11institutetext: European Southern Observatory, Karl-Schwarzschild-Str. 2,
85748 Garching bei München, Germany
11email<EMAIL_ADDRESS>22institutetext: Space sciences, Technologies and
Astrophysics Research (STAR) Institute, Université de Liège, 19c Allée du Six
Août, 4000 Liège, Belgium 33institutetext: Institut für Teilchen- und
Astrophysik ETH Zurich, Switzerland 44institutetext: Center for Astronomy
Research, University of Hertfordshire, Hatfield, United Kingdom
55institutetext: Stockholm University, Stockholm Observatory, Sweden
66institutetext: AIM, CEA, CNRS, Université Paris-Saclay, Université Paris
Diderot, Sorbonne Paris Cité, F-91191 Gif-sur-Yvette, France 77institutetext:
Astronomy Department, University of Michigan, Ann Arbor, MI 48109, USA
88institutetext: Tsung-Dao Lee Institute, Shanghai Jiao Tong University, 800
Dongchuan Road, Shanghai 200240, People’s Republic of China 99institutetext:
Department of Astronomy, School of Physics and Astronomy, Shanghai Jiao Tong
University, 800 Dongchuan Road, Shanghai 200240, People’s Republic of China

# High contrast imaging at 10 microns, a search for exoplanets around: Eps
Indi A, Eps Eri, Tau Ceti, Sirius A and Sirius B

P. Pathak 11 D. J. M. Petit dit de la Roche 11 M. Kasper 11 M. Sterzik 11 O.
Absil, F.R.S.-FNRS Research Associate22 A. Boehle 33 F. Feng 8899 V. D. Ivanov
11 M. Janson 55 H.R.A. Jones 44 A. Kaufer 11 H.-U. Käufl 11 A.-L. Maire 22 M.
Meyer 77 E. Pantin 66 R. Siebenmorgen 11 M. E. van den Ancker 11 G. Viswanath
55

(Received xx, 2020; accepted xx, 2020)

###### Abstract

Context. The direct imaging of rocky exoplanets is one of the major science
goals for upcoming large telescopes. The contrast requirement for imaging such
planets is challenging. However, the mid-IR (InfraRed) regime provides the
optimum contrast to directly detect the thermal signatures of exoplanets in
our solar neighbourhood.

Aims. We aim to exploit novel fast chopping techniques newly developed for
astronomy with the aid of adaptive optics to look for thermal signatures of
exoplanets around bright stars in the solar neighbourhood.

Methods. We use the upgraded VISIR (Very Large Telescope Imager and
Spectrometer for the mid-InfraRed) instrument with high contrast imaging (HCI)
capability optimized for observations at 10 $\mu$m to look for exoplanets
around five nearby ($d$ ¡ 4 pc) stars. The instrument provides an improved
signal-to-noise (S/N) by a factor of $\sim$4 in the N-band compared to
standard VISIR for a given S/N and time.

Results. In this work we achieve a detection sensitivity of sub-mJy, which is
sufficient to detect few Jupiter mass planets in nearby systems. Although no
detections are made we achieve most sensitive limits within
$<2^{\prime\prime}$ for all the observed targets compared to previous
campaigns. For $\epsilon$ Indi A and $\epsilon$ Eri we achieve detection
limits very close to the giant planets discovered by RV, with the limits on
$\epsilon$ Indi A being the most sensitive to date. Our non-detection
therefore supports an older age for $\epsilon$ Indi A. The results presented
here show the promise for high contrast imaging and exoplanet detections in
the mid-IR regime.

###### Key Words.:

exoplanets – instrumentation: adaptive optics, coronagraphy – methods: data
analysis

##  1 Introduction

The direct imaging of habitable exoplanets is one of the key science goals of
current and upcoming large telescopes (Meyer et al., 2018). The field of high-
contrast imaging (HCI), employing extreme adaptive optics (ExAO), coronagraphy
and state-of the art post-processing techniques, has enabled direct imaging of
young (up to about 30 Myr), several Jupiter-mass exoplanets with current
$8-10\leavevmode\nobreak\ m$ class telescopes (Marois et al., 2008; Macintosh
et al., 2015; Keppler et al., 2018; Chauvin et al., 2017; Nowak et al., 2020).
Examples of current HCI instruments include the Spectro-Polarimetric High-
contrast Exoplanet REsearch instrument (SPHERE), the Gemini Planet Imager
(GPI) and Subaru Coronagraphic Extreme Adaptive Optics (SCExAO), all of which
operate in the near-IR (1-2.5 $\mu$m) regime (Beuzit et al., 2019; Macintosh
et al., 2014; Jovanovic et al., 2015). Compared to the near-IR, the mid-IR
(8-13$\mu$m) is more sensitive to colder planets and allows to probe less
massive planets or, for a given mass, one is able to search around older stars
(Quanz et al., 2015). This is because the planet to star flux contrast is more
favourable in the mid-IR, where the thermal emission of the planet peaks in
the Rayleigh-Jeans tail of target stars (Baraffe et al., 2003; Sudarsky et
al., 2003; Marley et al., 2007; Fortney et al., 2008; Spiegel & Burrows,
2012). The key downsides of mid-IR HCI are reduced spatial resolution due to
the larger diffraction limit and large sky-background for ground-based
observations. Therefore, the mid-IR is best suited to look for exoplanets
around nearby stars.

New Earths in the $\alpha$ Cen Region (NEAR) experiment was a collaboration
between the Breakthrough Foundation and the European Southern Observatory
(ESO). The project involved upgrading the existing VISIR (Very Large Telescope
Imager and Spectrometer for the mid-InfraRed) instrument (Lagage et al., 2004)
at the VLT with adaptive optics (AO) using the deformable secondary mirror
(DSM) installed at UT4 (Arsenault et al., 2017), and a high-performance
annular groove phase mask (AGPM) coronagraph (Mawet et al., 2005). The aim of
the NEAR experiment was to enable HCI capability in the astronomical N-band
and to look for low mass exoplanets in the $\alpha$ Centauri binary system in
a $100$ hr campaign (for details see Kasper et al., 2017, 2019). The NEAR was
able to reach sensitivity and contrast sufficient for detection of Neptune
mass planets in the habitable zone of $\alpha$ Cen A, and a weak signal was
found whose nature (e.g., planet, part of a zodiacal disk, image artefact)
remains to be confirmed by follow-up observations (for details see Wagner et
al., 2021).

In this work, we report the results of observations with NEAR to look for
Jupiter size exoplanets around the nearest stars with spectral type earlier
than M: $\epsilon$ Indi A, $\epsilon$ Eri, $\tau$ Ceti, Sirius A and Sirius B.

In Sect. 2 we briefly describe observed targets, in Sect. 3 and 4 we describe
the data observation and reduction techniques. We discuss results in Sect. 5
and conclude with Sect. 6.

##  2 Target description

###  2.1 $\mathrm{\epsilon}$ Indi A

$\mathrm{\epsilon}$ Indi is a triple system at a distance of 3.6 pc (Gaia
Collaboration et al., 2020). It consists of the primary K5V star
$\mathrm{\epsilon}$ Indi A and a brown dwarf binary ($\mathrm{\epsilon}$ Indi
Ba and Bb) on a wide orbit of 1459 AU (Scholz et al., 2003; McCaughrean et
al., 2004). Age estimates of $1.4^{+1}_{-0.5}$ Gyr for $\epsilon$ Indi A were
published based on chromospheric activity indicators such as the calcium RHK
as a proxy for rotation (Lachaume et al., 1999). Given the well-known
relationships between rotation and age for FGK stars a similar value of $1.5$
Gyr was suggested by Kasper et al. (2009). However, Dieterich et al. (2018)
suggest an older age based on UVW kinematics and cooling curves for the brown
dwarf companions. Recently Feng et al. (2019) use extensive time-resolved
spectra to estimate a rotation period for the star of 36 days, suggesting an
age of $\sim$4 Gyr based on the rotation-age calibration of Eker et al.
(2015). This older age also agrees with the 3.7-4.3 Gyr estimated by King et
al. (2010) for the brown dwarf binary from the dynamical system mass and the
evolutionary models of Baraffe et al. (2003). The higher end of the age range
is therefore more likely.

Endl et al. (2002) first identified a long-period, low-amplitude radial
velocity signal in $\mathrm{\epsilon}$ Indi A, which could be explained by a
companion with P¿20 yr and a mass of at least 1.6 $M_{\mathrm{J}}\ $. This
signal has been confirmed by Janson et al. (2009) and Zechmeister et al.
(2013), who also find that the binary brown dwarf companions
$\mathrm{\epsilon}$ Indi Ba and Bb are too far away to induce the measured
trend. Feng et al. (2019) combine radial velocity data with astrometry to
confirm the existence of a $3.25^{+0.39}_{-0.65}$,$M_{\mathrm{J}}\ $planet on
an eccentric orbit with a period of $45.2^{+5.74}_{-4.77}$ yr. In September
2019, at the time of our observations the separation of this planet from the
host star is expected to be about 1.07$\arcsec$ (error bars are large due to
poorly constrained orbital solution).

###  2.2 $\mathrm{\epsilon}$ Eri

$\epsilon$ Eri is an adolescent K2V type dwarf star at a distance of $3.2$ pc
(Gaia Collaboration et al., 2020). The age of the star has been estimated
through various means and is generally thought to be around 0.4-0.9 Gyr, with
the higher end of the range being more likely (Henry et al., 1996; Song et
al., 2000; Di Folco et al., 2004; Mamajek & Hillenbrand, 2008). $\epsilon$ Eri
is surrounded by a narrow ring of debris located between 63 to 76 AU and a
possible inner belt at 12 to 16 AU (see Mawet et al., 2019, for a full
discussion of the disk structure).

A companion to $\mathrm{\epsilon}$ Eri was first suggested by Walker et al.
(1995) based on radial velocity data. Hatzes et al. (2000) argued that the
most likely explanation for the observed decade-long radial velocity (RV)
variations was the presence of a 1.5 $M_{\mathrm{J}}\ $giant planet with a
period P = 6.9 yr (3 AU orbit) and a high eccentricity (e=0.6). Very similar
parameters for the planet $\epsilon$ Eri b were derived from a comprehensive
set of RV as well HST astrometry data by Benedict et al. (2006). The most
recent mass estimate to date was done by Mawet et al. (2019) and combined 30
years of radial velocity data with deep direct imaging data in a Bayesian
analysis to constrain the properties of the companion. They found a mass of
$0.78^{+0.38}_{-0.12}$, $M_{\mathrm{J}}\ $at a separation of $3.48\pm 0.07$ AU
and an eccentricity of $0.007$, which is lower than previous reported values.
Direct imaging detections of $\epsilon$ Eri b in the L- and M-bands were
attempted by Janson et al. (2008) and Mawet et al. (2019) and yielded an upper
mass limits of around 4 $M_{\mathrm{J}}\ $(for an age of 320 Myr) and 2
$M_{\mathrm{J}}\ $(for 400 Myr), respectively. A second companion was first
suggested by Benedict et al. (2006) at 12-20 AU based on radial velocity
residuals, but this was not confirmed by Mawet et al. (2019). An alternative
additional companion of 0.4-1.2 $M_{\mathrm{J}}\ $has been suggested at 48 AU
by Booth et al. (2017) to explain the shape of the outer dust belt, and Mawet
et al. (2019) also require an additional planet to stir this belt. Janson et
al. (2015) are able to obtain sub-Jovian mass limits of 0.6-1 $M_{\mathrm{J}}\
$at these larger separations, but this cannot rule out the lower end of the
proposed mass range, so while the companion has not been confirmed, it can
also not been ruled out.

###  2.3 $\tau$ Ceti

$\tau$ Ceti is a nearby (3.7 pc), sun-like G8.5V star with an extended debris
disk (5-55 AU) that is more than 10 times as massive as the Kuiper belt (Gaia
Collaboration et al., 2020; Gray et al., 2006; Greaves et al., 2004; MacGregor
et al., 2016). There is a large range in the literature for ages of $\tau$
Ceti: based on stellar activity the age is 5.8$\pm$2.9 Gyr (Mamajek &
Hillenbrand, 2008), but astroseismological and interferometric measurements
suggest an age closer to 8-10 Gyr (Di Folco et al., 2004; Tang & Gai, 2011)
and chemical composition measurements point towards an age of
$7.63^{+0.87}_{-1.5}$ Gyr (Pagano et al., 2015).

Tuomi et al. (2013) discovered 5 Earth-like planets in radial velocity data
with periods from 14 to 642 days (0.1-1.35 AU). Two of these were confirmed by
Feng et al. (2017), who discovered two further planets at periods of 20 and 49
days. They also suggest that the 14 day signal could be the result of stellar
activity, rather than a planet and that candidates e, f and h might actually
be too eccentric to be planets. Dietrich & Apai (2020) use dynamical arguments
to provide statistical evidence for the existence of the remaining three
planets suggested by Tuomi et al. (2013) and one additional candidate that
could be located in the habitable zone. All the previously mentioned
candidates are expected to be super-Earths ($M\cdot sin(i)\approx
1-4M_{\oplus}$). However, Kervella et al. (2019) provided tentative evidence
of a giant planet candidate (1-2 $M_{\mathrm{J}}\ $, 3-20 AU) from Gaia data.
Near infrared direct imaging has not been able to detect any of the planets,
but has provided constraints of 10-20 $M_{\mathrm{J}}\ $at separations larger
than 2$\arcsec$ (7AU) and 30-50 $M_{\mathrm{J}}\ $at 1$\arcsec$ (Boehle et
al., 2019). The candidate detected by Kervella et al. (2019) is the only one
that is not too small and close to be detected with present-day mid-IR
facilities.

###  2.4 Sirius A

Sirius is a binary system at a distance of 2.7 pc, consisting of an A1Vm star
and a WD with an age of 225-250 Myr (Gaia Collaboration et al., 2020; Liebert
et al., 2005; Bond et al., 2017). While there are no known planets around
Sirius A or B, there are mass limits on possible companions from previous
imaging campaigns, covering wavelengths of roughly $0.5-5\,\mathrm{\mu}$m. The
most sensitive limits on Sirius A exclude giant planets down to 11
$M_{\mathrm{J}}\ $at 0.5 AU, 6-7 $M_{\mathrm{J}}\ $in the 1-2 AU range and 4
$M_{\mathrm{J}}\ $at 10 AU (Hunziker et al., 2020; Vigan et al., 2015;
Thalmann et al., 2011; Bonnet-Bidaud & Pantin, 2008). In any case, the long-
term orbital stability of planets around Sirius A or B would be impacted by
the binarity of the system, which has a semi-major axis of about 20 AU and
eccentricity 0.6. Bond et al. (2017) find that the longest periods for stable
planetary orbits in the Sirius system are about 2.24 yr for a planet orbiting
Sirius A, corresponding to a r = 2.2 AU circular orbit, and 1.79 yr for a
planet orbiting Sirius B, corresponding to a r = 1.5 AU circular orbit. WDs
are typically $10^{3}$ to $10^{4}$ times less luminous than their progenitor
stars. Thus, it would be much easier to achieve the contrast required to
detect a planetary companion (Burleigh et al., 2002). This idea sparked direct
imaging searches for planets around WDs (Gratton et al., 2020; Friedrich et
al., 2007). While no planets have been found using direct imaging to date, a
transiting planet was found around the white dwarf WD 1856+534 (Vanderburg et
al., 2020), and an evaporating Neptune was proposed to explain the chemical
fingerprints of hydrogen, oxygen and sulfur in the spectrum of WDJ0914+1914
(Gänsicke et al., 2019).

###  2.5 Sirius B

For Sirius B, as explained above a planet in a stable orbit would have a
period of 1.79 yr for a r = 1.5 AU. No limits have been placed on companions
within 3$\arcsec$, although near infrared imaging by Bonnet-Bidaud & Pantin
(2008) did set limits of 10-30 $M_{\mathrm{J}}\ $outside of that radius.
Sirius B is the only target in the sample to have been previously imaged in
the mid-IR at 8-10$\,\mu$m between 2003 and 2006, but no limits on companions
were determined from this dataset (Skemer & Close, 2011).

Target | Parallax | N-band (Jy) | Date | Observation | On-coronagraph | Seeing | Temp (∘C) | PWV (mm)
---|---|---|---|---|---|---|---|---
| (mas) | brightness | observed | time (hr) | time (hr) | (arcsec) |  |
$\epsilon$ Indi A | $274.84$ | 4.5 | 2019-09-14 | 2.35 | 0.81 | 0.8-2.0 | 10-11 | 0.8-2.2
|  |  | 2019-09-15 | 4.23 | 1.47 | 0.5-1.0 | 12-13 | 0.4-0.9
|  |  | 2019-09-17 | 3.31 | 1.33 | 0.5-0.9 | 9-12 | 0.9-3.0
$\epsilon$ Eri | $310.58$ | 7.6 | 2019-09-15 | 1.61 | 0.61 | 1.0-1.8 | 11-12 | 0.4-0.7
|  |  | 2019-09-17 | 2.63 | 1.01 | 0.5-0.9 | 9-10 | 0.8-1.4
$\tau$ Ceti | $273.81$ | 7.5 | 2019-09-16 | 1.81 | 0.65 | 0.8-1.6 | 10-11 | 3.0-5.0
Sirius A | $374.49$ | 118.8 | 2019-12-15 | 2.38 | 0.74 | 0.4-0.7 | 13-14 | 3.8-5.2

Table 1: Observing parameters for all the targets under various conditions.
All the observations were carried out using the NEAR N-band filter with a
bandpass of $10-12.5\leavevmode\nobreak\ \mu$m. The N-band brightness reported
in the table assumes the central wavelength of the NEAR filter of
$11.25\leavevmode\nobreak\ \mu$m.

111The on-coronagraph time is $40\%$ of the selected frames due to the
observing strategy based on chopping and nodding, for details see Sec. 3.

##  3 Observation and data reduction

All the observations employed a common observing strategy, including the use
of AO, an AGPM coronagraph, chopping and nodding. The chopping was done with
the DSM of the VLT. The chop throw of the DSM was $\leavevmode\nobreak\
4.5^{\prime\prime}$ and was performed at a speed of $8.33$ Hz to reduce the
excess low frequency noise common to the mid-IR arrays (Si:As array, Arrington
et al., 1998). The chopping subtracts two images taken at different position
on the sky thereby leaving a positive (coronagraphic, on-axis) and a negative
(off-axis) image of the source separated by the chop throw and removing most
of the sky and instrumental background flux bias. However, the optical path is
slightly different for both chopping positions, which leaves some small
residuals. In principle, these could be removed by nodding (for details see
Lagage et al., 2004), but our data reduction is not affected by the small
chopping residuals which are not point-like and do not degrade the point-
source sensitivity. At 8.33 Hz chopping, each half-cycle is 60 ms consisting
of $8\times 6$ ms DITs (=$48$ ms) and $2\times 6$ ms DITs (=$12$ ms) skipped
during the chopping transition. The other half-cycle is taken with the star
off the coronagraph. At each nodding position, 500 chopping frames half-cycles
were recorded for a total observing time of $500\times 60$ ms = $30$ seconds
out of which $250\times 48$ ms = 12 were spent with the target on the
coronagraph, that is, the observing efficiency was 40$\%$. A summary of the
observations and the atmospheric conditions affecting the sensitivity is
outlined in the Table 1. The atmospheric data were taken from Paranal
Astronomical Site Monitoring. To center the targets on the coronagraph and to
minimize the leakage, a dedicated correction using the science images with the
aid of the QACITS algorithm was used (for details see Maire et al., 2020). We
derived a pixel scale of $45.25$ mas/pixel using the $\alpha$ Cen campaign
data, utilizing the well known orbit of the binary from Kervella et al.
(2019). In the next section we discuss the steps employed for the data
reduction.

Figure 1: (a) Final derotated image of the $\epsilon$ Indi A target with high-
pass filter applied. (b) ADI processed image.

###  3.1 Data Reduction

For all the targets a common data reduction strategy was followed, which
included a chop subtraction of the off-axis from the on-axis source position
frames adjacent in time. This provided images where the source was positive on
the coronagraph and negative in the off-axis position.

Three selection criteria were employed to identify inferior frames and remove
them from the data analysis: AO correction (ratio of flux in an annulus of
radii 6-12 pix to flux in an aperture of r¡6 pix), coronagraphic leakage (flux
in an aperture of 20 pix) and sky-background noise variance calculated using
small regions of the non-chopped images. To further identify good, co-aligned
frames, an additional parameter based on the positions of the off-axis PSFs
was used. The employed selection criteria improved the overall sensitivity and
contrast, and reduced false positives, especially at small projected
separations. We lost about $14\%,\leavevmode\nobreak\ 5\%,\leavevmode\nobreak\
10\%$ and $22\%$ of the observed frames for $\epsilon$ Indi A, $\epsilon$ Eri,
$\tau$ Ceti and Sirius A respectively.

Once good chopped frames were identified, they were binned by averaging 250
frames. The binning of the frames to an exposure time of 30 seconds
($250\times 0.12$s) was chosen to be short enough to avoid smearing of
potential companions by the field rotation, and long enough to provide a good
sensitivity on binned frames and to reduce the data size for further post-
processing. The averaged frames still show some smoothly varying structures
(residual sky-background, left over after chopping), which was removed by
applying a spatial high-pass filter. This filtering process creates a smoothed
version of the image, by replacing each individual pixel by a median of
$15\times 15$ surrounding pixels, and then subtracts it from the image. The
effect of such filtering on the point source signal was a flux reduction of
less than $10\%$ and had a negligible effect on the noise variance. Figure 1
(a) shows a final averaged and derotated image for the target $\epsilon$ Indi
A, with the coronagraphic PSF at the center and the off-axis PSF’s
representing both the nod positions.

For the final Angular Differential Imaging (ADI) analysis (Marois et al.,
2006), night by night data was processed using a global annular Principal
component analysis (PCA) based algorithm. Specifically, for a given analysis
frame, we identify all the frames obtained during that night which differ in
field rotation angle by at least one PSF half width at half maximum (HWHM) at
the smallest angular separation of interest. We set this separation to 8
pixels (or 360 mas) which corresponds to the 1st minimum of the VLT’s N-band
Airy pattern. For this set of calibration frames, first the mean of the set
was subtracted from all individual frames. Then we select all pixels in an
annular area with an inner radius of 8 pixels and an outer radius of 25 pix,
corresponding to the 3rd minimum of the Airy pattern. As our images are
usually very smooth and without residual speckle structure outside a radius of
25 pix (see Figure 1 a), we do not benefit from a larger outer radius. We
perform the PCA analysis on these data, i.e., on the pixels in the annular
area for the set of calibration frames arranged in a matrix of size
$\\#$pixels $\times$ $\\#$frames. This yields the linear combinations of
calibration frames (the principle components) which best reproduces the
analysis frame. The optimization of the PCA parameters, such as inner and
outer radius of the annulus and number of principal components, was done with
artificial planet injection and recovery tests, to maximize the contrast
sensitivity. We observed that 15 principal components yielded the best
compromise between the reduction of PSF residuals and self-subtraction of
artificial planets inserted into the data. A further analysis was performed by
splitting the data into odd-even frames and dividing into different chunks, to
see if any strong speckles remain for different analysis. This helped to
identify suspected false positive detections such as a faint speckle visible
just right of the coronagraph center in the Figure 1 (b).

In the case of targets observed for more than one night, the final processed
image was produced by weighting each night’s combined image by the inverse of
the background noise as measured in the combined frame of the night, i.e., by
applying a noise weighted mean. This step was used to compensate for variable
atmospheric conditions (ambient temperature, humidity and precipitable water
vapor in the atmosphere), this helped to improve the final noise variance in
the image (Turchi et al., 2020).

Figure 2: (a) $\epsilon$ Indi A image with injected planets at contrast of
$10^{-4}$ with a separation from $1^{\prime\prime}$ to $2.5^{\prime\prime}$
marked with white arrows to left. On the right-hand side is a likely false
positive identified from examination of the odd-even frames. (b) S/N map
showing injected planets appearing with S/N in the range of $5-7$. The
approximate position of $\epsilon$ Indi Ab is shown by a circle, but the
uncertainties are large (for details see Feng et al., 2019)

.

##  4 Analysis

To quantify the results further, we calculate a background noise limited
sensitivity and contrast curve using artificial planet injections and recovery
tests for each target, which is discussed in the following sections.

###  4.1 Background noise limited imaging performance (BLIP)

We obtain a $5\sigma$ background noise limited imaging performance (BLIP) by
calculating the standard deviation in 4-pix radius (=1.25 $\lambda$/D)
apertures at various locations of the PCA reduced images. This value was then
multiplied by $5$ times the square root of the number of pixels in the
aperture ($5\times\sqrt{16\pi}$). To get the sensitivity with respect to the
target, we used the off-axis stellar PSF for relative flux-calibration. This
process was repeated for 20 angular and 17 radial distances separated by 7
pix. A mean of angular values was then calculated to get a background noise
limited sensitivity curve as shown by the dashed line in the Figure 3 panel
(a)-(d).

The background noise limited sensitivity steeply increases at small
separations ($\mathrm{\lesssim 1^{\prime\prime}}$) for $\epsilon$ Indi A,
$\epsilon$ Eri and $\tau$ Ceti, which is due to the coronagraphic glow.
Because the AGPM is not located downstream of a cold stop in VISIR, a part of
the thermal emission originating from outside the telescope pupil (incl. the
central obscuration) is diffracted back inside the pupil by the vortex effect
(see Absil et al. (2016) for details). This creates a significant additional
amount of thermal background close to the center of the AGPM on the detector.
Which could be mitigated by introducing a cold stop upstream of the AGPM.

The BLIP sensitivity would only be reached in the absence of coronagraphic PSF
residuals (quasi-static speckles –QSS–) from the central star. It can be
compared to the point source sensitivity contrast introduced above to evaluate
the angular separation beyond which BLIP sensitivity is reached. At such
angular separations, the sensitivity improves with the square-root of
integration time while sensitivity improvements in the inner regions dominated
by QSS are much harder to achieve.

Figures 3 and 4 show that the gap between BLIP sensitivity and point source
sensitivity contrast levels out at angular separations of around 1” or 3.5
lambda/D for the fainter stars of our sample ($\epsilon$ Indi A, $\epsilon$
Eri, $\tau$ Ceti and Sirius B. At such separations, QSS are no longer seen
(cf. Figure 1) and pixel-pixel noise dominates the sensitivity. The shallow
improvement of the point source sensitivity towards even larger angular
separations can be attributed to the PCA algorithm which does not conserve
flux and self-subtracts a diminishing fraction of the injected fake planets
signal.

The contrast around the very bright Sirius A instead is limited by QSS and PSF
residuals out to an angular separation of several arcseconds. This is due to a
slight misalignment between the star and the coronagraph during the
observation, and to the use of a conventional Lyot-stop (LS). While the
apodized LS used during the Alpha Cen observing campaign (Wagner et al., 2021)
suppresses the off-axis Airy pattern at angular separations similar to the
chopping throw of 4.5”, this conventional LS does not reduce the Airy pattern
of the off-axis chopping position and leaves residuals near the coronagraphic
center which reduce sensitivity.

###  4.2 Point Source Contrast Sensitivity

To compute the planet detection sensitivity, we injected artificial planets at
various angular and radial
($0.7^{\prime\prime},0.85^{\prime\prime},1^{\prime\prime},1.5^{\prime\prime},2^{\prime\prime},2.5^{\prime\prime}$)
separations. To estimate signal-to-noise (S/N), we used the approach of Mawet
et al. (2014), as implemented in the open source Vortex Image Processing
library (Gomez Gonzalez et al., 2017). We found that a S/N of $5$ using the
above criteria was sufficient to visually identify inserted artificial
planets, as can be seen from Figure 2. The Figure shows injected planets at a
contrast of $10^{-4}$ with respect to $\epsilon$ Indi A, with separations of
$1^{\prime\prime}$, $1.7^{\prime\prime}$, $2.5^{\prime\prime}$. Panel (b)
shows their S/N estimates, which varies from $5-7$ from the inner to the outer
planets.

The overall contrast curve sensitivity was calculated by azimuthally averaging
the contrast required to achieve $5\leavevmode\nobreak\ \sigma$ S/N. We used a
power law function to fit the radial points to obtain final contrast curves.
The contrast curves of all our targets are shown in the Figures 3 panel
(a)-(d). The contrast at small separation is affected by the coronagraphic
glow similar to background noise limited sensitivity, except for the target of
Sirius A, for the reason mentioned in the previous section.

Estimated contrasts of the known RV companions of $\epsilon$ Indi A and
$\epsilon$ Eri are included in the Figure 3 for comparison. Planet fluxes in
the NEAR filter are calculated from the ATMO 2020 spectral models (Phillips et
al., 2020, see section 4.3) assuming literature values for the planet mass
($3.25^{+0.39}_{-0.65}\,$$M_{\mathrm{J}}\ $and $0.77\pm 0.2$ $M_{\mathrm{J}}\
$) and the system age ($2^{+2}_{-1.3}\,$Gyr and $0.7\pm 0.3$ Gyr). These
values are plotted by blue points in the Figure 3. Since the masses are
determined by radial velocity, radius measurements are not available. Both the
planet radii and temperatures are taken from the ATMO evolutionary models.

###  4.3 Mass limits

The contrast curves were converted into mass limits using the ATMO 2020
exoplanet atmosphere models (Phillips et al., 2020). The models are computed
using a state-of-the-art one-dimensional radiative-convective equilibrium code
along a grid of self-consistent pressure–temperature profiles and chemical
equilibrium abundances for a range of effective temperatures (200 to 3000 K)
and gravities (2.5-5.5 dex). ATMO 2020 has key improvements over previous
model families, including the use of updated molecular line opacities which
results in warmer atmospheric temperature structures and improved emission
spectra. We use the non-equilibrium models with weak vertical mixing and the
isochrones of age-ranges obtained from literature to determine the masses
corresponding to the contrast curves.

For absolute flux value of Sirius A, we use reported value from ESO’s list of
mid-IR standard
stars222https://www.eso.org/sci/facilities/paranal/instruments/visir/tools/.
It provides a flux of 118.8 Jy in the PAH2 filter, which has the same central
wavelength (11.25 $\mu$m) as the broad NEAR filter with a bandpass of 10-12.5
$\mu$m. For the other stars, we estimated the absolute flux from the tabulated
K-band magnitude and applying the K-M correction from Allen’s astrophysical
quantities (Cox, 2000). The M-N color of main sequence stars with spectral
type earlier than K5 is vanishingly small as this wavelength regime is well
within the Rayleigh-Jeans part of the stellar spectrum. This procedure yields
the 11.25 $\mu$m fluxes of $\sim$4.5 Jy for $\epsilon$ Indi A, $\sim$7.6 Jy
for $\epsilon$ Eri and $\sim$7.5 Jy for $\tau$ Ceti. We also applied the
procedure to some standard stars with tabulated K-band magnitude and PAH2
fluxes and found the values to agree within a few percent. For Sirius A, the
estimate is $117$ Jy in a very good agreement with the tabulated 118.8 Jy. We
used Sirius A as a reference to calculate differential flux for other targets
and find values agree with the calculation. We find no evidence of mid-IR
excess in our targets consistent with previous work, Sirius A (White et al.,
2019), Sirius B (Skemer & Close, 2011), $\epsilon$ Indi A (Trilling et al.,
2008). $\epsilon$ Eri (Backman et al., 2009) and $\tau$ Ceti (Lawler et al.,
2014) are known to have some IR excess from their extended debris disks, but
this emission is mostly from cold dust and therefore at longer wavelengths.
Also, our high-spatial resolution imagery would resolve the debris disk from
the central star, such that no IR excess is measured on the central PSF.

##  5 Discussion

###  5.1 $\mathrm{\epsilon}$ Indi A

To constrain the mass limits of companions to $\epsilon$ Indi A, we adopt an
age range of 0.7-4 Gyr for our models and find limits of 3.3-10
$M_{\mathrm{J}}\ $beyond 1$\arcsec$. Since the mass of the known planet is
$3.25^{+0.39}_{-0.65}$, $M_{\mathrm{J}}\ $, we would have likely detected it
if the age of the system was 0.7 Gyr as shown in the Figure 3 (e). Our non-
detection therefore supports an older age for $\epsilon$ Indi A. This is
consistent with the majority of the age determinations as discussed in the
introduction above. We can calculate the required observation time to detect
the known giant planet by assuming a likely age of 3.8 Gyr, in a background
limited regime and improved sensitivity at small separations (without
coronographic glow). It will require 50 hrs of observing time to detect the
planet associated with the RV signal.

The limits we obtain are more sensitive than any previous near IR imaging
campaigns, which have constrained the masses of possible companions to 20
$M_{\mathrm{J}}\ $in the inner regions of the system (Geißler et al., 2007)
and 5-20 $\mathrm{M_{J}}$ at separations larger than 2$\arcsec$ (Janson et
al., 2009). Another independent reduction of $\epsilon$ Indi A combining the
NEAR and NaCO L′ data reaches similar mass limits as ours (Viswanath, 2021).

$\epsilon$ Indi Ba and Bb are not discussed in this paper, as their wide orbit
(1459 AU, Scholz et al., 2003; McCaughrean et al., 2004) corresponds to
approximately 6.7 arc minute separation, which is far outside the field of
view of the VISIR instrument.

Figure 3:  Panel (a), (b), (c), and (d) shows 5 $\sigma$ contrast curves and
background noise limited imaging performance. Panel (e), (f), (g) and (h)
shows the mass limits derived using contrast curves. The solid line is derived
using artificial injection and recovery tests, the thin line represents the 5
$\sigma$ BLIP sensitivity. The detection limits would improve with
$\sqrt{t_{obs}}$ and observing conditions. The different shape of the curves
in (h) is due to the strong irradiation of the planet by the star, as
discussed in Section 5.4

###  5.2 $\mathrm{\epsilon}$ Eri

We adopt an age range of 0.4-1 Gyr for our models. We obtained a mass limits
of 2-4 $M_{\mathrm{J}}\ $, as shown in the Figure 3 (f). The obtained limits
are more sensitive than most previous imaging data (Macintosh et al., 2003;
Janson et al., 2008; Mizuki et al., 2016; Hunziker et al., 2020), with the
exception of Mawet et al. (2019), who derive an upper mass limit of about 2
$M_{\mathrm{J}}\ $for an assumed system age of 400 Myr. Reaching similar mass
limits at different wavelengths does, however, reduce the dependency on the
planet atmosphere models. Our result therefore increases the confidence that
there is indeed no planet more massive than 2 $M_{\mathrm{J}}\ $around
$\epsilon$ Eri, for an age of 400 Myr old. The debris disk around $\epsilon$
Eri (Backman et al., 2009) is too large for our field of view and too cold and
faint at $11.25\leavevmode\nobreak\ \mu$m to be detected in our observations.
To estimate the required observing time for detecting $\epsilon$ Eri b for a
likely age of 0.7 Gyr, we find that 1 $M_{\mathrm{J}}\ $planet can be detected
in less than 70 hrs with the current setup and sensitivity will improve at
small separations, if the coronographic glow is eliminated (by introducing a
cold pupil stop in front of the AGPM coronagraph mask).

###  5.3 $\tau$ Ceti

Because of the large range of age suggested in the literature, we adopt a wide
range of 3-10 Gyr. The obtained mass limits of 15-30 $M_{\mathrm{J}}\ $shown
in the Figure 3 (g) are comparable to those of Boehle et al. (2019), who use a
combination of radial velocity and $3.8\,\mathrm{\mu}$m imaging data to find
limits of 10-20 $M_{\mathrm{J}}\ $beyond 2$\arcsec$ for a slightly younger age
range (2.9-8.7 Gyr). Within 2$\arcsec$ we are more sensitive, and the non-
detection of any of the known planets is consistent with the expectation, as
the various Earth-mass planets of the system are far too low mass and are
located within the inner working angle of our data and even the proposed giant
planet candidate is well below our detection threshold (1-2 $M_{\mathrm{J}}\
$at 3-20 AU).

###  5.4 Sirius A

For our models we assumed an age range of 0.2-0.3 Gyr for Sirius. For Sirius A
we have also included the irradiation from the star when determining the
expected magnitude of the planet, due to the brightness of the host star. We
accounted for the irradiation by counting both the flux arriving at the planet
surface and the intrinsic formation heat of the planet from the model as
incoming energy when calculating the equilibrium temperature, which in turn
determines the outgoing flux. Sirius A is 25 times more luminous than the Sun,
and a potential planet on a 2 AU orbit would be heated to more than 400 K
independent of the planet’s age or mass. This leads to the peculiar shape of
the mass contrast curve with better mass sensitivities at small separation
from Sirius A shown in the Figure 3 panel h. As a result, the curve of the
mass limit falls of sharply within $\sim$1$\arcsec$ or 2.6 AU, where the
stellar radiation dominates. Beyond this the irradiation quickly becomes
negligible due to falling off with the square of the distance and the curve
looks more similar to those of the other systems. The other systems have
smaller, fainter stars and therefore the amount of heating by the stellar flux
is negligible at the separations resolved by our imagery. While we do not
detect any planets, we do obtain the most sensitive mass limits to date within
1.5$\arcsec$ and comparable limits to the most sensitive limits of previous
imaging campaigns outside that radius (Bonnet-Bidaud & Pantin, 2008; Thalmann
et al., 2011; Vigan et al., 2015; Hunziker et al., 2020). We cannot rule out
the possibility of planets that could be hidden behind or too close to the
star.

###  5.5 Sirius B

No ADI reduction had to be applied to the Sirius B data, because the star is
$4\times 10^{-5}$ times fainter than Sirius A and no PSF residuals are seen
besides the PSF core. Also the target was far from Sirius A and the noise of
its coronagraphic PSF, so no further processing was necessary. The final image
of Sirius A and B is shown in the Figure 4. Sirius B was very close to edge of
the NEAR’s field of view, and even outside of it for some individual frames,
which were then excluded before derotation and averaging. To calculate the
sensitivity around Sirius B, we divided that area of the image into two
regions, an inner and an outer region, as shown in the Figure 4 (b). The inner
region provides a better sensitivity for both the background noise limited and
injected planet, as it includes more frames.

The astrometry measurements for Sirius B, put it at a separation of
$11.18^{\prime\prime}$ from Sirius A. Relative photometry with respect to
Sirius A has been performed using an optimum r=4 pix photometric aperture. The
$11.25\leavevmode\nobreak\ \mu$m contrast ratio between the two stars is
$4\times 10^{-5}$ corresponding to a Sirius B flux of 4.7 mJy at an S/N of
about 40. This value is consistent with the low S/N measurement of 4.9 mJy
reported for a similar observing band by Skemer & Close (2011).

For our models we have assumed the same age range as we did for Sirius A,
giving us limits of $1.5-1.8$ $M_{\mathrm{J}}\ $for the ”inner” region and
$3.1-3.6$ $M_{\mathrm{J}}\ $for the ”outer” region. The mass limits in the
inner region are comparable to previous near IR limits of 1.6 $M_{\mathrm{J}}\
$from Thalmann et al. (2011). According to the models and assuming the
sensitivity improving with $\sqrt{t_{obs}}$, a $4\times$ more observation time
would be enough to reach 0.5 $M_{\mathrm{J}}\ $.

Figure 4:  (a) Final derotated image showing Sirius A and Sirius B. (b) Zoomed
in on Sirius B, divided into two regions (inner and outer) based on the number
of frames in the outlined area.

Figure 5:  Sirius B 5 $\sigma$ contrast curves, same as in Figure 3. The outer
and inner regions are represented by red and black lines respectively. The
contrast curve for outer region increases at small separation due to edge of
the inner frames.

Figure 6:  Planet mass upper limits derived for Sirus B. The two mass limits
are based on the outer and inner region, see Figure 5.

##  6 Summary and Conclusions

In this work we demonstrate high-contrast imaging of a small sample of very
nearby (¡4 pc) stars with spectral type earlier than M at
$11.25\leavevmode\nobreak\ \mu m$ with NEAR. While we do not detect any known
or new planets, we are able to set upper mass limits of the order of a few
Jupiter masses for most of the targets and of $15-30$ $M_{\mathrm{J}}\ $for
the older $\tau$ Ceti. For $\epsilon$ Indi A and $\epsilon$ Eri we achieve
detection limits very close to the giant planets discovered by RV, with the
limits on $\epsilon$ Indi A being the most sensitive to date. Also for $\tau$
Ceti and Sirius A we obtain the most sensitive limits to date at small
separations (¡1.5$\arcsec$ and ¡2$\arcsec$ respectively). Our mass limit for
Sirius B is similar to the one achieved previously at a shorter wavelength.

The ADI analysis was performed using a PCA based algorithm with artificial
planet injections and recovery tests yielding some of the most stringent upper
mass limits to date. For $\epsilon$ Indi A and $\epsilon$ Eri, we almost reach
the detection limit for the known planets if they were at the young end of the
possible age estimates but fail to detect any signal. We achieve an
unprecedented sub-mJy detection sensitivity.

We demonstrate close to background noise limited imaging for most of our
target stars apart from the glaring Sirius A, for which the data is contrast
limited. Assuming likely ages and background noise limited imaging, the giant
planets orbiting $\epsilon$ Eri and $\epsilon$ Indi A can be imaged in 70 and
50 hrs respectively. Finally, for our closest and youngest (together with
Sirius A) target Sirius B, the sub-Jupiter mass regime could be reached by
merely doubling the observation time.

This work shows the potential of direct imaging in the mid-IR regime and
prospects for upcoming mid-IR HCI instruments. Upcoming mid-IR HCI instrument
such as METIS at the ELT would be able to detect known planets around
$\epsilon$ Indi A and $\epsilon$ Eri in a few minutes of observation time and
reach sensitivities to detect Earth size exoplanets in a few hours (Brandl et
al., 2018).

###### Acknowledgements.

The authors would like to thank the ESO and the Breakthrough Foundation and
all the people involved for making the NEAR project possible. The observations
were carried out under the ESO program id: 60.A-9107(D) and 60.A-9107(F). MRM
acknowledges the support of a grant from the Templeton World Charity
Foundation, Inc. The opinions expressed in this publication are those of the
authors and do not necessarily reflect the views of the Templeton World
Charity Foundation, Inc. Part of this work has received funding from the
European Research Council (ERC) under the European Union’s Horizon 2020
research and innovation programme (grant agreement No. 819155), and by the
Wallonia-Brussels Federation (grant for Concerted Research Actions).

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