# Instrumental Magnitude

One of the things that has puzzled me about one of the VPHOT functions is its reporting of instrumental magnitude of the target star. It always reports it as some negative number. For the current star I am observing, its instrumental magnitude is reported as - 6.667. Now if I take that number literally, it would imply that the VPHOT interprets the data from CCD camera on the SRO telescope of the AAVSOnet to mean that this star is about four orders of magnitude brighter than Venus. Which is obviously wrong....

So anyone have any idea how to interpret VPHOT's instrumental magnitude number correctly? I'd like to do some work with the photometric transforms for various filters on this scope, but I have no idea what (lower case) b, v, r, i, values I should be using in the various transform equations.

In order to distinguish between the names of the standard filters, standard magnitudes (i.e. magnitudes in the UBVRI system) and the instrumental magnitudes, i.e. the magnitudes measured from your images, we use the following convention:

filters are designated by upper case :U, B, V, R, I

standard magnitudes are designated by upper case italics: *U, B, V, R, I*

instrumental magnitudes are designated by lower case italics: *u, b, v, r, i*

Instrumental magnitudes are computed from the intensity of the star which is measured by your CCD as electrons. Pogson defines the instrumental difference in magnitude of the target star and the comparison star as:

m_{target} – m_{comparison }= -2.5 log(F_{target}/F_{comparison}),

where F is the flux of the object. This merely tells you the difference in the magnitudes. It can be a negative number. I would recommend __Astronomical Photometry __ by Arne Henden and Ron Kaitchuck . I hope this helps.

Robin (RROA)

There is nothing wrong with the reported instrumental magnitude. It is not a catalog magnitude as you expect. Instrumental magnitude is required by the AAVSO extended format when you have one target and one comp.

On the AAVSO web page do a search on instrumental magnitude (top left). See Matt Templeton's good data, good science.... link for a start on understanding. It has other links too.

VPHOT, like all photometry routines, measures the flux of the various targets, ie, the ADU count inside the aperture (maybe adjusted to electron count based on the camera gain value). Magnitudes are 2.5*log(ratio of two fluxes). The number reported as instrumental magnitude depends upon what flux the programmer chooses to be the "zero point." I'm guessing (don't really know) that Geir uses the value for the zero point as 1. Hence, any flux greater than one is going to "appear" to be much brighter than a zero magnitude star, ie, with a negative instrumental value.

He does the same thing to the comp star. To get the difference in magnitude between the target star and the comp star he simply subtracts one from the other. Knowing the difference (v_{c}-v) and the catalog value of the comp (Vc), he reports the value of the target as V = Vc -(v_{c }-v).

Note that if the instrumental value of the comp star goes up and down over, say, a time series, the difference (v_{c } - v) doesn't change (much, usually). The changing instrumental value would indicate changes in the sky (eg, passing light clouds).

To add to the mystery, when you ask VPHOT to produce the AAVSO format, it does list what would be considered "normal values" for the comp and check stars (e.g. 10.167), not the negative values shown for the instrumental magnitudes. So as you say, it depends on how Geir chose the zero point to do the various calculations.

This has alredy been explained well enough, but just for the records VPHOT calculate instrumental magnitude as

v = -2.5*log(F/t)

where F is the flux or intensity of the star and t the exposure time (so yes it is time corrected).

Instrumental magnitudes are on an arbitrary scale, and does not give much meaning before they are compared to other instr.mags. That is what you do in VPHOT, you compare the brightness of a target star with that of comp stars with known magnitude, so VPHOT does **differential** photometry.

Geir

Obviously VPHOT does differential photometry. But this discussion seems to have wandered from my original question. For a photometric transform equation:

V - R = T(vr) (v-r),

Where V = standard V magnitude, R = standard R magnitude

T(vr) = photometric transform coefficient for V&R (for the SRO50 scope)

v = instrumental V magnitude

r = instrumental R magnitude

Can the instrumental magnitude from VPHOT for an observation with a V filter (v), and the instrumental magnitude from VPHOT for an observation with a R filter (r) be used in this equation to produce a reliable result for observation with the SRO50 scope? In essence, if I know V for a star and T(vr) for SRO50, use v and r from VPHOT for SRO50 observations, can I produce a reasonably good R, using this equation?

The reason for my original question is that in other photometric analysis packages I own, the instrumental magnitudes are positive values, and usually close to the standard comp star magnitudes, while in VPHOT, the instrumental magnitudes are large negative values.

In essence, if I know V for a star and T(vr) for SRO50, use v and r from VPHOT for SRO50 observations, can I produce a reasonably good R, using this equation?

Yes.

As I mentioned yesterday, the transform coefficients for SRO are missing in VPHOT. Get Arne to provide that info and you can move forward on this. (Actually, all AAVSONet scopes appear to lack transform coefficients in VPHOT. Not good.)

The reason for my original question is that in other photometric analysis packages I own, the instrumental magnitudes are positive values, and usually close to the standard comp star magnitudes, while in VPHOT, the instrumental magnitudes are large negative values.

This is a function of zero point. In VPHOT you can not set/alter zero point...so the instrumental magnitudes can appear very strange when taken out of context. Your personal software, you can probably alter zero point so that instrumental magnitudes are 'close' to transformed magnitudes. This can be a helpful sanity check, if you use it that way. But don't be confused or fooled by the 'strange' values for instrumental magnitudes in VPHOT. Instead, look for signs of bad data/image quality: flat field problems, saturated/non-linear stars, focus, tracking, etc...and then look at transformed results (once Arne provides coefficients).

PS. I'll mention one more technique: 'pseudo transformed magnitudes'...when you only have data/images from one filter. You need the transform coefficient for that filter (R, for example) and associated color index (V-R). You need to know the R mags and V-R color index values for your comp stars (that is getting easier in the post-APASS world)...and you need to either know, or assume a V-R color index for your target star. (If it's a well-studied type of star...then this should not be a problem.) You can do this sort of 'transform' at home, and VPHOT can also perform this single-filter correction.

HJZ wrote:

"But this discussion seems to have wandered from my original question. "

The answer is encoded in my comment. I hit save before I fully explained the code. Sorry.

VPHOT reports V = Vc -(vc - v) where Vc is the catalog value for the comp star, vc is the instrumental value for the comp star and v is the instrumental value for the variable. You know Vc and vc is given to you (along with V) so you can get v = V - Vc + vc. If vc is negative, more than likely v will also be negative, but no matter. The same applies to getting r.

As Tom mentions, instrumental values are just that - they are just 2.5 log (flux), where typically "flux" for software packages is in ADU and so is several steps removed from a standard magnitude. IRAF, for example, has an adjustable zeropoint so that your resultant instrumental magnitudes look more realistic (or at least, always positive). The main point is to not change any applied zeropoint between frames, if you intend to use those frames in a combined manner for determining standard magnitudes.

Regarding AAVSOnet transformation coefficients: I have been careful to report on the AAVSOnet discussion all determined coefficients for all telescopes. I don't personally enter those numbers into VPHOT; someone else has to do that, and I think they were all set prior to the problems a few months ago that required things to be reloaded.

That said, what I derive for the telescopes are the traditional coefficients: those for V and those for the various color indices. I don't derive Tr, Ti, etc. If you have 4 filters (BVRI), what is normally calculated is:

Tv as a function of (B-V)

Tbv

Tvr

Tri

Tvi

since those coefficients are necessary for just about any other calculation, and by themselves form a complete set sufficient to determine the usual colors and all of the magnitudes. The problem arises when you want to determine individual magnitudes, like Rc or Ic. I typically do so by

Rc = V - (V-Rc)

but it could also be determined by

Rc = rc + zeropoint + Tr * (V-Rc)

(ignoring extinction). But it could also be determined by

Rc = rc + zeropoint + Tr * (V-Ic)

or

Rc - rc + zeropoint + Tr * (B-Ic)

etc., where each of those "Tr" coefficients is different from one another. The entire suite of such coefficients is quite large. One person may just be doing Rc/Ic imaging, while another might be doing V/Ic imaging for example. So I don't know a good solution to the problem right now, as determining coefficients is a human-required process to do it right, and adding more coefficients to the mix means someone has to manually derive those coefficients on multiple nights.

The exception to this is APASS (and other professional surveys, such as SDSS), where they derive magnitudes as the primary product and not color indices. For those, however, each object is carefully measured in each filter and so you can define a minimal set of coefficients rather than the general situation.

Arne

I don't personally enter those numbers into VPHOT; someone else has to do that, and I think they were all set prior to the problems a few months ago that required things to be reloaded.

If nobody else will do it, then I'll offer my services.

I don't derive Tr, Ti, etc.

The entire suite of such coefficients is quite large. One person may just be doing Rc/Ic imaging, while another might be doing V/Ic imaging for example. So I don't know a good solution to the problem right now, as determining coefficients is a human-required process to do it right, and adding more coefficients to the mix means someone has to manually derive those coefficients on multiple nights.

If you send me your tables of transformed magnitudes and catalog magnitudes/color indices, I'll extract all the various Tx coefficients, etc. and get that added to the telescope profiles in VPHOT.

Instrumental magnitude is typically normalized to time (i.e. flux value is divided by exposure time).

This means that instrumental magnitude should remain constant for a given comp star, no matter what exposure value you use.

Not sure if VPHOT uses instrumental magnitude that way? Take a short and long exposure of a star field and look at the instrumental magnitude values for the same star.

The AAVSONet SRO telescope....should have transform coeff's determined for it. Here's an example of an old post to that effect:

http://www.aavso.org/sro50-transformation-coefficients

But I see in VPHOT that there are no transform coefficients loaded into the telescope profiles for AAVSONet scopes. That's bad.

We need to tell Arne to fix this ASAP.