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Limiting magnitude

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spp
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Limiting magnitude

In the Photometry Report there is an option to report a target as fainter than the limiting magnitude of the image.  How does VPhot calculate the limiting magnitude of an image?  What is the SNR of a source that determines the limiting magnitude?

Phil

MZK
MZK's picture
Limiting Mag

Hi Phil:

SNR=10 is the value that is used to define the limiting magnitude. (Yields error about 0.1/10%).

If you want to use something else, you would need to report what is calculated without this checkbox or edit report by hand.

Ken

spp
spp's picture
Limiting Mag

Thanks, Ken.  There was a post on a different forum about calculating limiting magnitude, so the VPhot fainter-than option came to mind. 

Arne gave a really interesting presentation on this subject at the 2017 SAS meetings (How Faint Can You Go?).  Perhaps you were there.  I think the figures he used for limiting magnitude were SNR=5 for the whole image, but if you had the specific position to look for a source then SNR=3 could be considered a detection.

He was speaking about the detection of a source rather than a SNR below which any attempt at measurement would be  pointless.  As a measurable limit SNR=10 seems about right.

 Phil

MZK
MZK's picture
Final Choice?

Phil:

The final SNR choice was subjective. I prevailed in this specific discussion, and error was given more emphasis.  

IF you can confirm the identification of the target (!?) and REALLY want to report a value without much thought to the error, other criteria may be considered.

In VPhot, it is quite simple to leave the box unchecked, but one should understand how uncertain the magnitude is?

Ken

spp
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"limiting magnitude"

Ken,

I think using a SNR=10 cutoff is a good idea.  I’d be hard put to come up with a situation in which I would attempt a magnitude estimate for a star that faint.  My only question is using “limiting magnitude” for this in the Photometry Report.

Here’s a copy and paste from Arne’s paper on this subject presented at the 2017 joint AAVSO\SAS meeting:

“2.1   A Theoretical Definition

There are basically two types of limiting magnitude. First, if you are just trying to find the faintest object on a frame, most researchers define the faintest object to be one that is 5 standard deviations (5σ) above the sky background; or roughly equivalently, that has a signal-to-noise ratio (SNR or S/N) of 5. This may seem conservative to you, as it means (assuming a normal population) that the probability of the detection being real is 99.99994%. However, the assumption is that you have not properly accounted for everything, and there will be small, non-real, fluctuations in your background.

You can use a less-stringent requirement if you have additional information about the possible object. For example, if you know the position of a real object, most researchers will relax the requirement to 3σ, or SNR=3, as the probability of a small non-real fluctuation happening right at the known position is smaller.”

Later in the paper (Section 4) Arne discusses ways to estimate the magnitudes of these very faint sources.

Since there is already a (perhaps informal) consensus for the meaning of this term, I think using “limiting magnitude” in the Photometry Report to indicate something else (You shouldn't report magnitudes for stars fainter than this magnitude) could be misleading.  Some might reasonably think this means there is no detectable source fainter than the stated magnitude.  I suggest just leaving out the term “limiting magnitude”:  

“report the target as fainter than the limiting magnitude of 14.091”  would become,  “report the target as fainter than 14.091”, and leave it at that.

The SAS posts their symposium Proceedings, as well as videos of the presentations, in the public domain.  I’ve attached a PDF of the 2017 Proceedings.  Arne’s paper, How Faint Can You Go?,  starts on page 75.

I recommend this paper even to those who think this discussion is much ado about very little.

Phil  

MZK
MZK's picture
Changing Words!

Phil:

Changing the wording is a good idea. Even I can change such code in VPhot!  

Ken

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