Stellar Atmospheres: The Radiation Field 1 The Radiation Field.

Slides:

Advertisements

Similar presentations

1 The structure and evolution of stars Lecture 3: The equations of stellar structure Dr. Stephen Smartt Department of Physics and Astronomy

Advertisements

1 The structure and evolution of stars Lecture 2: The equations of stellar structure Dr. Stephen Smartt Department of Physics and Astronomy

Stellar Atmospheres: Hydrostatic Equilibrium 1 Hydrostatic Equilibrium Particle conservation.

ASTROPHYSICS SUMMARY.

3RF Sciences, LLC. Blackbody defined…  A blackbody is an object that absorbs all light that hits it  Also emits light provided that its temperature.

OC3522Summer 2001 OC Remote Sensing of the Atmosphere and Ocean - Summer 2001 Review of EMR & Radiative Processes Electromagnetic Radiation - remote.

Light. Photons The photon is the gauge boson of the electromagnetic force. –Massless –Stable –Interacts with charged particles. Photon velocity depends.

Blackbody radiation Goals: Understand properties of Black body radiation; Black body radiation Radiation power, intensity and angle dependence.

NJIT Physics 320: Astronomy and Astrophysics – Lecture VIII Carsten Denker Physics Department Center for Solar–Terrestrial Research.

Astronomy 1 – Winter 2011 Lecture 7; January

Lecture 27. Debye Model of Solids, Phonon Gas

Which picture shows the larger flux of blue circles? 1.Left 2.Right 3.Neither.

Quantum physics. Quantum physics grew out failures of classical physics which found some quantum remedies in the Planck hypothesis and wave-particle duality.

Color/Temperature Relation

Stars Introduction To “Atomic Astrophysics and Spectroscopy” (AAS) Anil Pradhan and Sultana Nahar Cambridge University Press 2011 Details at:

Ch. 5 - Basic Definitions Specific intensity/mean intensity Flux

Radiation Definitions and laws Heat transfer by conduction and convection required the existence of a material medium, either a solid or a.

Laws of Radiation Heat Transfer P M V Subbarao Associate Professor Mechanical Engineering Department IIT Delhi Macro Description of highly complex Wave.

Radiation: Processes and Properties -Basic Principles and Definitions- Chapter 12 Sections 12.1 through 12.3.

Blackbody Radiation & Atomic Spectra. “Light” – From gamma-rays to radio waves The vast majority of information we have about astronomical objects comes.

Now we begin…..

Basic Definitions Terms we will need to discuss radiative transfer.

Chapter 18 Bose-Einstein Gases Blackbody Radiation 1.The energy loss of a hot body is attributable to the emission of electromagnetic waves from.

Stellar structure equations

Radiative Equilibrium

Ch. 5 - Basic Definitions Specific intensity/mean intensity Flux

Lecture 4a. Blackbody Radiation Energy Spectrum of Blackbody Radiation - Rayleigh-Jeans Law - Rayleigh-Jeans Law - Wien’s Law - Wien’s Law - Stefan-Boltzmann.

Note that the following lectures include animations and PowerPoint effects such as fly-ins and transitions that require you to be in PowerPoint's Slide.

Stellar Atmospheres: Radiation Transfer 1 Radiation Transfer.

M.R.Burleigh 2601/Unit 1 DEPARTMENT OF PHYSICS AND ASTRONOMY LIFECYCLES OF STARS Option 2601.

Black Holes Escape velocity Event horizon Black hole parameters Falling into a black hole.

Lecture 24. Blackbody Radiation (Ch. 7) Two types of bosons: (a)Composite particles which contain an even number of fermions. These number of these particles.

The Sun and other stars. The physics of stars A star begins simply as a roughly spherical ball of (mostly) hydrogen gas, responding only to gravity and.

How to Make Starlight (part 1) Chapter 7. Origin of light Light (electromagnetic radiation) is just a changing electric and magnetic field. Changing electric.

Spectra What determines the “color” of a beam of light? The answer is its frequency, or equivalently, its wavelength. We see different colors because.

Photon Statistics Blackbody Radiation 1.The energy loss of a hot body is attributable to the emission of electromagnetic waves from the body. 2.The.

Radiation Fundamental Concepts EGR 4345 Heat Transfer.

Energy Transport Formal solution of the transfer equation Radiative equilibrium The gray atmosphere Limb darkening.

A short review The basic equation of transfer for radiation passing through gas: the change in specific intensity I is equal to: -dI /d  = I - j /  =

Starlight and Atoms, or How to Make Light. Origin of light (actually, electromagnetic radiation) Light is Electromagnetic Radiation (EMR) that we see.

{ Week 22 Physics.  Understand that a star is in equilibrium under the action of two opposing forces, gravitation and the radiation pressure of the star.

1 The structure and evolution of stars Lecture 3: The equations of stellar structure.

Blackbody Spectrum Remember that EMR is characterized by wavelength (frequency) Spectrum: distribution of wavelength (or frequency) of some EMR Blackbody:

ASTROPHYSICS. Physical properties of star 1.SIZE spherical depends on mass, temperature, gravity & age Range- 0.2R to 220 R, R- solar radius = 6.96 x.

Wavelength Intensity of emitted e/m radiation 6000K 2000K 1500K 1000K VIBGYOR Wien’s Displacement Law for black body radiation peak wavelength  1 / Temp.

Chapter 3 Stars: Radiation  Nick Devereux 2006 Revised 2007.

Note that the following lectures include animations and PowerPoint effects such as fly-ins and transitions that require you to be in PowerPoint's Slide.

PHY134 Introductory Astronomy Light and Matter 1.

Lecture 8 Radiative transfer.

Lecture 12 Stellar structure equations. Convection A bubble of gas that is lower density than its surroundings will rise buoyantly  From the ideal gas.

Hale COLLAGE (CU ASTR-7500) “Topics in Solar Observation Techniques” Lecture 2: Describing the radiation field Spring 2016, Part 1 of 3: Off-limb coronagraphy.

Oct. 9, Discussion of Measurement uncertainties (cont.) Measurements always have uncertainties, which can be estimated in our labs (and in your.

Basic Definitions Specific intensity/mean intensity Flux

Blackbody Radiation A blackbody is something that absorbs all radiation that shines on it Are all blackbodies black? - no!! - imagine a box full of lava.

Chapter 9 Bradt’s Astronomy Methods Outline of Chapter Concepts ASTR 402 Observational Astronomy Dr. H. Geller Department of Physics and Astronomy George.

Black Bodies Wien’s Law – Peak intensity Stefan-Boltzman Law – Luminosity Planck’s Law – Energy Distribution –Rayleigh-Jeans approximation –Wien approximation.

Lecture 8: Stellar Atmosphere 4. Stellar structure equations.

Remote sensing: the collection of information about an object without being in direct physical contact with the object. the collection of information about.

Chapter 4 – Radiation Essentials. Reconsider TE Consider a closed box (a ‘cavity’ at equilibrium) with no heat loss or gain, uniform T throughout. The.

Cool, invisible galactic gas (60 K, f peak in low radio frequencies) Dim, young star (600K, f peak in infrared) The Sun’s surface (6000K, f peak in visible)

Lecture 8: Stellar Atmosphere 3. Radiative transfer.

Lecture 8: Stellar Atmosphere

The Transfer Equation The basic equation of transfer for radiation passing through gas: the change in specific intensity In is equal to: dIl = intensity.

10: Electromagnetic Radiation

Radiative Field (Hubeny & Mihalas Chapter 3)

Modeling Stars.

Black Holes Escape velocity Event horizon Black hole parameters

Radiative Field (Hubeny & Mihalas Chapter 3)

Terms we will need to discuss radiative transfer.

Presentation transcript:

Stellar Atmospheres: The Radiation Field 1 The Radiation Field

Stellar Atmospheres: The Radiation Field 2 Description of the radiation field Macroscopic description: Specific intensity as function of frequency, direction, location, and time; energy of radiation field (no polarization) in frequency interval (, +d ) in time interval (t,t+dt) in solid angle d  around n through area element d  at location r  n

Stellar Atmospheres: The Radiation Field 3 The radiation field dA dd  dd

Stellar Atmospheres: The Radiation Field 4 Relation Energy in frequency interval (, +  ) Energy in wavelength interval (, +  ) i.e. thus with

Stellar Atmospheres: The Radiation Field 5 Invariance of specific intensity The specific intensity is distance independent if no sources or sinks are present. 

Stellar Atmospheres: The Radiation Field 6 Irradiance of two area elements dA dA´ d ´

Stellar Atmospheres: The Radiation Field 7 Specific Intensity Specific intensity can only be measured from extended objects, e.g. Sun, nebulae, planets Detector measures energy per time and frequency interval

Stellar Atmospheres: The Radiation Field 8 Special symmetries Time dependence unimportant for most problems In most cases the stellar atmosphere can be described in plane-parallel geometry Sun: z

Stellar Atmospheres: The Radiation Field 9 For extended objects, e.g. giant stars (expanding atmospheres) spherical symmetry can be assumed r=R outer boundary p r z

Stellar Atmospheres: The Radiation Field 10 Integrals over angle, moments of intensity The 0-th moment, mean intensity In case of plane-parallel or spherical geometry

Stellar Atmospheres: The Radiation Field 11 J is related to the energy density u l dV dA dd

Stellar Atmospheres: The Radiation Field 12 The 1st moment: radiation flux  x y z

Stellar Atmospheres: The Radiation Field 13 Meaning of flux: Radiation flux = netto energy going through area  z-axis Decomposition into two half-spaces: Special case: isotropic radiation field: Other definitions:

Stellar Atmospheres: The Radiation Field 14 Idea behind definition of Eddington flux In 1-dimensional geometry the n-th moments of intensity are

Stellar Atmospheres: The Radiation Field 15 Idea behind definition of astrophysical flux Intensity averaged over stellar disk = astrophysical flux R p=Rsin

Stellar Atmospheres: The Radiation Field 16 Idea behind definition of astrophysical flux Intensity averaged over stellar disk = astrophysical flux dp p

Stellar Atmospheres: The Radiation Field 17 Flux at location of observer 

Stellar Atmospheres: The Radiation Field 18 Total energy radiated away by the star, luminosity Integral over frequency at outer boundary: Multiplied by stellar surface area yields the luminosity 

Stellar Atmospheres: The Radiation Field 19 The photon gas pressure Photon momentum: Force: Pressure: Isotropic radiation field: 

Stellar Atmospheres: The Radiation Field 20 Special case: black body radiation (Hohlraumstrahlung) Radiation field in Thermodynamic Equilibrium with matter of temperature T

Stellar Atmospheres: The Radiation Field 21 Hohlraumstrahlung

Stellar Atmospheres: The Radiation Field 22 Asymptotic behaviour In the „red“ Rayleigh- Jeans domain In the „blue“ Wien domain

Stellar Atmospheres: The Radiation Field 23 Wien´s law x:=hv/kT

Stellar Atmospheres: The Radiation Field 24 Integration over frequencies Stefan-Boltzmann law Energy density of blackbody radiation:

Stellar Atmospheres: The Radiation Field 25 Stars as black bodies – effective temperature Surface as „open“ cavity (... physically nonsense) Attention: definition dependent on stellar radius!  

Stellar Atmospheres: The Radiation Field 26 Stars as black bodies – effective temperature

Stellar Atmospheres: The Radiation Field 27 Examples and applications Solar constant, effective temperature of the Sun Sun‘s center 

Stellar Atmospheres: The Radiation Field 28 Examples and applications Main sequence star, spectral type O Interstellar dust 3K background radiation

Stellar Atmospheres: The Radiation Field 29 Radiation temperature... is the temperature, at which the corresponding blackbody would have equal intensity Comfortable quantity with Kelvin as unit Often used in radio astronomy

Stellar Atmospheres: The Radiation Field 30 The Radiation Field - Summary -

Stellar Atmospheres: The Radiation Field 31 Summary: Definition of specific intensity dA dd  dd

Stellar Atmospheres: The Radiation Field 32 Summary: Moments of radiation field In 1-dim geometry (plane-parallel or spherically symmetric): Mean intensity Eddington flux K-integral

Stellar Atmospheres: The Radiation Field 33 Summary: Moments of radiation field