Download Hertzsprung-Russell Diagrams

Hertzsprung – Russell
Diagram
A plot of the luminosity as a function of the surface temperature for
different radii stars.
Hertzsprung - Russell Diagram
The Hertzsprung -Russell (H-R) Diagram is a graph that plots stars color
(spectral type or surface temperature) vs. its luminosity (intrinsic brightness or
absolute magnitude). On it, astronomers plot stars' color, temperature, luminosity,
spectral type, and evolutionary stage. There are 3 very different types of stars:
Most stars, including the sun, are "main sequence stars," fueled by nuclear fusion
converting hydrogen into helium. For these stars, the hotter they are, the brighter.
These stars are in the most stable part of their existence; this stage generally
lasts for about 5 billion years.
As stars begin to die, they become giants and supergiants (above the main
sequence). These stars have depleted their hydrogen supply and are very old.
The core contracts as the outer layers expand. These stars will eventually
explode (becoming a planetary nebula or supernova, depending on their mass)
and then become white dwarfs, neutron stars, or black holes (again depending on
their mass).
Smaller stars (like our Sun) eventually become faint white dwarfs (hot, white, dim
stars) that are below the main sequence. These hot, shrinking stars have
depleted their nuclear fuels and will eventually become cold, dark, black dwarfs.
Hertzsprung – Russell Diagram
Sometimes the labels are a little different:
The vertical position represents the star's luminosity.
This could be the luminosity in watts.
More commonly it is in units of the Sun's luminosity.
In either case, a ``ratio scale'' is used.
Absolute magnitude is also commonly used.
The horizontal position represents the star's surface temperature.
Sometimes this is labelled in by the temperature in Kelvins.
Highest temperatures go to the left. (It's traditional.)
Normally the temperature is given using a ``ratio scale.''
Sometimes the stars spectral class (OBAFGKM) is used.
One could also use a measure of color as seen through filters.
Basics of the HR diagram
In a Hertzsprung-Russell diagram, each star is represented by a dot. One uses data
from lots of stars, so there are lots of dots. The position of each dot on the diagram
corresponds to the star's luminosity and its temperature.
The vertical position represents the star's luminosity.
The horizontal position represents the star's surface temperature.
Hertzsprung – Russell Diagram
How it works:
Stefan-Boltzmann’s Law:
L
A
= 
T4
Where
L is the luminosity in Watts
A is the surface area
 is the Stefan-Boltzmann constant = 5.67 x 10-8 W/m2 –
K4
T is the surface temperature in Kelvin
Hertzsprung – Russell Diagram
How it works:
Stefan-Boltzmann’s Law:
L
A
= 
T4
L
= 4  R2 
T4
Hertzsprung – Russell Diagram
Some fancy stuff:
L
L = 4 
L

( )
L
( L )L


= 4

R2
(R )R ( )
2 
2 
R T4
2
But:
L = 4 

Where  is the symbol for the sun
T4
4
T

T4
R T4
2
R2
T4
(R )(T )
2 

4
Hertzsprung – Russell Diagram
Therefore:
L
=
L
( )
1
T4
R2
(R )T
4
2 
If luminosity and radius are given as the fraction of the luminosity and
radius of the sun, and recalling that T = 5800 K, then
Lfractional
1
2 T4
=
R
fractional
58004
Where Lfractional and Rfractional are the fraction of the suns luminosity and radius.
Hertzsprung – Russell Diagram
AND, using logarithms:
1
2 T4
Log (Lfractional) = Log
R
fractional
58004
(
1
2
Log (Lfractional) = Log
R
fractional
58004
(
Log (Lfractional) = 4 Log T + Log
(
)
) + Log (T
4
)
1
2
R
fractional
58004
)
Hertzsprung – Russell Diagram
AND, using logarithms:
Log (Lfractional) = 4 Log T + Log
(
1
2
R
fractional
58004
y = mx + b
On a Log – Log graph, the L vs T graph is a straight line for a given radius
star
)
Hertzsprung – Russell Diagram
Log (Lfractional) = 4 Log T + Log
y = mx + b
(
1
2
R
fractional
58004
)
Hertzsprung – Russell Diagram
H-R Diagram for the nearest stars to the solar system
Hertzsprung – Russell Diagram
Most stars fall on a band, called the main sequence.
Main sequence – the band on an H-R Diagram upon which most stars fall.
Hertzsprung – Russell Diagram
Log (Lfractional) = 4 Log T + Log
y = mx + b
(
1
2
R
fractional
58004
)
Determination of Masses
Binary Stars
R
X
Determination of Masses
Binary Stars
R
X
M=
v2 R
G
Determination of Masses
Binary Stars - Types
Visual Binaries – Binary stars which are far enough apart and bright enough to
be observed and monitored separately.
Spectroscopic Binaries – Binary stars which are too far away to be
distinguished visually. There motion can be determine though their spectra,
and the Doppler Shifts associated with the orbits of the stars.
Mass-Luminosity Relationship
Luminosity vs. Mass is plotted for the Sun and all Main Sequence stars in
binary systems that have good mass measurements shows that a Main
Sequence star's Luminosity is very strongly correlated with its Mass:
Data shows that L  M4
Using this relation, we can label regions on the HR diagram according to
the mass of the corresponding stars.
Our conclusion:
Different stars have different masses.
Among all stars with the same mass, almost all have the same properties.
The most massive stars are the most luminous.
Hertzsprung – Russell Diagram
Based on experimental evidence:
* Stars spend most of their lives as main sequence stars.
* During its lifetime, the surface temperature and luminosity stays pretty
much constant.
Something else could happen in the star birth process.
Something else could happen in the star death process.
* The star's mass determines what the temperature and luminosity is
during the star's main sequence lifetime.
More mass -> hotter.
More mass -> more luminous.
Also, more mass -> bigger.
The most prominent feature of
the H-R diagram is the Main
Sequence (M-S):
* Strong correlation between Luminosity and Temperature.
* Hotter stars are Brighter than cooler stars along the M-S.
* About 85% of nearby stars, including the Sun, are on the M-S.
All other stars differ in size:
Giants & Supergiants:
* Very large radius, but same masses as M-S stars
White Dwarfs:
* Very compact stars: ~ Rearth but with ~ Msun