Transcript Powerpoint

Measuring the Stars
How big are stars?
How far away are they?
How bright are they?
How hot?
How old, and how long do they live?
What is their chemical composition?
How are they moving?
Are they isolated or in clusters?
By answering these questions, we not only learn about stars, but
about the structure and evolution of galaxies they live in, and the
Universe.
How Far Away are the Stars?
Earth-baseline parallax useful in Solar System
Parallax demo
Earth-orbit parallax - useful
for nearest stars
New distance unit: the parsec (pc).
Using Earth-orbit parallax, if a star has a parallactic angle of 1",
it is 1 pc away.
Remember 1" (arcsecond) = 1/60 arcmin = 1/3600 degrees
If the angle is 0.5", the distance is 2 pc.
1
Distance (pc) = Parallactic angle (arcsec)
Closest star to Sun is Proxima Centauri. Parallactic angle is 0.7”, so
distance is 1.3 pc.
1 pc = 3.3 light years
= 3.1 x 10 18 cm
= 206,000 AU
1 kiloparsec (kpc) = 1000 pc
1 Megaparsec (Mpc) = 10 6 pc
The Solar Neighborhood
Nearest star to the Sun: Proxima Centauri, which is
a member of a 3-star system: Alpha Centauri
complex
Model of distances:
• Sun is a marble, Earth is a grain of sand orbiting 1
m away.
• Nearest star is another marble 270 km away.
• Solar system extends about 50 m from the Sun;
rest of distance to nearest star is basically empty.
Earth-orbit parallax using ground-based optical telescopes is
good for stars within 30 pc (1000 or so). Tiny volume of
Milky Way galaxy. Other methods later.
Our nearest stellar neighbors
Star Motion
Barnard’s Star (top) has the
largest proper motion of any –
proper motion is the actual shift
of the star in the sky, after
correcting for parallax.
The pictures (a) were taken 22
years apart. (b) shows the actual
motion of the Alpha Centauri
complex.
Clicker Question:
Suppose we observe a star with an annual
parallax of 600 milliarcseconds, what is its
distance in parsecs?
A: 100 parsecs
B: 1.7 parsecs
C: 0.1 parsecs
D: 0.01 parsecs
Question 2
The angle of stellar
parallax for a star
gets larger as the
a) distance to the star increases.
b) size of the star increases.
c) size of the telescope increases.
d) length of the baseline increases.
e) wavelength of light increases.
Question 2
The angle of stellar
parallax for a star
gets larger as the
a) distance to the star increases.
b) size of the star increases.
c) size of the telescope increases.
d) length of the baseline increases.
e) wavelength of light increases.
Astronomers typically make observations of
nearby stars 6 months apart, making the
baseline distance equal to 2 AU
(Astronomical Units).
How Luminous are Stars?
Remember, luminosity of the Sun is
LSun = 4 x10 33 erg/s
(amount of energy put out every second in form of radiation).
Luminosity also called “absolute brightness”.
How bright a star appears to us is the “apparent brightness”, which
depends on its luminosity and distance from us:
apparent brightness

luminosity
(distance) 2
So we can determine luminosity if apparent brightness and distance
are measured:
luminosity

apparent brightness x (distance) 2
This is an example of the inverse square law.
apparent brightness

luminosity
(distance) 2
Luminosity and Apparent Brightness
Therefore, two stars
that appear equally
bright might be a
closer, dimmer star
and a farther,
brighter one.
Luminosity and Apparent Brightness
Apparent luminosity is
measured using a magnitude
scale, which is related to our
perception.
It is a logarithmic scale; a
change of 5 in magnitude
corresponds to a change of a
factor of 100 in apparent
brightness.
It is also inverted – larger
magnitudes are dimmer.
Stellar Temperatures
The color of a star is indicative of its temperature.
Red stars are relatively cool, whereas blue ones
are hotter.
Stellar Temperatures
The radiation from stars is blackbody radiation; as the
blackbody curve is not symmetric, observations at two
wavelengths are enough to
define the temperature.
Spectral Classes
Strange lettering scheme is a historical accident.
Spectral Class
Surface Temperature
O
B
A
F
G
K
M
30,000 K
20,000 K
10,000 K
7000 K
6000 K
4000 K
3000 K
Examples
Rigel
Vega, Sirius
Sun
Betelgeuse
Further subdivision: BO - B9, GO - G9, etc. GO hotter than G9.
Sun is a G2.
Classification of Stars Through Spectroscopy
Ionized helium. Requires extreme UV
photons. Only hottest stars produce many of these.
Remember: stellar spectra show
black-body radiation and absorption
lines.
Pattern of absorption lines depends on
temperature (mainly) and chemical
composition.
Spectra give most accurate info on
these as well as:
density in atmosphere
gravity at surface
velocity of star towards or from us
Stellar Temperatures
The different spectral classes have distinctive
absorption lines.
Stellar Sizes
A few very large, very close stars can be imaged
directly; this is Betelgeuse.
Stellar Sizes - Indirect Method
Almost all stars too far away to measure their radii directly. Need
indirect method. For blackbodies, use Stefan's Law:
Energy radiated per cm2 of area on surface every second 
(T = temperature at star’s surface)
T4
And:
Luminosity = (energy radiated per cm2 per sec) x (area of surface in cm2)
So:
Luminosity 
(temperature) 4 x (surface area)
Determine luminosity from apparent brightness and distance,
determine temperature from spectrum (black-body curve or spectral lines),
then find surface area, Surface area  Luminosity / (temperature) 4
then find radius (sphere surface area is 4 R2)
The Wide Range of Stellar Sizes
How Massive are Stars?
1. Binary Stars. Orbital period depends on masses of two stars and
their separation.
2. Theory of stellar structure and evolution. Tells how spectrum and
color of star depend on mass.
Relationship of Luminosity, Size, and Temperature
Burner and Boiling Spaghetti Analogy
Which burner will cook the pot of spaghetti faster?
A. The one on the left
B. The one on the right
C. Neither, both will cook the spaghetti in the same amount of time
Relationship of Luminosity, Size, and Temperature
Luminosity α radius2 x temperature4
The Hertzsprung–Russell Diagram
The H–R diagram plots
stellar luminosity against
surface temperature.
This is an H–R diagram
of a few prominent stars.
Building the Hertzsprung-Russell (H-R) Diagram
Which is larger, S or T? => A.) S B.) T C.) same size D.) can’t tell
Building the Hertzsprung-Russell (H-R) Diagram
Which is larger, S or X? => A.) S B.) X C.) same size D.) can’t tell
Summary of Chapter 10
• Distance to nearest stars can be measured by
parallax.
• Apparent brightness is as observed from Earth;
depends on distance and absolute luminosity.
• Spectral classes correspond to different surface
temperatures.
• Stellar size is related to luminosity and temperature.
Summary of Chapter 10, cont.
• H–R diagram is plot of luminosity vs. temperature;
most stars lie on main sequence.
• Distance ladder can be extended using spectroscopic
parallax.
• Masses of stars in binary systems can be measured.
• Mass determines where star lies on main sequence.