Stars as blackbodies

1. 3RF Sciences, LLC Stars as blackbodies

2. Blackbody defined… • A blackbody is an object that absorbs all light that hits it • Also emits light provided that its temperature is above absolute zero • http://www.handprint.com/HP/WCL/IMG/bbody.gif

3. A Blackbody… • Perfect “black body” – something which absorbs all the radiation that falls on it • Good absorber of radiant heat is also a good emitter • Main scientist - 1859, G. Kirchhoff • Foundation of blackbody radiation lies in the idea that radiation is released from blackbodies in the form of "quanta" or discrete packets of light called photons • Main scientist – 1900, Max Planck

4. More about a Blackbody… • Is the best possible emitter of radiant energy • Must both radiate and absorb energy at the same rate in order to maintain a constant temperature • Total radiation from a black body depends only on temperature of the body, not on chemical or physical characteristics

5. Plotting Curves • A curve can be generated plotting the temperature, intensity, or brightness of the black body versus the wavelength coming from it. • These curves are sometimes called Planck curves.

6. Blackbody curves, 4 objects • Cool, invisible galactic gas cloud called Rho Ophiuchi. • Temperature of 60 K • Emits mostly low-frequency radio radiation • http://www.daf.on.br/jlkm/astron2e/AT_MEDIA/CH03/CHAP03AT/AT03FG13.JPG

7. Blackbody curves, 4 objects • A dim, young star (shown here in red) near the center of the Orion Nebula. • Temperature of star's atmosphere ~ 600 K • Radiates primarily in infrared (IR) • http://www.daf.on.br/jlkm/astron2e/AT_MEDIA/CH03/CHAP03AT/AT03FG13.JPG

8. Blackbody curves, 4 objects • The Sun • Surface ~ 6000 K • Brightest in the visible (v) region of the electromagnetic spectrum • http://www.daf.on.br/jlkm/astron2e/AT_MEDIA/CH03/CHAP03AT/AT03FG13.JPG

9. Blackbody curves, 4 objects • A cluster of very bright stars, called Omega Centauri, as observed by a telescope aboard the space shuttle • Temperature ~ 60,000 K • Radiate strongly in ultraviolet (UV) • http://www.daf.on.br/jlkm/astron2e/AT_MEDIA/CH03/CHAP03AT/AT03FG13.JPG

10. How is a star a blackbody? • Because blackbody radiation is solely dependent on temperature (simple) • And to maintain a constant temperature, a blackbody must emit radiation in the same amount as it absorbs

11. Wein’s Law • The hotter a blackbody becomes, the shorter its wavelength of peak emission becomes • The wavelength of peak emission is simply the wavelength at which a blackbody emits most of its radiation

12. Wein’s Law • 1893, German physicist Wilhelm Wien • Quantified relationship between blackbody temperature and wavelength of spectral peak • λmax = 2.9 x 10-3 (microns)/T • λmax (lambda max) = wavelength of Peak emission • 2898 microns • T = temperature of Blackbody in Kelvin (K)

13. Wein’s Law in action…

14. Plank Curves - 1 • 1900 , Max Planck • Electromagnetic radiation absorbed or emitted only in “chunks” of energy, quanta, E • Quanta are proportional to the frequency of the radiation E = h. (Constant of proportionality “h” is Planck's constant.) • Wanted to understand the shape of Wien's radiative energy distribution as a function of frequency. • http://abyss.uoregon.edu/~js/glossary/planck_curve.html

15. http://www.oglethorpe.edu/faculty/~m_rulison/Astronomy/Dictionary/Laws%20of%20Radiation_files/radiation_curve.gifhttp://www.oglethorpe.edu/faculty/~m_rulison/Astronomy/Dictionary/Laws%20of%20Radiation_files/radiation_curve.gif

16. Plank Curves - 2 • Postulated that radiators or oscillators can only emit electromagnetic radiation in finite amounts of energy of size. • At a given temperature T, there is not enough thermal energy available to create and emit many large radiation quanta. • More large energy quanta can be emitted when temperature is raised. • http://abyss.uoregon.edu/~js/glossary/planck_curve.html

17. Plank’s Law • The amount of blackbody radiative flux emitted by a blackbody for a given wavelength is given by Planck's Law: • Where T is object temperature (in degrees Kelvin); l is wavelength in microns; units are (W/m2) per micron • The wavelength of peak emission is:

18. Stefan–Boltzmann Law • Independently formulated by Josef Stefan (1879) and Ludwig Boltzmann (1884, 1889) • Relationship between radiant energy and temperature for a black body radiator • Relates total radiant flux (F) (in W/m2), from surface of black body to its temperature (T) • F= σ T4 • σ = 5.6703 x 10-8 watt / m2 K4

19. Stefan–Boltzmann Law 2 • How much power a blackbody radiates per unit area of its surface • For a blackbody of temperature T, the power radiated per unit area is: • P = constant x T4 • http://zebu.uoregon.edu/~imamura/122/images/stefanboltzmanlaw.jpg

20. Stefan–Boltzmann Law

21. Why use Stefan-Boltzmann(S-B) Law? • Using the Stefan-Boltzmann law in conjunction with other known quantities, it can be used to infer properties of a star • For example, if a star radiates like a blackbody, then the luminosity of the star can be written as • L = (Surface Area of the Star) x (power per unit area produced by the star)= 12.6 x R2 x constant x T4 So, if we know certain information (obtained through independent means) about a star, we can infer other properties. For example,

22. What can we learn from S-B law? • If we know the luminosity and temperature, we can infer the radius of the star; • If we know the luminosity and radius of a star, we can infer its temperature; • If we know the radius and temperature of a star, we can infer its luminosity

23. Blackbody Review • Stefan-Boltzmann Law - Area under the curve increases as the temperature is increased • Wien's Law – Peak of the curve in emitted energy changes wavelength • Planck’s Law – Peak of the curve or the peak emission wavelength of a blackbody is related to the temperature of the object – hotter objects emit in higher wavelengths.