A Protostar is Formed and Continues to Contract

Lecture 20: From Protostars to the Main Sequence

Recall that stars form from collapsing clouds and that we have plenty of evidence that stars are currently forming in the Milky Way (and in other galaxies, too!).

Stellar Lifetimes

• main sequence stars are burning H. How long can they remain in this stable state? Not quite as long as it would take to burn all the H in the star (details to come!), but its main sequence lifetime is proportional to its mass divided by its luminosity:

This gives the lifetime in years. Recall the relations between mass and luminosity for a stars:

If we use the mass-luminosity relation for stars of 0.4M_Sun and greater,

or

so a star with 10x the mass of the Sun will have a main sequence lifetime of only 10 million yrs!

So we know that O stars, the most massive stars, have main sequence lifetimes of only a million years so the fact that we see some O stars now means that star formation is still occuring in the Milky Way.

The Star Formation Process

From a variety of observations, it appears certain that stars form in the centers of dense molecular clouds.

--- clouds have cores which are hotter and denser than the surrounding material suggesting that the cloud is collapsing in its core.

-- Generally speaking, we think most star formation proceeds along the same lines as the formation of the Solar System:

1) A cold, dense molecular cloud begins to collapse

{ collapse may be triggered by gravity, a supernova blast, nearby hot stars}

2) Cloud fragments into stellar-sized clumps

3) Stars form in these clumps; planets may or may not form in the cloud material surrounding the star

Step 1: initial collapse

• If the cloud can cool sufficiently, gravity will always cause a contraction and subsequent collapse.
• Sequential star formation -- one star or group of stars forms in a cloud. Their energy heats the nearby cloud material which expands and thus compresses gas in the more distant part of the molecular cloud causing it to collapse.
• Supernovae explosions which happen when massive stars use up their H cause blast waves which can hit a molecular cloud and cause it to collapse.

[Abundances of some rare isotopes found in meteorites suggest that this was the triggering mechanism for the collapse of the cloud that became the Solar System]

• Rotation of the Milky Way can cause clouds to pile up and collisions between clouds can cause their collapse.

Step 2:  the GMC begins to collapse and it fragments into subcondensations which form individual stars. Although we don't know exactly why clouds like to fragment, it is obviously a common occurrence given the number of star clusters we see. It appears to be related to turbulence in the collapsing cloud.

Step 3: The clump collapses into a star

Consider the balance of forces in the collapsing cloud by looking at a gas sample in the cloud:

Gravity pulls gas towards the cloud center:

F_grav = GM_cloudm_gas/r²

r=distance from cloud center

F_pressure = C x density x T

T = temperature

While T is low (cloud is cool),

F_grav > F_pressure

and cloud collapses.

This collapse happens very fast. Eventually the gas gets sufficiently compressed that it is dense and hot enough that

F_pressure > F_grav

and the collapse stops.

The star is likely to be surrounded by gas and dust leftover from its formation, usually in the form of a circumstellar disk shape. The circumstellar disks are where planets form.

Many clouds in the galaxy cannot collapse to form stars because their temperatures are too high --

Cloud will collapse only if their gravitational force can overcome their internal pressure.

Recall from the lecture on the Sun that this equilibrium is fulfilled if

We can compute the mass of the cloud:

Recall also that P=nkT so the equilibrium condition becomes:

Substituting values for k and G and letting m equal mass of the H₂ molecule and converting to units of solar mass (M_Sun ) we get

named for Sir James Jeans. Clouds of larger mass than the Jeans mass can collapse while smaller ones cannot.

For a typical interstellar cloud with T=50°K and n =10⁶ particles/m³,

while for a dense cloud core with T=10°K and n=10¹² particles/m³:

During the initial parts of its contraction, a cloud won't heat up -- radiation escapes and carries away the energy. The Jeans mass decreases because T is staying constant but the density is increasing. Eventually the cloud breaks into fragments which in turn collapse to become stars.

An artist's idea of what the formation of the sun might have looked like.

Eventually the star will blow way the material surrounding it and become a regular visible star.

Cloud clumps with .08 M < M < 100 M can form stable, main sequence stars.

From protostar to main sequence:

--- after initial collapse, protostar is likely still to be surrounded by remnant of the cloud from which it formed (need to observe at long wavelengths to see through the dust)

• -- protostars are frequently observed to have circumstellar disks (are these where planets form?) and 'jets' or outflows from their poles

• -- eventually the star completes its collapse and begins to burn H, blows away surrounding material and it is then observed as a normal main sequence star

What happens if the collapsing cloud is too large?

If the mass of the cloud exceeds about 100 M, it will collapse and heat up very quickly. Nuclear reactions occur so rapidly that the star becomes very luminous and blows itself apart -- either catastrophically or more gently by blowing off only the outer layers.

What happens if the collapsing cloud is too small?

If the cloud has M < .08 M, it will contract, heat up, but the central temperature will never reach the 10,000,000°K limit required to start the conversion of H to He. The outer layers may get as hot as 2500°K and so appear similar to cool, dim stars, but they will have only a very brief lifetime in this luminous state. Such objects are called brown dwarfs.

Initial Mass Function

By observing the relative numbers of various masses of stars, we have been able to deduce something about the cloud fragmentation process even though we do not understand the details theoretically. The initial mass function (IMF) describes the relative numbers of each stellar mass:

Example of using this relationship:

Consider a cloud with a total mass of 1000M_Sun . How many 10M_Sun stars are formed if it follows the above IMF and forms stars over a range from 1 to 50M_Sun ?

Note that this is the number of stars with 10M_Sun in an interval of 1M_Sun .

After a cloud has contracted sufficiently, these steps describe its path to the main sequence:

Protostar will heat up due to Kelvin-Helmholtz contraction (review notes from on the Sun). The protostar is still rather cool and would appear at the extreme right of the HR diagram if at all. Because the protostar is still contracting, its diameter and hence surface area are quite large so its luminosity may be ~100x what it will be when it reaches the main sequence.

The protostar's relatively high luminosity means that it radiates away energy rapidly which in turns causes it to collapse gravitationally even faster. Its surface temperature hardly changes so its luminosity is declining rapidly because its radius is declining:

so the protostar moves almost straight downward in the HR diagram.

Due to the contraction, the core continues to heat up to several million ° K and H fusion begins. Energy production is not high enough to halt the collapse which continues although at a much slower rate. The increase in heating from the fusion is enough to increase the luminosity and surface temperature of the protostar so it moves leftward and slightly upward in the HR diagram.

The core continues to heat up and eventually the rate of energy release through fusion is sufficient to stop further collapse and the star enters a state of hydrostatic equilibrium on the main sequence.

Color Magnitude diagram for the cluster NGC2264

The track of where stars of different masses hit the main sequence is called the zero age main sequence.

Stars on the Main Sequence

While on the main sequence, a star is very stable, but its properties are slowly changing as the result of the composition of its core changing. For example, since P=nkT the pressure of the gas will respond to the smaller value of n because 4 H atoms have gone into one He atom. T increases to maintain hydrostatic equilibrium which in turn causes the luminosity to increase slightly.

Eventually the H loss is too large for the core to maintain hydrostatic equilibrium because the rate of energy generation drops due to a lack of H.

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Source: http://ircamera.as.arizona.edu/astr_250/Lectures/Lecture_20.htm

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