Download star

The Stars:
A Celestial Census
28 July 2005
AST 2010: Chapter 17
1
Stellar Questions
What’s a census?
What’s it for?
28 July 2005
AST 2010: Chapter 17
2
The Lives of Stars
Stars live for a very long time,
up to 100 million years or more
No humans can possibly
observe a star this long!
How can we learn about the
stages in a star’s life?
We can take a celestial census, getting a snapshot
of many stars at different stages of their life
We can then try to infer the stages that a star goes
through from the data we
assemble in the census
But we can be misled if the
star sample in the census is
biased (as in political
surveys)
28 July 2005
AST 2010: Chapter 17
3
A Stellar Census (1)
We measure distances in light years (LY)
Astronomical distances are difficult to measure, to
be discussed in Ch. 18
Small stars are less luminous and, therefore,
harder to see
If not corrected for these hard-to-see stars, our
sample of stars will be biased
Careful observation reveals that small stars (brown
dwarfs) are more common than large stars
While less numerous, large stars are easier to
see at large distances
Most of the stars visible to the naked eye are large
28 July 2005
AST 2010: Chapter 17
4
A Stellar Census (2)
Stars that appear very bright are not
necessarily very close to us, and those
appearing faint are not necessarily very
distant from us
In fact, the brightest stars are bright mainly
because they are intrinsically very luminous
Most of them are very far away
Moreover, most of the nearest stars are
intrinsically very faint
The luminosity (L) of stars ranges from more
than 106 LSun for the most luminous stars to
10-6 LSun for brown dwarfs
28 July 2005
AST 2010: Chapter 17
5
Measuring Stellar Masses
Mass is one of a star’s most important characteristics
Knowing the mass can help us estimate how long it will
shine and what its ultimate fate will be
Yet, a star’s mass is very difficult to measure directly
Indirect measurements of stellar masses can be done
for binary-star systems
Each system consists of two stars that orbit each
other, bound together by gravity
Strictly speaking, each of the binary stars orbits a
common point called the center of mass
Animation
About half of stars
are binary stars
Orbits and Masses of Binary Stars
The masses of the 2 stars can be
estimated using Kepler's third law
The orbital period P (in years) and
semimajor axis D (in AU) of the
ellipse are related to the masses
M1 and M2 (in units of the Sun’s
mass) by D3 = (M1+M2) P2
D
Thus, if D and P are measured, the
sum of the masses can be found
If the relative orbital speeds of the 2
stars are also measured, the mass of
each star separately can be
calculated as well
28 July 2005
AST 2010: Chapter 17
7
Visual Binaries
Binary-star systems in
which both of the stars
can be seen with a
telescope are called
visual binaries
Animation
Binary stars: Sirius A and B
28 July 2005
AST 2010: Chapter 17
8
Sirius A and B
Sirius A is normal star
Sirius B is a white dwarf companion
The orbits are drawn to scale, but the sizes of
the stars are exaggerated
Sirius A is considerably larger than the Sun,
while Sirius B is about the size of the Earth
28 July 2005
AST 2010: Chapter 17
9
Spectroscopic Binaries
In some binary-star
systems, only one of the
stars can be seen with a
telescope, but the presence
of the companion star is
revealed by spectroscopy
Such stars are called
spectroscopic binaries
The binary nature is
indicated in the periodic
Doppler-shift of their
spectral lines as they orbit
around each other
Animation
Doppler Effect in Binary Stars
If the line spectra of the spectroscopic
binaries can be observed, their motion
is reflected in the Doppler shifts of the
spectral lines
Radial velocities of spectroscopic binaries
28 July 2005
AST 2010: Chapter 17
11
Range of Stellar Masses
How large and small can stars’ masses be?
Stars with masses up to about 100 times that of the
Sun have been discovered
Some may have masses up to about 200 solar masses
Theoretical calculations suggest that the mass of a
true star must be at least 1/12 that of the Sun
A “true” star is one that becomes hot enough to fuse
protons to form helium (see Ch. 15)
Objects with masses between 1/100 and 1/12 that of
the Sun are called brown dwarfs
They may produce energy for a brief time by nuclear
reactions, but do not become hot enough to fuse protons
They are intermediate in mass between stars and planets
Objects with masses less than about 1/100 that of the
Sun are considered planets
28 July 2005
AST 2010: Chapter 17
12
Mass-Luminosity Relation
There is a correlation
between the mass and
luminosity of a star
The more massive
stars are generally
also the more
luminous (they give
off more energy)
For about 10% of the
stars, this relationship
is violated
They include the
white dwarfs
28 July 2005
AST 2010: Chapter 17
13
Diameters of Stars
The diameter of a star can be determined by
measuring the time it takes an object (the Moon, a
planet, or a companion star) to pass in front of it and
blocks its light
The blocking of the star’s light is an eclipse
The star’s brightness decreases gradually during the
eclipse
The time for the brightness decrease depends on the
size of the star
Accurate sizes for a large
number of stars come from
measurements of eclipsing
binaries
28 July 2005
AST 2010: Chapter 17
14
Eclipsing Binary System
Some binary stars are lined up in such a way that,
when viewed from the Earth, each star passes in front
of the other during every revolution
Thus, we can observe periodic eclipses in these
binary-star systems, which are therefore called
eclipsing binaries
28 July 2005
AST 2010: Chapter 17
15
Techniques for Measuring Characteristics of Stars
28 July 2005
AST 2010: Chapter 17
16
H-R Diagram
There is a relationship between the temperature
(color) and luminosity of 90% of stars
They lie along a
band called the
main sequence
The plot of stars’
luminosities versus
their temperatures
is called the
HertzsprungRussell diagram
(H-R diagram)
28 July 2005
AST 2010: Chapter 17
17
H-R Diagram for Many Stars
28 July 2005
AST 2010: Chapter 17
18
Features of H-R Diagram
The main-sequence band contains almost 90% of the
stars
Large blue stars
Medium yellow stars
Small red stars
About 10% of the
stars lie below the
main sequence
They are the hot, but
dim, white dwarfs
No more than 1% of
the stars lie above
the main sequence
They are cool and
very luminous
Hence they must be the giants and supergiants
28 July 2005
AST 2010: Chapter 17
19
Stellar Question
Where would you put a brown
dwarf on this diagram?
28 July 2005
AST 2010: Chapter 17
20
Characteristics of Main-Sequence Stars
The main sequence turns out to be a sequence of stellar
masses (for almost 90% of the stars)
The more massive stars have the more weight and can
thus compress their centers to the greater degree, which
implies that they are the hotter inside and the better at
generating energy from nuclear reactions deep within
28 July 2005
AST 2010: Chapter 17
21
The Other 10% of Stars
Roughly 10% of the stars
do not follow the mass-luminosity
relationship
do not lie on the main sequence
Betelgeuse
Giant and supergiant stars
lie on the upper-right section of the H-R
diagram
are very luminous because they are
large in diameter, although they are cool
make up less than 1% of the stars
White dwarfs
lie on the lower-left section of the H-R
diagram
are small in diameter (similar to Earth’s)
are hot, but dim
make up about 10% of the stars
28 July 2005
AST 2010: Chapter 17
22