(11.2-d was typically favoured, but alternative periods caused by a non-trivial window function at
13.6-d, 18.3-d were also found to be possible). The data taken in 2016 exclusively corresponds to
the new campaign specifically designed to address the sampling issues.
2.5
HARPS : Pale Red Dot campaign.
PRD was executed between Jan 18th and March 30th, 2016. Few nights interruptions were an-
ticipated to allow for technical work and other time-critical observations with HARPS. Of the 60
scheduled epochs, we obtained 56 spectra in 54 nights (two spectra were obtained in two of those
nights). Integration times were set to 1200 s, and observations were always obtained at the very end
of each night. All the HARPS spectra (raw, extracted and calibrated frames) are publicly available
in their reduced form via ESO’s archive at
http://archive.eso.org/cms.html
.
3
Spectroscopic indices
Stellar activity can be traced by features in the stellar spectrum. For example, changes in the line-
profile shapes (symmetry and width) have been associated to spurious Doppler shifts.
18, 51
Chromo-
spheric emission lines are tracers of spurious Doppler variability in the Sun and they are expected to
behave similarly for other stars.
52
We describe here the indices measured and used in our analyses.
3.1
Measurements of the mean spectral line profiles.
The HARPS Data Reduction Software provides two measurements of the mean-line profile shapes
derived from the cross-correlation function (CCF) of the stellar spectrum with a binary mask. These
are called the bisector span (or BIS) and full-width-at-half-maximum (or FWHM) of the CCF.
53
For
very late type stars like Proxima, all spectral lines are blended producing a non-trivial shape of the
CCF, and thus the interpretation of the usual line-shape measurements is not nearly as reliable as in
earlier type stars. We applied the Least-Squares Deconvolution (LSD) technique
54
to obtain a more
accurate estimate of the spectral mean line profile. This profile is generated from the convolution of
a kernel, which is a model spectrum of line positions and intensities, with the observed spectrum.
A description of our implementation of the procedure, applied specifically to crowded M-dwarf
spectra is described in.
55
The LSD profile can be interpreted as a probability function distribution
that can then be characterized by its central moments.
56
We computed the second (
m
2
) and third
(
m
3
) central moments of each LSD-profile of each observation. More details of these indices and
how they compare to other standard HARPS cross-correlation measurements can be found in.
11
To
eliminate the correlation of the profile moments with the slope of the spectral energy distribution,
11
we corrected the SED and blaze function to match the same spectral energy distribution of the highest
S/N observation obtained with HARPS. Uncertainties were obtained using an empirical procedure
as follows: we derived all the
m
2
and
m
3
measurements of the high-cadence night of May 7th 2013
and fitted a polynomial to each time-series. The standard deviation of the residuals to that fit was
then assumed to be the expected uncertainty for a S/N∼20 (at reference echelle aperture number
16
60), which was the typical value for that night’s observations. All other errors were then obtained by
scaling this standard deviation by a factor of
20
S/N
obs
for each observation.
3.2
Chromospheric indices.
Chromospheric emission lines are tracers of spurious Doppler variability in the Sun and they are
expected to behave similarly for other stars.
52
We describe here the indices computed and used in
our analyses.
3.3
Chromospheric CaII H+K S-index.
We calculated the CaII H+K fluxes following standard procedures,
57, 58
both the PRD data and the
pre-2016 data were treated the same. Uncertainties were calculated from the quadrature sum of the
variance in the data used within each bandpass.
3.4
Chromospheric H
α
emission.
This index was measured in a similar way to the
S-indices, such that we summed the fluxes in the
center of the lines, calculated to be 6562.808 ˚
A, this time utilising square bandpasses of 0.678 ˚
A
not triangular shapes, and those were normalized to the summed fluxes of two square continuum
band regions surrounding each of the lines in the time series. The continuum square bandpasses
were centered at 6550.870 ˚
A and 6580.309 ˚
A and had widths of 10.75 ˚
A and 8.75 ˚
A, respectively.
Again the uncertainties were calculated from the quadrature sum of the variance of the data within
the bandpasses.
4
Photometric datasets
4.1
Astrograph Southern Hemisphere II.
The ASH2 (Astrograph for the South Hemisphere II) telescope is a 40 cm robotic telescope with
a CCD camera STL11000 2.7K x 4K, and a field-of-view (FOV) of 54 x 82 arcmin. Observations
were obtained in two narrow-band filters centered on H
α
and SII lines, respectively (H
α
is centred
on 656 nm, SII is centered on 672 nm, and both filters have a Gaussian-like transmission with a
FWHM of 12 nm). The telescope is at SPACEOBS (San Pedro de Atacama Celestial Explorations
Observatory), at 2450 m above sea level, located in the northern Atacama Desert, in Chile. This
telescope is managed and supported by the Instituto de Astrof´ısica de Andaluc´ıa (Spain). During
the present work, only subframes with 40% of the total field of view were used, resulting in a useful
FOV of 21.6 × 32.8 arcmin. Approximately 20 images in each band of 100 s of exposure time were
obtained per night. In total, 66 epochs of about 100 min each were obtained during this campaign.
The number of images collected per night was increased during the second part of the campaign
(until about 40 images in each filter per night).
17