2
5
10
20
50
100
300
1000
Period [days]
0
10
20
30
40
∆
ln L
1% FAP
P
1
= 82.9 days
P
2
= 85 days
~317 days
m
2
- HARPS pre-2016
a
2
5
10
20
50
100
300
1000
Period [days]
0
10
20
30
40
∆
ln L
1% FAP
P
1
~ 75 days
P
2
~ 38 days
8.39 days
m
2
- HARPS PRD
b
Extended Data Figure 4:
Signal searches on the width of the spectral lines. Likelihood peri-
odogram searches on the width of the mean spectral line as measured by
m
2
for the HARPS pre-2016
(panel a) and HARPS PRD data (panel b). The signals in the HARPS pre-2016 data are comparable
to the photometric period reported in the literature and the variability in the HARPS PRD run com-
pares quite well to the photometric variability. Black, red and blue lines represent the search for a
first, second and third signal respectively.
correlations.
5.4
Width of the mean spectral line as measured by m
2
.
The
m
2
measurement contains a strong variability that closely mirrors the measurements from the
photometric time-series (see Figure 3 in the main manuscript). As in the photometry, the rotation
period and its first harmonic (∼
40 days) are clearly detected in the PRD campaign (see Extended
data Figure 4). This apparently good match needs to be verified on other stars as it might become
a strong diagnostic for stellar activity in M-stars. The analysis of the HARPS pre-2016 also shows
very strong evidence that
m
2
is tracing the photometric rotation period of 83 days. The modelling
of this HARPS pre-2016 requires a second sinusoid with
P
2
∼ 85 days, which is peculiar given how
close it is to
P
1
. We suspect this is caused by photospheric features on the surface changing over
time.
5.5
Asymmetry of the mean spectral lines as monitored by m
3
The periodogram analysis of
m
3
of the PRD run suggests a signal at 24 days which is close to twice
the Doppler signal of the planet candidate (see Extended Data Figure 5). However, line asymmetries
are expected to be directly correlated with Doppler signals, not at twice nor integer multiples of the
Doppler period. In addition, the peak has a FAP∼ 5% which makes it non-significantly different
from white noise. When looking at the HARPS pre-2016 data, some strong beating is observed
at 179 and 360 days, which is likely caused by a poorly sampled signal at that period or longer
(magnetic cycle?), or some residual systematic effect (contamination by tellurics?). In summary,
m
3
does not show evidence of any stable signal in the range of interest.
24
2
5
10
20
50
100
300
1000
Period [days]
0
10
20
30
40
50
60
∆
ln L
1% FAP
P
1
=179 or 360 days
16.9 days
m
3
- HARPS pre-2016
a
2
5
10
20
50
100
300
1000
Period [days]
0
5
10
15
20
25
∆
ln L
1% FAP
24.2 days
m
3
- HARPS PRD
b
Extended Data Figure 5:
Signal searches on the assymetry of the spectral lines. Likelihood
periodogram searches on the line asymmetry as measured by
m
3
from the HARPS pre-2016 (panel
a) and HARPS PRD (panel b) datasets. A signal beating at ∼ 1 year and 1/2 year is detected in the
HARPS pre-2016 data, possibly related to instrumental systematic effects or telluric contamination.
No signals are detected above 1% threshold in the HARPS PRD campaign. Black and red lines
represent the search for first and second signals respectively.
5.6
Signal searches in S-index.
While H
α
52
and other lines like the sodium doublet (NaD1 and NaD2)
63
have been shown to be the
best tracers for activity on M-dwarfs, analyzing the time-series of the S-index is also useful because
of its historical use in long term monitoring of main-sequence stars.
64
In Extended Data Figure 6
we show the likelihood ratio periodograms for the
S-indices of the HARPS pre-2016 and PRD
time-series. As can be seen, no signals were found around the 11 day period of the radial velocity
signal, however two peaks were found close the 1% false alarm probability threshold with periods
of ∼170 and 340 days. In order to further test the reality of these possible signals, we performed a
Lomb-Scargle (LS) periodogram analysis
44
of the combined PRD and pre-2016 HARPS data. This
test resulted in the marginal recovery of both the 170 and 340 day peaks seen in the likelihood
periodograms, with no emerging peaks around the proposed 11 day Doppler signal. The LS tests
revealed some weak evidence for a signal at much lower periods, ∼7 days and ∼30 days.
Given that there is evidence for significant peaks close to periods of 1 yr, its first harmonic,
and the lunar period, we also analysed the window function of the time-series to check if there
was evidence that these peaks are artefacts from the combination of the window function pattern
interfering with a real long-period activity signal in the data. The dominant power in the window
function is found to increase at periods greater than 100 days, with a forest of strong peaks found in
that domain, in comparison to sub-100 day periods which is very flat, representing the noise floor of
the time-series. This indicates that there is likely to be strong interference patterns from the sampling
in this region, and that the signal in the radial velocity data is also not due to the sampling of the
data. A similar study in the context of the HARPS M-dwarf program was also done on Proxima.
63
They compared several indices and finally decided to use the intensity of the chromospheric sodium
25