Download What is a Hertzsprung

Luminosity
What is a
HertzsprungRussell
diagram?
An H-R diagram
plots the
luminosity and
temperature of
stars
Temperature
Most stars fall
somewhere on
the main
sequence of
the H-R diagram
Large radius
Stars with lower
T and higher L
than mainsequence stars
must have larger
radii:
giants and
supergiants
Stars with higher
T and lower L
than mainsequence stars
must have
smaller radii:
white dwarfs
Small radius
Spectral lines of supergiants, giants, and mainsequence stars
Figure 8.9: Differences in widths and strengths of spectral lines distinguish
the spectra of supergiants, giants, and main-sequence stars. (Adapted
from H. A. Abt, A. B. Meinel, W. W. Morgan, and J. W. Tapscott, An Atlas of
Low-Dispersion Grating Stellar Spectra, Kitt Peak National Observatory,
1968)
Fig. 8-9, p. 141
A star’s full classification includes spectral type
(line identities) and luminosity class (line shapes,
related to the size of the star):
I - supergiant
II - bright giant
III - giant
IV - subgiant
V - main sequence
Examples:
Sun - G2 V
Sirius - A1 V
Proxima Centauri - M5.5 V
Betelgeuse - M2 I
Luminosity
classes
The approximate location of the luminosity
classes on the H–R diagram.
Fig. 8-10, p. 142
Stellar Sizes
A few stars are big enough to resolve in
the new telescopes.
Sizes for these can now be calculated
directly.
Betelguese is 600X larger than the Sun.
Indirect Size determinations
Using the luminosity and the temperature of a star the area
and hence the size of a star can be determined.
𝐿 = 𝜎𝐴𝑇 4 = 4𝜋𝜎𝑟 2 𝑇 4
𝑟=
𝐿
4𝜋𝜎𝑇 4
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.
𝐿 = 4𝜋𝜎𝑟 2 𝑇 4
Thus, Polaris is 100 times larger than the sun.
H-R diagram
depicts:
Temperature
Color
Luminosity
Spectral Type
Luminosity
Radius
Temperature
C
Luminosity
B
Which star
is the
hottest?
D
A
Temperature
C
Luminosity
B
Which star
is the
hottest?
D
A
A
Temperature
C
Luminosity
B
Which star is
the most
luminous?
D
A
Temperature
C
Which star is the most
luminous?
B
Luminosity
C
D
A
Temperature
C
Which star is a mainsequence star?
Luminosity
B
D
A
Temperature
C
Which star is a mainsequence star?
B
Luminosity
D
D
A
Temperature
C
Which star has the
largest radius?
Luminosity
B
D
A
Temperature
C
Which star has the
largest radius?
B
Luminosity
C
D
A
Temperature
What is the significance of the
main sequence?
Main-sequence
stars are fusing
hydrogen into
helium in their
cores like the Sun
Luminous mainsequence stars are
hot (blue)
Less luminous
ones are cooler
(yellow or red)
High-mass stars
Low-mass stars
Mass
measurements of
main-sequence
stars show that the
hot, blue stars are
much more
massive than the
cool, red ones
High-mass stars
Low-mass stars
The mass of a
normal, hydrogenburning star
determines its
luminosity and
spectral type!
Core pressure and
temperature of a
higher-mass star
need to be larger
in order to balance
gravity
Higher core
temperature
boosts fusion rate,
leading to larger
luminosity
For stars
Main regions
Some HR diagrams use the
magnitude instead of the
luminosity. While it looks like a
linear scale remember it’s
really a log scale.
The Distance Modulus
If we know a star’s absolute magnitude or
luminosity, we can infer its distance by comparing
absolute and apparent magnitudes:
Distance Modulus
= mV – MV
= -5 + 5 log10(d [pc])
Distance in units of parsec
Equivalent:
d = 10(mV – MV + 5)/5 pc
Stellar Distances. From parallax outward each new method is calibrated by data
from the earlier method. The methods overlap.
Stellar Properties Review
Luminosity: from brightness and distance
10-4 LSun - 106 LSun
Temperature: from color and spectral type
3,000 K - 50,000 K
Mass: from period (p) and average separation (a)
of binary-star orbit
0.08 MSun - 100 MSun
Stellar Properties Review
Luminosity: from brightness and distance
(0.08 MSun) 10-4 LSun - 106 LSun
(100 MSun)
Temperature: from color and spectral type
(0.08 MSun) 3,000 K - 50,000 K
(100 MSun)
Mass: from period (p) and average separation (a)
of binary-star orbit
0.08 MSun - 100 MSun
The most
visible stars
Notice the scales are log scales.
The diagonals are lines of
constant radius, from the
radius-luminosity-temperature
relationship.
Nearby
Stars
A random sample of stars
p. 151
There should be nothing special about our
local neighborhood. It therefore is useful as
a random sample of stars in the galaxy.
The larger our sample size the better our
conclusions. So a complete sample out to
greater distances gives a more accurate
picture of the galaxy as a whole.
A Census of the Stars
Faint, red dwarfs (low
mass) are the most
common stars.
Bright, hot, blue mainsequence stars (highmass) are very rare.
Giants and
supergiants are
extremely rare.
Mass & Lifetime
Sun’s life expectancy: 10 billion years
Until core hydrogen
(10% - 15% of total) is
used up
Life expectancy of 10 MSun star:
10 times as much fuel, uses it 104 times as fast
10 million years ~ 10 billion years x 10 / 104
Life expectancy of 0.1 MSun star:
0.1 times as much fuel, uses it 0.01 times as fast
100 billion years ~ 10 billion years x 0.1 / 0.01
Stellar Population Distribution Explained
Faint, red dwarfs
(low mass) are the
most common stars.
Long lived
Bright, hot, blue
main-sequence
stars (high-mass)
are very rare. Short
lived
Giants and
supergiants are
extremely rare.
Passing through a
stage.
Main-Sequence Star Summary
High Mass:
High Luminosity
Short-Lived
Large Radius
Blue
Low Mass:
Low Luminosity
Long-Lived
Small Radius
Red
What are giants, supergiants, and
white dwarfs?
Off the Main Sequence
• Stellar properties depend on both mass and age:
those that have finished fusing H to He in their cores
are no longer on the main sequence
• All stars become larger and redder after exhausting
their core hydrogen: giants and supergiants
• The core of most stars ends up small and white after
fusion has ceased: white dwarfs
A
Luminosity
D
B
C
Temperature
Which star is
most like our
Sun?
Which star is most like
our Sun?
A
Luminosity
D
B
C
Temperature
B
Which of these stars
will have changed the
least 10 billion years
from now?
A
Luminosity
D
B
C
Temperature
Which of these stars
will have changed the
least 10 billion years
from now?
A
Luminosity
D
B
C
C
Temperature
Which of these stars
can be no more than
10 million years old?
A
Luminosity
D
B
C
Temperature
Which of these stars
can be no more than
10 million years old?
A
Luminosity
D
A
B
C
Temperature
Why do the properties of some
stars vary?
Variable Stars
• Any star that varies significantly in brightness with
time is called a variable star
• Some stars vary in brightness because they cannot
achieve proper balance between power welling up
from the core and power radiated from the surface
• Such a star alternately expands and contracts,
varying in brightness as it tries to find a balance
Pulsating Variable Stars
• The light curve of this pulsating variable star shows
that its brightness alternately rises and falls over a
50-day period
Pulsating Variable Stars
• Most pulsating
variable stars
inhabit an instability
strip on the H-R
diagram
• The most luminous
ones are known as
Cepheid variables
Cepheid Variable Stars
• Cepheid variable’s magnitude will vary
between 0.5-2 magnitudes over a period from
days to months.
• They have been show to have a period of
variability that depends on luminosity.
• This allows Cepheid variables to be used as a
standard candle to measure distance.
Cepheid Variable Stars
• The accepted explanation for the pulsation of
Cepheids is called the Eddington valve
• Doubly ionized helium is more opaque than
singly ionized helium.
Eddington valve cont.
• The more helium is heated, the more ionized
it becomes.
• At the dimmest part of a Cepheid's cycle, the
ionized gas in the outer layers of the star is
opaque, and so is heated by the star's
radiation
• Due to the increased temperature the fusion
rate in the core increase resulting in an
increase in radiation pressure causing the star
to begin to expand.
Eddington valve cont.
• As it expands, the ionized helium cools, and
becomes less ionized and therefore more
transparent, allowing the radiation to escape
cooling the star and slowing the fusion rate.
• Then the expansion stops, and reverses due to
the star's gravitational attraction.
• The process then repeats.
What have we learned?
• What is a Hertzsprung-Russell diagram?
– An H-R diagram plots stellar luminosity of stars
versus surface temperature (or color or
spectral type)
• What is the significance of the main
sequence?
– Normal stars that fuse H to He in their cores
fall on the main sequence of an H-R diagram
– A star’s mass determines its position along the
main sequence (high-mass: luminous and blue;
low-mass: faint and red)
What have we learned?
• What are giants, supergiants, and white
dwarfs?
– All stars become larger and redder after core
hydrogen burning is exhausted: giants and
supergiants
– Most stars end up as tiny white dwarfs after
fusion has ceased
• Why do the properties of some stars vary?
– Some stars fail to achieve balance between
power generated in the core and power
radiated from the surface
Star Clusters
• Our goals for learning
• What are the two types of star clusters?
• How do we measure the age of a star cluster?
What are the two types of star
clusters?
Open cluster: A few thousand loosely packed stars, typically found is galactic disk,
and typically young in age <5 billion yrs.
Globular cluster: Up to a million or more stars in a dense ball bound together by gravity, most
found in the galactic halo with some in the disk, some of the oldest objects found in the galaxy.
How do we measure the age of a
star cluster?
Massive blue
stars die first,
followed by
white, yellow,
orange,
and
red stars
Mainsequence
turnoff point
of a cluster
tells us its age
Pleiades now
has no stars
with life
expectancy
less than
around 100
million years
Main-sequence
turnoff
Detailed
modeling of
the oldest
globular
clusters
reveals that
they are
about 13
billion years
old
What have we learned?
• What are the two types of star clusters?
– Open clusters are loosely packed and contain
up to a few thousand stars
– Globular clusters are densely packed and
contain hundreds of thousands of stars
• How do we measure the age of a star
cluster?
– A star cluster’s age roughly equals the life
expectancy of its most massive stars still on the
main sequence