STARS AS BLACKBODIES3RF Sciences, LLC

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

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

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

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.

Blackbody curves, 4 objects

a) 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

Blackbody curves, 4 objects

b) 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

c) 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

Blackbody curves, 4 objects

Blackbody curves, 4 objects

d) 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

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

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

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)

Wein’s Law in action…

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

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

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

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:

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

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

Stefan–Boltzmann Law

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,

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

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.