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We've got a hot star in the middle of a gas cloud. We point a spectrometer at the star, calculating the following attributes of our line of sight at the star through the cloud:

  • Total number of various elements and molecules (H, H2, C, O, N, CO, lots of ions of all of the above) along the line of sight (units are number/cm^2)
  • Average temperature of the atoms in our line of sight
  • Average radial velocity of the atoms in our line of sight

All the radial velocities are roughly the same, so we infer that the line of sight is more or less a single coherent blob of gas. Good!

Now, the star itself which illuminated the line of sight is moving about 40 km/s towards us, while the gas cloud chunk we observed is moving at around 20 km/s away. Also, from comparing the luminosity of the star to the temperature of the gas, we conclude that the gas cloud is a light year or two away from the star.

Given all this information, here is your task: If we take another spectrum of the same line of sight ten years from now, will it be the same blob of gas?

I will tell you right away that the radial velocity will only make the gas 0.002LY closer to the star, which is way less than what we need. So, in other words, given all the above, can you conclude anything about the transverse velocity of the cloud? Can you tell anything about the bulk flow and determine whether it is probable that the gas in our line of sight has moved with respect to the star?

My physical intuition says that you'd expect yes, since the radial velocities are so different, but I'm not totally sure - the radial velocity doesn't necessarily imply anything about the transverse velocity. Or does it?

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If you are going to look at one star only, you will have to make some assumptions about the cloud structure if you want to link signal variation to the transverse motion. – gigacyan Jan 29 '11 at 15:38
@gigacyan Right. What are those assumptions? – kharybdis Jan 29 '11 at 18:45
I'm not a specialist but there are people who model such gas clouds and maybe they could attribute your gas cloud to a particular type based on its chemical composition. – gigacyan Jan 29 '11 at 20:09
First of all:What is the difference between composition and the "Total number of various elements"? And then I completely do not understand the question. "I'm looking at the sun and see a cloud in between. Would it be the same cloud if I look at the sun after half an hour?" – Kostya Jan 31 '11 at 15:57
@Kostya Yes, those are redundant - edited to correct. As for the second question - that's the gist of it, but it's not as trivial as you would like to think. The cloud and the star are both moving. If they are moving with the same velocity, we're looking at the same patch of cloud. Even if they aren't, it's important to know how different the velocities are. Knowing this, we can estimate how far apart the two measurements are in space, not just in time; this turns out to be very important for understanding other properties of the cloud. – kharybdis Jan 31 '11 at 17:07

1 Answer

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The radial velocity can not give us any information about transverse velocity directly. But it provides a clue that the star and gas bulk are not belonging to the same dynamical system. So they are unlikely to keep still to each other on the projected 2-D plane. If the comparative transverse movement is at the same level of radial velocity, 60km/s for example, after 10 years the gas bulk will move $60 / 3E+5 * 10 = 0.018 ly$, which is 20 times larger than the Pluto's orbit (0.00085 ly at most). It is a small scale for a gas bulk. But it can be big enough for elements' column density to change (due to elements distribution and projection effect). You could observe slight shape changes of some absorption lines. But as mentioned by gigacyan, with only one star it is really hard to get the direction and velocity of transverse movement. If you make some assumption, like taking the bulk as a sphere, then you can explore something.

What's more, both star and gas bulk are not isolated in the space, there are velocity limitations due to their position in the Galaxy, on the disk, in the bulge or halo etc. You can give some reasonable estimates base on these.

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Good answer. You say they are unlikely to stay close w/r/t each other on the 2-D projected plane. Is it possible to even estimate how unlikely, though? Usually, you would want to do this sort of thing by calculating the expected value of the velocity by integrating over some distribution of velocities. Is there any distribution that would be approximately valid for this purpose, maybe? – kharybdis Jan 31 '11 at 18:11
Second comment - why would you say that the transverse motion is the same as the radial velocity? – kharybdis Jan 31 '11 at 18:15
The velocity example is only to get a feeling of possible scale. Don't take it seriously. As for the distribution of comparative transverse velocity, of course we can estimate the possibility of the velocity less than certain value for two independent objects. But this case may be simplified by their position, take a typical value of nearby object maybe a good approximation. – gerry Jan 31 '11 at 19:56

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