XO-1 is the sun-like star in the transiting exoplanet system in the constellation Corona Borealis, at RA = 16:02:11.6, Dec = +28:10:11. In the following image 9 stars are identified whose magnitudes have been measured with filters for the four bands B, V, Rc and Ic.

Figure 1. Finder chart for XO-1 (to left of X symbol) and 8 nearby candidate reference stars. FOV = 16 x 21 'arc, north up, east left. Faintest stars in this rendition have V ~ 18.0. [Celestron CGE-1400, 14-inch SCT, focal reducer, AO-7 image stabilizer, SBIG CFW8, SBIG ST-8XE CCD; four 60-second exposures, 2006.02.27, Hereford, AZ]

Magnitudes for the 9 stars identified in this image were determined from two all-sky photometry observing sessions, on 2006.02.25 and 2006.03.14. On each date 4-filter observations of the XO-1 star field and two Landolt star fields (at RA/Dec 04:52:30/+00:03.0 and 12:42:22/-00:33.5) were conducted at times when air mass was approximately the same. On the first date 28 Landolt stars were used to establish "simplified magnitude equation" constants for my telescope system, and on the second date 22 of these same stars were used. The "simple magnitude equation" with constants to be solved for is illustrated for V-band with the following equation:

    V = 19.887 - 2.5 * LOG ( S' / g ) - 0.12 * m -0.05 * C'

          where, the three parameters to be solved-for using Landolt stars are shown as bold and blue.
          19.887 is a zero shift constant (different for each filter, usually stable on month timescales),
          S'  is star flux using a large aperture [counts],
          g = exposure time [seconds],
          0.12 is zenith extinction constant [magnitudes per air mass], (different for each filter and often different for each date),
          m is air mass,
          -0.05 is a star color sensititivty constant to be solved for (different for each filter, stable over time), and
          C' = "linearized star color" defined as C' = C + 1.3 * C⁴, where C = 0.57 * (B-V) - 0.30 (for typical stars C' = C ~ zero).

A derivation and fuller description of "simple magnitude equations," SME, (including an additional term for "air mass times star color") is given at the web page SME_AllSkyPhotometry.

When observations of the target star field and Landolt star fields are at the same air mass it is not necessary to solve for the extinction constant. If there's a large separation in observing times for the two star fields then temporal trends of extinction can be important. For the calibrations described here the two star field observations were closely spaced in time.

As an aside, the 2006.02.25 all-sky calibration of SME constants were used to determine a photometric sequence for GRB060218. I noted an approximate 0.25 magnitude discrepancy with SDSS magnitudes for 5 stars for all 4 bands. The audacity of an amateur to question SDSS photometry was noted (Arne) so I kept quiet and merely described my results on a web page GRB060218. About a month later (2006.03.20) Malcolm Hicken announced (on behalf of the CfA's Supernova Group) via GCN 4898 that all-sky measurements taken at Mount Hopkins showed that the SDSS magnitudes for stars in this region are too bright by ~0.27 magnitude at V-band, and are too bright by similar amounts at other bands. Their web page referred to stars with my finder chart designation numbers, and they stated that their magnitudfes were in agreement with mine. Additional information on this announcement can be found at GCN 4898 Supporting Info. Amateurs don't get no respect! End of aside.

A sense of the quality of how well the SME solutions fit the star flux measurements can be conveyed by describing RMS residuals from the fitted equations. On the first calibration date the Landolt stars exhibited RMS differences from the SME solution of 0.0199, 0.031, 0.026 and 0.036 magnitude for B, V, Rc and Ic (N = 29, 35, 18 and 14). On the second date the RMS residuals were 0.018, 0.012, 0.008 and 0.026 magnitude for B, V, Rc and Ic (N = 36, 20, 6 and 14). The following graph illustrates the consistent correlation of a parameter related to "star color sensitivity" versus star color for B-band.

Figure 2. B-band star magnitude parameter versus known star color for 36 Landolt stars, 2006.03.14 observations. The slope of the fitted line is the "star color sensitivity" constant for B-band.

The all-sky Rc magnitudes for the XO-1 stars derived on two dates differed by only 0.003 magntude. The population SE for the differences (8 stars) was 0.005 magnitude. The following figure is a weighted-average solution for star magnitudes for the XO-1 star field.

The estimated SE accuracy for these stars is:

    B  SE = 0.04 magnitude
    V  SE = 0.03     "
    Rc SE = 0.020    "
    Ic SE = 0.03     "

This site opened:  May 16, 2006 .  Last Update:  May 18, 2006