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Gaia, Simbad and Ballesteros' Formula

Astrometry Astrophotography
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#1 BQ Octantis

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Posted 25 February 2024 - 09:43 AM

I'm down another color-matching rabbit hole—this one for reference star correlated color temperatures. I've been using Ballesteros' formula for CCT(B-V) for a couple of years now, thinking it was an accurate way to get star CCTs. Only this week did I first dig into the Gaia database of star spectra, now armed with the Colour-Science spectrum-to-XYZ and XYZ-to-CCT,∆uv functions.

 

And the result ain't pretty.

 

Now I'm not one to defend D65. But that's my image chain—the whole hog, calibrated from the rooter to the tooter. But ok, fine, the Universe is E, or something around 5500K. And everybody loves D50 (I guess because one day, they'll actually print their images for display indoors during the daytime). So I'll concede there are other white point options (although we can arm wrestle later about how to correctly display those on a D65 monitor).

 

And yet…the spectral outputs for D65 and E are nowhere near Ballesteros' output. Indeed, the closest white point that approximates his formula is 9100K:

 

(Click for full size)

comparison.png

 

Zhai and Luo in 2018 found that the native background white point for self-luminous colors is on the order of 9100K…so maybe Ballesteros was onto something?

 

Anyway, if 9100K is the right white point, then there's very little advantage to downloading each star's Gaia spectrum, interpolating to 1nm, sorting it, formatting it into Pythonese, and then running it through XYZ_to_CCT_Ohno2013(sd_to_XYZ). The CCTs from Ballesteros' formula applied to the B-V from Simbad is extremely close, and is two inputs into a spreadsheet:

 

comparison2.png

 

End of rant.

 

BQ

 



#2 yuzameh

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Posted 25 February 2024 - 11:10 AM

When you say GAIA spectra, do you mean the actual GAIA spectra and not the derived BP and RP?

 

Even so, have you read up on the full nature of the spectra?

 

They are relatively wide dispersion, quite wide, and very low resolution, not much better than the average amateur kit.

 

Also the brighter stuff in the catalogue may be ground based as bright stars are usually too bright for it (hence few having an accurate Gmag).

 

The red stuff starts about Halpha so most of it isn't optical, and the full stuff used for Gmag starts beyond blue and ends in the near infrared (somewhere in the Ic band range) so don't equate to optical.  The blue stuff goes roughly optical, a little too blue to just past Halpha (the blue and red stuff overlap so even if people are playing with fluxes derived from the spectral continua that's to be thought of).

 

The radial velocity stuff is now used for the GRVS mag which is certainly in the near infrared and quite a narrow range of wavelengths.

 

In the end for any of these "transformations" being clever with spectral continua summations or even different filter bandpasses and deriving relations that way are very clever but inherently so much juggling of maths with software.

 

What is really needed to equate filter bandpasses is to plot the things against each other.  You find yourself a primary source of Johnson B and V and possibly Rc (Cousins R, probably B and V will suffice, and if you can't find B AND V many sources of V and B-V exist so you can get B) standard or secondary standard magnitudes.  You cross correlate those to the GAIA catalogue (try CDS XMATCH service, websearch) on about an arcsec or two astrometric matching, then you simply plot things against things on a graph.  You can check the linearity of the plot (eg GAIA BP versus B and even V), derive a relation (no need to go mad, quadratic is often overkill, linear gradient with intercept will suffice).  Then you take your Johnson V or B mag or pick eg the GAIA BP mag and use that relation to derive the other values.  Then you take the difference, the residuals, of the observed (catalogue mag) and the calculated (derived) magnitude for the passband of interest and get the residuals.  For example Johnson B(standard) minus Johnson B(derived from BP).

 

Then you have a look at the scatter, derive the standard deviation, mean and median to see if the first is small enough to feel good, and the second and third are sufficiently near zero to suggest no real systematic offsets.

 

Then you plot the residual values as a function of B-V (or BP-RP) to see if there are colour dependencies of the transformation.

 

You can also plot the derived Johnson B against B-V to look for colour dependencies to the transformation (does it 'bend' or get broader at the red end, for example).

 

You should also plot the derived magnitude against the observed magnitude to see if there is a magnitude dependency as the faint end not only usually broadens out (increases spread) but often has a bias in one direction, a well known threshold effect (you will likely not be going to either the Johnson photometry source catalogue nor the GAIA catalogue limit so you may be spared this.

 

To see an example of threshold effects look up Malmquist Bias (it is an astronomical topic).  Or think of the quantum vacuum versions.  The former is covered well enough in wikipedia, the latter is of the ilk that at a threshold level of measurement based on energy you can get over representation at the limit, such as virtual pairs of electrons and positrons at the quantum vacuum limit where a pair instead of rejoining and turning back to gamma rays somehow the energy is found (interaction with real matter or magnetic field or electric field etc) to make one of the particles real, and these appear as a surplus on top of the nonvirtual (real) particles.  The Malmquist Bias will be a better read than my lame explanation.

 

Remember also that the GAIA system derives Teff from a very complex somewhat assumption laden model, which gets changed every data release.

 

Also, and most important, all data releases of GAIA so far have been optimised for FGK stars.  It says that in all the paper work.  For A and M stars completely different relations will likely be used as opposed to extrapolations of the FGK model and the non-continuum lines will differ markedly (albeit early F has some A type spectra characteristics at the Balmer end).

 

But check data against data not just from physics first principles and juggling formulae based thereon.

 

EDIT finally found this, I can never remember what to call it so websearch is tricky https://vizier.cds.u...?-source=II/374

 

That can also be used via CDS xmatch, just enter II/374/table2 as the source and upload a table of targets (with ra and dec first two rows) or choose one of the many VizieR photometric catalogues.  Possibly of more interest to yourself though may be the paper behind it.  For that you'll need to go to arxiv.org and search on the title of the catalogue (same as the paper title).  It was written and published in a technical venue, not an astronomy periodical.


Edited by yuzameh, 25 February 2024 - 11:17 AM.


#3 BQ Octantis

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Posted 25 February 2024 - 12:16 PM

Thanks for the quick and thorough reply, yuzameh! smile.gif

 

I have used the VizieR catalog many times in the past; however, its data is in very finite clumps, and very seldom does it have measurements for the southern hemisphere stars that comprise the majority of my data.

 

I was under the assumption that the Gaia data was simply prism-on-a-CCD. And Gaia is the new standard for stellar spectrophotometry, so my assumption was that it was good enough for this kind of work. But reading up on it, you're right: its operation and calibration seems quite complex:

 

https://www.aanda.or...aa41249-21.html

 

Regardless, the DR3 "XP mean sampled spectrum" data is 2nm-spaced flux measurements of the spectrum sampled from 336nm to 1020nm with the error included per sample. Even without futzing with the error, the Gaia-derived B-V values compare extremely well with the Simbad values (and the Simbad database is quite complete):

 

B-V.png

 

For me, that gives reasonable confidence in the consistency of the Gaia data with prior observations. However, the spectral distribution to (CCT, ∆uv) calculations via standard color matching methods cast serious doubts on Ballesteros' formula…


Edited by BQ Octantis, 25 February 2024 - 12:38 PM.


#4 BQ Octantis

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Posted 25 February 2024 - 01:14 PM

Hmmm…I have no idea how to read the Gaia DR3 data out of VizieR.

 

For instance, take the star HD 65152 a.k.a. Gaia DR3 5290926575075526784.

 

Simbad says

 

B = 9.07

V = 7.20

 

So B-V = 1.87. But there is nothing in the VizieR entry that correlates with any of those values.

 

However, downloading the spectrum from the Gaia DR3 archive (which looks well-behaved), summing the flux B (400 to 500nm), summing the flux V (500 to 700nm) and taking -5 times the log base 100 of the ratio gives me a B-V of 2.01. Those are well in the ballpark of each other—and fall within the category of "red" M-class star.

 

Of course, the bigger error is in the blue stars…

 

BQ



#5 BQ Octantis

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Posted 25 February 2024 - 01:39 PM

It looks like a lot of the Simbad data might have come from the Tycho catalog derived from the Hipparcos mission. It didn't even have Johnson B, V filters, but instead B_Tycho, V_Tycho. And B-V = 0.85*(BT-VT). crazy.gif

 

Amateur kit, indeed.


Edited by BQ Octantis, 25 February 2024 - 01:39 PM.


#6 BQ Octantis

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Posted 28 February 2024 - 06:14 PM

Turns out, B-V is somewhat arbitrary. The transmission shapes are pretty specific—and they're included in the AstroPy Speclite add-on:

 

BV.png

 

But as the RTFM states, "these do not represent the response of any actual instrument. Response values are normalized to have a maximum of one in each band."

 

And that's important, because every Johnson/Cousins UBVRI filter set has a different Vpeak/Bpeak. No matter—because Vega was chosen as the B-V=0 point by definition—which puts the sun at 0.656 relative to (B-V)Vega=0. The cool thing about it is that regardless of what filter brand you use, the B-V curve for your collection of star measurements will just be off from the reference stars by a constant, which you can easily calibrate out before adding newly studied stars to your Hertzprung-Russell Diagram (remember, this was the '50's on photographic plates).

 

The Vpeak/Bpeak that gives (B-V)Vega=0 is 1.864. However, B-V is not just some arbitrary number—it is literally -5*log100(B/V), where B and V are flux integrals. In order for that value to match the D65 CCT (which is the only one that will correctly display the colors on your D65 screen), the Vpeak/Bpeak must be set to 1.34. On the other hand, B-V as defined will work if Vega at 9600K is defined as white instead of its actual blue.

 

Not that any of you are using this method to match your star colors. Just thought you might find this interesting.

 

BQ


Edited by BQ Octantis, 28 February 2024 - 07:02 PM.



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