Is it this simple?

[Demonperformer]

I have a catalogue that lists star magnitudes as red magnitude (M_R) and blue magnitude (M_B).  Can I get the visual magnitude (M_V) - or at least a good approximation - by simply taking the mean?

Or is there some other calculation I should make?

Thanks.

[ronin]

Would be nice if it was but the only information I can locate that looks like it has no relationship stated:

http://astronomyonline.org/Astrophotography/CMDDiagram.asp

Not sure they are the same as the data you have either.

Would appear to be an astrophotography measurement.

[Demonperformer]

Thanks for the link, Ronin.

Fascinating read, but doesn't really solve my problem.

I am trying to extract data from the USNO B1.0 catalogue for CdC.  CdC requires a visual magnitude (and also has optional fields for red and blue magnitudes).  USNO only gives red and blue magnitudes (two readings of each) so I am trying to find a way of extracting a visual magnitude from that data.

Having had a bit more of a think about it, USNO also gives a TYC reference for stars that are that bright, so I could compare the M_R and M_B values, and the average, with the M_V value given in TYC2 and see if I can find a formula that will link them.

Thanks.

[jambouk]

If white light is made up of all wavelengths of light added together, is it possible to work out a white light magnitude if you don't know how much green there is? Or is green such a minor player it can be ignored?

It all sounds very complicated!

Good luck.

James

[Demonperformer]

Well, I was naively thinking that red is at one end of the spectrum and blue at the other, so there would probably be a reasonably even spread of light between them.  Yes, it does seem to be a bit more complicated than that, but in AP you can synthesize a green channel from red and blue, so I'm not sure why (if?) that same principle can't be applied to getting a M_G reading.  To add another issue into the mix, my reading has suggested that the M_V value is based on yellow light!

I will report back when I have done some investigation with the TYC stars.

[jambouk]

Does this help:

http://www.astro.ljmu.ac.uk/courses/phys134/magcol.html

James

[jambouk]

This is my last attempt to help:

http://elvis.rowan.edu/astronomy/observe/lesson14.htm

James

[Demonperformer]

Thank you, James for the links.

Results on the TYC test:

Vt is taken from the TYC catalogue (3 d.p.)

BR is the mean of the two blue and two red magnitudes quoted in USNO B1.0 (2 d.p.)

r is the range (min to max) of the 4 magnitudes quoted in USNO B1.0

D = Vt - BR (difference between estimate from USNO B1.0 and TYC-2)

From a sample of 97 TYC-2 stars:

The range of D: +0.1155 to -0.275 magnitudes

The mean of D: 0.01 magnitudes

The mean of ABS(D): 0.027 magnitudes

The standard deviation of D: 0.051 magnitudes

The standard error of D: 0.225 magnitudes

As one would expect from the above, when I plotted [100*]D against r, the majority of the stars had D<0.05 magnitudes.  For this majority of stars, it seems to show something like a sine-wave.  Why and whether this is at all significant, I don't know.

This would appear to suggest that if I derive a mean magnitude from the four magnitudes quoted in USNO B1.0 to just one d.p. this is likely to be pretty accurate 95% of the time.

Which I guess is reasonable enough for my needs!

[Astrobits]

Look up black body radiation. If the star temperature is very low ( when the peak of it's radiation is at a longer wavelength than that at which the red magnitude is taken ) or very high ( peak beyond the blue ) then it might be possible to estimate the V magnitude by interpolation between the R and B magnitudes. However, if the star is like the Sun then the peak of it's radiation comes between the red and blue magnitudes and will be higher than either. The V magnitude in these cases is likely to be nowhere near the simple interpolation between the R and B magnitudes.

Nigel

[Demonperformer]

I see what you are saying, Nigel, and it does seem to make sense.

However, my initial test did not seem to bear this out, so I have tried a larger, more random sample:

I used a random number generator to select 24 integers from 0 to 1799 (UNB zones [i/284]). They were in turn allocated to a 1 hour segment (0h-1h, 1h-2h, etc). For each zone-hour combination, a list was made of all the stars quoted as being in TYC-2 [i/259], the number of stars for each combination is listed below.

hh     zone     #
---     ------    ---
  0    1680    27
  1      932    39
  2      436    20
  3    1616    38
  4    1449    38
  5    1018    97
  6    1783      0
  7      137    18
  8    1649    23
  9      769    77

10    1100    27
11    1161    29
12    1578    17
13      512    65
14    1780      0
15    1393    32
16      543    67    
17    1353    56    
18      264    42    
19    1508    74    
20        84    10    
21      968    66    
22    1792      0    
23      764    34    

Total # stars    896

Of these 896, three were not found in the TYC catalogue:
TYC 3738-01256-1 (UNB 1449-0139123)
TYC 4496-02593-1 (UNB 1680-0002150)
TYC 9472-00193-2 (UNB 0084-0091257)

For the remaining 893 stars:
the mean of Vt-BR was 0.003 magnitudes,
the standard deviation was 0.030 magnitudes
the standard error was 0.174 magnitudes

How many stars were how accurate?
837 (93.7%) were within 0.1 magnitudes
788 (88.2%) were within 0.05 magnitudes
615 (68.9%) were within 0.025 magnitudes
364 (40.8%) were within 0.01 magnitudes

  9 (1.0%) showed a difference of >0.2 magnitudes
  2 (0.2%) showed a difference of >1.0 magnitudes

Attachments:

Chart2.jpg shows 100*D plotted against r for the entire data set
Chart3.jpg is the same with the 9 stars for which D>0.2 removed

results.txt is a full list of the data used
 

I don't have the knowledge to attempt to explain the above, but when over 2/3 of the sample produced results within 0.025 magnitudes of the figure quoted in TYC, and over 93% were within 0.1 magnitudes, it seems to me this can be used to provide a reasonable approximation.

The only thing that strikes me as exceptional about the data set is that, because I am limited by the nature of the test to TYC stars, this precludes the inclusion of any really faint (17-21 mag) stars.  But is there any reason why this should skew the results?  I don't know.

results.txt

[Astrobits]

Hmmmmm...

Nigel