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Spherical Cows

When scientists refer to a spherical cow, we are poking fun at ourselves. We are admitting that some of our models or descriptions of things are far more simple than the actual object, like to say that a cow has a spherical shape. The phenomena we study are often complex, and including too many details can hinder, rather than help our understanding. Often it is useful to study a simplified model which contains only the most important general characteristics. Such a model can be more easily studied using numerical or analytical methods and then compared to observations.

As an example of this kind of thinking, say we were aliens trying to understand "humans", a strange race of beings recently discovered on a small planet orbiting a medium-sized star. We might divide them into two groups, one which grows facial hair (men), one which does not (women). Within each group there is a lot of variety - each human in the first group group can have facial hair in a wide range of colors and textures, for example. However, we think that there is some underlying reason for the gross characteristic of having or not having facial hair. We might then make more observations to try and understand why this is so. These further observations might uncover more similarities (humans in the first group have both an X and a Y chromosome while humans in the second group have two X shaped chromosomes) that are more fundamental. In astronomy we try to do the same thing.

Often what we do is look at a limited number of characteristics, trying to understand each to put into our picture of the whole. Almost any astrophysical object is too complicated to try and understand everything at once. It makes more sense to look at only a few characteristics at one time and to try and understand how each one affects how the object appears or evolves.

"Flavors" of SNR - Different Viewpoints

Supernova Remnants (SNR) are one such complex astrophysical object. You can say that SNRs come in many different flavors, depending on who you talk to. Each flavor or "ideal" SNR isolates important features, giving scientists a piece of the puzzle in helping to figure out the entire SNR picture.

First there is the theorist's SNR, which is something of a spherical cow. In this model, a couple of thousand years after the star blew up in a supernova explosion, the ejected material has swept up a considerable amount of the ambient gas, leaving behind a big, hot hole. There is a little bit of gas inside the hole and that gas emits some thermal X-ray light. There is a lot more gas on the edges (because the swept-up gas was swept to the edge of the hole). This gas is also very hot and should emit thermal X-ray light.

Ambient Interstellar Medium drawing

Cartoon Model of a SNR

"Sounds reasonable, so where does the spherical cow business come in", you ask. The answer is that we often pretend that the SNR has a spherical shape, in spite of the fact that most of them are a bit out-of-round. We also pretend that all SNRs should look the same even though they don't. But, we do this for some good reasons -- we want to learn about what happens to SNRs in general as they mature and what SNRs as a whole class will do to the galaxy. Concentrating on their common features helps us to do that. Also, simplifying their shapes makes it easier for us to perform the mathematical computations that we do.

Another flavor of SNR is the observer's SNR. The observer generally has many pictures of the SNR, each taken with a different observing instrument, such as X-ray, radio, and even visible light detectors. Generally the SNR looks different "in each of these different wavelengths", just like you and I look different to another human being (who looks at the visible light) then we do to a bee or a snake (who are able to detect ultraviolet and infrared light, respectively). Also, even when using the same observing instrument, each SNR looks different from all of the other SNRs and often observers try to figure out what is causing the differences.

Scientists are indeed guilty of calling cows (or SNR) spherical. But there is good reason to do so. It is important to understand not only what makes a cow more or less spherical as well as to understand what it is that makes a cow, well, a cow.


Thank you to Robin Shelton for contributing to this article.

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Imagine the Universe! is a service of the High Energy Astrophysics Science Archive Research Center (HEASARC), Dr. Alan Smale (Director), within the Astrophysics Science Division (ASD) at NASA's Goddard Space Flight Center.

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This page last updated: Thursday, 11-Jan-2007 16:41:19 EST