caloric curve of King models
|
|
- Morris Lang
- 5 years ago
- Views:
Transcription
1 caloric curve of King models with a short-distance cutoff on the interactions Lapo Casetti Dipartimento di Fisica e Astronomia & CSDC, Università di Firenze, Italy INFN, sezione di Firenze, Italy Dynamics & Kinetic Theory of Self-Gravitating Systems IHP, Paris, France, November 6, 2013 joint work with Cesare Nardini (ENS Lyon) Physical Review E 85, (2012)
2 introduction & motivation self-gravitating systems: natural examples of long-range systems truly long-range interactions, unscreened almost ideal samples: globular clusters, elliptical galaxies... seemingly obvious testing ground for theoretical predictions standard equilibrium statistical mechanics does not work! short-distance singularity escape of particles idealized systems & toy models first step very interesting theoretical features clustering, phase transitions, ensemble inequivalence, C v < 0... encoded in the caloric curve T (E) relevant for real systems? caloric curve analysis of observationally probed models (King) introduction of a short-distance cutoff
3 equilibrium statistical mechanics of self-gravitating systems H (r 1,..., r N, v 1,..., v N ) = m 2 N v 2 i Gm 2 i=1 N N i=1 j>i 1 r i r j short-distance singularity = no true equilibrium state metastable states may still exist (local entropy maxima) easy solution: regularization via short-distance cutoff (more soon) unbounded space = escape of particles finite escape velocity incompatible with maxwellian velocity distribution stationary maxwellian distribution in unbounded space = infinite mass solution (not so easy...): put the system in a box or consider an expanding background, but that s another story regularized & confined = equilibrium exists [Kiessling, Chavanis]
4 equilibrium statistical mechanics of self-gravitating systems
5 isothermal sphere forget about regularization it is implied, and will come back shortly... continuum (mean-field) limit & spherical box of radius R (m = 1) S[f ] = dr dv f (r, v) log f (r, v) local extrema of S spherically symmetric that is, for given β and ϱ c = ϱ(0), d 2 ϕ(r) dr 2 f (r, v) = C e βv 2 /2 e βϕ(r) + 2 r ϱ(r) = dv f (r, v) 2 ϕ(r) = 4πGϱ(r) dϕ(r) dr = 4πGϱ ce β[ϕ(r) ϕ(0)] [Antonov, Lynden-Bell & Wood, Padmanabhan, Chavanis]
6 isothermal sphere: caloric curve energy & temperature (k B = 1) U = G 2 K = 1 2 dr dv v 2 f (r, v) = 3 2β = 3T 2 dr dv dr dv f (r, v)f (r, v ) r r E = K + U = 1 2 dr ϱ(r)ϕ(r) energy unit GM 2 /R M = dr ϱ(r) dimensionless energy & temperature ε = ϑ = RE GM 2 RT GM 2
7 isothermal sphere: caloric curve ϑ minimal energy & temperature ε ε min ϑ min 0.4 ε < ε min = gravothermal catastrophe [Antonov, Lynden-Bell & Wood, Padmanabhan, Chavanis]
8 short-distance cutoff short-distance regularization regularization + confinement = equilibrium states exist necessary to justify the mean-field procedure required by physics quantum particles: effective cutoff due to Pauli exclusion principle self-gravitating fermions [Chavanis & Ispolatov] classical particles: new interactions at small scales stars & planets have a finite size! many possible implementations hard-core/soft-core particles, truncated/softened potential... Gm 2 V (r i, r j ) = ri r j 2 + a [a] = l 2
9 models with cutoff mean-field in a spherical box (isothermal sphere + cutoff) [Aronson & Hansen, Chavanis, Ispolatov & Cohen, Alastuey & coworkers] shell model [Youngkins & Miller] self-gravitating ring [Sota et al., Tatekawa et al.] self-gravitating particles on S 2 [Kiessling] minimalistic models [Thirring, Lynden-Bell, Chavanis, LC & Nardini] N stars in a box (MC simulations of N self-gravitating particles in a 3D box) [De Vega & Sanchez] common features short-distance cutoff + confinement in a box or in a compact configuration space
10 caloric curve ϑ cutoff-dominated C < 0 gaslike ε common features (small cutoff) the cutoff stabilizes a low-energy phase (clustered phase) no gravothermal catastrophe, minimal energy related to real lower bound on potential energy negative specific heat in a region of the clustered phase phase transition to high-energy phase (quasi-uniform, perfect-gas-like) the order of the phase transition depends on the cutoff, as do the details of the phases
11 caloric curve ϑ cutoff-dominated C < 0 gaslike ε question what about real self-gravitating systems? no box, no thermal velocity distribution
12 globular clusters ω Cen the largest Milky Way globular cluster
13 King model phenomenological & stationary mean-field-like model spherically symmetric cluster of equal stars globulars & open clusters & elliptical galaxies... assumptions 1 single particle distribution function f (r, v) 2 ϱ(r) 0 if r r t 3 relaxed system = f (v) as close to thermal equilibrium as it can be 4 constraint: v v e(r) = escape velocity [King 1966]
14 King model ϱ(r) = f (r, v) = C M β T 1 { dv f (r, v) v 2 e(r) = 2ϕ(r) ϕ(r t) = 0 C e 2βϕ(r) [e βv 2 e βv 2 e (r)] if v 2 < v 2 e (r) 0 otherwise for the moment no short-distance cutoff on the gravitational interaction... 2 ϕ(r) = 4πGϱ(r)...and go on as in the isothermal sphere r t (M ) = King isothermal sphere [King 1966]
15 introduction self-gravitating systems King model statistical mechanics summary & outlook King model vs. observations good fit of density profiles for roughly 80% of Milky Way globulars bad fit or no fit for the remaining 20% of globulars post-core-collapsed globulars [Djorgovic & King 1986] M 13 in Hercules King cluster M 15 in Pegasus post-core-collapsed cluster
16 statistical mechanics of King models energy & temperature (k B = 1) K = 1 2 dr dv v 2 f (r, v) = 3T 2 U = G 2 dr dv dr dv f (r, v)f (r, v ) r r E = K + U = 1 2 dr ϱ(r)ϕ(r) energy unit GM 2 /r t dimensionless energy & temperature ε = ϑ = rte GM 2 rtt GM 2
17 caloric curve of King model without cutoff ϑ ε virial theorem for purely gravitational interactions energy & temperature are bounded K = E = ϑ = 2 3 ε ε [ 2.13, 0.60] ϑ [0.40, 1.42]
18 caloric curve of King model without cutoff ϑ ε increasing ϕ(r = 0) data points reach ε min then go back and forth in a collapsed spiral pattern plotting e.g. ϑ 0 = ϑ(r = 0) the spiral pattern opens up
19 switching on the cutoff short-range cutoff 1 r r 1 r r 2 + a all definitions of f, ϱ, ϕ, U, K, E, T formally as before same adimensionalization: dimensionless cutoff α α = a r t 2 no analogue of Poisson equation = no differential formulation self-consistent iterative procedure conceptually straightforward, numerically less efficient reasonable cutoff values star size < cutoff length < average interstellar separation 10 9 α
20 caloric curve with cutoff ϑ ε α = 10 3
21 caloric curve with cutoff ϑ ε α = 10 5
22 caloric curve with cutoff 1.5 ϑ ε α = 10 3 α = 10 5 no cutoff
23 caloric curve with cutoff effect of the short-distance cutoff stabilization of a low-energy phase energy range much larger than without cutoff high-energy region model without cutoff already for moderate cutoff α 10 5 close analogy to confined models with cutoff no gas-like phase at high energy (no container!) ϑ cutoff-dominated C < 0 gaslike ε
24 caloric curve with cutoff effect of the short-distance cutoff stabilization of a low-energy phase energy range much larger than without cutoff high-energy region model without cutoff already for moderate cutoff α 10 5 close analogy to confined models with cutoff no gas-like phase at high energy (no container!) ϑ cutoff-dominated C < 0 gaslike ε
25 density profiles α = ψ(x) x C < 0, high energy C < 0, intermediate energy C > 0, low energy
26 density profiles α = ψ(x) x C < 0, high energy C < 0, intermediate energy C > 0, low energy
27 phase transition? 4 3 ϑ ε α = no cutoff
28 phase transition? 3.5 α = ϑ ε
29 phase transition? α = ψ(x) x C < 0, high energy C < 0, intermediate energy C > 0, low energy
30 summary & outlook summary statistical-mechanical approach to King phenomenological model of star clusters study of the caloric curve short-range cutoff stabilizes a low-energy phase caloric curve analogous to confined self-gravitating systems, without high-energy gas phase low-energy density profile with core-halo structure qualitatively similar to post-core-collapsed clusters and many elliptical galaxies phase transition between King and core-halo structure for small cutoff? preliminary result precise understanding still lacking
31 summary & outlook summary statistical-mechanical approach to King phenomenological model of star clusters study of the caloric curve short-range cutoff stabilizes a low-energy phase caloric curve analogous to confined self-gravitating systems, without high-energy gas phase low-energy density profile with core-halo structure qualitatively similar to post-core-collapsed clusters and many elliptical galaxies phase transition between King and core-halo structure for small cutoff? preliminary result precise understanding still lacking outlook differential formulation using soft-core particles regularization (Yukawa-like)? improvement of numerics, test of robustness against different regularizations and better understanding of the phase transition (work in progress) possible physical origin of effective cutoff? e.g. formation of hard binaries (work in progress) quantitative comparison with observations of collapsed globulars and ellipticals? density profiles does not seem to work for globulars but might work for ellipticals improved models? (starting collaboration with A. Marconi)
32
33 globular clusters platonic self-gravitating systems clusters of stars, almost spherical orbiting (all?) galaxies # of Milky Way globulars in Andromeda galaxy, > 10 4 in giant elliptical M87 finite size r t 50 pc tidal effect of the host galaxy no gas, no dust no dark matter too... very old (age > 10 Gyr) may have undergone collisional relaxation
Kinetic Theory. Motivation - Relaxation Processes Violent Relaxation Thermodynamics of self-gravitating system
Kinetic Theory Motivation - Relaxation Processes Violent Relaxation Thermodynamics of self-gravitating system negative heat capacity the gravothermal catastrophe The Fokker-Planck approximation Master
More informationSpiral Structure. m ( Ω Ω gp ) = n κ. Closed orbits in non-inertial frames can explain the spiral pattern
Spiral Structure In the mid-1960s Lin and Shu proposed that the spiral structure is caused by long-lived quasistatic density waves The density would be higher by about 10% to 20% Stars, dust and gas clouds
More informationAY202a Galaxies & Dynamics Lecture 7: Jeans Law, Virial Theorem Structure of E Galaxies
AY202a Galaxies & Dynamics Lecture 7: Jeans Law, Virial Theorem Structure of E Galaxies Jean s Law Star/Galaxy Formation is most simply defined as the process of going from hydrostatic equilibrium to gravitational
More informationStellar Dynamics and Structure of Galaxies
Stellar Dynamics and Structure of Galaxies Gerry Gilmore H47 email: gil@ast.cam.ac.uk Lectures: Monday 12:10-13:00 Wednesday 11:15-12:05 Friday 12:10-13:00 Books: Binney & Tremaine Galactic Dynamics Princeton
More information1.1 Motivation. 1.2 The H-R diagram
1.1 Motivation Observational: How do we explain stellar properties as demonstrated, e.g. by the H-R diagram? Theoretical: How does an isolated, self-gravitating body of gas behave? Aims: Identify and understand
More informationRecent progress in the study of long-range interactions
Recent progress in the study of long-range interactions Thierry Dauxois 1 and Stefano Ruffo 1,2 1 Laboratoire de Physique de l École Normale Supérieure de Lyon, Université de Lyon, CNRS, 46 Allée d Italie,
More informationStellar-Dynamical Systems
Chapter 8 Stellar-Dynamical Systems A wide range of self-gravitating systems may be idealized as configurations of point masses interacting through gravity. But in galaxies, the effects of interactions
More informationNeutron Stars. Neutron Stars and Black Holes. The Crab Pulsar. Discovery of Pulsars. The Crab Pulsar. Light curves of the Crab Pulsar.
Chapter 11: Neutron Stars and Black Holes A supernova explosion of an M > 8 M sun star blows away its outer layers. Neutron Stars The central core will collapse into a compact object of ~ a few M sun.
More informationSlow dynamics in systems with long-range interactions
Slow dynamics in systems with long-range interactions STEFANO RUFFO Dipartimento di Energetica S. Stecco and INFN Center for the Study of Complex Dynamics, Firenze Newton Institute Workshop on Relaxation
More informationb a = 1 n 10. Surface brightness profile of most elliptical galaxies can be fit well by the R 1/4 (or de Vaucouleurs) law, (1 ɛ) 2 a 2 = 1.
7 Elliptical Galaxies Basic properties of elliptical galaxies Formation of elliptical galaxies 7.1 Photometric Properties Isophotes of elliptical galaxies are usually fitted by ellipses: Major axis a;
More informationMichela Mapelli. LECTURES on COLLISIONAL DYNAMICS: 1. RELEVANT TIMESCALES, FORMATION OF STAR CLUSTERS, EQUILIBRIUM MODELS
Michela Mapelli LECTURES on COLLISIONAL DYNAMICS: 1. RELEVANT TIMESCALES, FORMATION OF STAR CLUSTERS, EQUILIBRIUM MODELS COLLISIONAL/COLLISIONLESS? Collisional systems are systems where interactions between
More informationView of the Galaxy from within. Lecture 12: Galaxies. Comparison to an external disk galaxy. Where do we lie in our Galaxy?
Lecture 12: Galaxies View of the Galaxy from within The Milky Way galaxy Rotation curves and dark matter External galaxies and the Hubble classification scheme Plotting the sky brightness in galactic coordinates,
More informationDark matter and galaxy formation
Dark matter and galaxy formation Galaxy rotation The virial theorem Galaxy masses via K3 Mass-to-light ratios Rotation curves Milky Way Nearby galaxies Dark matter Baryonic or non-baryonic A problem with
More informationAim: Understand equilibrium of galaxies
8. Galactic Dynamics Aim: Understand equilibrium of galaxies 1. What are the dominant forces? 2. Can we define some kind of equilibrium? 3. What are the relevant timescales? 4. Do galaxies evolve along
More informationAstro 242. The Physics of Galaxies and the Universe: Lecture Notes Wayne Hu
Astro 242 The Physics of Galaxies and the Universe: Lecture Notes Wayne Hu Syllabus Text: An Introduction to Modern Astrophysics 2nd Ed., Carroll and Ostlie First class Wed Jan 3. Reading period Mar 8-9
More informationBinary star formation
Binary star formation So far we have ignored binary stars. But, most stars are part of binary systems: Solar mass stars: about 2 / 3 are part of binaries Separations from: < 0.1 au > 10 3 au Wide range
More informationAS1001:Extra-Galactic Astronomy
AS1001:Extra-Galactic Astronomy Lecture 5: Dark Matter Simon Driver Theatre B spd3@st-andrews.ac.uk http://www-star.st-and.ac.uk/~spd3 Stars and Gas in Galaxies Stars form from gas in galaxy In the high-density
More informationCHAPTER 20. Collisions & Encounters of Collisionless Systems
CHAPTER 20 Collisions & Encounters of Collisionless Systems Consider an encounter between two collisionless N-body systems (i.e., dark matter halos or galaxies): a perturber P and a system S. Let q denote
More informationGalaxies: Structure, Dynamics, and Evolution. Elliptical Galaxies (II)
Galaxies: Structure, Dynamics, and Evolution Elliptical Galaxies (II) Layout of the Course Feb 5: Review: Galaxies and Cosmology Feb 12: Review: Disk Galaxies and Galaxy Formation Basics Feb 19: Disk Galaxies
More informationPeculiar (Interacting) Galaxies
Peculiar (Interacting) Galaxies Not all galaxies fall on the Hubble sequence: many are peculiar! In 1966, Arp created an Atlas of Peculiar Galaxies based on pictures from the Palomar Sky Survey. In 1982,
More informationASTRON 331 Astrophysics TEST 1 May 5, This is a closed-book test. No notes, books, or calculators allowed.
ASTRON 331 Astrophysics TEST 1 May 5, 2003 Name: This is a closed-book test. No notes, books, or calculators allowed. Orders of Magnitude (20 points): simply circle the correct answer. 1. The brightest
More informationThe physical origin of stellar envelopes around globular clusters
The physical origin of stellar envelopes around globular clusters Phil Breen University of Edinburgh in collaboration with A. L. Varri, J. Peñarrubia and D. C. Heggie Current observational evidence Example:
More informationASTR 200 : Lecture 25. Galaxies: internal and cluster dynamics
ASTR 200 : Lecture 25 Galaxies: internal and cluster dynamics 1 Galaxy interactions Isolated galaxies are often spirals One can find small galaxy `groups' (like the Local group) with only a few large spiral
More informationLecture notes 17: The Milky Way ii: Kinematics and the galactic core
Lecture notes 17: The Milky Way ii: Kinematics and the galactic core Disk rotation & the local standard of rest In the galactic disk the mean orbital speed of the stars is much greater than the stars random
More informationGalaxy clusters. Dept. of Physics of Complex Systems April 6, 2018
Galaxy clusters László Dobos Dept. of Physics of Complex Systems dobos@complex.elte.hu É 5.60 April 6, 2018 Satellite galaxies Large galaxies are surrounded by orbiting dwarfs approx. 14-16 satellites
More informationClusters of Galaxies
Clusters of Galaxies Galaxies are not randomly strewn throughout space. Instead the majority belong to groups and clusters of galaxies. In these structures, galaxies are bound gravitationally and orbit
More informationThe Milky Way Galaxy
1/5/011 The Milky Way Galaxy Distribution of Globular Clusters around a Point in Sagittarius About 00 globular clusters are distributed in random directions around the center of our galaxy. 1 1/5/011 Structure
More informationGravitational Efects and the Motion of Stars
Gravitational Efects and the Motion of Stars On the largest scales (galaxy clusters and larger), strong evidence that the dark matter has to be non-baryonic: Abundances of light elements (hydrogen, helium
More informationChapter 15 The Milky Way Galaxy. The Milky Way
Chapter 15 The Milky Way Galaxy The Milky Way Almost everything we see in the night sky belongs to the Milky Way We see most of the Milky Way as a faint band of light across the sky From the outside, our
More informationA Guide to the Next Few Lectures!
Dynamics and how to use the orbits of stars to do interesting things chapter 3 of S+G- parts of Ch 11 of MWB (Mo, van den Bosch, White) READ S&G Ch 3 sec 3.1, 3.2, 3.4 we are skipping over epicycles 1
More informationSpatial distribution of stars in the Milky Way
Spatial distribution of stars in the Milky Way What kinds of stars are present in the Solar neighborhood, and in what numbers? How are they distributed spatially? How do we know? How can we measure this?
More informationAstronomy 330 Lecture Oct 2010
Astronomy 330 Lecture 10 06 Oct 2010 Outline Review Galactic dynamics Potentials Energetics Rotation curves Disk-halo degeneracy Characteristics of dynamical systems Dynamics of collisionless systems But
More informationClicker Question: Clicker Question: Clicker Question: Clicker Question: What is the remnant left over from a Type Ia (carbon detonation) supernova:
Test 3 results D C Grades posted in cabinet and Grades posted on-line B A F If you are not properly registered then come see me for your grade What is the ultimate origin of the elements heavier than helium
More informationA Guide to the Next Few Lectures!
Dynamics and how to use the orbits of stars to do interesting things chapter 3 of S+G- parts of Ch 11 of MWB (Mo, van den Bosch, White) READ S&G Ch 3 sec 3.1, 3.2, 3.4 we are skipping over epicycles 1
More informationWhy evolution? Why the Stars and the Universe Evolve?
Why evolution? Why the Stars and the Universe Evolve? @Kobe planetary school Daiichiro Sugimoto former affiliations: Univ. Tokyo & Open University of Japan Jan 10, 2011 Wärmetod or Emergence of structures?
More informationName Midterm Exam October 20, 2017
Name Midterm Exam October 20, 2017 This test consists of three parts. For the first and second parts, you may write your answers directly on the exam, if you wish. For the other parts, use separate sheets
More informationComponents of Galaxies Stars What Properties of Stars are Important for Understanding Galaxies?
Components of Galaxies Stars What Properties of Stars are Important for Understanding Galaxies? Temperature Determines the λ range over which the radiation is emitted Chemical Composition metallicities
More informationStatistical Mechanics of Gravitating Systems
Statistical Mechanics of Gravitating Systems...and some curious history of Chandra s rare misses! T. Padmanabhan (IUCAA, Pune, INDIA) Chandra Centenary Conference Bangalore, India 8 December 2010 Phases
More informationGalaxies: The Nature of Galaxies
Galaxies: The Nature of Galaxies The Milky Way The Milky Way is visible to the unaided eye at most place on Earth Galileo in 1610 used his telescope to resolve the faint band into numerous stars In the
More informationUniverse Now. 9. Interstellar matter and star clusters
Universe Now 9. Interstellar matter and star clusters About interstellar matter Interstellar space is not completely empty: gas (atoms + molecules) and small dust particles. Over 10% of the mass of the
More informationAstronomy: Division C Science Olympiad, Round 1 Tryout Test
Astronomy: Division C Science Olympiad, Round 1 Tryout Test Student Name : Student Number : DIRECTIONS 1. Write the answers that you want graded legibly on the answer sheet, along with your name and student
More informationASTRON 449: Stellar (Galactic) Dynamics. Fall 2014
ASTRON 449: Stellar (Galactic) Dynamics Fall 2014 In this course, we will cover the basic phenomenology of galaxies (including dark matter halos, stars clusters, nuclear black holes) theoretical tools
More information3 Hydrostatic Equilibrium
3 Hydrostatic Equilibrium Reading: Shu, ch 5, ch 8 31 Timescales and Quasi-Hydrostatic Equilibrium Consider a gas obeying the Euler equations: Dρ Dt = ρ u, D u Dt = g 1 ρ P, Dɛ Dt = P ρ u + Γ Λ ρ Suppose
More informationProbing Dark Matter Halos with Satellite Kinematics & Weak Lensing
Probing Dark Matter Halos with & Weak Lensing Frank C. van den Bosch (MPIA) Collaborators: Surhud More, Marcello Cacciato UMass, August 2008 Probing Dark Matter Halos - p. 1/35 Galaxy Formation in a Nutshell
More informationStar systems like our Milky Way. Galaxies
Galaxies Star systems like our Milky Way Galaxies Contain a few thousand to tens of billions of stars,as well as varying amounts of gas and dust Large variety of shapes and sizes Gas and Dust in
More informationASTR 610 Theory of Galaxy Formation Lecture 15: Galaxy Interactions
ASTR 610 Theory of Galaxy Formation Lecture 15: Galaxy Interactions Frank van den Bosch Yale University, spring 2017 Galaxy Interactions & Transformations In this lecture we discuss galaxy interactions
More informationChapter 23 The Milky Way Galaxy Pearson Education, Inc.
Chapter 23 The Milky Way Galaxy The Milky Way is our own galaxy viewed from the inside. It is a vast collection of more than 200 billion stars, planets, nebulae, clusters, dust and gas. Our own sun and
More informationBeyond the spherical dust collapse model
Beyond the spherical dust collapse model 1.5M 1.0M M=1.66 10 15 M 0.65M 0.4M 0.25M Evolution of radii of different mass shells in a simulated halo Yasushi Suto Department of Physics and RESCEU (Research
More informationAstronomy Stars, Galaxies and Cosmology Exam 3. Please PRINT full name
Astronomy 132 - Stars, Galaxies and Cosmology Exam 3 Please PRINT full name Also, please sign the honor code: I have neither given nor have I received help on this exam The following exam is intended to
More informationGalaxies and Star Systems
Chapter 5 Section 5.1 Galaxies and Star Systems Galaxies Terms: Galaxy Spiral Galaxy Elliptical Galaxy Irregular Galaxy Milky Way Galaxy Quasar Black Hole Types of Galaxies A galaxy is a huge group of
More informationDynamical friction, galaxy merging, and radial-orbit instability in MOND
Dynamical friction, galaxy merging, and radial-orbit instability in MOND Carlo Nipoti Dipartimento di Astronomia Università di Bologna Strasbourg, 29 June 2010 Outline MOND and Equivalent Newtonian Systems
More informationASTR Midterm 2 Phil Armitage, Bruce Ferguson
ASTR 1120-001 Midterm 2 Phil Armitage, Bruce Ferguson SECOND MID-TERM EXAM MARCH 21 st 2006: Closed books and notes, 1 hour. Please PRINT your name and student ID on the places provided on the scan sheet.
More informationAstronomy 1 Fall 2016
Astronomy 1 Fall 2016 Lecture11; November 1, 2016 Previously on Astro-1 Introduction to stars Measuring distances Inverse square law: luminosity vs brightness Colors and spectral types, the H-R diagram
More informationOur Solar System: A Speck in the Milky Way
GALAXIES Lesson 2 Our Solar System: A Speck in the Milky Way The Milky Way appears to be curved when we view it but in reality it is a straight line. It is curved due to the combination of pictures taken
More informationChapter 14 The Milky Way Galaxy
Chapter 14 The Milky Way Galaxy Spiral Galaxy M81 - similar to our Milky Way Galaxy Our Parent Galaxy A galaxy is a giant collection of stellar and interstellar matter held together by gravity Billions
More informationGravitational instability of polytropic spheres and generalized thermodynamics
A&A 386, 732 742 (22) DOI:.5/4-636:2236 c ESO 22 Astronomy & Astrophysics Gravitational instability of polytropic spheres and generalized thermodynamics P. H. Chavanis Laboratoire de Physique Quantique,
More informationarxiv: v1 [gr-qc] 19 Sep 2018
Relativistic Gravitational Phase Transitions and Instabilities of the Fermi Gas arxiv:189.7169v1 [gr-qc] 19 Sep 18 Zacharias Roupas Department of Mathematics, University of the Aegean, Karlovassi 83, Samos,
More informationDynamical Models of the Globular Clusters M4 and NGC 6397
Dynamical Models of the Globular Clusters M4 and NGC 6397 Douglas Heggie University of Edinburgh d.c.heggie@ed.ac.uk in collaboration with Mirek Giersz CAMK, Warsaw, Poland Outline Introduction: M4 and
More informationAST1100 Lecture Notes
AST1100 Lecture Notes 5 The virial theorem 1 The virial theorem We have seen that we can solve the equation of motion for the two-body problem analytically and thus obtain expressions describing the future
More informationThe Milky Way & Galaxies
The Milky Way & Galaxies The Milky Way Appears as a milky band of light across the sky A small telescope reveals that it is composed of many stars (Galileo again!) Our knowledge of the Milky Way comes
More informationPhysics 314 (Survey of Astronomy) Exam 3
Physics 314 (Survey of Astronomy) Exam 3 Please show all significant steps clearly in all problems. Please give clear, legible, and reasonably complete (although brief) responses to qualitative questions.
More informationMilky Way s Mass and Stellar Halo Velocity Dispersion Profiles
Milky Way s Mass and Stellar Halo Velocity Dispersion Profiles Shanghai Astronomical Observatory In collaboration with Juntai Shen, Xiang Xiang Xue, Chao Liu, Chris Flynn, Ling Zhu, Jie Wang Contents 1
More informationComponents of Galaxies Gas The Importance of Gas
Components of Galaxies Gas The Importance of Gas Fuel for star formation (H 2 ) Tracer of galaxy kinematics/mass (HI) Tracer of dynamical history of interaction between galaxies (HI) The Two-Level Atom
More informationBlack Holes in Globular Clusters
Black Holes in Globular Clusters Douglas Heggie University of Edinburgh d.c.heggie@ed.ac.uk Papers on black holes and globular clusters Spot the odd man out Cen M15 www.jb.man.ac.uk The pioneer phase:
More informationExam # 3 Tue 12/06/2011 Astronomy 100/190Y Exploring the Universe Fall 11 Instructor: Daniela Calzetti
Exam # 3 Tue 12/06/2011 Astronomy 100/190Y Exploring the Universe Fall 11 Instructor: Daniela Calzetti INSTRUCTIONS: Please, use the `bubble sheet and a pencil # 2 to answer the exam questions, by marking
More informationNeutron Stars. Chapter 14: Neutron Stars and Black Holes. Neutron Stars. What s holding it up? The Lighthouse Model of Pulsars
Neutron Stars Form from a 8-20 M Sun star Chapter 14: Neutron Stars and Black Holes Leftover 1.4-3 M Sun core after supernova Neutron Stars consist entirely of neutrons (no protons) Neutron Star (tennis
More informationGaia Revue des Exigences préliminaires 1
Gaia Revue des Exigences préliminaires 1 Global top questions 1. Which stars form and have been formed where? - Star formation history of the inner disk - Location and number of spiral arms - Extent of
More informationDark Matter Density Function Depending on Gravitational Field as Universal Law - M. Abarca
DARK MATTER DENSITY FUNCTION DEPENDING ON INTENSITY OF GRAVITATIONAL FIELD AS UNIVERSAL LAW Author Manuel Abarca Hernández e-mail mabarcaher1@gmail.com INDEX 1. ABSTRAT.... INTRODUCTION... 3 3. GALACTIC
More informationEinführung in die Astronomie II
Einführung in die Astronomie II Teil 12 Peter Hauschildt yeti@hs.uni-hamburg.de Hamburger Sternwarte Gojenbergsweg 112 21029 Hamburg 13. September 2017 1 / 77 Overview part 12 The Galaxy Historical Overview
More informationAstronomy 114. Lecture 29: Internal Properties of Galaxies. Martin D. Weinberg. UMass/Astronomy Department
Astronomy 114 Lecture 29: Internal Properties of Galaxies Martin D. Weinberg weinberg@astro.umass.edu UMass/Astronomy Department A114: Lecture 29 20 Apr 2007 Read: Ch. 26 Astronomy 114 1/16 Announcements
More informationThermodynamics of violent relaxation
UNIVERSITA DEGLI STUDI DI PADOVA Dipartimento di ASTRONOMIA Thermodynamics of violent relaxation Dr. Bindoni Daniele 13 of MAY 2011 Outlines The Aims Introduction Violent Relaxation Mechanism Distribution
More informationProbing Gravity in the Low Acceleration Regime with Globular Clusters
Probing Gravity in the Low Acceleration Regime with Globular Clusters By Riccardo Scarpa, Gianni Marconi & Roberto Gilmozzi European Southern Observatory The idea of this study sparked from the following
More informationEvolution of second generation stars in stellar disks of globular and nuclear clusters: ω Centauri as a test case
Evolution of second generation stars in stellar disks of globular and nuclear clusters: ω Centauri as a test case Alessandra Mastrobuono-Battisti & Hagai Perets Outline Dense stellar clusters: Nuclear
More informationLecture 7: the Local Group and nearby clusters
Lecture 7: the Local Group and nearby clusters in this lecture we move up in scale, to explore typical clusters of galaxies the Local Group is an example of a not very rich cluster interesting topics include:
More informationGalaxy interaction and transformation
Galaxy interaction and transformation Houjun Mo April 13, 2004 A lot of mergers expected in hierarchical models. The main issues: The phenomena of galaxy interaction: tidal tails, mergers, starbursts When
More informationBlack Holes. Jan Gutowski. King s College London
Black Holes Jan Gutowski King s College London A Very Brief History John Michell and Pierre Simon de Laplace calculated (1784, 1796) that light emitted radially from a sphere of radius R and mass M would
More informationPotential/density pairs and Gauss s law
Potential/density pairs and Gauss s law We showed last time that the motion of a particle in a cluster will evolve gradually, on the relaxation time scale. This time, however, is much longer than the typical
More informationGalaxies. The majority of known galaxies fall into one of three major classes: spirals (78 %), ellipticals (18 %) and irregulars (4 %).
Galaxies Collection of stars, gas and dust bound together by their common gravitational pull. Galaxies range from 10,000 to 200,000 light-years in size. 1781 Charles Messier 1923 Edwin Hubble The distribution
More informationElad Zinger Hebrew University Jerusalem Spineto, 12 June Collaborators: Avishai Dekel, Yuval Birnboim, Daisuke Nagai & Andrey Kravtsov
Elad Zinger Hebrew University Jerusalem IGM@50, Spineto, 12 June 2015 Collaborators: Avishai Dekel, Yuval Birnboim, Daisuke Nagai & Andrey Kravtsov They re still there! Account for most of the accretion.
More informationEvolution of Star Clusters on Eccentric Orbits
Evolution of Star Clusters on Eccentric Orbits Maxwell Xu CAI (NAOC/KIAA) Collaborators: Mark Gieles, Douglas Heggie, Anna Lisa Varri Cai et al. (2016), MNRAS, 455, 596 7th KCK meeting, NAOC, Dec 15, 2015
More informationStellar Dynamics and Structure of Galaxies
Stellar Dynamics and Structure of Galaxies. Spherically symmetric objects Vasily Belokurov vasily@ast.cam.ac.uk Institute of Astronomy Lent Term 2016 1 / 21 Outline I 1 2 Globular of galaxies 2 / 21 Why
More informationPreliminary Examination: Astronomy
Preliminary Examination: Astronomy Department of Physics and Astronomy University of New Mexico Spring 2017 Instructions: Answer 8 of the 10 questions (10 points each) Total time for the test is three
More informationClusters and Groups of Galaxies
Clusters and Groups of Galaxies Groups and clusters The Local Group Clusters: spatial distribution and dynamics Clusters: other components Clusters versus groups Morphology versus density Groups and Clusters
More informationThe Milky Way Galaxy. Some thoughts. How big is it? What does it look like? How did it end up this way? What is it made up of?
Some thoughts The Milky Way Galaxy How big is it? What does it look like? How did it end up this way? What is it made up of? Does it change 2 3 4 5 This is not a constant zoom The Milky Way Almost everything
More informationGasdynamical and radiative processes, gaseous halos
Gasdynamical and radiative processes, gaseous halos Houjun Mo March 19, 2004 Since luminous objects, such as galaxies, are believed to form through the collapse of baryonic gas, it is important to understand
More informationThe cosmic distance scale
The cosmic distance scale Distance information is often crucial to understand the physics of astrophysical objects. This requires knowing the basic properties of such an object, like its size, its environment,
More informationDistance Measuring Techniques and The Milky Way Galaxy
Distance Measuring Techniques and The Milky Way Galaxy Measuring distances to stars is one of the biggest challenges in Astronomy. If we had some standard candle, some star with a known luminosity, then
More informationThe Night Sky. The Universe. The Celestial Sphere. Stars. Chapter 14
The Night Sky The Universe Chapter 14 Homework: All the multiple choice questions in Applying the Concepts and Group A questions in Parallel Exercises. Celestial observation dates to ancient civilizations
More informationIntroduction to the Universe
What makes up the Universe? Introduction to the Universe Book page 642-644 Objects in the Universe Astrophysics is the science that tries to make sense of the universe by - describing the Universe (Astronomy)
More informationDYNAMICS OF GALAXIES
DYNAMICS OF GALAXIES 3. Piet van der Kruit Kapteyn Astronomical Institute University of Groningen the Netherlands Winter 2008/9 Contents Differential rotation Epicycle orbits Vertical motion Resonances
More informationDark Matter Density Function Depending on Gravitational Field as Universal Law - M. Abarca
DARK MATTER DENSITY FUNCTION DEPENDING ON INTENSITY OF GRAVITATIONAL FIELD AS UNIVERSAL LAW Author Manuel Abarca Hernández e-mail mabarcaher1@gmail.com INDEX 1. ABSTRAT.... INTRODUCTION... 4 3. GALACTIC
More informationGalaxies 626. Lecture 3: From the CMBR to the first star
Galaxies 626 Lecture 3: From the CMBR to the first star Galaxies 626 Firstly, some very brief cosmology for background and notation: Summary: Foundations of Cosmology 1. Universe is homogenous and isotropic
More information7/5. Consequences of the principle of equivalence (#3) 1. Gravity is a manifestation of the curvature of space.
7/5 Consequences of the principle of equivalence (#3) 1. Gravity is a manifestation of the curvature of space. Follow the path of a light pulse in an elevator accelerating in gravityfree space. The dashed
More informationHR Diagram, Star Clusters, and Stellar Evolution
Ay 1 Lecture 9 M7 ESO HR Diagram, Star Clusters, and Stellar Evolution 9.1 The HR Diagram Stellar Spectral Types Temperature L T Y The Hertzsprung-Russel (HR) Diagram It is a plot of stellar luminosity
More informationOrigin of Structure Formation of Structure. Projected slice of 200,000 galaxies, with thickness of a few degrees.
Origin of Structure Formation of Structure Projected slice of 200,000 galaxies, with thickness of a few degrees. Redshift Surveys Modern survey: Sloan Digital Sky Survey, probes out to nearly 1000 Mpc.
More informationIntroduction to the Universe. What makes up the Universe?
Introduction to the Universe What makes up the Universe? Objects in the Universe Astrophysics is the science that tries to make sense of the universe by - describing the Universe (Astronomy) - understanding
More informationStatistical Mechanics of Violent Relaxation in Stellar Systems
Statistical Mechanics of Violent Relaxation in Stellar Systems Pierre-Henri Chavanis Laboratoire de Physique Quantique, Université Paul Sabatier, 118 route de Narbonne, 31062 Toulouse, France Abstract.
More informationCo-Evolution of Central Black Holes and Nuclear Star Clusters
Co-Evolution of Central Black Holes and Nuclear Star Clusters Oleg Gnedin (University of Michigan) Globular clusters in the Galaxy median distance from the center is 5 kpc Resolved star cluster highest
More informationLecture 2: Molecular Clouds: Galactic Context and Observational Tracers. Corona Australis molecular cloud: Andrew Oreshko
Lecture 2: Molecular Clouds: Galactic Context and Observational Tracers Corona Australis molecular cloud: Andrew Oreshko Classification of Young Stellar Objects (YSOs) Spectral Index Hartmann: Accretion
More informationAstr 2310 Thurs. March 23, 2017 Today s Topics
Astr 2310 Thurs. March 23, 2017 Today s Topics Chapter 16: The Interstellar Medium and Star Formation Interstellar Dust and Dark Nebulae Interstellar Dust Dark Nebulae Interstellar Reddening Interstellar
More information