[Aavso-photometry] Differential vs. absolute magnitudes

[Jim Roe]

gianlucaros at gmail.com wrote:
> I still have some confusion about differential vs. absolute
> magnitudes. If I have understood properly transformation coefficients
> improves the accuracy of the measurements and zero point is necessary
> only for all sky photometry.

Let's see if I can put it differently to help you understand. 
Estimating star brightnesses (magnitudes) is all about comparisons.  In 
particular, certain standard stars have been measured by careful study 
and it is to these that we reference our own measurements.

But what we measure is "flux" (let's stick to CCDs for this discussion) 
which is in terms of ADUs which, in turn are, related to the electrons 
generated by the incoming photons and, which is related to the 
brightness of the star and length of the exposure (among other things). 
  Let's say we measure for a given star 100 flux units.  Then we turn 
our telescope and camera to, say, Vega and for the same exposure time we 
get 10,000 flux units.  Wouldn't you think it safe to say Vega is 100 
times brighter than our candidate star, or vice versa, our candidate 
star is 100 times fainter than Vega?  To convert this to magnitudes we 
would take 2.5*log(FluxofVega/FluxofCandidate) and get that our 
candidate star is 5 magnitudes fainter than Vega.  So what is the 
apparent magnitude of our candidate star?  It turns out that Vega has 
been *defined* to be magnitude zero - rather arbitrary but there it is. 
  So we would say our candidate star is magnitude 5.

But it ain't quite that simple.  Chiefly, our atmosphere does funny 
things to the starlight as it passes through it on the way to your 
telescope, camera, and detector.  To keep everybody on a level playing 
field, we want to know what the apparent brightness *above* our 
atmosphere is and that requires taking making adjustments for the 
different sky conditions that relate to the two different measurements. 
  It's complicated but can be done and we are fortunate that the pros 
(like Arne) do this and create "secondary standards" all around the sky 
that we can use.

So, if you can get one or more of these well-measured stars in your 
field of view with your variable, you can measure the two fluxes, 
calculate the magnitude difference between the variable and the 
reference star and be able to state with some confidence that the 
variable is Mag(reference) +/- (Mag difference) (depending on whether 
the variable is dimmer or brighter than the reference, of course). 
Because the two flux measurements were taken at the same time and with 
very little difference in the atmospheric conditions, we can safely 
assume that whatever affects the one affects the other identically and 
cancels out - it works beautifully in practice.

Now, you can report just the difference magnitudes that you get and, IF 
you report what the reference star was, anyone who wants to look up the 
magnitude of the reference star can figure out how bright the variable 
was when you measured it.  Just report your data as DIF magnitudes.  On 
the other hand, if you are a nice guy/gal, you can just add the known 
value for the reference star to your difference measurement and save 
folks that extra trouble.  Report these as ABS.

It was mentioned in another post that some folks (CBAT?) are only 
interested in changes in brightness and are happy with the difference 
values.  Check with them to see what is best.

The foregoing was greatly simplified (but is essentially correct, I 
believe).  There is a lot of stuff going on that your software usually 
take care of for you.  But the matter of color transformations (which is 
also complicated) needs a bit of a further look.

When I said you can get lucky with AAVSO charts in particular in that 
they have well-measured reference stars on them that you can use for you 
comparisons, I didn't mention the complication of how they got their 
estimate and how it affects you.  I will do so now.  The essence of this 
discussion is that you will want to have your measurements comparable to 
others - it's really no fun being an individualistic lone-wolf and doing 
your own thing in photometry.  This is a team sport! :-)

Arne and all the other pros who create the photometry for our reference 
stars use filters that pass different colors of light.  Most of the 
folks who submit data that you will be cooperating with also use these 
filters.  You can't hope to get comparable data if you don't use filters 
too.  Even if you buy filters with the same specifications used by Arne 
and others, you won't get identical results because it is not possible 
to make identical filters batch after batch - and the same goes for your 
detector chip.  It is *essential* that you use filters that have the 
same specs as everyone else and many folks just report the results they 
get this way - and it's usually pretty close.

But the Gold Standard is to figure out just how your filter results 
differ from the standard and to include these adjustments when you 
report your data.  The adjustments are usually small but can be quite 
significant and will allow your data to be melded with data from other 
observers who have transformed their data as well.

So, take your data with standard filters, get reference stars in the 
same field of view as your variable (calibrate your images with darks 
and flats to make the background uniform), measure the ratios of the 
variable flux to the reference star(s) flux, compute the magnitude 
difference, add the difference to the reference magnitude, transform the 
measurements if you can and have fun.  (Most of that will be done in 
software.)

Jim Roe [ROE]