Is there any limit to the radialvelocity precision

Only a couple of years ago, a part of the astronomical community believed that stellar noise would prevent reaching the 1 ms_1 precision level. Indeed, since such precision was not available then, the behavior of the stars below 3 ms-1 was completely unknown.

Reference

McArthur et al. (2004) Santos et al. (2004) Butler et al. (2004a) Udry et al. (2005) Bonfils et al. (2005) Rivera et al. (2005) Marcy et al. (2005)

Table 1. Summary table of the recently discovered Neptune-mass planets. The lowest m2 sin i of 5.9 ms-1 was obtained for Gl876d, while the lowest m2 sinijm\ of 4.2 x 10~5 was achieved on [ Arac.

Planet

P

m2 sin i

(o-c)

m2 sin i/m1

[days]

[M®]

[m s 1]

[x10~5]

55 Cnc e

2.81

14

5.4

4.7

H Ara c

9.6

14

0.9

4.2

Gl436b

2.6

21

5.26

16.0

HD 4308 b

15.6

14

1.3

5.4

Gl 581b

4.96

16.6

2.5

17.1

Gl 876 d

1.94

5.9

4.6

6.0

HD 190360 c

17.1

18

3.5

6.0

Table 1. Summary table of the recently discovered Neptune-mass planets. The lowest m2 sin i of 5.9 ms-1 was obtained for Gl876d, while the lowest m2 sinijm\ of 4.2 x 10~5 was achieved on [ Arac.

Figure 3. In order to illustrate the extraordinary stability of HARPS, we plot here the measured physical position of one single calibration spectrum line (thorium lamp) on the CCD as a function of time. The line position is expressed directly in the CCD pixel scale and does not include any calibration. It can be seen that the line remains at the same location on the CCD within ~1ms_1, which is the approximate photon-noise precision obtained on the centroid measurement of the spectral line. This diagram demonstrates that the instrument remained intrinsically stable during more than a month, without calibration!

Figure 3. In order to illustrate the extraordinary stability of HARPS, we plot here the measured physical position of one single calibration spectrum line (thorium lamp) on the CCD as a function of time. The line position is expressed directly in the CCD pixel scale and does not include any calibration. It can be seen that the line remains at the same location on the CCD within ~1ms_1, which is the approximate photon-noise precision obtained on the centroid measurement of the spectral line. This diagram demonstrates that the instrument remained intrinsically stable during more than a month, without calibration!

However, with the increased precision of the HARPS instrument (Pepe et al. 2005), suddenly it became possible to explore this new radial-velocity range.

In the laboratory, we could easily prove that the instrumental stability of HARPS is unequaled (see Figure 3). During the instrument commissioning period, intense astero-seismological observations were carried out to monitor its short-term (^nights) precision. Besides demonstrating that the short-time precision was better than 20cms~1, these observations also revealed the fact that almost every star presents p-mode oscillations at this precision level. Such p-modes could clearly and directly be identified in the high-frequency measurement series obtained on several sample stars (Figure 4).

Figure 4. Summary plot of the radial-velocity measurements of stars for which we have made long observations series. All of them show clear indications of stellar pulsations.

From these measurements it immediately became evident that HARPS' capability for planet search was not limited by the instrument's performance, but rather by the stars themselves. Indeed, stellar p-mode oscillations on a short-term scale, and stellar jitter on a long-term scale, introduce obvious radial-velocity noise that cannot be mistaken at the precision level of HARPS. For instance, even a very 'quiet' G or K dwarf shows oscillation modes of several 10 cms-1. These modes might combine and finally add up to radialvelocity amplitudes as large as several ms-1. Moreover, any exposure with an integration time shorter than the oscillation period of the star might arbitrarily fall on any phase of the pulsation cycle, leading to additional radial-velocity noise. This phenomenon may seriously compromise the ability to detect very low-mass planets around solar-type stars using radial-velocity measurements.

In June 2004, a group of European astronomers (Santos et al. 2004; Bouchy et al. 2005) proved that p-mode radial-velocity variability was not an issue for detecting very-low mass planets, providing some conditions are met. During asteroseismology campaigns on the star j Ara, they measured its p-oscillation modes, but in addition, they also observed an unexpected coherent night-to-night variation in very small semi-amplitude of 4.1ms_1. This was later confirmed to be the signature of a planetary companion of m2 sin i = 14 with an orbital period of P = 9.6 days (see Figure 5). This discovery demonstrated that oscillation noise can be averaged out to unveil a small radial-velocity signature of a Neptune-mass planet companion—if the total integration time chosen is sufficiently long when compared to the oscillation period. It must also be mentioned that

012345678 BJD - 2 453 160

Figure 5. Asteroseismology observations of j Ara. Although the dispersion of the radial velocity caused by stellar oscillations can rise 10 ms-1 amplitudes, one easily sees the 'low-frequency' variation induced by the planetary companion on the daily radial-velocity average.

012345678 BJD - 2 453 160

Figure 5. Asteroseismology observations of j Ara. Although the dispersion of the radial velocity caused by stellar oscillations can rise 10 ms-1 amplitudes, one easily sees the 'low-frequency' variation induced by the planetary companion on the daily radial-velocity average.

the pulsations of j Ara have high amplitudes up to 10 ms_1 P — V. This object represents, therefore, almost the worst case scenario if high precision is the aim. Despite this fact, the residuals could be decreased to the level of 0.4 ms-1 during the asteroseismology run (long integration time) and about 1ms-1 during "ordinary" runs (see Figure 6).

The semi-amplitude of the radial-velocity wobble of j Ara c-like objects is hardly larger than typical stellar p-mode oscillations. As mentioned above, the discovery of Neptune-mass planets may only be feasible when applying an adequate observation strategy that includes an integration time increased beyond the typical period of stellar oscillations (i.e., more than five minutes), in order to average them out. In practice, the total integration time was fixed to 15 minutes for all the stars of the high-precision HARPS sample, independent of the stellar magnitude. An example showing the success of this strategy is presented in Figure7, which shows the low residuals of 0.9ms-1 obtained on the radial-velocity curve of the planet-harboring star HD 102117 (Lovis et al. 2005).

We followed this strategy on a set of 200 selected stars of the HARPS planet-search program. For this very high-precision survey, an accuracy better than 1ms-1 is desired for each individual measurement. So far, the results obtained demonstrate that this strategy is successful. The distribution histogram of the radial-velocity dispersion (Figure 8) peaks at 2 ms-1 and decreases rapidly towards higher values. More than 80% of these stars show dispersion smaller than 5.5 ms-1, and more than 35% have dispersions below 2.5 ms-1. It must be noted that the presented dispersion values include photon noise, stellar oscillations and jitter, and, in particular, radial-velocity wobble induced by known extrasolar planets (j Arac, HD 102117b, HD4308b, etc.), or still-undetected planetary companions.

The increase in the performance of HARPS, combined with the new observation strategy, has led to discoveries of unequaled quality. This is best illustrated by the analyzing the residuals of the orbital fits to the measured data. Figure 9 shows the fit residuals for all extrasolar planets discovered since January 2004—about the time HARPS became fully operational. The planets discovered with HARPS are marked by the dashed area; those represented by the cross-dashed area are all part of the instrument's high-precision program. Note that all the planets with rms below 3 ms-1 have been discovered with

20 M. Mayor et al.: The quest for very low-mass planets

HD 160691 HARPS

20 M. Mayor et al.: The quest for very low-mass planets

HD 160691 HARPS

53160 53180 53200 53220 53240

JD-2400000 [days]

Figure 6. HARPS radial-velocity measurements of j Ara as a function of time. The filled line represents the best fit to the data, obtained with the sum of a keplerian function and a linear trend, representing the effect of the long-period companions to the system. The residuals of the fit to the data, only 0.9 m s-1 rms, are shown in the lower panel. Note that for the measurements obtained during the asteroseismology run (longer total integration), the residuals of the orbital fit to the data is as low as 0.4 ms-1.

53160 53180 53200 53220 53240

JD-2400000 [days]

Figure 6. HARPS radial-velocity measurements of j Ara as a function of time. The filled line represents the best fit to the data, obtained with the sum of a keplerian function and a linear trend, representing the effect of the long-period companions to the system. The residuals of the fit to the data, only 0.9 m s-1 rms, are shown in the lower panel. Note that for the measurements obtained during the asteroseismology run (longer total integration), the residuals of the orbital fit to the data is as low as 0.4 ms-1.

HARPS. This clearly demonstrates that the precision of HARPS is about a factor of two higher than any other existing instrument.

Since the discovery of the very low-mass companion of j Ara, similar objects have been discovered (see Table 1). These planetary companions begin to populate the lower end of the secondary-mass distribution, a region so far affected by detection incompleteness. The discovery of these very low-mass planets close to the detection threshold of radial-velocity surveys suggests that this kind of object may be rather frequent. But just the simple existence of such planets could cause headaches for the theoretician. Indeed, statistical considerations predict that planets with a mass 1-0.1 MSat and with semi-major axis of 0.1-1 AU must be rare (Ida & Lin 2004, see also next section for details). At least for the moment, the recent discoveries contradict these predictions. In any case, the continuous detection of planets with even lower masses will set new constraints to possible planetary system formation and evolution models.

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