The Sloppy Science of Astronomy
This is a little bit technical but here goes.
The above picture shows some data points we have on the shape of an astronomical object. The x-axis is distance from an arbitrary zero and the y-axis is how bright it is at that distance. You can see that it is brightest at around -10 and gets less bright as you move away to either side. The line that traces out the bell curve shape is a “best fit” line, which is the bell curve that minimizes how far away the data points are from it. A bell curve shape like this is called different things by different types of science geeks but it is generally know as a Gaussian, named after Gauss, who did a lot or work with it. It is more commonly called the normal distribution. So by “fitting” a Gaussian to these data points, we can turn them into a concise mathematical function. The assumption here, of course, is that this function closely approximates the actual shape of the object.
The question I’m trying to answer is: how far away is this object from my zero point. To answer that question you need to decide what you mean by that -- how far away is what from the zero point? The obvious answer to that question is: the center. If I can assume the shape is roughly a bell curve and then fit a bell curve to the data, I can then trivially find the center of that bell curve mathematically.
Anyway, I was doing all of this with R, which is a statistical software package. I had used it to fit polynomials to data (polynomials are just equations like f(x) = 2x2 + 3x). The equation for a Gaussian is quite a bit more complex:
I was having trouble getting R to do what I wanted so I asked the R-help email list, which is populated mainly with (obviously enough) statistics people. Apparently physicists and statisticians do not speak at all the same language. They thought I was trying to solve a statistics problem and they thought my data was horrendous. They also kind of politely assumed I was an idiot. The data in the picture above was collected with the Hubble Space Telescope (HST) using the STIS spectrograph. It is a faint object that is about 0.00006 degrees across. It is also 0.00006 degrees away from a super massive, ridiculously bright star. It is hard to measure. Really hard. For something like this we are lucky if we get data at all. The fact that we can pretty reliably figure out the center of that little blob and then watch it move over time, giving us its speed and its age, is truly amazing. It is sloppy and uncertain but still systematic and repeatable. It’s science, baby. Physical science. It might seem a bit ugly to people used to pure math and statistics but, to me, the ugliness just comes with the territory when you are pushing the envelope. Astronomy is always pushing the envelope.
Tuesday, August 29, 2006
