Introduction to Stars, Galaxies, & the Universe
Prof. Richard Pogge, MTWThF 9:30
Lecture 15: The Main Sequence
Readings: Chapter 20, section 20-4
- Main Sequence stars are those that "burn" Hydrogen
into Helium in their cores.
- Get slowly brighter with age.
- The Main Sequence is a Mass Sequence:
- Lower M-S: M < 1.1 Msun
- Upper M-S: M > 1.1 Msun
- The Main-Sequence Lifetime depends on the Mass:
- Larger Mass = Shorter Lifetime
Main Sequence Membership
For a star to be located on the Main Sequence in the H-R diagram:
- It must be in Hydrostatic Equilibrium (Pressure balances Gravity)
- It must be in Thermal Equilibrium (Energy Generation balances
- It must generate energy by "burning" Hydrogen into Helium in its core.
Relax any of these conditions and the star must leave the Main Sequence.
Main Sequence stars are in Hydrostatic
Equilibrium. This requires a high central Pressure.
Since we have an ideal gas, Pressure = Density x Temperature:
As Hydrogen is fused into Helium in the core there are fewer nuclei
around (4 H become 1 He). As a consequence:
- Temperature: mean speeds of the nuclei
- Density: number of nuclei per cubic centimeter
- The remaining nuclei must move faster to maintain the
same high Pressure as before.
- The gas at the center gets slowly hotter.
- This causes fusion to run faster as the temperature rises.
The result is that Main Sequence stars get slowly brighter as they age.
We would not notice this on a human timescale, but there is evidence of
changes in the Sun's brightness over geologic time (specifically the Sun
has gotten about 30% brighter over the last 4.5Gyr since the formation
of the Earth).
- It's a small effect: ~0.7% brighter every 100 Myr
The Main Sequence is a Mass Sequence
The location of a star along the M-S is determined by its Mass.
- Low-Mass Stars: Cooler and Fainter
- High-Mass Stars: Hotter and Brighter
As we saw in Lecture 11, M-S stars
obey a strong Mass-Luminosity Relation:
(In words: High-mass M-S stars are more luminous than low-mass
M-S stars proportional to the 4th power of their Mass.)
Nuclear reaction rates are very sensitive to core temperature:
The leads to:
The dividing line is at about 1.1 Msun, the mass at which the
P-P chain and CNO cycle both contribute equally to the total energy
generation in the core.
- Differences in internal structure.
- Division into Upper and Lower Main-Sequences by mass.
Upper Main Sequence
Upper Main-Sequence stars have
- M > 1.1 Msun
- TCore > 18 Million K
Hydrogen fusion occurs via the CNO Cycle
[Schematic of an Upper M-S Star interior]
- Internal Structure:
- Convective Core
- Radiative Envelope
Lower Main Sequence
Lower Main-Sequence stars have
- M < 1.1 Msun
- TCore < 18 Million K
Hydrogen fusion occurs via the
[Schematic of a Lower M-S Star interior]
- Internal Structure:
- Radiative Core
- Convective Envelope
The Lowest Mass Stars
Mass Range: 0.25 > M* > 0.08 Msun:
These stars have Fully Convective Interiors:
Genericaly called Red Dwarf Stars
- Convective Core and
- Convective Envelope
[Schematic of a red dwarf interior]
How long a star can continue to generate energy by fusing H into He in
its core depends upon how much fuel it has (total mass of the star),
and how fast it is burning it (luminosity).
We call this the Nuclear Timescale:
For the Sun:
- f = fraction of nuclear fuel available for fusion
- e = efficiency of matter-energy conversion
- M = mass of the star
- L = luminosity of the star
- tnuc = 10 Gyr given that f=10% of the Sun's H is
available for fusion into He with a matter-energy conversion
efficiency of e=0.7%
Main Sequence Lifetime
The Nuclear Timescale above depends on the Mass (M)
and Luminosity (L). But, we know from the Mass-Luminosity Relation for Main Sequence
If we combine this with the formula for the Nuclear
Timescale, we get the Main Sequence Lifetime:
- L = M4
The consequence is that the M-S lifetime is strongly dependent on the
Mass of the star, in the sense that:
tMS ~ 1 / M3
- High-Mass M-S Stars have short M-S lifetimes
- Low-Mass M-S Stars have long M-S lifetimes
- M = 1 Msun, and tMS = 10 Gyr
- Massive Star (10 Msun):
- tMS = 10 Gyr / (10 Msun)3 = 10 Million Years
- Low-Mass Star (0.1 Msun):
- tMS = 10 Gyr / (0.1 Msun)3 = 10 Trillion Years
Some observational consequences of the Main-Sequence lifetime
depending so strongly on the Mass of the star:
- If you see an O or B dwarf star, it must be relatively young
as O and B stars evolve very rapidly and live for only a few Million
- You can't tell how old an M dwarf is because their M-S lifetimes
are extremely long and they evolve very slowly.
- The Sun is ~5 Billion years old, so it will only last for about
another ~5 Billion years.
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Updated: 2006 August 1
Copyright © Richard W. Pogge, All Rights