Download DTU 8e Chap 11 Characterizing Stars

Neil F. Comins • William J. Kaufmann III
Discovering the Universe
Ninth Edition
CHAPTER 11
Characterizing Stars
Light echoes from dust
surrounding a mysterious star
Interstellar dust illuminated by a pulse of light emitted from the
red giant star, V838 Monocerotis, in the center of the image.
WHAT DO YOU THINK?
1.
2.
3.
4.
5.
6.
How near to us is the closest star other than
the Sun?
How luminous is the Sun compared with other
stars?
What colors are stars, and why do they have
these colors?
Are brighter stars hotter than dimmer stars?
Compared to the Sun, what sizes are other
stars?
Are most stars isolated from other stars, as the
Sun is?
In this chapter you will discover…
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that the distances to many nearby stars can be
measured directly, whereas the distances to farther ones
are determined indirectly
the observed properties of stars on which astronomers
base their models of stellar evolution
how astronomers analyze starlight to determine a star’s
temperature and chemical composition
how the total energy emitted by stars and their surface
temperatures are related
the different classes of stars
the variety and importance of binary star systems
how astronomers calculate stellar masses
Using Parallax to Determine Distance
Our eyes change the angle between their line of sight as we look at things
that are different distances away. Our eyes are adjusting for the parallax of
the things we see. This change helps our brain determine the distances to
objects and is analogous to how astronomers determine the distance to
objects in space.
Using Parallax to Determine Distance
As Earth orbits the Sun, a nearby star
appears to shift its position against
the background of distant stars. The
star’s parallax angle (p) is equal to
the angle between the Sun and
Earth, as seen from the star.
The closer the star is to us, the greater
the parallax angle p. The distance to
the star (in parsecs) is found by taking
the inverse of the parallax angle p (in
arcseconds), d = 1/p.
Apparent Magnitude Scale
(a) Several stars in and around the
constellation Orion, labeled with
their names and apparent
magnitudes.
(b) Astronomers denote the
brightnesses of objects in the sky by
their apparent magnitudes. Stars visible
to the naked eye have magnitudes
between m = –1.44 and about m = +6.
The Inverse-Square Law
The same amount of radiation from a light source must illuminate
an ever-increasing area as the distance from the light source
increases. The decrease in brightness follows the inverse-square
law, which means, for example, that tripling the distance
decreases the brightness by a factor of 9.
Absolute magnitude indicates:
A.
B.
C.
D.
The diameter of the star
The luminosity of the star
How bright the star looks from Earth
The temperature of the star
Apparent magnitude indicates:
A.
B.
C.
D.
The diameter of the star
The luminosity of the star
How bright the star looks from Earth
The temperature of the star
Which term is most similar to
“absolute magnitude:”
A.
B.
C.
D.
Apparent Brightness
Color
Variability
Luminosity
Temperature and Color
This beautiful
Hubble Space
Telescope image
shows the variety
of colors of stars.
Temperature and Color
These diagrams show the relationship between the color of a star and its
surface temperature. The intensity of light emitted by three stars is plotted
against wavelength. The range of visible wavelengths is indicated. The
location of the peak of each star’s intensity curve, relative to the visible-light
band, determines the apparent color of its visible light. The insets show
stars of about these surface temperatures. Ultraviolet (uv) extends to 10 nm.
Spectral
Types
As indicated on right and left, spectral type carries the same information as
temperature. The hydrogen Balmer lines are strongest in stars with surface
temperatures of about 10,000 K (called A-type stars). The hottest stars show
ionized Helium (He II) lines. Several of the broad, dark bands in the spectrum
of the coolest stars (M-type stars) are caused by titanium oxide (TiO)
molecules, which can exist only if the temperature is below about 3700 K.
If a star is moved 3 times
farther away:
A.
B.
C.
D.
It will look the same
It will look 3 times dimmer
It will look 6 times dimmer
It will look 9 times dimmer
Classifying the Spectra of Stars
(a) Williamina Fleming (standing)
(b) Annie Jump Cannon
The modern classification scheme for stars, based on their spectra, was
developed at the Harvard College Observatory in the late nineteenth century.
Female astronomers, initially led by Edward C. Pickering and Williamina
Fleming, and then by Annie Jump Cannon, analyzed hundreds of thousands of
spectra. Social conventions of the time prevented most women from using
research telescopes or receiving much recognition or comparable salaries.
Hertzsprung-Russell
Diagram
On an H-R diagram, the luminosities of
stars are plotted against their spectral
types. Each dot on this graph
represents a star whose luminosity
and spectral type have been
determined. The data points are
grouped in just a few regions of the
diagram, revealing that luminosity and
spectral type are correlated: Mainsequence stars fall along the red
curve, giants are to the right,
supergiants are on the top, and white
dwarfs are below the main sequence.
The absolute magnitudes and surface
temperatures are sometimes used on
H-R diagrams instead of luminosities
and spectral types.
The Types of Stars and Their Sizes
On this H-R diagram, stellar luminosities
are plotted against the surface
temperatures of stars. The dashed
diagonal lines indicate stellar radii. For
stars of the same radius, hotter stars
(corresponding to moving from right to
left on the HR diagram) glow more
intensely and are more luminous
(corresponding to moving upward on the
diagram) than cooler stars. While
individual stars are not plotted, we show
the regions of the diagram in which
main-sequence, giant, supergiant, and
white dwarf stars are found. Note that
the Sun is very much a middle-of-theroad star.
L = 4 π R2 σ T4
Stellar Size and Spectra
These spectra are from two stars of the same spectral type (B8) and, hence,
the same surface temperature (13,400 K) but different radii and luminosities:
(a) the B8 supergiant Rigel (58,000 solar luminosities) in Orion, and (b) the
B8 main-sequence star Algol (100 solar luminosities) in Perseus.
Luminosity Classes
Dividing the H-R diagram into
regions, called luminosity
classes, permits finer
distinctions between giants
and supergiants. Luminosity
classes Ia and Ib encompass
the supergiants. Luminosity
classes II, III, and IV indicate
giants of different brightness.
Luminosity class V indicates
main-sequence stars. White
dwarfs do not have their own
luminosity class.
The Hertzsprung-Russell Diagram:
A. maps the locations of stars within 100 LY
of the Sun
B. plots stars in terms of their mass and
distance
C. plots stars in terms of their surface
temperature and luminosity
D. plots stars in terms of their size and
chemical composition
Where on the H-R diagram are the majority
of stars located?
A.
B.
C.
D.
as white dwarves
on the main sequence
as giants
as supergiants
Size Comparison of Planets
(plus a dwarf planet)
Sun, Planets, and a
few Giant Stars
Giants and Supergiants
A Binary
Star System
About one-third of the visible “stars” in our region of the Milky Way are
actually double stars. Mizar in Ursa Major is a binary system with stars
separated by only about 0.01 arcsec. The images and plots show the relative
positions of the two stars over nearly half of their orbital period. The orbital
motion of the two binary stars around each other is evident. Either star can be
considered fixed in making such plots.
Center of Mass of a Binary Star System
(a) Two stars move in elliptical orbits around a common center of mass.
Although the orbits cross each other, the two stars are always on opposite
sides of the center of mass and thus never collide. (b) A seesaw balances if
the center of mass of the two children is at the fulcrum. When balanced, the
heavier child is always closer to the fulcrum, just as the more massive star
is closer to the center of mass of a binary star system.
Spectral Line Motion in Binary Star Systems
“Spectroscopic Binary”
The diagrams indicate the positions and motions of the stars, labeled A and
B, relative to Earth. Below each diagram is the combined spectrum we would
observe at each stage. Typically, we would not be able to distinguish two
stars in the image, but could infer that this is a binary from the shifting
spectral lines. The changes in colors (wavelengths) of the spectral lines are
due to changes in the stars’ Doppler shifts, as seen from Earth.
Spectral Line Motion in Binary Star Systems
This graph displays the radial-velocity curves of the binary HD 171978. The
entire binary is moving away from us at 12 km/s, which is why the pattern of
radial velocity curves is displaced upward from the zero-velocity line.
A Double-Line Spectroscopic Binary
The spectrum of the double-line
spectroscopic binary kappa Arietis
has spectral lines that shift back
and forth as the two stars revolve
around each other. (a) The stars
are moving parallel to the line of
sight, with one star approaching
Earth, the other star receding, as
in Stage 1 or 3 of Figure 11-15a.
These motions produce two sets
of shifted spectral lines. (b) Both
stars are moving perpendicular to
our line of sight, as in Stage 2 or 4
of Figure 11-15a. As a result, the
spectral lines of the two stars have
merged.
Representative Light Curves of Eclipsing Binaries
Illustrated here are (a) a partial eclipse and (b) a total eclipse. (c) The
binary star NN Serpens, indicated by the arrow, undergoes a total eclipse.
The telescope was moved during the exposure so that the sky drifted
slowly from left to right. During the 10.5-min eclipse, the dimmer but larger
star in the binary system (an M6 V star) passed in front of the more
luminous but smaller star (a white dwarf). The binary became so dim that it
almost disappeared.
The Mass-Luminosity Relation
Or, What Does the Mass Information Mean
For main-sequence stars, mass
and luminosity are directly
correlated—the more massive a
star, the more luminous it is. A
main-sequence star of 10 solar
masses has roughly 3000 times
the Sun’s luminosity ; one with
0.1 solar masses has a
luminosity of only about 0.001
solar luminosities. To fit them on
the page, the luminosities and
masses are plotted using
logarithmic scales.
The Mass-Luminosity Relation
.. Annotated on the H-R Diagram
On this H-R diagram, each dot
represents a main-sequence star.
The number next to each dot is the
mass of that star in solar masses. As
you move up the main sequence
from the lower right to the upper left,
the mass, luminosity, and surface
temperature of main-sequence stars
all increase.
How is stellar mass determined?
A. By radar reflection from satellites
B. By analyzing the orbit of companion stars
C. By sending gravimeter-equipped
spacecraft to them
D. By their gravitational influence on planets
in our solar system
Summary of Key Ideas
Magnitude Scales
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Determining stellar distances from Earth is the first step
to understanding the nature of the stars. Distances to the
nearer stars can be determined by stellar parallax, which
is the apparent shift of a star’s location against the
background stars while Earth moves along its orbit
around the Sun. The distances to more remote stars are
determined using spectroscopic parallax.
The apparent magnitude of a star, denoted m, is a
measure of how bright the star appears to Earth-based
observers. The absolute magnitude of a star, denoted M,
is a measure of the star’s true brightness and is directly
related to the star’s energy output, or luminosity.
Magnitude Scales
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The luminosity of a star is the amount of energy
emitted by it each second.
The absolute magnitude of a star is the apparent
magnitude it would have if viewed from a
distance of 10 pc. Absolute magnitudes can be
calculated from the star’s apparent magnitude
and distance from Earth.
The Temperatures of Stars
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Stellar temperatures can be determined from
stars’ colors or stellar spectra.
Stars are classified into spectral types (O, B, A,
F, G, K, and M) based on their spectra or,
equivalently, their surface temperatures.
Types of Stars
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The Hertzsprung-Russell (H-R) diagram is a graph on
which luminosities of stars are plotted against their
spectral types (or, equivalently, their absolute
magnitudes are plotted against surface temperatures).
The H-R diagram reveals the existence of four major
groupings of stars: main-sequence stars, giants,
supergiants, and white dwarfs.
The mass-luminosity relation expresses a direct
correlation between a main-sequence star’s mass and
the total energy it emits.
Distances to stars can be determined using their spectral
types and luminosity classes.
Stellar Masses
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Binary stars are fairly common. Those that can be
resolved into two distinct star images (even if it takes a
telescope to do this) are called visual binaries.
The masses of the two stars in a binary system can be
computed from measurements of the orbital period and
orbital dimensions of the system.
Some binaries can be detected and analyzed, even
though the system may be so distant (or the two stars so
close together) that the two star images cannot be
resolved with a telescope.
Stellar Masses
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A spectroscopic binary is a system detected from the
periodic shift of its spectral lines. This shift is caused by
the Doppler effect as the orbits of the stars carry them
alternately toward and away from Earth.
An eclipsing binary is a system whose orbits are viewed
nearly edge on from Earth, so that one star periodically
eclipses the other. Detailed information about the stars in
an eclipsing binary can be obtained by studying the
binary’s light curve.
Key Terms
absolute magnitude
apparent magnitude
binary star
center of mass
close binary
eclipsing binary
giant star
Hertzsprung-Russell
(H-R) diagram
initial mass function
inverse-square law
light curve
luminosity
luminosity class
main sequence
main-sequence star
mass-luminosity relation
OBAFGKM sequence
optical double
photometry
radial-velocity curve
red giant
spectral types
spectroscopic binary
spectroscopic parallax
stellar evolution
stellar parallax
stellar spectroscopy
supergiant
visual binary
white dwarf
WHAT DID YOU THINK?
How near to us is the closest star other
than the Sun?
 The closest star, Proxima Centauri, is
about 40 trillion km (25 trillion mi) away.
Light from there takes about 4 years to
reach Earth.
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WHAT DID YOU THINK?
How luminous is the Sun compared with
other stars?
 The most luminous stars are about a
million times brighter, and the least
luminous stars are about a hundred
thousand times dimmer than the Sun.
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WHAT DID YOU THINK?
What colors are stars, and why do they
have these colors?
 Stars are found in a wide range of colors,
from red through violet as well as white.
They have these colors because they
have different surface temperatures.
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WHAT DID YOU THINK?
Are brighter stars hotter than dimmer
stars?
 Not necessarily. Many brighter stars (such
as red giants) are cooler but larger than
hotter, dimmer stars (such as white
dwarfs).
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WHAT DID YOU THINK?
Compared to the Sun, what sizes are
other stars?
 Stars range from more than 1000 times
the Sun’s diameter to less than 1/100 the
Sun’s diameter.
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WHAT DID YOU THINK?
Are most stars isolated from other stars,
as the Sun is?
 No. In the vicinity of the Sun, one-third of
the stars are found in pairs or larger
groups.
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