Distance Modulus
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The Hubble Constant H0 --- Describing How Fast the Universe Is Expanding A˙ (T) H(T) = , A(T) = the Cosmic Scale Factor A(T)
Determining H0 and q0 from Supernova Data LA-UR-11-03930 Mian Wang Henan Normal University, P.R. China Baolian Cheng Los Alamos National Laboratory PANIC11, 25 July, 2011,MIT, Cambridge, MA Abstract Since 1929 when Edwin Hubble showed that the Universe is expanding, extensive observations of redshifts and relative distances of galaxies have established the form of expansion law. Mapping the kinematics of the expanding universe requires sets of measurements of the relative size and age of the universe at different epochs of its history. There has been decades effort to get precise measurements of two parameters that provide a crucial test for cosmology models. The two key parameters are the rate of expansion, i.e., the Hubble constant (H0) and the deceleration in expansion (q0). These two parameters have been studied from the exceedingly distant clusters where redshift is large. It is indicated that the universe is made up by roughly 73% of dark energy, 23% of dark matter, and 4% of normal luminous matter; and the universe is currently accelerating. Recently, however, the unexpected faintness of the Type Ia supernovae (SNe) at low redshifts (z<1) provides unique information to the study of the expansion behavior of the universe and the determination of the Hubble constant. In this work, We present a method based upon the distance modulus redshift relation and use the recent supernova Ia data to determine the parameters H0 and q0 simultaneously. Preliminary results will be presented and some intriguing questions to current theories are also raised. Outline 1. Introduction 2. Model and data analysis 3. -
AS1001: Galaxies and Cosmology Cosmology Today Title Current Mysteries Dark Matter ? Dark Energy ? Modified Gravity ? Course
AS1001: Galaxies and Cosmology Keith Horne [email protected] http://www-star.st-and.ac.uk/~kdh1/eg/eg.html Text: Kutner Astronomy:A Physical Perspective Chapters 17 - 21 Cosmology Title Today • Blah Current Mysteries Course Outline Dark Matter ? • Galaxies (distances, components, spectra) Holds Galaxies together • Evidence for Dark Matter • Black Holes & Quasars Dark Energy ? • Development of Cosmology • Hubble’s Law & Expansion of the Universe Drives Cosmic Acceleration. • The Hot Big Bang Modified Gravity ? • Hot Topics (e.g. Dark Energy) General Relativity wrong ? What’s in the exam? Lecture 1: Distances to Galaxies • Two questions on this course: (answer at least one) • Descriptive and numeric parts • How do we measure distances to galaxies? • All equations (except Hubble’s Law) are • Standard Candles (e.g. Cepheid variables) also in Stars & Elementary Astrophysics • Distance Modulus equation • Lecture notes contain all information • Example questions needed for the exam. Use book chapters for more details, background, and problem sets A Brief History 1860: Herchsel’s view of the Galaxy • 1611: Galileo supports Copernicus (Planets orbit Sun, not Earth) COPERNICAN COSMOLOGY • 1742: Maupertius identifies “nebulae” • 1784: Messier catalogue (103 fuzzy objects) • 1864: Huggins: first spectrum for a nebula • 1908: Leavitt: Cepheids in LMC • 1924: Hubble: Cepheids in Andromeda MODERN COSMOLOGY • 1929: Hubble discovers the expansion of the local universe • 1929: Einstein’s General Relativity • 1948: Gamov predicts background radiation from “Big Bang” • 1965: Penzias & Wilson discover Cosmic Microwave Background BIG BANG THEORY ADOPTED • 1975: Computers: Big-Bang Nucleosynthesis ( 75% H, 25% He ) • 1985: Observations confirm BBN predictions Based on star counts in different directions along the Milky Way. -
Aspects of Spatially Homogeneous and Isotropic Cosmology
Faculty of Technology and Science Department of Physics and Electrical Engineering Mikael Isaksson Aspects of Spatially Homogeneous and Isotropic Cosmology Degree Project of 15 credit points Physics Program Date/Term: 02-04-11 Supervisor: Prof. Claes Uggla Examiner: Prof. Jürgen Fuchs Karlstads universitet 651 88 Karlstad Tfn 054-700 10 00 Fax 054-700 14 60 [email protected] www.kau.se Abstract In this thesis, after a general introduction, we first review some differential geom- etry to provide the mathematical background needed to derive the key equations in cosmology. Then we consider the Robertson-Walker geometry and its relation- ship to cosmography, i.e., how one makes measurements in cosmology. We finally connect the Robertson-Walker geometry to Einstein's field equation to obtain so- called cosmological Friedmann-Lema^ıtre models. These models are subsequently studied by means of potential diagrams. 1 CONTENTS CONTENTS Contents 1 Introduction 3 2 Differential geometry prerequisites 8 3 Cosmography 13 3.1 Robertson-Walker geometry . 13 3.2 Concepts and measurements in cosmography . 18 4 Friedmann-Lema^ıtre dynamics 30 5 Bibliography 42 2 1 INTRODUCTION 1 Introduction Cosmology comes from the Greek word kosmos, `universe' and logia, `study', and is the study of the large-scale structure, origin, and evolution of the universe, that is, of the universe taken as a whole [1]. Even though the word cosmology is relatively recent (first used in 1730 in Christian Wolff's Cosmologia Generalis), the study of the universe has a long history involving science, philosophy, eso- tericism, and religion. Cosmologies in their earliest form were concerned with, what is now known as celestial mechanics (the study of the heavens). -
Measurements and Numbers in Astronomy Astronomy Is a Branch of Science
Name: ________________________________Lab Day & Time: ____________________________ Measurements and Numbers in Astronomy Astronomy is a branch of science. You will be exposed to some numbers expressed in SI units, large and small numbers, and some numerical operations such as addition / subtraction, multiplication / division, and ratio comparison. Let’s watch part of an IMAX movie called Cosmic Voyage. https://www.youtube.com/watch?v=xEdpSgz8KU4 Powers of 10 In Astronomy, we deal with numbers that describe very large and very small things. For example, the mass of the Sun is 1,990,000,000,000,000,000,000,000,000,000 kg and the mass of a proton is 0.000,000,000,000,000,000,000,000,001,67 kg. Such numbers are very cumbersome and difficult to understand. It is neater and easier to use the scientific notation, or the powers of 10 notation. For large numbers: For small numbers: 1 no zero = 10 0 10 1 zero = 10 1 0.1 = 1/10 Divided by 10 =10 -1 100 2 zero = 10 2 0.01 = 1/100 Divided by 100 =10 -2 1000 3 zero = 10 3 0.001 = 1/1000 Divided by 1000 =10 -3 Example used on real numbers: 1,990,000,000,000,000,000,000,000,000,000 kg -> 1.99X1030 kg 0.000,000,000,000,000,000,000,000,001,67 kg -> 1.67X10-27 kg See how much neater this is! Now write the following in scientific notation. 1. 40,000 2. 9,000,000 3. 12,700 4. 380,000 5. 0.017 6. -
Methods of Measuring Astronomical Distances
LASER INTERFEROMETER GRAVITATIONAL WAVE OBSERVATORY - LIGO - =============================== LIGO SCIENTIFIC COLLABORATION Technical Note LIGO-T1200427{v1 2012/09/02 Methods of Measuring Astronomical Distances Sarah Gossan and Christian Ott California Institute of Technology Massachusetts Institute of Technology LIGO Project, MS 18-34 LIGO Project, Room NW22-295 Pasadena, CA 91125 Cambridge, MA 02139 Phone (626) 395-2129 Phone (617) 253-4824 Fax (626) 304-9834 Fax (617) 253-7014 E-mail: [email protected] E-mail: [email protected] LIGO Hanford Observatory LIGO Livingston Observatory Route 10, Mile Marker 2 19100 LIGO Lane Richland, WA 99352 Livingston, LA 70754 Phone (509) 372-8106 Phone (225) 686-3100 Fax (509) 372-8137 Fax (225) 686-7189 E-mail: [email protected] E-mail: [email protected] http://www.ligo.org/ LIGO-T1200427{v1 1 Introduction The determination of source distances, from solar system to cosmological scales, holds great importance for the purposes of all areas of astrophysics. Over all distance scales, there is not one method of measuring distances that works consistently, and as a result, distance scales must be built up step-by-step, using different methods that each work over limited ranges of the full distance required. Broadly, astronomical distance `calibrators' can be categorised as primary, secondary or tertiary, with secondary calibrated themselves by primary, and tertiary by secondary, thus compounding any uncertainties in the distances measured with each rung ascended on the cosmological `distance ladder'. Typically, primary calibrators can only be used for nearby stars and stellar clusters, whereas secondary and tertiary calibrators are employed for sources within and beyond the Virgo cluster respectively. -
PHAS 1102 Physics of the Universe 3 – Magnitudes and Distances
PHAS 1102 Physics of the Universe 3 – Magnitudes and distances Brightness of Stars • Luminosity – amount of energy emitted per second – not the same as how much we observe! • We observe a star’s apparent brightness – Depends on: • luminosity • distance – Brightness decreases as 1/r2 (as distance r increases) • other dimming effects – dust between us & star Defining magnitudes (1) Thus Pogson formalised the magnitude scale for brightness. This is the brightness that a star appears to have on the sky, thus it is referred to as apparent magnitude. Also – this is the brightness as it appears in our eyes. Our eyes have their own response to light, i.e. they act as a kind of filter, sensitive over a certain wavelength range. This filter is called the visual band and is centred on ~5500 Angstroms. Thus these are apparent visual magnitudes, mv Related to flux, i.e. energy received per unit area per unit time Defining magnitudes (2) For example, if star A has mv=1 and star B has mv=6, then 5 mV(B)-mV(A)=5 and their flux ratio fA/fB = 100 = 2.512 100 = 2.512mv(B)-mv(A) where !mV=1 corresponds to a flux ratio of 1001/5 = 2.512 1 flux(arbitrary units) 1 6 apparent visual magnitude, mv From flux to magnitude So if you know the magnitudes of two stars, you can calculate mv(B)-mv(A) the ratio of their fluxes using fA/fB = 2.512 Conversely, if you know their flux ratio, you can calculate the difference in magnitudes since: 2.512 = 1001/5 log (f /f ) = [m (B)-m (A)] log 2.512 10 A B V V 10 = 102/5 = 101/2.5 mV(B)-mV(A) = !mV = 2.5 log10(fA/fB) To calculate a star’s apparent visual magnitude itself, you need to know the flux for an object at mV=0, then: mS - 0 = mS = 2.5 log10(f0) - 2.5 log10(fS) => mS = - 2.5 log10(fS) + C where C is a constant (‘zero-point’), i.e. -
The Distance to NGC 1316 \(Fornax
A&A 552, A106 (2013) Astronomy DOI: 10.1051/0004-6361/201220756 & c ESO 2013 Astrophysics The distance to NGC 1316 (Fornax A): yet another curious case,, M. Cantiello1,A.Grado2, J. P. Blakeslee3, G. Raimondo1,G.DiRico1,L.Limatola2, E. Brocato1,4, M. Della Valle2,6, and R. Gilmozzi5 1 INAF, Osservatorio Astronomico di Teramo, via M. Maggini snc, 64100 Teramo, Italy e-mail: [email protected] 2 INAF, Osservatorio Astronomico di Capodimonte, salita Moiariello, 80131 Napoli, Italy 3 Dominion Astrophysical Observatory, Herzberg Institute of Astrophysics, National Research Council of Canada, Victoria BC V82 3H3, Canada 4 INAF, Osservatorio Astronomico di Roma, via Frascati 33, Monte Porzio Catone, 00040 Roma, Italy 5 European Southern Observatory, Karl–Schwarzschild–Str. 2, 85748 Garching bei München, Germany 6 International Centre for Relativistic Astrophysics, Piazzale della Repubblica 2, 65122 Pescara, Italy Received 16 November 2012 / Accepted 14 February 2013 ABSTRACT Aims. The distance of NGC 1316, the brightest galaxy in the Fornax cluster, provides an interesting test for the cosmological distance scale. First, because Fornax is the second largest cluster of galaxies within 25 Mpc after Virgo and, in contrast to Virgo, has a small line-of-sight depth; and second, because NGC 1316 is the single galaxy with the largest number of detected Type Ia supernovae (SNe Ia), giving the opportunity to test the consistency of SNe Ia distances both internally and against other distance indicators. Methods. We measure surface brightness fluctuations (SBF) in NGC 1316 from ground- and space-based imaging data. The sample provides a homogeneous set of measurements over a wide wavelength interval. -
Observational Cosmology - 30H Course 218.163.109.230 Et Al
Observational cosmology - 30h course 218.163.109.230 et al. (2004–2014) PDF generated using the open source mwlib toolkit. See http://code.pediapress.com/ for more information. PDF generated at: Thu, 31 Oct 2013 03:42:03 UTC Contents Articles Observational cosmology 1 Observations: expansion, nucleosynthesis, CMB 5 Redshift 5 Hubble's law 19 Metric expansion of space 29 Big Bang nucleosynthesis 41 Cosmic microwave background 47 Hot big bang model 58 Friedmann equations 58 Friedmann–Lemaître–Robertson–Walker metric 62 Distance measures (cosmology) 68 Observations: up to 10 Gpc/h 71 Observable universe 71 Structure formation 82 Galaxy formation and evolution 88 Quasar 93 Active galactic nucleus 99 Galaxy filament 106 Phenomenological model: LambdaCDM + MOND 111 Lambda-CDM model 111 Inflation (cosmology) 116 Modified Newtonian dynamics 129 Towards a physical model 137 Shape of the universe 137 Inhomogeneous cosmology 143 Back-reaction 144 References Article Sources and Contributors 145 Image Sources, Licenses and Contributors 148 Article Licenses License 150 Observational cosmology 1 Observational cosmology Observational cosmology is the study of the structure, the evolution and the origin of the universe through observation, using instruments such as telescopes and cosmic ray detectors. Early observations The science of physical cosmology as it is practiced today had its subject material defined in the years following the Shapley-Curtis debate when it was determined that the universe had a larger scale than the Milky Way galaxy. This was precipitated by observations that established the size and the dynamics of the cosmos that could be explained by Einstein's General Theory of Relativity. -
Lecture 12: Galaxy Evolution
Lecture 12: Galaxy Evolution • An empirically driven subject: – The Mass versus Age plot of all surveys • Completing the local census: – New dwarf galaxies in the local group – The dwarf galaxy problem • Comparative evolution: – Luminosity function evolution • Luminosity evolution • Number evolution • Practicalities – K-correction – Dust Galaxies – AS 3011 1 MASS ASSEMBLY V. SMOOTH NO METALS V. LUMPY, METAL RICH Galaxies – AS 3011 2 1 The Mass-Age plot 1. Completing the local census 2. Comparative studies Galaxies – AS 3011 3 Dwarf galaxies • Dwarf galaxies are a crucial part of the galaxy evolution puzzle but we know very little about them. • Main theory (see later) proposes that galaxies built-up from smaller units through repeated merging. • Numerical simulations typically predict several thousand dark matter haloes in the local group. • ~ 55 Local Group galaxies known. • ~ 1 new Local Group dwarf galaxy discovered every 18 months. • Very wide range of properties = a combination of late- starters, relics, debris and stunted systems. • Space-density extremely poorly constrained, I.e., important to appreciate that our current backyard census is woefully incomplete. Galaxies – AS 3011 4 2 2 New Local Group galaxies discovered recently… • Bootes • Mv=-5.7 mag • µo=28.1 mag/sq arcsec • Belokurov et al (2006) • Canes Venatici • MV=-7.9 mag • µo=27.8 mag/sq arcsec • Zuker et al (2006) Galaxies – AS 3011 5 The Luminosity-Surface Brightness Plane Galaxies – AS 3011 6 3 Comparative studies • Many comparisons are possible, e.g., – Profile shapes – Gas, dust, plasma and stellar content – Fundamental plane and Faber-Jackson relation – Tully-Fischer relation – Star-formation rates – Line indices, metallicity and colours – Morphologies and luminosity-size relations – Overall and component luminosity functions • Main issues are sample selection bias and demonstrating that a comparison of the high and low z samples is valid, comprehensive and complete. -
The Distance to Andromeda
How to use the Virtual Observatory The Distance to Andromeda Florian Freistetter, ARI Heidelberg Introduction an can compare that value with the apparent magnitude m, which can be easily Measuring the distances to other celestial measured. Knowing, how bright the star is objects is difficult. For near objects, like the and how bright he appears, one can use moon and some planets, it can be done by the so called distance modulus: sending radio-signals and measure the time it takes for them to be reflected back to the m – M = -5 + 5 log r Earth. Even for near stars it is possible to get quite acurate distances by using the where r is the distance of the object parallax-method. measured in parsec (1 parsec is 3.26 lightyears or 31 trillion kilometers). But for distant objects, determining their distance becomes very difficult. From Earth, With this method, in 1923 Edwin Hubble we can only measure the apparant was able to observe Cepheids in the magnitude and not how bright they really Andromeda nebula and thus determine its are. A small, dim star that is close to the distance: it was indeed an object far outside Earth can appear to look the same as a the milky way and an own galaxy! large, bright star that is far away from Earth. Measuring the distance to As long as the early 20th century it was not Andrimeda with Aladin possible to resolve this major problem in distance determination. At this time, one To measure the distance to Andromeda was especially interested in determining the with Aladin, one first needs observational distance to the so called „nebulas“. -
The Distance Modulus in the Presence of Absorption Is Given by from Appendix 4 Table 3, We Have, for an A0V Star, Where the Magn
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 of the star? The distance modulus in the presence of absorption is given by mM–5= logd– 5 + A From Appendix 4 Table 3, we have, for an A0V star, M = 0.6 BV–0= where the magnitudes and absorption are in the visual (V) band. Therefore, the color excess is 1.5−0=1.5, and so A=3×1.5=4.5. This gives m==0.6+ 5log 100 – 5 + 4.5 10.1 for the apparent magnitude. Problem 3: Imagine that all of the Sun’s mass is concentrated in a thin spherical shell at the Sun’s radius. Imagine further that the Sun is powered by this mass slowly falling piece by piece into a black hole at the center of the sphere. If 100% of this energy is radiated away from the surface of the Sun, calculate the lifetime of the Sun, given its observed luminosity. Comment on your answer. If a small bit of mass ∆m falls from a radius r onto a radius R, then the energy released is given by GM∆m GM∆m GM∆m ∆E = – ------------------ –– ------------------ ≈ ------------------ r R R where, in this case, the black hole radius R is much smaller than the Sun’s radius r. 2 Using the Schwarzschild radius R=2GM/c for the black hole, we calculate the luminosity as ∆ E GM ∆ m 1 ∆ m L ==------- --------------------------- -------- =--- -------- c 2 ∆ t ()2GM ⁄c2∆ t 2 ∆ t This is precisely the same relationship used when we studied Cygnus X-1 and also appeared on the second class exam. -
Studying the Ultraviolet Spectrum of the First Spectroscopically Confirmed Supernova at Redshift
The Astrophysical Journal, 854:37 (14pp), 2018 February 10 https://doi.org/10.3847/1538-4357/aaa126 © 2018. The American Astronomical Society. All rights reserved. Studying the Ultraviolet Spectrum of the First Spectroscopically Confirmed Supernova at Redshift Two M. Smith1 , M. Sullivan1 , R. C. Nichol2, L. Galbany3 ,C.B.D’Andrea4, C. Inserra1 , C. Lidman5,6 , A. Rest7,8, M. Schirmer9 , A. V. Filippenko10,11 , W. Zheng10, S. Bradley Cenko12 , C. R. Angus1, P. J. Brown13,14 , T. M. Davis5,15, D. A. Finley16, R. J. Foley17, S. González-Gaitán18,19 , C. P. Gutiérrez1 , R. Kessler20,21 , S. Kuhlmann22, J. Marriner16, A. Möller5,23, P. E. Nugent10,24 , S. Prajs1 , R. Thomas24, R. Wolf4, A. Zenteno25, T. M. C. Abbott25, F. B. Abdalla26,27, S. Allam16, J. Annis16 , K. Bechtol28, A. Benoit-Lévy26,29,30, E. Bertin29,30, D. Brooks26 , D. L. Burke31,32 , A. Carnero Rosell33,34, M. Carrasco Kind35,36, J. Carretero37, F. J. Castander38 , M. Crocce38, C. E. Cunha31, L. N. da Costa33,34, C. Davis31, S. Desai39, H. T. Diehl16, P. Doel26,T.F.Eifler40,41, B. Flaugher16, P. Fosalba38, J. Frieman16,20, J. García-Bellido42 , E. Gaztanaga38, D. W. Gerdes43,44 , D. A. Goldstein10,24 , D. Gruen31,32 , R. A. Gruendl35,36 , J. Gschwend33,34, G. Gutierrez16, K. Honscheid45,46, D. J. James47 , M. W. G. Johnson36, K. Kuehn6 , N. Kuropatkin16,T.S.Li16, M. Lima33,48, M. A. G. Maia33,34, J. L. Marshall13,14 , P. Martini45,49 , F. Menanteau35,36, C. J. Miller43,44, R. Miquel37,50 , R. L. C. Ogando33,34, D.