DOCSLIB.ORG

Radiative Transfer in Stellar Atmospheres

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Radiative Transfer in Stellar Atmospheres 3. Transport of energy: radiation specific intensity, radiative flux optical depth absorption & emission equation of transfer, source function formal solution, limb darkening temperature distribution grey atmosphere, mean opacities 1 Energy flux conservation No sinks and sources of energy in the atmosphere all energy produced in stellar interior is transported through the atmosphere at any given radius r in the atmosphere: 4().rFr2 const L F is the energy flux per unit surface and per unit time. Dimensions: [erg/cm2/sec] The energy transport is sustained by the temperature gradient. The steepness of this gradient is dependent on the effectiveness of the energy transport through the different atmospheric layers. 2 Transport of energy Mechanisms of energy transport a. radiation: Frad (most important) b. convection: F (important especially in cool stars) conv c. heat production: e.g. in the transition between solar cromosphere and corona d. radial flow of matter : corona and stellar wind e. sound waves: cromosphere and corona We will be mostly concerned with the first 2 mechanisms: F(r)=Frad(r) + Fconv(r). In the outer layers, we always have Frad >> Fconv 3 The specific intensity Measures of energy flow: Specific Intensity and Flux The amount of energy dEν transported through a surface area dA is proportional to dt (length of time), dν (frequency width), dω (solid angle) and the projected unit surface area cos θ dA. The proportionality factor is the specific Intensity Iν(cosθ) dEν = Iν (cos θ ) cos θ dA dω dν dt 2 1 1 1 ([Iν ]: erg cm− sr− Hz− s− ) c Iλ = λ2 Iν (from Iλdλ = Iν dν and ν = c/λ) Intensity depends on location in space, direction and frequency 4 Invariance of the specific intensity The area element dA emits radiation towards dA’. In the absence of any matter between emitter and receiver (no absorption and emission on the light paths between the surface elements) the amount of energy emitted and received through each surface elements is: dEν = Iν (cos θ) cos θ dA dω dν dt dEν0 = Iν0 (cos θ0) cos θ0 dA0 dω0 dν dt 5 Invariance of the specific intensity projected area dA0 cos θ0 dω = distance2 = r2 energy is conserved: dEν = dEν0 and dA cos θ dω0 = r2 dE = I (cos θ) cos θ dA dω dν dt and ν ν dEν0 = Iν0 (cos θ0) cos θ0 dA0 dω0 dν dt Specific intensity is constant along rays - as long as there is no absorption and emission Iν = Iν0 of matter between emitter and receiver In TE: I = B 6 Spherical coordinate system and solid angle dω dA solid angle : dω = r2 4πr2 Total solid angle = = 4π r2 dA = (r dθ)(r sin θ dφ) dω = sin θ dθ dφ → define μ = cos θ dμ = sin θ dθ − dω = sin θ dθ dφ = dμ dφ − 7 Radiative flux How much energy flows through surface element dA? dE ~ I cosθ dω integrate over the whole solid angle (4): 2π π πFν = Iν (cos θ) cos θ dω = Iν (cos θ) cos θ sin θdθdφ 0 0 “astrophysical flux” 4Zπ Z Z Fν is the monochromatic radiative flux. The factor π in the definition is historical. Fν can also be interpreted as the net rate of energy flow through a surface element. 8 Radiative flux The monochromatic radiative flux at frequency gives the net rate of energy flow through a surface element. dE ~ I cosθ dω integrate over the whole solid angle (4): 2π π π Fν = Iν (cos θ) cos θ dω = Iν (cos θ) cos θ sin θdθdφ “astrophysical flux” 0 0 4Zπ Z Z We distinguish between the outward direction (0 < < /2) and the inward direction (/2 < so that the net flux is + πF = πF πF − = ν ν − ν 2π π/2 2π π = Iν (cos θ) cos θ sin θdθdφ + Iν (cos θ) cos θ sin θdθdφ Z0 Z0 Z0 Zπ/2 Note: for /2 < cosθ < 0 second term negative !! 9 Total radiative flux Integral over frequencies ∞ πF dν = ν Frad Z0 Frad is the total radiative flux. It is the total net amount of energy going through the surface element per unit time and unit surface. 10 Stellar luminosity At the outer boundary of atmosphere (r = Ro) there is no incident radiation Integral interval over θ reduces from [0,π] to [0,π/2]. 2π π/2 + πFν (Ro) = πFν (Ro) = Iν (cos θ) cos θ sin θdθdφ Z0 Z0 This is the monochromatic energy that each surface element of the star radiates in all directions 2 If we multiply by the total stellar surface 4πR0 2 4πRo πFν (Ro)= Lν monochromatic stellar luminosity at frequency · and integrating over total stellar luminosity 2 ∞ + 4πRo πFν (Ro)dν = L (Luminosity) · 11 Z0 Observed flux What radiative flux is measured by an observer at distance d? integrate specific intensity Iν towards observer over all surface elements note that only half sphere contributes Eν = dE = ∆ω ∆ν ∆ t Iν(cos θ) cos θ dA 1/2 sZphere 1/2 sZphere 2 in spherical symmetry: dA = Ro sin θ dθ dφ 2π π/2 E = ∆ω ∆ν ∆t R2 I (cos θ) cos θ sin θ dθ dφ → ν o ν Zo Z0 + πFν because of spherical symmetry the integral of intensity towards + the observer over the stellar surface is proportional to F , the flux emitted into all directions by one surface element !! 12 Observed flux Solid angle of telescope at distance d: ∆ω = ∆A/d2 + 2 + Eν = ∆ω ∆ν ∆t Ro πFν (Ro) flux received = flux emitted x (R/r)2 radiative energy R2 unlike I , decreases with obs = = o πF +(R ) F Fν area frequency time d2 ν o increasing distance · · This, and not I, is the quantity generally measured for stars. For the Sun, whose disk is resolved, we can also measure I ∞ obs 2 0 ν, dν = 1.36 KW/m F ¯ (the variation of I over the solar disk is called the limb R darkening) 13 Mean intensity, energy density & radiation pressure Integrating over the solid angle and dividing by 4: 1 J = I dω mean intensity ν 4π ν 4Zπ radiation energy 1 4π u = = I dω = J energy density ν volume c ν c ν 4Zπ 1 p = I cos2 θ dω radiation pressure ν c ν 4Zπ (important in hot stars) force d momentum(= E/c) 1 pressure = = area dt area 14 Moments of the specific intensity 1 1 2π 1 1 1 0th moment Jν = Iν dω = dφ Iν dμ = Iν dμ 4π 4π 0 1 2 1 Z Z Z− Z− for azimuthal symmetry 1 1 1 Fν st Hν = Iν cos θ dω = Iν μ dμ = 1 moment 4π 2 1 4 Z Z− (Eddington flux) 1 1 2 1 2 c Kν = Iν cos θ dω = Iν μ dμ = pν 2nd moment 4π 2 1 4π Z Z− 15 InteractionsInteractions betweenbetween photonsphotons andand mattermatter absorption of radiation ds dI = κ I ds ν − ν ν κν : absorption coefficient I 1 [κν ] = cm− microscopical view: n loss of intensity in the beam (true absorption/scattering) Over a distance s: s κν ds s o − 0 o Iν (s) = Iν e R I I(s) s optical depth τν := κν ds Convention: = 0 at the outer edge (dimensionless) of the atmosphere, increasing Z0 16 inwards or: d = ds optical depth The optical thickness of a layer o τν determines the fraction of the Iν (s) = I e− ν intensity passing through the layer o Iν o We can see through if τν = 1 Iν = 0.37 Iν → e ' atmosphere until ~ 1 optically thick (thin) medium: > (<) 1 The quantity has a geometrical interpretation in terms of mean free path of photons s¯ : s¯ τν = 1 = κν ds Zo photons travel on average for a length s¯ before absorption 17 photon mean free path What is the average distance over which photons travel? ∞ expectation value < τν >= τν p(τν ) dτν Z0 probability of absorption in interval [+d] = probability of non-absorption between 0 and and absorption in d ∆I(τ) Io I(τν ) I(τν ) - probability that photon is absorbed: p(0, τν ) = = − = 1 Io Io − Io I(τ ) ν τν - probability that photon is not absorbed: 1 p(0, τν ) = = e− − Io dIν - probability that photon is absorbed in [τν , τν + dτν ] : p(τν , τν + dτν ) = = dτν I(τν ) τν total probability: e− dτν 18 photon mean free path ∞ ∞ x x τν xe− dx = (1 + x) e− < τν >= τν p(τν ) dτν = τν e− dτν = 1 − Z Z0 Z0 mean free path corresponds to <>=1 1 if κν (s) = const : ∆τν = κν ∆s ∆s = s¯ = → κν (homogeneous material) 19 Principle of line formation observer sees through the atmospheric layers up to 1 In the continuum is smaller than in the line see deeper into the atmosphere T(cont) > T(line) 20 radiative acceleration In the absorption process photons release momentum E/c to the atoms, and the corresponding force is: momentum(=E/c) force =dfphot = dt The infinitesimal energy absorbed is: abs dEν = dIν cos θ dA dω dt dν = κν Iν cosθ dA dω dt dν ds The total energy absorbed is (assuming that κν does not depend on ω): ∞ ∞ abs E = κν Iν cos θ dω dν dA dt ds = π κν Fν dν dA dt ds Z0 4Zπ Z0 F 21 radiative acceleration ∞ κν Fν dν π df = 0 dA dt ds = g dm (dm = ρ dA ds) phot c R dt rad π ∞ g = κ F dν rad cρ ν ν Z0 22 emission of radiation ds d dA dV=dA ds energy added by emis sion processes within dV em dEν = ²ν dV dω dν dt ²ν : emission coefficient 3 1 1 1 [²ν ] = erg cm− sr− Hz− s− 23 TheThe equationequation ofof radiativeradiative tranfertranfer If we combine absorption and emission together: dEabs = dIabs dA cos θ dω dν dt = κ I dA cos θ dω dt dν ds ν ν − ν ν em em dEν = dIν dA cos θ dω dν dt = ²ν dA cos θ dω dν dt ds dEabs+dEem = (dIabs+dI em) dA cos θ dω dν dt = ( κ I +² ) dA cos θ dω dν dt ds ν ν ν ν − ν ν ν dI = dIabs + dIem = ( κ I + ² ) ds ν ν ν − ν ν ν differential equation dIν = κ I + ² describing the flow of ds − ν ν ν radiation through matter 24 TheThe equationequation ofof radiativeradiative tranfertranfer Plane-parallel symmetry dx = cos θ ds = μ ds d d = μ ds dx μ dIν (μ,x) = κ I (μ, x) + ² dx − ν ν ν 25 TheThe equationequation ofof radiativeradiative tranfertranfer Spherical symmetry d dr ∂ dθ ∂ = + ds ds ∂r ds ∂θ dr dr = ds cos θ = cos θ (as in plane parallel) → ds − dθ sin θ r dθ = sin θ ds (dθ < 0) = − → ds − r ∂ ∂μ ∂ ∂ = = sin θ ∂θ ∂θ ∂μ − ∂μ d ∂ sin2 θ ∂ ∂ 1 μ2 ∂ = = μ + = μ + − ⇒ ds ∂r r ∂μ ∂r r ∂μ ∂ 1 μ2 ∂ μ ∂r Iν (μ, r) + −r ∂μ Iν (μ, r) = κν Iν (μ, r) + ²ν angle between ray and radial direction − is not constant 26 TheThe equationequation ofof radiativeradiative tranfertranfer Optical depth and source function optical depth increasing In plane-parallel symmetry: towards interior: κν dx = dτν dI (μ,x) − μ ν = κ (x) I (μ, x) + ² (x) x dx − ν ν ν τ = κ dx ν − ν RZo dIν (μ,τν ) μ = Iν (μ, τν ) Sν (τν ) dτν − S = ²ν ν κν source function Observed emerging intensity I(cos ,= 0) depends on = cos , (R ) and S dim [S] = [I] i dτν ∆τν 1 = 1 corresponds to free mean path of κν = The physics of S is crucial for radiative transfer ds ≈ ∆s ≈ s¯ photons ²ν S = ² s¯ source function S corresponds to intensity ν κν ν ≈ · emitted over the free mean path of photons 27 TheThe equationequation ofof radiativeradiative tranfertranfer Source function: simple cases a.
Load more

Recommended publications
  • Glossary Physics (I-Introduction)
    1 Glossary Physics (I-introduction) - Efficiency: The percent of the work put into a machine that is converted into useful work output; = work done / energy used [-]. = eta In machines: The work output of any machine cannot exceed the work input (<=100%); in an ideal machine, where no energy is transformed into heat: work(input) = work(output), =100%. Energy: The property of a system that enables it to do work. Conservation o. E.: Energy cannot be created or destroyed; it may be transformed from one form into another, but the total amount of energy never changes. Equilibrium: The state of an object when not acted upon by a net force or net torque; an object in equilibrium may be at rest or moving at uniform velocity - not accelerating. Mechanical E.: The state of an object or system of objects for which any impressed forces cancels to zero and no acceleration occurs. Dynamic E.: Object is moving without experiencing acceleration. Static E.: Object is at rest.F Force: The influence that can cause an object to be accelerated or retarded; is always in the direction of the net force, hence a vector quantity; the four elementary forces are: Electromagnetic F.: Is an attraction or repulsion G, gravit. const.6.672E-11[Nm2/kg2] between electric charges: d, distance [m] 2 2 2 2 F = 1/(40) (q1q2/d ) [(CC/m )(Nm /C )] = [N] m,M, mass [kg] Gravitational F.: Is a mutual attraction between all masses: q, charge [As] [C] 2 2 2 2 F = GmM/d [Nm /kg kg 1/m ] = [N] 0, dielectric constant Strong F.: (nuclear force) Acts within the nuclei of atoms: 8.854E-12 [C2/Nm2] [F/m] 2 2 2 2 2 F = 1/(40) (e /d ) [(CC/m )(Nm /C )] = [N] , 3.14 [-] Weak F.: Manifests itself in special reactions among elementary e, 1.60210 E-19 [As] [C] particles, such as the reaction that occur in radioactive decay.
    [Show full text]
  • THE EVOLUTION of SOLAR FLUX from 0.1 Nm to 160Μm: QUANTITATIVE ESTIMATES for PLANETARY STUDIES
    View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by St Andrews Research Repository The Astrophysical Journal, 757:95 (12pp), 2012 September 20 doi:10.1088/0004-637X/757/1/95 C 2012. The American Astronomical Society. All rights reserved. Printed in the U.S.A. THE EVOLUTION OF SOLAR FLUX FROM 0.1 nm TO 160 μm: QUANTITATIVE ESTIMATES FOR PLANETARY STUDIES Mark W. Claire1,2,3, John Sheets2,4, Martin Cohen5, Ignasi Ribas6, Victoria S. Meadows2, and David C. Catling7 1 School of Environmental Sciences, University of East Anglia, Norwich, UK NR4 7TJ; [email protected] 2 Virtual Planetary Laboratory and Department of Astronomy, University of Washington, Box 351580, Seattle, WA 98195, USA 3 Blue Marble Space Institute of Science, P.O. Box 85561, Seattle, WA 98145-1561, USA 4 Department of Physics & Astronomy, University of Wyoming, Box 204C, Physical Sciences, Laramie, WY 82070, USA 5 Radio Astronomy Laboratory, University of California, Berkeley, CA 94720-3411, USA 6 Institut de Ciencies` de l’Espai (CSIC-IEEC), Facultat de Ciencies,` Torre C5 parell, 2a pl, Campus UAB, E-08193 Bellaterra, Spain 7 Virtual Planetary Laboratory and Department of Earth and Space Sciences, University of Washington, Box 351310, Seattle, WA 98195, USA Received 2011 December 14; accepted 2012 August 1; published 2012 September 6 ABSTRACT Understanding changes in the solar flux over geologic time is vital for understanding the evolution of planetary atmospheres because it affects atmospheric escape and chemistry, as well as climate. We describe a numerical parameterization for wavelength-dependent changes to the non-attenuated solar flux appropriate for most times and places in the solar system.
    [Show full text]
  • Lecture 5. Interstellar Dust: Optical Properties
    Lecture 5. Interstellar Dust: Optical Properties 1. Introduction 2. Extinction 3. Mie Scattering 4. Dust to Gas Ratio 5. Appendices References Spitzer Ch. 7, Osterbrock Ch. 7 DC Whittet, Dust in the Galactic Environment (IoP, 2002) E Krugel, Physics of Interstellar Dust (IoP, 2003) B Draine, ARAA, 41, 241, 2003 1. Introduction: Brief History of Dust Nebular gas long accepted but existence of absorbing interstellar dust controversial. Herschel (1738-1822) found few stars in some directions, later extensively demonstrated by Barnard’s photos of dark clouds. Trumpler (PASP 42 214 1930) conclusively demonstrated interstellar absorption by comparing luminosity distances & angular diameter distances for open clusters: • Angular diameter distances are systematically smaller • Discrepancy grows with distance • Distant clusters are redder • Estimated ~ 2 mag/kpc absorption • Attributed it to Rayleigh scattering by gas Some of the Evidence for Interstellar Dust Extinction (reddening of bright stars, dark clouds) Polarization of starlight Scattering (reflection nebulae) Continuum IR emission Depletion of refractory elements from the gas Dust is also observed in the winds of AGB stars, SNRs, young stellar objects (YSOs), comets, interplanetary Dust particles (IDPs), and in external galaxies. The extinction varies continuously with wavelength and requires macroscopic absorbers (or “dust” particles). Examples of the Effects of Dust Extinction B68 Scattering - Pleiades Extinction: Some Definitions Optical depth, cross section, & efficiency: ext ext ext τ λ = ∫ ndustσ λ ds = σ λ ∫ ndust 2 = πa Qext (λ) Ndust nd is the volumetric dust density The magnitude of the extinction Aλ : ext I(λ) = I0 (λ) exp[−τ λ ] Aλ =−2.5log10 []I(λ)/I0(λ) ext ext = 2.5log10(e)τ λ =1.086τ λ 2.
    [Show full text]
  • Light and Illumination
    ChapterChapter 3333 -- LightLight andand IlluminationIllumination AAA PowerPointPowerPointPowerPoint PresentationPresentationPresentation bybyby PaulPaulPaul E.E.E. Tippens,Tippens,Tippens, ProfessorProfessorProfessor ofofof PhysicsPhysicsPhysics SouthernSouthernSouthern PolytechnicPolytechnicPolytechnic StateStateState UniversityUniversityUniversity © 2007 Objectives:Objectives: AfterAfter completingcompleting thisthis module,module, youyou shouldshould bebe ableable to:to: •• DefineDefine lightlight,, discussdiscuss itsits properties,properties, andand givegive thethe rangerange ofof wavelengthswavelengths forfor visiblevisible spectrum.spectrum. •• ApplyApply thethe relationshiprelationship betweenbetween frequenciesfrequencies andand wavelengthswavelengths forfor opticaloptical waves.waves. •• DefineDefine andand applyapply thethe conceptsconcepts ofof luminousluminous fluxflux,, luminousluminous intensityintensity,, andand illuminationillumination.. •• SolveSolve problemsproblems similarsimilar toto thosethose presentedpresented inin thisthis module.module. AA BeginningBeginning DefinitionDefinition AllAll objectsobjects areare emittingemitting andand absorbingabsorbing EMEM radiaradia-- tiontion.. ConsiderConsider aa pokerpoker placedplaced inin aa fire.fire. AsAs heatingheating occurs,occurs, thethe 1 emittedemitted EMEM waveswaves havehave 2 higherhigher energyenergy andand 3 eventuallyeventually becomebecome visible.visible. 4 FirstFirst redred .. .. .. thenthen white.white. LightLightLight maymaymay bebebe defineddefineddefined
    [Show full text]
  • ASTR 545 Module 2 HR Diagram 08.1.1 Spectral Classes: (A) Write out the Spectral Classes from Hottest to Coolest Stars. Broadly
    ASTR 545 Module 2 HR Diagram 08.1.1 Spectral Classes: (a) Write out the spectral classes from hottest to coolest stars. Broadly speaking, what are the primary spectral features that define each class? (b) What four macroscopic properties in a stellar atmosphere predominantly govern the relative strengths of features? (c) Briefly provide a qualitative description of the physical interdependence of these quantities (hint, don’t forget about free electrons from ionized atoms). 08.1.3 Luminosity Classes: (a) For an A star, write the spectral+luminosity class for supergiant, bright giant, giant, subgiant, and main sequence star. From the HR diagram, obtain approximate luminosities for each of these A stars. (b) Compute the radius and surface gravity, log g, of each luminosity class assuming M = 3M⊙. (c) Qualitative describe how the Balmer hydrogen lines change in strength and shape with luminosity class in these A stars as a function of surface gravity. 10.1.2 Spectral Classes and Luminosity Classes: (a,b,c,d) (a) What is the single most important physical macroscopic parameter that defines the Spectral Class of a star? Write out the common Spectral Classes of stars in order of increasing value of this parameter. For one of your Spectral Classes, include the subclass (0-9). (b) Broadly speaking, what are the primary spectral features that define each Spectral Class (you are encouraged to make a small table). How/Why (physically) do each of these depend (change with) the primary macroscopic physical parameter? (c) For an A type star, write the Spectral + Luminosity Class notation for supergiant, bright giant, giant, subgiant, main sequence star, and White Dwarf.
    [Show full text]
  • STELLAR SPECTRA A. Basic Line Formation
    STELLAR SPECTRA A. Basic Line Formation R.J. Rutten Sterrekundig Instituut Utrecht February 6, 2007 Copyright c 1999 Robert J. Rutten, Sterrekundig Instuut Utrecht, The Netherlands. Copying permitted exclusively for non-commercial educational purposes. Contents Introduction 1 1 Spectral classification (“Annie Cannon”) 3 1.1 Stellar spectra morphology . 3 1.2 Data acquisition and spectral classification . 3 1.3 Introduction to IDL . 4 1.4 Introduction to LaTeX . 4 2 Saha-Boltzmann calibration of the Harvard sequence (“Cecilia Payne”) 7 2.1 Payne’s line strength diagram . 7 2.2 The Boltzmann and Saha laws . 8 2.3 Schadee’s tables for schadeenium . 12 2.4 Saha-Boltzmann populations of schadeenium . 14 2.5 Payne curves for schadeenium . 17 2.6 Discussion . 19 2.7 Saha-Boltzmann populations of hydrogen . 19 2.8 Solar Ca+ K versus Hα: line strength . 21 2.9 Solar Ca+ K versus Hα: temperature sensitivity . 24 2.10 Hot stars versus cool stars . 24 3 Fraunhofer line strengths and the curve of growth (“Marcel Minnaert”) 27 3.1 The Planck law . 27 3.2 Radiation through an isothermal layer . 29 3.3 Spectral lines from a solar reversing layer . 30 3.4 The equivalent width of spectral lines . 33 3.5 The curve of growth . 35 Epilogue 37 References 38 Text available at \tthttp://www.astro.uu.nl/~rutten/education/rjr-material/ssa (or via “Rob Rutten” in Google). Introduction These three exercises concern the appearance and nature of spectral lines in stellar spectra. Stellar spectrometry laid the foundation of astrophysics in the hands of: – Wollaston (1802): first observation of spectral lines in sunlight; – Fraunhofer (1814–1823): rediscovery of spectral lines in sunlight (“Fraunhofer lines”); their first systematic inventory.
    [Show full text]
  • Black Body Radiation and Radiometric Parameters
    Black Body Radiation and Radiometric Parameters: All materials absorb and emit radiation to some extent. A blackbody is an idealization of how materials emit and absorb radiation. It can be used as a reference for real source properties. An ideal blackbody absorbs all incident radiation and does not reflect. This is true at all wavelengths and angles of incidence. Thermodynamic principals dictates that the BB must also radiate at all ’s and angles. The basic properties of a BB can be summarized as: 1. Perfect absorber/emitter at all ’s and angles of emission/incidence. Cavity BB 2. The total radiant energy emitted is only a function of the BB temperature. 3. Emits the maximum possible radiant energy from a body at a given temperature. 4. The BB radiation field does not depend on the shape of the cavity. The radiation field must be homogeneous and isotropic. T If the radiation going from a BB of one shape to another (both at the same T) were different it would cause a cooling or heating of one or the other cavity. This would violate the 1st Law of Thermodynamics. T T A B Radiometric Parameters: 1. Solid Angle dA d r 2 where dA is the surface area of a segment of a sphere surrounding a point. r d A r is the distance from the point on the source to the sphere. The solid angle looks like a cone with a spherical cap. z r d r r sind y r sin x An element of area of a sphere 2 dA rsin d d Therefore dd sin d The full solid angle surrounding a point source is: 2 dd sind 00 2cos 0 4 Or integrating to other angles < : 21cos The unit of solid angle is steradian.
    [Show full text]
  • Spectral Classification and HR Diagram of Pre-Main Sequence Stars in NGC 6530
    A&A 546, A9 (2012) Astronomy DOI: 10.1051/0004-6361/201219853 & c ESO 2012 Astrophysics Spectral classification and HR diagram of pre-main sequence stars in NGC 6530,, L. Prisinzano, G. Micela, S. Sciortino, L. Affer, and F. Damiani INAF – Osservatorio Astronomico di Palermo, Piazza del Parlamento, Italy 1, 90134 Palermo, Italy e-mail: [email protected] Received 20 June 2012 / Accepted 3 August 2012 ABSTRACT Context. Mechanisms involved in the star formation process and in particular the duration of the different phases of the cloud contrac- tion are not yet fully understood. Photometric data alone suggest that objects coexist in the young cluster NGC 6530 with ages from ∼1 Myr up to 10 Myr. Aims. We want to derive accurate stellar parameters and, in particular, stellar ages to be able to constrain a possible age spread in the star-forming region NGC 6530. Methods. We used low-resolution spectra taken with VLT/VIMOS and literature spectra of standard stars to derive spectral types of a subsample of 94 candidate members of this cluster. Results. We assign spectral types to 86 of the 88 confirmed cluster members and derive individual reddenings. Our data are better fitted by the anomalous reddening law with RV = 5. We confirm the presence of strong differential reddening in this region. We derive fundamental stellar parameters, such as effective temperatures, photospheric colors, luminosities, masses, and ages for 78 members, while for the remaining 8 YSOs we cannot determine the interstellar absorption, since they are likely accretors, and their V − I colors are bluer than their intrinsic colors.
    [Show full text]
  • Multidisciplinary Design Project Engineering Dictionary Version 0.0.2
    Multidisciplinary Design Project Engineering Dictionary Version 0.0.2 February 15, 2006 . DRAFT Cambridge-MIT Institute Multidisciplinary Design Project This Dictionary/Glossary of Engineering terms has been compiled to compliment the work developed as part of the Multi-disciplinary Design Project (MDP), which is a programme to develop teaching material and kits to aid the running of mechtronics projects in Universities and Schools. The project is being carried out with support from the Cambridge-MIT Institute undergraduate teaching programe. For more information about the project please visit the MDP website at http://www-mdp.eng.cam.ac.uk or contact Dr. Peter Long Prof. Alex Slocum Cambridge University Engineering Department Massachusetts Institute of Technology Trumpington Street, 77 Massachusetts Ave. Cambridge. Cambridge MA 02139-4307 CB2 1PZ. USA e-mail: [email protected] e-mail: [email protected] tel: +44 (0) 1223 332779 tel: +1 617 253 0012 For information about the CMI initiative please see Cambridge-MIT Institute website :- http://www.cambridge-mit.org CMI CMI, University of Cambridge Massachusetts Institute of Technology 10 Miller’s Yard, 77 Massachusetts Ave. Mill Lane, Cambridge MA 02139-4307 Cambridge. CB2 1RQ. USA tel: +44 (0) 1223 327207 tel. +1 617 253 7732 fax: +44 (0) 1223 765891 fax. +1 617 258 8539 . DRAFT 2 CMI-MDP Programme 1 Introduction This dictionary/glossary has not been developed as a definative work but as a useful reference book for engi- neering students to search when looking for the meaning of a word/phrase. It has been compiled from a number of existing glossaries together with a number of local additions.
    [Show full text]
  • The Sun's Dynamic Atmosphere
    Lecture 16 The Sun’s Dynamic Atmosphere Jiong Qiu, MSU Physics Department Guiding Questions 1. What is the temperature and density structure of the Sun’s atmosphere? Does the atmosphere cool off farther away from the Sun’s center? 2. What intrinsic properties of the Sun are reflected in the photospheric observations of limb darkening and granulation? 3. What are major observational signatures in the dynamic chromosphere? 4. What might cause the heating of the upper atmosphere? Can Sound waves heat the upper atmosphere of the Sun? 5. Where does the solar wind come from? 15.1 Introduction The Sun’s atmosphere is composed of three major layers, the photosphere, chromosphere, and corona. The different layers have different temperatures, densities, and distinctive features, and are observed at different wavelengths. Structure of the Sun 15.2 Photosphere The photosphere is the thin (~500 km) bottom layer in the Sun’s atmosphere, where the atmosphere is optically thin, so that photons make their way out and travel unimpeded. Ex.1: the mean free path of photons in the photosphere and the radiative zone. The photosphere is seen in visible light continuum (so- called white light). Observable features on the photosphere include: • Limb darkening: from the disk center to the limb, the brightness fades. • Sun spots: dark areas of magnetic field concentration in low-mid latitudes. • Granulation: convection cells appearing as light patches divided by dark boundaries. Q: does the full moon exhibit limb darkening? Limb Darkening: limb darkening phenomenon indicates that temperature decreases with altitude in the photosphere. Modeling the limb darkening profile tells us the structure of the stellar atmosphere.
    [Show full text]
  • Aerosol Optical Depth Value-Added Product
    DOE/SC-ARM/TR-129 Aerosol Optical Depth Value-Added Product A Koontz C Flynn G Hodges J Michalsky J Barnard March 2013 DISCLAIMER This report was prepared as an account of work sponsored by the U.S. Government. Neither the United States nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise, does not necessarily constitute or imply its endorsement, recommendation, or favoring by the U.S. Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the U.S. Government or any agency thereof. DOE/SC-ARM/TR-129 Aerosol Optical Depth Value-Added Product A Koontz C Flynn G Hodges J Michalsky J Barnard March 2013 Work supported by the U.S. Department of Energy, Office of Science, Office of Biological and Environmental Research A Koontz et al., March 2013, DOE/SC-ARM/TR-129 Contents 1.0 Introduction .......................................................................................................................................... 1 2.0 Description of Algorithm ...................................................................................................................... 1 2.1 Overview
    [Show full text]
  • STHF-R Ultra High Flux Gamma Probe Data Sheet
    Features STHF-R™ Ultra High ■ Measurement of H*(10) Flux Gamma Probe ambient gamma dose equivalent rate up to 1000 Sv/h (100 000 R/h) Description ■ To be connected to The STHF-R ultra high flux Radiagem™, MIP 10 Digital™ probe is designed for the or Avior ® meters measurements of very high ■ Waterproof: 80 m (262.5 ft) gamma dose-equivalent rates water depth up to 1000 Sv/h. ■ Detector: Silicon diode This probe is especially ■ 5 kSv maximum integrated designed for ultra high flux dose measurement which can be found in pools in nuclear ■ Compact portable design for power plants or in recycling detector and detector cable facilities. Effectively this on reel probes box is stainless steel based and waterproof up to 80 m (164 ft) underwater. It can be laid underwater in the storage pools Borated water. An optional ballast weight can be supplied to ease underwater measurements. The STHF-R probe is composed of two matched units: ■ The measurement probe including the silicon diode and the associated analog electronics. ■ An interface case which houses the processing electronics that are more sensitive to radiation; this module can be remotely located up to 50 m (164 ft) from the measurement spot. ■ An intermediate connection point with 50 m length cable to which the interface case can be connected. The STHF-R probe can be connected directly to Avior, Radiagem or MIP 10 Digital meters. The STHF-R unit receives power from the survey meter during operation. STHF-R instruments include key components of hardware circuitry (high voltage power supply, amplifier, discriminator, etc.).
    [Show full text]