Zero Point Calibrations

Hi Grant,

You want to precisely zeropoint multi-night observations of the same star, or do this with many different stars on different nights?  Those are two separate problems.  Also, what kind of accuracy do you need for this calibration?  Are you using one filter, or multifilter with transformation?

Arne

"You want to precisely zeropoint multi-night observations of the same star, or do this with many different stars on different nights?"

Sorry, I didn't clarify. I have many nights of observation for a single star. I need to do a calibration amoungst these.

 "what kind of accuracy do you need for this calibration?"

The endgoal is to calculate six decimal accuracy of the period of a Cepheid. So essentially there isn't a specific accuracy needed for the calibration, but as the accuracy of the period relies partially on the accuracy of the calibration, I just need to do this as accurately as possible while staying within a reasonable difficulty level if possible.

"Are you using one filter, or multifilter with transformation?"

I'm not sure what this means, I don't have a lot of experience with this kind of thing. Could you clarify this for me?

Thank you very much for the response!

Hi Grant,

I don't know your background, so please excuse me if I state something well-known.  What you are describing is called "differential photometry", available in almost every software package such as VPHOT (from the AAVSO home page).  It uses a known constant star (and its known magnitude) as a reference star, with which the target star is compared.  If you do aperture photometry and obtain the "instrumental magnitude" (whatever magnitude your software produces) for both the target and the constant (or comparison) star, you obtain

Vtarget = (Vtarget_instrumental - Vcomp_instrumental) + Vcomp_standard

If the comparison star is constant, then (Vtarget_instrumental - Vcomp_instrumental) shows any variation of the target object and is immune to night-to-night sky or equipment changes.  Performing this differenced magnitude+zeropoint_offset (the Vcomp_standard) works over multiple nights.

There are two embellishments to this technique.  First, perhaps the assumed constancy of the comparison star is wrong.  You can additionally perform the same analysis using a "check star" instead of your target.  That gives

Vcheck = (Vcheck_instrumental - Vcomp_instrumental) + Vcomp_standard

and you can look at Vcheck and see if it varies.  If the check star varies in the same manner as the target star, then this check star tells you that the comp star is variable.  Second, you can expand the differential photometry technique to multiple comp stars, each one providing a target star magnitude which you can average together to obtain a more robust estimate.  This technique is called "ensemble photometry".

Both of these approaches can be found in the "CCD Photometry Guide" underneath the Observing tab on the AAVSO home page.  Read that guide, and then ask any additional questions you might have.

As for 6-digit accuracy on Cepheid periods, that can be accomplished in two ways (assuming that the period is constant over long time intervals).  You can either get exquisite photometry over a few pulsational cycles, and with a very good model of the light curve shape, obtain a fit to the period; or you can obtain times of maximum over many cycles, and even though the accuracy for any given cycle may be relatively poor, the long time interval and many cycles of monitoring work to improve the period estimation.  The "exquisite photometry" method relies on an accurate model for the light curve, because, unlike eclpsing binaries, there is no sharp feature on the light curve that can be precisely measured.  Most period-determining techniques were developed for eclipsing binaries, and rely on the symmetry of the dip.

I started work on Cepheids as an undergraduate, because a subclass (the double-mode Cepheids) had both interesting light curves as well as a theoretical explanation that gave clues as to the star's structure.  I'm glad that you are interested in Cepheids as well!

I hope that I read your question correctly!

Arne

Hi Arne,

Thank you very much for such a detailed response! I think this was exactly what I needed. I really appreciate you taking the time to explain all of this. 

Thanks again!

Grant

I'm doing what I'd call 'broadband' differential photometry.  That is, unfiltered.  In truth, of course, it is filtered because I'm using the frequency response of my CCD camera as a filter.  I'm sort of being forced to do broadband because all I have (at the moment) are RGB filters which I don't consider scientifically valid.  I'm using an SBIG ST7-ME on a Celestron Nexstar 8se.  I've collected images of the open cluster NGC 7243 which gives me a nice selection of stars at many different magnitudes.

In order to determine whether my magnitude measurements are accurate and precise, I'm wanting to compare these measurements to a known and trusted standard.  I've chosen the GAIA DR2 'G Broadband Filter' magnitudes as that standard because these most closely match my broadband system.

To do the comparison correctly, however, it does seem as though I need to do a transform between my system and GAIA, as I see a linear relationship between my instrumental magnitude differences and GAIA magnitude differences.  As you can see in the attached plot, I've plotted these differences (GAIA vs Mine) and done a LSF to the data to get the linear equation you see.

I've been carefully reading the AAVSO CCD Photometry Guide (thank you, BTW, for making this available!!!) and I see in Chapter 6 the procedure for doing transformations.  The problem I'm having is that in my particular case, I'm not measuring colors -- so I'm not quite sure how to properly do the transformation.  Or, more specifically, I'm not sure what I'm doing is correct.

What I'm doing is simply taking my magnitude differences (I've chosen 10 stars, with one used as the reference), plugging them into this equation, and coming up with results that do indeed very closely match the GAIA magnitude differences (some 10's of milli-magnitudes -- pretty nice!).  Naturally I'm going to get closely matching results, but how I'm doing it doesn't quite go (as far as I can tell) with the procedure laid out in the Guide.

So I have some questions.  Is what I'm doing correct?  Do I need to take into account stellar color, and if so, how to do that when I'm not necessarily measuring color?

First-time post.  Very glad to be here.  I've been aware of AAVSO for decades but have never gotten involved.  Would like to start contributing if possible, but I need to be convinced that my measurements are as accurate and precise as possible.

Cheers!

You're asking a good question.  There are two ways one might answer it.

First, one might ask "Is there some significant color term in my observations, relative to Gaia?"  You can answer this question without making any additional observations.  All you need is some measurements of the colors of the stars you are using as references.  You can use Gaia measurements of their colors, or colors from some other catalog.  Simply make a graph which shows the colors of the stars on the x-axis, and the difference (Gaia mag - my mag) on the vertical axis.  If you see random scatter as a function of stellar color, then your system and Gaia's system of "broadband" magnitudes are similar.  That would be nice.

But if you see a clear trend in the graph -- say, red stars are consistently fainter in your measurements than in the Gala catalog -- then your system's response has some systematic difference from Gaia's system.

How can you correct your measurements so that they are close to Gaia's at all colors?  Ah, that's more difficult.  For this, you _do_ need to make more measurements.  It's okay to use those RGB filters you mentioned, if you don't want to buy others.  Use your system to measure, say, R and G for each star; then compute your own (R-G) color. 

Now, again, make a graph.  This time, put your own (R-G) color on the x-axis, and the difference (Gaia G - your G) on the y-axis.  Measure the slope of the relationship in this diagram. You can use it to correct your "G" magnitudes so that they are close to the Gaia "G" magnitudes. 

If you have the time, give it a try.  See how well you can correct your own measurements.

Phil asked about using the tricolor green filter.  Its main bandpass is similar to Johnson V, and so in theory can be used, with transformation, to create V magnitudes.  The devil is in the details as always.  The foremost problem is that most tricolor green filters have a substantial red leak.  This means that measurements of red stars will be compromised.  You can experiment with this by just measuring a bright red variable, like R Leo.  The differential photometry will show a magnitude that is much brighter than others on the same date, if the filter has a red leak.  This can be eliminated to a large degree by adding an IR blocker to the optical path.  This is one reason why one-shot-color cameras often have an entrance window that serves as an IR blocker.

The best method to see if your green filter can be transformed is by imaging a standard cluster and doing the TG process.  Note, however, that the result can only be valid over the color range in the cluster.  For bluer or redder stars, you never know if the results are the same.

As for Gaia G magnitude results:  I don't recommend transforming onto the Gaia magnitude system.  It is nonstandard, and researchers will have difficulty comparing your results vs. TESS or Kepler or ground-based photometry like ASAS.  Transform to Johnson/Cousins or to Sloan.  As you mention, you need two filters to do this properly, so unfiltered systems are hard to transform.  They are great for some projects, such as determining eclipsing star or superhump periods.

I do have a few Johnson V filters that were restored by John Menke, so if you want to try imaging with a true Johnson filter, just let me know and I'll send one to you.  Welcome to the variable-star community!

Arne

Thanks you everyone for your very kind and useful help!  My apologies to the IP for sorta taking over this thread.

I understand that to properly submit data to AAVSO, I'll have to collect data either using a standard filter set, or at least take data with the filters I have and transform them to a standard.  That is, of course, my intention.  In fact I'll be going beyond that and actually dive into the database to do my own scientific analysis.  Data collection, for me, is only step #1.  But of course is has to the right.

But what I'm doing now is mearly evaluating the performance of my system.  I want / need to know how accurate and precise the system is to determine whether going to the next step and getting a proper filter set and then collecting the data will be worth it.  So with the equipment that I've got, I need to be able to compare apples to apples, which is why I decided that comparing my measurements to GAIA was the best path.  I couldn't find any other surveys that had magnitudes measured across the entire visible band.

So instead what I'm looking for right now is whether or not you folks think how I'm doing the comparison is valid.  I've found a very linear relationship between my magnitude differences and the GAIA magnitude differences for the same stars, which tells me that a transformation is possible.  See my first post above for details.

Arne -- for sure I'll take you up on your very generous offer, if I can!  I have an SBIG CFW-8A filter wheel that uses 1.25-inch "thread in" filters.  Not quite sure what kind of thread it actually has.  TBH I've never gotten into the filter wheel to look.

Cheers and thanks again!

- MC