Download • This chapter concentrates on five goals:

• This chapter concentrates on five
goals:
•
•
•
•
•
Knowing how far away stars are
How much energy they emit
What their surface temperatures are
How big they are
How much mass they contain
Star Distances
• Distance is the most important,
and the most difficult,
measurement in astronomy.
• Astronomers have many different
ways to find the distances to stars.
Each of those ways depends on a simple and direct
geometrical method that is much like the method
surveyors would use to measure the distance across
a river they cannot cross.
p. 44
Figure 9-1 p182
You can measure the parallax of a nearby star by photographing it from two points along
Earth’s orbit. For example, you might photograph it now and again in six months.
Figure 9-2 p182
Distances to Stars
Trigonometric Parallax:
A star appears slightly shifted from
different positions of the Earth on its orbit.
The further away the star is (larger d),
the smaller the parallax angle p.
1 pc = 3.26 LY
• Imagine a dime two miles away from you, the
dime covers an angle of 1 arcsec
If you know how far away something is you can use this
relationship to figure out how bright it is
Intrinsic Brightness /
Absolute Magnitude
The more distant a light source
is, the fainter it appears.
The same amount of light falls
onto a smaller area at distance
1 than at distance 2 => smaller
apparent brightness
Area increases as square of distance => apparent
brightness decreases as inverse of distance squared
Distance and
Intrinsic Brightness
Rigel appears 1.28 times
brighter than Betelgeuze.
Betelgeuze
But, Rigel is 1.6 times
further away than
Betelgeuze.
Thus, Rigel is actually
(intrinsically)
1.28 x (1.6)2 = 3.3 times
brighter than Betelgeuze.
Rigel
Absolute Visual Magnitude
• Astronomers use 10 pc as the standard
distance.
• They refer to the intrinsic brightness of the
star as its absolute visual magnitude (MV).
– This is the apparent visual magnitude that the star would
have if it were 10 pc away.
– The subscript V informs you it is a visual magnitude—
referring to only the wavelengths of light your eye can see.
Betelgeuse 0.43
Bellatrix 1.62
51 Orionis 4.87
Saiph 2.06
Rigel 0.15
Apparent brightness of
some stars in Orion.
Our Sun’s absolute
brightness, that is how
bright it would be if it
was 10 pc, is +4.8 ~ 51
Orionis
Luminosity
The second goal for the chapter is
to find out how much energy the
stars emit.
• Absolute visual magnitude refers to visible
light.
• However, you want to know the total
output—including all types of radiation.
– Hot stars emit a great deal of ultraviolet radiation that you
can’t see.
– Cool stars emit plenty of infrared radiation.
Luminosity
• To add in the energy you can’t see, astronomers
make a mathematical correction that depends
on the temperature of the star.
• With that correction, they can find the total
electromagnetic energy output of a star.
– They refer to this as its luminosity (L).
Star Temperatures
• Your third goal in the chapter
is to learn about the
temperatures of stars.
Star Temperatures
• The surprising fact is that stellar
spectral lines can be used as a
sensitive star thermometer.
Temperature, Heat, and Blackbody Radiation (CH 5)
• The figure shows plots of
the intensity of radiation
versus wavelength for
three objects with
different temperatures.
– This illustrates both
Wien’s law and the
Stefan–Boltzmann law.
Spectral Lines and Temperature
• As you have learned, hydrogen Balmer
absorption lines are produced by hydrogen
atoms with electrons initially in the second
energy level.
It takes a specific amount of energy
to get an electron from one energy
Level to another
Spectral Lines and Temperature
• One, if the surface of a star is as cool as the sun
or cooler, there are few violent collisions
between atoms to excite the electrons.
• Most atoms will have their electrons in the
ground (lowest) state.
– These atoms can’t absorb photons in the Balmer series.
– Thus, you should expect to find weak hydrogen Balmer
absorption lines in the spectra of very cool stars.
Spectral Lines and Temperature
• Two, in the surface layers of stars hotter than
about 20,000 K, there are many violent collisions
between atoms.
• These excite electrons to high energy levels or
knock the electrons completely out of most
atoms—so they become ionized.
– In this case, few hydrogen atoms will have electrons in the
second energy level to form Balmer absorption lines.
– So, you should also find weak hydrogen Balmer absorption
lines in the spectra of very hot stars.
Spectral Lines and Temperature
• Finally, at an intermediate temperature—
roughly 10,000 K—the collisions have the
correct amount of energy to excite large
numbers of electrons into the second energy
level.
– With many atoms excited to the second level, the gas
absorbs Balmer wavelength photons well—producing
strong hydrogen Balmer lines.
Spectral Lines and Temperature
• Thus, the strength of the hydrogen
Balmer lines depends on the temperature
of the star’s surface layers.
– Both hot and cool stars have weak Balmer lines.
– Medium-temperature stars have strong Balmer lines.
Spectral Lines and Temperature
• Each type of atom or molecule produces spectral
lines that are weak at high and low
temperatures and strong at some intermediate
temperature.
• The temperature at which the lines reach
maximum strength
is different for
each type of atom
or molecule.
Spectral Lines and Temperature
Theoretical calculations of the type first
made by Cecilia Payne can predict just how
strong various spectral lines should be for
stars of different temperatures.
First mentioned in
CH 5 in relation to
solar spectra
Temperature Spectral Classification
• Astronomers classify stars by the lines
and bands in their spectra.
• For example, if it has weak Balmer lines and lines of ionized
helium, it must be an O star.
Temperature Spectral Classification
• The star classification system now used by
astronomers was devised at Harvard during the
1890s and 1900s.
• One of the astronomers there, Annie J. Cannon,
personally inspected and classified the spectra
of over 250,000 stars.
Edward Charles Pickering (director of the Harvard Observatory from 1877 to 1919)
decided to hire women as skilled workers to process astronomical data. Among these
women were Williamina Fleming, Annie Jump Cannon, Henrietta Swan Leavitt and
Antonia Maury. This staff came to be known as the Harvard Computers.[1
Annie Jump Cannon
1863-1941
she applied a division of
stars into the spectral classes
O, B, A, F, G, K, M. Her
scheme was based on the
strength of the Balmer
absorption lines.
Cannon manually classified
more stars in a lifetime than
anyone else, with a total of
around 350,000 stars
Table 9-1 p186
Temperature Spectral Classification
The figure shows color images of 13 stellar spectra—ranging
from the hottest at the top to the coolest at the bottom.
Temperature Spectral Classification
• Compare the figures and
notice how the strength
of spectral lines depends
on temperature.
The Size (Radius) of a Star
Once you know Luminosity you can calculate size
We already know: hotter stars are brighter
But brightness also increases with size:
A
B
Star B will be
brighter than
star A.
Absolute brightness is proportional to the surface area
of the star, and thus its radius squared, L ~ R2.
Example:
Polaris has just about the same spectral type
(and thus surface temperature) as our sun, but
it is 10,000 times brighter than our sun.
Thus, Polaris is 100 times larger than the sun.
This causes its luminosity to be 1002 =
10,000 times more than our sun’s.
The Hertzsprung-Russell Diagram
• The Hertzsprung–Russell diagram, abbreviated H–R
diagram or HRD, is a scatter graph of stars showing the
relationship between the stars' absolute magnitudes or
luminosities versus their spectral classifications or
effective temperatures.
• More simply, it plots each star on a graph
measuring the star's brightness against its
temperature (color). It does not map any
locations of stars.
Luminosity, Temperature, and Diameter
• Before discussing the details of the H–R
diagram, look at a similar diagram you might
use to compare automobiles.
– You can plot a diagram
to show horsepower
versus weight for
various makes of cars.
Figure 9-7 p189
Luminosity, Temperature, and Diameter
• An H-R diagram
has luminosity on
the vertical axis
and temperature
on the horizontal
axis.
• A star is represented
by a point on the
graph that shows its
luminosity and
temperature.
In an H-R Diagram, stars
with the smallest radius
are found in the
__________ of the
diagram.
a. center
b. upper left corner
c. upper right corner
d. lower left corner
e. lower right corner
______
Figure 9-8 p190
Betelgeuse is a very
bright red star in the
constellation of Orion. It
is known as a supergiant.
Where on the diagram
would it be found.
a. center
b. upper left corner
c. upper right corner
d. lower left corner
e. lower right corner
Figure 9-8 p190
______13. A team of astronomers
discovers one of its most massive
stars ever found. If the star is just
settling down in the stage of its life
where it will be peacefully
converting hydrogen to helium in
its core. Draw where it would be
found.
____
14.
Stars on the
main sequence with the greatest
mass. are a. spectral type M stars.
b. are spectral type O stars. c. are
located at the bottom of the main
sequence in the HR diagram.
d. have masses very similar to the
sun. e. both b and c (see also fig.
on the next pg.)
Figure 9-8 p190
In an H-R Diagram, stars with the
smallest radius are found in the
__________ of the diagram.
a. center b. upper left corner
c. upper right corner d. lower left
corner e. lower right corner
______12. Betelgeuse is a very
bright red star in the constellation
of
Orion. It is known as a
supergiant. Draw on the diagram
where it would be
found.
______13. A team of astronomers
discovers one of its most massive
stars ever found. If the star is just
settling down in the stage of its life
where it will be peacefully
converting hydrogen to helium in
its core. Draw where it would be
found.
Figure 9-8 p190
Luminosity Spectral Classification
• The widths of spectral lines are
partially determined by the density
of the gas.
• If the atoms collide often in a dense gas, their energy levels
become distorted, and the spectral lines are broadened.
Luminosity effects on the width
of spectral lines
Same
spectral type,
but different
luminosity
Gas less dense near the surfaces of giants
smaller effect of broadening
narrower lines
A main sequence star’s atmosphere is dense and the hydrogen
atoms collide often
Luminosity Spectral Classification
• Thus, an astronomer can look closely at a
star’s spectrum and tell roughly how big
it is.
Luminosity Spectral Classification –
Can be used for spectroscopic parallax
• From spectral type and luminosity class,
astronomers can estimate the star’s absolute
magnitude, compare with its apparent
magnitude, and compute its distance.
• Although this process finds distance and not
true parallax, it is called spectroscopic parallax.
Masses of Stars—Binary Stars
• More than 50 percent of the stars in the universe may
occur in pairs or multiples. The mass of a body can be
calculated if it is attached by gravity to a partner. Finding
the masses of stars involves studying binary stars.
Our nearest star, proxima
Centauri, is part of a
visual binary (actually
trinary)
binary star simulator
Figure 9-11 p192
HDE 226868 – Cygnus X-1
At the bend of the handle of the Big
Dipper lies a pair of stars, Mizar and
Alcor. Through a telescope you can
discover that Mizar has a fainter
companion and so is a member of a
visual binary system. Adaptive optics
observations have discovered a faint
close companion of Alcor, not
pictured in this diagram. (b) Spectra
of Mizar recorded at different times
show that it is a spectroscopic binary
system rather than a single star.
Figure 9-10 p192
Figure 9-13 p195
Doppler shift in absorption lines
From Earth, an eclipsing binary looks like a
single point of light, but changes in brightness
reveal that two stars are eclipsing each other.
The light curve, shown here as magnitude
versus time, combined with Doppler shift
information from spectra, can reveal the size
and mass of the individual stars.
Figure 9-14 p195
Figure 9-15 p196
Figure 9-16 p197
p198
p199