MBCAA Observatory

Transformation coefficients (with weights): V, Rc measurements

Observed: 7 Jan 2005, 24 Dec 2006, 12 Jan, 19 July, 5 Aug, 5, 6, 12, 15 Sept 2007

Michel Bonnardeau
29 Sept 2007

Abstract

The transformation coefficients for my telescope and camera and V,Rc filters are measured and computed from weighted averages and weighted standard deviations.

Introduction

For an introduction to transformation equations and coefficients for differential photometry, see HERE.

The transformation coefficients for my telescope and camera and V,Rc filters are derived by multiple observations of Landolt's fields (1992, VizieR II/183A), spanning over several nights. The stability of these coefficients can then be assessed.

Observations

Run Session Field Nb of
stars V-Rc
range Tvr Tv Tr

value error value error value error

0 20050107 L95 14 1.087 1.056 0.011 -0.020 0.036 -0.162 0.010

1 20061224 L98 8 0.607 1.118 0.024 -0.050 0.010 -0.143 0.009

2 20070112 L95 9 0.663 1.026 0.011 -0.014 0.005 -0.041 0.006

3 20070719 L110 7 1.038 1.154 0.011 0.041 0.008 -0.111 0.001

4 20070805 L111 3 0.730 1.135 0.020 -0.054 0.008 -0.173 0.008

5 20070905 L110 North 8 1.038 1.105 0.007 0.004 0.006 -0.107 0.001

6 20070905 L110 South 9 1.148 1.157 0.034 0.006 0.019 -0.145 0.006

7 20070906 L110 North 8 1.038 1.105 0.007 -0.008 0.006 -0.115 0.001

8 20070906 L110 South 9 0.999 1.131 0.024 -0.001 0.015 -0.132 0.003

9 20070912 L110 North 8 1.038 1.132 0.007 0.021 0.006 -0.109 0.001

10 20070912 L113 7 0.362 0.979 0.020 -0.116 0.024 -0.049 0.024

11 20070912 L95 8 0.644 1.097 0.073 0.005 0.026 -0.085 0.034

12 20070915 L110 North 6 0.462 1.184 0.099 0.071 0.042 -0.073 0.029

There is only one subfield observed per session, except for 20050107 which has 3 subfields and 20070112 with 2 subfields.

The transformed V,R magnitudes of the star being studied are computed the following way:

V = v + Tv*Tvr*((v-r)-(Vo-Ro))
R = V - [(Vo-Ro) + Tvr*((v-r)-(Vo-Ro))]

or

R = r + Tr*Tvr*((v-r)-(Vo-Ro))
V = R + (Vo-Ro) + Tvr*((v-r)-(Vo-Ro))

where Vo,Ro are the magnitudes of the comparison star and v,r the observed magnitudes of the star being studied. The only coefficients that are useful for the transformations are then Tvr, Tv*Tvr, Tr*Tvr:

The coefficients are fairly stable. The adopted values and uncertainties are the weighted average values and the weighted standard deviations:

(m the number of observations, deltaTi the uncertainty/error on observation i)

Tvr = 1.104 +/- 0.039
Tv*Tvr = -0.010 +/- 0.032
Tr*Tvr = -0.134 +/- 0.017