6 Results

Resulting barycentric radial-velocity measures for the Sun (lunar spectra) are given in the rightmost columns of Table 1, and for the stars in Table 2. The indicated uncertainties are internal standard errors. The lunar observations show an apparent change by 39 m s^-1 between February and October. We believe this is related to the instrumental changes discussed in Sect. 5.5 and therefore indicative of a minimum level of external errors in these results as well as for the stars. The unweighted mean from the two periods gives $cz_{\rm B}=+0.257$ km s^-1 as our best estimate of the full-disk solar radial-velocity measure (its standard error, including the zero-point uncertainty $\sigma_0$, is 0.011 m s^-1). This is consistent with typical shifts of medium-strong Fe I lines (equivalent width $\simeq$6 pm) as measured in the Solar Flux Atlas by Allende Prieto & García López (1998b), although their data refer to the line bottoms while our results are for points higher up towards the continuum (cf. Sect. 7.2). Subtracting the gravitational redshift for an observer at infinity (636.5 m s^-1) gives a net blueshift of -379 m s^-1 relative to the Fe I template due to convection and possibly other effects.

 

 

Table 2: Results of the stellar observations, given in the form of barycentric radial-velocity measures $cz_{\rm B}$ (referring to the synthetic Fe I template), and a comparison with published radial velocities $v_{\rm r}$. Note that for HIP 20205, 20889, 87079 there are two lines of data per star, one for each observing period. The columns contain: HIP - Hipparcos Catalogue number; HD/HDE/BD - alternative designation; Sp - spectral type; B-V - colour index (Sp and B-V from Hipparcos Catalogue Turon et al. 1998); Date - mean epoch of observation, given as the barycentric Julian Ephemeris Date (JED) minus 2450000.0; $cz_{\rm B}$ - (mean) radial-velocity measure and estimated internal standard error; N - number of observations; $v_{\rm r}({\rm CDS})$ and $v_{\rm r}({\rm other})$ - radial velocity from the SIMBAD data base (CDS, Strasbourg) and other sources; Ref. - reference for radial velocity (see below); Rem. - remark concerning cluster membership (Hyades or Ursa Major), radial-velocity standard star (std), metal-poor star (mp), or other. For Hyades stars in Griffin et al. (1988) we also give the designation used in their Table IV. See text for comments on the (variable) stars HIP 71284 and 113357.

HIP	HD/HDE	Sp	B-V	Date	$cz_{\rm B}$	N	$v_{\rm r}({\rm CDS})$	Ref.	$v_{\rm r}({\rm other})$	Ref.	Rem.
	BD		mag	2450000+	km s-1		km s-1		km s-1
910	693	F5V	0.487	741.4221	+15.107$~\pm~$0.027	1	+14.4$~\pm~$0.9	2	+14.50$~\pm~$0.04	6	std
2413	2665	G5IIIwe	0.747	745.3761	-382.472$~\pm~$0.026	1	-379.0$~\pm~$2.0	8			mp
13806	+29 503	G5	0.855	740.6419	+26.472$~\pm~$0.027	1	+22.7$~\pm~$2.0	1	+26.62$~\pm~$0.21	3	Hya (vB 153)
13834	18404	F5IV	0.415	501.2739	+27.974$~\pm~$0.106	1	+28.1$~\pm~$2.0	2			Hya
15720	-	-	1.431	739.5265	+30.066$~\pm~$0.085	1			+28.90$~\pm~$0.45	5	Hya
16529	+23 465	G5	0.844	745.4760	+32.188$~\pm~$0.030	1	+32.0$~\pm~$5.0	1	+32.72$~\pm~$0.28	3	Hya (vB 4)
19148	25825	G0	0.593	740.4366	+37.657$~\pm~$0.026	1	+36.1$~\pm~$2.0	1	+38.04$~\pm~$0.17	3	Hya (vB 10)
19504	26345	F6V	0.427	737.4273	+36.379$~\pm~$0.449	1	+34.5$~\pm~$2.0	2	+37.10$~\pm~$0.30	5	Hya (vB 13)
19655	-	M0V:	1.216	739.5412	-10.156$~\pm~$0.022	2					UMa
19786	26767	G0	0.640	741.5809	+38.420$~\pm~$0.027	1	+39.1$~\pm~$2.0	1	+38.29$~\pm~$0.03 $\dag$	9	Hya (vB 18)
19796	26784	F8V	0.514	738.4939	+38.302$~\pm~$0.089	1	+36.8$~\pm~$2.0	2	+38.50$~\pm~$0.15	3	Hya (vB 19)
20205	27371	G8III	0.981	498.3456	+38.696$~\pm~$0.014	2	+38.7$~\pm~$0.9	2	+39.28$~\pm~$0.11	3	Hya (vB 28)
20205	27371	G8III	0.981	745.5277	+38.693$~\pm~$0.014	1	+38.7$~\pm~$0.9	2	+39.28$~\pm~$0.11	3	Hya (vB 28)
20237	27406	G0V	0.560	498.3996	+38.514$~\pm~$0.061	1	+39.5$~\pm~$2.0	2	+38.81$~\pm~$0.18	3	Hya (vB 31)
20357	27561	F5V	0.412	741.5211	+39.252$~\pm~$0.148	1	+37.7$~\pm~$2.0	1	+39.20$~\pm~$0.33	3	Hya (vB 37)
20557	27808	F8V	0.518	738.5569	+38.339$~\pm~$0.025	1	+34.8$~\pm~$2.0	2	+38.94$~\pm~$0.13	3	Hya (vB 48)
20889	28305	K0III	1.014	498.3724	+38.641$~\pm~$0.013	2	+39.0$~\pm~$5.0	2	+39.37$~\pm~$0.06	3	Hya (vB 70)
20889	28305	K0III	1.014	745.5351	+38.541$~\pm~$0.013	1	+39.0$~\pm~$5.0	2	+39.37$~\pm~$0.06	3	Hya (vB 70)
20899	28344	G2V	0.609	501.3387	+39.426$~\pm~$0.027	1	+39.8$~\pm~$2.0	2	+39.15$~\pm~$0.03 $\ddag$	9	Hya (vB 73)
20949	283704	G5	0.766	737.5852	+38.795$~\pm~$0.030	1	+36.8$~\pm~$2.0	1	+39.02$~\pm~$0.17	3	Hya (vB 76)
21261	285837	-	1.197	745.6615	+40.335$~\pm~$0.058	1			+41.43$~\pm~$0.15	3	Hya (J 291)
21317	28992	G1V	0.631	737.4956	+40.427$~\pm~$0.026	1	+42.0$~\pm~$5.0	1	+40.78$~\pm~$0.21	3	Hya (vB 97)
21637	29419	F5	0.576	502.3667	+39.289$~\pm~$0.023	1	+40.0$~\pm~$5.0	1	+39.86$~\pm~$0.29	3	Hya (vB 105)
21741	284574	K0V	0.811	738.6277	+40.395$~\pm~$0.032	1	+39.5$~\pm~$2.0	1	+41.34$~\pm~$0.16	3	Hya (vB 109)
22654	284930	K0	1.070	745.5827	+41.852$~\pm~$0.033	1			+42.88$~\pm~$0.25	3	Hya (L 98)
23214	31845	F5V	0.450	739.5863	+42.561$~\pm~$0.436	1	+44.1$~\pm~$2.0	1	+42.50$~\pm~$1.50	5	Hya
23312	+04 810	K2	0.957	739.6266	+43.173$~\pm~$0.037	1			+42.21$~\pm~$0.40	5	Hya
27913	39587	G0V	0.594	499.4425	-11.705$~\pm~$0.018	2	-13.5$~\pm~$0.9	1	-13.00$~\pm~$0.20	7	UMa
36704	59747	G5	0.863	500.4986	-15.438$~\pm~$0.026	1			-15.74$~\pm~$0.03	9	UMa
37279	61421	F5IV-V	0.432	738.6816	-2.475$~\pm~$0.013	3	-3.2$~\pm~$0.9	1			Procyon
59496	238087	K5	1.277	500.5753	-10.581$~\pm~$0.034	2	-15.0$~\pm~$10.	2			UMa
61946	110463	K3V	0.955	498.5152	-9.493$~\pm~$0.023	1	-6.3$~\pm~$2.0	1	-9.70$~\pm~$0.30	4	UMa
64532	115043	G1V	0.603	498.4531	-8.383$~\pm~$0.027	1	-8.9$~\pm~$0.9	2	-8.50$~\pm~$0.10	4	UMa
71284	128167	F3Vwvar	0.364	739.2596	+0.307$~\pm~$0.053	2	+0.2$~\pm~$0.9	2	+0.14$~\pm~$0.03	9	std (var?)
74702	135599	K0	0.830	501.6353	-2.856$~\pm~$0.018	2			-3.15$~\pm~$0.03	9	UMa
84195	155712	K0	0.941	738.2800	+19.991$~\pm~$0.027	1					UMa
87079	163183	G0	0.619	499.6231	-4.544$~\pm~$0.024	2					UMa
87079	163183	G0	0.619	738.7318	-4.572$~\pm~$0.025	6					UMa
95447	182572	G8IVvar	0.761	740.3722	-100.104$~\pm~$0.017	1	-100.1$~\pm~$0.9	2	-100.29$~\pm~$0.03	9	std
97675	187691	F8V	0.563	738.4285	+0.217$~\pm~$0.031	1	-0.2$~\pm~$0.9	2	+0.04$~\pm~$0.03	6	std
102040	197076	G5V	0.611	745.3125	-35.215$~\pm~$0.021	1	-37.0$~\pm~$2.0	1	-35.41$~\pm~$0.03	9	std
106278	204867	G0Ib	0.828	737.3641	+6.911$~\pm~$0.013	2	+6.5$~\pm~$0.9	1	+6.36$~\pm~$0.06	6	std
113357	217014	G5V	0.666	739.5116	-33.048$~\pm~$0.012	4	-31.2$~\pm~$2.0	1	-33.23$~\pm~$0.03	9	51 Peg (var)
115949	221170	G2IV	1.027	739.3436	-121.696$~\pm~$0.027	1	-119.0$~\pm~$5.0	1	-121.40$~\pm~$0.90	7	mp
116771	222368	F7V	0.507	739.3876	+5.776$~\pm~$0.016	3	+5.0$~\pm~$0.9	1	+5.66$~\pm~$0.03	9	std

$\dag$ Griffin et al. (1988) give $v_{\rm r}=+39.32\pm 0.30$.     $\ddag$ Griffin et al. (1988) give $v_{\rm r}=+39.99\pm 0.35$.
References: 1. GCSRV (Wilson 1953); 2. Revised GCRV (Evans 1967); 3. Griffin et al. (1988, quoted error is the larger of the internal and external errors);
4. Soderblom & Mayor (1993); 5. Perryman et al. (1998); 6. Stefanik et al. (1999); 7. Barbier-Brossat & Figon (2000); 8. Beers et al. (2000);
9. Nidever et al. (2002).

When more than one good spectrum was obtained of the same star in the same observation period, Table 2 gives the weighted mean radial-velocity measure at the similarly weighted mean observation epoch; the internal standard error of the mean was calculated from the total statistical weight. The chi-square of the residuals with respect to the mean value was acceptable in all except two of these cases. For HIP 71284 (28 Boo, a known variable star) the two observations separated by only 40 min were marginally discordant ( $cz_{\rm B}=+0.472\pm 0.091$ and $+0.225\pm 0.064$ km s^-1). The other case is HIP 113357, the well-known exoplanet system 51 Peg (Mayor & Queloz 1995), where the four measurements gave $\chi^2=32$ (3 degrees of freedom). This was reduced to a satisfactory $\chi^2=2.5$ (3 degrees of freedom) after correction for the planet-induced velocity using the orbital period and phase from Bundy & Marcy (2000), whose observations span our data, and the velocity amplitude from Marcy et al. (1997). The mean value in Table 2 is for the corrected values and thus refers to the centre of gravity of the system.

Three stars (besides the Sun) were observed in both observation periods, for which (mean) results are given on separate lines in Table 2. For two of them (HIP 20205 and 87079) there is excellent agreement between the two measures. For the Hyades K giant HIP 20889 ($=\epsilon$ Tau = vB 70) the two measures differ by 0.1 km s^-1, significant at the $5\sigma$ level. This star was separately discussed by Griffin et al. (1988), who remarked upon its possible variability on the level of a few tenths of a km s^-1.

Table 2 also gives radial velocities from various other sources. The column $v_{\rm r}({\rm CDS})$ contains values from the SIMBAD data base (Centre de Données astronomiques de Strasbourg), while $v_{\rm r}({\rm other})$contains more precise values from the literature when available. A comparison of these data with our radial-velocity measures is shown in Fig. 5. The location of the Sun in the diagram is shown by the solar symbol at $B\!-\!V=0.65$, $v_{\rm r}-cz_{\rm B}=-0.257$ km s^-1. Two sets of differences are especially worth noting. (1) The crosses are for the photoelectric radial velocities of Hyades stars by Griffin et al. (1988). The mean difference for the stars with $B\!-\!V<0.9$ (which excludes the two giants) is +0.45 km s^-1, with some apparent trend depending on colour index or magnitude. Compared with the solar value, this suggests that the Griffin et al. velocities require a correction of $\simeq$-0.7 km s^-1for the late F and G stars in order to put them on the kinematic velocity scale. (2) The filled triangles are for the nine stars in common with the list of very precise absolute radial velocities by Nidever et al. (2002). Here, the mean difference is -0.21 km s^-1 and the RMS scatter of differences only 0.07 km s^-1. Nidever et al. use the Solar Flux Atlas as a template for the F, G and K stars, so the mean difference is expected to be close to the solar value -0.257 km s^-1. Thus their velocity scale is consistent with ours to within 0.05 km s^-1. The differences based on radial velocities from various other sources agree on the average with the Nidever et al. data, although the scatter is substantial.

Ultimately the present radial-velocity measures may be compared with astrometric radial velocities, such as those obtained by Madsen et al. (2002), in order to derive the spectral line shifts caused by convection and other intrinsic stellar effects. However, such a comparison requires detailed consideration of many additional factors, and is therefore beyond the scope of this paper.

 

 

Table 3: Typical (median) random errors of the various reduction steps contributing to the final standard errors of the radial-velocity measures in Table 2, and estimated systematic errors. A cautionary note: while the random errors are well quantified using theory (e.g. based on photon statistics) or the results of repeated measurements, the systematic errors are little more than order-of-magnitude estimates as discussed in Sect. 7.1.

Random errors (median values):
- cross-correlation ( $\sigma_{\rm N}$), Appendix A	13 m s-1
- short-term drift ( $\sigma_{\rm D}$), Eqs. (7)-(8)	17 m s-1
- barycentric correction ( $\sigma_{\rm LOS}$), Sect. 5.4	13 m s-1
- long-term drift ($\sigma_0$), Sect. 5.5	10 m s-1
total median standard error	27 m s-1
Estimated systematic errors:
- long-term instability of the solar spectrum	30 m s-1
- long-term instability of the instrument	50 m s-1
- wavelength scale of the Solar Flux Atlas	100 m s-1
- laboratory Fe I wavelengths	30 m s-1
total systematic error	120 m s-1