a) If you let the size of your body represent the size of the star forming complex, how big would the
forming stars be? Can you come up with an analogy that would help a layperson understand
this di fference in scale? For example, if the cloud is the size of a human, then a star is the size
of what?
Our first step was to draw a big formless shape on the board, representing a molecular cloud with a radius of 30 parsecs. We then converted that into centimeters so that we could more easily compare it to the size of the sun.
We found that the Taurus region is about $10^9$ times as large as our Sun.
If we take this down to a human size scale, assuming the average sphere-shaped (because everything's a sphere) has a radius of about 1 m, the typical star would have a radius of $1\times 10^{-9}$ m, or 1 nanometer.
To give a point of reference, this is a close-up image of a human hair
which has a width of of about 10 micrometers. This means that, if I were a star forming molecular cloud, the average star formed from my gases would be smaller than $\frac{1}{1000}$ of a single hair.
b) Within the Taurus complex there is roughly $3\times 10^4 M_\odot$ of gas. To order of magnitude, what is the average density of the region? What is the average density of a typical star (use the Sun as a model)? How many orders of magnitude diff erence is this? Consider the di fference between lead and air.
The average density of the region can be found using
$\rho=\frac{M}{V}=\frac{M}{\frac{4}{3}\pi r^3}$
Just by plug-and-chugging provided values into the above equation, we find that the average density of the Taurus region is $1.5\times 10^{-23}$ grams per cm cubed.
We plugged in the sun's values to find the average density of the sun, which we found to be $5\times 10^{-1}$ grams per cm cubed.
This means that the sun is $10^{22}$ times as dense as the Taurus region. This ratio is a lot bigger than the ratio of the densities of lead and air, which are of the same order of magnitude.
Nice work - I especially like the "star formed from my gases" sentence...
ReplyDeleteJokes aside - something's off with your average density of the Sun, it should be more along the lines of 1.4 g per cm cubed. Fortunately it doesn't really affect your answer though. A molecular cloud is actually less dense than the best man-made vacuums on Earth - cool, right?