4.1: Star Formation

Background: the law of gravity

The story of star formation begins with gravity. Aristotle believed that the movement of objects depends on their nature (earth, water, air, fire) and their intrinsic gravitas (heaviness). More than a millennia passed before Galileo and then Isaac Newton improved the physical description of gravity. In 1687, Newton published his Universal Law of Gravity, a predictive and mathematical description of gravitational forces that appears in most physics textbooks:

$F=\frac{GMm}{d^2}$

This equation tells us that the gravitational force is proportional to the mass $$M$$ of the attracting body and inversely proportional to the square of the distance between the attracting body and a particle with mass $$m$$. Double the mass, $$M$$, and the gravitational force is doubled. Double the distance, $$d$$, and the gravitational force drops by a factor of four.

Consider the example of a ball tossed into the air in the figure below. In this example, the ball is at a maximum height and is just about to reverse it's upward trajectory before falling back to the Earth. The gravitational force is between the Earth with mass $$M_{\oplus}$$ and the ball with mass m. The distance used in Eqn 1 must be calculated between the center of the Earth and the height of the ball: $$d=(R_{\oplus}+h)$$. The gravitational force between the Earth and the ball is:

$F_{grav}\,=\frac{GM_{\oplus}m_{ball}}{R_{\oplus}+h^2}$

At every point in it's trajectory, the ball has gravitational potential energy. That potential energy can do work, increasing the velocity (the kinetic energy) of the ball as it falls back toward the Earth. Because the ball stops at the surface of the Earth, the gravitational potential energy is relative to the Earth surface and proportional to the height of the ball relative to the surface of the Earth: $$U=mgh$$.

Gravity and General Relativity

In 1915, Einstein published his General Theory of Relativity, treating gravity as a warping of the space-time continuum and an attribute of mass rather than a fundamental force. Einstein's description of gravity employs mathematically sophisticated metric tensors, while Newtonian gravity uses more commonly accessible algebra or calculus. On the scales that humans are accustomed to working (and certainly for the physics included in this course) general relativity converges to the Newtonian description so we are justified in defaulting to the Newtonian description of gravity.

Star Formation

Spiral galaxies like the Milky Way contain about 1000 giant molecular clouds (GMCs), all located in the mid-plane of the galaxy. The GMCs are among the largest objects in galaxies with physical dimensions spanning 3 - 300 parsecs. It takes about 100 million years for the GMCs to dissipate. GMCs accumulate a mass that is roughly 100,000 times the mass of the Sun and are produced when aging stars shed their outer layers as red giants or supernovae. GMCs are comprised of hydrogen (mostly H2, hence the "molecular" cloud), helium and other gases as well as dust particles. Ultimately, this concentration of gas and dust collapses to form hundreds of thousands new stars and planets.

At first, the density of the GMC is low and the gravitational force is not strong enough to overcome the random thermal motion of molecules. It is likely that a shock wave - perhaps from the evolution of a nearby stars - compresses gas locally in the GMC. If the compressed regions reach a critical density, then gravity takes over. Look at Eqn (4.1.1) to understand why this is a runaway process: collapse means that the mean distance between particles is decreasing and this (decreasing $$d$$ ) results in an increase in the gravitational force. Increasing the gravitational force increases the collapse, which further increases the strength of the gravitational force, and so on.

The collapse of a critically dense region in the GMC does not produce a single star. Instead, the gas cloud fragments and smaller, denser clouds begin to collapse to form thousands of stars. Initially, the cloud is transparent to radiation and the gravitational collapse proceeds quickly. As the cloud fragment contracts, the density and the collision rate between particles increases so that the core of the cloud begins to heat up. Gravitational potential energy is doing work at this stage and some of the gravitational potential energy is emitted as infrared energy. As the density of the core is increasing, it becomes more opaque, trapping thermal energy in the core. At this point, the core of the cloud is a protostar with a temperature of a few thousand degrees, embedded in an obscuring shroud of cooler gas. Images of a star-forming region at visible and infrared wavelengths show different features. The infrared wavelengths of light penetrate the cooler gas and dust, allowing us to see the embedded protostars.

Star formation is a very inefficient process. Giant molecular clouds can churn out thousands of stars, but only a small fraction of the cloud (less than 10%) ends up in these stars. Once the stars form, the gas and dust is cleared out and on timescales of tens of millions of years, gravitational interactions begin to kick stars out of the cluster -- the cluster begins to dissipate.

When a protostar is contracting, there are two physical forces at work: gravity, which tries to collapse the protostar, and the kinetic energy of colliding particles, which resists contraction. Initially, gravity wins this battle. The protostar continues to contract and the density, temperature and pressure in the core continue to build. As the star contracts, angular momentum is conserved and the star spins up. Kinetic energy is released as increasingly strong polar winds and turbulence in the plasma of the protostar spawn magnetic fields. Young protostars in the Orion nebula are shown below. These objects are beginning to clear the dark cloud of gas and dust and the infrared light of the star, which is beginning to burn deuterium, shines through.

When the temperature in the core of the protostar climbs to 10 million K, the inward pressure overcomes electrostatic repulsion between the hydrogen nuclei (protons) and hydrogen fuses to form helium. With the onset of hydrogen fusion, the protostar becomes a bonafide star. The rate of hydrogen fusion continues to increase until the core generates enough energy to stabilize the gravitational collapse. If the star expands too much, then the gravitational pressure decreases, and hydrogen fusion rate slows down a bit. This self-regulating process acts like a thermostat to keep the star in balance. When the amount of energy that is being produced by hydrogen fusion is equal and opposite to the gravitational potential energy of the star, we say that the star is in hydrostatic equilibrium. These are the two defining characteristics of this "main sequence" star: hydrogen fusion in the core and hydrostatic equilibrium between the energy production from fusion reactions and gravity.

The role of massive stars in star-forming regions

The mass of the star determines its future evolution. More massive protostars collapse more quickly. Gravity is running the star formation show and as the mass increases, the gravitational force increases. More massive stars contain more hydrogen, but the rate of hydrogen fusion (also called "hydrogen burning") is so much faster in high mass stars that they have much shorter lifetimes.

At the end of the life cycle of a star, nuclear fusion can no longer support the star against gravity. The star begins to collapse. As the outermost layers of the star fall in, they bounce off a dense wall of imploding material and the heavy elements inside the star are expelled, enriching the interstellar medium. Stars that are about the mass of the Sun will puff off a shell of material into a nebula containing atomic elements from hydrogen up to iron. This material is eventually swept up into molecular clouds and incorporated in the next generation of star formation. The subsequent generation of stars inherits a larger fraction of heavy elements that allows them to build planets and living organisms. Stars that are significantly more massive than the Sun have a more violent ending in a supernova explosion.

Images of the star-forming region in the Serpens constellation show spectacular dust structures called "the Pillars of Creation." New stars are being formed inside these structures. However, there are some rare stars that are about 80 times the mass of the Sun, and the giant molecular dust cloud is being sculpted by the high energy radiation of these stars.

Can you hear me now?

The velocity of dust in the surface of the pillars has been measured and indicates that these structures are experiencing significant mass loss. The shapes we see in the image above would have changed significantly in the 7000 years that it has taken their light to travel to us. Indeed, it is very likely that one of the massive stars in the region has already "gone supernova" and blown the pillars away completely. However, it will take many years before we get an update that revises our picture.

Spiral arms and young stars

It is interesting to map out the location of star formation. Stars are distributed nearly uniformly in the disks of spiral galaxies, but you would never know it looking at the composite image of the Whirlpool galaxy. The bright spiral arms are regions of enhanced density where new star formation is triggered. Because the massive stars are the most luminous, they light up the arms during their relatively short lives and are never seen far from the molecular clouds. The youngest stars are born in clusters located along the spiral arms of the galaxy and the giant molecular clouds are seen as dark dust lanes along the trailing edge of the spiral arms. The spiral density waves that cause turbulence and large scale coherent structure are only observed in flattened galaxies but the forcing mechanism that causes the spiral density waves is complicated and still controversial.

Star Formation in Open Clusters

Recall that open clusters are fundamentally different from globular clusters. Globular clusters are among the oldest objects in the Milky Way galaxy and are distributed in a spherical volume above and below the galactic plane. Open clusters are concentrated in the thin disk of our galaxy. They consist of a group of hundreds of stars (compared to many thousands of stars in globular clusters). Because open clusters are smaller, they are not as tightly bound by gravity and they tend to have an irregular morphology. Open clusters are the product of new star formation from giant molecular clouds. Because open clusters contain short-lived massive stars, the most visible stars in open clusters appear bright and blue. The most luminous stars in the old globular clusters are red giants and that stellar population lends an orange cast to the cluster.

The collapse of molecular clouds is triggered in the leading edge of spiral arms in galaxies where the dust and gas is compressed. Young bright stars in open clusters light up the arms of spiral galaxies, like sparkling diamonds. Open clusters last for a few hundred million years. Ultimately, their stars slowly disperse because of random velocities. The Sun must have formed in an open cluster of stars, but 4.5 Gyr is a long time. All of the sibling stars of the Sun have long left the nest. In contrast, globular clusters do not disperse because of the larger self-gravity of the group.

Best Friends Forever: Binary Stars

Our Sun is a loner - a single star. However, roughly half of the stars in our galaxy are gravitationally bound to another star. Such stars are called "binary" stars and they can have orbital periods as short as an hour or as long as thousands of years. Remarkably, a series of papers in the 1990's showed that the fraction of binary star systems depends on the spectral type of the stars. The O and B type stars are exceedingly rare. However, roughly 75% of these massive stars are gravitationally bound in binary star systems. In contrast, about 60% of stars like our Sun have a gravitationally-bound stellar buddy and only 40% of the smallest stars - the low mass M dwarfs - have binary stellar companions.