Lecture 15: The Main Sequence

Readings: Box 21-2, Figure 20-11

 

Key Ideas

 

Main Sequence stars ÒburnÓ hydrogen into helium in their cores

         Get slowly brighter with age

 

The Main Sequence is a Mass Sequence

         Low M-S: M < 1.2 MSun

         Upper M-S: M > 1.2 MSun

 

The M-S lifetime depends on the Mass

         Larger Mass = Shorter Lifetime

 

Main Sequence Membership

 

To be a main sequence star:

         It must be in Hydrostatic Equilibrium (Pressure=Gravity)

         It must be in Thermal Equilibrium (Energy Generation=Luminosity)

         It must generate energy by ÒburningÓ H into He in its core

 

If any of these conditions is not met, the star is not on the main-sequence.

These conditions define a region on the H-R diagram where stars hang out for long periods of time. ThatÕs why so many stars in the sky (85%) are on the main sequence.

 

The Main Sequence is a Mass Sequence

 

The location of a star along the main sequence is determined by its mass.

 

         Low-mass stars: Cool & Low Luminosity

         High-mass stars: Hot & High Luminosity

 

Result of the Mass-Luminosity Relation:

 

 

Internal Structure

 

Nuclear reaction rates are very sensitive to core temperature

         Proton-proton chain: fusion rate ~T4

         CNO cycle fusion rate~T18!

 

Leads to

         Difference in internal structure

         Division into upper & lower M-S by mass

         Dividing line is at ~1.2 MSun

 

Upper Main Sequence

M > 1.2 MSun

Tcore > 18 Million K

CNO Cycle fusion

Structure

         Convective Core

         Radiative Envelope

 

Lower Main Sequence

M < 1.2MSun

Tcore< 18 million K

P-P Chain

Structure

         Radiative Core

         Convective Envelope

 

The Lowest Mass Stars

 

0.25 > MSun < 0.08 MSun

P-P Chain fusion

Fully Convective

         Convective Core and Envelope

 

The Nuclear Timescale

 

 

 

The nuclear timescale is

 

 

f=fraction of nuclear fuel available for fusion (~10% in most cases)

e= efficiency of matter-energy conversion (0.7% for hydrogen-helium fusion)

M=mass of star

L=luminosity of star

 

For the Sun:

         t=10 Gyr

 

Stars=Cars? Part I

A low-mass star is like an economy car:

         Small fuel tank

         Low-power engine (low energy output)

         Excellent Ògas mileageÓ

Consumes fuel very slowly

Result: Low-Mass stars stay on the Main Sequence for a very long time.

 

Stars=Cars? Part II

 

A high-mass star is like a Hummer

         Large fuel tank

         High power engine (high energy output)

         Low Ògas mileageÓ

Consumes fuel very quickly

Result: High-Mass stars run out of fuel and leave the Main Sequence after a very short time.

 

Main-Sequence Lifetime

 

Nuclear Timescales:

 

Mass-Luminosity Relation:

 

 

Combine them

 

 

Another way to think of this

 

 

(note this is a little different than the relation in Box 21-2. Use this relation)

 

Consequences:

         High-Mass M-S stars have short M-S lifetimes

         Low-Mass M-S stars have long M-S lifetimes

        

More massive main-sequence stars need higher pressures to support themselves against gravitational collapse. Higher pressure=higher temperatures. The higher temperatures lead to greater rates of nuclear fusion which means higher luminosity.

 

Example:

Low-mass Star (0.1 MSun)

 

 

 

 

 

Question: what is the lowest mass star that has left the main sequence?

 

 

 

 

 

 

Consequences

 

If you see an O or B dwarf (=main sequence) star, it must be young as they die after only a few million years.

 

You canÕt tell how old an M dwarf is because they live long and age slowly

 

The Sun is ~5 billion years old, so it will last only for ~5 billion years longer.

Start packing!

 

Brighter with AgeÉ.

Hydrostatic Equilibrium requires a high central pressure:

         Pressure=density x temperature

As H is fused into He, there are fewer nuclei:

         Remaining nuclei must move faster to maintain the same pressure

         The gas gets hotter, so fusion runs faster

 

M-S stars get slowly brighter with age

         Small effect: ~1% brighter every 100 Myr years

 

Compared to 4.5 billion years agao, the radius of the Sun ahs increased by 6% and the luminosity by 40%

 

Running out of Fuel—Low Mass

 

The star begins its life on the M-S with 70% H and 30% He.

Temperature is highest at the center, so nuclear reactions eat up H there faster.

H is gradually used up further and further away from the center.

It is a slow adjustment

 

 

Running out of Fuel – High Mass

 

Similar to low-mass stars, except convection brings new H from lower temperature regions. H is used up all throughout the core at a constant rate. When it is gone, it is all gone, so this leads to a rapid adjustment.