Converting Tycho magnitudes to the standard scale

March 8, 2008

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?

you can read an older version of this page


The following information comes from Brian Skiff, who keeps it at ftp://ftp.lowell.edu/pub/bas/starcats/bessell.tyc

Mamajek, Meyer, & Liebert (2002AJ....124.1670M), appendix C, claim the following equations fit Bessell's relations to 1-2 millimag. The second equation, for the redder B-V colors, is corrected per the erratum in 2006AJ....131.2360M).


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


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Date: Fri, 10 Jan 2003 13:16:03 -1000 (HST)
From: Michael Linnolt 
Subject: Re: Bessell lookup table
To: Brian Skiff 

Brian,

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. Clear skies, Mike Linnolt =============================================================================== Corrections to put Hipparcos/Tycho data on the standard V and B system from: 2000PASP..112..961B BESSELL M.S. Publ. Astron. Soc. Pac., 112, 961-965 (2000) [July 2000 issue] The Hipparcos and Tycho photometric system passbands. TABLE 2 RELATION BETWEEN BT-VT AND HIPPARCOS/TYCHO DATA FOR B-G MAIN-SEQUENCE STARS AND K-M GIANTS BT-VT V-VT del(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