(correction made Sep 30, 2003 -- thanks, Eric!)
The Tycho-1 and Tycho-2 catalogs provide magnitudes for many stars over the entire sky in two passbands: Bt and Vt. These are not very far from the standard Johnson-Cousins B and V passbands, but there are differences. How can one convert the Tycho values to the standard scale?
The Tycho-2 catalog is described in an article in Astronomy and Astrophysics, 355L, 27 (2000). In the documentation which accompanies the catalog on the SIMBAD site, Hog et al. provide a conversion:
Approximate Johnson photometry may be obtained as:
V = VT - 0.090*(BT-VT)
B-V = 0.850*(BT-VT)
Consult Sect 1.3 of Vol 1 of "The Hipparcos and Tycho Catalogues",
ESA SP-1200, 1997, for details.
In Feb, 2001, Arne Henden wrote an E-mail message to the TASS mailing list in which he states:
For those of you that are interested in using the Tycho2 catalog for photometric as well as astrometric calibration, here are the results from my latest fits vs. Landolt standards (about 270 stars, V brighter than 10.5, B-V bluer than 1.8): U = Bt - 0.325 + 0.8034*(Bt-Vt) B = Bt + 0.018 - 0.2580*(Bt-Vt) V = Vt + 0.008 - 0.0988*(Bt-Vt) R = Vt - 0.014 - 0.5405*(Bt-Vt) I = Vt - 0.039 - 0.9376*(Bt-Vt) U has terrible systematics; I has systematics as well. The BVR fits are quite good. For these fits, I have not made any discrimination on luminosity class and have assumed a purely linear relationship.
Mike Bessell compared Tycho magnitudes to those of primary standards in the E-regions. You can read his paper in PASP (112, 961, 2000). Here is his Table 2. The column labelled "d(B-V)" provides the difference defined as follows:
d(B-V) = (B-V) - (BT-VT)
The column labelled "V-HP" shows the difference between
standard V-band magnitudes and those measured through the
wide passband of the Hipparcos instrument.
BT-VT V-VT Īd(B-V) V-HP
--------------------------------
-0.250 0.038 0.031 0.066
-0.200 0.030 0.021 0.051
-0.150 0.022 0.011 0.036
-0.100 0.015 0.005 0.021
-0.050 0.008 0.002 0.006
-0.000 0.001 -0.005 -0.011
0.050 -0.005 -0.010 -0.025
0.100 -0.012 -0.017 -0.038
0.150 -0.018 -0.020 -0.048
0.200 -0.024 -0.021 -0.058
0.250 -0.029 -0.023 -0.069
0.300 -0.035 -0.025 -0.079
0.350 -0.040 -0.025 -0.087
0.400 -0.045 -0.026 -0.094
0.450 -0.050 -0.030 -0.101
0.500 -0.054 -0.035 -0.108
0.550 -0.059 -0.045 -0.114
0.600 -0.064 -0.051 -0.120
0.650 -0.068 -0.060 -0.127
0.700 -0.072 -0.068 -0.131
0.750 -0.077 -0.076 -0.134
0.800 -0.081 -0.085 -0.137
0.850 -0.085 -0.094 -0.142
0.900 -0.089 -0.104 -0.147
0.950 -0.093 -0.113 -0.151
1.000 -0.098 -0.122 -0.155
1.050 -0.102 -0.131 -0.158
1.100 -0.106 -0.142 -0.157
1.150 -0.110 -0.154 -0.160
1.200 -0.115 -0.166 -0.162
1.250 -0.119 -0.178 -0.164
1.300 -0.124 -0.189 -0.166
1.350 -0.128 -0.199 -0.166
1.400 -0.133 -0.210 -0.165
1.450 -0.138 -0.222 -0.164
1.500 -0.143 -0.234 -0.161
1.550 -0.148 -0.245 -0.157
1.600 -0.154 -0.256 -0.153
1.650 -0.160 -0.266 -0.148
1.700 -0.165 -0.277 -0.143
1.750 -0.172 -0.288 -0.137
1.800 -0.178 -0.299 -0.131
1.850 -0.185 -0.309 -0.125
1.900 -0.191 -0.320 -0.119
1.950 -0.199 -0.331 -0.112
2.000 -0.206 -0.342 -0.106
Mike Linnolt provides a convenient polynomial to convert VT to V magnitudes:
While working on loading the Bessel data table into my charting program, I noticed that the (V-Vt) vs. (Bt-Vt) is almost perfectly fit by a single cubic polynomial! V-Vt = -0.02(Bt-Vt)^3 + 0.0549(Bt-Vt)^2 - 0.1334(Bt-Vt) + 0.001 R^2 = 0.99998 Unfortunately the del(B-V) vs. (Bt-Vt) cannot be fit so perfectly by a polynomial, but a 5th order is within R^2=0.99965 with significant departures around (Bt-Vt)~0.4 and (Bt-Vt)~0.15.
In a paper by Mamajek et al. (AJ, 124, 1670, 2002) , the authors provide a polynomial fit to Bessell's table shown above. They find
for -0.25 < (BT-VT) < 2.0: V = VT + 9.7E-04 - 1.334E-01(BT-VT) + 5.486E-02(BT-VT)^2 - 1.998E-02(BT-VT)^3 for 0.5 < (BT-VT) < 2.0: B-V = (BT-VT) - 7.813E-03(BT-VT) - 1.489E-01(BT-VT)^2 + 3.384E-02(BT-VT)^3 for -0.25 < (BT-VT) < 0.5: B-V = (BT-VT) - 0.006 -1.069E-01(BT-VT) + 1.459E-01(BT-VT)^2