Simple Radiation Transfer for Spherical Stars

Total Page:16

File Type:pdf, Size:1020Kb

Simple Radiation Transfer for Spherical Stars SIMPLE RADIATION TRANSFER FOR SPHERICAL STARS Under LTE (Local Thermodynamic Equilibrium) condition radiation has a Planck (black body) distribution. Radiation energy density is given as 8πh ν3dν U dν = , (LTE), (tr.1) r,ν c3 ehν/kT 1 − and the intensity of radiation (measured in ergs per unit area per second per unit solid angle, i.e. per steradian) is c I = B (T )= U , (LTE). (tr.2) ν ν 4π r,ν The integrals of Ur,ν and Bν (T ) over all frequencies are given as ∞ 4 Ur = Ur,ν dν = aT , (LTE), (tr.3a) Z 0 ∞ ac 4 σ 4 c 3c B (T )= Bν (T ) dν = T = T = Ur = Pr, (LTE), (tr.3b) Z 4π π 4π 4π 0 4 where Pr = aT /3 is the radiation pressure. Inside a star conditions are very close to LTE, but there must be some anisotropy of the radiation field if there is a net flow of radiation from the deep interior towards the surface. We shall consider intensity of radiation as a function of radiation frequency, position inside a star, and a direction in which the photons are moving. We shall consider a spherical star only, so the dependence on the position is just a dependence on the radius r, i.e. the distance from the center. The angular dependence is reduced to the dependence on the angle between the light ray and the outward radial direction, which we shall call the polar angle θ. The intensity becomes Iν (r, θ). The specific intensity is the fundamental quantity in classical radiative transfer. The radiation energy density is its zeroth angular moment, the flux is its first angular moment, and the radiation pressure is its second angular moment. tr — 1 Let us consider a change in the intensity of radiation in the direction θ at the radial distance r when we move along the beam by a small distance dl = dr/ cos θ. The intensity will be reduced by the amount proportional to the opacity per unit volume, κν ρ multiplied by dl, where ρ is density of 2 −1 matter and κν is monochromatic total opacity in units cm g . κν is comprised of an absorptive a s (κν ) and a scattering (κν ) part. The former is connected to the emissivity by Kirchhoff’s law and the intensity will increase by the amount proportional to the emissivity of gas. Under nearly a LTE condition the emissivity per unit volume is given as a product κν ρBν (T ). The equation of monochromatic radiation transfer is written as s ∂Iν (θ, r) ∂Iν (θ, r) a κ ′ ′ ′ = cos θ = κν ρIν (θ, r)+ κ ρBν (T )+ I (θ, r)Φ(Ω , Ω)dΩ , (tr.4) ∂l ∂r − ν 4π Z ν where the last term represents the redistribution of radiation by scattering back into the beam with angular indicatrix (coupling) Φ(Ω′, Ω). Note that the dependence of the various opacities on photon frequency, as well as on the density, temperature, and chemical composition of the gas, is implied. Monochromatic radiation energy density may be calculated as 1 Ur,ν = Iν (θ, r) dΩ, (tr.5) c Z 4π where the integration is extended over the whole 4π solid angle. This is the zeroth angular moment of the radiation field. Because of azimuthal symmetry this integral may be written as π 2π Ur,ν = Iν (θ, r) sin θdθ. (tr.6) c Z 0 The total radiation energy density is given as ∞ Ur = Ur,ν dν. (tr.7) Z 0 tr — 2 Monochromatic flux of radiation in the direction r is the first angular moment of the specific intensity and may be calculated as π Fν = Iν (θ, r)cos θdω =2π Iν (θ, r)cos θ sin θdθ, (tr.8) Z Z 4π 0 and the total flux of radiation, measured in erg cm −2 s −1, is given as ∞ F = Fν dν. (tr.9) Z 0 The radiation pressure is the second angular moment of Iν , integrated over frequency. In the Eddington/diffusive approximation, the second moment is one-third of the zeroth moment. It can then be shown that the flux is driven by the spatial gradient of the Planck function: 4π ∂Bν (T ) 4π ∂Bν (T ) dT Fν = = . −3κνρ ∂r −3κνρ ∂T dr The total radiative energy flux is an integral of Fν over all frequencies, i.e ∞ 4π dT 1 ∂B (T ) 4π dB (T ) c dP F = ν dν = = r , (tr.10) − 3ρ dr Z κν ∂T −3κRρ dr −κRρ dr 0 where the Rosseland mean opacity, κR, is defined as ∞ ∞ 1 ∂Bν (T ) dν 1 ∂Bν (T ) dν 1 κν ∂T κν ∂T R0 R0 ∞ = ac 3 . (tr.11) κR ≡ ∂Bν (T ) π T ∂T dν R0 Of course, the Rosseland mean opacity is a function of density, temperature and chemical composi- tion, κR(ρ,T,X). We shall at times write the Rosseland opacity as κ. tr — 3 We now have L c dU 4acT 3 dT dT r = F = r = = λ , (tr.12) 4πr2 −3κρ dr − 3κρ dr − dr 2 where Lr = 4πr F is stellar luminosity at a radius r, i.e. the total amount of radiation energy flowing across a spherical surface with a radius r, and Ur is the radiation energy density. The last equation looks just like the equation for heat diffusion, with the coefficient of thermal conductivity λ related to the coefficient of opacity with a relation 4acT 3 λ = . (tr.13) 3κρ As heat may be transferred not only by photons, but also by electrons, it may be safer to write the last equation as 4acT 3 λrad = , (tr.14) 3κradρ where λrad and κrad are explicitly related to radiation. We may write a similar relation for electrons: 4acT 3 λel = , (tr.15) 3κelρ where λel and κel are the coefficients of thermal conductivity and ”opacity” for the electrons. In general, we may have some heat transferred by photons, and some by electrons. As the two means of heat transport are additive, the combined coefficient of thermal conductivity may by calculated as λ = λrad + λel, (tr.16) or equivalently, we may write a formula for the combined coefficient of opacity as 1 1 1 = + . (tr.17) κ κrad κel tr — 4 Near the stellar surface the luminosity and radius can be taken as L and R, and the radiation energy flux is F = L/4πR2. Let us define optical depth τ as dτ κρdr, τ =0 at r = R. (tr.18) ≡− Now, we may write the equation as dT 4 3F = const, (tr.19) dτ ac ≈ and therefore 3F T 4 = T 4 + τ, (tr.20) 0 ac where T0 is the temperature at the stellar surface. Consider now a surface radiating as a black body with a temperature T. At a point just above the surface the radiation comes from one hemisphere only, and we may use equations (tr.7), (tr.6), and (tr.2) to calculate ∞ π 2π Ur = Iν (θ) sin θdθ dν = (tr.21) Z c Z 0 0 ∞ π/2 2π 2π 1 4 Bν (T ) sin θdθ dν = B (T )= aT . Z c Z c 2 0 0 We obtained only one half of the radiation energy density expected under LTE conditions for the temperature T , because radiation was coming from one hemisphere only. The radiative energy flux may be calculated for our case: ∞ π ∞ π/2 F = 2π Iν (θ) sin θ cos θdθ dν = 2π Bν (T ) sin θ cos θdθ dν = (tr.22) Z Z Z Z 0 0 0 0 ac πB (T )= T 4 = σT 4. 4 We shall define the effective temperature of a star with a relation L = F σT 4 . (tr.23) 4πR2 ≡ eff This is a temperature that a black body would have if it radiated just as much energy per unit area as the star does. tr — 5 The radiation energy density at the surface of a black body is half of the LTE energy density corresponding to the temperature T . We shall adopt an approximation that at the stellar surface, 4 i.e. at τ = 0 the radiation energy density is aTeff /2, by analogy with a black body case. We find that 1 T 4 = T 4 , (tr.24) 0 2 eff and the temperature distribution close to the stellar surface is given as 1 3F 1 3 T 4 = T 4 + τ = T 4 + τ . (tr.25) 2 eff ac eff 2 4 Therefore, we have T = Teff at τ = 2/3. The optical depth 2/3 corresponds to a photosphere. This formula is the origin of the classic τ =2/3 condition for photospheres. Note that in the diffusion/Eddington approximation the surface temperature is 21/4 times lower than the effective temperature. The exact value is (4/√3)1/4, when the opacity is independent of frequency. The radiation diffusion equation may be written as dP κρ κρ L r = F = r . (tr.26) dr − c − c 4πr2 This may be combined with the equation of hydrostatic equilibrium to obtain dP dP dP GM κρ L g = r = r ρ + r = (tr.27) dr dr − dr − r2 4πc r2 GMr κLr 2 ρ 1 . − r − 4πcGMr The emergence of the local Eddington luminosity, 4πcGMr/κ is not a coincidence and is gratifying. tr — 6 Near the stellar surface we have Lr = L, and Mr = M. We shall find later on that when luminosity is very high then density in a stellar atmosphere is very low, and the opacity is dominated by scattering of photons on free electrons.
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]
  • 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]
  • 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]
  • 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]
  • 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]
  • Retrieval of Cloud Optical Thickness from Sky-View Camera Images Using a Deep Convolutional Neural Network Based on Three-Dimensional Radiative Transfer
    remote sensing Article Retrieval of Cloud Optical Thickness from Sky-View Camera Images using a Deep Convolutional Neural Network based on Three-Dimensional Radiative Transfer Ryosuke Masuda 1, Hironobu Iwabuchi 1,* , Konrad Sebastian Schmidt 2,3 , Alessandro Damiani 4 and Rei Kudo 5 1 Graduate School of Science, Tohoku University, Sendai, Miyagi 980-8578, Japan 2 Department of Atmospheric and Oceanic Sciences, University of Colorado, Boulder, CO 80309-0311, USA 3 Laboratory for Atmospheric and Space Physics, University of Colorado, Boulder, CO 80303-7814, USA 4 Center for Environmental Remote Sensing, Chiba University, Chiba 263-8522, Japan 5 Meteorological Research Institute, Japan Meteorological Agency, Tsukuba 305-0052, Japan * Correspondence: [email protected]; Tel.: +81-22-795-6742 Received: 2 July 2019; Accepted: 17 August 2019; Published: 21 August 2019 Abstract: Observation of the spatial distribution of cloud optical thickness (COT) is useful for the prediction and diagnosis of photovoltaic power generation. However, there is not a one-to-one relationship between transmitted radiance and COT (so-called COT ambiguity), and it is difficult to estimate COT because of three-dimensional (3D) radiative transfer effects. We propose a method to train a convolutional neural network (CNN) based on a 3D radiative transfer model, which enables the quick estimation of the slant-column COT (SCOT) distribution from the image of a ground-mounted radiometrically calibrated digital camera. The CNN retrieves the SCOT spatial distribution using spectral features and spatial contexts. An evaluation of the method using synthetic data shows a high accuracy with a mean absolute percentage error of 18% in the SCOT range of 1–100, greatly reducing the influence of the 3D radiative effect.
    [Show full text]
  • LFC-050-LE Light Flux Color and Luminous Efficacy Measurement Systems Why Choose Lightfluxcolor
    LFC-050-LE Light Flux Color and Luminous Efficacy Measurement Systems Why Choose LightFluxColor • Calibrations are traceable to NIST (USA) which are accepted and recognized globally. Ideal For Flux, Color & AC/DC The most economical and • Calibrated lamp standards NVLAP Electrical Characterization of: reliable solution for photometry accreditation Lab Code 200951-0 of light source needs! Automotive Lamps Traffic Lighting (ISO 17025) LED Clusters Architectural Lighting • Spectral flux standards (calibration LightFluxColor-LE Series Systems are the performed at each wavelength) are LED Bulbs Railway Lighting most affordable and reliable systems for testing supplied with each system for highest LED lighting products. Whether you are a possible accuracy. manufacturer of LED luminaires, street lights, • Single software controls all electronics and solar powered LED lanterns, LED bulbs, LightFluxColor-LE Series Systems also include provides optical and electrical data. or any other type of LED lighting product, a highly sensitive mini-calibrated CCD Array Spectrometer with spectral range from LightFluxColor Systems will meet all your testing • Competitive systems only provide 250 to 850 nm. This low noise and broad spectral requirements. LightFluxColor Systems allow luminous flux standards with CCT luminaire manufacturers to test LED products response spectrometer provide instantaneous calibration which limits overall for photometric performance. measurement of radiometric, photometric, and system accuracy. color characteristics of the LED sources. • AC/DC operation in one packaged LightFluxColor-LE Series Systems allow testing system users to test AC/DC characterization of lamps The fast results from the spectrometer helps at various input frequencies along with lumens to increase the rate of product development, • An auxiliary lamp is provided for and color parameters.
    [Show full text]
  • Radiometry of Light Emitting Diodes Table of Contents
    TECHNICAL GUIDE THE RADIOMETRY OF LIGHT EMITTING DIODES TABLE OF CONTENTS 1.0 Introduction . .1 2.0 What is an LED? . .1 2.1 Device Physics and Package Design . .1 2.2 Electrical Properties . .3 2.2.1 Operation at Constant Current . .3 2.2.2 Modulated or Multiplexed Operation . .3 2.2.3 Single-Shot Operation . .3 3.0 Optical Characteristics of LEDs . .3 3.1 Spectral Properties of Light Emitting Diodes . .3 3.2 Comparison of Photometers and Spectroradiometers . .5 3.3 Color and Dominant Wavelength . .6 3.4 Influence of Temperature on Radiation . .6 4.0 Radiometric and Photopic Measurements . .7 4.1 Luminous and Radiant Intensity . .7 4.2 CIE 127 . .9 4.3 Spatial Distribution Characteristics . .10 4.4 Luminous Flux and Radiant Flux . .11 5.0 Terminology . .12 5.1 Radiometric Quantities . .12 5.2 Photometric Quantities . .12 6.0 References . .13 1.0 INTRODUCTION Almost everyone is familiar with light-emitting diodes (LEDs) from their use as indicator lights and numeric displays on consumer electronic devices. The low output and lack of color options of LEDs limited the technology to these uses for some time. New LED materials and improved production processes have produced bright LEDs in colors throughout the visible spectrum, including white light. With efficacies greater than incandescent (and approaching that of fluorescent lamps) along with their durability, small size, and light weight, LEDs are finding their way into many new applications within the lighting community. These new applications have placed increasingly stringent demands on the optical characterization of LEDs, which serves as the fundamental baseline for product quality and product design.
    [Show full text]
  • • Flux and Luminosity • Brightness of Stars • Spectrum of Light • Temperature and Color/Spectrum • How the Eye Sees Color
    Stars • Flux and luminosity • Brightness of stars • Spectrum of light • Temperature and color/spectrum • How the eye sees color Which is of these part of the Sun is the coolest? A) Core B) Radiative zone C) Convective zone D) Photosphere E) Chromosphere Flux and luminosity • Luminosity - A star produces light – the total amount of energy that a star puts out as light each second is called its Luminosity. • Flux - If we have a light detector (eye, camera, telescope) we can measure the light produced by the star – the total amount of energy intercepted by the detector divided by the area of the detector is called the Flux. Flux and luminosity • To find the luminosity, we take a shell which completely encloses the star and measure all the light passing through the shell • To find the flux, we take our detector at some particular distance from the star and measure the light passing only through the detector. How bright a star looks to us is determined by its flux, not its luminosity. Brightness = Flux. Flux and luminosity • Flux decreases as we get farther from the star – like 1/distance2 • Mathematically, if we have two stars A and B Flux Luminosity Distance 2 A = A B Flux B Luminosity B Distance A Distance-Luminosity relation: Which star appears brighter to the observer? Star B 2L L d Star A 2d Flux and luminosity Luminosity A Distance B 1 =2 = LuminosityB Distance A 2 Flux Luminosity Distance 2 A = A B Flux B Luminosity B DistanceA 1 2 1 1 =2 =2 = Flux = 2×Flux 2 4 2 B A Brightness of stars • Ptolemy (150 A.D.) grouped stars into 6 `magnitude’ groups according to how bright they looked to his eye.
    [Show full text]
  • Use and Measurement of Mass Flux and Mass Discharge
    Technology Overview Use and Measurement of Mass Flux and Mass Discharge Mass Discharge (Md) = Sum of Mass Flux (J) Estimates MdB MdA B Flux JAi,j Flux J i,j Transect A Transect B August 2010 Prepared by The Interstate Technology & Regulatory Council Integrated DNAPL Site Strategy Team ABOUT ITRC Established in 1995, the Interstate Technology & Regulatory Council (ITRC) is a state-led, national coalition of personnel from the environmental regulatory agencies of all 50 states and the District of Columbia, three federal agencies, tribes, and public and industry stakeholders. The organization is devoted to reducing barriers to, and speeding interstate deployment of, better, more cost-effective, innovative environmental techniques. ITRC operates as a committee of the Environmental Research Institute of the States (ERIS), a Section 501(c)(3) public charity that supports the Environmental Council of the States (ECOS) through its educational and research activities aimed at improving the environment in the United States and providing a forum for state environmental policy makers. More information about ITRC and its available products and services can be found on the Internet at www.itrcweb.org. DISCLAIMER ITRC documents and training are products designed to help regulators and others develop a consistent approach to their evaluation, regulatory approval, and deployment of specific technologies at specific sites. Although the information in all ITRC products is believed to be reliable and accurate, the product and all material set forth within are provided without warranties of any kind, either express or implied, including but not limited to warranties of the accuracy or completeness of information contained in the product or the suitability of the information contained in the product for any particular purpose.
    [Show full text]