Reading - Chapter 4 pp75-95
What was the size of the cloud that collapsed? We know that the total mass of the cloud had to be at least the mass of the current solar system - basically the Sun. The process of making solar systems is a messy business - and we do not understand all the steps. Let's assume that the efficiency is about 1 % (yes, this is a fuzzy number - but lots of material escapes out of the poles of the Sun (that's how it looses angular momentum, remember) and a large amount just does not make it into the planets and Sun - it is kicked out or blown away - or just fails to make it for one reason or another).
So, let's take Mcloud ~ 1032 kg. Now, think about the criterion for collapse - that the gravitational potential energy is greater than twice the thermal energy (see Class 5 notes and page 81 of the book). If you then look at the figure on page 80, you can see that, if we take an estimate of the temperature of the initial cloud (say, 10 K - probably more realistic than 1000K) - then we can take this Mcloud ~ 1032 kg on the left of the plot, go across to the 10K line and go down to an estimate of the density of gas needed to make the cloud collapse. We find that the cloud needs to be denser than about 10-18 kg/ m3 in order for the cloud to collapse.
Now we have the mass of the cloud and the density of the cloud.
For T~ 10 K this is R~(1032/4 x 10-18)1/3 ~ 3 x 1016 meters. Dividing by 1 AU = 160 million km = 1.5x1011meters, we get R ~ 200,000 AU.
[Someone asked in class how many light years this is - 1 LY = 60x60x24x365 x 3 x 108 =9 x 1015 meters = 65,000 AU - so the cloud would be about 3 LY in radius - comparable to the nearest star]
For T~ 1000 K this is R~(1032/4 x 10-12)1/3 ~ 3 x 1014 meters. Dividing by 1 AU = 160 million km = 1.5x1011meters, we get R ~ 2000 AU (confirming our suspicion that 1000 K is probably too high - the cloud would be no bigger than the current Oort cloud).
How long did the cloud take to collapse? Again, we can try to make a simple estimate - the cloud starts off with gravitational potential energy and this is converted into kinetic energy as it collapses (true, some of this energy is lost as heat, radiation, friction - but we get an order of magnitude estimate this way).
THAT's JUST 1-2 Million years!!! A tiny time compared with the 4.6 Billion years age of the solar system.
NOTE - this time for collapse does not depend on the size of the cloud - just its density.
Alternatively, one could make a similarly crude estimate by saying the gravitational acceleration of the cloud is g = GM/R2. Then we say that the distance traveled while under constant acceleration is S = 1/2 a t2 and the time to fall Rcloud under the cloud's own gravitational acceleration is then
t ~ (2 Rcloud3/GM)1/2 ~ (6/4Gpr)1/2 - basically the same formula as above (just 6/4 instead of 3/8).
Disk formation - conservation of angular momentum, collisions -> disk - it is collisions, not gravity, that causes the cloud to form a disk as it collapses - just as in making galaxies and ring systems.
Multiple systems - see Figure 4-4 - greater initial angular momentum -> multiple system.
How did the Sun loose angular momentum? Polar Jet - Image of polar jet - planetary disk is at the bottomPolar jets - explanation - de-spinning of the star/Sun - diagram - and Figure 4-11
What about double/multiple systems? What's the difference between double star systems and a star-Jupiter system?
E.g. here is the latest table of extra-solar planets -
Failed stars / successful planets - see Figure 4-8 - and figure from Class 1.
The Astronomer's Periodic Table - cosmic composition. Where do these elements come from? They are the products of recycling stars - large stars going through a super-nova and then recycling as new stars.
Cosmic abundance table - It is usually assumed as the initial composition of the solar nebula. Where did this come from? This cosmic abundance table comes from spectroscopic studies of molecular clouds and of stars AND spectroscopic studies of the Sun - See Table 4-1. Notice the difference in Table 4-1 between cosmic abundance (actually, the composition of the sun - see caption) and the GAS part of the clouds. The difference is the material locked up in dust grains - notice the 3rd column of the table has large numbers next to metals and silicon - the building blocks of rock.
Here is a spectrum of interstellar dust - showing molecular species. A spectrum from the Orion nebula looks like soot. The list of 2-, 3-...7-atom molecules detected in molecular clouds is huge - many are organic molecules. Here is another list of the Composition of molecular clouds. Most exciting are the Polycyclic-Aromatic-Hydrocarbons PAHs which suggest pre-biotic chemistry - the building blocks of life. PAHs are a major focus of astrobiology studies - as laboratory and orion spectra of PAHs are compared.
Did a supernova trigger the collapse of the molecular cloud that made out solar system? What is the evidence? Could these isotopes be made other ways? Latest Chandra results from a star-forming region in Orion say yes - in solar flares.
Also:
UC Berkeley page - for scientists
