Download The Mass-Luminosity Relationship and Stellar Lifetimes

Survey
yes no Was this document useful for you?
   Thank you for your participation!

* Your assessment is very important for improving the work of artificial intelligence, which forms the content of this project

Document related concepts

Astronomical spectroscopy wikipedia, lookup

Aquarius (constellation) wikipedia, lookup

Ursa Minor wikipedia, lookup

Corvus (constellation) wikipedia, lookup

Boötes wikipedia, lookup

Perseus (constellation) wikipedia, lookup

Corona Australis wikipedia, lookup

Canis Major wikipedia, lookup

Auriga (constellation) wikipedia, lookup

Cygnus (constellation) wikipedia, lookup

Canis Minor wikipedia, lookup

Cassiopeia (constellation) wikipedia, lookup

Corona Borealis wikipedia, lookup

Timeline of astronomy wikipedia, lookup

Hipparcos wikipedia, lookup

Observational astronomy wikipedia, lookup

Lyra wikipedia, lookup

Serpens wikipedia, lookup

International Ultraviolet Explorer wikipedia, lookup

Planetary habitability wikipedia, lookup

CoRoT wikipedia, lookup

Ursa Major wikipedia, lookup

Stellar evolution wikipedia, lookup

Star formation wikipedia, lookup

Stellar kinematics wikipedia, lookup

Dyson sphere wikipedia, lookup

Stellar classification wikipedia, lookup

Star catalogue wikipedia, lookup

Star wikipedia, lookup

H II region wikipedia, lookup

Star of Bethlehem wikipedia, lookup

Drake equation wikipedia, lookup

Transcript
The Mass-Luminosity
Relationship
and Stellar Lifetimes
Gee, since we’re already
examining how things are related…
Masses of Stars
• Just like we plotted color (temperature)
against luminosity…(the HR diagram!)
• If the mass of the stars is plotted against
their luminosities, the graph reveals
another relationship.
• (We’ll cover just how the masses of stars
are determined in a couple of days.)
http://www-astronomy.mps.ohio-state.edu/~pogge/Ast162/Unit2/Images/mlrel.gif
The Equation
• A star has a luminosity that is proportional
to its mass to the 4th power. In other
words, the brightness of a star increases
much faster than its mass does.
• In equation form, the mass-luminosity
relationship is…
Lstar / Lsun
=
(Mstar / Msun)4
• The equation is only true for stars that are
bigger than 0.43 Msun.
• If the star is very small, smaller than 0.43
Msun, then the equation is modified:
Lstar / Lsun = (Mstar / Msun)2.3
Slight change
This doesn’t seem right…
• Our intuition would seem to say that since
big stars have a lot more fuel to consume,
they should last a lot longer than smaller
stars.
• It doesn’t work this way, however. If the
luminosity of a star increases with the 4th
power of the mass, that means that the
star is producing energy and using its fuel
at the same faster rate.
Here’s an example
• A star of 2 solar masses has twice the H
fuel available, but uses it 24 or 16 times
faster.
• Mathematically, 21/24 = 2/16 = 1/8. A star
of 2 solar masses would last only 1/8th as
long as a 1 solar mass star.
• This is like a bonfire burning all its fuel and
being out in an hour, where a small
campfire still has hot embers the next
morning!
Burns out quickly!
Still burning slowly
the next morning…
So How Long Do Stars Last?
• We estimate that a 1-solar-mass star like
our sun will live a total of about 10 billion
or 1 x 1010 years.
• Larger stars will live
(1 / Mstar)3 x 1010 years
• This equation is good for all stars 0.43
Msun and above.
What about very small stars?
• For small stars, their lifetimes are given by
(1 / Mstar)1.3 x 1010 years
A couple of examples
• How long would a 10-solar-mass star live?
(1 / 10)3 x 1010 = 1/1000 x 1010 =
1 x 107 or 10 million years.
• The smallest a star can be is about 0.08
solar masses. How long would a star like
this live?
(1 / 0.08)1.3 x 1010 = 26.7 x 1010 =
267 billion years
• This means that the universe isn’t yet old
enough for small red dwarf stars to have
begun dying. Some red dwarfs may have
been around since the universe began!
• The very largest a star can be (we think) is
about 100 solar masses.
• How luminous would a star like this be?
Lstar = 1004 = 100 million Lsun
• How long would a star this size live?
(1/100)3 x 1010 = 10,000 years
• Huge stars may actually live a little longer
than this due to other factors, but you get
the point!
Time to do the Homework!