The Cosmic Distance Scale
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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. -
The Impact of the Astro2010 Recommendations on Variable Star Science
The Impact of the Astro2010 Recommendations on Variable Star Science Corresponding Authors Lucianne M. Walkowicz Department of Astronomy, University of California Berkeley [email protected] phone: (510) 642–6931 Andrew C. Becker Department of Astronomy, University of Washington [email protected] phone: (206) 685–0542 Authors Scott F. Anderson, Department of Astronomy, University of Washington Joshua S. Bloom, Department of Astronomy, University of California Berkeley Leonid Georgiev, Universidad Autonoma de Mexico Josh Grindlay, Harvard–Smithsonian Center for Astrophysics Steve Howell, National Optical Astronomy Observatory Knox Long, Space Telescope Science Institute Anjum Mukadam, Department of Astronomy, University of Washington Andrej Prsa,ˇ Villanova University Joshua Pepper, Villanova University Arne Rau, California Institute of Technology Branimir Sesar, Department of Astronomy, University of Washington Nicole Silvestri, Department of Astronomy, University of Washington Nathan Smith, Department of Astronomy, University of California Berkeley Keivan Stassun, Vanderbilt University Paula Szkody, Department of Astronomy, University of Washington Science Frontier Panels: Stars and Stellar Evolution (SSE) February 16, 2009 Abstract The next decade of survey astronomy has the potential to transform our knowledge of variable stars. Stellar variability underpins our knowledge of the cosmological distance ladder, and provides direct tests of stellar formation and evolution theory. Variable stars can also be used to probe the fundamental physics of gravity and degenerate material in ways that are otherwise impossible in the laboratory. The computational and engineering advances of the past decade have made large–scale, time–domain surveys an immediate reality. Some surveys proposed for the next decade promise to gather more data than in the prior cumulative history of astronomy. -
Distances and Magnitudes Distance Measurements the Cosmic Distance
Distances and Magnitudes Prof Andy Lawrence Astronomy 1G 2011-12 Distance Measurements Astronomy 1G 2011-12 The cosmic distance ladder • Distance measurements in astronomy are a chain, with each type of measurement relative to the one before • The bottom rung is the Astronomical Unit (AU), the (mean) distance between the Earth and the Sun • Many distance estimates rely on the idea of a "standard candle" or "standard yardstick" Astronomy 1G 2011-12 Distances in the solar system • relative distances to planets given by periods + Keplers law (see Lecture-2) • distance to Venus measured by radar • Sun-Earth = 1 A.U. (average) • Sun-Jupiter = 5 A.U. (average) • Sun-Neptune = 30 A.U. (average) • Sun- Oort cloud (comets) ~ 50,000 A.U. • 1 A.U. = 1.496 x 1011 m Astronomy 1G 2011-12 Distances to nearest stars • parallax against more distant non- moving stars • 1 parsec (pc) is defined as distance where parallax = 1 second of arc in standard units D = a/✓ (radians, metres) in AU and arcsec D(AU) = 1/✓rad = 206, 265/✓00 in parsec and arcsec D(pc) = 1/✓00 nearest star Proxima Centauri 1.30pc Very hard to measure less than 0.1" 1pc = 206,265 AU = 3.086 x 1016m so only good for stars a few parsecs away... until launch of GAIA mission in 2014..... Astronomy 1G 2011-12 More distant stars : standard candle technique If a star has luminosity L (total energy emitted per sec) then at L distance D we will observe flux density F (i.e. energy per second F = 2 per sq.m. -
Standard Candles in Cosmology
Standard Candles: Distance Measurement in Astronomy Farley V. Ferrante Southern Methodist University 5/3/2017 PHYS 3368: Principles of Astrophysics & Cosmology 1 OUTLINE • Cosmic Distance Ladder • Standard Candles Parallax Cepheid variables Planetary nebula Most luminous supergiants Most luminous globular clusters Most luminous H II regions Supernovae Hubble constant & red shift • Standard Model of Cosmology 5/3/2017 PHYS 3368: Principles of Astrophysics & Cosmology 2 The Cosmic Distance Ladder - Distances far too vast to be measured directly - Several methods of indirect measurement - Clever methods relying on careful observation and basic mathematics - Cosmic distance ladder: A progression of indirect methods which scale, overlap, & calibrate parameters for large distances in terms of smaller distances • More methods calibrate these distances until distances that can be measured directly are achieved 5/3/2017 PHYS 3368: Principles of Astrophysics & Cosmology 3 Standard Candles • Magnitude: Historical unit (Hipparchus) of stellar brightness such that 5 magnitudes represents a factor of 100 in intensity • Apparent magnitude: Number assigned to visual brightness of an object; originally a scale of 1-6 • Absolute magnitude: Magnitude an object would have at 10 pc (convenient distance for comparison) • List of most luminous stars 5/3/2017 PHYS 3368: Principles of Astrophysics & Cosmology 4 5/3/2017 PHYS 3368: Principles of Astrophysics & Cosmology 5 The Cosmic Distance Ladder 5/3/2017 PHYS 3368: Principles of Astrophysics & Cosmology 6 The -
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. -
5. Cosmic Distance Ladder Ii: Standard Candles
5. COSMIC DISTANCE LADDER II: STANDARD CANDLES EQUIPMENT Computer with internet connection GOALS In this lab, you will learn: 1. How to use RR Lyrae variable stars to measures distances to objects within the Milky Way galaxy. 2. How to use Cepheid variable stars to measure distances to nearby galaxies. 3. How to use Type Ia supernovae to measure distances to faraway galaxies. 1 BACKGROUND A. MAGNITUDES Astronomers use apparent magnitudes , which are often referred to simply as magnitudes, to measure brightness: The more negative the magnitude, the brighter the object. The more positive the magnitude, the fainter the object. In the following tutorial, you will learn how to measure, or photometer , uncalibrated magnitudes: http://skynet.unc.edu/ASTR101L/videos/photometry/ 2 In Afterglow, go to “File”, “Open Image(s)”, “Sample Images”, “Astro 101 Lab”, “Lab 5 – Standard Candles”, “CD-47” and open the image “CD-47 8676”. Measure the uncalibrated magnitude of star A: uncalibrated magnitude of star A: ____________________ Uncalibrated magnitudes are always off by a constant and this constant varies from image to image, depending on observing conditions among other things. To calibrate an uncalibrated magnitude, one must first measure this constant, which we do by photometering a reference star of known magnitude: uncalibrated magnitude of reference star: ____________________ 3 The known, true magnitude of the reference star is 12.01. Calculate the correction constant: correction constant = true magnitude of reference star – uncalibrated magnitude of reference star correction constant: ____________________ Finally, calibrate the uncalibrated magnitude of star A by adding the correction constant to it: calibrated magnitude = uncalibrated magnitude + correction constant calibrated magnitude of star A: ____________________ The true magnitude of star A is 13.74. -
Astronomy (ASTR) 1
Astronomy (ASTR) 1 ASTR 330 The Cosmic Distance Scale 3 Credit Hours ASTRONOMY (ASTR) An exploration of the cosmic distance ladder focusing on the systems and techniques that astronomers use in establishing the distances to ASTR 130 Introduction to Astronomy 3 Credit Hours celestial objects. Direct measures using radar ranging and trigonometric A one-term introduction for those interested in learning about the present parallax will be discussed for objects in the solar system and for stars state of knowledge of the Universe, its origin, evolution, organization, within about 3000 light-years of the Sun, respectively. For more remote and ultimate fate. Exciting new discoveries concerning extrasolar systems in or just outside the Milky Way, methods based spectroscopic planets, star birth, supermassive black holes, dark matter/dark energy, parallax and the period-luminosity relation for various types of variable and cosmology are discussed. Two years of high school math or its stars will be introduced. For the extra-galactic objects, use of the Hubble equivalent recommended. relation and the light curves of Type Ia supernovae will be made to assess ASTR 131 Introductory Astronomy Lab 1 Credit Hour the distances. At each rung of the ladder, emphasis will be placed on the An introduction to some of the important observational techniques and astrophysical principles and processes underlying the methodology being analytical methods used by astronomers. Ground-based and satellite applied. 3 hours lecture data will be used to reveal physical and chemical properties of the moon, Prerequisite(s): (MATH 113 or MATH 115) and (PHYS 126 or PHYS 151) planets, stars, and the Milky Way. -
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. -
Cosmic Distance Ladder
Cosmic Distance Ladder How do we know the distances to objects in space? Jason Nishiyama Cosmic Distance Ladder Space is vast and the techniques of the cosmic distance ladder help us measure that vastness. Units of Distance Metre (m) – base unit of SI. 11 Astronomical Unit (AU) - 1.496x10 m 15 Light Year (ly) – 9.461x10 m / 63 239 AU 16 Parsec (pc) – 3.086x10 m / 3.26 ly Radius of the Earth Eratosthenes worked out the size of the Earth around 240 BCE Radius of the Earth Eratosthenes used an observation and simple geometry to determine the Earth's circumference He noted that on the summer solstice that the bottom of wells in Alexandria were in shadow While wells in Syene were lit by the Sun Radius of the Earth From this observation, Eratosthenes was able to ● Deduce the Earth was round. ● Using the angle of the shadow, compute the circumference of the Earth! Out to the Solar System In the early 1500's, Nicholas Copernicus used geometry to determine orbital radii of the planets. Planets by Geometry By measuring the angle of a planet when at its greatest elongation, Copernicus solved a triangle and worked out the planet's distance from the Sun. Kepler's Laws Johann Kepler derived three laws of planetary motion in the early 1600's. One of these laws can be used to determine the radii of the planetary orbits. Kepler III Kepler's third law states that the square of the planet's period is equal to the cube of their distance from the Sun. -
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. -
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“.