Bruce L. Gary, Hereford Arizona Observatory (G95)
Last updated 2011.06.04

0.05 mag SE, Convert Carlsberg r' and 2MASS JK to B,V,Rc,Ic,i',z' (10 Minutes)

This method will only work for stars between -30 and +50 degrees declination. There are two situations for which this procedure can be used: 1) you don't have an image of the target star field, and 2) you do have an image (or image set) of the target star field. Slightly better results can be obtained using an actual image of the target star and nearby stars, but it entails more work and may not be worth the extra effort for most users. It also involves use of a free program, DS9.exe. (If you don't have DS9.exe installed on your computer, go to the bottom of this page for instructions on doing it; it's a free program.) This procedure is meant for "main sequence" stars (~90%) and star fields that are not highly reddened by interstellar dust. However, for Rc, Ic, i' and z' there shouldn't be a problem for even non-main sequence stars or reddened star fields.

Procedure When You Don't Have An Image of Target Star Field

Browse to the VizieR web site:  

Here's what the (new portal) VizieR web page looks like (after user enters desired catalogs and target star coordinates):

Figure 1. VizieR input page, where user enters desired catalogs and star coordinates.

User first enters "CMC14, 2MASS, LONEOS, Tycho-2" (case doesn't matter) and RA/DE coord's, then clicks Go. This will produce an output that looks like this:

Figure 2. VizieR result page, showing star mag's at the requested RA/DE coordinates. Nothing was found for LONEOS and Tycho-2.

In the CMC14 section the first entry is closest to the target coord's, so this is the row from which we note that r' = 12.498.

In the 2MASS section the first entry is closest to the target coord's, so this is the row from which we note that J = 11.011 ± 0.018 and K = 10.389 ± 0.018.

The LONEOS section can be ignored for now. It's used to assess whether this star is suitable for use with the rJK conversion algorithm (because of the star's spectral energy distribution, SED, departing from normal for main sequence stars). This is treated in a later section of this web page.

Download a small spreadsheet for converting magnitudes from this link: Converting-rJK-to-BVRcIci'z'.zip  
Unzip and run it. Enter mag's and SE's in the input section light blue cells; it will then look like this:

Figure 3. Spreadsheet input (light blue cells) and output results for B, V, Rc, Ic, g', i' and z' (yellow cells).

Note the answers in the yellow cells for B, V, Rc, Ic, g',  i' and z'.

Don't enter an SE for r' because it's calculated automatically by the spreadsheet using the SE(r') relation reported by the CMC14 project:

Figure 4. r' accuracy SE [mmag] versus r' (according to a CMC14 project report).

The spreadsheet calculates most-likely mag's for B, V etc using results of a multiple-regression analysis that I performed using stars calibrated in BVRcIc bands by Landolt (2009) and calibrated in u'g'r'i'z' bands at the USNO by Smith et al (2002). Of the 158 stars in the Smith et al catalog only 94 stars are in common with the Landolt (2009) catalog. My analysis uses 93 of these stars (my bookkeeping lost track of one of them); these are the best fully-calibrated stars in the sky, having Landolt (2009) magnitudes for BVRcIc and Smith et al (2002) magnitudes for u'g'r'i'z'. The J-K colors are within the range -0.2 to +1.2. Each filter band was subjected to an objective and iterative outlier rejection procedure. An outlier for this analysis is defined as a value that departs from a model fit by more than 2.7 × RMSi, where RMSi is the population RMS (including the candidate outlier) for that iteration. When the total number of values ~ 93 this outlier criterion will typically reject a valid datum once per 10 uses. This assumes the set of values consist of two populations: a Gaussian and outliers.

The entire list of 94 stars can be found in a spreadsheet at: 1335 & 94 star This spreadsheet also includes a listing of 1335 stars that have been calibrated by Landolt (1992), Landolt (2009) and Smith et al (2002).

If you don't want to use this spreadsheet you may use the equations and constants shown in the following figures:

Figure 5. Scatter plot of true B magnitude minus equation B magnitude versus J-K star color. Note that 3 B-mag's were "outliers" (3%, due to actual star perculiarities, not measurement errors), being brighter than the rJK equation predicts.

Figure 6. Note that 6 V-mag's were "outliers."

Figure 7. Note that only 2Rc-mag's were "outliers."

Figure 8. Note that 3 Ic-mag's were "outliers."

Figure 9. Note that 5% of g'-mag's were "outliers" (due to actual star perculiarities, not measurement errors).  

Figure 10. Note that 3 i'-mag's were "outliers."  
Figure 11. Note that 5 z'-mag's were "outliers."  

These figures show error scatter for ~ 90 well-calibrated stars after calculating B, V, Rc, Ic, i' and z' (using the equations shown) when good quality r'-band mag's were used (SE < ~0.004, ?). The measured RMS values are 0.059, 0.019, 0.008 and 0.020 mag for B, V, Rc and Ic. These RMS values are the orthogonal sum of errors propogated by r'_SE, J_SE, K_SE and star spectral energy distribution differences (including a small amount of interstellar reddening). I calculate that the last component (star SED differences and reddening) = 0.050, 0.017, 0.007 and 0.019 mag for B, V, Rc and Ic. For a specific target star situation, where we are using a single Carlsberg r' magnitude and J & K magnitudes with specific SE values, we can orthogonally add a Carlsberg r' SE (typically ~ 0.025 ) to the other two sources of SE to arrive at a final SE. This is done in the above spreadsheet. Typical final SE values are 0.068, 0.035, 0.025 and 0.025 mag for for B, V, Rc and Ic. In the next table note how these SE values compare when using the JK-only procedure (as reported by Warner and Harris, 2007), the rJK with CMC14 r' procedure and the rJK with USNO Smith et al 2002 r' procedure.

  Table 1 - Typical Final SE's When Using CMC14 r'

          JK-only    rJK      rJK
                   CMC14 r'  USNO r'

      B    0.080    0.067    0.059
      V    0.050    0.033    0.019
      Rc   0.040    0.022    0.008
      Ic   0.035    0.025    0.020

All bands exhibit significantly improved SEs using the rJK equations compared with the JK-only equations.

More About "Outlier" Stars

The so-called "outlier" stars must have "spectral energy density" (SED) functions that differ from the average. The approximate outlier percentages (for the group of 93 fully-calibrated stars) are given in the following table.

  Table 2 - Typical "Outlier" Incidence

       B   3%
       V   6%
       Rc  2%
       Ic  3%
       g'  5%
       i'  3%
       z'  5%

One star was an ooutlier in every one of the previous 7 figures, and another was an outlier in 6 of the 7 figures. This should serve as a warning about using the rJK conversion equations and expecting the SE accuracies cited above to be correct. To investigate the outlier matter further, consider again the B-band scatter plot (repeated below).

Figure 5 Repeat. Scatter plot of true B magnitude minus equation B magnitude versus J-K star color.

The outlier star with J-K = 0.90  will be used as an example of a "bad star." The star with J-K = 0.91, that agrees with the model, will be used as an example of a "good star" in what follows.

The stated SEs will only be valid if something is explicitly done to guard against the star-of-interest being an outlier star. One precaution is to compare the rJK-derived B-mag with the Tycho-2 based B-band magnitude, and if they differ by more than 0.25 magnitude, for example, the star-of-interest will probably be an outlier. If the star is an outlier on this basis then it should be viewed as a probable outlier for all other bands.

Here's an illustration of how to identify the "bad star" in the above figure (at J-K = 0.90) as an outlier. The rJK-converted B-mag for this star is 13.483, while the Tycho-2 catalog has Bt =  13.663 and Vt = 11.376. Using the conversion equation Tycho-2 based B = Vt + 0.760 * (Bt - Vt), we derive Tycho-2 based B = 13.114. Therefore, B(Tycho-2) - B(rJK) = -0.369, and this confirms the star to be an outlier. These calculations can be performed easily with the rJK spreadsheet, starting with the VizieR input and then the rJK spreadsheet:

Figure 12. VizieR input fgor the "bad star" showing the catalog selection that I recommend for any use of the rJK spreadsheet.

Figure 13. rJK spreadsheet for "bad star" showing a discrepancy of -0.369 mag comparing Tycho-2 based B-mag with the rJK-based B-mag (cell G15).

In this figure both the B- and V-mag values based on Tycho-2 differ from the rJK-based values by large amounts. The "Quality" score (simply a probability function using an assumed FWHM based on the RMS from Fig's 5 and 6) is close to zero, suggesting that the rJK magnitudes not be used because this star is a "SED ooutlier." 

The Tycho-2 catalog is limited to V ~ 11, approximately, so for fainter stars another catalog has to be relied upon for determining if the star is a SED outlier. I've tentatively chosen to use the LONEOS (2003) catalog for this purpose.

To show that the rJK spreadsheet identifies good stars a good, here's the rJK result for the "good star" identified in Fig. 5 at J-K = 0.91.

Figure 14. rJK spreadsheet for "good star" showing only small discrepancies between LONEOS-based B- & V-mags and the rJK-based B- & V-mags (cells G13:G14).

For this star there are no Tycho-2 magnitudes, because it is fainter than the 11th V-mag limit, but LONEOS does have entries for V and B-V.  The Quality score for this star is close to one, so it is not a SED outlier.

Scoring the rJK Algorithm Using Landolt Stars Not Used in Determining rJK Coefficients

The USNO by Smith et al (2002) catalog contains u'g'r'i'z' magnitudes for 158 stars, 94 of which are found in the Landolt (2009) catalog of BVRcIc magnitudes for 598 stars. Let's calculate BVRcIc using the rJK algorithm for some of the 1207 Landolt (2009) stars that weren't included in the USNO SDSS catalog, and therefore weren't included in deriving rJK coefficients. For r' we'll use the CMC14 catalog, as before. This will be a labor-intensive evaluation, so the following table will be updated as my time permits.

Figure 15. Assessment of rJK algorithm using Landolt stars not used for determining conversion coefficients. Magnitude errors columns AF:AL are bold when the magnitude error is less than 2.7 x RMS for the band in question.

An assessment for "SED Outlier" status can be made for only about 1/3 of stars (11 out of 28, so far) because the Tycho-2 and LONEOS cataloges aren't comprehensive enough. When an assessment can be made it is usually correct (11 out of 11, so far).

Finally, here's a result for a faint "flare star."

Figure 15. rJK spreadsheet for a star that's too faint to be included in either the Tycho-2 or LONEOS catalogs but is present in the UCAC3 catalog.

This illustrates the reality for faint stars; they can't be identified as "SED normal" or "SED outliers" based on B-magnitude differences. At least in this case we can assess the target star's suitability for rJK use based on the V-magnitude difference with the UCAC3 catalog's f.mag (an attempt to approximate V-mag). The differenceof 0.129 mag is large compared with the 0.019 mag RMS in Fig. 6, so we should assume that this star could be a SED outlier. If the star really is 0.129 mag brighter in V than the rJK algorithm solution, and if you're desperate for estimating the other magnitudes, try assuming that the departure from rJK increases monotonically in going to shorter wavelength bands starting at r'.  I think it should be safe to adopt the rJK solutions for Rc, Ic, r', i' and z' since they're all within the region covered by r' toK.

If the star were fainter than those in the UCAC3 catalog then all we could say is that the rJK results just have to be viewed as having a ~94% probability of being acceptable, which assumes that the star wasn't identified for evaluation for a reason that could be related to a SED anomaly (e.g., "flare star"). That's when a single image with any of the short wavelength filtes can "come to the rescue." This is treated in the next section.

Procedure When You Do Have An Image of Target Star Field

If you use an image of the target star field it's possible to improve the accuracy of the target star's V, Rc, Ic, i' and z' magnitudes (there's a small improvement for B). These improvements are due to the fact that many nearby stars with CMC14 r'-mag's can be used to establish a set of telescope photometry constants associated with the image. Instead of r' SE being ~ 0.025 mag it is possible to achieve a smaller value for the ensemble of CMC14 stars. Consider the example of using 25 nearby stars with CMC14 r' mag's. The SE on r' for the target star would decrease from 0.025 to ~ 0.005 mag if the system of Carlsberg stars had zero systematic error. This won't be the case, of course, since individual CMC14 stars are uncertain by an amount that's the orthogonal sum of the star field's systematic error and the individual star's measurement by the CMC14 reduction pipeline. Using many CMC14 stars in an image reduces only the individual star SEs, and as the number of stars increaes the underlying systematic error for this star field becomes the dominant component of SE for the average of all stars. If many CMC14 stars in an image are used then maybe the SE for the target star might decrease to an asymptotic value as low as ~ 0.010 mag, for example. The corresponding SEs for B, V, Rc, Ic, i' and z' would then be ~ 0.057, 0.022, 0.012, 0.022, 0.020 and 0.024 mag (assuming typical SEs for J and K).

There's a caveat that should be repeated here. If the target is an "outlier" (not a main sequence star, or if the star field is in a region of the sky with high interstellar reddening) then the conversion equations (from r'JK to BVRcIc) will yield target star magnitudes that are systematically offset from true. This effect will be smallest for Rc, a little larger for Ic and i', larger for V and largest for B.

Here's a brief description f the CMC14. It contains ~ 94 million stars, and in a typical image (FOV 13 x 19 'arc) there are 2 to 4 dozen stars with r' < 14. The r' accuracy varies with r' as shown in Fig. 4, above. It is safe to use r' < ~14.5. For fainter stars it is advisable to use an image with the target star in the FOV, as described in this section.

All-Sky Alternative

For more accurate mag's at all bands consider performing an all-sky observing session, as described at


Disregard the following.

    R-mag = (20.0 +/- 0.1) - 2.5 * LOG10 ( FLUXr / g ) - (0.13 +/- 0.01 ) * m

where FLUXr = "intensity" of the asteroid using the R-band filter, g = exposure time, m = air mass. The constant 0.13 +/- 0.01 is my site's extinction {magnitudes per air mass). The constant 20.0 +/- 0.1 is unique to my telescope system and is the number that must be calibrated once per year (or whenever the configuration changes). Each filter has a different pair of constants, and I'm just illustrating the equation for converting intensity to magnitude for one filter.

Procedure for Downloading Free Program DS9.exe



Smith, J. Allyn, et al, 2009, AJ, 123, 2121-2144.
Landolt, Arlo U., 2009, AJ, 137, 4186-4269.

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This site opened:  January 1, 2005 Last Update:  2011.06.13a