activity has been observed to influence RV in M
stars without producing spots with high optical
contrast. Striking similarities exist with our ob-
served activity-RV correlation results for GJ 581
and those reported for Barnard’s star, a slow-
rotating, photometrically quiet M dwarf of sim-
ilar spectral type. Observations with the Ultra-
violet and Visual Echelle Spectrograph (UVES)
found an RV-IHa anticorrelation value of r = –
0.498, almost identical to that observed herein
(22). Kürster et al. attribute this phenomenon to
magnetically active regions that stimulate Ha
emission but do not produce spots of high
contrast. These regions impede local convection,
leading to an RV shift. Evidence for a relation
between chromospheric activity, Ha emission,
and convective suppression has also been
observed in the form of a temperature/radius
dependence on Ha activity for low-mass stars
(23). The anticorrelation (i.e., the negative
slope) for RV versus IHa suggests that the stellar
lines used for RV determination are emitted
from a region of convective overshoot.
Although the activity-induced RV we observe
may not be due to “typical” dark starspots, localized, rotating regions that magnetically alter
the convective velocity field would create RV signatures equivalent to spots. In the absence of
simultaneous high-precision photometric monitoring, it is difficult to deduce the relative contributions of these different mechanisms. We
therefore refer to these as active regions (ARs)
hereafter. A single rotating starspot creates an
RV signal at the rotation period and injects
power at a number of its harmonics, primarily
Prot/2, Prot/3, and Prot/4 (24). For the purposes
of exploring the qualitative impact of such ARs
on RV, a starspot model should suffice. For a ro-
tation period of 130 days, the activity-induced RV
signal always includes significant power near the
period of planet d. We present two hypotheses for
the lack of an observed signal at the periodogram
around 130 days. One explanation lies in the
geometry of the star and its ARs. The shape of
an activity-induced RV signal changes as a func-
tion of the stellar inclination and the latitudes of
the ARs, sometimes transferring RV power out
of the rotation period into its harmonics. As an
illustration, in an analysis using the SOAP (Spot
Oscillation and Planet) code (24) (fig. S7), for an
inclination of 50° for the star [consistent with
that of its debris disk (4)] and spots near the
stellar equator, the spot-induced RVs are domi-
nated by the 66-day signal. A more important
factor, though, is that for the 2010 to 2011 ob-
serving epoch, the Ha activity contains two sig-
nals of roughly equal power at 128 and 69 days,
indicating the presence of two ARs instead of
one. In this epoch, we find (fig. S4) that the
activity-RV correlation is driven by the 69-day
signal rather than the rotation period, indicat-
ing that activity is injecting RV power at half
the rotation period while two ARs are present.
The addition of power at half the rotation period
for 109 of 240 observations explains the domi-
nance of the Prot/2 signal.
Our activity analysis also helps explain why
the signal ascribed to planet d is not observed
in the Keck/HIRES RVs alone (11). We have computed IHa for the HIRES spectra, which we show
alongside the HARPS measurements in Fig. 3.
The HIRES data only cover the last portion of the
active phase from December 2005 to September
2007 and have very little coverage in 2010 to
2011, where two ARs drive the 66-day period.
Coupled with the higher reported error bars of
HIRES compared with HARPS, this yields a non-detection of the 66-day signal.
The signal of the 33- or 36-day “planet g,” the
existence of which has already been called into
question, is also an artifact of stellar rotation
because no hint of it remains after the activity
correction. Close to P = Prot/4, it is another harmonic of the rotation period. Furthermore, the
signal is only observed when fitting a circular
orbit to “planet d,” as shown in the bottom panel
of Fig. 2 (7–9). By fitting a circular Keplerian
model to the 66-day signal, Vogt et al. (7) essentially performed an incomplete stellar activity
correction, and the signal of “planet g” was simply leftover noise created by stellar activity.
The impact of stellar activity on the GJ 581
system demonstrates the crucial importance of
understanding and treating the presence of activity signals in the quest for low-mass planets.
Our activity correction clearly distinguishes between planetary and stellar signals and reduces
the astrophysical noise in the data sufficiently
that the signals of very low-mass planets are
recovered at much higher significance. This analysis also naturally explains the correlated (red)
noise seen in analysis of the HARPS and HIRES
data (11).
Given the advantages of RV surveys of slow-rotating low-mass M dwarfs for RV searches, the
physical mechanism that inhibits the convective
motion in the stellar atmosphere should be the
Fig. 3. Ha indices from HARPS (red) and HIRES (purple). The periods of greatest rotational modulation are shaded. Note the sparse HIRES coverage in the last shaded region, where the signal of the
66-day signal is strongest in both RV and IHa.
Table 1. Orbital solution for GJ 581 planets after correcting for stellar activity. AU, astronomical
units; BJD, barycentric Julian date.
Orbital parameter Planet b Planet c Planet e
Period P(days) 5.3686 T0.0001 12.914 T0.002 3.1490 T0.0002
Periastron passage T0
(BJD –2, 450,000)
4751.76 T0.01 4759.2 T0.1 4752.33 T0.05
RV amplitude K (m/s) 12.6 T 0.2 3.3 T 0.2 1.7 T 0.2
Eccentricity e 0.00 T0.03 0.00 T0.06 0.00 T0.06
Semimajoraxis a(AU) 0.04061 T0.00003 0.0721 T0.0003 0.02815 T0.00006
Minimum mass M sin i (M⊕) 15.8 T 0.3 5.5 T 0.3 1.7 T 0.2
Zero-point RV offset (m/s) –0.52 T 0.1
RMS (m/s) 2.12
