Useful Constants
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PHYS 633: Introduction to Stellar Astrophysics Spring Semester 2006 Rich Townsend ([email protected])
PHYS 633: Introduction to Stellar Astrophysics Spring Semester 2006 Rich Townsend ([email protected]) Governing Equations In the foregoing analysis, we have seen how a star usually maintains a state of hydrostatic equilibrium. We have seen how the energy created in the star through nuclear reactions, or released through contraction, makes its way out in the form of the star’s luminosity. We have seen how the physical processes responsible for transporting this energy can either be radiation or convection. And, finally, we have seen how nuclear reactions within the star, and transport processes such as convective mixing, can alter the stars chemical composition. These four key pieces of physics lead to 3 + I of the differential equations governing stellar structure (here, I is the number of elements whose evolution we are following). Let’s quickly review these equations. First, we have the most general (spherically-symmetric) form for the equation governing momen- tum conservation, ∂P Gm 1 ∂2r = − − . (1) ∂m 4πr2 4πr2 ∂t2 If the second term on the right-hand side vanishes, then we recover the equation of hydrostatic equilibrium, expressed in Lagrangian form (i.e., derivatives with respect to the mass coordinate m, rather than the radial coordinate r). If this term does not vanish at some point in the star, then the mass shells at that point will being to expand or contract, with an acceleration given by ∂2r/∂t2. Second, we have the most general form for the energy conservation equation, ∂l ∂T δ ∂P = − − c + . (2) ∂m ν P ∂t ρ ∂t The first and second terms on the right-hand side come from nuclear energy gen- eration and neutrino losses, respectively. -
Used Time Scales GEORGE E
PROCEEDINGS OF THE IEEE, VOL. 55, NO. 6, JIJNE 1967 815 Reprinted from the PROCEEDINGS OF THE IEEI< VOL. 55, NO. 6, JUNE, 1967 pp. 815-821 COPYRIGHT @ 1967-THE INSTITCJTE OF kECTRITAT. AND ELECTRONICSEN~INEERS. INr I’KINTED IN THE lT.S.A. Some Characteristics of Commonly Used Time Scales GEORGE E. HUDSON A bstract-Various examples of ideally defined time scales are given. Bureau of Standards to realize one international unit of Realizations of these scales occur with the construction and maintenance of time [2]. As noted in the next section, it realizes the atomic various clocks, and in the broadcast dissemination of the scale information. Atomic and universal time scales disseminated via standard frequency and time scale, AT (or A), with a definite initial epoch. This clock time-signal broadcasts are compared. There is a discussion of some studies is based on the NBS frequency standard, a cesium beam of the associated problems suggested by the International Radio Consultative device [3]. This is the atomic standard to which the non- Committee (CCIR). offset carrier frequency signals and time intervals emitted from NBS radio station WWVB are referenced ; neverthe- I. INTRODUCTION less, the time scale SA (stepped atomic), used in these emis- PECIFIC PROBLEMS noted in this paper range from sions, is only piecewise uniform with respect to AT, and mathematical investigations of the properties of in- piecewise continuous in order that it may approximate to dividual time scales and the formation of a composite s the slightly variable scale known as UT2. SA is described scale from many independent ones, through statistical in Section 11-A-2). -
Arxiv:2007.13451V2 [Gr-Qc] 24 Nov 2020 on GR and Its Modifications [31–33], but Also Delivers Model Particles As Well As Dark Matter Candidates [56– Drawbacks
Early evolutionary tracks of low-mass stellar objects in modified gravity Aneta Wojnar1, ∗ 1Laboratory of Theoretical Physics, Institute of Physics, University of Tartu, W. Ostwaldi 1, 50411 Tartu, Estonia Using a simple model of low-mass stellar objects we have shown modified gravity impact on their early evolution, such as Hayashi tracks, radiative core development, effective temperature, masses, and luminosities. We have also suggested that the upper mass' limit of fully convective stars on the Main Sequence might be different than commonly adopted. I. INTRODUCTION is, in the so-called mass gap [38]), which merged with a black hole of 23M , provided even more questions for Working on modified gravity does not make one to for- theoretical physics of compact objects. get the elegance and success of Einstein's theory of grav- However, it turns out that there is a class of stellar ity, being already confirmed by many observations [1]; objects, with the internal structure much better under- even more, General Relativity (GR) still delights when stood than that of neutron stars, which might be used to one of its mysterious predictions, such as the existence of constrain theories of gravity. It is a family of low-mass black holes, is directly affirmed by the finding of gravi- stars (LMS) [39{41] which includes such ordinary objects tational waves as a result of black holes' binary mergers as M dwarfs (also called red dwarfs), which are cool Main [2] as well as soon after the imaging of the shadow of the Sequence stars with masses in the range [0:09 − 0:6]M , supermassive black hole of M87 [3] (see [4] for a review). -
Revisiting the Pre-Main-Sequence Evolution of Stars I. Importance of Accretion Efficiency and Deuterium Abundance ?
Astronomy & Astrophysics manuscript no. Kunitomo_etal c ESO 2018 March 22, 2018 Revisiting the pre-main-sequence evolution of stars I. Importance of accretion efficiency and deuterium abundance ? Masanobu Kunitomo1, Tristan Guillot2, Taku Takeuchi,3,?? and Shigeru Ida4 1 Department of Physics, Nagoya University, Furo-cho, Chikusa-ku, Nagoya, Aichi 464-8602, Japan e-mail: [email protected] 2 Université de Nice-Sophia Antipolis, Observatoire de la Côte d’Azur, CNRS UMR 7293, 06304 Nice CEDEX 04, France 3 Department of Earth and Planetary Sciences, Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro-ku, Tokyo 152-8551, Japan 4 Earth-Life Science Institute, Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro-ku, Tokyo 152-8551, Japan Received 5 February 2016 / Accepted 6 December 2016 ABSTRACT Context. Protostars grow from the first formation of a small seed and subsequent accretion of material. Recent theoretical work has shown that the pre-main-sequence (PMS) evolution of stars is much more complex than previously envisioned. Instead of the traditional steady, one-dimensional solution, accretion may be episodic and not necessarily symmetrical, thereby affecting the energy deposited inside the star and its interior structure. Aims. Given this new framework, we want to understand what controls the evolution of accreting stars. Methods. We use the MESA stellar evolution code with various sets of conditions. In particular, we account for the (unknown) efficiency of accretion in burying gravitational energy into the protostar through a parameter, ξ, and we vary the amount of deuterium present. Results. We confirm the findings of previous works that, in terms of evolutionary tracks on the Hertzsprung-Russell (H-R) diagram, the evolution changes significantly with the amount of energy that is lost during accretion. -
Solar Radius Determined from PICARD/SODISM Observations and Extremely Weak Wavelength Dependence in the Visible and the Near-Infrared
A&A 616, A64 (2018) https://doi.org/10.1051/0004-6361/201832159 Astronomy c ESO 2018 & Astrophysics Solar radius determined from PICARD/SODISM observations and extremely weak wavelength dependence in the visible and the near-infrared M. Meftah1, T. Corbard2, A. Hauchecorne1, F. Morand2, R. Ikhlef2, B. Chauvineau2, C. Renaud2, A. Sarkissian1, and L. Damé1 1 Université Paris Saclay, Sorbonne Université, UVSQ, CNRS, LATMOS, 11 Boulevard d’Alembert, 78280 Guyancourt, France e-mail: [email protected] 2 Université de la Côte d’Azur, Observatoire de la Côte d’Azur (OCA), CNRS, Boulevard de l’Observatoire, 06304 Nice, France Received 23 October 2017 / Accepted 9 May 2018 ABSTRACT Context. In 2015, the International Astronomical Union (IAU) passed Resolution B3, which defined a set of nominal conversion constants for stellar and planetary astronomy. Resolution B3 defined a new value of the nominal solar radius (RN = 695 700 km) that is different from the canonical value used until now (695 990 km). The nominal solar radius is consistent with helioseismic estimates. Recent results obtained from ground-based instruments, balloon flights, or space-based instruments highlight solar radius values that are significantly different. These results are related to the direct measurements of the photospheric solar radius, which are mainly based on the inflection point position methods. The discrepancy between the seismic radius and the photospheric solar radius can be explained by the difference between the height at disk center and the inflection point of the intensity profile on the solar limb. At 535.7 nm (photosphere), there may be a difference of 330 km between the two definitions of the solar radius. -
100 Closest Stars Designation R.A
100 closest stars Designation R.A. Dec. Mag. Common Name 1 Gliese+Jahreis 551 14h30m –62°40’ 11.09 Proxima Centauri Gliese+Jahreis 559 14h40m –60°50’ 0.01, 1.34 Alpha Centauri A,B 2 Gliese+Jahreis 699 17h58m 4°42’ 9.53 Barnard’s Star 3 Gliese+Jahreis 406 10h56m 7°01’ 13.44 Wolf 359 4 Gliese+Jahreis 411 11h03m 35°58’ 7.47 Lalande 21185 5 Gliese+Jahreis 244 6h45m –16°49’ -1.43, 8.44 Sirius A,B 6 Gliese+Jahreis 65 1h39m –17°57’ 12.54, 12.99 BL Ceti, UV Ceti 7 Gliese+Jahreis 729 18h50m –23°50’ 10.43 Ross 154 8 Gliese+Jahreis 905 23h45m 44°11’ 12.29 Ross 248 9 Gliese+Jahreis 144 3h33m –9°28’ 3.73 Epsilon Eridani 10 Gliese+Jahreis 887 23h06m –35°51’ 7.34 Lacaille 9352 11 Gliese+Jahreis 447 11h48m 0°48’ 11.13 Ross 128 12 Gliese+Jahreis 866 22h39m –15°18’ 13.33, 13.27, 14.03 EZ Aquarii A,B,C 13 Gliese+Jahreis 280 7h39m 5°14’ 10.7 Procyon A,B 14 Gliese+Jahreis 820 21h07m 38°45’ 5.21, 6.03 61 Cygni A,B 15 Gliese+Jahreis 725 18h43m 59°38’ 8.90, 9.69 16 Gliese+Jahreis 15 0h18m 44°01’ 8.08, 11.06 GX Andromedae, GQ Andromedae 17 Gliese+Jahreis 845 22h03m –56°47’ 4.69 Epsilon Indi A,B,C 18 Gliese+Jahreis 1111 8h30m 26°47’ 14.78 DX Cancri 19 Gliese+Jahreis 71 1h44m –15°56’ 3.49 Tau Ceti 20 Gliese+Jahreis 1061 3h36m –44°31’ 13.09 21 Gliese+Jahreis 54.1 1h13m –17°00’ 12.02 YZ Ceti 22 Gliese+Jahreis 273 7h27m 5°14’ 9.86 Luyten’s Star 23 SO 0253+1652 2h53m 16°53’ 15.14 24 SCR 1845-6357 18h45m –63°58’ 17.40J 25 Gliese+Jahreis 191 5h12m –45°01’ 8.84 Kapteyn’s Star 26 Gliese+Jahreis 825 21h17m –38°52’ 6.67 AX Microscopii 27 Gliese+Jahreis 860 22h28m 57°42’ 9.79, -
2. Astrophysical Constants and Parameters
2. Astrophysical constants 1 2. ASTROPHYSICAL CONSTANTS AND PARAMETERS Table 2.1. Revised May 2010 by E. Bergren and D.E. Groom (LBNL). The figures in parentheses after some values give the one standard deviation uncertainties in the last digit(s). Physical constants are from Ref. 1. While every effort has been made to obtain the most accurate current values of the listed quantities, the table does not represent a critical review or adjustment of the constants, and is not intended as a primary reference. The values and uncertainties for the cosmological parameters depend on the exact data sets, priors, and basis parameters used in the fit. Many of the parameters reported in this table are derived parameters or have non-Gaussian likelihoods. The quoted errors may be highly correlated with those of other parameters, so care must be taken in propagating them. Unless otherwise specified, cosmological parameters are best fits of a spatially-flat ΛCDM cosmology with a power-law initial spectrum to 5-year WMAP data alone [2]. For more information see Ref. 3 and the original papers. Quantity Symbol, equation Value Reference, footnote speed of light c 299 792 458 m s−1 exact[4] −11 3 −1 −2 Newtonian gravitational constant GN 6.674 3(7) × 10 m kg s [1] 19 2 Planck mass c/GN 1.220 89(6) × 10 GeV/c [1] −8 =2.176 44(11) × 10 kg 3 −35 Planck length GN /c 1.616 25(8) × 10 m[1] −2 2 standard gravitational acceleration gN 9.806 65 m s ≈ π exact[1] jansky (flux density) Jy 10−26 Wm−2 Hz−1 definition tropical year (equinox to equinox) (2011) yr 31 556 925.2s≈ π × 107 s[5] sidereal year (fixed star to fixed star) (2011) 31 558 149.8s≈ π × 107 s[5] mean sidereal day (2011) (time between vernal equinox transits) 23h 56m 04.s090 53 [5] astronomical unit au, A 149 597 870 700(3) m [6] parsec (1 au/1 arc sec) pc 3.085 677 6 × 1016 m = 3.262 ...ly [7] light year (deprecated unit) ly 0.306 6 .. -
Cygnus OB2 – a Young Globular Cluster in the Milky Way Jürgen Knödlseder
Cygnus OB2 – a young globular cluster in the Milky Way Jürgen Knödlseder To cite this version: Jürgen Knödlseder. Cygnus OB2 – a young globular cluster in the Milky Way. Astronomy and Astrophysics - A&A, EDP Sciences, 2000, 360, pp.539 - 548. hal-01381935 HAL Id: hal-01381935 https://hal.archives-ouvertes.fr/hal-01381935 Submitted on 14 Oct 2016 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. Astron. Astrophys. 360, 539–548 (2000) ASTRONOMY AND ASTROPHYSICS Cygnus OB2–ayoung globular cluster in the Milky Way J. Knodlseder¨ INTEGRAL Science Data Centre, Chemin d’Ecogia 16, 1290 Versoix, Switzerland Centre d’Etude Spatiale des Rayonnements, CNRS/UPS, B.P. 4346, 31028 Toulouse Cedex 4, France ([email protected]) Received 31 May 2000 / Accepted 23 June 2000 Abstract. The morphology and stellar content of the Cygnus particularly good region to address such questions, since it is OB2 association has been determined using 2MASS infrared extremely rich (e.g. Reddish et al. 1966, hereafter RLP), and observations in the J, H, and K bands. The analysis reveals contains some of the most luminous stars known in our Galaxy a spherically symmetric association of ∼ 2◦ in diameter with (e.g. -
Single Star Implementation Notes
Mon. Not. R. Astron. Soc. 000, 000{000 (0000) Printed 8 November 2017 (MN LATEX style file v2.2) Single Star Implementation Notes PFH 8 November 2017 1 METHODS 1=2 − 1 times the cloud diameter Lcloud) are driven as an Ornstein-Uhlenbeck process in Fourier space, with the com- Our simulations use GIZMO (?),1, and include full self- pressive part of the modes projected out via Helmholtz de- gravity, adaptive resolution, ideal and non-ideal magneto- composition so that we can specify the ratio of compress- hydrodynamics (MHD), detailed cooling and heating ible and incompressible/solenoidal modes. Unless otherwise physics, protostar formation, accretion, and feedback in the specified we adopt pure solenoidal driving, appropriate for form of protostellar jets and radiative heating, and main- e.g. galactic shear (so that we do not artificially \force" com- sequence stellar feedback in the form of photo-ionization pression/collapse), but we vary this. The specific implemen- and photo-electric heating, radiation pressure, stellar winds, tation here has been verified in ????. and supernovae. A subset of our runs include explicit treat- The driving specifies the large-scale steady-state (one- ment of the dust particle and cosmic ray dynamics as well dimensional) turbulent velocity σ ≡ hv2 i1=2 and as radiation-hydrodynamics; otherwise these are included in 1D turb; 1D Mach number M ≡ h(v =c )2i1=2, where v is simplified form. turb; 1D s turb; 1D an (arbitrary) projection (in detail we average over all 1.1 Gravity random projections). Unless otherwise specified, we initial- ize our clouds on the linewidth-size relation from ?, with All our simulations include full self-gravity for gas, stars, −1 1=2 σ1D ≈ 0:7 km s (Lcloud=pc) and dust. -
POSTERS SESSION I: Atmospheres of Massive Stars
Abstracts of Posters 25 POSTERS (Grouped by sessions in alphabetical order by first author) SESSION I: Atmospheres of Massive Stars I-1. Pulsational Seeding of Structure in a Line-Driven Stellar Wind Nurdan Anilmis & Stan Owocki, University of Delaware Massive stars often exhibit signatures of radial or non-radial pulsation, and in principal these can play a key role in seeding structure in their radiatively driven stellar wind. We have been carrying out time-dependent hydrodynamical simulations of such winds with time-variable surface brightness and lower boundary condi- tions that are intended to mimic the forms expected from stellar pulsation. We present sample results for a strong radial pulsation, using also an SEI (Sobolev with Exact Integration) line-transfer code to derive characteristic line-profile signatures of the resulting wind structure. Future work will compare these with observed signatures in a variety of specific stars known to be radial and non-radial pulsators. I-2. Wind and Photospheric Variability in Late-B Supergiants Matt Austin, University College London (UCL); Nevyana Markova, National Astronomical Observatory, Bulgaria; Raman Prinja, UCL There is currently a growing realisation that the time-variable properties of massive stars can have a funda- mental influence in the determination of key parameters. Specifically, the fact that the winds may be highly clumped and structured can lead to significant downward revision in the mass-loss rates of OB stars. While wind clumping is generally well studied in O-type stars, it is by contrast poorly understood in B stars. In this study we present the analysis of optical data of the B8 Iae star HD 199478. -
Star Systems in the Solar Neighborhood up to 10 Parsecs Distance
Vol. 16 No. 3 June 15, 2020 Journal of Double Star Observations Page 229 Star Systems in the Solar Neighborhood up to 10 Parsecs Distance Wilfried R.A. Knapp Vienna, Austria [email protected] Abstract: The stars and star systems in the solar neighborhood are for obvious reasons the most likely best investigated stellar objects besides the Sun. Very fast proper motion catches the attention of astronomers and the small distances to the Sun allow for precise measurements so the wealth of data for most of these objects is impressive. This report lists 94 star systems (doubles or multiples most likely bound by gravitation) in up to 10 parsecs distance from the Sun as well over 60 questionable objects which are for different reasons considered rather not star systems (at least not within 10 parsecs) but might be if with a small likelihood. A few of the listed star systems are newly detected and for several systems first or updated preliminary orbits are suggested. A good part of the listed nearby star systems are included in the GAIA DR2 catalog with par- allax and proper motion data for at least some of the components – this offers the opportunity to counter-check the so far reported data with the most precise star catalog data currently available. A side result of this counter-check is the confirmation of the expectation that the GAIA DR2 single star model is not well suited to deliver fully reliable parallax and proper motion data for binary or multiple star systems. 1. Introduction high proper motion speed might cause visually noticea- The answer to the question at which distance the ble position changes from year to year. -
The Future Life Span of Earth's Oxygenated Atmosphere
In press at Nature Geoscience The future life span of Earth’s oxygenated atmosphere Kazumi Ozaki1,2* and Christopher T. Reinhard2,3,4 1Department of Environmental Science, Toho University, Funabashi, Chiba 274-8510, Japan 2NASA Nexus for Exoplanet System Science (NExSS) 3School of Earth and Atmospheric Sciences, Georgia Institute of Technology, Atlanta, GA 30332, USA 4NASA Astrobiology Institute, Alternative Earths Team, Riverside, CA, USA *Correspondence to: [email protected] Abstract: Earth’s modern atmosphere is highly oxygenated and is a remotely detectable signal of its surface biosphere. However, the lifespan of oxygen-based biosignatures in Earth’s atmosphere remains uncertain, particularly for the distant future. Here we use a combined biogeochemistry and climate model to examine the likely timescale of oxygen-rich atmospheric conditions on Earth. Using a stochastic approach, we find that the mean future lifespan of Earth’s atmosphere, with oxygen levels more than 1% of the present atmospheric level, is 1.08 ± 0.14 billion years (1σ). The model projects that a deoxygenation of the atmosphere, with atmospheric O2 dropping sharply to levels reminiscent of the Archaean Earth, will most probably be triggered before the inception of moist greenhouse conditions in Earth’s climate system and before the extensive loss of surface water from the atmosphere. We find that future deoxygenation is an inevitable consequence of increasing solar fluxes, whereas its precise timing is modulated by the exchange flux of reducing power between the mantle and the ocean– atmosphere–crust system. Our results suggest that the planetary carbonate–silicate cycle will tend to lead to terminally CO2-limited biospheres and rapid atmospheric deoxygenation, emphasizing the need for robust atmospheric biosignatures applicable to weakly oxygenated and anoxic exoplanet atmospheres and highlighting the potential importance of atmospheric organic haze during the terminal stages of planetary habitability.