4 Transformation of 2MASS magnitudes to the Bessell-Brett (BB) homogenized system

The 2MASS data used in this paper are from the Second Incremental Data Release (Cutri et al. 2000). Thirty nine of the stars with (V-K) < 1.50 for which Di B98 gives K magnitudes on the TCS system have 2MASS $K_{\rm s}$ magnitudes. For 18 stars with (V-K) $_{\rm J} < 0.50$, $K_{\rm s}$ minus $K_{\rm TCS} = -0.075\pm0.007$ mag. For the 21 stars with $0.50\leq(V-K)_{\rm J}\leq1.50$, $K_{\rm s}$ minus $K_{\rm TCS} = -0.064\pm0.006$ mag. We conclude that there is no significant colour term in the transformation and for all 39 stars we obtain:

$$K_{\rm TCS} K_{\rm s} +0.069\pm0.005.$$ (3)

The differences between the 2MASS and Di B98 magnitudes are shown in Fig. 4 where the error bars are those given for the 2MASS data alone; the differences seem reasonable since the Di B98 magnitudes have errors of about $\pm$0.02 mag. In this plot, it seems that the differences are greater for the very brightest stars. No similar effect was found in a larger sample of these stars (Carpenter 2001a) and so no systematic magnitude effect is likely to be present.

Figure 4: The difference ($\Delta$K) (2MASS $K_{\rm s}$ minus K magnitude on the TCS system (Di Benedetto 1998) as function of $(V-K)_{\rm0}$ (above) and $K_{\rm s}$ (below).

Carpenter (2001b) gives colour transformations for the 2MASS Second Incremental Data Release to various other photometric systems, including the Bessell & Brett (BB) homogenized system (Bessell & Brett 1988). Carpenter (Eq. (A1)) finds:

$$(K_{\rm s})_{\rm 2MASS} = K_{\rm BB} + (0.000\pm0.005)(J-K)_{\rm BB} + (-0.044\pm0.003).$$ (4)

The difference between the constants in Eqs. (4) and (5) is greater than their quoted errors. We assume that this is an indication of the looseness of the definition of the Johnson system for hot stars (e.g. Fig. 1 of Di B98). In this paper we have chosen to adopt Eq. (4) and so have:

$$K_{\rm BB} = (K_{\rm s})_{\rm 2MASS} + 0.044.$$ (5)

Using Carpenter's Eqs. (A4) and (A3), we further obtain:

$$H_{\rm BB} = H_{\rm 2MASS} +0.016$$ (6)

$$J_{\rm BB} = J_{\rm 2MASS} +0.029(J-K_{\rm s})_{\rm 2MASS} +0.055 .$$ (7)

Hawarden et al. (2001) have given a list of faint IR standard stars on the UKIRT system. Seven of these are blue ( $-0.01\leq(B-V)\leq0.020$) and have 9.9<K< 13.5 and have 2MASS magnitudes. The mean differences in the sense 2MASS minus UKIRT magnitudes for these seven stars are:

$$\Delta J = -0.022\pm0.015~~~~~~~~~~~(-0.007\pm0.007 )$$ (8)

$$\Delta H = +0.008\pm0.013~~~~~~~~~~~(+0.019\pm0.006 )$$ (9)

$$\Delta K = -0.009\pm0.011~~~~~~~~~~~(+0.002\pm0.004 )$$ (10)

where the quantities in parentheses were calculated from Carpenter's transformation Eqs. (38), (40) and (41). The agreement is satisfactory and shows that the 2MASS magnitudes for fainter and bluer stars are on the same system as for the brighter stars and that their quoted errors are realistic for these relatively faint stars.

 

 

Table 6: Data for the Hyades Dwarf stars discussed in Sect. 5.1.

HD	HIP	$T_{\rm eff}$a	$\log g$a	Vb	$J_{\rm 2MASS}$	$H_{\rm 2MASS}$	$K_{\rm 2MASS}$	(V-J)$_{\rm BB}$c	(V-H)$_{\rm BB}$c	(V-K)$_{\rm BB}$c
		(K)
(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)	(11)
24098	17950	6624	4.431	6.473	5.711	5.552	5.470	0.700	0.905	0.959
		$\pm$51.8	$\pm$0.029	$\pm$0.006	$\pm$0.023	$\pm$0.064	$\pm$0.033	$\pm$0.024	$\pm$0.064	$\pm$0.034
26345	19504	6660	4.336	6.612	5.822	5.622	5.557	0.727	0.974	1.011
		$\pm$44.4	$\pm$0.036	$\pm$0.007	$\pm$0.057	$\pm$0.039	$\pm$0.041	$\pm$0.057	$\pm$0.040	$\pm$0.042
26737	19789	6674	4.334	7.049	6.225	6.091	5.999	0.762	0.942	1.006
		$\pm$44.4	$\pm$0.037	$\pm$0.004	$\pm$0.078	$\pm$0.043	$\pm$0.037	$\pm$0.078	$\pm$0.043	$\pm$0.037
27524	20349	6628	4.340	6.807	5.968	5.791	5.741	0.777	1.000	1.022
		$\pm$67.2	$\pm$0.039	$\pm$0.022	$\pm$0.036	$\pm$0.032	$\pm$0.039	$\pm$0.042	$\pm$0.039	$\pm$0.045
27534	20350	6598	4.345	6.791	5.951	5.802	5.727	0.779	0.973	1.020
		$\pm$62.3	$\pm$0.038	$\pm$0.021	$\pm$0.036	$\pm$0.032	$\pm$0.037	$\pm$0.042	$\pm$0.038	$\pm$0.043
27731	20491	6507	4.361	7.175	6.253	6.117	6.072	0.862	1.042	1.059
		$\pm$29.9	$\pm$0.039	$\pm$0.009	$\pm$0.022	$\pm$0.025	$\pm$0.025	$\pm$0.024	$\pm$0.027	$\pm$0.027
28406	20948	6554	4.352	6.915	6.066	5.901	5.786	0.786	0.998	1.085
		$\pm$43.7	0.039	$\pm$0.007	$\pm$0.039	$\pm$0.053	$\pm$0.038	$\pm$0.040	$\pm$0.053	$\pm$0.039
28911	21267	6651	4.337	6.619	5.757	5.635	5.528	0.800	0.968	1.047
		$\pm$53.6	$\pm$0.039	$\pm$0.004	$\pm$0.027	$\pm$0.036	$\pm$0.030	$\pm$0.027	$\pm$0.036	$\pm$0.030
29225	21474	6593	4.346	6.647	5.785	5.608	5.552	0.800	1.023	1.051
		$\pm$78.9	$\pm$0.043	$\pm$0.010	$\pm$0.054	$\pm$0.030	$\pm$0.046	$\pm$0.055	$\pm$0.032	$\pm$0.047
31845	23214	6558	4.352	6.753	5.818	5.645	5.617	0.874	1.092	1.092
		$\pm$66.5	$\pm$0.041	$\pm$0.005	$\pm$0.032	$\pm$0.035	$\pm$0.040	$\pm$0.032	$\pm$0.035	$\pm$0.040
33400	24116	6580	4.348	7.856	7.003	6.852	6.797	0.792	0.988	1.015
		$\pm$66.8	$\pm$0.048	$\pm$0.031	$\pm$0.033	$\pm$0.034	$\pm$0.044	$\pm$0.045	$\pm$0.046	$\pm$0.054

$\parbox{15.7cm}{ $^{a}$ ~Data taken from de Bruijne et~al. (\cite{d... ...gue (Turon et~al. \cite{hip92}). \\ $^{c}$ ~On the Bessell-Brett system. \\ }$