Name _______________________________
Partners _____________________________
Light and Starlight
Introduction
Light is electromagnetic radiation that propagates through space. It is emitted from charged
matter, particles such as electrons in atoms being excited (absorption) or de-excited (emission) in
stars and nebula, from nuclei (Gamma-ray), and during powerful stellar phenomena (e.g., supernovae, black-holes).
When a lot of light is emitted we can see it from a great distance. Stars emit tremendous
amounts of light – enough to sustain life here on earth, and can be seen from stars in our galaxy
tens of thousands of light years (ly) away, and from other galaxies millions of ly away.
Stars generate light because they are incredibly hot – thousands of degrees on the surface,
millions of degrees in the core. The heat is generated by thermonuclear fusion in the star’s core
that requires extreme density. The density is typically provided by gravity, compressing
hydrogen gas until fusion occurs. Fusion accelerates until the resulting heat and high pressure
balance gravity. A stable star is born.
How bright a star appears in the sky is related not only to how fast it is burning fuel, but how far
away it is. The farther away, the dimmer it appears. This is related to the “apparent magnitude”
scale you see on star charts.
Light is both wave and particle
Light can be thought of as a wave or particle. It exhibits both characteristics in different
situations. Light as a wave (the wave theory) was proven primarily by Young, Huygens,
Maxwell and Hertz prior to the 20th century. Light as a particle (the quantum theory) was proven
primarily by Einstein, Compton, Feynman, Schwinger and Tomonaga in the last century.
A wave is characterized by its frequency (in cycles/sec or Hertz (Hz)), wavelength, intensity and
speed. The frequency f and wavelength λ are related to each other by the formula
fλ=c
(1)
where c is the speed of light.
Different frequencies differences are seen as color differences. Visible light, for example, ranges
from a wavelength of 400nm (violet) to 700nm (red), and frequency from 7 x 1014Hz to 4 x
1014Hz, respectively. Brightness, on the other hand, is proportional to intensity, which is the
energy falling on a unit area per unit time.
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The spectrum of light is the range of frequencies (or by (1), wavelengths) it can have. All manner
of things we might think are different (like X-rays, “red light” or radio waves) are just different
frequency manifestations of the same thing – electromagnetic radiation.
1. Use (1) and your text or web to fill in the frequency, wavelength and type blanks in Table I
(below)
Type
Gamma-ray (γ)
X-ray
UV
Infrared
Microwave
Table I. The Light Spectrum in Astronomy
Frequency
Astrophysical Source
Wavelength
(Hz)
Black-holes, super10pm or
novae, solar flares,
shorter
γ-ray bursts(?)
Extremely hot gases,
1017-1018
neutron stars, blackholes, super-novae
Stars
10-400nm
Stars
400nm
Stars
700nm
12
14
Stars
10 -10
Synchrotron radiation,
1cm-100cm
masers, stars
Synchrotron radiation,
1m or longer
pulsars, stars, galaxies,
quasars, 30 background
Photon
energy(eV)
The particle nature of light is best illustrated by light’s energy. Light is emitted and absorbed by
charged matter only in discrete amounts of energy called quanta. Einstein received his Nobel
prize for this discovery.
A single quantum of light has been given the name “photon”. A photon has energy
E = hf
(2)
where “h” is Planck’s constant
h = 6.63 x 10-34 Joule-sec or
h = 4.14 x 10-15eV-sec
Both “Joule” and “eV” (electron volt) are units of energy. “eV” is typically used for atomic
spectra where energies are very small. A “joule” is related to “Watts” which you’ve heard of.
“1 Watt” (or 1W) is a Joule per second – a unit of “power” – the rate of energy production or
expenditure.
For example, using (2) the photon energy for a frequency of a 1018 Hz X-ray is
E = (4.14 x 10-15eV-sec) (1018Hz) = 4.14 keV
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where keV is 1000-eV (kilo-electron-volt).
To an observer, the apparent brightness of an object is the energy the observer sees from that
object per second. In terms of photons, it is directly proportional to the rate of photons emitted
by that object into that “seeing area” (e.g., our eyes). When we “see” a star, we are receiving
photons traveling for perhaps thousands of years into our eyes that are absorbed by our retina and
transferred as signals to our mind that “sees” the image of the star.
2. Fill in the Table I for the photon energies. Use keV for thousand-eV, MeV for million-eV, GeV
for billion-eV.
Note: pm = pico-meter = 10-12 m
nm = nano-meter = 10-9 m
μm = micro-meter = 10-6 m
3. Which type of photon in table I has the highest energy and in what range (of eV) is that energy?
Which type has the lowest energy and in what range (of eV) is that energy?
a) highest energy photon (eV/type) _____________________
b) lowest energy photon (eV/type) ______________________
Light Speed
The theory of relativity says that no mass can be accelerated to the speed of light – it is a barrier
that cannot be broken as far as we know at the present time. It is hard for us to imagine building a
rocket that could travel any where near the speed of light, so having an idea of how long light takes
to travel tells us it would take us thousands of times longer to cover that distance with our current
technology.
3. Since distance d = ct where t is time, find the distance light travels in a year in mi, km, AU, and
light-years (ly).
4. Calculate out how much time it takes light to travel from the Sun
a) to Earth (1 AU = 1.5 x 108km) in minutes _____________________
b) to Neptune (30.0 AU) in hours
_____________________
c) to the center of the Milky Way (37.5 x 1012 km) in years __________________
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d) to the Andromeda Galaxy (1.58 x 1011 AU) in years ______________________
Light Intensity – Luminosity, Brightness and Magnitudes of Stars
The brightness of an object is the energy per second per unit area. We see a star’s “apparent
brightness”. But it is far away from us, and its intensity is spread all over an expanding sphere of
area 4πd2 where d is the distance traveled.
At the source, we talk about the “luminosity” of a star, which is its rate of energy production
or “wattage” – 1 Watt = 1 Joule/sec. Our sun’s luminosity is
L = 3.9 x 1026 W
(3)
Where L is the standard symbol for the sun’s luminosity. Other stars’ luminosities are typically
expressed in terms of L .
Of course, the farther we are away from the sun, the less bright it appears. It is not because it is
producing less energy, but that its energy is spread out over a bigger and bigger area the farther we
go from the sun. The apparent brightness b of a star (which has the dimensions of Watts/m2 ) is
how much energy per unit time reaches us within a 1 square meter area. Starlight is a point source
that spreads its light over the surface area 4πd2 of a sphere radius d surrounding it. Then
b
L
4 d 2
(4)
5. Compute the apparent brightness of the sun from the earth with d being the distance from the
earth to the sun (in m). Use (3) and (4)
b of sun at earth ____________________W/m2
6. Compute the sun’s apparent brightness if it were as far away as alpha centauri (4.3 ly away)?
b of sun 4.3 ly away ____________________W/m2
Stars are often depicted on a star chart with varying sizes proportional to their apparent
brightness. They may also have a number by it which is the “apparent magnitude”. The
magnitude system was devised by Hipparchus long ago. It stuck, and we are stuck with it as a
result. His magnitude system gave numbers 0 to 6, where 0 was the brightest, 6 the dimmest.
Vega, a star always visible to us in the Northern Hemisphere, is magnitude 0.03. The faintest
stars visible to the naked eye are magnitude 6.
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It was later expanded as fainter stars needed larger + magnitudes, and brighter solar system
objects had to get negative magnitudes. Venus is about -4, the moon -13 and the sun -27. So the
smaller (or more negative) the magnitude, the brighter it is. A star with magnitude 4 is brighter
than a star with magnitude 6!
The question is how much brighter? Well, the magnitude scale is constructed so a difference of 5
in apparent magnitudes means 1 star is 100 times as bright as another star. This implies that a
difference 1 in apparent magnitude corresponds to 1001/5 = 2.512. So, a star of magnitude 3 is
2.512 brighter than a star with magnitude 4. In general, in terms of brightness bA and bB of stars A
and B, with apparent magnitudes A and B, respectively
bA
 2.512 B  A
bB
(5)
So, if star A has apparent magnitude 4, start B magnitude 6, the ratio of the apparent brightness of
A and B is 2.5126-4 = 6.3. That means A is 6.3 times as bright as B. (see here for reference).
The “summer triangle” is a famous for its appearance in the night sky of summer. It is a set of 3
bright stars: Vega, Altair and Deneb, which are present in their respective constellations Lyra,
Aquila, and Cygnus (the swan). Deneb has an apparent magnitude of 1.25, Altair 0.77 and Vega is
the brightest with 0.03.
Use (5) to find
7. a) the brightness of Vega relative to Deneb _____________________
b) which is brighter Vega or Deneb?
8. a) the brightness of Vega relative to Altair _____________________
b) which is brighter Vega or Altair?
9. a) the brightness of Altair relative to Deneb _____________________
b) which is brighter Deneb or Altair?
10. How much brighter is Venus (-4.4) than Vega? ____________________
11. How much brighter is the moon (-12.6) than Venus? ________________
12. How much brighter is the sun (-26) than the moon? _________________
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The primary source of light emission in the universe
Where does all the light in the night sky come from? From stars! According to Einstein’s theory
of relativity, a star converts matter to energy by thermonuclear fusion according to
E = mc2
(6)
where m is the mass and interestingly, the speed c of light appears. The sun converts mass into
energy some of which is light, the rest into the high kinetic energies of helium nuclei and nuclear
particles that result. The latter bounce around with other helium nuclei to produce the very high
temperatures of about 14 million oC in the core of the sun.
13. Calculate the amount of mass (kg/s) converted to energy within our sun each second to
produce the luminosity given by (3).
mass conversion kg/sec ________________________________
14. Given the mass of the sun is 1.99 × 1030 kilograms, use equation (6) to find the percent of the
sun used up each year
% sun fuel expended /yr ________________________________
Fusion happens in the core of a star. But the core comprises only 10% of the hydrogen in the
star. Also, only 1% of the mass of hydrogen is converted to energy, the rest is converted to
helium (and other elements). This means the time that available fuel remains for burning, and in
turn, the sun’s lifetime, can be estimated by multiplying the answer to #13 by .1 x .01 = .001.
15. From #13 multiplied by 0.001, estimate how many years sun will last as a powerful source of
light
sun’s lifetime ___________________________________
Star Formation
Stars form when giant molecular clouds (almost all hydrogen) are compressed enough to
cause thermonuclear reactions to accelerate. When gas is compressed, it heats up. A cloud
can either be gradually squeezed by gravity under its own collective weight (gravitational
collapse) , or be suddenly compressed by the shock wave of an exploding star (super-nova). The
result of both can be seen as nebula.
One example of a “gravitationsis the famous Eagle Nebula. Here is a view from the Hubble
Space Telescope (HST) – which by the way, your professor helped fix in 1993!
16. View a picture of the Eagle Nebula ______________ (check when viewed)
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In the next view a small portion of the Eagle Nebula is viewed, and has been named “Pillars of
Creation”. Enhanced (not actual) colors gave hydrogen emissions a green color, oxygen
emissions a blue color, and sulfur emissions reddish colors.
17. View the “Pillars of Creation” ______________ (check when viewed)
18. View a “Pillars” close-up ______________ (check when viewed)
19. Use the web to find facts about the Eagle Nebula:
a) Messier number _____________________
b) Age ______________________
c) Located in which constellation _________________________
d) How far away is it (ly)? ____________________
e) How big are the pillars (ly)? __________________
f) How big is the whole nebula (ly)? _________________
Use this link to answer the following questions on the Pillars
21. The star forming globules projecting from the pillars are called ________________
22. The process of stripping dust away from the globules is called ________________
The Color Of The Sun, The Color Of The Sky, and Why We Don’t See Stars In The Daytime
The sun’s emissions are greatest in the visible, with the maximum emission is right in the middle
of the visible range so all colors are present in roughly equal proportions. Therefore, we expect the
sun to be white. And to an astronaut, it is white!
But on earth the sun appears yellowish. How come? When white sunlight goes through the
atmosphere, some photons of shorter wave colors are subtracted out, leaving slightly more
intensity in long wavelengths in what we see.
23. A yellowish sun implies what colors are subtracted out?
_______________________________________
Air scatters light preferentially at shorter wavelengths. This is called “Rayleigh scattering”.
Scattering of light is like what happens when a ball hits some target – it deflects or changes
direction. It may change energy too. Light from the sun is a stream of quanta at all different
wavelengths.
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But the photons of light bounce off air molecules into different directions. The higher the
frequency the more likely light is to scatter. The result is a light beam coming directly to us from
the sun has a lot more green, blue and violet “scattered out” of the beam than red, orange or
yellow. The result is a yellowish tinge, since the longer wavelengths now predominate in the beam
itself.
What happens to the scattered photons? They’re going off in different directions from their
original beam. If we look away from the sun, we see some of those photons from beams going by
us. The mix of the scattered colors is “sky-blue”. The lower in the sky we look, the more
atmosphere there is (we’re looking at an angle through the lower atmosphere instead of directly up
through it). The more atmosphere there is, the more light that is scattered and the brighter it is.
So, overhead (the atmosphere is not as thick) the sky appears a little darker than closer to the
horizon. If there were no air to scatter light, we’d see a black sky, like night (but pitch, ink black),
except of course, for the sun.
So, during the day, a lot of sunlight is bouncing off molecules and coming at us from all directions
– not just directly from the sun. All this light is coming from parts of the sky where starlight is
also arriving at the same time. But so much scattered sunlight is coming from the area of starlight
that it drowns out the starlight, so we can’t see it. We see only the blue scattered sunlight. But the
moon is so bright (-13 magnitude), we can see it during the day.
24. When we see a blue sky it means we are seeing
a) direct sunlight
b) scattered sunlight
25. Since we can see the moon (apparent magnitude -13) but not Venus (-4) during the day,
estimate the brightness of the daytime sky.
sky’s daytime magnitude ____________________
After the sun goes down, there is much less light to scatter, so gradually the sky darkens. If it
darkens enough we can see objects with magnitudes lower (i.e., that are brighter) than the sky.
26. Estimate the sky’s brightness when you can first see Venus.
sky’s magnitude when Venus appears ____________________
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Name ______________________________
Pre-lab Questions – Light and Starlight
1. A photon is a type of
a) particle
b) wave
c) electromagnetic radiation
d) all of the above
e) none of the above
2. Different frequencies of visible light correspond to
a) different speeds of light
b) different colors of light
c) different intensities of light
d) white light
3. Electromagnetic radiation includes
a) X-rays and Gamma-Rays
b) radio waves and microwaves
c) UV rays and visible light
d) all of the above
e) none of the above
4. Most light in the universe is generated
a) in nebula
b) in stars
c) by black-holes
d) by the big-bang
5. In the vacuum a 2000-m light wave travels
a) faster than a 1000-m light wave
b) slower than a 1000-m light wave
c) the same speed as the 1000-m light wave
6. The speed of light is
a) infinitely fast
b) about ten times the speed of sound
c) faster than anything else in the universe
d) slower than matter can travel
7. Heat in stars is generated by
a) burning elements
b) burning electrons
c) fissioning nuclei
d) fusing nuclei
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