3. Radial velocity determinations

3.1. fitted by a lorentz profile

Some stars of the sample rotate very fast and some are very hot, with effective temperature of about 8000 K. Therefore, these stars cannot be measured with an instrument such as Coravel, which needs many narrow lines. The adopted technique consists in fitting a lorentz profile on the line [4861.331 Å] minimising the , i.e. the differences between the lorentz profile and the observed line. The advantage of a lorentz function over a gaussian is to be more peaked at the centre, so hydrogen lines are better fitted.

A lorentz profile is defined by 3 parameters (Eq. 1): is the centre, i₀ the intensity or height and b the half-intensity width of the profile.

The three parameters of are fitted by least-squares; meanwhile the optimum choice will depend on the limits fixing the spectral range on which the fit is made. To avoid too subjective a choice, we fix on both sides of the line two points determining a segment on which the limit is randomly chosen (Fig. 1 (click here)). Thus, we generate 100 lorentz profiles with different limits on each line. A profile is taken into account only if the value does not exceed 0.05 in order to avoid hazardous fits. Then, we define for each line the mean value of the central wavelength and the dispersion:

  
Figure 1: The limits fixing the spectral range on which the fit is made are randomly chosen on two segments symmetrically placed with respect to the centre of the line

The dispersion depends on the physical properties of the star, essentially the temperature, the surface gravity and the rotation but also the quality of the spectrum, i.e. the signal-to-noise. We have chosen to distribute the measurements into categories of decreasing discrete precision on the basis of values (see Table 1 (click here)): measurements with between 0 and 3 mÅ will be considered as having , those with between 3 and 6 mÅ will have , etc. The value of 3 mÅ\ is completely arbitrary, corresponding to a radial velocity of about 0.2 kms^-1. The and the central wavelength also depend on the choice of the limits for the fit. This effect is discussed in detail in Appendix A.

 

[0.000, 0.003] 0.19

[0.003, 0.006] 0.38

[0.006, 0.009] 0.56

[0.009, 0.012] 0.74 ...

Table 1: Dispersion in radial velocity from the dispersion in wavelength

 

The term is defined as the internal error due to the effective temperature, the surface gravity, the rotation and the S/N ratio. The total internal error includes an additional term due to the instrumental drift during the night. This variability was similar for the four missions and Figs. 2 (click here) and 3 (click here) show the fluctuations of the position of the thorium lines during the night of 6 and 7 November and during the night of 5 and 6 December 1994 for 3 lines. When we filled up the nitrogen tank, at the beginning and in the middle of the night, a strong variation appeared as shown on these figures. Between these jumps, we observe a regular variation of about 0.12 pixels per hour. We therefore have a variation of 0.16 kms^-1 per 12 minutes which corresponds to the average time of stellar exposure. For this reason, the internal error due to this factor () is estimated at 0.16 kms^-1. Finally, the total internal error is written by .

  
Figure 2: Variation of the position of three lines of thorium during 6 and 7 November 1994. The vertical shift is arbitrary. The vertical line corresponds to the filling of nitrogen

  
Figure 3: Same as Fig. 2 (click here), but for the night of 5 and 6 December 1994

3.2. Standard stars

For standard stars, we prefer to use Coravel values in the system of faint IAU standard stars (Mayor & Maurice 1985) than IAU values listed in the Astronomical Almanach because the latter are taken from various authors and sometimes not updated. For example, the IAU radial velocity for HD 114762 has been listed as in the Astronomical Almanach since at least 1981, while combined data from the Cfa and Coravel give a systemic velocity of (Latham et al. 1989).

For the four observing runs, Fig. 4 (click here) shows the difference between radial velocities measured with Aurélie and the Coravel value for each standard star. Our values are higher than the Coravel ones by about 2.75 kms^-1. The error bars are defined by the quadratic sum of the internal error (see Sect. 3.1) and the dispersion on the Coravel values. The internal precision of our measurements is very impressive: we obtain a scatter of about 0.4 kms^-1 around the mean radial velocity.

  
Figure 4: Difference between Aurélie radial velocities and Coravel velocities for the runs of May, June, November and December 1994. HD 693: open squares. HD 22484: open triangles. HD 89449: crosses. HD 114762: full circles. HD 136202: full triangles. HD 222368: open circles

Notice that is clearly smaller for HD 114762 by about 1.4 kms^-1. Such a difference can partly be due to the nature of this star, which has a very small amplitude (Latham et al. 1989 and Cochran et al. 1991) and to the fact that our measurements were made precisely when the radial velocity was minimum: in this way we can explain a shift of about 0.6 kms^-1 with respect to the other standard stars. Unfortunately, we do not find any explanation for the remaining shift of 0.8 kms^-1. The reduction of the spectra was made again with MIDAS software, only to find the same shift. So, we cannot question the reduction.

We have simply subtracted the mean from the measured velocities. The average are 2.80, 2.49, 2.69 and 2.90 kms^-1 for the runs of May, June, November and December respectively. For the first run, the values of HD 114762 are not taken into account in the average value. Table 2 (click here) gives the individual corrected radial velocities and the mean velocity for standard stars; Table 3 lists the individual corrected radial velocities for the 50 giant A and F stars.

 

HD HJD I

(+2449000) kms^-1 kms^-1

693 663.367 15.12 0.28

693 692.408 15.99 0.48

693 693.411 15.57 0.28

22484 663.507 27.59 0.28

22484 663.528 27.97 0.48

22484 665.610 28.11 0.28

22484 689.403 27.45 0.28

22484 689.450 28.05 0.48

22484 692.473 27.73 0.28

22484 692.544 27.07 0.48

22484 693.546 28.62 0.28

89449 470.375 6.07 0.28

89449 471.311 6.13 0.28

89449 472.383 5.04 0.48

89449 472.433 6.87 0.69

89449 473.347 5.39 0.28

89449 474.319 6.19 0.28

89449 505.366 6.49 0.28

89449 506.346 5.83 0.28

89449 507.345 4.69 0.28

89449 509.356 6.03 0.28

89449 663.674 5.62 0.48

89449 692.618 5.88 0.28

89449 692.681 5.65 0.28

89449 693.668 5.72 0.48

89449 693.722 6.13 0.28

114762 470.503 47.51 0.48

114762 471.411 47.38 0.28

114762 472.526 47.75 0.48

114762 473.420 48.02 0.28

114762 474.432 48.01 0.28

136202 470.593 54.33 0.48

136202 471.499 54.22 0.48

136202 472.597 54.16 0.48

136202 473.555 54.30 0.48

136202 474.504 54.37 0.28

136202 505.503 54.89 0.48

136202 506.474 54.93 1.56

136202 508.381 54.48 0.48

187691 470.642 -0.58 0.28

187691 471.638 -0.07 0.28

187691 472.638 0.21 0.28

187691 473.640 -0.01 0.48

187691 474.639 -0.86 0.28

187691 505.598 0.23 0.28

187691 506.558 -0.08 0.48

187691 507.599 -0.39 0.28

187691 509.501 -1.30 0.48

222368 663.287 4.76 0.28

222368 663.395 5.67 0.28

222368 689.321 4.98 0.48

222368 690.296 4.39 0.28

222368 692.320 5.23 0.28

222368 693.300 5.62 0.28

 

 

(+2449000) kms^-1 kms^-1

1671 663.445 10.53 0.48

1671 689.354 10.55 0.28

1671 693.444 10.34 0.48

2628 663.451 -10.86 0.28

2628 689.366 -10.67 1.12

2628 693.448 -10.40 0.28

4338 663.410 2.08 0.69

4338 689.381 -0.47 1.34

4338 693.470 5.84 0.94

6706 663.426 23.81 0.28

6706 692.487 23.57 0.69

10845 663.458 -13.97 0.48

10845 689.412 -13.67 0.90

11522 663.436 1.16 0.69

11522 693.514 1.99 1.34

12573 663.471 8.62 0.69

12573 692.522 7.38 0.90

17584 689.423 18.41 0.94

17584 663.481 18.60 0.90

17584 692.387 19.42 0.69

17918 663.491 17.21 0.48

17918 663.552 18.40 0.69

17918 689.434 17.11 0.90

17918 692.396 18.08 0.90

21770 663.500 -46.18 0.28

21770 689.444 -46.35 0.48

21770 692.469 -46.01 0.28

24832 663.538 20.61 1.56

24832 692.433 18.20 0.90

24832 693.569 22.67 0.69

30020 663.570 34.31 0.69

30020 692.567 37.19 0.48

30020 693.609 37.87 0.90

34045 663.591 29.89 0.48

34045 689.467 26.19 0.94

34045 692.587 29.18 0.48

48737 663.606 26.12 0.90

48737 665.620 26.30 0.48

48737 689.459 25.77 0.48

48737 692.598 27.35 0.69

48737 693.630 27.56 0.48

50019 663.611 31.17 0.69

50019 664.643 30.75 0.69

50019 665.626 30.30 0.69

50019 692.601 30.04 0.69

50019 693.633 32.39 0.90

60489 663.617 52.67 0.69

60489 665.645 53.42 0.69

60489 692.608 30.81 0.48

60489 693.650 31.65 0.28

62437 663.627 11.13 0.48

62437 665.677 14.46 1.34

Table 3: Radial velocities of A and F giants

 

 

(+2449000) kms^-1 kms^-1

62437 692.628 15.99 0.28

62437 693.639 14.12 0.69

69997 663.642 31.67 0.28

69997 692.641 32.79 0.28

69997 692.703 33.18 0.28

69997 693.661 32.59 0.28

82043 663.652 12.25 0.48

82043 692.649 1.73 0.69

82043 692.712 1.41 0.69

82043 693.679 0.14 0.48

84607 663.660 13.65 0.48

84607 692.660 12.25 0.69

84607 692.723 13.50 0.69

84607 693.690 13.09 0.48

86611 663.688 26.47 0.90

86611 692.669 24.42 0.90

86611 692.732 25.79 0.69

86611 693.699 25.04 1.34

89025 692.676 -21.20 0.69

89025 693.710 -22.07 0.28

92787 692.689 4.47 0.90

92787 692.692 4.47 0.90

92787 693.715 3.82 0.48

100418 470.406 1.02 0.69

100418 471.327 0.76 0.58

100418 471.390 -0.57 0.69

100418 472.398 2.28 0.28

100418 473.336 0.22 0.69

100418 474.359 -1.81 0.48

100418 506.372 -0.28 0.28

103313 470.461 16.10 0.69

103313 471.340 16.75 0.48

103313 471.463 14.71 0.28

103313 472.413 19.14 0.90

103313 473.359 17.59 0.69

103313 473.440 17.88 0.90

103313 474.378 16.54 0.69

103313 474.414 16.72 0.48

103313 505.387 22.17 1.56

103313 507.364 18.64 0.48

103313 507.397 15.74 2.01

104827 470.475 10.21 0.48

104827 471.352 8.07 0.90

104827 471.399 7.33 0.48

104827 472.443 7.70 0.48

104827 473.373 7.60 0.48

104827 473.482 8.42 0.48

104827 474.332 7.37 0.69

104827 474.479 6.93 0.48

104827 506.394 8.89 0.48

108382 470.486 -2.33 0.48

108382 471.364 -1.97 0.48

108382 471.471 -1.82 0.48

108382 472.457 -2.86 0.69

108382 473.383 -1.97 0.90

108382 473.430 -2.71 0.69

108382 474.345 -1.55 0.90

 

(+2449000) kms^-1 kms^-1

118295 470.535 -20.00 0.69

118295 471.375 -19.63 0.69

118295 471.447 -17.52 1.56

118295 472.470 -20.59 0.69

118295 473.401 -18.46 0.94

118295 474.394 -17.76 0.69

118295 505.410 -24.23 0.94

118295 506.420 -19.84 1.34

108382 474.446 -1.89 0.90

122703 470.522 -17.63 0.69

122703 471.430 -13.34 0.90

122703 471.485 -21.60 0.69

122703 472.509 -19.21 2.01

122703 473.455 -15.39 0.69

122703 474.464 -17.16 0.94

150453 471.521 0.82 0.69

150453 471.620 0.47 0.69

150453 472.586 0.12 0.28

150453 473.541 0.64 0.48

150453 474.568 -0.10 0.28

150453 506.486 1.54 0.28

150557 471.510 -49.75 0.48

150557 472.492 -49.42 0.69

150557 473.496 -48.36 0.90

150557 474.494 -49.64 0.69

150557 474.540 -50.22 0.48

150557 505.532 -48.20 0.48

150557 506.412 -48.49 0.94

150557 506.467 -50.15 0.28

150557 509.393 -49.60 0.48

155646 470.552 59.76 0.48

155646 471.535 61.08 0.48

155646 472.542 62.36 0.48

155646 473.518 59.78 0.28

155646 474.524 58.64 0.48

155646 505.545 60.05 0.48

155646 506.445 59.95 0.28

155646 506.547 60.70 0.28

159561 470.565 10.69 0.69

159561 471.543 11.10 0.48

159561 472.550 12.23 0.69

159561 472.631 10.25 0.94

159561 473.527 12.03 0.90

159561 474.510 10.82 0.69

159561 505.431 11.46 0.90

159561 506.457 10.65 0.48

159561 507.608 9.68 0.69

159561 509.446 8.29 0.48

171856 470.639 -5.56 2.01

171856 473.620 -5.96 1.34

171856 506.584 -21.70 0.48

171856 508.544 -19.14 0.69

174866 470.625 -39.39 0.94

174866 472.615 -38.50 0.69

174866 473.606 -40.45 0.48

174866 505.585 -40.89 0.90

174866 506.571 -43.56 1.34

174866 509.521 -42.08 0.69

 

(+2449000) kms^-1 kms^-1

176971 470.575 -34.62 0.90

176971 471.553 -34.28 0.48

176971 472.559 -31.63 0.69

176971 473.560 -35.13 0.48

176971 474.579 -33.63 0.69

176971 474.625 -34.88 1.34

176971 505.461 -34.60 0.94

176971 506.517 -32.51 0.69

176971 509.414 -29.47 1.78

177392 470.608 10.13 0.48

177392 471.577 9.51 1.56

177392 472.603 12.38 0.69

177392 473.580 10.12 0.90

177392 474.593 6.75 0.90

177392 505.481 11.21 0.90

177392 506.502 10.31 2.01

177392 508.525 6.75 0.90

177392 509.459 8.69 0.28

177392 509.539 7.37 0.90

178187 470.600 -24.85 0.69

178187 471.563 -24.43 0.69

178187 472.568 -24.82 0.48

178187 473.570 -25.11 0.94

178187 474.602 -24.69 0.90

178187 505.440 -24.69 0.69

178187 505.518 -25.04 0.90

178187 506.531 -25.03 0.90

178187 507.585 -22.70 0.48

178187 508.506 -23.06 0.69

186005 472.623 -40.39 1.34

186005 474.634 -39.98 0.90

186005 506.593 -39.50 0.90

186005 509.593 -42.63 0.48

187764 471.598 -8.02 0.69

187764 473.589 -5.96 0.48

187764 474.551 -8.39 0.90

187764 474.612 -4.71 0.90

187764 505.560 -6.14 0.69

187764 506.554 -3.10 0.69

187764 509.477 -4.64 0.69

190172 471.628 2.82 0.48

190172 473.628 6.00 0.28

190172 506.602 3.11 0.48

203842 663.228 -25.94 0.69

203842 665.246 -27.74 0.48

203842 690.313 -26.43 0.69

203842 692.296 -24.73 0.90

203842 693.243 -23.22 0.48

204577 663.245 -10.45 0.48

204577 693.273 -8.69 0.69

205852 663.262 -31.90 0.90

205852 692.307 -31.83 0.69

205852 693.308 -32.48 0.69

209166 663.275 5.22 0.28

209166 692.314 6.36 0.28

209166 693.322 6.82 0.48

 

(+2449000) kms^-1 kms^-1

210516 663.295 10.46 0.69

210516 692.332 11.38 0.94

210516 693.339 12.16 0.94

216701 663.314 12.70 0.48

216701 692.352 15.26 0.69

216701 693.355 11.36 0.48

217131 663.334 -12.12 0.28

217131 693.374 -11.35 0.48

219891 663.352 -3.04 0.90

219891 689.338 -3.01 2.01

219891 693.396 -0.48 0.94

224995 663.383 8.13 0.48

224995 689.302 7.14 0.90

224995 693.431 7.48 0.69