| MadSci Network: Astronomy |
First, a bit of history. Magnitudes are a system of measuring the brightness of astronomical objects that dates back to the ancient Greek astronomer Hipparchus. He assigned the brightest stars to be first magnitude, the next brightest to be second, and so forth, down to sixth magnitude, which is about the faintest that the human eye can see.
Radio astronomy is a much younger branch of astronomy, having only been around since the 1930s. The brightness of objects that emit radio light was described originally by using (the rather unimaginative term) flux units. In the 1970s, astronomers decided to rename the flux unit as the Jansky, after the first radio astronomer.
In order to compare these, we must be a bit more quantitative. By the 1850s astronomers were able to measure the (visual) brightness of stars well enough that Hipparchus' system was in need of improvement. In doing so, it was discovered that the human eye is a rather peculiar measuring device. It works on a logarithmic scale. What this means is that a sixth magnitude star is 100 times fainter than a first magnitude star.
By this time, however, the magnitude system had been in use for nearly 2000 years. Changing 2000 years of practice is extremely difficult, so the following formula was suggested to relate the magnitude system and the actual brightness of an object:
m = 2.5*log(F0/F)where
F is the brightness of an object or the amount of energy
we are receiving from it, F0 is a zero point, and
log(.) is the logarithm function. A star that emits an amount
of energy equal to F0 will have a magnitude of 0. (If
F0 = F, then F0/F = 1. The logarithm of 1 is
log(1) = 0, so such a star will have a magnitude of 0.) It
was also decided that the star Vega would be defined to have a magnitude of
0.00. In the V (visual) band, F0 = 3.2 x 10-9
Watts per square meter. (A full listing of various visual and infrared
observing bands and their zero points is given in the
Handbook of
Space Astronomy and Astrophysics.)
(One effect of choosing Vega as the zero point is that some stars are brighter than first magnitude. For instance, Sirius has a magnitude of about -1.5.)
In contrast, radio astronomy uses a linear scale. Thus an object that has a brightness of 10 Janskys (Jy) is 10 times as bright as an object with a brightness of 1 Jy.
Let's compare the "brightnesses" of objects in radio and visual light. I put "brightness" in quotes because we are comparing the amount of energy from different objects. In visual light, we typically see stars or the combined light of stars from a galaxy. In radio light, we typically see the light from free, high-speed electrons spiraling around a magnetic field in a galaxy's core. Nonetheless, let's compare the brightness of the faintest objects we can detect.
The faintest objects ever seen in the V band were in the Hubble Deep Field. These objects were distant galaxies of about 30th magnitude (or about 10 billion times fainter than the faintest object your eye can see in a dark sky!) Using our formula above, we receive an amount of energy about equal to 3.2 x 10-21 Watts per square meter from these distant galaxies. The faintest radio objects detected (of which I'm aware) have a brightness of about 10 microJanskys or about 5 x 10-24 Watts per square meter or about 1000 times fainter than the faintest object in the V band.
Alternately, we can ask the question of how faint would the Hubble Space Telescope (or some similar telescope) have to reach to equal the faintest objects seen by radio telescopes. Again, using our value of 10 microJanskys and the formula above, we find a V magnitude of about 37. That is, an object with a V magnitude of 37 has about the same brightness as an object with a brightness of 10 microJanskys.
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