Free-fall Collapse Times in Cosmology

Transcription

1 Astro 2299 The Search for Life in the Universe Lecture 9 Last time The Sun, hydrogen fusion Virial theorem and internal temperatures of stars Jeans mass This time: Star formation Formation of protostars and planetary systems Magnetic fields Assignment 2 posted Summary about stars posted Instructors: Jim Cordes & Shami Chatterjee 1 Free-fall Collapse Times in Cosmology We have 1/2 1 t = G Today, the mean matter density is about 30% of the critical density c = 3H2 0 8 G g cm 3 At redshifts z = 10 the universe was (1+z) 3 = 11 3 more dense than today. This gives t ff ~ 6 x sec ~ 2 Gyr Useful: 1 yr ~ π x 10 7 s To form the Galaxy an overdensity was needed (i.e. higher than average). A factor of 10 would yield t ff < 1 Gyr. 1

2 2/27/ Sudden decrease in MJ by > 12 orders of magnitude Why? 2

3 Jeans Mass vs Epoch One form for the Jeans length is: R J = C s p G Corresponding to a Jeans mass: M J R 3 J = C 3 s Prior to decoupling of radiation and matter, the universe was radiation dominated so the sound speed was C s ~ c / 3 1/2. Afterwards the sound speed in matter was C s~ (kt/m) 1/2 with T ~ 10 4 K, or about 10 km/s G 3/2 1/2 The ratio of sound speeds cubed is: apple Cs (before) C s (after) Formation of stars in the Galaxy In the Milky Way there are cold dense clouds that are actively forming stars today Typical temperatures are 10 K and densities g/cm 3 Evaluating R J ~ (kt/m) 1/2 (1 / (G!) 1/2 ~ 3 pc We can also calculate the Jeans mass as M J ~ R J 3 and we get about 50 M Interpretation: Relatively large mass regions collapse. Subregions inside them fragment as their temperatures fall and their densities increase. à A wide range of stellar masses 3

4 Other factors in cloud collapse and fragmentation So far we assumed (simplisticly) gas pressure from a monoatomic-like gas radial motion inward Realistic situations have additional contributions to gas pressure: Turbulent gas motions Magnetic pressure B 2 /2π Discuss magnetic fields Angular momentum also impedes collapse because It is conserved if there are no applied torques Discuss angular momentum Centrifugal forces work against gravity (rotationally-supported clouds) Successful collapse to protostars requires removal of both angular momentum and magnetic pressure. Magnetic fields can help extract angular momentum (viscosity) and later the fields can dissipate by ohmic diffusion. Solar System Formation Prime ingredients: Metals for solar abundances and for rocky planets Gas cloud that can collapse to form a protostar and protoplanetary disk Magnetic fields to help redistribute angular momentum Particulars: Giant planets further out Terrestrial (i.e. rocky) planets close in, one in the habitable zone (liquid water) Benign part of the Milky Way to provide orbital stability of the planets over 4.6 Gyr and adequate distance from catastrophic events (supernovae, gammaray bursts) 4

5 Salient Points Structure formation is very similar on large and small scales Galaxies in disks + debris (satellite galaxies) Supermassive black holes with disks + jets Planetary systems + debris around central star Protoplanetary systems with disks + jets Planets, asteriods have orbits in ecliptic plane today Comets (and other objects) can have highly inclined orbits Þ different origin Kinetic energy is king (in impacts): KE = MV 2 /2 Much larger for comets than asteroids per unit mass Minimum mass solar nebula: M(gas+dust) = 0.01 to 0.1 solar masses = 10 to 100 Jupiter Þ most mass has been lost, remainder is in planets, residual amount in debris Star Formation in the Galaxy Star formation is ongoing About 1 to 10 new stars formed each year in the Milky Way The rate of new star formation is much larger in some galaxies and was also much larger at earlier times (10 billion years ago) The Eagle Nebula (Hubble image) 5

6 2/27/18 Star Formation in the Galaxy Star formation is ongoing About 1 to 10 new stars formed each year in the Milky Way The rate of new star formation is much larger in some galaxies and was also much larger at earlier times (10 billion years ago) The Eagle Nebula (Hubble image) Star and Planet Formation 6

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8 b Pictoris A Nascent Solar System 8

9 What is the smallest mass that can collapse? Depends on gravity vs. pressure Jeans Mass Gravity tries to pull mass inward Pressure from gas at temperature T tries to resist gravity AstronomyOnline.org J Interstellar cloud ~ pc or more in size Net angular momentum [universe likely has no net angular momentum] Collapse to angular momentum vector requires radiation only (a la virial theorem) Disk structures are a natural outcome of collapse + angular momentum Viscosity allows gas+dust in the inner disk transfer angular momentum outward Viscosity is from gas collisions + turbulence in the gas, including the magnetic field Collapse inward requires 1. Radiation 2. Removal of angular momentum 3. Ultimately requires dissipation of magnetic field Outward transport of angular momentum Jets remove radiation and angular momentum Magnetic pressure: P ~ B 2 /8π B grows as cloud collapses and can aid removal of angular momentum Ohmic dissipation of field: Currents dissipate. 9

10 PE = Angular Momentum Barrier Object in circular orbit: we have the usual potential, kinetic, and total energy GMm r KE = 1 2 mv2 = GMm 2r E = 1 2 PE = 1 2 KE The potential energy V(r) = PE is a negative going potential well. For an object moving with arbitrary velocity we can write an effective potential Let v φ = azimuthal velocity and v r = radial velocity The object can be on an elliptical, hyperbolic, or parabolic orbit. Let J = angular momentum = mv φ r Then the energy of the particle can be written as E = (1/2) m v r2 + J 2 /2mr 2 GMm / r The last two terms comprise an effective potential V(r) = J 2 /2mr 2 GMm / r where the first term is a centrigugal barrier at small r Effective Potential that includes angular momentum 10

11 Ubiquity of Disks and Jets in Astrophysics 1. Accretion disks around supermassive black holes (SMBH) Centers of galaxies Disk temperature related to GPE of SMBH Disks are fed episodically by gas and stars from the host galaxy 2. Accretion disks around stellar mass BH, NS, and white dwarfs (10 M, ~1.4 M and <1.2 M, respectively) 3. Accretion disks around protostars In all cases, radiation has to occur for material to move inward (virial theorem) and angular momentum has to be transferred outward (angular momentum barrier) Active Galactic Nuclei 11

12 Unified model for AGNs AGN = Active galactic nucleus Note that there is a counter jet pointing downward (not shown) Figure 1.1 Schematic representation of our understanding of the AGN phenomenon and its main components. Note that this is a simplified view and not to scale. Graphic courtesy of Marie-Luise Menzel. 23 Unified model for AGNs AGN = Active galactic nucleus The AGN phenomenon Volker Beckmann low power high power BL Lac FSRQ BLRG, radio-loud (RL) AGN BLRG jet Type I QSO NLRG NLRG, Type II QSO reflected absorbed Seyfert 2 transmitted radio-quiet (RQ) AGN scattered dusty absorber accretion disc electron plasma black hole broad line region narrow line region Seyfert 1 Figure 1: Schematic representation of our understanding of the AGN phenomenon in the unified scheme [1]. The type of object we see depends on the viewing angle, whether or not the AGN produces a significant jet emission, and how powerful the central engine is. Note that radio loud objects are generally thought to display symmetric jet emission. Graphic courtesy of Marie-Luise Menzel (MPE)

13 25 Cygnus A Radio image VLA, NM 13

14 2/27/18 Cygnus A Radio image VLA, NM Accretion onto Compact Objects (WD, NS, BH) 14

15 Fig. 1 An artist s impression of a low-mass BHXRB. The major components of the binary, accretion flow, and outflows are indicated. R Fender, and T Belloni Science 2012;337: Published by AAAS Protoplanetary Disks and Jets 15

16 Protostar, disk and jet Image credit: Brooks/Cole Thomson Learning Basic Features of a New Star and Protoplanetary Disk Envelope Disk Protostar Jet/wind/outflow T. Greene 16

17 Planet formation was as follows: Collapse of the protoplanetary disk from an interstellar gas cloud while the inner part was collapsing to form the sun Formation of planetesimals to form protoplanets in about 10 5 yr in the inner solar system and 10 7 yr in the outer SS. Orbits stabilize as bigger objects deflect smaller ones or collisionally merge with them Final configuration of planetary orbits after a few hundred million years Cleanup: ongoing Considerable material ejected to the ISM or into the Sun Interstellar comets and asteroids: e.g. Oumuamua Protoplanetary disk ALMA observations Star = TW Hydrae ~60 pc distance young: ~10 Myr Large dark rings = gaps at distances equivalent to Uranus and Pluto Inset: gap ~ 1 AU radius (Earth like planet forming?) ALMA = Atacama Large Millimeter/Submillimeter Array 34 17

18 2/27/18 ALMA = Atacama Large Millimeter/Submillimeter Array 35 Protoplanetary disk ALMA observations Star = HL Tau ~150 pc distance < 105 yr old ALMA = Atacama Large Millimeter/Submillimeter Array 36 18

19 Magnetic Fields 37 Relevance of Magnetic Fields Magnetic fields are important for formation and evolution of protoplanetary disks (transferring angular momentum so that the disk can contract Cosmic rays are trapped in the Galaxy by its magnetic field; some CRs cause mutations in the biosphere Earth s magnetic field protects the biosphere from most (but not all) CRs and from particles from the Sun Navigation: some birds (magnetite in their brains) human 19