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“You really should keep a personal log. Why bore others needlessly?” The Doctor, Star Trek Voyager Announcements Midterm in one week. Draft of your paper A rough draft of your paper will be due on March 23. This draft does NOT need to be complete. However, it should include ALL of the references you plan to use and outline ALL of the sections you think your paper will include. The more complete it is, the more I can comment. It will be worth 25 points. Star formation The basic idea is that stars form from the widely dispersed clouds around the galaxy. Both the gas and stars in the Milky Way are not evenly distributed. So we start with the ISM The ISM The ISM comes in different densities and temperatures. However, since H is the most abundant atom by a longshot, we can concentrate on that. H can be ionized, neutral, or molecular (H2). The ISM The number density of the ISM depends on what form H takes. If H is ionized, then nISM=2nH or if H is molecular, then nISM= ½nH. The ISM But nH does give a good indicator of the mass density, r. So for any sample of ISM, r~nHmH. Various types of gases distinguished By number density and temperature. Note the general trend in this plot. The cold gases tend to be more dense and the hotter ones less dense. And the ranges; from 100/m3 to 1017/m3 and from 10K to over a million K. We will explore these different types of gas. Starting here. Intercloud Medium The intercloud medium is the diffuse gas that accounts for most of the volume of the ISM. It is the gas between the stars and all other type of ISM are within this one. Hot Intercloud Medium The hot intercloud medium is very widespread, but very diffuse. This is ionized H. This medium is highly transparent Warm Intercloud Medium Same as the hot stuff, but neutral H. Still very diffuse. This medium is optically transparent. Typical densities are 1 H /cc (a nice number to remember!) This is the gas that makes the 21cm radio line. We use it to map galaxies. Interesting note The 21cm line cannot be produced in Earth-based labs as our vacuums cannot get low enough, so collisions dominate and lab atoms de-excite prior to emitting 21cm photons. Intercloud medium But this gas is not involved directly in star formation. So we are not so interested in it now. The rest The other types are compact, but are either associated with stars (planetary nebulae and supernova remnants) or are not (the ones we're interested in now) Those associated with individual stars And those we're interested in now. Diffuse clouds. Diffuse Clouds These regions are cold and of moderate density. You can see stars through them at visible wavelengths and so are typically not apparent. H is both neutral and in molecular form. These typically have temperatures of 30 – 80 K and number densities of 100 – 800 /cc (divide by a million to get mks units) and masses of 1 – 100 solar masses with sizes of 3 - 100pc. Diffuse Clouds H2 is not easily mapped (diatomic molecule), but typically where you find H2, you find CO, which can be. Dense clouds Dense clouds Unless very thin, these are opaque at visible and UV wavelengths. These are therefore often called dark clouds. Dense clouds Most of this gas exists in molecular form. The clouds are usually mapped in CO, HC, or OH molecules. Temperatures are 15 – 50 K, n~ 500 – 5,000/cc, and masses of ~3 – 1000 solar masses with sizes of 0.1 – 20pc. So ALL dense clouds are also molecular clouds. Part of Orion mapped in CO. Regions of dense clouds are usually surrounded by diffuse clouds. HII regions. These are again regions of ionized H, caused by very hot O or B stars. HII regions (aka Stromgren spheres) UV photons from hot stars ionize the H in the nearby cloud. This creates bubbles of HII gas. These spheres are called Stromgren spheres. At the outer boundary, there is some recombination. With the short lifetime of massive, UV-creating stars, the size of Stromgren spheres often reaches a limit. Other times, it can break out. The pretty pictures are caused by recombination at the boundary regions, where the electron cascades down through shells. This is the n=3 to 2 transition (Ha). A beautifully complex slice of the Orion nebula. Giant molecular clouds These consist of diffuse and dense clouds that span large regions. Attributes are typically T~20K, n~100-300/cm3, m~10-10,000 solar masses and sizes are around 50pc (but up to 100pc). Thousands of these are known in our galaxy. Most in the spiral arms. Orange are GMCs, green is an HII region, Pink is an SNR. Scale is 1500 light years per side. You can see how GMCs trace the spiral arms (or is it the other way round?). Dense cores or Bok globules. These are dense regions inside GMCs which have the densest gases. T~10K, n>104/cm3, m~1-1,000 solar mass and r~1pc. Dense cores or Bok globules. Infrared surveys reveal that these are regions of active star formation These regions are usually associated with OB associations. Another indication of their youth. How dense is dense? Space is pretty empty and so comparing a giant molecular cloud to space, it seems pretty dense. However, even the densest cloud is about a million times less dense than the best vacuum we can create on Earth. They make up for it in volume. Dense clouds These make up about 45% of the total mass of the ISM. Connections between clouds and star formation. 1) We see young stars near clouds. We only see OB associations near clouds and never alone. And of course these are the stars with the shortest lifetimes, and so cannot travel as far from their birth place. Or even still embedded in the gas. We see large regions of dust surrounding very young stars These are often called cocoon nebulae, as they surround and hide the star inside. They are heated to 100s of K. HR diagrams of these regions also show that while massive stars have reached the MS, most stars have not. Theoretical isochrones date regions like this at a few million years (Orion is 1 million) The basics of star formation Gravity acts everywhere and on/from every particle with mass. As such, even though the density is very low, each particle does pull on other particles. While these forces are very, very, VERY small, we cannot ignore them. 1) Because there are no other large masses around, and 2) because taken as a whole, the clouds can be very massive. Gas balance. James Jeans sorted a lot of this out in 1902. Here are the basics: 1) Ignore galactic rotation and magnetic fields 2) Put the cloud in hydrostatic equilibrium (a balance between gravity and pressure) 3) just overcome the pressure. Volume is area x radius Pressure is force over area. Gravitational force is GM2/r2 Density is M/V ~M/r3 Higher pressre → expansion (stability against contraction). Higher density → contraction (gravity wins). Higher pressre → expansion (stability against contraction). Higher density → contraction (gravity wins). The virial theorem The virial theorem describes the condition of equilibrium for a stable, gravitationally bound, system: 2K + U = 0 Where K is the kinetic energy of the gas and U is the gravitational potential energy of the gas. The virial theorem 2K + U = 0 If twice the kinetic energy of a molecular cloud exceeds the gravitational potential, the cloud will expand. If the internal kinetic of the cloud is too low, the cloud will collapse. The virial theorem 2K + U = 0 The boundary between those two cases is the critical condition for stability. Deriving the Jean's criterion. The gravitational potential energy of a spherical cloud of constant density is: The gravitational potential energy of a test particle of mass dmi at a distance r from the center is Deriving the Jean's criterion. The gravitational potential energy of a spherical cloud of constant density is: The mass within the shell of dr is dm=4pdrr which makes the potential energy Deriving the Jean's criterion. The gravitational potential energy of a spherical cloud of constant density is: To sum all the potential energy, integrate over the entire cloud Deriving the Jean's criterion. The gravitational potential energy of a spherical cloud of constant density is: At uniform density, we can integrate over the total mass, which is (4/3)pr3r Deriving the Jean's criterion. The gravitational potential energy of a spherical cloud of constant density is: Substituting back to M, this becomes. Which is the gravitational potential energy of a uniform sphere. Deriving the Jean's criterion. The gravitational potential energy of a spherical cloud of constant density is: Where Mc and Rc are the mass and radius of the cloud. Deriving the Jean's criterion. The internal kinetic energy of a spherical cloud of constant density, ideal gas is: Where N is the total number of particles. We may rewrite N as where m is the mean molecular weight and then Deriving the Jean's criterion. Putting it back together, we have Yet we can also eliminate Rc using the initial mass density of the cloud ro. Deriving the Jean's criterion. And finally, we can get the Jean's mass and the Jean's length So the conditions for cloud collapse are Mc>MJ or Rc>RJ. Example 1 A typical diffuse cloud has T=50 K, n=5x10108/m3 which, if entirely composed of H, is ro=nHmH=8.4x10-20kg/m3. Then m=1 too. mH=1.67x10-27kg, G=6.67x10-11, k=1.38x10-23. What then is the Jean's mass? Example 1 A typical diffuse cloud has T=50 K, n=5x10108/m3 which, if entirely composed of H, is ro=nHmH=8.4x10-20kg/m3. Then m=1 too. mH=1.67x10-27kg, G=6.67x10-11, k=1.38x10-23. What then is the Jean's mass? The pressure from the large star on the left has caused the four stars on the right to condense from their proto-cloud.