Download Chapter10 (with interactive links)

Lecture Slides
CHAPTER 10: Measuring the Stars
Understanding Our Universe
SECOND EDITION
Stacy Palen, Laura Kay, Brad Smith, and George Blumenthal
Prepared by Lisa M. Will,
San Diego City College
Copyright © 2015, W. W. Norton & Company
Measuring the Stars
 Understand the properties
of light and atoms.
 Determine stellar
properties – brightness,
mass, temperature, size,
composition.
 Organize stars on the
HR diagram.
Distance
Distance (Cont.)
 Our brains compare views of our left and right eyes to
get nearby distances.
 Depth perception comes from stereoscopic vision.
Distance: Parallax
 Parallax: change in position caused by a change in
the position of the observer.
 The only direct way to measure the distance to a star
is from the parallax.
Distance: Nearby Stars
 As Earth orbits the Sun, nearby stars change their
positions against the background stars.
 Comparing the position six months apart yields the
distance.
Distance: Parallax Vs. Distance
 The greater the parallax, the smaller the distance.
 The parallaxes of real stars are tiny and are typically
measured in small fractions of a degree known as
arcseconds.
Distance: Definitions and Conversion Factors
Some useful definitions and conversion factors:
 1 arcminute = 1/60 of a degree.
 1 arcsecond = 1/60 of an arcminute = 1/3600 of
a degree.
 Parsec: distance at which the parallax is equal to
one arcsecond.
 1 parsec = 3.26 light-years.
Calculating distance from parallax
 If Distance d in parsecs and parallax p is in
arcseconds,
 Then d(pc) = 1/p(arcsec)
 Remember, 1parsec (parallax-second) = 3.26 light
years.
 Example: the parallax of a star is measured to be
0.75 arcsec. What is the star’s distance from earth?
 Answer: d = 1/(.75) = 1.33 parsecs
 Answer in light years = 1.33*3.26 = 4.34 light years
 (this is about the distance to the nearest star)
Brightness
 Luminosity: the amount of light emitted by an object.
=> Luminosity is a star’s intrinsic brightness.
Brightness: Luminosity and Distance
 Observed brightness depends on both the luminosity
and the distance.
=> A dim star could have a low luminosity or be far
away; A bright star could be close or have a high
luminosity.
Brightness: Magnitude
Some useful definitions:
 Brightness of a star is measured by logarithmic
magnitude.
=> Brighter objects have a smaller magnitude.
 Apparent magnitude: how bright the star appears to
us in the sky. This generally a number between 0
(very bright) and 6 (faintest human eye can see in a
dark sky). A difference in magnitude of 1 is a factor
in brightness of 2.5. Venus can have a negative
apparent magnitude!
 Absolute magnitude: how bright the star would be at a
fixed distance of 10 parsecs from us. This is useful
because it allows us to quickly compare the true
luminosity of each object if we imagine that every
object is at the same distance from us!
M = m – 5log(d) +5 or
m-M = 5log(d) -5
M = absolute magnitude
M = apparent (observed) magnitude.
You will not have to calculate logarithms on the the
exam, but you need to understand magnitudes.
Class Question
Which of the following apparent magnitudes is the
brightest?
A.
B.
C.
D.
2
1
0
-3
Which star is the brightest? Which is the
faintest?
Star
m (apparent magnitude)
Rigel
0.12
Sirius
-1.46
Betelgeuse
0.42
Regulus
1.35
Deneb
1.25
•Star A has m = 2.3. Star B has m = 5.3
•Which is brighter, and by how much?
Answer: Star A is brighter by exactly 3
magnitudes. 2 magnitudes is 2.5*2.5*2.5=
15.6 times brighter!
•Note that 5 magnitudes difference is a
factor of 100 in brightness!
Brightness: Luminosity
 Luminosity is usually
expressed in terms of the solar
luminosity: 1 L
 The most luminous stars are
106 L.
 The least luminous are 10-4 L.
 Low-luminosity stars are more
common than high luminosity
stars.
Composition
 Atoms consist of protons,
neutrons, and electrons.
 Protons and neutrons are
found in the nucleus.
 Electrons surround the
nucleus in a “cloud.”
Composition: Energies
 Electrons can only have certain energies; other
energies are not allowed.
 Each type of atom has a unique set of energies,
typically illustrated with an energy level diagram.
Composition: Energies (Cont.)
Composition: Energies (Cont.)
Composition: Energy State
 The lowest energy state is
called the ground state.
 Energy levels above the
ground state are called
excited states.
 The atom can go from one
energy state to another,
but never have an energy
in between.
Composition: Visual Analogy
Composition: Emission
 Emission: an electron emits a photon and drops to a
lower energy state, losing energy.
 The photon’s energy is equal to the energy difference
between the two levels.
Composition: Absorption
 Absorption: an electron absorbs the energy of a
photon to jump to a higher energy level.
 The photon’s energy must be equal to the energy
difference between the two levels.
Composition: Spectral Fingerprints of Atoms
 The wavelengths at which atoms emit and
absorb radiation form unique spectral
fingerprints for each atom.
Composition: Spectral Fingerprints of Atoms (Cont.)
Composition: Spectral Fingerprints of Atoms (Cont.)
Composition: Spectral Fingerprints of Atoms (Cont.)
Composition: Absorption Lines
 For stars, astronomers look at the dark absorption lines
in stars’ spectra.
 These absorption lines help determine a star’s
temperature, composition, density, pressure, and more.
Composition: Absorption and Emission Lines
Composition: Classification of Stars
 The spectra of stars were first classified during the
late 1800s.
 Stars with the strongest hydrogen lines were labelled
“A,” stars with somewhat weaker hydrogen lines were
labelled “B stars,” and …
Composition: Spectral Types of Stars
 Hottest stars: weak absorption by hydrogen and
helium (type O).
 Middle: strong hydrogen absorption (type A).
 Cool stars: many different heavy elements or
molecules (type M).
Composition: Spectral Types Subclasses
 Absorption lines depend mainly on the temperature.
 Full sequence: OBAFGKM
 Each spectral type is broken down into 10: 0-9.
=> The Sun is type G2.
Class Question
Which of the following spectral types is the hottest?
A.
B.
C.
D.
A
G
M
O
Class Question
Which of the following spectral types has the
weakest hydrogen lines?
A.
B.
C.
D.
A
G
M
O
Temperature
 Measuring the color of a star tells
us the surface temperature.
 The spectrum shifts to shorter
wavelengths at higher temperatures.
 Wien’s law: “Hotter means bluer.”
Size
 With luminosity and temperature, we can calculate
the size of a star.
 Stars have radii measuring from 1% of the Sun’s to
1000 times its radius!
Size (Cont.)
Size (Cont.)
Mass
 To measure mass, astronomers
look for the effects of gravity.
 Many stars are binary stars orbiting
a common center of mass.
 A less massive star moves
faster on a larger orbit.
Mass: Measuring the Mass
 Measure velocities from
Doppler shift.
 Calculate total mass of both
stars from Kepler’s third law.
 Lowest-mass stars have
M = 0.08 M.
 Highest-mass stars appear to
be greater than 200 M, but
are rare.
Mass: Visual Binary System
 If we can take pictures showing the two stars
separately, the system is called a visual binary.
 We can directly measure the size and period of the
orbits of the two stars.
Mass: Spectroscopic Binary Stars
 Spectroscopic binary: individual stars cannot be
resolved in images.
 Pairs of Doppler-shifted lines trade places indicating
the presence of two stars.
Mass: Spectroscopic Binary Stars (Cont.)
Mass: Spectroscopic Binary Stars (Cont.)
Mass: Doppler Velocity
 The Doppler shifts can be converted into radial
velocities, leading to the ratio of the masses of
the two stars.
Size: Eclipsing Binary System
 Eclipsing binary: the total light coming from the star
system decreases when one star passes in front of
the other.
 This allows us to determine the relative sizes of the
two stars.
H-R Diagram
 Hertzsprung-Russell
(H-R) diagram = Plot
of luminosity vs.
temperature.
 Key to unraveling
stellar evolution:
how stars change
with time.
H-R Diagram: Properties of Stars
 Top = brightest.
 Left = hottest.
 Some stars are cool
but very luminous.
 Some are hot with
low luminosity.
H-R Diagram: O and M Stars
 On far left end of the
main sequence are the
O stars: hotter, larger,
and more luminous
than the Sun.
 On far right end of the
main sequence are the
M stars: cooler,
smaller, and fainter
than the Sun.
H-R Diagram: Mass Determining the Location
 The mass of a star determines
its characteristics.
 Most stars, including the Sun,
exist on the main sequence.
H-R Diagram: Determining Characteristics
 Knowing where a star lies on
the main sequence, you can
determine its approximate
luminosity, surface
temperature, and size.
Class Question
Which of the following statements about the main
sequence is not correct?
A.
B.
C.
D.
Hotter stars are more massive.
More massive stars are more luminous.
Hotter stars are more luminous.
Cooler stars are more luminous.
Chapter Summary
 By understanding light, the properties of stars can be
determined: distance, brightness, mass, size,
composition, temperature.
 The H-R diagram is a key to understanding stars.
Astronomy in Action
Parallax
Click the image to launch the Astronomy in Action Video
(Requires an active Internet connection)
Astronomy in Action
Emission and Absorption
Click the image to launch the Astronomy in Action Video
(Requires an active Internet connection)
AstroTour
Atomic Energy Levels and Light Emission and Absorption
Click here to launch this AstroTour
(Requires an active Internet connection)
AstroTour
Atomic Energy Levels and the Bohr Model
Click here to launch this AstroTour
(Requires an active Internet connection)
AstroTour
H-R Diagram
Click here to launch this AstroTour
(Requires an active Internet connection)
AstroTour
Stellar Spectrum
Click here to launch this AstroTour
(Requires an active Internet connection)
Nebraska Applet
Spectrum Explorer
Click the image to launch the Nebraska Applet
(Requires an active Internet connection)
Nebraska Applet
Ecliptic Binary Stars Simulator
Click the image to launch the Nebraska Applet
(Requires an active Internet connection)
Nebraska Applet
H-R Diagram Explorer
Click the image to launch the Nebraska Applet
(Requires an active Internet connection)
Nebraska Applet
Spectroscopic Parallax Simulator
Click the image to launch the Nebraska Applet
(Requires an active Internet connection)
Nebraska Applet
Parallax Calculator
Click the image to launch the Nebraska Applet
(Requires an active Internet connection)
Nebraska Applet
Stellar Luminosity Calculator
Click the image to launch the Nebraska Applet
(Requires an active Internet connection)
Nebraska Applet
Center of Mass Simulator
Click the image to launch the Nebraska Applet
(Requires an active Internet connection)
Nebraska Applet
Parallax Explorer
Click the image to launch the Nebraska Applet
(Requires an active Internet connection)
Understanding Our Universe
SECOND EDITION
Stacy Palen, Laura Kay, Brad Smith, and George Blumenthal
Prepared by Lisa M. Will,
San Diego City College
This concludes the Lecture slides for
CHAPTER 10: Measuring
the Stars
wwnpag.es/uou2
Copyright © 2015, W. W. Norton & Company