Download Lecture 5: Light as a tool

Light and how we observe the
Universe
How do atoms emit and absorb light?
 Each atom has a specific pattern of allowed
orbits.
Electrons jump between allowed orbits
http://spaceplace.nasa.gov/ir-photoalbum/en/
Why is the sky blue at mid-day and red at sunset?
The sky on Earth
appears blue because
blue (and violet)
photons are scattered
as they collide with air
particles.
The sky on Earth
appears red at sunset
because the light must
pass through a lot of
atmosphere.
Earth’s
Atmospher
e
Brainstorm!
1) Why does our sky appear to be mostly
blue, and not violet, at mid-day?
2) What color would our sky be if
atmospheric particles were slightly larger?
3) Why is the sky black on the moon?
Why do stars have a particular color?
All objects emit
electromagnetic
radiation.
Color depends
on temperature.
Energy Output  Surface Temperature  "Color"
 In science, the standard measure of
temperature is the Kelvin.
0 Kelvin = ─273o C = ─460o F
Object
Human Body
Sun
Blue Star
Kelvin
310.15 K
5800 K
35000 K
Fahrenheit
98.6 ºF
9,980 ºF
62,540 ºF
Energy, Temperature, & Wavelength
Stefan-Boltzman Law
Wien’s Law
E = T4
T = 3,000,000
max
2T → 16E
3T → 81 E
4T → 256 E
 Every star emits
photons in all colors.
 The color emitted most
is related to the surface
temperature.
Brainstorm!
1) What do you think the surface
temperature of a red star would be?
2) A blue star has a wavelength of
maximum emission at 434 nm.
What is the surface temperature of
this star?
Brainstorm!
1. If the Doppler shift is used to
measure the radial velocity, how do
we measure the tangential velocity?
2. What is the effect of the Doppler
shift for light coming from the sun?
The Magnitude Scale
First introduced by Hipparchus
(160–127 B.C.):
• Brightest stars: ~1st magnitude
• Faintest stars (unaided eye): 6th magnitude
More quantitative:
• 1st magnitude stars appear 100 times
brighter than 6th magnitude stars
• 1 magnitude difference gives a factor of
2.512 in apparent brightness
(larger magnitude => fainter object!)
Example:
Magnitude
Difference
Flux Ratio
1
2.512
2
2.512 × 2.512 =
(2.512)2 = 6.31
…
…
5
(2.512)5 = 100
For a magnitude difference
of 0.41 – 0.14 = 0.27, we
find an flux ratio of
(2.512)0.27 = 1.28
Betelgeuse
Magnitude = 0.41 mag
Rigel
Magnitude = 0.14 mag
The Magnitude Scale
The magnitude scale system can be extended towards
negative numbers (very bright) and numbers > 6 (faint
objects):
Sirius (brightest star in the sky): mv = –1.42
Full Moon: mv = –12.5
Sun: mv = –26.5
The Absolute Magnitude
A star’s absolute magnitude Mv is the apparent magnitude it
would have if it were at a distance of 10 parsecs (32.6 lightyears) from Earth.
– The Sun’s absolute magnitude is Mv = 4.8
– Sirius: Mv = +1.4
– Betelgeuse: Mv = -5.1
•
•
Apparent magnitude tells us nothing about the luminosity of
the objects, but it tell us how difficult it is to see the objects in
the sky.
Absolute magnitude, on the other hand, is directly related to
the luminosity of the object. But it does not tell us how bright
they appear in the sky.
Determination of Distance
Stellar Parallax
Knowledge of the distance to the
stars is crucial for our
determination of the luminosity
of stars…
• Current technology allows us to
determine the distance
accurately to within a few
hundred light-years.
• Hipparcos mission (European
Space Agency) measured the
stellar parallax of roughly
100,000 stars with precision of a
few milli-arcseconds. So, it can
measure distance of star up to
1,000 light-years away…
Many methods are used to determine distance
Spectroscopy
Kirchhoff’s Laws of Radiation
1. A solid, liquid, or dense gas excited to emit
light will radiate at all wavelengths and
thus produce a continuous spectrum.
Kirchhoff’s Laws of Radiation
2. If light comprising a continuous spectrum
passes through a cool, low-density gas, the
result will be an absorption spectrum.
Light excites electrons in
atoms to higher energy
states,
The frequencies of light correspond to the transition
energies absorbed from the continuous spectrum.
Kirchhoff’s Laws of Radiation
3. A low-density gas excited to emit light will
do so at specific wavelengths and thus
produce an emission spectrum.
Light excites electrons in
atoms to higher energy states,
Which transition back to lower states,
emitting light at specific frequencies.
The Spectra of Stars
Inner, dense layers of a
star produce a continuous
(blackbody) spectrum.
Cooler surface layers absorb light at specific frequencies.
=> Spectra of stars are absorption spectra.
Thermal source plus cool gas
Lines of Hydrogen
Most prominent lines
in many astronomical
objects: Balmer lines
of hydrogen
The Balmer Lines
Transitions
from 2nd to
higher levels
of hydrogen
n=1
H
H
H
The only hydrogen
lines in the visible
wavelength range
2nd to 3rd level = H (Balmer alpha line)
2nd to 4th level = H (Balmer beta line)
…
Absorption Spectrum
Dominated by Balmer Lines
Modern spectra are usually recorded
digitally and represented as plots of
intensity vs. wavelength.
Emission nebula,
dominated by the red
H line
Emission Spectra (“nonthermal”)
from hot, transparent gases
Spectral Lines from
Sunlight
Wollaston (1802)
– sunlight through slit to prism
– spectrum = rainbow with
holes
Fraunhofer (~1812)
– cataloged over
600 dark lines
Doppler-shifted absorption spectra
% shift in wavelength = speed of
source,
as % of
Doppler-shifted absorption spectra
% shift in wavelength = speed of
source,
as % of
Doppler-shifted absorption spectra
Shorter wavelengths implies it’s moving
toward us are shifted by about 10 units
Wavelengths
(Angstroms) out of 4000, or 1 part in 400.
Therefore this object is moving toward us at
Dispersion
Splitting up light in its spectral components achieved by
one of two ways:
• differential refraction
– prism
• interference
– reflection/transmission grating
– fourier transform
– (Fabry-Perot)
71
Diffraction grating