Download The portion of light we detect from a star/blackbody depends on

Amount of Light
The portion of light we detect from a star/blackbody depends on
several factors that have nothing to do with the star!
--The area of our detector
--The wavelengths to which it is sensitive (visible? IR? just green?)
--The fraction of the star’s area whose light we receive.
--The angle of our detector with respect to the incoming light.
We need a way to translate the light we observe to the object’s
intrinsic properties. So we consider:
only light falling on 1 square meter in one second (1/m2)
only a specific wavelength range: [λ, λ + dλ] (nanometers)
only light entering a given solid angle: dΩ (steradians)
We then can measure energy received
as:
Joules per second per m2 per unit
wavelength per unit solid angle.
Watts/m2/nm/steradian.
That’s: Bλ(T)
Catastrophe!!!
Classical physics was used to predict the amount of
light produced by a blackbody at various wavelengths.
These predictions were utterly wrong!
Since the discrepancy was greatest at UV
wavelengths, this problem was called the:
“ultraviolet catastrophe.”
Quantum Physics
Planck tried to explain blackbody radiation anyway he could.
He postulated that energy came only in discrete units:
E=hν
Where h = 6.67 x 10-34 J s became known as Planck’s constant.
(these units are now called photons)
This guess allowed him to derive the dependence of the light from the
BB on temperature and wavelength. He found...
...That intensity of light Bλ(Τ) at each
specific wavelength (λ) produced by
a blackbody of temperature T is:
“Planck function”
Q: “At which wavelength does this function reach a maximum?” (λMAX,)
A: To see, define: x = (kT/hc) λ. x will max. out where λ maxes out.
The numerical value of x will give you Wien’s Law:
Amount of Light
Each spectrum shows the
light output of an object
at a different temperature.
Wein’s Law: how
astronomers measure
temperature.
Warm objects (black bodies) emit light at various wavelengths.
But the peak of this spectrum is inversely proportional to Temp.
Amount of Light
The Total Luminosity of the
star is the sum (integral over all
wavelengths) of Bλ(T)
Where R = star’s radius. (So larger stars give off more light)
Also, a hotter star is more luminous, at all wavelengths.
Stephan Boltzmann Law
Not all objects emit a perfect “Black-body” spectrum.
Still we we can define an effective temperature, Teff for them.
Group Activity:
Using the Stephan-Boltzman Law, estimate your body’s
luminosity (in Watts). Make any approximation that helps!
Conversions: [K] = ([°F] + 459.67) × 5⁄9
Bolometric Magnitude
So far, we have assumed we could detect light at all wavelengths.
Then, from a measured flux, we could define the apparent
magnitude of a star using:
Mags. defined this way are called bolometric.
In practice we observe: Fλ the flux of light within a certain
wavelength range, bandwidth.
E.g.: Observe all light between: [500,505 nm]
The bandwidth is Δλ = 5 nm
Filters
We may wish to deliberately restrict the wavelength range we
observe using filters. Filters used in visible astronomy are:
U filter: “ultraviolet”, 365 nm
B filter: “blue” 440 nm
V filter: “visible”: 550 nm
Each filter has a range in wavelengths.
Absolute mags. observed in these filters are: MU, MB, MV.
Apparent mags. observed in these filters are: mU, mB, mV, or more
commonly: U, B, V
(note these are capital letters!)
Sensitivity of the 3 common filters.
Color Temperature
By observing at two wavelengths we
“pick off” two points on the star’s light
output.
This is often sufficient to give an
indication of the color of the star.
In fact, Mag. differences are referred to
as the star’s “color”: U-B, B-V, U-V
BV
Challenge Question: Which of the stars above has a larger B-V??
Recall that lower mags = brighter!
The Spectrograph
A spectrograph uses a prism or
grating to split light up into
different wavelengths
A Spectrum
Modern spectra are recorded
digitally as plots of intensity vs.
wavelength
Brightness (or Intensity)
Spectrum of the Sun
Wavelength
The Sun emits light at UV, Visible and Infrared wavelengths
Like the Sun, most stars’s spectra show dark absorption lines
Spectroscopy
We can spread the light of a star out into its component
colors.
We find that these spectra fall into three categories:
• Continuum -- Rainbow
• Absorption -- Dark Lines
• Emission -- Bright Lines
We can compare a star’s spectrum to lab experiments.
The type of spectrum tells us about the star.
Video on discovery of spectral lines:
https://vimeo.com/113614651
Absorption Spectrum
Emission Spectrum
Measuring Velocities
Stars move through space in all directions.
We can define a star’s velocity vector V, in two ways:
1.) with a x,y,z coordinate system based on the Milky Way Galaxy
[Vx, Vy, Vz] = [U,V,W]
(see Croswell, p.40)
(where x-axis is the direction to the galactic center)
2.) with a spherical coordinate system [vθ, vr] where:
vr = radial velocity: speed along the line of sight to the star
vθ = tangent velocity, related to proper motion μ).
Doppler Effect
Proper motion can be measured by observing a star’s location for several years.
Radial velocity is usually measured using the Doppler effect.
Δλ
Δλ