Experiments in photometry

[VictordeHolland]

If you get a Rsquared of >0.5 in a social/economics model you would be dancing all day .

Guess mode ON:
Do the residuals vs. fitted look different if you exclude double/multiple stars and/or variable stars?
Do the stars with high residuals have anything in common? Place in the sky, maybe a frame with a slightly longer exposure? Aliens sending laser signals?

[xilman]

Originally Posted by VictordeHolland

If you get a Rsquared of >0.5 in a social/economics model you would be dancing all day .

Guess mode ON:
Do the residuals vs. fitted look different if you exclude double/multiple stars and/or variable stars?
Do the stars with high residuals have anything in common? Place in the sky, maybe a frame with a slightly longer exposure?

It's not easy to remove variables and/or doubles from the catalogue data. However your question about properties in common led me to do something I should have done long before: plot the estimated magnitudes against the catalogued magnitudes. The plot is attached. One thing that is obvious, and I sort of knew before hand, is that the data with very large residues are almost always the very faintest and the densely packed linearly aligned data corresponds to V<14 or thereabouts. This agrees with examination of the images: stars fainter than 14th magnitude are barely distinguishable from noise.

Next phase is to crop the data at V=14 and remove a few obvious outliers such as the one at V=4, M=13. The purpose of this exercise, remember, is to find a usable relationship between M and V so that the brightness of variable stars and uncatalogued objects can be measured as accurately as possible.

[fivemack]

I'm really pleased how tight a fit you're getting on the magnitude 8 to 10 stars ... these results look pretty decent given the kind of casual kit and murky skies that I'm giving you to work with.

Would it make sense to plot 'M from the best frame' against 'M from the second-best frame' to get some idea of the intrinsic noise in the data?

[xilman]

Originally Posted by VictordeHolland

Do the stars with high residuals have anything in common? Place in the sky, maybe a frame with a slightly longer exposure?

The image on which photometry was performed is a stack of several images. One was of much shorter exposure than the others but it was, of course, co-added with appropriate weight.

Place on sky may have a bearing though I've not examined in detail and my gut feeling is that it is rather doubtful. The attached JPG shows a contrast enhanced
image of the entire frame and the matched NOMAD-1 catalogued stars marked in red. The latter is a 4x4 degree patch centred on RA 3h 52m, Dec +26. The curious RA figure perhaps makes more sense if expressed as 58 degrees.

As can be seen the region is mostly clear of any edge effects but does overlap with the reflection nebulae. Whether that is significant remains to be seen.

[VictordeHolland]

Originally Posted by xilman

The attached JPG shows a contrast enhanced
image of the entire frame and the matched NOMAD-1 catalogued stars marked in red. The latter is a 4x4 degree patch centred on RA 3h 52m, Dec +26. The curious RA figure perhaps makes more sense if expressed as 58 degrees.

Ecliptic Longtitude/Latitude (J2000)
+58^o 00' 00"
+26^o 00' 00"
that would be near the constellation Perseus?

Or RA/Dec (J2000)
Right Ascension +3h 52m 00s
Declination +26^o 00' 00"
Which is near the Pleiades (which would make more sense as you're talking about nebulae) ?

Looks like you're getting a good fit if you exclude objects V>14. Higher than that there is probably just too much noise. V=14 is already very dim! The apparent magnitude scale is logarithmic with 1 magnitude higher ⁵Root(100) ~2.5 times dimmer. So you're detecting objects which are a 1000 times fainter than can be seem by the naked eye on a clear night (V=6)!

[xilman]

Originally Posted by VictordeHolland

Or RA/Dec (J2000)
Right Ascension +3h 52m 00s
Declination +26^o 00' 00"
Which is near the Pleiades (which would make more sense as you're talking about nebulae) ?

My use of the phrase "RA 3h 52m, Dec +26" is a bit of a give away...


Anyway, you mean you don't instantly recognize the Pleiades in the images I posted?

[VictordeHolland]

Originally Posted by xilman

My use of the phrase "RA 3h 52m, Dec +26" is a bit of a give away...


Anyway, you mean you don't instantly recognize the Pleiades in the images I posted?

RA/Dec is what I usually use in Stellarium, but I'm still unsure what you mean with the 58 deg??

You posted pics of the Pleiades before, but I wasn't 100% sure the dataset you're working with now was of the same skies. Now that I look more closely at the NOMAD fitted jpeg, yeah it's obvious .

[xilman]

Originally Posted by VictordeHolland

RA/Dec is what I usually use in Stellarium, but I'm still unsure what you mean with the 58 deg??

You posted pics of the Pleiades before, but I wasn't 100% sure the dataset you're working with now was of the same skies. Now that I look more closely at the NOMAD fitted jpeg, yeah it's obvious .

RA can be measured in degrees as well as hours ...

[xilman]

Originally Posted by xilman

Place on sky may have a bearing though I've not examined in detail and my gut feeling is that it is rather doubtful.

With roughly three times the number of data points the behaviour of the residuals is largely the same, even though 2/3 of the data now comes from other positions.

The larger set now contains not only magnitudes but also x-y positions of the star image centroids, the distance and angle to the nearest catalogue position, an estimage of the sky back ground and a couple of morphological measures of the star images.

I'm now faced with a classification problem and my R skills are not yet up to the task. If you refer back to the residuals vs. observed magnitude (M) plot, there's a linear region with slope close to 1.0. These are the "good" points in that they agree with the naive expectation. There's another region, not quite as well clustered, with a negative slope. The large data set shows the same behaviour but the second region appears to be better correlated.

The classification problem is: how do I determine what measured quantities best model the data in that second region? IOW, how can I exploit both regions of data to make accurate estimates for the magnitude in what appears at first glance to be a largely bimodal distribution?

Apologies if my terminology is unconventional for this field but, as noted earlier, I'm uneducated but trying to alleviate that deficiency. All help gratefully received.

[xilman]

Originally Posted by xilman

I'm now faced with a classification problem and my R skills are not yet up to the task. If you refer back to the residuals vs. observed magnitude (M) plot, there's a linear region with slope close to 1.0. These are the "good" points in that they agree with the naive expectation. There's another region, not quite as well clustered, with a negative slope. The large data set shows the same behaviour but the second region appears to be better correlated.

The classification problem is: how do I determine what measured quantities best model the data in that second region? IOW, how can I exploit both regions of data to make accurate estimates for the magnitude in what appears at first glance to be a largely bimodal distribution?

The two regions corresponded to residuals being positive or negative. I played around with classification algorithms but decided that brute force and ignorance was likely to be a better bet for my purely utilitarian purposes.

First step was to feed in every bit of observational data I could find and use that as a maximal model for M_V and used the mean of the catalogued M_V as the minimal. Then running R's step() function with every possible sub-model produced what it thought was the best model in some sense. Yes, I freely admit I don't know what I'm doing but I don't much care (at the moment, I will eventually) as long as it works.

The best model produced the following residuals plot and the same for the predictions and their standard errors for the original data set. It seems to me that the measurements of Tom's images can be used for half-way decent photometry for visual magnitudes between 6 and 14 or so. That's plenty good enough for me! I'm rather amazed that the faintest magnitude is so faint, given that with eyeball inspection of the image stack it's hard to distinguish 14th mag stars from background noise. I'm even more amazed that this is achievable with images taken from near the centre of a light-polluted city with a ~5cm telescope.

Next step, perhaps, is to analyse the R and B channels (only the camera's G data has been used so far) and see how well the standard BVR magnitudes can be estimated when differential colour data is available.

[xilman]

Just for kicks I searched for a bright, but not too bright, variable star near the Pleiades, one with a range of at least half a magnitude, and SY Tau turned up.

Plugging the measured quantities into the model produced an estimate of M = 10.04 \pm 0.04 on the date in question. Returning to Tom's original data, the latter was 2016-10-26.

The extracted photometry data is:

   PHOT_id   NOMAD.1_id    Mag  Merr   M_B   M_V  M_R      sky  chi2        x        y     r  theta iter class
1 I-008153 1135-0043297 13.238 0.014 10.84 9.617 8.88 12360.86 2.668 3737.947 2786.696 0.095 -1.112    5  TRUE

where M_x are the NOMAD-1 catalogued values, Mag is the DAOPHOT-derived magnitude on a scale with an arbitrary zero point and everything after chi2 is essentially irrelevant.

The AAVSO doesn't (yet?) have any estimate for the date in question but the star is noted as varying between 9.0 and 10.3 by visual observers since the turn of the millenium.