Nemesis to WZ Sagittae

by Joe Patterson


August 23, 2001

No, not the weather. That too, maybe. But now that WZ has faded, it's time to worry more about the nefarious little companion star.

All previous studies have had to do something about the companion, and we do too. If feasible, you could just exclude it from your aperture or psf photometry. In our photoelectric photometry from the 1970s, that's what usually did. The enclosed discussion by Arne Henden gives the relevant numbers which indicate how to do this, and are also a measure of the severity of the problem.


WZ Sge 20:07:36.53 +17:42:15.2 J2000
companion 20:07:35.77 +17:42:17.1 J2000

with typical errors of 100mas. This gives a separation of 10.9 arcsec.

Magnitudes of the companion alone:

(0.03mag total errors except for U-B which has 0.07mag error).

You should not have problems with contamination as long as your aperture is 12 arcsec in diameter or smaller. I'd suggest either using a small aperture or else one large enough to encompass both stars; the inbetween ranges will have some weird results. Remember, however, that the contamination is highly dependent on your passband, worse at red wavelengths or with unfiltered photometry.


Most of us observe unfiltered, which approximates an R passband, implying that full contamination means an extra unwanted R=13.11 star. Looking at the data you've sent, it's pretty easy for me to tell which observers have cleanly excluded or included this star. But in-between cases are hard to identify, and will inevitably give noisy data since the amount of contamination will depend drastically on the instantaneous seeing. Don't mess with Mister Inbetween (Sinatra 1942).

Unless your telescope drive and/or seeing are really bad, I recommend excluding the companion. This is because background from sky and companion will start to overwhelm you beyond about magnitude 13.5 - and the light curves will suffer greatly. We're interested in the detailed light curves on the approach to quiescence. A too-small aperture hurts light curves too, but you'll be able to study those problems, gain experience, and maybe even fix them... whereas a too-large aperture just swamps everything in the ocean of Poisson noise.

In any case, send me a note describing how you've extracted your delta-magnitudes so far, and whether you can do OK with a box that excludes the companion. Our emphasis is time-series, so this is not the most critical issue for us... but now's the time to report the details, and find the right strategy for WZ Sge's fainter days ahead.

Thanks, Arne, for your measurements, and for improving our attention to this issue!

................. joe

Lew's Method to Remove Nemesis

Doing photometry sometimes requires we measure two stars at once when we want data on only one of them. If star A and star B are too close to resolve or to exclude from our aperture photometry circles, we measure both. When we convert the measurements to magnitudes, we have a result which gives a magnitude too small (too bright) by the amount of the contaminating star's light. To get the magnitude of the star of interest, we must convert the observed magnitude to light units, subtract the light from star B from the total light and convert the remaining light units - representing the contribution of star A - back into a magnitude (because we usually - but not always - deal with mangitudes). We realize that our removal of the light of star B willbe done as a mathematical constant, and the noise from the star B and star A will still remain and will be magnified on the magnitude scale.

Here's how we do it:

We have stars A and B that we measure, but B is a close companion to A and we can't separate it from A with our photometry system. So we measure both stars at the same time. Now we've got to do something to remove that extra light that compromises our results.

The total light (L.t) from 2 stars measured simultaneously is given by

L.t = L.a + L.b

where L.a and L.b are the light (in light units) from star A and star B, respectively.

The magnitude of the star A (mag.a) as measured in aperture photometry is too bright (too small) due to the contamination from B.

We need a good value for star B - alone - related to either our comparison star (if we are using differential photometry or) in absolute terms, and it needs to be a valid magnitude in our photometric system. We add the comparison star's magnitude to the differential magnitudes forming an (instrumental) all sky magnitude (mag.t) for the variable plus the companion.

Next we convert the measured magnitudes to light units using the formula

l.t = (2.51189)^(-1*mag.t)

The carat (^) means "raised to the power of".

Then subtract the light units for the contaminating star from our measurements of both stars:

l.b = (2.51189)^(-1*mag.b) (always constant for this star)


l.a = l.t - l.b

and we convert back to a magnitude:

mag.a = -2.5*log(l.a)

And that's all there is to it.

Here's a spreadsheet to remove the contamination from one constant star included in the photometry diaphragm when you are after the magnitude of another star.

Download nemesis.xls

One note of caution: the nemesis star must always be fainter than the star of interest, else you end up trying to take the logarithm of a negative number. This is a subject best explored in astrology rather than astronomy.

It will do 1001 measurements. If you want more, unprotect the sheet (instructions given on the sheet) and Copy & paste the formulae into more rows. You can't simply copy and paste the values you get into another spreadsheet - they must be copied and "paste special - Values" into the destination spreadsheet. You can do that in the plotting spreadsheet


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