Turner et al.Follow-up NenuFAR observations of the $\tau$ Boo

# Follow-up radio observations of the $\tau$ Boötis exoplanetary system:
Preliminary results from NenuFAR

J.D. TurnerDepartment of Astronomy and Carl Sagan Institute, Cornell
University, Ithaca, NY, USA ,NHFP Sagan Fellow ∗ P. ZarkaObservatoire
Radioastronomique de Nançay (ORN), Observatoire de Paris, PSL Research
University, CNRS, Univ. Orléans, OSUC, 18330 Nançay, France ,LESIA,
Observatoire de Paris, CNRS, PSL, Meudon, France  J-M. Grießmeier3,Laboratoire
de Physique et Chimie de l’Environnement et de l’Espace (LPC2E) Université
d’Orléans/CNRS, Orléans, France
E. Mauduit4 L. Lamy3,4,Aix Marseille Université, CNRS, CNES, LAM, Marseille,
France  J.N. Girard4
T. KimuraDepartment of Physics, Tokyo University of Science, Tokyo, Japan  B.
Cecconi4 L.V.E. KoopmansKapteyn Astronomical Institute, University of
Groningen, Groningen, The Netherlands
∗Corresponding author<EMAIL_ADDRESS>
###### Abstract

Studying the magnetic fields of exoplanets will provide valuable information
about their interior structures, atmospheric properties (escape and dynamics),
and potential habitability. One of the most promising methods to detect
exoplanetary magnetic fields is to study their auroral radio emission.
However, there are no confirmed detections of an exoplanet in the radio
despite decades of searching. Recently, Turner et al. (2021) reported a
tentative detection of circularly polarized bursty emission from the $\tau$
Boötis ($\tau$ Boo) exoplanetary system using LOFAR low-frequency beamformed
observations. The likely source of this emission was presumed to be from the
$\tau$ Bootis planetary system and a possible explanation is radio emission
from the exoplanet $\tau$ Boo b, produced via the cyclotron maser mechanism.
Assuming the emission is from the planet, Turner et al. (2021) found that the
derived planetary magnetic field is compatible with theoretical predictions.
The need to confirm this tentative detection is critical as a conclusive
detection would have broad implications for exoplanetary science. In this
study, we performed a follow-up campaign on the $\tau$ Boo system using the
newly commissioned NenuFAR low-frequency telescope in 2020. We do not detect
any bursty emission in the NenuFAR observations. There are many different
degenerate explanations for our non-detection. For example, the original
bursty signal may have been caused by an unknown instrumental systematic.
Alternatively, the planetary emission from $\tau$ Boo b is variable. As
planetary radio emission is triggered by the interaction of the planetary
magnetosphere with the magnetized stellar wind, the expected intensity of the
planetary radio emission varies greatly with stellar rotation and along the
stellar magnetic cycle. More observations are needed to fully understand the
mystery of the possible variability of the $\tau$ Boo b radio emission.

##  1 Introduction

The search for auroral radio emissions from exoplanets has been ongoing for
many decades. In analogy with the magnetized Solar System planets and moons,
these radio emissions are expected to be produced via the cyclotron maser
instability (CMI) mechanism (Wu & Lee 1979; Zarka 1998; Treumann 2006) and be
highly circularly polarized, beamed, and time-variable (e.g., Zarka 1998;
Zarka et al. 2004). CMI emission is produced at the local electron cyclotron
frequency ($\omega_{c}$) in the source region and the maximum gyrofrequency
$\nu_{g}$ is determined by the maximum magnetic field $B_{p}$ near the
planetary surface, as $\nu_{g}[MHz]=2.8\times B_{p}[G]$, where the frequency
is measured in MHz and the magnetic field is measured in Gauss. Therefore,
radio observations can be used to probe the magnetic fields of exoplanets
(e.g. Farrell et al. 1999; Zarka et al. 2001; Zarka 2007).

Low-frequency radio observations are indeed among the most promising methods
to detect their magnetic fields (Grießmeier 2015) as many of the other
techniques are prone to false-positives (e.g. Grießmeier 2015; Alexander et
al. 2016; Turner et al. 2016a; Route 2019; Strugarek et al. 2022). Measuring
the magnetic field of an exoplanet will give valuable constraints on its
interior structure, atmospheric escape, and star-planet interactions (Zarka et
al. 2015; Lazio et al. 2016; Grießmeier 2018; Zarka 2018; Lazio et al. 2019).
Also, atmospheric dynamics may be altered by the presence of a planetary
magnetic field (e.g., Perna et al. 2010; Rauscher & Menou 2013; Hindle et al.
2021) and Ohmic dissipation may contribute to the anomalously large radii of
hot Jupiters (e.g. Perna et al. 2010; Knierim et al. 2022). Finally, a
magnetic field might be one of the many properties needed on Earth-like
exoplanets to sustain their habitability (e.g., Grießmeier et al. 2005a;
Lammer et al. 2009; Meadows & Barnes 2018; McIntyre et al. 2019).

Much work has been done to search for exoplanet radio emission for many
decades and a thorough overview of the theory and observations can be found in
the reviews by Zarka et al. (2015), Grießmeier (2015), and Grießmeier (2017).
Following several seminal papers (Zarka et al. 1997; Farrell et al. 1999;
Zarka et al. 2001; Zarka 2007), a large body of theoretical work has been
published (e.g., Lazio et al. 2004; Grießmeier et al. 2005b, 2007b; Hess &
Zarka 2011; Nichols 2012; Weber et al. 2017; Lynch et al. 2018; Ashtari et al.
2022; Grießmeier et al. 2023). In parallel to these theoretical studies, a
number of ground-based observations have been conducted to find exoplanet
radio emissions and most of them resulted in unambiguous non-detections (e.g.
Yantis et al. 1977; Winglee et al. 1986; Zarka et al. 1997; Bastian et al.
2000; Hallinan et al. 2013; Turner et al. 2017; Lynch et al. 2018; Cendes et
al. 2022; Narang et al. 2023). There are many degenerate reasons for the non-
detections that are discussed in Grießmeier (2017) and references therein.
Currently, there are a few tentative detections (Lecavelier des Etangs et al.
2013; Sirothia et al. 2014; Vasylieva 2015; Bastian et al. 2018) but none of
these have been confirmed by follow-up observations. By contrast, progress has
been made in detecting free-floating planets near the brown dwarf boundary
(Kao et al. 2016, 2018) and stellar emission, which could potentially
originate from star-planet interactions (e.g., Vedantham et al. 2020;
Callingham et al. 2021; Pérez-Torres et al. 2021; Pineda & Villadsen 2023;
Trigilio et al. 2023; Blanco-Pozo et al. 2023, and references within).

Recently, Turner et al. (2021, hereafter T21) tentatively detected circularly
polarized bursty and slow emission from the $\tau$ Boötis ($\tau$ Boo)
exoplanetary system using LOFAR beamformed observations. The slow and bursty
emissions were only seen around a phase (relative to the periastron) of 0.65
and 0.8, respectively (see Figure 1). The slow emission was detected between
21–30 MHz, while the bursty emission was detected between 15–21 MHz. For the
slow emission the signal could neither be confirmed with certainty nor could
it be fully refuted; however, for the bursty emission T21 found no potential
cause of a false positive. T21 determined that the signal originated from the
$\tau$ Boo system and that CMI radio emission from the exoplanet $\tau$ Boo b
is the most likely explanation. Assuming their radio signals originated from
the planet, T21 derived constraints on the magnetic field of $\tau$ Boo b that
are consistent with theoretical predictions (Grießmeier et al. 2007b;
Grießmeier 2017). More recent calculations with a new implementation of such
predictions also find compatible values for the planetary magnetic moment and
flux density (Ashtari et al. 2022; Mauduit et al. 2023) and the phases that
have been observed to have emission (Ashtari et al. 2022). On the other hand,
the derived constraints on the magnetic field of $\tau$ Boo b by T21 are in
conflict with the field strength derived by Cauley et al. (2019) via optical
star-planet interaction (SPI) observations. However, several new studies have
shown that the original SPI signatures are not statistically robust and need
to be re-evaluated(Route 2019; Strugarek et al. 2022). Therefore, more work is
needed before we can compare the SPI and radio observations. More follow-up
observations were highly advocated by T21 to confirm their tentative
detections and to search for periodicity in the signal.

Motivated by the tentative detection of radio emission from $\tau$ Boo, we
performed a large follow-up campaign at low-frequencies. This campaign was
coordinated between four different radio telescopes including LOFAR and
NenuFAR. In this paper, we only present the NenuFAR data of $\tau$ Boo. The
LOFAR data will be presented elsewhere.

##  2 Observations

All observations in this paper were taken with NenuFAR (New Extension in
Nançay Upgrading LOFAR) (Zarka et al. 2020), a large phased array located at
the Nançay Radio observatory. The data streams from all mini-arrays (each
composed of 19 individual antennas) were coherently summed together during the
observations. All beamformed observations are obtained with the UnDySPuTeD
receiver (described in Bondonneau et al. 2021), which provides the full Stokes
parameters. As part of the Early Science Phase (2019–2022), NenuFAR observed a
large sample of exoplanets and radio-active stars through a dedicated Key
Project. The $\tau$ Boo observations presented in the following were taken as
part of this Key Project.

We observed $\tau$ Boo for 64 hours with NenuFAR from 14-52 MHz in beamformed
mode with full Stokes in April and May 2020. In this study, we will only
concentrate on the Stokes V (circularly polarized flux) data since auroral
radio emissions are expected to be circularly polarized (Zarka 1998; Zarka et
al. 2004), Turner et al. (2019) showed that Stokes V data is an order of
magnitude more sensitive than Stokes I (total intensity) data for the
detection of attenuated Jovian radio bursts, and the T21 tentative detection
was in Stokes V. The observations consist of an on-target beam (“ON-beam”) and
three beams pointing to a nearby location in the sky (“OFF-beam 1”, “OFF-beam
2”, and “OFF-beam 3”). As in Turner et al. (2017, 2019); Turner et al. (2021),
we use the OFF-beams to characterize any terrestrial ionospheric fluctuations,
RFI (radio frequency interference), and instrumental systematics in the data.
In the final analysis, the OFF-beams are used to remove all these signals from
the ON-beam. Therefore, any remaining signal in the ON-beam should be
astrophysical in nature. The setup of the observations can be found in Table 1
and the positions of the ON- and OFF-beams can be found in Table 2. The
location of the OFF-beams were chosen such that they are located at an angular
distance of 2.8$\pm$0.4∘ (the second null location of NenuFAR’s PSF; Zarka et
al. 2020) from $\tau$ Boo and that they are devoid of point radio sources from
the LOFAR Multifrequency Snapshot Sky Survey (MSSS; Heald et al. 2015) with a
flux $\geq$ 300 mJy. Our observations used the 53 mini-arrays available during
the Early Science Phase. We performed the observations at night to avoid
strong contamination by RFI. The exact dates and times of each observation can
be found in Table 3 and the orbital phases111With the error bars of Wang &
Ford (2011), the orbital phase shifts by $\sim$10$\%$ over a period of 100
years. covered by the observations can be found in Figure 1. Before each
observation, we observed the pulsar B0809+74 for 17 mins using the exact same
setup. We use the pulsar observations to ensure the reliability of the data
reduction pipeline (e.g. adequate RFI masking), compare the ON and OFF beams,
and to search for systematics effects in the data. In T21, similar B0809+74
observations were used to understand and rule out certain systematics as the
cause of the detected signals (see their Appendix G). Three of the
observations (April 29, May 1, and May 2) experienced technical difficulties
resulting in only one OFF beam being recorded to disk. Due to this problem,
these observations were not used in our analysis. Therefore, the useful set of
observations covered 50$\%$ of $\tau$ Boo’s orbit. This is twice the coverage
of the T21 LOFAR observations. Most importantly, the NenuFAR observations
cover the same orbital phases as the tentative detections in T21 (Figure 1).

Table 1: Setup of NenuFAR observations

Parameter | Value | Units
---|---|---
Beams | ON, 3 OFF |
Stokes parameters | IQUV |
Number of mini-arrays | 53 |
Antennas per mini-array | 19 |
Total number of antennas | 1007 |
Minimum Frequency | 14.8 | MHz
Maximum Frequency | 52.1 | MHz
Frequency Resolution | 3.05 | kHz
Time Resolution | 10 | msec
Subbands | 192 |
Channels per Subband | 64 |
Beam diametera | 2.39 | ∘

  * •

aCalculated at 15 MHz (Zarka et al. 2020)

Table 2: Beam coordinates used for the observations

Beam | RA (J2000) | DEC (J2000) | Distance
---|---|---|---
| (h:m:s) | (∘:’:”) | ($\mathrm{\SIUnitSymbolDegree}$)
ON | 13:47:17 | 17:27:22 | —
OFF 1 | 13:49:04 | 20:20:37 | 2.9
OFF 2 | 13:38:50 | 15:23:37 | 2.9
OFF 3 | 13:55:48 | 15:21:22 | 2.9

  * •

Note: Column 1: beam name. Column 2: right ascension (RA) of the beam. Column
3: declination (DEC) of the beam. Column 4: distance of the beam from the ON-
beam.

Table 3: Summary of NenuFAR observations

Obs $\\#$ | Start Date | Time | Duration | Phase
---|---|---|---|---
| (UT) | (UT) | (hrs) |
$\tau$ Boötis [64 hrs]
1 | April 11, 2020 | 20:00-04:00 | 8 | 0.60–0.70
2 | April 15, 2020 | 20:00–04:00 | 8 | 0.81–0.91
3 | April 23, 2020 | 19:30–03:30 | 8 | 0.22–0.32
4 | April 24, 2020 | 19:00–03:00 | 8 | 0.51–0.61
5 | April 28, 2020 | 19:00–03:00 | 8 | 0.72–0.82
6a | April 29, 2020 | 19:00–03:00 | 8 | 0.02–0.12
7a | May 1, 2020 | 18:30–02:30 | 8 | 0.62–0.72
8a | May 2, 2020 | 18:30–02:30 | 8 | 0.92–0.02
B0809+74 [2.27 hrs]
1 | April 11, 2020 | 19:41–19:58 | 0.28 | –
2 | April 15, 2020 | 19:42–19:59 | 0.28 | –
3 | April 23, 2020 | 19:11–19:28 | 0.28 | –
4 | April 24, 2020 | 18:41–18:58 | 0.28 | –
5 | April 28, 2020 | 18:41–18:58 | 0.28 | –
6a | April 29, 2020 | 18:41–18:58 | 0.28 | –
7a | May 1, 2020 | 18:11–18:28 | 0.28 | –
8a | May 2, 2020 | 18:11–18:28 | 0.28 | –

  * •

aOnly 1 OFF beam was recorded

Figure 1: Orbital phase coverage for the observations of $\tau$ Boo b. The
orbital phase was calculated using the ephemeris from Wang & Ford (2011) and
is relative to periastron of $\tau$ Boo b. The LOFAR and NenuFAR observations
are labeled in red and orange, respectively. The original LOFAR observations
were taken between February 18, 2017 and March 25, 2017. The $\tau$ Boo LOFAR
observations with the tentative detections are displayed as large dark-blue
rectangles. The tentative detection of burst emission was seen on February 18,
2017 and the slow emission was seen on March 6, 2017. An arbitrary number of
days was placed between the 2020 and 2017 observations for clarity.

##  3 Data Reduction

The raw beamformed exoplanet observations from NenuFAR are produced by
coherently summing all the signals from each dipole antenna. They represent
125 GB / hour stored at the Nançay data center. The reduction pipeline applied
to our data consisted in computing the 4 Stokes parameters (I, Q, U, and V),
and applying RFI mitigation and correction of the time variations of the
instrumental gain, before integrating the measurements on 250 ms $\times$ 48
kHz bins (i.e. 24 $\times$ 16 raw bins). The purpose of the RFI mitigation is
to prevent polluted 3.05 $\times$ 10 ms bins to be included in the integrated
250 ms $\times$ 48 kHz bins, thus it is restricted to scales smaller than 250
ms in time and 48 kHz in frequency. RFI at larger scales are not eliminated at
the reduction stage, and must be flagged in the post-processing stage. For the
2020 data, only the intensity (I), circular polarization (V) and linear
polarization ($L=(Q^{2}+U^{2})^{1/2}$ were stored. The reduced data, flag
masks, time and frequency ranges, and housekeeping data are stored as standard
fits files, of volume $\sim$400 times smaller than the raw data, thus easy to
post-process. This data is labeled as level 2 data (L2) whereas the level 1
data (L1) is the raw data. The raw data are then erased.

An example dynamic spectra of the L2 data for $\tau$ Boo can be found in
Figure 2A. In this figure, lots of systematics are still clearly visible in
the data. The source of many of the features is not yet well understood but
several have a known origin. For example, the analog beams of NenuFAR are re-
pointed every 6 minutes to ensure accurate source tracking. These re-pointings
are clearly visible in the data as the baseline changes after every new
pointing. The blobs above 30 MHz are caused by bright-sources in the grating
lobes of NenuFAR.

(A)

(B)

Figure 2: The dynamic spectra in Stokes V for the April 23, 2020 $\tau$ Boo
observation with NenuFAR. (A.) Example of a pre-processed (L2) dynamic
spectra. The intensity in the dynamic spectrum is in arbitrary units. (B.)
Example of a high-pass filtered dynamic spectra. The dynamic spectrum is
normalized by the standard deviation of the observations.

Next, the L2 data were processed using the BOREALIS (BeamfOrmed Radio Emission
AnaLysIS) pipeline (Turner et al. 2017, 2019; Turner et al. 2021). We
performed RFI mitigation using a similar setup as in T21. Due to the
complexity of the NenuFAR data (e.g. six-minute pointing jumps), we did not
correct for the time-frequency background of the observations. This will be
done in future work. This limitation is the reason why we only search for
bursty emission in this study. After RFI mitigation we re-binned the data to a
time and frequency resolution of 1 second and 45 kHz, respectively. This
rebinned data was then fed into the post-processing part of BOREALIS.

In order to determine the reliability of the NenuFAR data, we processed the
pulsar (B0809+74) through the BOREALIS pipeline. In order to detect B0809+74
we perform an FFT on the RFI masked, de-dispersed (the data is de-disperse
using the pulsar’s known dispersion measure), and rebinned data (we only
rebinned the data in frequency). The FFT was computed using data from 40-50
MHz. Figure 3 shows an FFT of B0809+74 using NenuFAR data taken on April 23,
2020. The pulsar is detected with a signal-to-noise of $\sim$6 at its known
period. Based on this result, we are confident that the pipeline masks the RFI
adequately and will allow for the search for bursty signals from the
exoplanet.

Figure 3: FFT of the pulsar B0809+74 for the NenuFAR data taken on taken on
April 23, 2020. The known period is denoted as the dashed line and the pulsar
is detected with a signal-to-noise of $\sim$6 around this period.

In the post-processing, we only searched for burst emission. A very detailed
description of the burst emission observables can be found in Turner et al.
(2019) and T21 and we describe them briefly below. The post-processing is
performed on the absolute value of the corrected Stokes V data as defined in
Turner et al. (2019). For burst emission, we only use the Q2 and Q4a-f
observable quantities. The Q2 observable consists of one time series per beam
(ON, OFF1, OFF2, and OFF3). It is obtained by high-pass filtering the dynamic
spectrum. An example of a high-pass filtered dynamic spectrum for $\tau$ Boo
can be found in Figure 2B. To search for faint emission, the high-pass
filtered dynamic spectrum is integrated over a large frequency range (e.g.,
bin sizes of 10 MHz) to produce a time series. Q2 can be represented by a
“scatter plot” comparing a pair of beams (e.g., the ON and one of the OFF
beams) and is designed to find bursty emission (with time scales $<\sim$ 1
minute). The quantities Q4a to Q4f provide statistical measures of the bursts
identified by the Q2 quantity. When examining Q4a-f, the ON and OFF time
series are compared to each other; for this, we introduce the difference curve
Q4f${}_{\text{Diff}}$=Q4f(ON)-Q4f(OFF). We then plot this curve against a
reference curve computed from 10000 draws of purely Gaussian noise.

The post-processing was performed separately over 4 different frequency ranges
(15 - 21 MHz, 15-52 MHz, 15-33 MHz, and 33-52 MHz). All other post-processing
parameters are similar to those of T21. In this paper, we search for burst
emission in the data that has binned to 1 second and highpass filtered with a
smoothing timescale of 10 seconds. Therefore, only emission less than 10
seconds can be searched for in the data. T21 only observed burst emission at
this same timescale.

##  4 Results

We searched for excess signal in the ON-beam both by eye and using the
automated search procedure outlined in T21. We applied the same criteria as in
Turner et al. 2019; Turner et al. 2021 for a possible detection. We do not
find any burst emission in the NenuFAR observations for any of the probed
wavelength ranges. The burst statistics were similar between all ON and OFF
beams. An example of the diagnostics for a non-detection can be found in
Figure 4, based on the April 23, 2020 NenuFAR observation, analyzed between
15-32 MHz. The ON-OFF and OFF-OFF difference curves are very similar to each
other and all curves are systematically non-Gaussian. We performed a red-noise
analysis on the Q2 time series for the ON and OFF beams using the wavelet
technique of Carter & Winn (2009) as implemented in the EXOMOP code by Turner
et al. (2016b). The wavelet technique assumes that the time series is an
additive combination of noise with Gaussian white noise and red noise
(characterized as a power spectral density proportional to $1/f^{\alpha}$). We
find that the red and white noise components are nearly equal in magnitude. We
will investigate this systematic noise in the data in future work.

|
---|---
|
|

(a)

(b)

(c)

(d)

(e)

(f)

Figure 4: Non-detection of burst emission for $\tau$ Boo in the April 15, 2020
NenuFAR observation between 15-32 MHz in Stokes V. Panel a: Q2 for the ON-beam
vs the OFF-beam 2. Panel b: Q2 for the OFF-beam 1 vs the OFF-beam 2. Panel c:
Q4a (number of peaks). Panel d: Q4b (power of peaks). Panel e: Q4e (peak
offset). Panel f: Q4f (peak offset). For panels c to f the black lines are the
ON-beam difference with the OFF beam 2 and the red lines are the OFF-beam
difference. The dashed lines are statistical limits (1, 2, 3$\sigma$) of the
difference between all the Q4 values derived using two different Gaussian
distributions (each performed 10000 times). We do not see any excess signal in
the ON-beam compared to the OFF-beams.

##  5 Discussion

We do not detect any burst emission in our NenuFAR observations. This is
consistent with the simultaneous LOFAR observations that also did not detect
any bursty emission that will be presented elsewhere. The original LOFAR
observations (T21) only detected burst emission flux during one four-hour
observation centered around an orbital phase of 0.8 (Figure 1). All the
NenuFAR observations besides April 15, 2020 are consistent with this finding.
Based on T21, one might have expected to detect bursty emission at orbital
phase 0.8, i.e. for the NenuFAR observation of April 15, 2020.

There are many different degenerate reasons for our non-detection of burst
emission from $\tau~{}$Boo:

  1. (a)

It is possible that the original 3.2$\sigma$ bursty signal detected by T21 was
caused by an unknown instrumental systematic or statistical anomaly. An
extensive systematic study was undertaken by T21 and no plausible cause for a
false positive signal could be identified for the bursty emission signature.
In the future, a statistical comparison between many LOFAR and NenuFAR
datasets may shed light on this issue.

  2. (b)

An extended, evaporating atmosphere can lead to conditions in the planetary
magnetosphere that doesn’t allow the CMI mechanism to operate (the local
electron plasma frequency is greater than the local electron cyclotron
frequency, $\omega_{p}$ $>$ $\omega_{c}$; Grießmeier et al. 2023, e.g.).
However, for a planet as massive as $\tau~{}$Boo b, this effect is not
expected (Weber et al., 2018). On the other hand, if the planetary magnetic
field is as low as estimated by Reiners & Christensen (2010), the condition
for the CMI to operate is only marginally fulfilled (Weber et al., 2018,
Figure 5), and temporal variations could, in principle, lead to a situation
where the emission does not operate continuously. It is worth noting that Kao
et al. (2016, 2018) showed that the Reiners & Christensen (2010) magnetic
field predictions may not be applicable for all brown dwarfs. However, it is
currently unclear if the contradiction found by Kao et al. (2016, 2018)
extends to hot Jupiters such as $\tau$ Boo b. More work is needed to
understand this limitation.

  3. (c)

The observations could have been taken at an unfavorable rotational phase of
the star. Planetary radio emission is triggered by the interaction of the
planetary magnetosphere with the magnetized stellar wind (Zarka et al. 2001;
Zarka 2018). For this reason, the expected intensity of the planetary radio
emission differs greatly with stellar rotation (e.g. Grießmeier et al. 2005b;
Grießmeier et al. 2007a; Fares et al. 2010; Vidotto et al. 2012; See et al.
2015; Strugarek et al. 2022). See et al. (2015) showed that the expected radio
flux of $\tau~{}$Boo b can disappear entirely for certain stellar rotation
phases. We cannot rule out variability in the radio signal due to observing at
different stellar rotation phases (no stellar differential rotation
constraints exist during our 2020 observing campaign).

  4. (d)

The observations could have been taken at an unfavorable time in the stellar
magnetic cycle. The host star $\tau~{}$Boo is known to undergo a rapid
magnetic cycle of 120 days (Jeffers et al. 2018). Similarly to the stellar
rotation, this is expected to modulate the planetary radio emission (e.g.
Fares et al. 2009; Vidotto et al. 2012; See et al. 2015; Elekes & Saur 2023).
See et al. (2015) also found that the expected radio flux of $\tau~{}$Boo b
(at optimal stellar longitude) can vary by a factor of $\sim$5 along the
stellar magnetic cycle. Most recently, Elekes & Saur (2023) showed that a
magnetic polarity reversal of the host star towards an anti-aligned field
configuration would result in the planetary radio emission being below the
detection threshold of NenuFAR. However, no stellar magnetic field data of
$\tau$ Boo exists during our 2020 observing campaign. Therefore, we cannot
rule out variability in the radio signal due to observing at different moments
of the stellar magnetic cycle.

  5. (e)

Unlike Jupiter’s decametric emission (Zarka 1998), the planetary emission from
$\tau$ Boo might not always be on. This would imply that the magnetosphere
dynamics of $\tau$ Boo b would be different than that of Jupiter. For example,
the density of the magnetosphere could be variable and perhaps temporarily
become void of particles.

A large follow-up campaign is needed to disentangle the true cause of the
possible variability of the planetary radio emission. Multi-site observations
are highly encouraged to rule out instrumental systematics. Monitoring the
planet throughout its orbit and the stellar magnetic cycle is necessary to
disentangle the competing effects. There is also a need for measurements of
the stellar magnetic field taken throughout the radio follow-up campaign. Such
a coordinated campaign is currently ongoing, using NenuFAR for the radio
emission, and the TBL/Neo-Narval to monitor the magnetic field of the host
star.

With our non-detection, we can place an upper limit on the radio emission from
the $\tau$ Boo system at the time of the observations. Since NenuFAR is still
in early commissioning the system equivalent flux density (SEFD) is currently
not well characterized. Therefore, we will approximate our upper limit of
NenuFAR based-off the sensitivity limit found for LOFAR in Turner et al.
(2019). The theoretical sensitivity limit of LOFAR for broadband bursts

$\displaystyle\sigma_{LOFAR}=$ $\displaystyle\frac{S_{Sys}}{N\sqrt{b\tau}},$
(1) $\displaystyle\sigma_{LOFAR}=$ $\displaystyle\frac{40kJy}{24\sqrt{1\
sec\times 18\ MHz}}=393\ mJy$ (2)

where $N$ is the number of stations (24), $b$ is the bandwidth (18 MHz using
the 15-33 MHz frequency range), $\tau$ is the timing resolution (1 sec), and
$S_{Sys}$ is the station SEFD with a value of 40 kJy (van Haarlem et al.
2013). Turner et al. (2019) measured the sensitivity limit of LOFAR to be
$1.3\times\sigma_{LOFAR}$ and we will use this value below. For the burst
emission from NenuFAR, we find a 3$\sigma$ flux upper limit of 1.5 Jy and 590
mJy assuming NenuFAR is as sensitive and twice as sensitive as LOFAR,
respectively. This limit is a conservative preliminary estimate as NenuFAR is
expected to be more sensitive (at least 2–5$\times$) than LOFAR between 15–30
MHz. In the future, the SEFD of NenuFAR will be accurately measured and we
will perform a comprehensive sensitivity estimation using Jupiter radio
emission simulated as if it was an exoplanet (using the same method used to
obtain the sensitivity limit for LOFAR observations in Turner et al. 2019).
Therefore, we expect to have a more precise upper limit in future work.

The current NenuFAR observations are informative on the nature of $\tau$ Boo
b’s radio emission. The original tentative detection of burst emission from
T21 was observed to have a flux density of 890 mJy. Therefore, we would have
detected the burst emission of $\tau$ Boo b (in the absence of variability,
see above) at $\sim$4.5 $\sigma$ using the NenuFAR conservative sensitivity
limit (2$\times$ as sensitive as LOFAR) of $\sim$200 mJy. We also expected to
observe bursty emission at an orbital phase (e.g. 0.8) similar to that found
in T21 and validated in the model by Ashtari et al. (2022). Therefore, the
observed phases and the current upper limits can be used as priors in
theoretical predictions (e.g Elekes & Saur 2023; Ashtari et al. 2022) in the
expected variability of $\tau$ Boo b’s radio emission.

##  6 Conclusions and Perspectives

In this study, we search for bursty emission from the $\tau$ Boo exoplanetary
system using NenuFAR during its commissioning phase in 2020. This is the first
exoplanet observation from NenuFAR to be published. These observations are
part of a large ongoing follow-up campaign to confirm the tentative detections
of radio emission from $\tau$ Boo observed by LOFAR (Turner et al. 2021). We
do not detect any bursty emission in the NenuFAR observations and the reason
for this non-detection is degenerate. Possible interpretations include the
possibility that the original burst detection was an unknown systematic error
or that radio emission from $\tau$ Boo b is variable in time. Further analysis
on the NenuFAR data and more observations are needed to fully understand the
radio emission from the $\tau$ Boo system. Such observations are currently
ongoing.

## Acknowledgements

J.D. Turner was supported for this work by NASA through the NASA Hubble
Fellowship grant $\\#$HST-HF2-51495.001-A awarded by the Space Telescope
Science Institute, which is operated by the Association of Universities for
Research in Astronomy, Incorporated, under NASA contract NAS5-26555.

This paper is based on data obtained using the NenuFAR radio-telescope. The
development of NenuFAR has been supported by personnel and funding from:
Observatoire Radioastronomique de Nançay, CNRS-INSU, Observatoire de Paris-
PSL, Université d’Orléans, Observatoire des Sciences de l’Univers en Région
Centre, Région Centre-Val de Loire, DIM-ACAV and DIM-ACAV+ of Région Ile-de-
France, Agence Nationale de la Recherche.

We acknowledge the use of the Nançay Data Center computing facility (CDN -
Centre de Données de Nançay). The CDN is hosted by the Station de
Radioastronomie de Nançay in partnership with Observatoire de Paris,
Université d’Orléans, OSUC and the CNRS. The CDN is supported by the Region
Centre-Val de Loire, Département du Cher.

This work was supported by the Programme National de Planétologie (PNP) of
CNRS/INSU co-funded by CNES and by the Programme National de Physique
Stellaire (PNPS) of CNRS/INSU co-funded by CEA and CNES. PZ acknowledges
funding from the ERC under the European Union’s Horizon 2020 research and
innovation programme (grant agreement no. 101020459 - Exoradio).

The Nançay Radio Observatory is operated by the Paris Observatory, associated
with the French Centre National de la Recherche Scientifique (CNRS).

This research has made use of the Extrasolar Planet Encyclopaedia
(exoplanet.eu) maintained by J. Schneider (Schneider et al. 2011), the NASA
Exoplanet Archive, which is operated by the California Institute of
Technology, under contract with the National Aeronautics and Space
Administration under the Exoplanet Exploration Program, and NASA’s
Astrophysics Data System Bibliographic Services. In this paper, all the
physical characteristics for the pulsar B0809+74 were taken from the ATNF
Pulsar Catalogue (Manchester et al., 2005) located at
http://www.atnf.csiro.au/research/pulsar/psrcat.

We thank the anonymous referees for their useful and thoughtful comments.

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