Questions about Apparent magnitude

[Stingray21]

For my science experiment at school I am researching whether light pollution affects the number of stars that are visible exponentially or linearly. To test my hypothesis (I think that the effect is exponential) measured the apparent magnitude of the sky in diffrent areas and then took a picture of M45 to see how the number of stars within its boundary changed. 

The number did not change a lot (from 11 stars to 7 stars). I came up with a new hypothesis, that only stars of a magnitude lower (brighter stars) than that of the sky glow would be visible.

I proceeded to test this by looking at the stars that were not longer visible as the sky glow magnitude increase and comparing their apparent magnitude to that of the light pollution. 

The results confused me because even though these stars were very dim (magnitude 8 or 9 stars) they were still visible when the apparent magnitude of the sky was around a 5.

Could anyone explain why this is.

* The light pollution was measured using an iphone app called dark sky meter and the apparent magnitude of the stars was taken from the stellarium program. I took pictures with a camera of 300 mm focal length, a crop factor of 2 and an exposure time of 1 second

[Tiny Small]

This is to do with magnitude and surface brightness. Andromeda has a magnitude of 3.44 but as it is spread over a large area (150,000 light years) its surface brightness is relatively low. If you were to take a star of mag 3.44, it would give off the same amount of light that we see from Andromeda, but as the light emitting surface is much smaller, the light source is more concentrated and so appears brighter. This means if you have sky glow you would still be able to see lots of things unless their magnitude AND surface brightness combined made them equal to or dimmer than the sky glow.

I don't know how old you are or at what level of maths you have, but remember that a linear sequence is a mixture of a geometric AND arithmetic sequence and therefore generally creates vastly different results to an exponential sequence. You could probably model this on a linear relation given enough data.

[jambouk]

This sounds like a fascinating project; good luck with it.

I'm not very bright (probably magnitude 19 on the IQ scale), but my three thoughts on this are:

- is the app measuring in exactly the same units as the star catalogue data for "magnitude"; like saying, "the oven is hot at 180" (which is the same as saying "it's hot at 356", just that the two units of "temperature" are different). Is there a way to check the calibration of the app against the established and fixed magnitude scale?

- is the project about visible stars using ones eyes, or using a dslr sensor, as the sensor will be more sensitive once you get past a second or two exposure.

- look at the definition of the magnitude scale of star brightness closely once you work out which stars are visible and which are not.

But do report back on how you solve the issues and your results. Fascinating.

James

[dph1nm]

The results confused me because even though these stars were very dim (magnitude 8 or 9 stars) they were still visible when the apparent magnitude of the sky was around a 5.

I suspect the sky app gives the limiting visible magnitude. If you start taking photographs then this will (a) be fainter and ( depend on your exposure time.

NigelM

[itmo]

Since you are talking about the number of stars visible, your result will vary also on the magnitude distribution of the stars. So if you only look at a certain part of the sky, you might get funny results. So you will have to see how the pollution affects the visibility of stars of different magnitudes, then correct the result for the "whole sky". So what you need is a histogram of all stars' magnitudes. So what you are assuming now , is that the magnitude distribution is pretty linear and that M45 is representative of the whole visible star population?