Unified Schemes for Radio-Loud Active Galactic Nuclei
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Expanding Space, Quasars and St. Augustine's Fireworks
Universe 2015, 1, 307-356; doi:10.3390/universe1030307 OPEN ACCESS universe ISSN 2218-1997 www.mdpi.com/journal/universe Article Expanding Space, Quasars and St. Augustine’s Fireworks Olga I. Chashchina 1;2 and Zurab K. Silagadze 2;3;* 1 École Polytechnique, 91128 Palaiseau, France; E-Mail: [email protected] 2 Department of physics, Novosibirsk State University, Novosibirsk 630 090, Russia 3 Budker Institute of Nuclear Physics SB RAS and Novosibirsk State University, Novosibirsk 630 090, Russia * Author to whom correspondence should be addressed; E-Mail: [email protected]. Academic Editors: Lorenzo Iorio and Elias C. Vagenas Received: 5 May 2015 / Accepted: 14 September 2015 / Published: 1 October 2015 Abstract: An attempt is made to explain time non-dilation allegedly observed in quasar light curves. The explanation is based on the assumption that quasar black holes are, in some sense, foreign for our Friedmann-Robertson-Walker universe and do not participate in the Hubble flow. Although at first sight such a weird explanation requires unreasonably fine-tuned Big Bang initial conditions, we find a natural justification for it using the Milne cosmological model as an inspiration. Keywords: quasar light curves; expanding space; Milne cosmological model; Hubble flow; St. Augustine’s objects PACS classifications: 98.80.-k, 98.54.-h You’d think capricious Hebe, feeding the eagle of Zeus, had raised a thunder-foaming goblet, unable to restrain her mirth, and tipped it on the earth. F.I.Tyutchev. A Spring Storm, 1828. Translated by F.Jude [1]. 1. Introduction “Quasar light curves do not show the effects of time dilation”—this result of the paper [2] seems incredible. -
The Special Theory of Relativity Lecture 16
The Special Theory of Relativity Lecture 16 E = mc2 Albert Einstein Einstein’s Relativity • Galilean-Newtonian Relativity • The Ultimate Speed - The Speed of Light • Postulates of the Special Theory of Relativity • Simultaneity • Time Dilation and the Twin Paradox • Length Contraction • Train in the Tunnel paradox (or plane in the barn) • Relativistic Doppler Effect • Four-Dimensional Space-Time • Relativistic Momentum and Mass • E = mc2; Mass and Energy • Relativistic Addition of Velocities Recommended Reading: Conceptual Physics by Paul Hewitt A Brief History of Time by Steven Hawking Galilean-Newtonian Relativity The Relativity principle: The basic laws of physics are the same in all inertial reference frames. What’s a reference frame? What does “inertial” mean? Etc…….. Think of ways to tell if you are in Motion. -And hence understand what Einstein meant By inertial and non inertial reference frames How does it differ if you’re in a car or plane at different points in the journey • Accelerating ? • Slowing down ? • Going around a curve ? • Moving at a constant velocity ? Why? ConcepTest 26.1 Playing Ball on the Train You and your friend are playing catch 1) 3 mph eastward in a train moving at 60 mph in an eastward direction. Your friend is at 2) 3 mph westward the front of the car and throws you 3) 57 mph eastward the ball at 3 mph (according to him). 4) 57 mph westward What velocity does the ball have 5) 60 mph eastward when you catch it, according to you? ConcepTest 26.1 Playing Ball on the Train You and your friend are playing catch 1) 3 mph eastward in a train moving at 60 mph in an eastward direction. -
(Special) Relativity
(Special) Relativity With very strong emphasis on electrodynamics and accelerators Better: How can we deal with moving charged particles ? Werner Herr, CERN Reading Material [1 ]R.P. Feynman, Feynman lectures on Physics, Vol. 1 + 2, (Basic Books, 2011). [2 ]A. Einstein, Zur Elektrodynamik bewegter K¨orper, Ann. Phys. 17, (1905). [3 ]L. Landau, E. Lifschitz, The Classical Theory of Fields, Vol2. (Butterworth-Heinemann, 1975) [4 ]J. Freund, Special Relativity, (World Scientific, 2008). [5 ]J.D. Jackson, Classical Electrodynamics (Wiley, 1998 ..) [6 ]J. Hafele and R. Keating, Science 177, (1972) 166. Why Special Relativity ? We have to deal with moving charges in accelerators Electromagnetism and fundamental laws of classical mechanics show inconsistencies Ad hoc introduction of Lorentz force Applied to moving bodies Maxwell’s equations lead to asymmetries [2] not shown in observations of electromagnetic phenomena Classical EM-theory not consistent with Quantum theory Important for beam dynamics and machine design: Longitudinal dynamics (e.g. transition, ...) Collective effects (e.g. space charge, beam-beam, ...) Dynamics and luminosity in colliders Particle lifetime and decay (e.g. µ, π, Z0, Higgs, ...) Synchrotron radiation and light sources ... We need a formalism to get all that ! OUTLINE Principle of Relativity (Newton, Galilei) - Motivation, Ideas and Terminology - Formalism, Examples Principle of Special Relativity (Einstein) - Postulates, Formalism and Consequences - Four-vectors and applications (Electromagnetism and accelerators) § ¤ some slides are for your private study and pleasure and I shall go fast there ¦ ¥ Enjoy yourself .. Setting the scene (terminology) .. To describe an observation and physics laws we use: - Space coordinates: ~x = (x, y, z) (not necessarily Cartesian) - Time: t What is a ”Frame”: - Where we observe physical phenomena and properties as function of their position ~x and time t. -
Lecture Notes 17: Proper Time, Proper Velocity, the Energy-Momentum 4-Vector, Relativistic Kinematics, Elastic/Inelastic
UIUC Physics 436 EM Fields & Sources II Fall Semester, 2015 Lect. Notes 17 Prof. Steven Errede LECTURE NOTES 17 Proper Time and Proper Velocity As you progress along your world line {moving with “ordinary” velocity u in lab frame IRF(S)} on the ct vs. x Minkowski/space-time diagram, your watch runs slow {in your rest frame IRF(S')} in comparison to clocks on the wall in the lab frame IRF(S). The clocks on the wall in the lab frame IRF(S) tick off a time interval dt, whereas in your 2 rest frame IRF( S ) the time interval is: dt dtuu1 dt n.b. this is the exact same time dilation formula that we obtained earlier, with: 2 2 uu11uc 11 and: u uc We use uurelative speed of an object as observed in an inertial reference frame {here, u = speed of you, as observed in the lab IRF(S)}. We will henceforth use vvrelative speed between two inertial systems – e.g. IRF( S ) relative to IRF(S): Because the time interval dt occurs in your rest frame IRF( S ), we give it a special name: ddt = proper time interval (in your rest frame), and: t = proper time (in your rest frame). The name “proper” is due to a mis-translation of the French word “propre”, meaning “own”. Proper time is different than “ordinary” time, t. Proper time is a Lorentz-invariant quantity, whereas “ordinary” time t depends on the choice of IRF - i.e. “ordinary” time is not a Lorentz-invariant quantity. 222222 The Lorentz-invariant interval: dI dx dx dx dx ds c dt dx dy dz Proper time interval: d dI c2222222 ds c dt dx dy dz cdtdt22 = 0 in rest frame IRF(S) 22t Proper time: ddtttt 21 t 21 11 Because d and are Lorentz-invariant quantities: dd and: {i.e. -
Massachusetts Institute of Technology Midterm
Massachusetts Institute of Technology Physics Department Physics 8.20 IAP 2005 Special Relativity January 18, 2005 7:30–9:30 pm Midterm Instructions • This exam contains SIX problems – pace yourself accordingly! • You have two hours for this test. Papers will be picked up at 9:30 pm sharp. • The exam is scored on a basis of 100 points. • Please do ALL your work in the white booklets that have been passed out. There are extra booklets available if you need a second. • Please remember to put your name on the front of your exam booklet. • If you have any questions please feel free to ask the proctor(s). 1 2 Information Lorentz transformation (along the xaxis) and its inverse x� = γ(x − βct) x = γ(x� + βct�) y� = y y = y� z� = z z = z� ct� = γ(ct − βx) ct = γ(ct� + βx�) � where β = v/c, and γ = 1/ 1 − β2. Velocity addition (relative motion along the xaxis): � ux − v ux = 2 1 − uxv/c � uy uy = 2 γ(1 − uxv/c ) � uz uz = 2 γ(1 − uxv/c ) Doppler shift Longitudinal � 1 + β ν = ν 1 − β 0 Quadratic equation: ax2 + bx + c = 0 1 � � � x = −b ± b2 − 4ac 2a Binomial expansion: b(b − 1) (1 + a)b = 1 + ba + a 2 + . 2 3 Problem 1 [30 points] Short Answer (a) [4 points] State the postulates upon which Einstein based Special Relativity. (b) [5 points] Outline a derviation of the Lorentz transformation, describing each step in no more than one sentence and omitting all algebra. (c) [2 points] Define proper length and proper time. -
Radio Galaxies and Quasars
Published in "Galactic and Extragalactic Radio Astronomy", 1988, 2nd edition, eds. G.L. Verschuur and K.I. Kellerman. 13. RADIO GALAXIES AND QUASARS Kenneth I. Kellermann and Frazer N. Owen Table of Contents INTRODUCTION Optical Counterparts Radio Source Properties Radio Spectra Energy Considerations LOW-LUMINOSITY SOURCES Spiral, Seyfert, and Irregular Galaxies Elliptical Galaxies COMPACT SOURCES Self-Absorption Inverse Compton Radiation Polarization Structure Variability Source Dynamics and Superluminal Motion Relativistic Beaming EXTENDED SOURCES Jets, Lobes, and Hot Spots Jet Physics SUMMARY REFERENCES 13.1. INTRODUCTION All galaxies and quasars appear to be sources of radio emission at some level. Normal spiral galaxies such as our own galactic system are near the low end of the radio luminosity function and have radio luminosities near 1037 erg s-1. Some Seyfert galaxies, starburst galaxies, and the nuclei of active elliptical galaxies are 100 to 1000 times more luminous. Radio galaxies and some quasars are powerful radio sources at the high end of the luminosity function with luminosities up to 1045 erg s-1. For the more powerful sources, the radio emission often comes from regions well removed from the associated optical object, often hundreds of kiloparsecs or even megaparsecs away. In other cases, however, particularly in active galactic nuclei (AGN) or quasars, much of the radio emission comes from an extremely small region with measured dimensions of only a few parsecs. The form of the radio- frequency spectra implies that the radio emission is nonthermal in origin; it is presumed to be synchrotron radiation from ultra-relativistic electrons with energies of typically about 1 GeV moving in weak magnetic fields of about 10-4 gauss (see Section 1.1). -
General Relativity General Relativity Relativistic Momentum Mass Equivalence Principle
College Physics B Einstein’s Theories of Relativity Special Relativity Reminder: College Physics B - PHY2054C Time Dilation Length Contraction Special & General Relativity General Relativity Relativistic Momentum Mass Equivalence Principle 11/12/2014 My Office Hours: Tuesday 10:00 AM - Noon 206 Keen Building College Physics B Outline Einstein’s Theories of Relativity Special Relativity 1 Einstein’s Theories of Relativity Reminder: Time Dilation Special Relativity Length Contraction General 2 Reminder: Time Dilation Relativity Relativistic Momentum Mass Equivalence 3 Length Contraction Principle 4 General Relativity Relativistic Momentum Mass Equivalence Principle College Physics B Galilean Relativity and Light Einstein’s Theories of Relativity Galilean Relativity and electromagnetism do predict different Special Relativity results for observers in different inertial frames: Reminder: Time Dilation Experiments showed that Maxwell’s theory was correct. • Length The speed of light in the vacuum is always c. Contraction • General Galilean relativity for how the speed of light depends on Relativity • Relativistic the motion of the source is wrong. Momentum Mass ➜ Equivalence Einstein developed theory of relativity: Special Relativity. Principle Two Postulates 1 All laws of physics are the same in all inertial reference frames. 2 The speed of light in the vacuum is a constant. College Physics B Inertial Reference Frames Einstein’s Theories of Relativity Special Relativity Reminder: Time Dilation Length Contraction General Relativity Relativistic Momentum Mass The modern definition of an inertial reference is one in Equivalence Principle which Newton’s First Law holds: If a particle moves with a constant velocity, then the reference frame is inertial. ➜ Earth’s acceleration is small enough that it can be ignored (can be considered an inertial system). -
Relativistic Effects
Relativistic Effects 1 Introduction The radio-emitting plasma in AGN contains electrons with relativistic energies. The Lorentz factors of the emitting elec- trons are of order 1026– . We now know that the bulk motion of the plasma is also moving relativistically – at least in some regions although probably “only” with Lorentz factors about 10 or so. However, this has an important effect on the prop- erties of the emitted radiation – principally through the ef- fects of relativistic beaming and doppler shifts in frequency. This in turn affects the inferred parameters of the plasma. Relativistic Effects ©Geoffrey V. Bicknell 2 Summary of special relativity For a more complete summary of 4-vectors and Special Rel- ativity, see Rybicki and Lightman, Radiative Processes in As- trophysics, or Rindler, Special Relativity High Energy Astrophysics: Relativistic Effects 2/93 2.1 The Lorentz transformation y S y S V x x The primed frame is moving wrt to the unprimed frame with a velocity v in the x–direction. The coordinates in the primed frame are related to those in the unprimed frame by: High Energy Astrophysics: Relativistic Effects 3/93 Vx x= xvt– t= t – ------ c2 y = y z = z (1) v 1 = -- = ------------------- c 1 – 2 We put the space-time coordinates on an equal footing by putting x0 = ct. The the xt– part of the Lorentz transforma- tion can be written: x= x – x0 x0= x0 – x (2) The reverse transformation is: High Energy Astrophysics: Relativistic Effects 4/93 x = x + Vt yy= zz= Vx (3) t = t + -------- c2 i.e., x = x+ x0 x0 = x0+ x (4) High Energy Astrophysics: Relativistic Effects 5/93 2.2 Lorentz–Fitzgerald contraction 2.3 Time dilation y y V S S x x High Energy Astrophysics: Relativistic Effects 6/93 y y S S V L0 x x 2 1 x – x = L0 2 1 x – x = x2 – x1 – Vt2 – t1 –1 L0 = L L = L0 High Energy Astrophysics: Relativistic Effects 7/93 Consider a clock at a stationary position in the moving frame which registers a time interval T0. -
Relativity Chap 1.Pdf
Chapter 1 Kinematics, Part 1 Special Relativity, For the Enthusiastic Beginner (Draft version, December 2016) Copyright 2016, David Morin, [email protected] TO THE READER: This book is available as both a paperback and an eBook. I have made the first chapter available on the web, but it is possible (based on past experience) that a pirated version of the complete book will eventually appear on file-sharing sites. In the event that you are reading such a version, I have a request: If you don’t find this book useful (in which case you probably would have returned it, if you had bought it), or if you do find it useful but aren’t able to afford it, then no worries; carry on. However, if you do find it useful and are able to afford the Kindle eBook (priced below $10), then please consider purchasing it (available on Amazon). If you don’t already have the Kindle reading app for your computer, you can download it free from Amazon. I chose to self-publish this book so that I could keep the cost low. The resulting eBook price of around $10, which is very inexpensive for a 250-page physics book, is less than a movie and a bag of popcorn, with the added bonus that the book lasts for more than two hours and has zero calories (if used properly!). – David Morin Special relativity is an extremely counterintuitive subject, and in this chapter we will see how its bizarre features come about. We will build up the theory from scratch, starting with the postulates of relativity, of which there are only two. -
Analysis of Kepler Active Galactic Nuclei Using a Revised Kirk, Rieger, Mastichiadis (1998) Model Sarah M
Florida International University FIU Digital Commons FIU Electronic Theses and Dissertations University Graduate School 6-12-2014 Analysis of Kepler Active Galactic Nuclei Using A Revised Kirk, Rieger, Mastichiadis (1998) Model Sarah M. Dhalla Florida International University, [email protected] DOI: 10.25148/etd.FI14071133 Follow this and additional works at: https://digitalcommons.fiu.edu/etd Recommended Citation Dhalla, Sarah M., "Analysis of Kepler Active Galactic Nuclei Using A Revised Kirk, Rieger, Mastichiadis (1998) Model" (2014). FIU Electronic Theses and Dissertations. 1521. https://digitalcommons.fiu.edu/etd/1521 This work is brought to you for free and open access by the University Graduate School at FIU Digital Commons. It has been accepted for inclusion in FIU Electronic Theses and Dissertations by an authorized administrator of FIU Digital Commons. For more information, please contact [email protected]. FLORIDA INTERNATIONAL UNIVERSITY Miami, Florida ANALYSIS OF KEPLER ACTIVE GALACTIC NUCLEI USING A REVISED KIRK, RIEGER, MASTICHIADIS (1998) JET MODEL A thesis submitted in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE in PHYSICS by Sarah Mohammed Dhalla 2014 To: Interim Dean Michael R. Heithaus College of Arts and Sciences This thesis, written by Sarah Mohammed Dhalla, and entitled Analysis of Kepler Active Galactic Nuclei Using a Revised Kirk, Rieger, & Mastichiadis (1998) Jet Model, having been approved in respect to style and intellectual content, is referred to you for judgment. We have read this thesis and recommend that it be approved. Caroline Simpson Walter Van Hamme James R. Webb, Major Professor Date of Defense: June 12, 2014 The thesis of Sarah Mohammed Dhalla is approved. -
Special Relativity Length, Momentum, Ami Energy
Special Relativity Length, Momentum, ami Energy he speed of light is the speed limit for all matter. Suppose that two spaceships are T both traveling at nearly the speed of light and they are moving directly toward each other. The realms of space-time for each spaceship differ in such a way that the relative speed of approach Mass converts to energy and is still less than the speed of light! For example, if both spaceships vice versa. are traveling toward each other at 80% the speed of light with respect to Earth, an observer on each spaceship would measure the speed of approach of the other spaceship as 98% the speed of light. There are no circumstances where the relative speeds of any material objects surpass the speed of light. Why is the speed of light the universal speed limit? To under- stand this, we must know how motion through space affects the length, momentum, and energy of moving objects. 16.1 Length Contraction For moving objects, space as well as time undergoes changes. When viewed by an outside observer, moving objects appear to contract along the direction of motion. The amount of contraction is related to the amount of time dilation. For everyday speeds, the amount of contraction is much too small to be measured. For relativistic speeds, the contraction would be noticeable. A meter stick aboard a Figure 16.1 1 spaceship whizzing past you at 87% the speed of light, for example, A meter stick traveling at 87% would appear to you to be only 0.5 meter long. -
11 Jets and Gamma-Ray Burst Unification Schemes
11 Jets and Gamma-Ray Burst Unification Schemes Jonathan Granot1 and Enrico Ramirez-Ruiz2 (1) Centre for Astrophysics Research, University of Hertfordshire, College Lane, Hatfield, Herts, AL10 9AB, UK (2) Astronomy and Astrophysics Department, University of California, Santa Cruz, CA 95064, USA 11.1 Evidence for bulk relativistic motion in gamma-ray bursts The first line of evidence for ultra-relativistic bulk motion of the outflows that produce GRBs arises from the compactness argument. It relies on the observed short and intense pulses of gamma rays and their non-thermal en- ergy spectrum that often extends up to high photon energies. Together, these facts imply that the emitting region must be moving relativistically. In order to understand this better, let us first consider a source that is either at rest or moves at a Newtonian velocity, β v/c 1, corresponding to a ≡ ≪ bulk Lorentz factor Γ (1 β2)−1/2 1. For such a source the observed ≡ − ≈ variability timescale (e.g., the width of the observed pulses) ∆t, implies a typical source size or radius R < c∆t, due to light time travel effects (for sim- plicity we ignore here cosmological effects, such as redshift or time dilation). GRBs often show significant variability down to millisecond timescales, im- plying R< 3 107(∆t/ 1 ms) cm. At cosmological distances their isotropic × equivalent luminosity, L, is typically in the range of 1050 1053 ergs−1. − In addition, the (observed part of the) εFε GRB spectrum typically peaks around a dimensionless photon energy of ε E /m c2 1, so that (for ≡ ph e ∼ a Newtonian source) a good fraction of the total radiated energy is carried by photons that can pair produce with other photons of similar energy.