as high as during the “quiescent” periods in
2005 and 2009. The sinusoidal models yield an
average rotation period of 130 T 2 days, whereas
the phase and (to a lesser extent) amplitude vary.
The changing phase and amplitude of the
activity-induced stellar rotation signal induce a
variable effect on the RVs, implying that the
slope of the RV-activity correlation is not strictly constant. Instead of evaluating the RV-activity
correlation as one fit over the entire data set,
we have examined RV as a function of IHa over
each observing season in the HARPS archive.
For the December 2005 to September 2007 and
January 2010 to July 2011 time frames, we have
combined two seasons, because IHa shows a
coherent rotation signal across the seasons,
suggesting that the activity behavior remains
approximately constant over these times.
We find significant RV-IHa anticorrelations
(r = –0.45, –0.55, and –0.48) for three of the five
epochs. These three epochs have RMS values of
1.22 × 10–3, 1.10 × 10–3, and 1.31 × 10–3 in IHa, as
opposed to RMSIHa = 4.81 × 10–4 and 4.19 × 10–4
in the other seasons, suggesting that the star is
approximately twice as active during these times.
Although we have removed planets b, c, and e
from the RVs, we find that once planet b has
been removed, the correlation coefficients do not
change significantly before and after removing c
and e. The anticorrelation is particularly striking
for the 2010 season, shown in Fig. 1.
We correct the HARPS RVs by subtracting
the best-fit RV-IHa relation from each of the
three epochs for which we observed a significant anticorrelation, leaving the other epochs
unchanged. A new RV model then can be used
to evaluate the effect of the activity correction
on the known exoplanets and to determine
whether any additional signals exist. We detect
the known planets b, c, and e using the generalized Lomb-Scargle periodogram (19) (Fig. 2).
For planets c and e, we observe significant increases in signal power upon correcting for activity. The power of planet c increases from 53.5
to 57.6, while the power of e increases from 23.5
to 30.3. Formally, false-alarm probability (FAP)
[from (11)] scales approximately as e–P ffiffiffi P p for a
Lomb-Scargle periodogram with power P; thus,
the power increase translates to a decrease in
FAP by a factor of 60 for planet c and 800 for
In contrast, the power of planet d drops from
31.4 to 11.6 after we apply our activity correction.
As shown in Fig. 1, the periodogram power increases as a planet would during periods of high
activity but decreases over the epoch with lowest
RMSIHa. Planet d has a reported period of 66 days,
which is roughly equal to half the stellar rotation
period, suggesting that it is a harmonic that loses
significance when the rotation signal is removed
via decorrelating with IHa.
In Table 1, we list the parameters of our three-planet model to the activity-corrected HARPS
RVs. We fit the RVs using the GaussFit (20) and
Systemic (21) software packages, finding good
agreement between the two. Our model does
not differ much from previous fits to planets b,
c, and e (3, 8, 9), except that planet e no longer
shows any eccentricity after the activity correction. In the corrected RVs, the 66-day signal appears only at the 1.5-SD significance level in the
residual periodogram, and the 33- or 36-day
signal does not appear at all. We conclude that
the three-planet solution with activity-induced
variability fully explains the observations.
We assert that the periodic RV signal at 66 days
is an artifact induced by the stellar rotation rather than an exoplanet. Previous studies (3, 7) discounted starspot-induced rotational modulation
as the origin of RV signals corresponding to planets
d and g because the low photometric variability of the star suggests that any spots present
should be too small to create the observed signals. However, spatially localized magnetic
442 25 JULY 2014 • VOL 345 ISSUE 6195
Fig. 2. Periodograms for the HARPS RVs before (blue) and after (red) correcting for stellar activity, with the planets successively subtracted. In the
bottom panel, we also show (pink) the periodogram after subtracting four circular Keplerian signals, illustrating that the signal interpreted as 581 g (7, 9) was
caused by fitting a sinusoidal signal to the 581d signal and performing, in essence, an incomplete correction for stellar activity.