeans Length : The minimum radius for collapse of a cloud of density 𝜌0 Rc > RJ 14  FREE-FALL COLLAPSE TIME ▪ The estimate is for the special case of a non-rotating cloud, and requires that the particles of the cloud do not collide ▪ In the case of such a non-rotating cloud, all of the particles can be considered initially at rest with respect to the center ▪ And once the gravitational force begins to take effect, each particle can be considered to be in a long, narrow elliptical orbit ▪ It will fall from its initial radius to the center in a “free-fall” time, 1ൗ 3π 2 t ff = 32Gρ0 15  HOMOLOGOUS COLLAPSE ▪ Free fall time is independent from the initial radius of the sphere 1ൗ 3π 2 t ff = 32Gρ0 ▪ What is interesting is that every particle in the cloud takes exactly this same amount of time (because the inner particles feel less gravitational attraction, but have a smaller distance to fall) ▪ So this type of collapse is called homologous collapse 16 ▪ Gravitational Potential Energy converts into thermal energy when the cloud contracts ▪ While the dust in the core is optically thin, the core is transparent to IR wavelengths, and the core stays cool ▪ This phase of contraction is called isothermal collapse (temperature remains about constant) 17 ADIABATIC COLLAPSE ▪ The increase in density during the collapse, however, causes the optical depth to increase and eventually makes the cloud opaque to IR, trapping the thermal energy ▪ This is called the adiabatic collapse phase ▪ The temperature increases as the cloud collapses ▪ The trapped thermal energy heats the core, which builds up the internal pressure until hydrostatic equilibrium is reached ▪ At this stage the core is officially called a protostar 18 ▪ Momentum and Energy have to be conserved ▪ Potential Energy (P.E) = Kinetic Energy (1/2mv 2 ) ▪ Angular momentum to be conserved 19 ▪ The core stars to heat up and rotates faster as it collapses ▪ This rapid rotation creates large centrifugal forces ▪ These centrifugal forces are greatest at the equator and the core starts to spread out and form a disk 20 Shining, But not burning 21 YOUNG STARS ▪ Protostar: Protostars are central dense region of slowly collapse clouds (core) where collapse is adiabatic. Therefore the protostars are embedded sources ▪ Pre-main sequence stars (PMS): stars that are in the process of contracting but are not yet burning hydrogen in their cores. They have broken free from their parent cloud core ▪ T Tauri stars: Low mass (M < 2M0 ) PMS with stellar spectral class F to M (corresponding to Teff 7,000 – 3,000 K) ▪ Herbig stars: High mass (2 – 10 M) PMS are called Herbig stars. The high mass stars evolve so rapidly 22  ACCRETION PHASE ▪ The core gradually grows more massive by accreting in-falling material from the surrounding envelope ▪ However, the accreting material must first dissipate its gravitational potential energy, which is converted into accretion luminosity, given by: GMcore Macc Lacc = R core ▪ The accretion luminosity can dominate the protostar’s luminosity during this phase of evolution 23 ▪ While the in-fall continues, the temperature and radius of the protostar is increased 24 ▪ At this stage, the Hydrogen in the protostar’s core is still molecular ▪ At temperatures of about 2,000 K, molecular hydrogen dissociates in to hydrogen atoms ▪ This process, however, absorbs energy ▪ Since there is not enough pressure in the core to support the surrounding material, it suffers a second collapse phase Deuterium burning ▪ As the core grows via accretion, the central temperature increases and nuclear reactions begin in the core, converting deuterium into helium (He) via the reaction: 2 3 25 H+P He + γ HAYASHI TRACK ▪ Hayashi realized that the presence of H− ions in the envelope of a protostar enhances the opacity and forces the protostar to become convective ▪ As a result, the temperature only increases slowly while the core is collapsing, and therefore the luminosity of the protostar decreases ▪ In the HR diagram, this behaviour appears as a nearly vertical decline in the evolutionary track, known as the Hayashi track 26 27 ▪ The density and temperature of hydrogen nuclei in the core are enough to overcome their electrostatic repulsion ▪ The temperatures reach about 107 K at this moment and finally hydrogen is ignited in the stellar core 28 END OF THE CHAPTER 29