M67 Secondary Standards
Bruce Gary, Hereford Arizona Observatory; 2012.05.31

This web page provides a list of B, V, g', r', i', z' magnitudes for 47 stars in M67, based on two all-sky observations of six Landolt star fields with primary standard stars for B- and V-bands (Landolt, 2009) and g'r'i'z'-bands (Smith et al, 2002). The coordinates for the center of this star field (Star#2) is 08:51:23 +11:48:02 (J2000). The "observing season for M67 is centered on January 30 (when it crosses the meridian at local midnight). I'm currently preparing a table of 40 stars with calibrated BVg'r'i'z' magnitudes for an open cluster n Perseus (NGC 1342), with an observing season centered on November 19; a web page with these results can be found at link.

Figure 1. Finder chart for the 47 stars with secondary calibrations determined by Bruce Gary at the Hereford Arizona Observatory.  

Estimating Total SE for Each Star

As described below, the magnitudes in the Fig. 2 listing (and downloadable text file) have been corrected for small effects determined by treating each Landolt star field as an "unknown" and compiling "errors" from the true magnitudes and those solved for using my analysis procedure with the other Landolt stars. For the first all-sky observing session (2012 Apr 16) these corrections were small for B, V, g', r' and i' (-3, +0, -12, -9, +4 mmag), but for z'-band, which had the poorest SNR, the corrections was significant (-49 mmag). For the second all-sky observing session (2012 May 2) these corrections were small for all bands B, V, g', r', i' and z' (-9, +1, +5, +2, -2, +11 mmag). Each of the corrections from the "Landolt unknown" procedure has an uncertainty, and the orthogonal sum of the correction and associated uncertainty, for each band, can be used as an estimate of that band's systematic error. Total SE for each star will depend on the star's brightness, since stochastic SE varies with star brightness and total SE is the orthogonal sum of stochastic SE and estimated systematic SE. For each band the stochstic SE versus magnitude was modeled such that reduced chi-square was close to 1 (see Fig. 4, upper-right panel). The following listing is an average of  the two all-sky observing sessions. 

Figure 2.
Secondary standards magnitude listing, including total SE, based on two all-sky observing sessions. If systematic offsets for each band were removed the values in the SE columns would be much smaller. 

Here's a downloadable text version of the above list: M67GBL v2515    

Comparison With Other Catalogues

The above magnitudes are in approximate agreement with Henden 2000 for B- and V-bands (average difference = +15 and +12 mmag). I converted the Henden 2000 B- and V-band mag's to g'r'i'z' using conversion equations given by Jester 2005 (http://www.sdss.org/dr6/algorithms/sdssUBVRITransform.html). The results were compared with my g'r'i'z' masurements and differences are given in Table 1.

The AAVSO web site has APASS magnitudes (DR5) for BVg'r'i'. My magnitudes differ from APASS for these bands by amounts shown in the following table. Apparently the APASS magnitudes are very preliminary.

The old Priscilla Benson mag's for M67 agree with Henden 2000; my V-mag's differ from hers by amounts given in the following table.

Brian Skiff has a short catalog of M67 magnitudes for BVRcIc (N = 20), and only 6 stars are included in my Fig. 2 list. My magnitudes are compared with his in the following table.

Here's a summary of Fig. 2 magniutde comparisons with these catalogs.

Table 1. Comparison of Fig.2 Magnitudes With Other Catalogs (Fig. 2 Magnitude Minus Catalog Magnitude)

Henden 2000, N=23
+0.015 ± 0.006
(RMSi = 0.027) 
+0.012 ± 0.003
(RMSi = 0.015)
-0.006 ± 0.006
(RMSi = 0.027)
+0.019 ± 0.005
(RMSi = 0.023)
-0.006 ± 0.005
(RMSi = 0.024)
+0.005 ± 0.006
(RMSi = 0.029)
APASS (DR5, N=2), N=27
-0.053 (RMS=0.039)
-0.035 (RMS=0.039)
-0.229 (RMS=0.104)
-0.022 (RMS=0.087)
-0.141 (RMS=0.036)

Priscilla Benson, N=6
+0.038 (RMS=0.010)
+0.016 (RMS=0.008)
+0.015 (RMS=0.035)
+0.018 (RMS=0.014)
-0.004 (RMS=0.024)

Brian Skiff, N=6
+0.024 (RMS=0.011)
+0.016 (RMS=0.009)
+0.018 (RMS=48)
+0.018 (RMS=0.020)
+0.004 (RMS=0.024)

Consensus difference
+0.022 ± 0.012
+0.014 ± 0.007
+0.000 ± 0.010
+0.018 ± 0.005
-0.004 ± 0.007
+0.005 ± 0.006
Suggested Correction to Fig. 2

In this table the italicised entries are based on converting BVRcIc to g'r'i'z' using conversion equations given by Jester 2005 (http://www.sdss.org/dr6/algorithms/sdssUBVRITransform.html). The last row is my suggested correction to the Fig. 2 listing based on my subjective "consensus" of comparisons with other catalogs. I've been "conservative" iwth the g'r'i'z' adjustments because most of the the catalog comparisons use conversion equations. Here's a listing of the "adjusted" magnitudes.

Figure 3. Secondary standards magnitude listing, including total SE, based on two all-sky observing sessions and adjusted for compatibility with other catalogs. The brightness differences between stars (within a band) is much smaller than implied by the total SE values.

Here's a downloadable text version that contains the magnitude adjustments in the table's last: M67GBLa v2515  

Information on the All-Sky Observing and Analysis Procedures Used

My observing procedure is described elsewhere, http://brucegary.net/allsky2011/, as is my hardware: http://www.brucegary.net/HAO/. Briefly, I use a 14-inch Meade with a SBIG ST-10XME CCD. The telescope is housed in a dome, and both are controlled from my residence office using buried control cables. I use MaxIm DL for control of the telescope, CCD, focuser and dome. Flat fields are taken of the sky before sunset. Bias and dark exposures are also taken before observations. All imaging is unbinned.

The April 16 all-sky observing session consisted of "observing cycles" of Landolt star fields and M67. All exposure times are 10 seconds, unguided. An "observing cycle" consists of 4 B-band images, 4 at V-band, 4 at g', 3 at r', 3 at i' and 5 at z'. Two observing cycles are made whenever a Landolt star field is acquired (some fields are acquired at different times of the night for sampling a large range of air mass). On April 16 I observed the following star fields: L0652, L0558, M67, L0724, L0853, M67, L0853, L1637 (note that L0652 means the Landolt star field at RA = 06:52, DE ~ 0). After this sequence I observed L1637 for the rest of the night for the purpose of detecting the presence of sub-visible cirrus and aerosol patchiness (one events of ~15 mmag lasting 1/2 hour was found, as was another with 5 - 10 mag). This 6-hour run also provided extinction trend information (that was useful in constraining subsequent analyses involving extinction change modeling).

The rationale for including B and V observations when only g'r'i'z' magnitudes are to be determined has to do with the need for an accurate star color for each star. There are many more B and V standard magnitudes (Landolt 2009) than g'r'i'z' magnitudes (Smith et al 2002) at each of the observed Landolt star fields.

I use an artificial star for all image analysis, which permits monitoring of extinction variations. I have come to view the presence of sub-visible cirrus and aerosol patchiness as very important for all-sky observing, and the only way I know how to deal with these extinction variations is with the use of an artificial star (that occupies an unused 0.1% corner of each image). The artificial star magnitude won't vary during an observing session, so it allows star magnitude readings to be converted to star flux.

All photometry readings correct for "flux capture fraction" - the ratio of flux within the circular photometry circle when the radius is small (~ 2.5 times FWHM) versus large (~5 times FWHM). The small aperture is used for exporting to a spreadsheet for subsequent analysis. The incentive for using a small photometry aperture is twofold: bettyer SNR for faint Landolt stars, and reduced interference from nearby stars. This correction is usually 20 or 30 mmag.

The spreadsheet calculates air mass from JD, my site location and the target coordinates. All star fluxes are processed with guidance from the following generic magnitude equation:

   Magnitude = Z - 2.5 × LOG10 ( Flux / g ) - K' × AirMass + S × StarColor  + S2  × AirMass × StarColor                                                                               (1)

    where Z is a zero-shift constant, specific to each telescope system and filter (which should remain the same for many months),
    Flux is the star's flux (sum of counts associated with the star). It's called "Intensity" in MaxIm DL,
    g is exposure time ("g" is an engineering term meaning "gate time"),
    K' is zenith extinction (units of magnitude per air mass),
    S is "star color sensitivity." S is specific to each telescope system (and should remain the same for many months),
    StarColor can be defined using any two filter bands. B-V is in common use; I use 0.57 × (B-V) - 0.39,
    S2 is a second-order term that is usually ignored because it is only important for high air mass and extremely blue or red stars.

This general equation is true for all filter bands (even unfiltered), though there are different values for the constants for each filter. For example, the magnitude equation for V-band (omitting the last term in Eqn 1) is:

    V = Zv - 2.5 × LOG ( Flux / g ) - Kv' × AirMass + Sv × StarColor                                                                                                                                            (2)

Similar equations exist for bands B, g', r', i' and z'.

Because Kv' may vary throughout the night it has to be represented using a temporal trend term. I have found it useful to also solve for a 3rd-order fit to residuals that result from use of only a trend term.

My choice of StarColor = 0.57 × (B-V) - 0.39 is motivated by the simplicity of beginning an iteration with a StarColor value that is typically zero for the first iteration. This definition choice is arbitrary and won't affect results provided the same definition is used for all bands.

Extinction at each filter band is represented by a zenith value at mid-observing session time, a temporal trend parameter, and a 3rd order fit to residuals (identified as aerosol patches drifting overhead).

Figure 4. Screen capture of a spreadsheet section for V-band fitting of Landolt stars (N=54, total of 173 photometry readings). Lower-left panel shows solution for zenith extinction; upper-left panel shows solution for star color sensitivity; upper-right panel shows residuals of measured magnitude with respect to modeled magnitude versus V-magnitude. Lower-right area ahs slide bars for matching RMS versus magnitude (upper-right) with a stochastic SE model.

"Landolt Unknown" Analysis

A final adjustment was made by treating each Landolt star field as an "unknown" and processing it using the other Landolt stars to solve for telescope system photometry constants. Since five Landolt star fields were used for the April 16 observing session there were five estimates of "average star field error" for each filter band. For example, the V-band average errors were +8, -2, +8, -21 and +5 mmag. Some star fields had more standard stars than others, and the average of the 54 Landolt stars in all star fields for V-mag was +0 ± 11 mmag. For B, g', r', i' the average errors were +3, +12, +9 and -4 mmag. z'-band was less well behaved, with +49 mmag average error. Apparently there is something about my analysis procedure for z'-band that was underestimating star brightness when all Landolt star fields were involved in the parameter solution. Until I figure this out I have decided to adopt the correction values called for by the exercise of treating Landolt star fields as unknown. This is what was done in obtaining Fig. 2, above. The following table lists the "Landolt Bias Corrections" for each band based on treating each of the Landolt star fields as an "unknown."

Table 2. "Landolt Bias Correction" for Apr 16 (Based on Treating Landolt Star Fields as Unknown)

Apr 16 Bias [mmag]
+3 ± 12
+0 ± 11
+12 ± 7
+9 ± 4
-4 ± 4
+49 ± 25
Apr 16 Nr. Comparisons
May 02 Bias [mmag]
+9 ± 6
-1 ± 3
-5 ± 5
-2 ± 4
+2 ± 3
-11 ± 9
May 02 Nr. Comparisons

Total SE for each star will depend on the star's brightness, since stochastic SE varies with star brightness and total SE is the orthogonal sum of stochastic and estimated systematic SE. I estimate that the systematic error for each band is the orthogonal sum of the applied half of the "Landolt Bias Correction" correction (above table) and the SE of that correction.


 Henden, A. 2000, JAAVSO, 29, 35-43.
 Landolt, A. U., 2009, AJ, 137, 4186-4269, May.
 Smith, J. Allyn, et al, 2009, AJ, 123, 2121-2144.
 Skiff, B., 1997, M67 catalog: http://stupendous.rit.edu/tass/catalogs/m67.html 

    AAVSO photometry manual: http://www.aavso.org/observing/programs/ccd/manual/4.shtml#2
    Lou Cohen's 2003 tutorial: http://www.aavso.org/observing/programs/ccd/ccdcoeff.pdf
    Priscilla Benson's (1990's) CCD transformation equations tutorial: http://www.aavso.org/observing/programs/ccd/benson.pdf
    Bruce Gary's CD Transformation Equations derived from basic princples: http://reductionism.net.seanic.net/CCD_TE/cte.html
    Bruce Gary's All-Sky Photometry for Dummies: http://brucegary.net/dummies/x.htm
    Bruce Gary's All-Sky Photometry for Smarties - v1.0:
    Bruce Gary's All-Sky Photometry for Smarties - v2.0:  http://brucegary.net/ASX/x.htm
    Bruce Gary's Differential Alternative Equations: http://brucegary.net/DifferentialPhotometry/dp.htm
    Bruce Gary's Astrophotos home page: http://reductionism.net.seanic.net/brucelgary/AstroPhotos/x.htm
    Bruce Gary's all-sky observing session of 2011.10.28 (BVRcIcg'r'i'z', 60 Landolt stars, 22 SDSS stars):  http://brucegary.net/yygem/all-sky/index.htm  
    Bruce Gary's 2011 version of all-sky observing and analysis procedure: http://brucegary.net/allsky2011/  
    Bruce Gary resume: http://brucegary.net/resume.html


WebMaster: B. GaryNothing on this web page is copyrighted. This site opened:  2012.04.24 Last Update:  2013.02.19