Reverberation Mapping
|
|
- Emory Waters
- 5 years ago
- Views:
Transcription
1 Reverberation Mapping Astro 7B Spring 2016, Lab 101 GSI: Goni Halevi SOLUTIONS 1 What is it? As a quick review, let s recall that the purpose of reverberation mapping is to measure black hole masses. In order to use reverberation mapping, you need to know that the black hole is accreting, so it s used often for AGN (active galactic nuclei). The basic equation for the mass of an object is M = v2 R G where v is the velocity of a circular orbit at radius R. Reverberation mapping is particularly cool because it s independent of distance, and measuring distances is tough. 2 Recalling Equations Note: try to do this part without looking at your notes. a) Look at Equation 1. To find mass, we need to measure radius (R) and velocity (v). In reverberation mapping, we measure R. How? What is the formula to find for R? Find the time lag between the continuum and a spectral line of choice. The radius of the broad line region (BLR) for the spectral line you look at is given by R = c t where t is the average time lag measured. b) What method do we use to find the velocity v? What formula do we obtain? Be sure to explain what the variables in your formula represent. Doppler shift! We need to use the same spectral line as we did to find radius, let s say it has rest wavelength (as measured in labs) denoted by λ 0. Then, the line we actually see in the spectrum will have some broadness that comes from the fact that the region is rotating around the black hole, so different parts are moving at different velocities along our line of site. This causes the line to broaden as it is made up of components with different velocities and thus slightly different wavelengths. We typically measure the thickness of this spectral line as the full width half-maximum (FWHM), which just means we take the full width of the line at a point halfway to the peak. Denoting this broadness as λ, we have a velocity v given by v c = λ v = λ c λ 0 λ 0 (1) c) What are the limitations of this method for finding velocities? (Hint: consider inclinations). Doppler shift allows us to measure velocities along our line of sight, so we measure the true rotational velocity if the disk is edge on, but can t measure it at all if it is face on, and measure less than the true velocities for all other possible inclinations since we can only measure one component. 1
2 d) Plug in your formulas from a) and b) to rewrite Equation 1. M = v2 R G = ( λc λ 0 M = λ c 3 t λ 0 G ) 2 c t G e) Use dimensional analysis to make sure that your equation in part d) makes sense. The ratio of broadness to rest wavelength is dimensionless. c 3 has dimensions of cubic length over cubic time, while t has units of time, so we have cubic length over time squared in the numerator. The units of G, if you don t have them memorized, can be found by considering the equation for Newtonian gravitational force. F g = GMm R 2, so the units of G must be the units of force times length squared divided by mass squared. Force is mass times acceleration, so mass times length divided by time squared. Multiplying by length squared and dividing by mass squared, we find that G has units of inverse mass times length cubed times time squared. Overall, we have cubic length and time squared in the numerator, and then inverse mass, cubic length, and time squared in the denominator. Cancelling like dimensions, we are left with mass, as desired. 3 Real Reverberation Mapping: Time Lag You ve derived the formula for determining mass. However, in practice, things are hardly that simple. We re going to examine the case of a particular active galactic nucleus, the one in a galaxy called Mrk 40. To measure time lags, we gather data on the AGN over time and compare spectral line flux to that of the continuum, looking for delays we can measure. From the way we ve talked about the method in class, it seems like it d be straightforward to measure time lags, but it isn t really. To illustrate this, I ve included Figure 1, which I ll leave to your interpretation. a) Interpret Figure 1 using your knowledge of reverberation mapping. What does each subplot represent? What are the axes? The x-axis is time (NOT WAVELENGTH) in days, with a constant offset. The y-axes are flux measurements. Each subplot represents a different spectral line (the one labeled in the top left of the subplot), except for the top-most subplot. That one shows the continuum in UV wavelengths. From the data presented in Figure 1, you can determine the radius of the broad line region (BLR), but it s not such a simple task. To determine time lags, we do something called crosscorrelation. Mathematically, the cross-correlation of two functions f(t) and g(t) is f g(τ) + f (t)g(t + τ)dt where f (t) is the complex conjugate of f(t) and τ is the lag. 2
3 Figure 1: Some data for the reverberation mapping of Mrk 40. b) How would cross-correlation techniques simplify the calculation of lag times? Explain. You find out how much the two light curves overlap as you shift them. If they are the same, except for a time lag the overlap is maximized for a lag equal to the time lag. Note that because you re dealing with real data, your cross-correlation function is not maximized at 1 (which would indicate total overlap), but near 1. Do look up cross-correlation and read more about it if you d like. Also feel free to ask me about it. c) Given that Figure 2 shows the cross-correlation functions for different spectral lines as compared to the V band magnitude (shown in black), approximate the time lag for each line and sketch an accretion disk labeled by element that would create this array of time lags. This is just a matter of looking at Figure 2 and determining the approximate locations of the peaks for each curve (except for the V curve, which is the continuum and peaks at 1 because it is being cross-correlated with itself). Here are my estimates (don t worry if yours aren t identical): 3
4 Hα: 9 10 days Hβ: 5 days Hγ: 4 days Hδ: 3 days HeII: 0 days F eii: days d) Which line would be the best to use for reverberation mapping of Mrk 40? Why? The Hβ line is by far the best choice, for a number of reasons. For example, Its peak is clearly defined in the cross-correlation function. It has a discernible time lag, not too short. Its overall flux is much more than Hγ s or Hδ s (see Figure 1). It peaks at the highest cross-correlation, indicating that it resembles the continuum more closely than the rest of the spectral lines do. Figure 2: Cross-correlation functions for Mrk Thinking about Limitations... Figure 3 shows a correlation between the size of the BLR for Hβ and the luminosity at a specific wavelength of 5100 Å. 4
5 Figure 3: There is a correlation between BLR size and luminosity of AGNs. Note that this is a log-log plot and that the x-axis has units of ergs/second. a) Determine the Hβ BLR size in light days for Mrk 40. Don t over-think this one. I approximated the time lag for Hβ as t = 5 days, so the radius of the Hβ broad line region is R = c t = 5 light days. b) What value of λl λ (5100 Å) does this BLR size correspond to, approximately? Going up to 5 light days on the y-axis and across to the black least-squares fit line, then down to the x-axis, I find λl λ (5100 Å) ergs/second. c) If you wanted to use reverberation mapping for an AGN with λl λ (5100 Å) two orders of magnitude greater than that of Mrk 40, what is the minimum time you would need to collect data for? Two orders of magnitude more luminous ergs/second. Going to this value on the y-axis, up to the black line, and across to the x-axis, I approximate a BLR radius of 70 days. d) What does this tell you about what kind of AGN are easier to find BH masses for? Less luminous AGN Need to watch for a shorter time period Easier to get your telescope time proposal approved Easier to obtain data Easier to calculate BH masses for. 5
6 5 Real Reverberation Mapping: Mass Measurement a) Suppose you measure the Hβ line of Mrk 40 to have a FWHM of 0.06 nanometers, given that the rest wavelength of Hβ is nanometers. What mass do you determine for the BH in Mrk 40, assuming it is edge on? (Answer in solar masses). I worded this badly before. We don t care about the absolute location of the spectral line, because that s caused by cosmic redshift distant galaxies move away from us, so their spectra are shifted to redder wavelengths. Instead, we care about the spread of the Hβ line, representing the various velocities contributing to that line and thus the rotation of the accretion disk. Thus, λ = 0.06nm, λ 0 = nm M = λ c 3 t λ 0 G = 0.06 c 3 (5 days) G M = kg 10 7 M. b) If instead, we have no idea what the inclination of the accretion disk is, what is the range of possible masses for the BH in Mrk 40? We measure only the line-of-sight component of the velocity. Let s call the true velocity v and the one we measure v. Then, we see v = v sin i where i is the inclination (π/2 for edge-on, zero for face-on). This can be determined through simple trigonometry, draw some triangles if you don t know where I got this. Inverting, the true velocity is related to the measured velocity by v = v sin i. This is consistent because when the disk is edge-on, we get v = v and the velocity we calculate is the true velocity. In the case where the disk is face-on, sin i is zero so we can t use this equation, because we can t measure any velocities. Since sin i can be less than 1, but never more, v < v for all i. This tells us that the velocity we use, v, is always less than the true velocity. Since the formula for mass depends on this velocity as M v 2, we can only get masses less than the true mass if we don t know the inclination. Thus, the mass we calculated is a lower-limit on the possible mass of the black hole. c) In the next LAMP campaign, we want to measure black holes with masses that are an order of magnitude greater than that in Mrk 40. How does this affect the telescope time proposal? Well, more massive black holes have more luminous accretion disks. This is intuitive since assuming the same efficiency, more mass means more light to make. It can also be shown mathematically since we ve investigated in part 4 of this worksheet that the BLR radius grows with luminosity, and we know M R, so mass must also be positively correlated with luminosity. Like we said before, more luminous AGN need to be watched for more time because their time lags are longer since the BLR radius is greater. Thus, we needed to ask for much more telescope time this time around. 6
7 Congratulations on making it to the end of this quite long worksheet! If you re particularly interested in reverberation mapping, talk to me about it and I can show you the LAMP proposal and elaborate on it even more than this worksheet does. I may be biased, but time domain astrophysics is the coolest astrophysics and reverberation mapping is just one example of a much larger sub-field that s very actively researching right now. Also, if you liked the cross-correlation technique presented in this worksheet, it s just one example of how computational programming can simplify data analysis dramatically, and if you re an intended astro major planning to take optical lab, you ll get to use it cross-correlation for a totally different application. 7
Black Hole and Host Galaxy Mass Estimates
Black Holes Black Hole and Host Galaxy Mass Estimates 1. Constraining the mass of a BH in a spectroscopic binary. 2. Constraining the mass of a supermassive BH from reverberation mapping and emission line
More informationMeasuring the Properties of Stars (ch. 17) [Material in smaller font on this page will not be present on the exam]
Measuring the Properties of Stars (ch. 17) [Material in smaller font on this page will not be present on the exam] Although we can be certain that other stars are as complex as the Sun, we will try to
More informationACTIVE GALACTIC NUCLEI: optical spectroscopy. From AGN classification to Black Hole mass estimation
ACTIVE GALACTIC NUCLEI: optical spectroscopy From AGN classification to Black Hole mass estimation Second Lecture Reverberation Mapping experiments & virial BH masses estimations Estimating AGN black hole
More informationQuasars ASTR 2120 Sarazin. Quintuple Gravitational Lens Quasar
Quasars ASTR 2120 Sarazin Quintuple Gravitational Lens Quasar Quasars Quasar = Quasi-stellar (radio) source Optical: faint, blue, star-like objects Radio: point radio sources, faint blue star-like optical
More informationHubble Space Telescope ultraviolet spectroscopy of blazars: emission lines properties and black hole masses. E. Pian, R. Falomo, A.
Hubble Space Telescope ultraviolet spectroscopy of blazars: emission lines properties and black hole masses E. Pian, R. Falomo, A. Treves 1 Outline Extra Background Introduction Sample Selection Data Analysis
More informationMethods of Measuring Black Hole Masses: Reverberation Mapping. Misty C. Bentz Georgia State University
Methods of Measuring Black Hole Masses: Reverberation Mapping Misty C. Bentz Georgia State University Black Hole Masses in AGNs Dynamical methods generally not feasible in AGNs AGNs rare = distant, poor
More informationStructure and Kinematics of the central BLR in AGN
Structure and Kinematics of the central BLR in AGN Wolfram Kollatschny, Göttingen Divcibare, 2011 University Observatory Institute for Astrophysics Broad Line Region Size? radius: - 10-4...10-1 pc - 1...
More informationInfow and Outfow in the Broad Line Region of AGN
Infow and Outfow in the Broad Line Region of AGN Anna Pancoast (Harvard-Smithsonian Center for Astrophysics) Einstein Fellows Symposium, October 13, 2017 Collaborators: Catherine Grier (PSU) Michael Fausnaugh
More informationActive Galactic Nuclei
Active Galactic Nuclei Optical spectra, distance, line width Varieties of AGN and unified scheme Variability and lifetime Black hole mass and growth Geometry: disk, BLR, NLR Reverberation mapping Jets
More informationLine Profile Variability in AGNs
Line Profile Variability in AGNs Wolfram Kollatschny, Göttingen Serbia, 2007 University Observatory Institute for Astrophysics Scale Sizes of an AGN HST : 0.1 2pc R. Blandford 1pc = 3.3 ly = 1190. ld =
More informationHubble s Law: Finding the Age of the Universe
Lab 16 Name: Hubble s Law: Finding the Age of the Universe 16.1 Introduction In your lecture sessions (or the lab on spectroscopy), you will find out that an object s spectrum can be used to determine
More informationActive Galactic Nuclei
Active Galactic Nuclei How were they discovered? How common are they? How do we know they are giant black holes? What are their distinctive properties? Active Galactic Nuclei for most galaxies the luminosity
More informationAlgebra & Trig Review
Algebra & Trig Review 1 Algebra & Trig Review This review was originally written for my Calculus I class, but it should be accessible to anyone needing a review in some basic algebra and trig topics. The
More informationDISTANCES ON COSMOLOGICAL SCALES WITH VLTI. 1. Introduction
DISTANCES ON COSMOLOGICAL SCALES WITH VLTI MARGARITA KAROVSKA, MARTIN ELVIS and MASSIMO MARENGO Harvard-Smithsonian Center for Astrophysics Abstract. We present here a new method using interferometric
More informationChapter 1 Review of Equations and Inequalities
Chapter 1 Review of Equations and Inequalities Part I Review of Basic Equations Recall that an equation is an expression with an equal sign in the middle. Also recall that, if a question asks you to solve
More informationFrequency of Seyfert Type Transitions in a Sample of 102 Local Active Galactic Nuclei
Frequency of Seyfert Type Transitions in a Sample of 102 Local Active Galactic Nuclei Jordan Runco A Thesis presented for the degree of Physics Department of Physics California Polytechnic State University
More informationPhysics 161 Homework 7 - Solutions Wednesday November 16, 2011
Physics 161 Homework 7 - s Wednesday November 16, 2011 Make sure your name is on every page, and please box your final answer Because we will be giving partial credit, be sure to attempt all the problems,
More informationPartial Fractions. June 27, In this section, we will learn to integrate another class of functions: the rational functions.
Partial Fractions June 7, 04 In this section, we will learn to integrate another class of functions: the rational functions. Definition. A rational function is a fraction of two polynomials. For example,
More informationIntroduction. So, why did I even bother to write this?
Introduction This review was originally written for my Calculus I class, but it should be accessible to anyone needing a review in some basic algebra and trig topics. The review contains the occasional
More informationTo factor an expression means to write it as a product of factors instead of a sum of terms. The expression 3x
Factoring trinomials In general, we are factoring ax + bx + c where a, b, and c are real numbers. To factor an expression means to write it as a product of factors instead of a sum of terms. The expression
More informationActive Galaxies & Quasars
Active Galaxies & Quasars Normal Galaxy Active Galaxy Galactic Nuclei Bright Active Galaxy NGC 5548 Galaxy Nucleus: Exact center of a galaxy and its immediate surroundings. If a spiral galaxy, it is the
More informationSection 5-7 : Green's Theorem
Section 5-7 : Green's Theorem In this section we are going to investigate the relationship between certain kinds of line integrals (on closed paths) and double integrals. Let s start off with a simple
More information1 Light from all distant galaxies is found to be shifted towards longer wavelengths. The more distant the galaxy, the greater the shift in wavelength.
1 Light from all distant galaxies is found to be shifted towards longer wavelengths. The more distant the galaxy, the greater the shift in wavelength. State the conclusions that we can draw from this.
More informationBlack Holes and Active Galactic Nuclei
Black Holes and Active Galactic Nuclei A black hole is a region of spacetime from which gravity prevents anything, including light, from escaping. The theory of general relativity predicts that a sufficiently
More informationQuasars: Back to the Infant Universe
Quasars: Back to the Infant Universe Learning Objectives! What is a quasar? What spectral features tell us quasars are very redshifted (very distant)? What spectral features tell us they are composed of
More informationGalaxies with Active Nuclei. Active Galactic Nuclei Seyfert Galaxies Radio Galaxies Quasars Supermassive Black Holes
Galaxies with Active Nuclei Active Galactic Nuclei Seyfert Galaxies Radio Galaxies Quasars Supermassive Black Holes Active Galactic Nuclei About 20 25% of galaxies do not fit well into Hubble categories
More informationAGN Central Engines. Supermassive Black Holes (SMBHs) Masses and Accretion Rates SMBH Mass Determinations Accretion Disks
AGN Central Engines Supermassive Black Holes (SMBHs) Masses and Accretion Rates SMBH Mass Determinations Accretion Disks 1 Supermassive Black Holes Need to generate L > 10 43 ergs/sec inside radius < 10
More informationSection 4.6 Negative Exponents
Section 4.6 Negative Exponents INTRODUCTION In order to understand negative exponents the main topic of this section we need to make sure we understand the meaning of the reciprocal of a number. Reciprocals
More informationLine Broadening. φ(ν) = Γ/4π 2 (ν ν 0 ) 2 + (Γ/4π) 2, (3) where now Γ = γ +2ν col includes contributions from both natural broadening and collisions.
Line Broadening Spectral lines are not arbitrarily sharp. There are a variety of mechanisms that give them finite width, and some of those mechanisms contain significant information. We ll consider a few
More informationAST Cosmology and extragalactic astronomy. Lecture 20. Black Holes Part II
AST4320 - Cosmology and extragalactic astronomy Lecture 20 Black Holes Part II 1 AST4320 - Cosmology and extragalactic astronomy Outline: Black Holes Part II Gas accretion disks around black holes, and
More informationNeutrinos, nonzero rest mass particles, and production of high energy photons Particle interactions
Neutrinos, nonzero rest mass particles, and production of high energy photons Particle interactions Previously we considered interactions from the standpoint of photons: a photon travels along, what happens
More informationQuadratic Equations Part I
Quadratic Equations Part I Before proceeding with this section we should note that the topic of solving quadratic equations will be covered in two sections. This is done for the benefit of those viewing
More informationAppendix A Powers of Ten
Conclusion This has been a theory book for observational amateur astronomers. This is perhaps a bit unusual because most astronomy theory books tend to be written for armchair astronomers and they tend
More informationAstronomy 102: Stars and Galaxies Final Exam Review Problems Revision 2
Astronomy 102: Stars and Galaxies Final Exam Review Problems Revision 2 Multiple Choice Questions: The first eight questions are multiple choice. Except where explicitly noted, only one answer is correct
More informationJodrell Bank Discovery Centre
A-level Physics: Radio Telescopes Consolidation questions For these questions, we will be considering galaxy NGC 660 (below), a rare polar-ring galaxy in the constellation of Pisces. NGC 660 consists of
More informationPhysics Lab #2: Spectroscopy
Physics 10263 Lab #2: Spectroscopy Introduction This lab is meant to serve as an introduction to the science of spectroscopy. In this lab, we ll learn about how emission and absorption works, and we ll
More informationASTR240: Radio Astronomy
ASTR240: Radio Astronomy HW#3 Due Feb 27, 2013 Problem 1 (4 points) (Courtesy J. J. Condon & S. M. Ransom) The GBT (Green Bank Telescope, a steerable radio telescope roughly the size of a football field
More information18 An Eclipsing Extrasolar Planet
Name: Date: 18 An Eclipsing Extrasolar Planet 18.1 Introduction One of the more recent new fields in astronomy is the search for (and discovery of) planets orbiting around stars other than our Sun, or
More information2. Active Galaxies. 2.1 Taxonomy 2.2 The mass of the central engine 2.3 Models of AGNs 2.4 Quasars as cosmological probes.
2. Active Galaxies 2.1 Taxonomy 2.2 The mass of the central engine 2.3 Models of AGNs 2.4 Quasars as cosmological probes Read JL chapter 3 Active galaxies: interface with JL All of JL chapter 3 is examinable,
More informationClusters: Context and Background
Clusters: Context and Background We re about to embark on a subject rather different from what we ve treated before, so it is useful to step back and think again about what we want to accomplish in this
More informationCenters of Galaxies. = Black Holes and Quasars
Centers of Galaxies = Black Holes and Quasars Models of Nature: Kepler Newton Einstein (Special Relativity) Einstein (General Relativity) Motions under influence of gravity [23] Kepler The planets move
More informationLesson 21 Not So Dramatic Quadratics
STUDENT MANUAL ALGEBRA II / LESSON 21 Lesson 21 Not So Dramatic Quadratics Quadratic equations are probably one of the most popular types of equations that you ll see in algebra. A quadratic equation has
More informationPhotographs of a Star Cluster. Spectra of a Star Cluster. What can we learn directly by analyzing the spectrum of a star? 4/1/09
Photographs of a Star Cluster Spectra of a Star Cluster What can we learn directly by analyzing the spectrum of a star? A star s chemical composition dips in the spectral curve of lines in the absorption
More informationDIFFERENTIAL EQUATIONS
DIFFERENTIAL EQUATIONS Basic Concepts Paul Dawkins Table of Contents Preface... Basic Concepts... 1 Introduction... 1 Definitions... Direction Fields... 8 Final Thoughts...19 007 Paul Dawkins i http://tutorial.math.lamar.edu/terms.aspx
More informationParticle acceleration and generation of high-energy photons
Particle acceleration and generation of high-energy photons For acceleration, see Chapter 21 of Longair Ask class: suppose we observe a photon with an energy of 1 TeV. How could it have been produced?
More informationPart I Electrostatics. 1: Charge and Coulomb s Law July 6, 2008
Part I Electrostatics 1: Charge and Coulomb s Law July 6, 2008 1.1 What is Electric Charge? 1.1.1 History Before 1600CE, very little was known about electric properties of materials, or anything to do
More informationF q. Gas at radius R (cylindrical) and height z above the disk midplane. F z. central mass M
Accretion Disks Luminosity of AGN derives from gravitational potential energy of gas spiraling inward through an accretion disk. Derive structure of the disk, and characteristic temperatures of the gas.
More information3 The lives of galaxies
Discovering Astronomy : Galaxies and Cosmology 24 3 The lives of galaxies In this section, we look at how galaxies formed and evolved, and likewise how the large scale pattern of galaxies formed. But before
More informationPage 1. These are all fairly simple functions in that wherever the variable appears it is by itself. What about functions like the following, ( ) ( )
Chain Rule Page We ve taken a lot of derivatives over the course of the last few sections. However, if you look back they have all been functions similar to the following kinds of functions. 0 w ( ( tan
More informationWhat is a galaxy made of?
Weighing a Galaxy What is a galaxy made of? STARS GAS DUST DARK MATTER! Weighing a Galaxy 2 What is HI? p + e - Majority of gas is atomic hydrogen (HI) It is the fuel for stars One proton and one electron
More informationX-ray time lags and reverberation from accreting black holes
X-ray time lags and reverberation from accreting black holes Phil Uttley University of Amsterdam Thanks to: Ed Cackett, Erin Kara, Andy Fabian, Dan Wilkins (Review paper: arxiv:1405.6575) 1. Background
More informationLecture Outline: Spectroscopy (Ch. 4)
Lecture Outline: Spectroscopy (Ch. 4) NOTE: These are just an outline of the lectures and a guide to the textbook. The material will be covered in more detail in class. We will cover nearly all of the
More informationEdited from the online virtual version available at
Produced for NASA's Office of Space Science by the Smithsonian Astrophysical Observatory 2001 Smithsonian Institution Edited from the online virtual version available at http://www.cfa.harvard.edu/seuforum/galspeed/
More informationBlack Holes in Hibernation
Black Holes in Hibernation Black Holes in Hibernation Only about 1 in 100 galaxies contains an active nucleus. This however does not mean that most galaxies do no have SMBHs since activity also requires
More informationPreface. Here are a couple of warnings to my students who may be here to get a copy of what happened on a day that you missed.
alculus III Preface Here are my online notes for my alculus III course that I teach here at Lamar University. espite the fact that these are my class notes, they should be accessible to anyone wanting
More informationOPEN CLUSTER PRELAB The first place to look for answers is in the lab script!
NAME: 1. Define using complete sentences: Globular Cluster: OPEN CLUSTER PRELAB The first place to look for answers is in the lab script! Open Cluster: Main Sequence: Turnoff point: Answer the following
More informationReview Questions for the new topics that will be on the Final Exam
Review Questions for the new topics that will be on the Final Exam Be sure to review the lecture-tutorials and the material we covered on the first three exams. How does speed differ from velocity? Give
More informationChapter 19 Galaxies. Hubble Ultra Deep Field: Each dot is a galaxy of stars. More distant, further into the past. halo
Chapter 19 Galaxies Hubble Ultra Deep Field: Each dot is a galaxy of stars. More distant, further into the past halo disk bulge Barred Spiral Galaxy: Has a bar of stars across the bulge Spiral Galaxy 1
More informationHigh-Energy Astrophysics Lecture 6: Black holes in galaxies and the fundamentals of accretion. Overview
High-Energy Astrophysics Lecture 6: Black holes in galaxies and the fundamentals of accretion Robert Laing Overview Evidence for black holes in galaxies and techniques for estimating their mass Simple
More informationThus Far. Intro / Some Definitions Hubble Classification Components of Galaxies. Specific Galaxy Types Star Formation Clusters of Galaxies
Thus Far Intro / Some Definitions Hubble Classification Components of Galaxies Stars Gas Dust Black Holes Dark Matter Specific Galaxy Types Star Formation Clusters of Galaxies Components of Galaxies:
More informationMath101, Sections 2 and 3, Spring 2008 Review Sheet for Exam #2:
Math101, Sections 2 and 3, Spring 2008 Review Sheet for Exam #2: 03 17 08 3 All about lines 3.1 The Rectangular Coordinate System Know how to plot points in the rectangular coordinate system. Know the
More informationVariability in AGN polarized spectra - a view to the BLR and torus structure
Variability in AGN polarized spectra - a view to the BLR and torus structure Luka Č. Popović Astronomical Observatory, Serbia Coll. V. L. Afanasiev, A. I. Shapovalova, SAO, Russia Dj. Savi ć, AOB, Serbia
More informationFig. 1. On a sphere, geodesics are simply great circles (minimum distance). From
Equation of Motion and Geodesics The equation of motion in Newtonian dynamics is F = m a, so for a given mass and force the acceleration is a = F /m. If we generalize to spacetime, we would therefore expect
More informationLecture 10: Powers of Matrices, Difference Equations
Lecture 10: Powers of Matrices, Difference Equations Difference Equations A difference equation, also sometimes called a recurrence equation is an equation that defines a sequence recursively, i.e. each
More informationAstro2010 Science White Paper: Tracing the Mass Buildup of Supermassive Black Holes and their Host Galaxies
Astro2010 Science White Paper: Tracing the Mass Buildup of Supermassive Black Holes and their Host Galaxies Anton M. Koekemoer (STScI) Dan Batcheldor (RIT) Marc Postman (STScI) Rachel Somerville (STScI)
More informationSpectra of a Star Cluster. Photographs of a Star Cluster. What can we learn directly by analyzing the spectrum of a star? 4/1/09
Photographs of a Star Cluster Spectra of a Star Cluster What can we learn directly by analyzing the spectrum of a star? A star s chemical composition dips in the spectral curve of lines in the absorption
More informationClassification of Galaxies
Name: Partner(s): 1102 or 3311: Desk # Date: Classification of Galaxies Purpose Study and classify galaxies Learn how to measure their distance, mass and radius. Equipment Pictures from online lab manual
More informationPHY2048 Physics with Calculus I
PHY2048 Physics with Calculus I Section 584761 Prof. Douglas H. Laurence Exam 1 (Chapters 2 6) February 14, 2018 Name: Solutions 1 Instructions: This exam is composed of 10 multiple choice questions and
More informationASTRO-H Studies of Accretion Flow onto Supermassive Black Hole
ASTRO-H Studies of Accretion Flow onto Supermassive Black Hole 2015 October 21 The Institute of Physical and Chemical Research (RIKEN) Nishina center Hirofumi Noda 1. Contents I. Introduction II. Geometry
More informationII. Unit Speed Curves
The Geometry of Curves, Part I Rob Donnelly From Murray State University s Calculus III, Fall 2001 note: This material supplements Sections 13.3 and 13.4 of the text Calculus with Early Transcendentals,
More informationA brief outline of the lab procedure, the steps will be walked through later on.
Name: Partner(s): Lab #12 The Hubble Law Objectives In this lab you will use simple observational evidence to recreate the most profound discovery in cosmology. By calculating the distance to other galaxies
More informationbase 2 4 The EXPONENT tells you how many times to write the base as a factor. Evaluate the following expressions in standard notation.
EXPONENTIALS Exponential is a number written with an exponent. The rules for exponents make computing with very large or very small numbers easier. Students will come across exponentials in geometric sequences
More informationLONG TERM SPECTRAL OPTICAL MONITORNIG OF
LONG TERM SPECTRAL OPTICAL MONITORNIG OF ACTIVE GALACTIC NUCLEI Dragana Ilić DepartmentofAstronomy Astronomy, Faculty ofmathematics Mathematics, University of Belgrade Luka Č. Popović, Astronomical Observatory,
More informationQuasars and AGN. What are quasars and how do they differ from galaxies? What powers AGN s. Jets and outflows from QSOs and AGNs
Goals: Quasars and AGN What are quasars and how do they differ from galaxies? What powers AGN s. Jets and outflows from QSOs and AGNs Discovery of Quasars Radio Observations of the Sky Reber (an amateur
More informationarxiv:astro-ph/ v1 23 Dec 2005
3D spectroscopy as a tool for investigation of the BLR of lensed QSOs Luka Č. Popović Astronomical Observatory, Volgina 7, 11160 Belgrade, Serbia lpopovic@aob.bg.ac.yu arxiv:astro-ph/0512594v1 23 Dec 2005
More informationLecture 2: Galaxy types, spectra
Lecture 2: Galaxy types, spectra Galaxies AS 3011 1 Hubble tuning fork this is really just descriptive, but Hubble suggested galaxies evolve from left to right in this picture not unreasonable, perhaps
More informationLecture 2: Galaxy types, spectra. Galaxies AS
Lecture 2: Galaxy types, spectra Galaxies AS 3011 1 Hubble tuning fork this is really just descriptive, but Hubble suggested galaxies evolve from left to right in this picture not unreasonable, perhaps
More informationThe Hubble Law & The Structure of the Universe
Name: Lab Meeting Date/Time: The Hubble Law & The Structure of the Universe The Hubble Law is a relationship between two quantities the speed of and distance to a galaxy. In order to determine the Hubble
More informationMASSACHUSETTS INSTITUTE OF TECHNOLOGY Physics Department Earth, Atmospheric, and Planetary Sciences Department. Quiz 2
MASSACHUSETTS INSTITUTE OF TECHNOLOGY Physics Department Earth, Atmospheric, and Planetary Sciences Department Astronomy 8.282J 12.402J April 13, 2005 Quiz 2 Name Last First (please print) 1. Work any
More informationReverberation Mapping in the Era of MOS and Time-Domain Surveys: from SDSS to MSE
Reverberation Mapping in the Era of MOS and Time-Domain Surveys: from SDSS to MSE Yue Shen Carnegie Obs -> University of Illinois at Urbana-Champaign MSE Science Team Meeting, July 29-31 2015, Big Island
More informationModern Observations: the Accelerating Universe
Modern Observations: the Accelerating Universe So far we re caught up to the early or possibly mid 1990s in basic cosmological observations. In this lecture, however, we are going to address the greatest
More informationCarbon Dating The decay of radioactive nuclei can be used to measure the age of artifacts, fossils, and rocks. The half-life of C 14 is 5730 years.
Carbon Dating The decay of radioactive nuclei can be used to measure the age of artifacts, fossils, and rocks. The half-life of C 14 is 5730 years. a) If a sample shows only one-fourth of its estimated
More information! p. 1. Observations. 1.1 Parameters
1 Observations 11 Parameters - Distance d : measured by triangulation (parallax method), or the amount that the star has dimmed (if it s the same type of star as the Sun ) - Brightness or flux f : energy
More informationMASSACHUSETTS INSTITUTE OF TECHNOLOGY Physics Department Earth, Atmospheric, and Planetary Sciences Department. Final Exam
MASSACHUSETTS INSTITUTE OF TECHNOLOGY Physics Department Earth, Atmospheric, and Planetary Sciences Department Physics 8.282J EAPS 12.402J May 20, 2005 Final Exam Name Last First (please print) 1. Do any
More informationQuasars in the SDSS. Rich Kron NGC June 2006 START CI-Team: Variable Quasars Research Workshop Yerkes Observatory
Quasars in the SDSS Rich Kron 28 June 2006 START CI-Team: Variable Quasars Research Workshop Yerkes Observatory NGC 1068 About 10% of all of the spectra in the SDSS database are of quasars (as opposed
More informationA New Mass Estimate of the Central Supermassive Black Hole in NGC with Reverberation Mapping
A New Mass Estimate of the Central Supermassive Black Hole in NGC 4051 with Reverberation Mapping Kelly D. Denney 1 ABSTRACT There is increasingly strong evidence from observations of the local universe
More informationAstro 3 Lab Exercise
Astro 3 Lab Exercise Lab #4: Measuring Redshifts of Galaxies Dates: August 5 6 Lab Report due: 5 pm Friday August 15 Summer 2014 1 Introduction This project involves measuring the redshifts of distant
More informationActive Galactic Nuclei - Zoology
Active Galactic Nuclei - Zoology Normal galaxy Radio galaxy Seyfert galaxy Quasar Blazar Example Milky Way M87, Cygnus A NGC 4151 3C273 BL Lac, 3C279 Galaxy Type spiral elliptical, lenticular spiral irregular
More information[10] Spectroscopy (9/28/17)
1 [10] Spectroscopy (9/28/17) Upcoming Items 1. Homework #5 due on Tuesday 2. Midterm #1 October 10 3. Read Ch. 6.2 & 6.3 by next class (skim the rest of Ch. 6). Do the selfstudy quizzes APOD 9/28/16 2
More informationBUILDING GALAXIES. Question 1: When and where did the stars form?
BUILDING GALAXIES The unprecedented accuracy of recent observations of the power spectrum of the cosmic microwave background leaves little doubt that the universe formed in a hot big bang, later cooling
More informationWorksheet 1.4: Geometry of the Dot and Cross Products
Boise State Math 275 (Ultman) Worksheet 1.4: Geometry of the Dot and Cross Products From the Toolbox (what you need from previous classes): Basic algebra and trigonometry: be able to solve quadratic equations,
More informationLARGE QUASAR GROUPS. Kevin Rahill Astrophysics
LARGE QUASAR GROUPS Kevin Rahill Astrophysics QUASARS Quasi-stellar Radio Sources Subset of Active Galactic Nuclei AGNs are compact and extremely luminous regions at the center of galaxies Identified as
More informationPh211 Summer 09 HW #4, week of 07/13 07/16. Ch6: 44, 46, 52; Ch7: 29, 41. (Knight, 2nd Ed).
Solutions 1 for HW #4: Ch6: 44, 46, 52; Ch7: 29, 41. (Knight, 2nd Ed). We make use of: equations of kinematics, and Newton s Laws. You also (routinely) need to handle components of a vector, in nearly
More informationMath 121 (Lesieutre); 9.1: Polar coordinates; November 22, 2017
Math 2 Lesieutre; 9: Polar coordinates; November 22, 207 Plot the point 2, 2 in the plane If you were trying to describe this point to a friend, how could you do it? One option would be coordinates, but
More informationUnit 1: Equilibrium and Center of Mass
Unit 1: Equilibrium and Center of Mass FORCES What is a force? Forces are a result of the interaction between two objects. They push things, pull things, keep things together, pull things apart. It s really
More informationRELATIVISTIC SPECTROSCOPY OF BLACK HOLES
RELATIVISTIC SPECTROSCOPY OF BLACK HOLES Michael Parker ESAC science seminar 24/5/18 BLACK HOLES 101 For an object to just escape a massive body, it needs the sum: Kinetic energy + gravitational binding
More informationClusters: Context and Background
Clusters: Context and Background We reabouttoembarkon asubjectratherdifferentfrom what we vetreatedbefore, soit is useful to step back and think again about what we want to accomplish in this course. We
More informationSchwarzchild Radius. Black Hole Event Horizon 30 km 9 km. Mass (solar) Object Star. Star. Rs = 3 x M (Rs in km; M in solar masses)
Schwarzchild Radius The radius where escape speed = the speed of light. Rs = 2 GM/c2 Rs = 3 x M (Rs in km; M in solar masses) A sphere of radius Rs around the black hole is called the event horizon. Object
More informationSystematic Uncertainty Max Bean John Jay College of Criminal Justice, Physics Program
Systematic Uncertainty Max Bean John Jay College of Criminal Justice, Physics Program When we perform an experiment, there are several reasons why the data we collect will tend to differ from the actual
More informationWhy Doesn t the Moon Hit us? In analysis of this question, we ll look at the following things: i. How do we get the acceleration due to gravity out
Why Doesn t the oon Hit us? In analysis of this question, we ll look at the following things: i. How do we get the acceleration due to gravity out of the equation for the force of gravity? ii. How does
More information