The size of a modest star forming molecular cloud, like the Taurus region, is about 30 pc. The size of a typical star is, to an order of magnitude, the size of the Sun.
(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 difference in scale? For example, if the cloud is the size of a human, then a star is the size of what?
(b) Within the Taurus complex there is roughly 3ˆ104M* 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 difference is this? Consider the difference between lead (ρlead =11.34 g cm ́3) and air (ρair =0.0013 g cm ́3). This is four orders of magnitude, which is a huge difference!
(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 difference in scale? For example, if the cloud is the size of a human, then a star is the size of what?
(b) Within the Taurus complex there is roughly 3ˆ104M* 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 difference is this? Consider the difference between lead (ρlead =11.34 g cm ́3) and air (ρair =0.0013 g cm ́3). This is four orders of magnitude, which is a huge difference!
Okay, so let's try to make a comparison as to the size of star forming molecular cloud and an average star.
To do so, we will use a proportion.
\[\frac{d_{star}}{d_{cloud}}=\frac{d_{human}}{d_{?}}\]
\[d_{?}=\frac{d_{human} d_{cloud}}{d_{star}}\]
So the radius of the cloud is 30 pc. A parsec is a unit of distance that corresponds to the distance away an observer must be such that 1 AU (the distance between the Earth and Sun) is angularly 1 arcsecond or about 0.004 degrees. 1 parsec is about 3.26 lightyears, or \(3\times 10^{18}cm\). A human is roughly 100 cm in diameter if we were to curl up into a ball. The sun's diameter is \(1.4\times 10^{11} cm\).
\[d_{?}=\frac{(1\times 10^2 cm)(1.4\times 10^{11}cm)}{9\times 10^{19}cm}=1.6\times 10^{-7}cm\approx \boxed{2nm}\]
So, how big is 2nm exactly? This fantastic website can help: http://htwins.net/scale2/
This site lets us explore all sorts of length scales, from the size of the universe down to the planck length. I encourage you to play with it.
Based off of this site, if a star forming cloud was the size of a human, a star would be the size of a single glucose sugar molecule.
Alternatively, if a star forming cloud was the size of a football field, a star would be the size of a single HIV virus.
Still not comprehendible? Let's keep trying. We are looking for things with a difference in scale of about 10,000,000x.
So, if a star forming cloud was the size of Texas, a star would be the size of a baseball.
Let's do this again for density of the cloud.
\[\rho_{cloud}=\frac{M}{V}=\frac{3\times 10^4M_*}{\frac{4}{3}\pi r^3}=\frac{3\times 10^4 \times 2\times 10^{33}g}{\frac{4}{3}\pi (5\times 10^{19}cm)^3}=\boxed{1\times 10^{-22}\frac{g}{cm^3}}\]
For the sun we get:
\[\rho_{star}=\frac{M}{V}=\frac{M_*}{\frac{4}{3}\pi r^3}=\frac{2\times 10^{33}g}{\frac{4}{3}\pi (7\times 10^{10}cm)^3}=\boxed{1.4\frac{g}{cm^3}}\]
This shows that a star is 10,000,000,000,000,000,000,000 times more dense than a star forming cloud.
This problem done in collaboration with G. Grell and S. Morrison.
For the sun we get:
\[\rho_{star}=\frac{M}{V}=\frac{M_*}{\frac{4}{3}\pi r^3}=\frac{2\times 10^{33}g}{\frac{4}{3}\pi (7\times 10^{10}cm)^3}=\boxed{1.4\frac{g}{cm^3}}\]
This shows that a star is 10,000,000,000,000,000,000,000 times more dense than a star forming cloud.
This problem done in collaboration with G. Grell and S. Morrison.
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