"Comparison between Bessell-Brett (1988, "BB88") V-K colors and
Johnson-2MASS V-Ks colors for dwarf stars, or a check on the Carpenter
(2001) transformation from 2MASS Ks to BB88 K-band"

Eric Mamajek
6/22/2011

In this short memo, I basically confirm the transformation between
2MASS Ks and Bessell & Brett K-band by Carpenter (2001) appears to be
valid, through comparison of Bessell-Brett (BB88) intrinsic V-K colors
for dwarf stars and the author's Johnson-2MASS V-Ks colors for field
dwarfs, and that one can simply apply an offset of ~0.04 mag when
comparing BB88 intrinsic V-K colors to V-Ks colors measured using
2MASS and any V-band photometry which is claimed to be tied to
Johnson's system.

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Bessell & Brett (1988; PASP 100, 1134; hereafter "BB88") lists a table
(Table II) of "Intrinsic Colors for Dwarfs". Given the systematic
differences between the numerous near-IR natural JHK photometric
systems that appeared during the 1960s-1980s, BB88 generated a
homogenized system, "essentially the Johnson-Glass system", and
estimated conversions between the other near-IR photometric system and
this new homogenized system. BB88 "decided to adopt the system of
Glass (with zero-point corrections) as the base system for
homogenizing the photometry". Many authors use the BB88 colors as the
basis for their modeling of spectral energy distributions and
estimates of interstellar reddening and extinction (e.g. perhaps most
notably Kenyon & Hartmann 1995 ApJS 101, 117, which itself is heavily
cited as a source for intrinsic dwarf stellar colors).

Surprisingly little published work has been done on the intrinsic
colors of stars on the 2MASS JHKs system, which given its extensive
reach (99.998% sky coverage, 0.47 billion point sources; Skrutskie et
al 2006, AJ, 131, 1163). The author (EEM) has derived median (V-Ks;
i.e. Johnson V minus 2MASS "Ks") colors for normal dwarf stars based
on examination of the median colors for nearby, unreddened field
dwarfs classified on the MK system, and the colors of well-accepted
dwarf MK standard stars (see extensive notes, listed by spectral type,
in directory at http://www.pas.rochester.edu/~emamajek/spt/ ). The
majority of median V-Ks colors for a given spectral type were in fact
estimated by adopting a best Johnson B-V color, and then referring to
a dense stellar B-V vs. V-Ks locus of stellar dwarf colors generated
by the author. The inferred V-Ks colors also agree well with straight
median colors of samples of nearby dwarfs with MK classifications by
expert classifiers Gray, Corbally, Garrison, Houk, and their
collaborators (e.g. Gray et al. 2003 AJ 126, 2048; Gray et al. 2006 AJ
132, 161; Houk & Cowley 1975 "University of Michigan Catalogue of
two-dimensional spectral types for the HD stars. Volume
I. Declinations -90o to -53o" and subsequent volumes, etc.)

Here is a table of the V-K colors from Bessell & Brett (1988) listed
by dwarf (V) spectral type and the median colors estimated by Mamajek.

#SpT  V-K(BB88)  V-Ks(EEM)
B8    -0.36      -0.261
A0    0.00       0.042
A2    0.14       0.192
A5    0.38       0.404
A7    0.50       0.528
F0    0.70       0.732
F2    0.82       0.925
F5    1.10       1.079
F7    1.32       1.244
G0    1.41       1.421
G2    1.46       1.545
G4    1.53       1.621
G6    1.64       1.693
K0    1.96       1.953
K2    2.22       2.155
K4    2.63       2.733
K5    2.85       2.835
K7    3.16       3.407
M0    3.65       3.790
M1    3.87       4.099
M2    4.11       4.265
M3    4.65       4.660
M4    5.26       5.240
M5    6.12       5.942
M6    7.30       7.230

Let's quantify the differences in the BB88 V-K and Johnson-2MASS V-Ks
colors as derived by Mamajek. 

A least-squares fit to the data suggests:

(V-Ks) = (0.064+-0.030) + (0.9907+-0.0097)*(V-K_BB88)

The slope is within 1sigma of "1", so our analysis does not present
convincing evidence of a color term in the transformation.  If we
further assume that the V magnitudes are identical (a safe assumption
at the <0.01 mag level, as Cousins and Hipparcos V magnitudes are tied
to Johnson's system; see documentation on V-band photometry
from Hipparcos; ESA 1997), then this suggests:

Ks = (-0.064+-0.030) + (0.9907+-0.0097)*(K_BB88)

Looking at the 25 spectral type bins as an ensemble, and
neglecting any color effects (which appear to be negligible
given the near unity slope in the previous equation), 
we find that via median statistics (Gott et al. 2001 ApJ 549,
1):

Ks = (-0.032+-0.018) + K_BB88

This agrees remarkably well with equation A1 of Carpenter 
(2001; AJ, 121, 2851):

Ks = (-0.044+-0.003) + K_BB88 + (0.000+-0.005)*(J-K)_BB88

BB88 tied their homogenized system to the SAAO photometry
from Glass (1974), but since these stars were saturated
in 2MASS, Carpenter tied 2MASS to the Glass system
via his own transformations and those listed in BB88. 

Unsurprisingly then, Carpenter (2001) also found a similar
transformation (his equation 4) between the SAAO system and 2MASS,
but with a slight color term:

Ks = (-0.032+-0.012) + K_AAO + (-0.021+0.008)(J-K)_AAO

Conclusion: 

We have shown using an independent method (comparing intrinsic dwarf
colors for 25 spectral subclasses) that Carpenter's (2001) conversion
between the 2MASS Ks magnitudes and Bessell-Brett (BB88) K magnitudes
is validated. This can be helpful in converting between other colors
dependent on either the BB88 K band or 2MASS Ks band and other colors
published in the pre-2MASS literature.

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