ASTR240: Radio Astronomy

Size: px
Start display at page:

Download "ASTR240: Radio Astronomy"

Transcription

1 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 see photo below!) has sensitive receivers covering the frequency ranges 18 to 26.5 GHz and 26 to 40 GHz. Show that this frequency coverage is sufficient to detect CO emission from galaxies at any redshift from z 1.9 to at least z 10 (the estimated redshift at which stars started producing significant amounts of interstellar CO). You can look up the rest frequency of CO lines using splatalogue (note that the low-j lines are most likely to be excited in the cold ISM): The most commonly observed CO emission lines arise either from the J=1 0 or J=2 1 transition, with rest frequencies 115 and 230 GHz. For the upper limit on the redshift, z For the lower limit on the redshift, z

2 Problem 2 (17 points) You go to Prof. Novick s lab and measure the rest frequency of the J=3 2 transition of the CO molecule to be GHz. A) Estimate the distance between the C and O atoms in the molecule. (2 points) Recall that the frequency of the rotational line of a small molecule is given by ν = hj 4π 2 µre 2 (1) In this case, J=3 and µ = m1m2 m 1+m 2 = m H. Solving for r e gives cm Now you go to a telescope and observe the following CO line emission from a giant molecular cloud in the Milky Way galaxy (rest frame is LSR, position on the sky is α=18 h 30 m, δ=-10 6, in B1950 coordinates): B) What is the cloud s velocity relative to the sun? Is it moving towards or away from the sun? Remember that the conversion between LSR and heliocentric velocity is: V LSR = V heliocentric + V [cos(α α 0 ) cos δ 0 cos δ + sin δ 0 sin δ], where V = 19.7 km/s, and the direction of motion is towards (α 0 = 271, δ 0 = +30 ) in B1950 coordinates. (3 points) First, calculate LSR velocity: ν/ν = v/c. Solving for v gives 50 km/s. Note that the emission is redshifted (lower frequency) and has an amplitude larger than the maximum LSR-heliocentric velocity difference, so it must be moving away from the sun. To get the object s velocity relative to the sun, we must convert to the heliocentric rest frame. Using the values provided in the problem (with V LSR =50 km/s), the heliocentric conversion gives V hel = 35 km/s C) At what galactic longitude l do you observe this cloud? (One good calculator to help you out is the NED Coordinate and Extinction calculator at ). At what distance(s) from the earth might it be located? Assume that the galactic rotation curve exhibits a constant velocity of 220 km/s as a function of radius (i.e., ΩR = constant = 220 km/s). (4 points) 2

3 Plugging the coordinates into the calculator (converting from equatorial to galactic in epoch B1950) gives l = 21.9 Now comes the exciting part... Solve for the galactocentric distance R of the source based on its recessional velocity, using the assumption that ΩR = constant = 220 km/s: v = R 0 (Ω Ω 0 ) sin l (2) ΩR = constant = 220km/s (3) v = (R 0 Ω Ω 0 R 0 ) sin l (4) = 220km/s( R 0 1) sin l R (5) R = R 0 v 220km/s sin l + 1 (6) Plugging in the appropriate numbers (R 0 = 8.5 kpc, v = 35 km/s) gives R = 6 kpc. Once we have calculated R, we can use geometry to show that the distance of the cloud from earth must be x ± y, where x = R 2 (R 0 sin l) 2 and y = R 2 0 (R 0 sin l) 2. Here is a drawing of how that relationship is derived: (7) Plugging in appropriate values for x and y indicates that the cloud must be 8.4±5.9 kpc from earth, or either 2.5 or 14.4 kpc from earth D) Assuming the line is thermally broadened, estimate the temperature of the cloud. Check to make sure the cloud is hot enough to excite the CO J=3-2 line. (2 points) 3

4 8kT ln 2 Recall: ν D (F W HM) = ν 0 mc. From the drawing, ν 2 D (F W HM) = MHz, implying that the temperature is roughly 100 K. The estimated minimum temperature at which a line will be excited is given by T min = νh(j+1) 2k =33 K. Yes, the kinetic temperature indicated by the FWHM is high enough to excite the CO(3 2) line. E) Assume that the source fills the beam. Is the cloud optically thick, or optically thin? (2 points) Spectral line is characterized by thermal emission at temperature T s. When the source fills the beam, the antenna temperature T A is equal to the brightness temperature T B. If the source were optically thin, T A = T B τ ν, with τ ν < 1. However, in this case we see that T A = T B = T K (the kinetic temperature measured in part B), so the line has achieved its maximum brightness and is most likely optically thick. F) Can you measure the total column density of material through the cloud? If so, do it! If not, why not? (2 points) Can t measure column density for an optically thick line, because the object is opaque and so you can t see all the material along the line of sight. Instead you see surface temperature. G) The Einstein A coefficient for the CO J=3-2 line is s 1. Estimate the critical density of the line. Do you think the cloud is collisionally or radiatively excited? Why? Does this tell you anything about the density of material in the cloud? (2 points) n crit A21 σ calculate n crit cm 3 m kt k. With A 21 given in the problem, σ cm 2, T K 100 K, and m = (6 + 12)m H, we Since we know the kinetic temperature T K 100 K from the width of the line, and the flux of the line indicates optically thick emission at T S =100 K, it appears that the line is collisionally excited. This tells us that the density of material in the cloud must be higher than the critical density calculated above. Problem 3 (8 points) (Courtesy M. Faison) Qualitatively sketch the beam pattern of this aperture: 4

5 There are effectively four elements to this pattern: The beam pattern will be the combination of the Fourier transformations of these four functions: Note: (1) is a narrow peak with Airy rings, (2) is a broad trough with Airy rings, and for (3) and (4) the long axis FTs to a narrow sinc function, while the short axis FTs to a broad sinc function. The total should look something like this: 5

6 And in case you don t believe me, here is the actual FT, done in Mathematica: Problem 4 (6 points) Derive the expressions for α ν and j ν in terms of the Einstein coefficients that we used in class: Some helpful hints: α ν = g 2 + g 2 nc 2 h 8πkT s ν f(ν)a 21 (8) j ν = g 2 + g 2 nhν 4π f(ν)a 21 (9) I ν α ν is the number of net absorptions per unit time (i.e., absorption minus stimulated emission), times the energy hν, per unit solid angle (4π). Similarly, j ν is the number of spontaneous emissions per unit time, times the energy, per unit solid angle. Use the Rayleigh-Jeans approximation liberally. 6

7 n is defined as n 1 + n 2, and can also be written as n 1 (1 + n 2 /n 1 ). Don t give up: j ν is much simpler to derive than α ν! Number of net absorptions per unit time = number of absorptions - number of stimulated emissions: = (n 1 B 12 n 2 B 21 )f(ν)i ν Note that B 21 = g1 g 2 B 12 and n2 n 1 = g2 exp ( hν kt ) Then, = n 1 B 12 I ν f(ν)[1 exp ( hν kt )] Now use R-J approximation: hν kt << 1: = n 1 B 12 I ν f(ν) hν kt Now, I ν α ν = net absorptions per unit time hν 4π, implying: α ν = h2 ν 2 4πkT n 1B 12 f(ν) Recall: B 12 = g2 c 2 n 2 n 1 = g2 exp ( hν kt ) g2 Then, n = n 1 (1 + g2 2hν A 3 21 and n = n 1 + n 2 = n 1 (1 + n2 when hν << kt ) and n 1 = n 1+ g 2 = g1 g 1+g 2 n Substituting for B 12 and n 1 in the expression for α ν above gives: α ν = h2 ν 2 g 2 nc 2 4πkT +g 2 2hν A 3 21 = Now for j ν... g2 +g 2 nc 2 h 8πkT ν A 21f(ν) j ν = number of stimulated emissions per unit time hν 4π : j ν = n 2 hν 4π f(ν)a 21 Once again, express n 2 in terms of n and statistical weights: n 2 = Substitute in: j ν = g2 nhν +g 2 4π f(ν)a 21 n 1 ) g2 +g 2 n 7

Components of Galaxies Gas The Importance of Gas

Components 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 information

Radio Astronomy An Introduction

Radio Astronomy An Introduction Radio Astronomy An Introduction Felix James Jay Lockman NRAO Green Bank, WV References Thompson, Moran & Swenson Kraus (1966) Christiansen & Hogbom (1969) Condon & Ransom (nrao.edu) Single Dish School

More information

ASTR2050 Spring Please turn in your homework now! In this class we will discuss the Interstellar Medium:

ASTR2050 Spring Please turn in your homework now! In this class we will discuss the Interstellar Medium: ASTR2050 Spring 2005 Lecture 10am 29 March 2005 Please turn in your homework now! In this class we will discuss the Interstellar Medium: Introduction: Dust and Gas Extinction and Reddening Physics of Dust

More information

Lecture 19 CO Observations of Molecular Clouds

Lecture 19 CO Observations of Molecular Clouds Lecture 9 CO Observations of Molecular Clouds. CO Surveys 2. Nearby molecular clouds 3. Antenna temperature and radiative transfer 4. Determining cloud conditions from CO References Tielens, Ch. 0 Myers,

More information

An Introduction to Radio Astronomy

An Introduction to Radio Astronomy An Introduction to Radio Astronomy Bernard F. Burke Massachusetts Institute of Technology and Francis Graham-Smith Jodrell Bank, University of Manchester CAMBRIDGE UNIVERSITY PRESS Contents Preface Acknowledgements

More information

ASTR240: Radio Astronomy

ASTR240: Radio Astronomy AST24: adio Astronomy HW#1 Due Feb 6, 213 Problem 1 (6 points) (Adapted from Kraus Ch 8) A radio source has flux densities of S 1 12.1 Jy and S 2 8.3 Jy at frequencies of ν 1 6 MHz and ν 2 1415 MHz, respectively.

More information

- Synchrotron emission: A brief history. - Examples. - Cyclotron radiation. - Synchrotron radiation. - Synchrotron power from a single electron

- Synchrotron emission: A brief history. - Examples. - Cyclotron radiation. - Synchrotron radiation. - Synchrotron power from a single electron - Synchrotron emission: A brief history - Examples - Cyclotron radiation - Synchrotron radiation - Synchrotron power from a single electron - Relativistic beaming - Relativistic Doppler effect - Spectrum

More information

Preliminary Examination: Astronomy

Preliminary 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 information

MASSACHUSETTS INSTITUTE OF TECHNOLOGY HAYSTACK OBSERVATORY WESTFORD, MASSACHUSETTS

MASSACHUSETTS INSTITUTE OF TECHNOLOGY HAYSTACK OBSERVATORY WESTFORD, MASSACHUSETTS To: From: Subject: EDGES MEMO # 220 MASSACHUSETTS INSTITUTE OF TECHNOLOGY HAYSTACK OBSERVATORY WESTFORD, MASSACHUSETTS 01886 November 29, 2016 Telephone: 781-981-5414 Fax: 781-981-0590 EDGES Group Alan

More information

Spectral Line Observing

Spectral Line Observing Spectral Line Observing Measurement goals Spectral line formation processes Line Shapes / Doppler effect Spectrometers Observing techniques Calibration Data reduction / Data products Data visualization

More information

Ay 20 Basic Astronomy and the Galaxy Problem Set 2

Ay 20 Basic Astronomy and the Galaxy Problem Set 2 Ay 20 Basic Astronomy and the Galaxy Problem Set 2 October 19, 2008 1 Angular resolutions of radio and other telescopes Angular resolution for a circular aperture is given by the formula, θ min = 1.22λ

More information

Some HI is in reasonably well defined clouds. Motions inside the cloud, and motion of the cloud will broaden and shift the observed lines!

Some HI is in reasonably well defined clouds. Motions inside the cloud, and motion of the cloud will broaden and shift the observed lines! Some HI is in reasonably well defined clouds. Motions inside the cloud, and motion of the cloud will broaden and shift the observed lines Idealized 21cm spectra Example observed 21cm spectra HI densities

More information

An Introduction to Radio Astronomy

An Introduction to Radio Astronomy An Introduction to Radio Astronomy Second edition Bernard F. Burke and Francis Graham-Smith CAMBRIDGE UNIVERSITY PRESS Contents Preface to the second edition page x 1 Introduction 1 1.1 The role of radio

More information

Measurement of Galactic Rotation Curve

Measurement of Galactic Rotation Curve Measurement of Galactic Rotation Curve Objective: The 21-cm line produced by neutral hydrogen in interstellar space provides radio astronomers with a very useful probe for studying the differential rotation

More information

Lecture 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 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 information

Some recent work I. Cosmic microwave background, seeds of large scale structure (Planck) Formation and evolution of galaxies (Figure: Simpson et al.

Some recent work I. Cosmic microwave background, seeds of large scale structure (Planck) Formation and evolution of galaxies (Figure: Simpson et al. Radio astronomy Radio astronomy studies celestial objects at wavelengths longward of λ 100 µm (frequencies below ν 3 THz) A radio telecope can see cold gas and dust (Wien s displacement law of BB emision,

More information

Characteristic temperatures

Characteristic temperatures Characteristic temperatures Effective temperature Most sources are only roughly blackbodies (if that). So we integrate the flux over frequency and define: F = I cosθ dω d = σ T e 4 i.e. a source of effective

More information

Reverberation Mapping

Reverberation Mapping 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

More information

RADIO SPECTRAL LINES. Nissim Kanekar National Centre for Radio Astrophysics, Pune

RADIO SPECTRAL LINES. Nissim Kanekar National Centre for Radio Astrophysics, Pune RADIO SPECTRAL LINES Nissim Kanekar National Centre for Radio Astrophysics, Pune OUTLINE The importance of radio spectral lines. Equilibrium issues: kinetic, excitation, brightness temperatures. The equation

More information

Astrochemistry and Molecular Astrophysics Paola Caselli

Astrochemistry and Molecular Astrophysics Paola Caselli School of Physics and Astronomy FACULTY OF MATHEMATICS & PHYSICAL SCIENCES Astrochemistry and Molecular Astrophysics Paola Caselli Outline 1. The formation of H 2 2. The formation of H 3 + 3. The chemistry

More information

Active Galactic Nuclei OIII

Active Galactic Nuclei OIII Active Galactic Nuclei In 1908, Edward Fath (1880-1959) observed NGC 1068 with his spectroscope, which displayed odd (and very strong) emission lines. In 1926 Hubble recorded emission lines of this and

More information

VI. 21cm Radiation. 1 AY230-21cm. A. History

VI. 21cm Radiation. 1 AY230-21cm. A. History 1 AY230-21cm VI. 21cm Radiation A. History B. Physics van der Hulst 1941 Collq in a bunker! Ground state of HI: l = 0, s = 1/2, j = 1/2 Degeneracy of the G.S. is removed by the interaction of the magnetic

More information

Recombination onto Doubly-Ionized Carbon in M17

Recombination onto Doubly-Ionized Carbon in M17 Recombination onto Doubly-Ionized Carbon in M17 (Old dog; new trick) L. J Rickard, B. McEwen, and Y. Pihlström (University of New Mexico) New Mexico Symposium 4 November, 2016 Advantages to using radio

More information

Line 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. 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 information

ASTRONOMY 460: PROJECT INTRO - GALACTIC ROTATION CURVE

ASTRONOMY 460: PROJECT INTRO - GALACTIC ROTATION CURVE ASTRONOMY 460: PROJECT INTRO - GALACTIC ROTATION CURVE Snežana Stanimirović, October 6, 2014 1. Introduction This project has two goals: we want to measure the Milky Way (or Galactic) rotation curve by

More information

Astronomy 113. Dr. Joseph E. Pesce, Ph.D. Distances & the Milky Way. The Curtis View. Our Galaxy. The Shapley View 3/27/18

Astronomy 113. Dr. Joseph E. Pesce, Ph.D. Distances & the Milky Way. The Curtis View. Our Galaxy. The Shapley View 3/27/18 Astronomy 113 Dr. Joseph E. Pesce, Ph.D. Distances & the Milky Way 14-2 Historical Overview: the Curtis-Shapley Debate ³What is the size of our galaxy? ³What is the nature of spiral nebula? The Curtis

More information

Astronomy 113. Dr. Joseph E. Pesce, Ph.D. Dr. Joseph E. Pesce, Ph.D.

Astronomy 113. Dr. Joseph E. Pesce, Ph.D. Dr. Joseph E. Pesce, Ph.D. Astronomy 113 Dr. Joseph E. Pesce, Ph.D. Distances & the Milky Way Historical Overview: the Curtis-Shapley Debate ³What is the size of our galaxy? ³What is the nature of spiral nebula? 14-2 ³Occurred in

More information

CHAPTER 27. Continuum Emission Mechanisms

CHAPTER 27. Continuum Emission Mechanisms CHAPTER 27 Continuum Emission Mechanisms Continuum radiation is any radiation that forms a continuous spectrum and is not restricted to a narrow frequency range. In what follows we briefly describe five

More information

Lecture 2 Line Radiative Transfer for the ISM

Lecture 2 Line Radiative Transfer for the ISM Lecture 2 Line Radiative Transfer for the ISM Absorption lines in the optical & UV Equation of transfer Absorption & emission coefficients Line broadening Equivalent width and curve of growth Observations

More information

Astro 201 Radiative Processes Problem Set 6. Due in class.

Astro 201 Radiative Processes Problem Set 6. Due in class. Astro 201 Radiative Processes Problem Set 6 Due in class. Readings: Hand-outs from Osterbrock; Rybicki & Lightman 9.5; however much you like of Mihalas 108 114, 119 127, 128 137 (even skimming Mihalas

More information

Radiation Processes. Black Body Radiation. Heino Falcke Radboud Universiteit Nijmegen. Contents:

Radiation Processes. Black Body Radiation. Heino Falcke Radboud Universiteit Nijmegen. Contents: Radiation Processes Black Body Radiation Heino Falcke Radboud Universiteit Nijmegen Contents: Planck Spectrum Kirchoff & Stefan-Boltzmann Rayleigh-Jeans & Wien Einstein Coefficients Literature: Based heavily

More information

The distance modulus in the presence of absorption is given by

The distance modulus in the presence of absorption is given by Problem 4: An A0 main sequence star is observed at a distance of 100 pc through an interstellar dust cloud. Furthermore, it is observed with a color index B-V = 1.5. What is the apparent visual magnitude

More information

Sources of radiation

Sources of radiation Sources of radiation Most important type of radiation is blackbody radiation. This is radiation that is in thermal equilibrium with matter at some temperature T. Lab source of blackbody radiation: hot

More information

Lecture 10. Lidar Effective Cross-Section vs. Convolution

Lecture 10. Lidar Effective Cross-Section vs. Convolution Lecture 10. Lidar Effective Cross-Section vs. Convolution q Introduction q Convolution in Lineshape Determination -- Voigt Lineshape (Lorentzian Gaussian) q Effective Cross Section for Single Isotope --

More information

Very Long Baseline Interferometry (VLBI) Wei Dou Tutor: Jianfeng Zhou

Very Long Baseline Interferometry (VLBI) Wei Dou Tutor: Jianfeng Zhou Very Long Baseline Interferometry (VLBI) Wei Dou Tutor: Jianfeng Zhou 2017 03-16 Content Introduction to interferometry and VLBI VLBA (Very Long Baseline Array) Why VLBI In optics, airy disk is a point

More information

If light travels past a system faster than the time scale for which the system evolves then t I ν = 0 and we have then

If light travels past a system faster than the time scale for which the system evolves then t I ν = 0 and we have then 6 LECTURE 2 Equation of Radiative Transfer Condition that I ν is constant along rays means that di ν /dt = 0 = t I ν + ck I ν, (29) where ck = di ν /ds is the ray-path derivative. This is equation is the

More information

Physics of the Interstellar and Intergalactic Medium: Problems for Students

Physics of the Interstellar and Intergalactic Medium: Problems for Students Physics of the Interstellar and Intergalactic Medium: Problems for Students Version 2017.03.03 Bruce T. Draine PRINCETON UNIVERSITY PRESS PRINCETON AND OXFORD c 2011,2017 by Bruce T. Draine Preface I

More information

Radio Searches for Interstellar Carbon Chains HC 4 OH and H 2 CCC

Radio Searches for Interstellar Carbon Chains HC 4 OH and H 2 CCC Radio Searches for Interstellar Carbon Chains HC 4 OH and H 2 CCC Tokyo Univ. of Science a Nobeyama Radio Observatory b Shizuoka Univ. c Sophia Univ. d M. Araki, a S. Takano, b H. Yamabe, a N. Koshikawa,

More information

Gas 1: Molecular clouds

Gas 1: Molecular clouds Gas 1: Molecular clouds > 4000 known with masses ~ 10 3 to 10 5 M T ~ 10 to 25 K (cold!); number density n > 10 9 gas particles m 3 Emission bands in IR, mm, radio regions from molecules comprising H,

More information

GBT LO and Doppler Corrections

GBT LO and Doppler Corrections GBT LO and Doppler Corrections Rick Fisher June 3, 2000 1 Introduction This note outlines the methods by which GBT observers can specify observing frequencies or velocities and the equations that are used

More information

de = j ν dvdωdtdν. (1)

de = j ν dvdωdtdν. (1) Transfer Equation and Blackbodies Initial questions: There are sources in the centers of some galaxies that are extraordinarily bright in microwaves. What s going on? The brightest galaxies in the universe

More information

Journal Club Presentation on The BIMA Survey of Nearby Galaxies. I. The Radial Distribution of CO Emission in Spiral Galaxies by Regan et al.

Journal Club Presentation on The BIMA Survey of Nearby Galaxies. I. The Radial Distribution of CO Emission in Spiral Galaxies by Regan et al. Journal Club Presentation on The BIMA Survey of Nearby Galaxies. I. The Radial Distribution of CO Emission in Spiral Galaxies by Regan et al. ApJ, 561:218-237, 2001 Nov 1 1 Fun With Acronyms BIMA Berkely

More information

Problem Set 3, AKA First midterm review Astrophysics 4302 Due Date: Sep. 23, 2013

Problem Set 3, AKA First midterm review Astrophysics 4302 Due Date: Sep. 23, 2013 Problem Set 3, AKA First midterm review Astrophysics 4302 Due Date: Sep. 23, 2013 1. δ Cephei is a fundamental distance scale calibrator. It is a Cepheid with a period of 5.4 days. A campaign with the

More information

φ(ν)dν = 1. (1) We can define an average intensity over this profile, J =

φ(ν)dν = 1. (1) We can define an average intensity over this profile, J = Ask about final Saturday, December 14 (avoids day of ASTR 100 final, Andy Harris final). Decided: final is 1 PM, Dec 14. Rate Equations and Detailed Balance Blackbodies arise if the optical depth is big

More information

Lecture Outline: Spectroscopy (Ch. 4)

Lecture 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 information

ETA Observations of Crab Pulsar Giant Pulses

ETA Observations of Crab Pulsar Giant Pulses ETA Observations of Crab Pulsar Giant Pulses John Simonetti,, Dept of Physics, Virginia Tech October 7, 2005 Pulsars Crab Pulsar Crab Giant Pulses Observing Pulses --- Propagation Effects Summary Pulsars

More information

Diffuse Interstellar Medium

Diffuse Interstellar Medium Diffuse Interstellar Medium Basics, velocity widths H I 21-cm radiation (emission) Interstellar absorption lines Radiative transfer Resolved Lines, column densities Unresolved lines, curve of growth Abundances,

More information

2. NOTES ON RADIATIVE TRANSFER The specific intensity I ν

2. NOTES ON RADIATIVE TRANSFER The specific intensity I ν 1 2. NOTES ON RADIATIVE TRANSFER 2.1. The specific intensity I ν Let f(x, p) be the photon distribution function in phase space, summed over the two polarization states. Then fdxdp is the number of photons

More information

Astronomy 114. Lecture 27: The Galaxy. Martin D. Weinberg. UMass/Astronomy Department

Astronomy 114. Lecture 27: The Galaxy. Martin D. Weinberg. UMass/Astronomy Department Astronomy 114 Lecture 27: The Galaxy Martin D. Weinberg weinberg@astro.umass.edu UMass/Astronomy Department A114: Lecture 27 18 Apr 2007 Read: Ch. 25,26 Astronomy 114 1/23 Announcements Quiz #2: we re

More information

Jodrell Bank Discovery Centre

Jodrell 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 information

Thermal Equilibrium in Nebulae 1. For an ionized nebula under steady conditions, heating and cooling processes that in

Thermal Equilibrium in Nebulae 1. For an ionized nebula under steady conditions, heating and cooling processes that in Thermal Equilibrium in Nebulae 1 For an ionized nebula under steady conditions, heating and cooling processes that in isolation would change the thermal energy content of the gas are in balance, such that

More information

Atomic Physics 3 ASTR 2110 Sarazin

Atomic Physics 3 ASTR 2110 Sarazin Atomic Physics 3 ASTR 2110 Sarazin Homework #5 Due Wednesday, October 4 due to fall break Test #1 Monday, October 9, 11-11:50 am Ruffner G006 (classroom) You may not consult the text, your notes, or any

More information

Galaxy Ecosystems Adam Leroy (OSU), Eric Murphy (NRAO/IPAC) on behalf of ngvla Working Group 2

Galaxy Ecosystems Adam Leroy (OSU), Eric Murphy (NRAO/IPAC) on behalf of ngvla Working Group 2 Next Generation Very Large Array Working Group 2 HI in M74: Walter+ 08 CO in M51: Schinnerer+ 13 Continuum in M82: Marvil & Owen Galaxy Ecosystems Adam Leroy (OSU), Eric Murphy (NRAO/IPAC) on behalf of

More information

Spectroscopy and Molecular Emission. Fundamental Probes of Cold Gas

Spectroscopy and Molecular Emission. Fundamental Probes of Cold Gas Spectroscopy and Molecular Emission Fundamental Probes of Cold Gas Atomic Lines Few atoms have fine structure transitions at low enough energy levels to emit at radiofrequencies Important exceptions HI

More information

The Interstellar Medium

The Interstellar Medium http://www.strw.leidenuniv.nl/~pvdwerf/teaching/ The Interstellar Medium Lecturer: Dr. Paul van der Werf Fall 2014 Oortgebouw 565, ext 5883 pvdwerf@strw.leidenuniv.nl Assistant: Kirstin Doney Huygenslaboratorium

More information

1. Why photons? 2. Photons in a vacuum

1. Why photons? 2. Photons in a vacuum Photons and Other Messengers 1. Why photons? Ask class: most of our information about the universe comes from photons. What are the reasons for this? Let s compare them with other possible messengers,

More information

Physics H7C Midterm 2 Solutions

Physics H7C Midterm 2 Solutions Physics H7C Midterm 2 Solutions Eric Dodds 21 November, 2013 1 Qualitative questions a) The angular resolution of a space based telescope is limited by the wave properties of light, that is, by diffraction.

More information

Active Galactic Nuclei

Active 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 information

6: Observing Warm Phases: Dispersion ( n e dl ) & Emission ( n

6: Observing Warm Phases: Dispersion ( n e dl ) & Emission ( n 6: Observing Warm Phases: Dispersion ( n e dl ) & Emission ( n 2 e dl ) Measure James R. Graham University of California Berkeley NGC 891 NGC 891 AY 216 2 Techniques & Components The Warm Ionized Medium

More information

Review 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 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 information

M.Phys., M.Math.Phys., M.Sc. MTP Radiative Processes in Astrophysics and High-Energy Astrophysics

M.Phys., M.Math.Phys., M.Sc. MTP Radiative Processes in Astrophysics and High-Energy Astrophysics M.Phys., M.Math.Phys., M.Sc. MTP Radiative Processes in Astrophysics and High-Energy Astrophysics Professor Garret Cotter garret.cotter@physics.ox.ac.uk Office 756 in the DWB & Exeter College Radiative

More information

6. Interstellar Medium. Emission nebulae are diffuse patches of emission surrounding hot O and

6. Interstellar Medium. Emission nebulae are diffuse patches of emission surrounding hot O and 6-1 6. Interstellar Medium 6.1 Nebulae Emission nebulae are diffuse patches of emission surrounding hot O and early B-type stars. Gas is ionized and heated by radiation from the parent stars. In size,

More information

Temperature Scales and Telescope Efficiencies

Temperature Scales and Telescope Efficiencies Temperature Scales and Telescope Efficiencies Jeff Mangum (NRAO) April 11, 2006 Contents 1 Introduction 1 2 Definitions 1 2.1 General Terms.................................. 2 2.2 Efficiencies....................................

More information

Lecture 2: Transfer Theory

Lecture 2: Transfer Theory Lecture 2: Transfer Theory Why do we study transfer theory? The light we detect arrives at us in two steps: - first, it is created by some radiative process (e.g., blackbody, synchrotron, etc etc ) -

More information

Astronomy 242: Review Questions #3 Distributed: April 29, 2016

Astronomy 242: Review Questions #3 Distributed: April 29, 2016 Astronomy 242: Review Questions #3 Distributed: April 29, 2016 Review the questions below, and be prepared to discuss them in class next week. Modified versions of some of these questions will be used

More information

OPTI 511R, Spring 2018 Problem Set 10 Prof. R.J. Jones Due Thursday, April 19

OPTI 511R, Spring 2018 Problem Set 10 Prof. R.J. Jones Due Thursday, April 19 OPTI 511R, Spring 2018 Problem Set 10 Prof. R.J. Jones Due Thursday, April 19 1. (a) Suppose you want to use a lens focus a Gaussian laser beam of wavelength λ in order to obtain a beam waist radius w

More information

The formation of stars and planets. Day 1, Topic 2: Radiation physics. Lecture by: C.P. Dullemond

The formation of stars and planets. Day 1, Topic 2: Radiation physics. Lecture by: C.P. Dullemond The formation of stars and planets Day 1, Topic 2: Radiation physics Lecture by: C.P. Dullemond Astronomical Constants CGS units used throughout lecture (cm,erg,s...) AU = Astronomical Unit = distance

More information

Spontaneous Emission, Stimulated Emission, and Absorption

Spontaneous Emission, Stimulated Emission, and Absorption Chapter Six Spontaneous Emission, Stimulated Emission, and Absorption In this chapter, we review the general principles governing absorption and emission of radiation by absorbers with quantized energy

More information

X-ray Radiation, Absorption, and Scattering

X-ray Radiation, Absorption, and Scattering X-ray Radiation, Absorption, and Scattering What we can learn from data depend on our understanding of various X-ray emission, scattering, and absorption processes. We will discuss some basic processes:

More information

Galactic Structure Mapping through 21cm Hyperfine Transition Line

Galactic Structure Mapping through 21cm Hyperfine Transition Line Galactic Structure Mapping through 21cm Hyperfine Transition Line Henry Shackleton MIT Department of Physics (Dated: May 14, 2017) Using a Small Radio Telescope (SRT), we measure electromagnetic radiation

More information

Understanding the early stages of star formation in Perseus using CS and N 2 H + tracers

Understanding the early stages of star formation in Perseus using CS and N 2 H + tracers Understanding the early stages of star formation in Perseus using CS and N 2 H + tracers Sebastien GUILLOT September 17, 2006 Harvard-Smithsonian Center For Astrophysics Work Term supervisors: Pr. Paola

More information

Interstellar Medium and Star Birth

Interstellar Medium and Star Birth Interstellar Medium and Star Birth Interstellar dust Lagoon nebula: dust + gas Interstellar Dust Extinction and scattering responsible for localized patches of darkness (dark clouds), as well as widespread

More information

HOW TO GET LIGHT FROM THE DARK AGES

HOW TO GET LIGHT FROM THE DARK AGES HOW TO GET LIGHT FROM THE DARK AGES Anthony Smith Lunar Seminar Presentation 2/2/2010 OUTLINE Basics of Radio Astronomy Why go to the moon? What should we find there? BASICS OF RADIO ASTRONOMY Blackbody

More information

Synchrotron Radiation II

Synchrotron Radiation II Synchrotron Radiation II Cyclotron v

More information

Astronomy 203 practice final examination

Astronomy 203 practice final examination Astronomy 203 practice final examination Fall 1999 If this were a real, in-class examination, you would be reminded here of the exam rules, which are as follows: You may consult only one page of formulas

More information

If we see a blueshift on one side and a redshift on the other, this is a sign of rotation.

If we see a blueshift on one side and a redshift on the other, this is a sign of rotation. Galaxies : dynamics, masses, and formation Prof Andy Lawrence Astronomy 1G 2011-12 Overview Spiral galaxies rotate; this allows us to measure masses But there is also a problem : spiral arm winding Elliptical

More information

Radiation processes and mechanisms in astrophysics I. R Subrahmanyan Notes on ATA lectures at UWA, Perth 18 May 2009

Radiation processes and mechanisms in astrophysics I. R Subrahmanyan Notes on ATA lectures at UWA, Perth 18 May 2009 Radiation processes and mechanisms in astrophysics I R Subrahmanyan Notes on ATA lectures at UWA, Perth 18 May 009 Light of the night sky We learn of the universe around us from EM radiation, neutrinos,

More information

3: Interstellar Absorption Lines: Radiative Transfer in the Interstellar Medium. James R. Graham University of California, Berkeley

3: Interstellar Absorption Lines: Radiative Transfer in the Interstellar Medium. James R. Graham University of California, Berkeley 3: Interstellar Absorption Lines: Radiative Transfer in the Interstellar Medium James R. Graham University of California, Berkeley Interstellar Absorption Lines Example of atomic absorption lines Structure

More information

Chemistry 795T. Lecture 7. Electromagnetic Spectrum Black body Radiation. NC State University

Chemistry 795T. Lecture 7. Electromagnetic Spectrum Black body Radiation. NC State University Chemistry 795T Lecture 7 Electromagnetic Spectrum Black body Radiation NC State University Black body Radiation An ideal emitter of radiation is called a black body. Observation: that peak of the energy

More information

Chemistry 795T. Black body Radiation. The wavelength and the frequency. The electromagnetic spectrum. Lecture 7

Chemistry 795T. Black body Radiation. The wavelength and the frequency. The electromagnetic spectrum. Lecture 7 Chemistry 795T Lecture 7 Electromagnetic Spectrum Black body Radiation NC State University Black body Radiation An ideal emitter of radiation is called a black body. Observation: that peak of the energy

More information

Low Density Ionized Gas in the Inner Galaxy Interpretation of Recombination Line Observations at 325 MHz

Low Density Ionized Gas in the Inner Galaxy Interpretation of Recombination Line Observations at 325 MHz J. Astrophys. Astr. (1985) 6, 203 226 Low Density Ionized Gas in the Inner Galaxy Interpretation of Recombination Line Observations at 325 MHz K. R. Anantharamaiah Raman Research Institute, Bangalore 560080

More information

Astrophysics of Gaseous Nebulae and Active Galactic Nuclei

Astrophysics of Gaseous Nebulae and Active Galactic Nuclei SECOND EDITION Astrophysics of Gaseous Nebulae and Active Galactic Nuclei Donald E. Osterbrock Lick Observatory, University of California, Santa Cruz Gary J. Ferland Department of Physics and Astronomy,

More information

Dark Matter. ASTR 333/433 Spring Today Stars & Gas. essentials about stuff we can see. First Homework on-line Due Feb. 4

Dark Matter. ASTR 333/433 Spring Today Stars & Gas. essentials about stuff we can see. First Homework on-line Due Feb. 4 Dark Matter ASTR 333/433 Spring 2016 Today Stars & Gas essentials about stuff we can see First Homework on-line Due Feb. 4 Galaxies are made of stars - D. Silva (1990) private communication Stars Majority

More information

A MULTI-TRANSITION SEARCH FOR CLASS I METHANOL MASERS

A MULTI-TRANSITION SEARCH FOR CLASS I METHANOL MASERS A MULTI-TRANSITION SEARCH FOR CLASS I METHANOL MASERS Cara Denise Battersby MIT Haystack Observatory REU Summer 2004 Mentors: Preethi Pratap and Phil Shute ABSTRACT Class I methanol masers have been detected

More information

Review: Properties of a wave

Review: Properties of a wave Radiation travels as waves. Waves carry information and energy. Review: Properties of a wave wavelength (λ) crest amplitude (A) trough velocity (v) λ is a distance, so its units are m, cm, or mm, etc.

More information

a few more introductory subjects : equilib. vs non-equil. ISM sources and sinks : matter replenishment, and exhaustion Galactic Energetics

a few more introductory subjects : equilib. vs non-equil. ISM sources and sinks : matter replenishment, and exhaustion Galactic Energetics Today : a few more introductory subjects : equilib. vs non-equil. ISM sources and sinks : matter replenishment, and exhaustion Galactic Energetics photo-ionization of HII assoc. w/ OB stars ionization

More information

Lecture 3: Specific Intensity, Flux and Optical Depth

Lecture 3: Specific Intensity, Flux and Optical Depth Lecture 3: Specific Intensity, Flux and Optical Depth We begin a more detailed look at stellar atmospheres by defining the fundamental variable, which is called the Specific Intensity. It may be specified

More information

Electromagnetic Spectra. AST443, Lecture 13 Stanimir Metchev

Electromagnetic Spectra. AST443, Lecture 13 Stanimir Metchev Electromagnetic Spectra AST443, Lecture 13 Stanimir Metchev Administrative Homework 2: problem 5.4 extension: until Mon, Nov 2 Reading: Bradt, chapter 11 Howell, chapter 6 Tenagra data: see bottom of Assignments

More information

80 2 Observational Cosmology L and the mean energy

80 2 Observational Cosmology L and the mean energy 80 2 Observational Cosmology fluctuations, short-wavelength modes have amplitudes that are suppressed because these modes oscillated as acoustic waves during the radiation epoch whereas the amplitude of

More information

Ay Fall 2004 Lecture 6 (given by Tony Travouillon)

Ay Fall 2004 Lecture 6 (given by Tony Travouillon) Ay 122 - Fall 2004 Lecture 6 (given by Tony Travouillon) Stellar atmospheres, classification of stellar spectra (Many slides c/o Phil Armitage) Formation of spectral lines: 1.excitation Two key questions:

More information

PROBLEM SET #1. Galactic Structure 37 pts total. due Tuesday, 2/19/2019

PROBLEM SET #1. Galactic Structure 37 pts total. due Tuesday, 2/19/2019 PROBLEM SET #1 Galactic Structure 37 pts total due Tuesday, 2/19/2019 1. Stellar cluster problem [26 pts] The following refers to a star cluster observed on Aug 15, 2010 at about 4am UT. The cluster is

More information

MASSACHUSETTS INSTITUTE OF TECHNOLOGY HAYSTACK OBSERVATORY WESTFORD, MASSACHUSETTS

MASSACHUSETTS INSTITUTE OF TECHNOLOGY HAYSTACK OBSERVATORY WESTFORD, MASSACHUSETTS VSRT MEMO #033 MASSACHUSETTS INSTITUTE OF TECHNOLOGY HAYSTACK OBSERVATORY WESTFORD, MASSACHUSETTS 01886 July 20, 2010 Updated April 9, 2012 Telephone: 781-981-5407 Fax: 781-981-0590 To: VSRT Group From:

More information

ASTR-1010: Astronomy I Course Notes Section IV

ASTR-1010: Astronomy I Course Notes Section IV ASTR-1010: Astronomy I Course Notes Section IV Dr. Donald G. Luttermoser Department of Physics and Astronomy East Tennessee State University Edition 2.0 Abstract These class notes are designed for use

More information

Synchrotron Radiation: II. Spectrum

Synchrotron Radiation: II. Spectrum Synchrotron Radiation: II. Spectrum Massimo Ricotti ricotti@astro.umd.edu University of Maryland Synchrotron Radiation: II. Spectrum p.1/18 ds=v dt_em dt=ds cos(theta)/c=v/c cos(theta)dt_em Synchrotron

More information

Neutral Gas. Chapter Absorption lines. Absorption coefficient. κ ν = c2 n l g u 8π ν 2 A ul 1 exp hν )] φ ul (ν) (3.1)

Neutral Gas. Chapter Absorption lines. Absorption coefficient. κ ν = c2 n l g u 8π ν 2 A ul 1 exp hν )] φ ul (ν) (3.1) Chapter 3 Neutral Gas 3.1 Absorption lines Absorption coefficient [ ( κ ν = c2 n l g u 8π ν 2 A ul 1 exp hν )] φ ul (ν) (3.1) g l k B T ex n l = number density of particles in lower state g u = statistical

More information

Class #4 11 September 2008

Class #4 11 September 2008 Class #4 11 September 2008 Review Stellar evolution/nucleosynthesis/h-r diagrams Phases of the Interstellar Medium The Hydrogen Atom H-R diagram for 47 Tuc Evolution+nucleosynt hesis each box is a different

More information

Lecture 6: Continuum Opacity and Stellar Atmospheres

Lecture 6: Continuum Opacity and Stellar Atmospheres Lecture 6: Continuum Opacity and Stellar Atmospheres To make progress in modeling and understanding stellar atmospheres beyond the gray atmosphere, it is necessary to consider the real interactions between

More information

High Redshift Universe

High Redshift Universe High Redshift Universe Finding high z galaxies Lyman break galaxies (LBGs) Photometric redshifts Deep fields Starburst galaxies Extremely red objects (EROs) Sub-mm galaxies Lyman α systems Finding high

More information

Active Galactic Nuclei

Active 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 information

Astrophysical Radiation Processes

Astrophysical Radiation Processes PHY3145 Topics in Theoretical Physics Astrophysical Radiation Processes 5:Synchrotron and Bremsstrahlung spectra Dr. J. Hatchell, Physics 406, J.Hatchell@exeter.ac.uk Course structure 1. Radiation basics.

More information