# You’re Gonna Be A Star, Kid

So, you want to be a star? Well, you’ve got a long way to go. But don’t worry. Stick with me and you’ll go far.

The first thing you’ve got to do is be a huge cloud of gas, out in interstellar space. It’ll especially help if you’re a Giant Molecular Cloud. These are regions of the interstellar medium which have very high densities and very low temperatures. That will help you out when it’s time to begin collapsing.

The Pillars of Creation in the Eagle Nebula, an area where giant molecular clouds are collapsing to form stars. Image Credit: NASA Hubble Space Telescope

Speaking of which, that’s the next step. Once you are dense enough, the inward pull of gravity will overcome the outward push caused by heat. This can be calculated using the Virial Theorem.

$\frac{3}{5}\frac{GM^2}{R} > \frac{3Mk_BT}{\mu m_H}$

In this equation, the force of gravity is on the left side and the pressure caused by the cloud’s temperature is on the right. Sometimes this is quantified in terms of a mass, known as the Jeans Mass.

$M_J \simeq (\frac{5k_BT}{G\mu m_H})^{3/2}(\frac{3}{4\pi \rho_0})^{1/2}$

Are you not quite dense enough to achieve this? Don’t worry. All you have to do is wait for a supernova to create a shockwave and cause you to collapse. Or you can take advantage of a tidal interaction with another galaxy to give you the push (or in this case, pull) you need. Once you’ve gotten the initial push, you can relax for a bit. As the collapse happens, your density, $\rho_0$ will be increasing. Since the Jeans Mass depends inversely on density, as your density increases, the collapse will speed up.

You just need to sit back and wait for a bit until your temperature starts to go up. During the initial part of your collapse, you don’t really need to worry about this. The excess heat caused by the collapse is easily radiated away as infrared radiation, so your temperature will remain relatively constant. However, as your density starts to increase, your opacity will go up as well. This means that light will have a harder time escaping. Since infrared radiation is the way you get rid of heat, that means that your temperature will start increasing.

If you’ve attained a high enough density at this point, your core will continue contracting as the temperature goes up. At this point, you have successfully become a protostar! Once you’ve reached this point, you’re almost there. But don’t get complacent, you aren’t done yet. As a protostar, you should continue gaining mass from the surrounding cloud via accretion.

An ALMA image of the protoplanetary disk surrounding the growing protostar, HL Tau. Image Credit: ALMA

As mass accretes, your temperature will begin to rise. Remember the Virial Theorem from earlier? Well, you can see that since the left side depends on $M^2$ and the right side depends on $M$, if your mass is increasing, the left side will grow faster than the right side. For a protostar to remain in equilibrium, the left side and right side should remain equal. Since the radius doesn’t change much, the temperature must increase.

Be careful not to run out of mass at this point, because if you do you will only become a brown dwarf. You need to have a mass of at least 0.085 solar masses to be able to fuse hydrogen into helium. Once you reach a temperature of $10^7$ Kelvin, you will be all set to begin fusion! As you reach the onset of fusion, you will be a fully fledged star. Congratulations, you’ve made down a difficult road. Now you can put up your feet, form a planet (or nine), and clean up any leftover gas and dust. Then, for the next few hundred million to tens of billions of years, you can sit back, relax, and shine away!

(Adapted from a paper I wrote for a class.)

Cover Image: The Westerlund 2 star forming region, from APOD.