DOCSLIB.ORG

Relativistic Dynamics and Extreme Mass Ratio Inspirals

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text

Load more

Living Rev Relativ (2018) 21:4 https://doi.org/10.1007/s41114-018-0013-8 REVIEW ARTICLE Relativistic dynamics and extreme mass ratio inspirals Pau Amaro-Seoane1,2,3,4 Received: 13 July 2017 / Accepted: 16 February 2018 © The Author(s) 2018 Abstract It is now well-established that a dark, compact object, very likely a massive black hole (MBH) of around four million solar masses is lurking at the centre of the Milky Way. While a consensus is emerging about the origin and growth of supermas- sive black holes (with masses larger than a billion solar masses), MBHs with smaller masses, such as the one in our galactic centre, remain understudied and enigmatic. The key to understanding these holes—how some of them grow by orders of magnitude in mass—lies in understanding the dynamics of the stars in the galactic neighbourhood. Stars interact with the central MBH primarily through their gradual inspiral due to the emission of gravitational radiation. Also stars produce gases which will subsequently be accreted by the MBH through collisions and disruptions brought about by the strong central tidal field. Such processes can contribute significantly to the mass of the MBH and progress in understanding them requires theoretical work in preparation for future gravitational radiation millihertz missions and X-ray observatories. In particular, a unique probe of these regions is the gravitational radiation that is emitted by some compact stars very close to the black holes and which could be surveyed by a milli- hertz gravitational-wave interferometer scrutinizing the range of masses fundamental to understanding the origin and growth of supermassive black holes. By extracting B Pau Amaro-Seoane [email protected] 1 Institute of Space Sciences (ICE, CSIC), Institut d’Estudis Espacials de Catalunya (IEEC) at Campus UAB, Carrer de Can Magrans s/n, 08193 Barcelona, Spain 2 Institute of Applied Mathematics, Academy of Mathematics and Systems Science, CAS, Beijing 100190, China 3 Kavli Institute for Astronomy and Astrophysics, Beijing 100871, China 4 Zentrum für Astronomie und Astrophysik, TU Berlin, Hardenbergstraße 36, 10623 Berlin, Germany 123 4 Page 2 of 150 P. Amaro-Seoane the information carried by the gravitational radiation, we can determine the mass and spin of the central MBH with unprecedented precision and we can determine how the holes “eat” stars that happen to be near them. Keywords Black holes · Gravitational waves · Stellar dynamics Glossary 1 M 1 solar mass = 1.99 × 1030 kg M• Mass of super- or massive black hole 1 pc 1 parsec ≈ 3.09 × 1016 m 1 Myr/Gyr One million/billion years AGN Active galactic nucleus BH Black hole CO Compact object (a white dwarf or a neutron star), or a stellar- mass black hole. In general, a collapsed star with a mass ∈ [1.4, 10] M in this work DCO Dark compact object DF Dynamical friction EMRI Extreme mass ratio inspiral GC Galactic centre GPU Graphics processing unit GW/GWs Gravitational wave/s HB Giant stars in the horizontal branch HST Hubble space telescope IMBH Intermediate-mass black hole (M ∈[102, 105] M) IMF Initial mass function IMRI Intermediate mass ratio inspiral LISA Laser interferometer space antenna LSO Last stable orbit MBH Massive black hole (M ≈ 106 M) MC Monte carlo MW Milky Way NB6 Direct-summation N-body6 NS Neutron star PN Post-Newtonian RG Red giant RMS Root mean square SMBH Super massive black hole (M > 106 M) SNR Signal-to-noise ratio SPH Smoothed particle hydronamics TDE Tidal disruption event UCD Ultra-compact dwarf galaxy z Redshift 123 Relativistic dynamics and extreme mass ratio inspirals Page 3 of 150 4 Contents Foreword .................................................. 1 Massive dark objects in galactic nuclei ................................. 1.1 Active galactic nuclei ........................................ 1.2 Massive black holes and their possible progenitors ......................... 1.3 Tidal disruptions ........................................... 1.4 Extreme mass ratio inspirals .................................... 2 GWs as a probe to stellar dynamics and the cosmic growth of SMBHs ................. 2.1 GWs and stellar dynamics ...................................... 2.2 The mystery of the growth of MBHs ................................ 2.3 A magnifying glass ......................................... 2.3.1 A problem of ∼ 10 orders of magnitude ........................... 2.4 How stars distribute around MBHs in galactic nuclei ........................ 3 A taxonomy of orbits in galactic nuclei ................................. 3.1 Spherical potentials ......................................... 3.2 Non-spherical potentials ...................................... 4 Two-body relaxation in galactic nuclei ................................. 4.1 Introduction ............................................. 4.2 Two-body relaxation ........................................ 4.3 Dynamical friction ......................................... 4.4 The difussion and loss-cone angles ................................. 5 “Standard” mass segregation ....................................... 5.1 Introduction ............................................. 5.2 Single-mass clusters ......................................... 5.3 Mass segregation in two mass-component clusters ......................... 5.4 Clusters with a broader mass spectrum with no MBH ....................... 5.5 Core-collapse evolution ....................................... 5.6 Clusters with a broader mass spectrum with a MBH ........................ 6 Two-body extreme mass ratio inspirals ................................. 6.1 A hidden stellar population in galactic nuclei ............................ 6.2 Fundamentals of EMRIs ...................................... 6.3 Orbital evolution due to emission of gravitational waves ...................... 6.4 Decoupling from dynamics into the relativistic regime ....................... 7 Beyond the standard model of two-body relaxation ........................... 7.1 The standard picture ......................................... 7.2 Coherent or resonant relaxation ................................... 7.3 Strong mass segregation ....................................... 7.4 The cusp at the Galactic Centre ................................... 7.5 Tidal separation of binaries ..................................... 7.6 A barrier for captures ignored by rotating MBHs .......................... 7.7 Extended stars EMRIs ........................................ 7.8 The butterfly effect ......................................... 7.9 Role of the gas ............................................ 8 Integration of dense stellar systems and EMRIs ............................. 8.1 Introduction ............................................. 8.2 The Fokker–Planck approach .................................... 8.3 Moment models ........................................... 8.3.1 Equation of continuity .................................... 8.3.2 Momentum balance equation ................................. 8.3.3 Radial energy equation .................................... 8.3.4 Tangential energy equation .................................. 8.4 Solving conducting, self-gravitating gas spheres .......................... 8.5 The local approximation ...................................... 8.6 Monte Carlo codes ......................................... 8.7 Applications of Monte Carlo and Fokker–Planck simulations to the EMRI problem ....... 8.8 Direct-summation N-body codes .................................. 123 4 Page 4 of 150 P. Amaro-Seoane 8.8.1 Relativistic corrections: the post-Newtonian approach .................... 8.8.2 Relativistic corrections: a geodesic solver .......................... 8.8.3 N-body units and conversion ................................. A Comment on the use of the Ancient Greek word barathron and bathron to refer to a black hole .... References .................................................. Foreword The volume where capture orbits are produced is so small in comparison to other typical length scales of interest in astrodynamics that it has usually been seen as unimportant and irrelevant to the global dynamical evolution of the system. The only exception has been the tidal disruption of stars by massive black holes. Only when it transpired that the slow, adiabatic inspiral of compact objects onto massive black holes provides us with valuable information, did astrophysicists start to address the question in more detail. Since the problem of EMRIs (extreme mass ratio inspiral) started to draw our attention, there has been a notable progress in answering fundamental questions of stellar dynamics. The discoveries have been numerous and some of them remain puzzling. The field is developing very quickly and we are making important breakthroughs even before a millihertz mission flies. When I was approached and asked to write this review, I was glad to accept it without realising the dimensions of the task. I was told that it should be similar to a plenary talk for a wide audience. I have a personal problem with instructions like this. I remember that when I was nine years old, our Spanish teacher asked us to summarise a story we had read together in class. I asked her to define “summarise”, because I could easily produce a summary of one, two or fifty pages, depending on what she was actually expecting from us. She was confused and I never got a clear answer. She replied that “A summary is a summary and that’s it”. On this occasion, I am afraid that I have run into the same snag and I have gone for the many-pages
Recommended publications
  • The Solar System and Its Place in the Galaxy in Encyclopedia of the Solar System by Paul R

    The Solar System and Its Place in the Galaxy in Encyclopedia of the Solar System by Paul R

    Giant Molecular Clouds http://www.astro.ncu.edu.tw/irlab/projects/project.htm Æ Galactic Open Clusters Æ Galactic Structure Æ GMCs The Solar System and its Place in the Galaxy In Encyclopedia of the Solar System By Paul R. Weissman http://www.academicpress.com/refer/solar/Contents/chap1.htm Stars in the galactic disk have different characteristic velocities as a function of their stellar classification, and hence age. Low-mass, older stars, like the Sun, have relatively high random velocities and as a result c an move farther out of the galactic plane. Younger, more massive stars have lower mean velocities and thus smaller scale heights above and below the plane. Giant molecular clouds, the birthplace of stars, also have low mean velocities and thus are confined to regions relatively close to the galactic plane. The disk rotates clockwise as viewed from "galactic north," at a relatively constant velocity of 160-220 km/sec. This motion is distinctly non-Keplerian, the result of the very nonspherical mass distribution. The rotation velocity for a circular galactic orbit in the galactic plane defines the Local Standard of Rest (LSR). The LSR is then used as the reference frame for describing local stellar dynamics. The Sun and the solar system are located approxi-mately 8.5 kpc from the galactic center, and 10-20 pc above the central plane of the galactic disk. The circular orbit velocity at the Sun's distance from the galactic center is 220 km/sec, and the Sun and the solar system are moving at approximately 17 to 22 km/sec relative to the LSR.
  • Arxiv:1611.06573V2

    Arxiv:1611.06573V2

    Draft version April 5, 2017 Preprint typeset using LATEX style emulateapj v. 01/23/15 DYNAMICAL FRICTION AND THE EVOLUTION OF SUPERMASSIVE BLACK HOLE BINARIES: THE FINAL HUNDRED-PARSEC PROBLEM Fani Dosopoulou and Fabio Antonini Center for Interdisciplinary Exploration and Research in Astrophysics (CIERA) and Department of Physics and Astrophysics, Northwestern University, Evanston, IL 60208 Draft version April 5, 2017 ABSTRACT The supermassive black holes originally in the nuclei of two merging galaxies will form a binary in the remnant core. The early evolution of the massive binary is driven by dynamical friction before the binary becomes “hard” and eventually reaches coalescence through gravitational wave emission. We consider the dynamical friction evolution of massive binaries consisting of a secondary hole orbiting inside a stellar cusp dominated by a more massive central black hole. In our treatment we include the frictional force from stars moving faster than the inspiralling object which is neglected in the standard Chandrasekhar’s treatment. We show that the binary eccentricity increases if the stellar cusp density profile rises less steeply than ρ r−2. In cusps shallower than ρ r−1 the frictional timescale can become very long due to the∝ deficit of stars moving slower than∝ the massive body. Although including the fast stars increases the decay rate, low mass-ratio binaries (q . 10−3) in sufficiently massive galaxies have decay timescales longer than one Hubble time. During such minor mergers the secondary hole stalls on an eccentric orbit at a distance of order one tenth the influence radius of the primary hole (i.e., 10 100pc for massive ellipticals).
  • An Atomic Physics Perspective on the New Kilogram Defined by Planck's Constant

    An Atomic Physics Perspective on the New Kilogram Defined by Planck's Constant

    An atomic physics perspective on the new kilogram defined by Planck’s constant (Wolfgang Ketterle and Alan O. Jamison, MIT) (Manuscript submitted to Physics Today) On May 20, the kilogram will no longer be defined by the artefact in Paris, but through the definition1 of Planck’s constant h=6.626 070 15*10-34 kg m2/s. This is the result of advances in metrology: The best two measurements of h, the Watt balance and the silicon spheres, have now reached an accuracy similar to the mass drift of the ur-kilogram in Paris over 130 years. At this point, the General Conference on Weights and Measures decided to use the precisely measured numerical value of h as the definition of h, which then defines the unit of the kilogram. But how can we now explain in simple terms what exactly one kilogram is? How do fixed numerical values of h, the speed of light c and the Cs hyperfine frequency νCs define the kilogram? In this article we give a simple conceptual picture of the new kilogram and relate it to the practical realizations of the kilogram. A similar change occurred in 1983 for the definition of the meter when the speed of light was defined to be 299 792 458 m/s. Since the second was the time required for 9 192 631 770 oscillations of hyperfine radiation from a cesium atom, defining the speed of light defined the meter as the distance travelled by light in 1/9192631770 of a second, or equivalently, as 9192631770/299792458 times the wavelength of the cesium hyperfine radiation.
  • Stellar Dynamics and Stellar Phenomena Near a Massive Black Hole

    Stellar Dynamics and Stellar Phenomena Near a Massive Black Hole

    Stellar Dynamics and Stellar Phenomena Near A Massive Black Hole Tal Alexander Department of Particle Physics and Astrophysics, Weizmann Institute of Science, 234 Herzl St, Rehovot, Israel 76100; email: [email protected] | Author's original version. To appear in Annual Review of Astronomy and Astrophysics. See final published version in ARA&A website: www.annualreviews.org/doi/10.1146/annurev-astro-091916-055306 Annu. Rev. Astron. Astrophys. 2017. Keywords 55:1{41 massive black holes, stellar kinematics, stellar dynamics, Galactic This article's doi: Center 10.1146/((please add article doi)) Copyright c 2017 by Annual Reviews. Abstract All rights reserved Most galactic nuclei harbor a massive black hole (MBH), whose birth and evolution are closely linked to those of its host galaxy. The unique conditions near the MBH: high velocity and density in the steep po- tential of a massive singular relativistic object, lead to unusual modes of stellar birth, evolution, dynamics and death. A complex network of dynamical mechanisms, operating on multiple timescales, deflect stars arXiv:1701.04762v1 [astro-ph.GA] 17 Jan 2017 to orbits that intercept the MBH. Such close encounters lead to ener- getic interactions with observable signatures and consequences for the evolution of the MBH and its stellar environment. Galactic nuclei are astrophysical laboratories that test and challenge our understanding of MBH formation, strong gravity, stellar dynamics, and stellar physics. I review from a theoretical perspective the wide range of stellar phe- nomena that occur near MBHs, focusing on the role of stellar dynamics near an isolated MBH in a relaxed stellar cusp.
  • Units and Magnitudes (Lecture Notes)

    Units and Magnitudes (Lecture Notes)

    physics 8.701 topic 2 Frank Wilczek Units and Magnitudes (lecture notes) This lecture has two parts. The first part is mainly a practical guide to the measurement units that dominate the particle physics literature, and culture. The second part is a quasi-philosophical discussion of deep issues around unit systems, including a comparison of atomic, particle ("strong") and Planck units. For a more extended, profound treatment of the second part issues, see arxiv.org/pdf/0708.4361v1.pdf . Because special relativity and quantum mechanics permeate modern particle physics, it is useful to employ units so that c = ħ = 1. In other words, we report velocities as multiples the speed of light c, and actions (or equivalently angular momenta) as multiples of the rationalized Planck's constant ħ, which is the original Planck constant h divided by 2π. 27 August 2013 physics 8.701 topic 2 Frank Wilczek In classical physics one usually keeps separate units for mass, length and time. I invite you to think about why! (I'll give you my take on it later.) To bring out the "dimensional" features of particle physics units without excess baggage, it is helpful to keep track of powers of mass M, length L, and time T without regard to magnitudes, in the form When these are both set equal to 1, the M, L, T system collapses to just one independent dimension. So we can - and usually do - consider everything as having the units of some power of mass. Thus for energy we have while for momentum 27 August 2013 physics 8.701 topic 2 Frank Wilczek and for length so that energy and momentum have the units of mass, while length has the units of inverse mass.
  • Estimation of Forest Aboveground Biomass and Uncertainties By

    Estimation of Forest Aboveground Biomass and Uncertainties By

    Urbazaev et al. Carbon Balance Manage (2018) 13:5 https://doi.org/10.1186/s13021-018-0093-5 RESEARCH Open Access Estimation of forest aboveground biomass and uncertainties by integration of feld measurements, airborne LiDAR, and SAR and optical satellite data in Mexico Mikhail Urbazaev1,2* , Christian Thiel1, Felix Cremer1, Ralph Dubayah3, Mirco Migliavacca4, Markus Reichstein4 and Christiane Schmullius1 Abstract Background: Information on the spatial distribution of aboveground biomass (AGB) over large areas is needed for understanding and managing processes involved in the carbon cycle and supporting international policies for climate change mitigation and adaption. Furthermore, these products provide important baseline data for the development of sustainable management strategies to local stakeholders. The use of remote sensing data can provide spatially explicit information of AGB from local to global scales. In this study, we mapped national Mexican forest AGB using satellite remote sensing data and a machine learning approach. We modelled AGB using two scenarios: (1) extensive national forest inventory (NFI), and (2) airborne Light Detection and Ranging (LiDAR) as reference data. Finally, we propagated uncertainties from feld measurements to LiDAR-derived AGB and to the national wall-to-wall forest AGB map. Results: The estimated AGB maps (NFI- and LiDAR-calibrated) showed similar goodness-of-ft statistics (R­ 2, Root Mean Square Error (RMSE)) at three diferent scales compared to the independent validation data set. We observed diferent spatial patterns of AGB in tropical dense forests, where no or limited number of NFI data were available, with higher AGB values in the LiDAR-calibrated map. We estimated much higher uncertainties in the AGB maps based on two-stage up-scaling method (i.e., from feld measurements to LiDAR and from LiDAR-based estimates to satel- lite imagery) compared to the traditional feld to satellite up-scaling.
  • Galaxies at High Z II

    Galaxies at High Z II

    Physical properties of galaxies at high redshifts II Different galaxies at high z’s 11 Luminous Infra Red Galaxies (LIRGs): LFIR > 10 L⊙ 12 Ultra Luminous Infra Red Galaxies (ULIRGs): LFIR > 10 L⊙ 13 −1 SubMillimeter-selected Galaxies (SMGs): LFIR > 10 L⊙ SFR ≳ 1000 M⊙ yr –6 −3 number density (2-6) × 10 Mpc The typical gas consumption timescales (2-4) × 107 yr VIGOROUS STAR FORMATION WITH LOW EFFICIENCY IN MASSIVE DISK GALAXIES AT z =1.5 Daddi et al 2008, ApJ 673, L21 The main question: how quickly the gas is consumed in galaxies at high redshifts. Observations maybe biased to galaxies with very high star formation rates. and thus give a bit biased picture. Motivation: observe galaxies in CO and FIR. Flux in CO is related with abundance of molecular gas. Flux in FIR gives SFR. So, the combination gives the rate of gas consumption. From Rings to Bulges: Evidence for Rapid Secular Galaxy Evolution at z ~ 2 from Integral Field Spectroscopy in the SINS Survey " Genzel et al 2008, ApJ 687, 59 We present Hα integral field spectroscopy of well-resolved, UV/optically selected z~2 star-forming galaxies as part of the SINS survey with SINFONI on the ESO VLT. " " Our laser guide star adaptive optics and good seeing data show the presence of turbulent rotating star- forming outer rings/disks, plus central bulge/inner disk components, whose mass fractions relative to the total dynamical mass appear to scale with the [N II]/H! flux ratio and the star formation age. " " We propose that the buildup of the central disks and bulges of massive galaxies at z~2 can be driven by the early secular evolution of gas-rich proto-disks.
  • Improving the Accuracy of the Numerical Values of the Estimates Some Fundamental Physical Constants

    Improving the Accuracy of the Numerical Values of the Estimates Some Fundamental Physical Constants

    Improving the accuracy of the numerical values of the estimates some fundamental physical constants. Valery Timkov, Serg Timkov, Vladimir Zhukov, Konstantin Afanasiev To cite this version: Valery Timkov, Serg Timkov, Vladimir Zhukov, Konstantin Afanasiev. Improving the accuracy of the numerical values of the estimates some fundamental physical constants.. Digital Technologies, Odessa National Academy of Telecommunications, 2019, 25, pp.23 - 39. hal-02117148 HAL Id: hal-02117148 https://hal.archives-ouvertes.fr/hal-02117148 Submitted on 2 May 2019 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Improving the accuracy of the numerical values of the estimates some fundamental physical constants. Valery F. Timkov1*, Serg V. Timkov2, Vladimir A. Zhukov2, Konstantin E. Afanasiev2 1Institute of Telecommunications and Global Geoinformation Space of the National Academy of Sciences of Ukraine, Senior Researcher, Ukraine. 2Research and Production Enterprise «TZHK», Researcher, Ukraine. *Email: [email protected] The list of designations in the text: l
  • Astr-Astronomy 1

    Astr-Astronomy 1

    ASTR-ASTRONOMY 1 ASTR 1116. Introduction to Astronomy Lab, Special ASTR-ASTRONOMY 1 Credit (1) This lab-only listing exists only for students who may have transferred to ASTR 1115G. Introduction Astro (lec+lab) NMSU having taken a lecture-only introductory astronomy class, to allow 4 Credits (3+2P) them to complete the lab requirement to fulfill the general education This course surveys observations, theories, and methods of modern requirement. Consent of Instructor required. , at some other institution). astronomy. The course is predominantly for non-science majors, aiming Restricted to Las Cruces campus only. to provide a conceptual understanding of the universe and the basic Prerequisite(s): Must have passed Introduction to Astronomy lecture- physics that governs it. Due to the broad coverage of this course, the only. specific topics and concepts treated may vary. Commonly presented Learning Outcomes subjects include the general movements of the sky and history of 1. Course is used to complete lab portion only of ASTR 1115G or ASTR astronomy, followed by an introduction to basic physics concepts like 112 Newton’s and Kepler’s laws of motion. The course may also provide 2. Learning outcomes are the same as those for the lab portion of the modern details and facts about celestial bodies in our solar system, as respective course. well as differentiation between them – Terrestrial and Jovian planets, exoplanets, the practical meaning of “dwarf planets”, asteroids, comets, ASTR 1120G. The Planets and Kuiper Belt and Trans-Neptunian Objects. Beyond this we may study 4 Credits (3+2P) stars and galaxies, star clusters, nebulae, black holes, and clusters of Comparative study of the planets, moons, comets, and asteroids which galaxies.
  • Globular Clusters and Galactic Nuclei

    Globular Clusters and Galactic Nuclei

    Scuola di Dottorato “Vito Volterra” Dottorato di Ricerca in Astronomia– XXIV ciclo Globular Clusters and Galactic Nuclei Thesis submitted to obtain the degree of Doctor of Philosophy (“Dottore di Ricerca”) in Astronomy by Alessandra Mastrobuono Battisti Program Coordinator Thesis Advisor Prof. Roberto Capuzzo Dolcetta Prof. Roberto Capuzzo Dolcetta Anno Accademico 2010-2011 ii Abstract Dynamical evolution plays a key role in shaping the current properties of star clus- ters and star cluster systems. We present the study of stellar dynamics both from a theoretical and numerical point of view. In particular we investigate this topic on different astrophysical scales, from the study of the orbital evolution and the mutual interaction of GCs in the Galactic central region to the evolution of GCs in the larger scale galactic potential. Globular Clusters (GCs), very old and massive star clusters, are ideal objects to explore many aspects of stellar dynamics and to investigate the dynamical and evolutionary mechanisms of their host galaxy. Almost every surveyed galaxy of sufficiently large mass has an associated group of GCs, i.e. a Globular Cluster System (GCS). The first part of this Thesis is devoted to the study of the evolution of GCSs in elliptical galaxies. Basing on the hypothesis that the GCS and stellar halo in a galaxy were born at the same time and, so, with the same density distribution, a logical consequence is that the presently observed difference may be due to evolution of the GCS. Actually, in this scenario, GCSs evolve due to various mechanisms, among which dynamical friction and tidal interaction with the galactic field are the most important.
  • Download Full-Text

    Download Full-Text

    International Journal of Theoretical and Mathematical Physics 2021, 11(1): 29-59 DOI: 10.5923/j.ijtmp.20211101.03 Measurement Quantization Describes the Physical Constants Jody A. Geiger 1Department of Research, Informativity Institute, Chicago, IL, USA Abstract It has been a long-standing goal in physics to present a physical model that may be used to describe and correlate the physical constants. We demonstrate, this is achieved by describing phenomena in terms of Planck Units and introducing a new concept, counts of Planck Units. Thus, we express the existing laws of classical mechanics in terms of units and counts of units to demonstrate that the physical constants may be expressed using only these terms. But this is not just a nomenclature substitution. With this approach we demonstrate that the constants and the laws of nature may be described with just the count terms or just the dimensional unit terms. Moreover, we demonstrate that there are three frames of reference important to observation. And with these principles we resolve the relation of the physical constants. And we resolve the SI values for the physical constants. Notably, we resolve the relation between gravitation and electromagnetism. Keywords Measurement Quantization, Physical Constants, Unification, Fine Structure Constant, Electric Constant, Magnetic Constant, Planck’s Constant, Gravitational Constant, Elementary Charge ground state orbital a0 and mass of an electron me – both 1. Introduction measures from the 2018 CODATA – we resolve fundamental length l . And we continue with the resolution of We present expressions, their calculation and the f the gravitational constant G, Planck’s reduced constant ħ corresponding CODATA [1,2] values in Table 1.
  • Systematic Motions in the Galactic Plane Found in the Hipparcos

    Systematic Motions in the Galactic Plane Found in the Hipparcos

    Astronomy & Astrophysics manuscript no. cabad0609 September 30, 2018 (DOI: will be inserted by hand later) Systematic motions in the galactic plane found in the Hipparcos Catalogue using Herschel’s Method Carlos Abad1,2 & Katherine Vieira1,3 (1) Centro de Investigaciones de Astronom´ıa CIDA, 5101-A M´erida, Venezuela e-mail: [email protected] (2) Grupo de Mec´anica Espacial, Depto. de F´ısica Te´orica, Universidad de Zaragoza. 50006 Zaragoza, Espa˜na (3) Department of Astronomy, Yale University, P.O. Box 208101 New Haven, CT 06520-8101, USA e-mail: [email protected] September 30, 2018 Abstract. Two motions in the galactic plane have been detected and characterized, based on the determination of a common systematic component in Hipparcos catalogue proper motions. The procedure is based only on positions, proper motions and parallaxes, plus a special algorithm which is able to reveal systematic trends. Our results come o o o o from two stellar samples. Sample 1 has 4566 stars and defines a motion of apex (l,b) = (177 8, 3 7) ± (1 5, 1 0) and space velocity V = 27 ± 1 km/s. Sample 2 has 4083 stars and defines a motion of apex (l,b)=(5o4, −0o6) ± o o (1 9, 1 1) and space velocity V = 32 ± 2 km/s. Both groups are distributed all over the sky and cover a large variety of spectral types, which means that they do not belong to a specific stellar population. Herschel’s method is used to define the initial samples of stars and later to compute the common space velocity.