STIS Survey of Far-Ultraviolet Coronal Forbidden Lines In
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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). -
Surface Curvature-Quantized Energy and Forcefield in Geometrochemical Physics
Title: Surface curvature-quantized energy and forcefield in geometrochemical physics Author: Z. R. Tian, Univ. of Arkansas, Fayetteville, AR 72701, USA, (Email) [email protected]. Text: Most recently, simple-shape particles’ surface area-to-volume ratio has been quantized into a geometro-wavenumber (Geo), or geometro-energy (EGeo) hcGeo, to quantitatively predict and compare nanoparticles (NPs), ions, and atoms geometry- quantized properties1,2. These properties range widely, from atoms’ electronegativity (EN) and ionization potentials to NPs’ bonding energy, atomistic nature, chemical potential of formation, redox potential, surface adsorbates’ stability, and surface defects’ reactivity. For countless irregular- or complex-shaped molecules, clusters, and NPs whose Geo values are uneasy to calculate, however, the EGeo application seems limited. This work has introduced smaller surfaces’ higher curvature-quantized energy and forcefield for linking quantum mechanics, thermodynamics, electromagnetics, and Newton’s mechanics with Einstein’s general relativity. This helps quantize the gravity, gravity-counterbalancing levity, and Einstein’s spacetime, geometrize Heisenberg’s Uncertainty, and support many known theories consistently for unifying naturally the energies and forcefields in physics, chemistry, and biology. Firstly, let’s quantize shaper corners’ 1.24 (keVnm). Indeed, smaller atoms’ higher and edges’ greater surface curvature (1/r) into EN and smaller 0-dimensional (0D) NPs’ a spacetime wavenumber (ST), i.e. Spacetime lower melting point (Tm) and higher (i.e. Energy (EST) = hc(ST) = hc(1/r) (see the Fig. more blue-shifted) optical bandgap (EBG) (see 3 below), where the r = particle radius, h = the Supplementary Table S1)3-9 are linearly Planck constant, c = speed of light, and hc governed by their greater (1/r) i.e. -
Gravitational Redshift/Blueshift of Light Emitted by Geodesic
Eur. Phys. J. C (2021) 81:147 https://doi.org/10.1140/epjc/s10052-021-08911-5 Regular Article - Theoretical Physics Gravitational redshift/blueshift of light emitted by geodesic test particles, frame-dragging and pericentre-shift effects, in the Kerr–Newman–de Sitter and Kerr–Newman black hole geometries G. V. Kraniotisa Section of Theoretical Physics, Physics Department, University of Ioannina, 451 10 Ioannina, Greece Received: 22 January 2020 / Accepted: 22 January 2021 / Published online: 11 February 2021 © The Author(s) 2021 Abstract We investigate the redshift and blueshift of light 1 Introduction emitted by timelike geodesic particles in orbits around a Kerr–Newman–(anti) de Sitter (KN(a)dS) black hole. Specif- General relativity (GR) [1] has triumphed all experimental ically we compute the redshift and blueshift of photons that tests so far which cover a wide range of field strengths and are emitted by geodesic massive particles and travel along physical scales that include: those in large scale cosmology null geodesics towards a distant observer-located at a finite [2–4], the prediction of solar system effects like the perihe- distance from the KN(a)dS black hole. For this purpose lion precession of Mercury with a very high precision [1,5], we use the killing-vector formalism and the associated first the recent discovery of gravitational waves in Nature [6–10], integrals-constants of motion. We consider in detail stable as well as the observation of the shadow of the M87 black timelike equatorial circular orbits of stars and express their hole [11], see also [12]. corresponding redshift/blueshift in terms of the metric physi- The orbits of short period stars in the central arcsecond cal black hole parameters (angular momentum per unit mass, (S-stars) of the Milky Way Galaxy provide the best current mass, electric charge and the cosmological constant) and the evidence for the existence of supermassive black holes, in orbital radii of both the emitter star and the distant observer. -
A Stellar Flare-Coronal Mass Ejection Event Revealed by X-Ray Plasma Motions
A stellar flare-coronal mass ejection event revealed by X-ray plasma motions C. Argiroffi1,2⋆, F. Reale1,2, J. J. Drake3, A. Ciaravella2, P. Testa3, R. Bonito2, M. Miceli1,2, S. Orlando2, and G. Peres1,2 1 University of Palermo, Department of Physics and Chemistry, Piazza del Parlamento 1, 90134, Palermo, Italy. 2 INAF - Osservatorio Astronomico di Palermo, Piazza del Parlamento 1, 90134, Palermo, Italy. 3 Smithsonian Astrophysical Observatory, MS-3, 60 Garden Street, Cambridge, MA 02138, USA. ⋆ costanza.argiroffi@unipa.it May 28, 2019 Coronal mass ejections (CMEs), often associ- transported along the magnetic field lines and heats ated with flares 1,2,3, are the most powerful mag- the underlying chromosphere, that expands upward netic phenomena occurring on the Sun. Stars at hundreds of kms−1, filling the overlying magnetic show magnetic activity levels up to 104 times structure (flare rising phase). Then this plasma gradu- higher 4, and CME effects on stellar physics and ally cools down radiatively and conductively (flare de- circumstellar environments are predicted to be cay). The flare magnetic drivers often cause also large- significant 5,6,7,8,9. However, stellar CMEs re- scale expulsions of previously confined plasma, CMEs, main observationally unexplored. Using time- that carry away large amounts of mass and energy. resolved high-resolution X-ray spectroscopy of a Solar observations demonstrate that CME occurrence, stellar flare on the active star HR 9024 observed mass, and kinetic energy increase with increasing flare with Chandra/HETGS, we distinctly detected energy 1,2, corroborating the flare-CME link. Doppler shifts in S xvi, Si xiv, and Mg xii lines Active stars have stronger magnetic fields, higher that indicate upward and downward motions of flare energies, hotter and denser coronal plasma 12. -
Hertzsprung-Russell Diagram and Mass Distribution of Barium Stars ? A
Astronomy & Astrophysics manuscript no. HRD_Ba c ESO 2019 May 14, 2019 Hertzsprung-Russell diagram and mass distribution of barium stars ? A. Escorza1; 2, H.M.J. Boffin3, A.Jorissen2, S. Van Eck2, L. Siess2, H. Van Winckel1, D. Karinkuzhi2, S. Shetye2; 1, and D. Pourbaix2 1 Institute of Astronomy, KU Leuven, Celestijnenlaan 200D, 3001 Leuven, Belgium 2 Institut d’Astronomie et d’Astrophysique, Université Libre de Bruxelles, ULB, Campus Plaine C.P. 226, Boulevard du Triomphe, B-1050 Bruxelles, Belgium 3 ESO, Karl Schwarzschild Straße 2, D-85748 Garching bei München, Germany Received; Accepted ABSTRACT With the availability of parallaxes provided by the Tycho-Gaia Astrometric Solution, it is possible to construct the Hertzsprung-Russell diagram (HRD) of barium and related stars with unprecedented accuracy. A direct result from the derived HRD is that subgiant CH stars occupy the same region as barium dwarfs, contrary to what their designations imply. By comparing the position of barium stars in the HRD with STAREVOL evolutionary tracks, it is possible to evaluate their masses, provided the metallicity is known. We used an average metallicity [Fe/H] = −0.25 and derived the mass distribution of barium giants. The distribution peaks around 2.5 M with a tail at higher masses up to 4.5 M . This peak is also seen in the mass distribution of a sample of normal K and M giants used for comparison and is associated with stars located in the red clump. When we compare these mass distributions, we see a deficit of low-mass (1 – 2 M ) barium giants. -
Observation of Exciton Redshift-Blueshift Crossover in Monolayer WS2
Observation of exciton redshift-blueshift crossover in monolayer WS2 E. J. Sie,1 A. Steinhoff,2 C. Gies,2 C. H. Lui,3 Q. Ma,1 M. Rösner,2,4 G. Schönhoff,2,4 F. Jahnke,2 T. O. Wehling,2,4 Y.-H. Lee,5 J. Kong,6 P. Jarillo-Herrero,1 and N. Gedik*1 1Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States 2Institut für Theoretische Physik, Universität Bremen, P.O. Box 330 440, 28334 Bremen, Germany 3Department of Physics and Astronomy, University of California, Riverside, California 92521, United States 4Bremen Center for Computational Materials Science, Universität Bremen, 28334 Bremen, Germany 5Materials Science and Engineering, National Tsing-Hua University, Hsinchu 30013, Taiwan 6Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States *Corresponding Author: [email protected] Abstract: We report a rare atom-like interaction between excitons in monolayer WS2, measured using ultrafast absorption spectroscopy. At increasing excitation density, the exciton resonance energy exhibits a pronounced redshift followed by an anomalous blueshift. Using both material-realistic computation and phenomenological modeling, we attribute this observation to plasma effects and an attraction-repulsion crossover of the exciton-exciton interaction that mimics the Lennard- Jones potential between atoms. Our experiment demonstrates a strong analogy between excitons and atoms with respect to inter-particle interaction, which holds promise to pursue the predicted liquid and crystalline phases of excitons in two-dimensional materials. Keywords: Monolayer WS2, exciton, plasma, Lennard-Jones potential, ultrafast optics, many- body theory Table of Contents Graphic Page 1 of 13 Main Text: Excitons in semiconductors are often perceived as the solid-state analogs to hydrogen atoms. -
Gravitational Redshift/Blueshift of Light Emitted by Geodesic Test Particles
Eur. Phys. J. C (2021) 81:147 https://doi.org/10.1140/epjc/s10052-021-08911-5 Regular Article - Theoretical Physics Gravitational redshift/blueshift of light emitted by geodesic test particles, frame-dragging and pericentre-shift effects, in the Kerr–Newman–de Sitter and Kerr–Newman black hole geometries G. V. Kraniotisa Section of Theoretical Physics, Physics Department, University of Ioannina, 451 10 Ioannina, Greece Received: 22 January 2020 / Accepted: 22 January 2021 © The Author(s) 2021 Abstract We investigate the redshift and blueshift of light 1 Introduction emitted by timelike geodesic particles in orbits around a Kerr–Newman–(anti) de Sitter (KN(a)dS) black hole. Specif- General relativity (GR) [1] has triumphed all experimental ically we compute the redshift and blueshift of photons that tests so far which cover a wide range of field strengths and are emitted by geodesic massive particles and travel along physical scales that include: those in large scale cosmology null geodesics towards a distant observer-located at a finite [2–4], the prediction of solar system effects like the perihe- distance from the KN(a)dS black hole. For this purpose lion precession of Mercury with a very high precision [1,5], we use the killing-vector formalism and the associated first the recent discovery of gravitational waves in Nature [6–10], integrals-constants of motion. We consider in detail stable as well as the observation of the shadow of the M87 black timelike equatorial circular orbits of stars and express their hole [11], see also [12]. corresponding redshift/blueshift in terms of the metric physi- The orbits of short period stars in the central arcsecond cal black hole parameters (angular momentum per unit mass, (S-stars) of the Milky Way Galaxy provide the best current mass, electric charge and the cosmological constant) and the evidence for the existence of supermassive black holes, in orbital radii of both the emitter star and the distant observer. -
Lecture 21: the Doppler Effect
Matthew Schwartz Lecture 21: The Doppler effect 1 Moving sources We’d like to understand what happens when waves are produced from a moving source. Let’s say we have a source emitting sound with the frequency ν. In this case, the maxima of the 1 amplitude of the wave produced occur at intervals of the period T = ν . If the source is at rest, an observer would receive these maxima spaced by T . If we draw the waves, the maxima are separated by a wavelength λ = Tcs, with cs the speed of sound. Now, say the source is moving at velocity vs. After the source emits one maximum, it moves a distance vsT towards the observer before it emits the next maximum. Thus the two successive maxima will be closer than λ apart. In fact, they will be λahead = (cs vs)T apart. The second maximum will arrive in less than T from the first blip. It will arrive with− period λahead cs vs Tahead = = − T (1) cs cs The frequency of the blips/maxima directly ahead of the siren is thus 1 cs 1 cs νahead = = = ν . (2) T cs vs T cs vs ahead − − In other words, if the source is traveling directly towards us, the frequency we hear is shifted c upwards by a factor of s . cs − vs We can do a similar calculation for the case in which the source is traveling directly away from us with velocity v. In this case, in between pulses, the source travels a distance T and the old pulse travels outwards by a distance csT . -
Module 14 H. R. Diagram TABLE of CONTENTS 1. Learning Outcomes
Module 14 H. R. Diagram TABLE OF CONTENTS 1. Learning Outcomes 2. Introduction 3. H. R. Diagram 3.1. Coordinates of H. R. Diagram 3.2. Stellar Families 3.3. Hertzsprung Gap 3.4. H. R. Diagram and Stellar Radii 4. Summary 1. Learning Outcomes After studying this module, you should be able to recognize an H. R. Diagram explain the coordinates of an H. R. Diagram appreciate the shape of an H. R. Diagram understand that in this diagram stars appear in distinct families recount the characteristics of these families recognize that there is a real gap in the horizontal branch of the diagram, called the Hertzsprung gap explain that during their evolution stars pass very rapidly through this region and therefore there is a real paucity of stars here derive the shape of the 퐥퐨퐠 푻 − 퐥퐨퐠 푳 plot at a given stellar radius explain that the stellar radius (and mass) increases upwards in the H. R. Diagram 2. Introduction In the last few modules we have discussed the stellar spectra and spectral classification based on stellar spectra. The Harvard system of spectral classification categorized stellar spectra in 7 major classes, from simple spectra containing only a few lines to spectra containing a huge number of lines and molecular bands. The major classes were named O, B, A, F, G, K and M. Each major class was further subdivided into 10 subclasses, running from 0 to 9. Considering the bewildering variety of stellar spectra, classes Q, P and Wolf-Rayet had to be introduced at the top of the classification and classes R and N were introduced at the bottom of the classification scheme. -
On the Effect of Global Cosmological Expansion on Local Dynamics
AEC ALBERT EINSTEIN CENTER FOR FUNDAMENTAL PHYSICS INSTITUTE FOR THEORETICAL PHYSICS On the Effect of Global Cosmological Expansion on Local Dynamics Masterarbeit der Philosophisch-naturwissenschaftlichen Fakultät der Universität Bern vorgelegt von Adrian Oeftiger im Frühjahr 2013 Leiter der Arbeit Prof. Dr. Matthias Blau Abstract Our Universe is subject to a global intrinsic expansion that becomes appar- ent e.g. when observing the redshift of distant galaxies or the cosmic mi- crowave background radiation. The Friedmann-Lemaître-Robertson-Walker metric approximately models this behaviour on large scales where galaxies are averaged out, i.e. the scale of galaxy superclusters and larger. How- ever, zooming into the more complex local structure in galaxies, solar sys- tems and even atoms, gravitational attraction and other fundamental forces dominate the situation. Throughout the course of this master thesis, the effect of global cosmological expansion on local dynamics will be examined in different frameworks: first, a Newtonian approach will provide for a ba- sic discussion of the phenomenon. Subsequently, the full general relativistic framework will be employed starting with the analysis of the Einstein-Straus vacuole. Finally, the thesis is rounded off by a study of the local dynamics in the k = 0 McVittie space-time, which depicts a mass-particle embedded in an expanding spatially flat cosmos. In each of these situations, the respec- tive predictions for the evolution of local binary systems are elaborated. The corresponding scales, from which on systems follow the Hubble flow, con- sistently indicate an apparent recession of intergalactic objects from proper distances of about 10 million light years on. -
Structure and Evolution of FK Comae Corona
A&A 383, 919–932 (2002) Astronomy DOI: 10.1051/0004-6361:20011810 & c ESO 2002 Astrophysics Structure and evolution of FK Comae corona P. Gondoin, C. Erd, and D. Lumb Space Science Department, European Space Agency – Postbus 299, 2200 AG Noordwijk, The Netherlands Received 16 October 2001 / Accepted 17 December 2001 Abstract. FK Comae (HD 117555) is a rapidly rotating single G giant whose distinctive characteristics include a quasisinusoidal optical light curve and high X-ray luminosity. FK Comae was observed twice at two weeks interval in January 2001 by the XMM-Newton space observatory. Analysis results suggest a scenario where the corona of FK Comae is dominated by large magnetic structures similar in size to interconnecting loops between solar active regions but significantly hotter. The interaction of these structures themselves could explain the permanent flaring activity on large scales that is responsible for heating FK Comae plasma to high temperatures. During our observations, these flares were not randomly distributed on the star surface but were partly grouped within a large compact region of about 30 degree extent in longitude reminiscent of a large photospheric spot. We argue that the α − Ω dynamo driven activity on FK Comae will disappear in the future with the effect of suppressing large scale magnetic structures in its corona. Key words. stars: individual: FK Comae – stars: activity – stars: coronae – stars: evolution – stars: late-type – X-ray: stars 1. Introduction ments and their temporal behaviour during the observa- tions. Sections 5 and 6 describe the spectral analysis of the FK Comae (HD 117555) is the prototype of a small group EPIC and RGS datasets. -
1) You Are Given a Ticket for Running a Red Traffic Light. for an Observer
1) You are given a ticket for running a red traffic light. For an observer halted at the red light, the light emits a wavelength λ0 = 700 nm. You tell the traffic cop that because you were approaching the light, the Doppler shift made it appear green (λ = 500 nm). How fast would you have been going if this smart-aleck explanation had been true? Please express this speed in units of miles per hour. [Hint: There are 1.6093 kilometers in a mile.] First, ∆λ = λ − λ0 = 500 nm − 700 nm = −200 nm. In words, the wavelength decreased by 200 nm, making it appear green (we would call this a blueshift). ∆λ < 0 implies that we’re moving toward the traffic light (as expected). This is a useful consistency check. By convention, if the relative velocity of two objects is negative (i.e., v < 0), then they are getting closer together. This is because the distance that separates them is decreasing as time goes on. Next we determine the driver’s velocity (v). The wavelength change is related to velocity by the following formula: ∆λ v = , λ0 c where ∆λ is the change in wavelength, λ0 is the wavelength at rest (in the lab), c is the speed of light, and v is radial velocity (along the line of sight). Multiplying both sides of the equation by c, we find: ∆λ v = c . λ0 Plugging in the numbers from above and c =3.0 × 105 km/s, we have: −200 nm −2 v = (3.0×105 km/s) = (3.0×105 km/s)× = −8.571×104 km/s 700 nm 7 Note that the units of wavelength (nm) canceled out.