# Nonlinear force-free coronal magnetic stereoscopy

Iulia Chifu,1,2 Thomas Wiegelmann1, Bernd Inhester1 1 Max-Planck-Institut für
Sonnensystemforschung, Justus-von-Liebig-Weg 3, 37077 Göttingen, Germany;
<EMAIL_ADDRESS>
2 Astronomical Institute of Romanian Academy, Cutitul de Argint 5, Bucharest,
Romania

(Draft version December 20, 2016.)

###### Abstract

Getting insights into the 3D structure of the solar coronal magnetic field
have been done in the past by two completely different approaches: (1.)
Nonlinear force-free field (NLFFF) extrapolations, which use photospheric
vector magnetograms as boundary condition. (2.) Stereoscopy of coronal
magnetic loops observed in EUV coronal images from different vantage points.
Both approaches have their strength and weaknesses. Extrapolation methods are
sensitive to noise and inconsistencies in the boundary data and the accuracy
of stereoscopy is affected by the ability of identifying the same structure in
different images and by the separation angle between the view directions. As a
consequence, for the same observational data, the computed 3D coronal magnetic
field with the two methods do not necessarily coincide. In an earlier work
(Paper I) we extended our NLFFF optimization code by the inclusion of
stereoscopic constrains. The method was successfully tested with synthetic
data and within this work we apply the newly developed code to a combined
data-set from SDO/HMI, SDO/AIA and the two STEREO spacecraft. The extended
method (called S-NLFFF) contains an additional term that monitors and
minimizes the angle between the local magnetic field direction and the
orientation of the 3D coronal loops reconstructed by stereoscopy. We find that
prescribing the shape of the 3D stereoscopically reconstructed loops the
S-NLFFF method leads to a much better agreement between the modeled field and
the stereoscopically reconstructed loops. We also find an appreciable decrease
by a factor of two in the angle between the current and the magnetic field
which indicates the improved quality of the force-free solution obtained by
S-NLFFF.

Sun: corona, Sun: magnetic fields, methods: numerical

iint iiint iiiint idotsint AMSiint AMSiiint AMSiiiint AMSidotsint

##  1 Introduction

Knowledge of the 3D structure of the solar coronal magnetic field is essential
to understand basically all physical processes in the corona. The reason is
that the magnetic field clearly dominates and structures the corona, because
the plasma $\beta$ (ratio of plasma and magnetic pressure) is very small.
Unfortunately direct measurements of the coronal magnetic field are not
routinely available and two distinct methods have been developed to
reconstruct the coronal magnetic field: 1.) extrapolations of photospheric
vector fields into the corona under the force-free assumption (see Wiegelmann
& Sakurai, 2012, for a review) and 2.) Stereoscopy of coronal images (see
Aschwanden, 2011, for a review). Both methods are not perfect if applied to
observational data. Photospheric vector magnetograms contain noise and are not
necessarily force-free consistent because of the mixed plasma $\beta$ in the
lower solar atmosphere (Gary, 1990). For a stereoscopic reconstruction from
different vantage points one first has to extract loop-like structures from
EUV-images, identify the same loop in both images (association problem) and
finally perform the 3D stereoscopy (large error at loop-top for East-West
loops). Consequently the output of NLFFF and stereoscopy can be different (see
De Rosa et al., 2009, for a comparison of NLFFF-models and stereoscopy).

It is therefore natural to combine photospheric measurements and stereoscopy
to obtain coronal magnetic field measurements which comply with both data
sets. Several such attempts have been made, whereas the methods developed so
far use the photospheric line-of-sight field, rather than the full vector
field, as boundary condition. First attempts have been made about one and a
half decade ago by Wiegelmann & Neukirch (2002) using linear force-free fields
with SOHO/MDI magnetograms as boundary conditions. In this approach the linear
force-free parameter $\alpha$ was computed by comparing the resulting fields
with 3D-loops from dynamic stereoscopy (see Aschwanden et al., 1999). That
time, well before the launch of STEREO, images from different vantage points
have been observed using the rotation of the Sun, and it was therefore
necessary to limit the method to almost stationary structures. The method was
later extended by Carcedo et al. (2003) to compute the linear force-free
$\alpha$ also directly from coronal images from one viewpoint only. In
subsequent works, still within the limitations of linear force-free models,
projections of the magnetic field loops have been used to solve the
stereoscopic association and ambiguity problem. The method was dubbed magnetic
stereoscopy (see Wiegelmann & Inhester, 2006; Feng et al., 2007, for details)

Linear force-free fields have their limitation (see, e.g., Wiegelmann, 2008)
and in particular the best fit value of $\alpha$ for different loops within
one active region are different and $\alpha$ can even change it’s sign.
Aschwanden et al. (2012) incorporated a forward fitting method, which uses
analytic expressions and different values of $\alpha$ along different loops,
thereby approximating a nonlinear force-free field. The method was refined in
Aschwanden (2013a, c) and subsequent code versions allow using 2D-loop
projections rather than 3D-stereo-loops. The method was intensively tested,
compared with extrapolations from vector magnetograms and further refined in a
number of subsequent paper, (e.g. Aschwanden & Malanushenko, 2013; Aschwanden,
2013b; Aschwanden et al., 2014; Aschwanden, 2016). It was dubbed Vertical-
Current Approximation Nonlinear Force-Free Field (VCA-NLFFF) code.

While VCA-NLFFF avoids several problems of magnetic field extrapolations from
photospheric vector magnetograms, e.g. the assumption that the boundary data
are force-free consistent is not necessary, the method uses only the line-of-
sight photospheric magnetic field and not the full vector field.

Malanushenko et al. (2012, 2014) proposed a NLFF field extrapolation method,
called Quasi-Grad-Rubin, which uses the line-of-sight component of the surface
magnetic field and the 2D shapes of the coronal loops from a single image as
constraints for their extrapolation. They tested the method with a semi-
analytic solution and also applied it on observational data.

Within this work, we propose a new method which we call Stereoscopic Nonlinear
force-free field code (S-NLFFF). The method uses both photospheric vector
magnetograms (here from SDO/HMI) and stereoscopic reconstructed 3D-loops as
input. Necessarily providing all these conditions over-imposes the boundary
condition and one cannot find a solution which strictly fulfills constraints
which probably contradicts each other. The advantage of our new method is that
the different constraints (force-freeness, photospheric magnetic field vector,
3D-stereo-loops) are all considered as terms of one functional, each weighted
with certain Lagrangian multipliers. These free parameters allow to specify
measurement errors (both in the photospheric field as well as in the
prescribed 3D-loops) and the code iterates for an optimal solution in the
sense that deviation from the boundary conditions are allowed in regions with
a substantial measurement error (photospheric field vector) and reconstruction
error (stereo-loops). The method was described and tested with synthetic data
in Chifu et al. (2015) (Paper-I).

The paper is outlined as follows: in section 2 we make a short description of
the methods used for the reconstruction of the 3D coronal loops and of the 3D
magnetic field, in section 3 we present the data used for the reconstructions,
in section 4 we show the 3D reconstruction, in section 5 we present the
results and in section 6 we discuss the results.

##  2 Methods

###  2.1 Multiview B-spline Stereoscopic Reconstruction (MBSR)

The 3D shape of solar loop-like structures (e.g. coronal loops, prominences,
leading edge of coronal mass ejections) can be performed using stereoscopic
reconstruction. Two-view directions are sufficient for a 3D reconstruction
from an ideal data set. The use of more views brings more accuracy to the
reconstruction if the data are noisy. The main steps in the stereoscopic
reconstruction are: the identification of the object to be reconstructed in
all of the available views; matching the object by tie-pointing; the
reconstruction (Inhester, 2006). Usually, as a final step the stereoscopically
reconstructed points from the loop-like structure often needs to be smoothed
by fitting a polynomial or a spline curve (Chifu, 2016).

The main idea of the MBSR method is the reconstruction in one go of an entire
loop-like structure. Instead of calculating pairwise reconstructions from
multiple views which in the end needs to be averaged, our code is able to
reconstruct tie-pointed curves from two or more views directly. The tie-points
do not have to be related by a common epipolar coordinate and therefore be
used directly in more than 2 views. It is designed to yield a unique 3D
B-spline as approximation to the reconstructed loop curve, the projections of
which optimally matches all tie-points in all images. The local error depends
only on the projected distances of the tie-points position to the final spline
curve (Chifu, 2016).

###  2.2 Stereoscopic-Nonlinear Force-Free Field extrapolation (S-NLFFF)

The modeling of the magnetic field in the solar corona is possible under
certain assumptions. The plasma $\beta$ model by Gary (2001) shows that in the
corona the magnetic pressure dominates over the plasma pressure and gravity
effects and the kinematic ram pressure of plasma flows are small (Wiegelmann &
Sakurai, 2012), too. In this approach, called the force-free field assumption,
the Lorentz-force vanishes and has to fulfill the non-linear equation
($\mathbf{j}\times\mathbf{B}=0$) together with the solenoidal condition
($\nabla\cdot\mathbf{B}=0$).

To model the coronal magnetic field using nonlinear force-free field
extrapolations, one needs surface observations of all three components of the
magnetic field as boundary condition. We solve the force-free equations with
the help of an optimization approach, which has originally been proposed by
Wheatland et al. (2000) and extended by Wiegelmann (2004); Wiegelmann &
Inhester (2010). Recently, the NLFFF optimization method was extended by
constraining the magnetic field to be aligned to the 3D coronal loops
stereoscopically reconstructed from EUVI images (Chifu et al., 2015).

The essential approach of the extended S-NLFFF method is to minimize a scalar
cost function ($\mathrm{L_{tot}}$) which consists of a number of terms
quantifying constraints the final solution should satisfy. The terms of the
functional are

$\displaystyle\text{L}_{\textit{1}}=\int_{V}w_{f}\frac{|(\nabla\times\mathbf{B})\times\mathbf{B}|^{2}}{B^{2}}\;d^{3}r,$
(1)
$\displaystyle\text{L}_{\textit{2}}=\int_{V}w_{f}|\nabla\cdot\mathbf{B}|^{2}\;dr^{3},$
(2)
$\displaystyle\text{L}_{\textit{3}}=\int_{S}(\mathbf{B}-\mathbf{B}_{obs})\cdot\mathrm{diag(\sigma^{-2}_{\alpha})}\cdot(\mathbf{B}-\mathbf{B}_{obs})\;d^{2}r,$
(3)
$\displaystyle\text{L}_{\textit{4}}=\sum_{i}\int_{\mathbf{c}_{i}}\frac{1}{\sigma^{2}_{c}}{|\mathbf{B}\times\mathbf{t}_{i}|^{2}}\;ds,$
(4) $\displaystyle\text{where}\quad\mathbf{t}_{i}=\frac{d\mathbf{c}_{i}}{ds}.$
(5)

The function to be minimized is

$\mathrm{L_{tot}}=\sum_{n}\xi_{n}L_{n},$ (6)

where $\xi_{i}$ are regularization weights. Our experience from Chifu et al.
(2015) suggests $\xi_{i}=1$ as an acceptable choice for the weights.

The computational box has an inner physical domain surrounded by a buffer zone
on the top and lateral boundaries. The force-free and divergence-free
conditions are satisfied if the first two terms (Eq. 1 and 2) are minimized to
zero. $w_{f}$ is a boundary weight function which is set to unity in the
physical domain and it decreases monotonically to zero towards the outer
buffer zone (see Wiegelmann, 2004, for more details). The third term (Eq. 3)
minimizes the differences between the observed and modeled magnetic field at
the bottom boundary, while the fourth term (Eq. 4) minimizes the angles
between the modeled magnetic field and the tangents of the stereoscopically
reconstructed loops. In Eq. 3, $\sigma_{q}(\mathbf{r})$ are estimated
measurement errors for the three field components $\textit{q}=x,y,z$ on $S$
(see Tadesse et al., 2011, for more details). In Eq. 4, $\sigma_{c_{i}}(s)$ is
a relative measure of the estimated error of the tangent direction
$\mathbf{t}_{i}(s)$ along the loop $i$. A detailed description of the NLFFF
optimization method (the L${}_{\textit{1}}$, L${}_{\textit{2}}$,
L${}_{\textit{3}}$ terms) can be found in Wheatland et al. (2000); Wiegelmann
(2004); Wiegelmann & Inhester (2010) and about S-NLFFF method (the
L${}_{\textit{4}}$ term) can be found in Chifu et al. (2015).

##  3 Observational data

One of the criteria for selecting the data set was the separation angle
between the two STEREO spacecraft.The stereoscopic reconstruction requires a
separation angle between the view points larger than zero degrees and less
than 180∘. For the selected event, the separation angle with respect to the
center of the Sun between the two STEREO spacecraft was approximately 147∘,
between STEREO A and SDO 77∘, between STEREO B and SDO 70∘ (Fig. 1) .

Figure 1: Images of the Sun with the active region AR 11087 from three
different views observed on 2010 July 15 at 08:14 UT in 171 Å wavelength. The
red rectangle marks the active region. In the left panel we display the
EUVI/STEREO B image, in the middle panel, the AIA/SDO image and in the right
panel, the EUVI/STEREO A image.

Figure 2: HMI/SDO vector magnetogram observed on 2010 July 15 at 08:14 UT.

Another selection criteria was the position of the active region on the solar
surface as seen from the SDO spacecraft. As the accuracy of the photospheric
field measurements become strongly reduced towards the limb, we choose ARs
close to the disk center as seen from SDO (Fig. 1, middle panel). A data set
which fulfills these criteria is the active region AR 11087 observed on 2010
July 15. We performed the 3D stereoscopic reconstruction using simultaneously
extreme ultra-violet ($\lambda$ = 171 Å) images recorded by the EUVI telescope
onboard STEREO A and B and by the AIA telescope onboard SDO. The EUVI
telescope has a FOV up to 1.7 R⊙ ($\backsimeq$ 1182.7 Mm) and a spatial
sampling of 1.6 arcsec pixel-1 (Wuelser et al., 2004). AIA onboard SDO takes
EUV images with a FOV of 1.5 R⊙ and 0.6 arcsec pixel-1 spatial sampling at
each 12 seconds (Lemen et al., 2012). For the extrapolation of the NLFFF we
used vector magnetograms provided by HMI/SDO (Fig. 2).

##  4 Data reconstruction

###  4.1 Two and three view stereoscopic reconstruction

One of the very important steps in 3D stereoscopic reconstruction is the
correct identification and matching of the objects for reconstruction (e.g.
coronal loops). In an ideal case, the objects for reconstruction have to be
clearly visible and therefore easily identifiable.

In many of the solar EUV observations the objects for reconstruction are not
traceable in a straight forward manner. According to Stenborg et al. (2008)
the major reasons for poor visualization of the data are the low contrast
between the coronal structures and the background and the multiscale nature of
the coronal features. Another reason is that in the EUV images we see the
line-of-sight (LOS) integration of the radiation emitted by all the loops in a
particular wavelength band. A variety of data processing procedures exists to
enhance the visibility of the loop structures (Stenborg et al., 2008). The
best method for our data processing we found to be the noise adaptive fuzzy
equalization (NAFE) method developed by Druckmüller (2013). The method is
based on histogram equalization and unsharp masking. We have applied this
method for all of the three EUV images used in our 3D reconstructions.

Figure 3: Projection of the 3D stereoscopically reconstructed loops overploted
over the STEREO B (left panel), SDO (middle panel) and STEREO A (right panel).
The magenta loops are reconstructed using all of the three spacecraft, the
green loops are reconstructed using STEREO A and SDO and the light blue loops
are reconstructed using STEREO B and SDO.

While some of the visualization problems can be resolved with image processing
techniques, other problems such as saturated pixels cannot be resolved. In the
data from STEREO A and B patches of saturated pixels restrained our
identification and matching possibilities required by the reconstruction.

The configuration of the three spacecraft does not provide images with a
visibility of the entire AR from all three vantage points simultaneously. Even
though the data captured by the spacecraft fulfills our criteria of selection,
the position of the three telescopes limits the number of loops which we can
identify, trace and reconstruct. While the SDO satellite (see Fig. 1, middle
panel) has a full view of the AR, the STEREO A (see Fig. 1, right panel) and B
(see Fig. 1, left panel) spacecraft were viewing a limited common area. In
spite of all these above difficulties we could identify ten loops. Three loops
were traced in all of the three images, three more loops in STEREO A and SDO
and four loops in STEREO B and SDO.

In Fig. 3 we show the projection of the 3D stereoscopically reconstructed
loops together with their tie-points (the black crosses) on each of the EUV
images. In Fig. 4 we present the 3D configuration of the Sun, represented as a
gray sphere, and the direction of the three spacecraft together with the 3D
reconstructed loops. The red loops are reconstructed using simultaneously all
three spacecraft, the blue loops are reconstructed using the data from STEREO
A and SDO while the green loops are based on the data from STEREO B and SDO.

Figure 4: Solar toy model with the 3D reconstructed loops on top. The blue
segments represents the direction towards the three spacecraft.

###  4.2 S-NLFFF reconstruction

The S-NLFFF reconstruction uses as input the photospheric vector-magnetograms
provided by SDO/HMI and the 3D reconstructed loops described above. The HMI
vector-magnetograms are mapped from the Helioprojective Cartesian to the
Carrington Heliographic - Cylindrical Equal Area (CRLT/CRLN-CEA) coordinate
system (Bobra et al., 2014) in which we compute the 3D field reconstruction.
The stereoscopically reconstructed loops were first calculated in HEEQ
(Heliospheric Earth EQuatorial) coordinates and then mapped to the Carrington
Heliographic coordinate system.

Figure 5: Plot of the 3D stereoscopically reconstructed loops inside the
S-NLFFF computation box. At the bottom of the box, the radial component of the
magnetic field is displayed.

The computational box is 480$\times$272$\times$240 (pixels)3 which is the
equivalent of 350$\times$198$\times$175 (Mm)3. In the Fig. 5 we show a 3D plot
of the radial component of the magnetic field, color-coded at the bottom
surface, along with the 3D stereoscopically reconstructed loops above.

The NLFF field reconstructions are calculated iteratively from an initial
magnetic field until the field has relaxed to a force-free state. In order to
find out how the final solution depends on the initial field and also to
determine the impact of the loop data, we present alternative solution
strategies.

Typically, the initial field for the iteration is the potential field
$\mathbf{B_{\text{pot}}}$ determined in the entire box from the normal
component of the surface field. As an alternative, we iterate
$\mathbf{B_{\text{pot}}}$ first on a coarse 240$\times$136$\times$120 grid and
map the force-free field thus obtained from the coarse to the final
480$\times$272$\times$240 grid (so called multiscale approach). This
interpolated force-free field is then used as initial field for the final
iteration. For the coarse grid iteration, the boundary data is resampled
accordingly from the original vector-magnetogram data. To see the effect of
the loop data, we switch the loop constraint on, at different stages of the
iteration.

We present here the result from five different setups

Setup 1

Starting from $\mathbf{B_{\text{pot}}}$ we iterate the force-free solution
using the NLFFF on the final 480$\times$272$\times$240 grid without loop data.
This is the conventional approach.

Setup 2

Starting from $\mathbf{B_{\text{pot}}}$ we use S-NLFFF on the final grid,
i.e., we include the loop data from the beginning of the iterations.

Setup 3

We use the solution from Setup 1 as initial field for an iteration with
S-NLFFF.

Setup 4

We start from $\mathbf{B_{\text{pot}}}$ on the coarse grid and interpolate the
coarse-grid force-free solution as initial field
($\mathbf{B^{coarse}_{\text{NLFFF}}}$) for NLFFF on the final grid. No loop
data is used.

Setup 5

We use the interpolated coarse-grid field from Setup 4 as initial field
($\mathbf{B^{coarse}_{\text{NLFFF}}}$) for S-NLFFF.

The natural approach would be to apply the S-NLFFF method on the fine grid
(the Setup 2) and to evaluate the L${}_{\textit{1}}$..L${}_{\textit{4}}$ (Eq.
1..4) and the angles between the magnetic field and the tangents of the 3D
loops. We apply the S-NLFFF method to the Setup 2, 3 and 5 to see which one
provides the best solution. We run the Setup 3 to see if the force-freeness is
maintained and in the same time the angles are minimized. Metcalf et al.
(2008) claimed that the solution of the multiscale version of the NLFFF
converges to a lower L (Eq. 6) value when compared with the single grid
solution. For this reason we considered the multiscale approach for the NLFFF
and S-NLFFF method.

##  5 Results

We calculated the angles ($\theta_{\textbf{Bt}_{\textit{i,j}}}$) between the
magnetic field ($\mathbf{B}_{\text{NLFFF}}$) obtained with the NLFFF
optimization method and the tangents ($\mathbf{t_{\textit{i,j}}}$, j=1…10,
i=1..100) of the 3D stereoscopically reconstructed loops (see Fig. 6, 7). The
angles are calculated for each position i along the j${}^{\text{th}}$ loop.
Different colors represent different loops. The misalignment angles between
$\mathbf{B}_{\text{NLFFF}}$ and $\mathbf{t_{\textit{i,j}}}$ are on average 20∘
and reach a maximum of approximately 60∘ (see Fig. 6). The angles from Fig. 6
are obtained using $\mathbf{B}_{\text{NLFFF}}$ as a result of Setup 1, but the
same profile is obtained using $\mathbf{B}_{\text{NLFFF}}$ from Setup 4.

Figure 6: Angles between the NLFF magnetic field and the tangent of the 3D
loops obtained as a result of Setup 1. Different colors represent different
loops.

By applying the S-NLFFF method, the angles
$\theta_{\mathbf{Bt_{\textit{i,j}}}}$ between $\mathbf{B}_{\text{S-NLFFF}}$
and $\mathbf{t}_{\textit{i,j}}$ were reduced by a factor of more then 20 as
shown in Fig. 7. For the calculation of the final angles
$\theta_{\mathbf{Bt_{\textit{i,j}}}}$ from Fig. 7 we used
$\mathbf{B}_{\text{S-NLFFF}}$ as a result of Setup 5. Nevertheless, Fig. 7 is
representative also for the angles between the 3D loop tangents and the
$\mathbf{B}_{\text{S-NLFFF}}$ obtained as a result of Setup 2 and 3.

Figure 7: The final angles between the S-NLFFF extrapolated magnetic field and
the tangents of the 3D loops obtained as a result of Setup 5. Different colors
represent different loops.

With the S-NLFFF method we could recover a magnetic field which is closer to
the force-free condition. In Table 1 we present the values for the terms of
the functional (see the detailed description of the terms in Wiegelmann
(2004); Wiegelmann & Inhester (2010); Chifu et al. (2015)), namely the force-
free ($L_{\textit{1}}$) term, the divergence of the magnetic field
($L_{\textit{2}}$) term, the closeness with the bottom boundary observation
($L_{\textit{3}}$) term and the closeness with coronal observable
($L_{\textit{4}}$) term. The residual values of the functional terms when
applying the S-NLFFF method are lower than those obtained with the NLFFF
method for the Setup 2 and 3 but a slightly larger for the Setup 5.

Table 1: The residual values of each of the functional terms  Configuration | No. grids | Initialization | Methods | $L_{1}$ | $L_{2}$ | $L_{3}$ | $L_{4}$
---|---|---|---|---|---|---|---
Setup 1 | one | B${}_{\text{pot}}$ | NLFFF | $5.2$ | $3.2$ | $12.9$ | $-$
Setup 2 | one | B${}_{\text{pot}}$ | S-NLFFF | $4.6$ | $2.7$ | $12.2$ | $0.0011$
Setup 3 | one | B${}_{\text{NLFFF}}$ | S-NLFFF | $4.9$ | $3.0$ | $11.5$ | $0.0041$
Setup 4 | two | B${}_{\text{pot}}$ | NLFFF | $3.7$ | $2.2$ | $12.2$ | $-$
Setup 5 | two | B${}^{coarse}_{\text{NLFFF}}$ | S-NLFFF | $4.0$ | $2.3$ | $11.9$ | $0.0007$

We evaluated the angles ($\phi_{\mathbf{JB}}$) between the magnetic field and
the current for each loop, along the loop. We derived the $\phi_{\mathbf{JB}}$
angles between the potential, NLFF and S-NLFF field and the current. For
comparing the three cases, we calculated the root mean square (RMS) of the
angles $\phi_{\mathbf{JB}}$ for each loop. This is a critical test because the
current $\mathbf{J}$ is derived by differentiation from the magnetic field
$\mathbf{B}$ which amplifies the noise, especially where the field strength is
low. In Fig. 8 we show the RMS of $\phi_{\mathbf{JB}}$ for each loop. Here we
present the angles derived using the $\mathbf{B}_{\text{NLFFF}}$ obtained as a
solution of Setup 1 and the $\mathbf{B}_{\text{S-NLFFF}}$ obtained as a
solution of Setup 5. The evolution of the $\phi_{\mathbf{JB}}$ from Fig. 8 is
representative also for angles derived using the NLFFF solution of Setup 4 and
the S-NLFFF solution of setups 2, 3 and 5. The current is more aligned with
the magnetic field after using the reconstructed 3D loops as constrain for the
S-NLFFF method.

Figure 8: Root mean square of the angles between the current and the potential
field (orange rhombus), the extrapolated NLFFF (magenta squares) and the
extrapolated S-NLFFF (green triangles) for each of the 3D loops.

##  6 Discussions

De Rosa et al. (2009) compared different coronal NLFFF models with EUV coronal
loops observations. The conclusion of the study was that the misalignment
angles between the extrapolated NLFF field and the 3D stereoscopically
reconstructed loops reaches a maximum of approximately 45∘. In agreement with
the results of De Rosa et al. (2009) we derived similar angles between the
magnetic field ($\mathbf{B}_{\text{NLFFF}}$) obtained with the NLFFF
optimization method (for Setup 1 and 4) and the tangents $\mathbf{t}_{i,j}$ of
the 3D stereoscopically reconstructed loops (see Fig. 6).

In a previous paper (Chifu et al., 2015) we presented and tested the S-NLFFF
method with semi-analytic data. The results of the tests predicts that the
S-NLFFF method is capable of reducing the values of the
$\theta_{\mathbf{Bt}_{\textit{i,j}}}$ angles below 2∘. In all of the cases
studied in this paper, the S-NLFFF method was capable to reduce the angles
even further (see Fig. 7).

In an ideal case, the residual values of the functional terms
L${}_{\textit{1}}$..L${}_{\textit{4}}$ (Eq. 1…4) would be zero. Since the
observational data contains errors and the magnetic field model is based on
certain assumptions, the residual values cannot exactly be minimized to zero.
The smaller the residual value L${}_{\textit{1}}$ (Eq. 1), the close is the
field to the force-free condition. For the setups 2 and 3, the S-NLFFF could
bring the magnetic field closer to a force-free solution when compared with
the reference field (Setup 1).

From the evaluation of the root mean square angles ($\phi_{\mathbf{JB}}$)
between the current and the magnetic field, we could see an improvement in the
average alignment for all of the three setups. The large values in the angle
between the force-free magnetic field and current are probably due to the
large uncertainties in the horizontal vector field component, in particular in
the weak regions of magnetic field. Even for the Setup 5 for which the
residual values for the force-free terms did not improve when applying
S-NLFFF, the average angle along the loop between the field and the current
became smaller. Over all we can say that the new method which includes the
constraints from the corona improves not only the agreement between modeling
and observations, but it also improves the force-freenes of the obtained
magnetic field.

For most of the 3D stereoscopically reconstructed loops used as constraint for
the magnetic field, the S-NLFFF method is able to reduce the angles between
the magnetic field and the 3D loop tangents below 2∘. Nevertheless, there are
few loops for which the angles between $\mathbf{B}_{\text{S-NLFFF}}$ and
$\mathbf{t}_{i}$ remain large after S-NLFFF treatment. These loops have a
deviation of $\gtrsim$ 65∘ when compared with the NLFFF model field (Setup 1
and 4). When this field was used as initial condition for S-NLFFF (Setup 3)
the average angle could be reduced by a factor of 2-10 but not below 5∘.

In this paper we present the performance of the S-NLFFF method using ten 3D
coronal loops as a constraint for modeling the coronal magnetic field. For
these ten loops we show that the S-NLFFF method can obtain a good agreement
between the modeled coronal magnetic field and the coronal loops observations.
The S-NLFFF method can also obtain a much better alignment between the current
and the magnetic field which is an indication that we obtain a better field in
terms of force-freenes. The residual value of force-free integral value (Eq.
1) decreases only little. The reason is probably that the few loops we
included improve the field in their local environment but have limited impact
on metrics which average over a much larger volume. We believe that more loops
which occupy a larger fraction of the computational box will also improve the
quality measures over the entire box.would have a larger impact on the
improvement of the force-freenes.

Data are courtesy of NASA/SDO and the AIA and HMI science teams. The authors
thank the STEREO SECCHI consortia for supplying their data. STEREO is a
project of NASA. I.C is grateful to Hans-Peter Doerr for helpful suggestions.
This work was supported by DLR fund 50 OC 1301

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# A Green Bank Telescope search for narrowband technosignatures between 1.1 –
1.9 GHz during 12 Kepler planetary transits

Sofia Z. Sheikh SETI Institute, 339 Bernardo Avenue, Suite 200, Mountain View,
CA 94043, USA  Berkeley SETI Research Center, University of California,
Berkeley, CA 94720, USA  Penn State Extraterrestrial Intelligence Center, 525
Davey Laboratory, The Pennsylvania State University, University Park, PA,
16802, USA  Shubham Kanodia Earth and Planets Laboratory, Carnegie Institution
for Science, 5241 Broad Branch Road, NW, Washington, DC 20015, USA  Department
of Astronomy & Astrophysics, 525 Davey Laboratory, The Pennsylvania State
University, University Park, PA, 16802, USA  Center for Exoplanets and
Habitable Worlds, 525 Davey Laboratory, The Pennsylvania State University,
University Park, PA, 16802, USA  Penn State Extraterrestrial Intelligence
Center, 525 Davey Laboratory, The Pennsylvania State University, University
Park, PA, 16802, USA  Emily Lubar Department of Astronomy, University of Texas
at Austin, Austin, TX, USA  William P. Bowman Department of Astronomy &
Astrophysics, 525 Davey Laboratory, The Pennsylvania State University,
University Park, PA, 16802, USA  Institute for Gravitation and the Cosmos, The
Pennsylvania State University, University Park, PA 16802, USA  Caleb I. Cañas
Department of Astronomy & Astrophysics, 525 Davey Laboratory, The Pennsylvania
State University, University Park, PA, 16802, USA  Center for Exoplanets and
Habitable Worlds, 525 Davey Laboratory, The Pennsylvania State University,
University Park, PA, 16802, USA  Christian Gilbertson Department of Astronomy
& Astrophysics, 525 Davey Laboratory, The Pennsylvania State University,
University Park, PA, 16802, USA  Center for Exoplanets and Habitable Worlds,
525 Davey Laboratory, The Pennsylvania State University, University Park, PA,
16802, USA  Mariah G. MacDonald Center for Exoplanets and Habitable Worlds,
525 Davey Laboratory, The Pennsylvania State University, University Park, PA,
16802, USA  Department of Physics, The College of New Jersey, 2000 Pennington
Road, Ewing, NJ 08628, USA  Jason Wright Department of Astronomy &
Astrophysics, 525 Davey Laboratory, The Pennsylvania State University,
University Park, PA, 16802, USA  Center for Exoplanets and Habitable Worlds,
525 Davey Laboratory, The Pennsylvania State University, University Park, PA,
16802, USA  Penn State Extraterrestrial Intelligence Center, 525 Davey
Laboratory, The Pennsylvania State University, University Park, PA, 16802, USA
David MacMahon  Radio Astronomy Lab, University of California, Berkeley, CA
94720, USA  Berkeley SETI Research Center, University of California, Berkeley,
CA 94720, USA  Steve Croft Radio Astronomy Lab, University of California,
Berkeley, CA 94720, USA  Berkeley SETI Research Center, University of
California, Berkeley, CA 94720, USA  SETI Institute, 339 Bernardo Avenue,
Suite 200, Mountain View, CA 94043, USA  Danny Price Berkeley SETI Research
Center, University of California, Berkeley, CA 94720, USA  International
Centre for Radio Astronomy Research, 1 Turner Ave, Bentley WA 6102, Australia
Andrew Siemion Berkeley SETI Research Center, University of California,
Berkeley, CA 94720, USA  SETI Institute, 339 Bernardo Avenue, Suite 200,
Mountain View, CA 94043, USA  Department of Physics and Astronomy, University
of Manchester, UK  Institute of Space Sciences and Astronomy, University of
Malta  Jamie Drew  Breakthrough Initiatives, NASA Research Park, Moffett
Field, CA 94035, USA  S. Pete Worden  Breakthrough Initiatives, NASA Research
Park, Moffett Field, CA 94035, USA  Elizabeth Trenholm University of
Greenwich, School of Computing and Mathematical Sciences, Park Row SE10 9LS
London, UK Sofia Sheikh<EMAIL_ADDRESS>
(Accepted November 24, 2022)

###### Abstract

A growing avenue for determining the prevalence of life beyond Earth is to
search for “technosignatures” from extraterrestrial intelligences/agents.
Technosignatures require significant energy to be visible across interstellar
space and thus intentional signals might be concentrated in frequency, in
time, or in space, to be found in mutually obvious places. Therefore, it could
be advantageous to search for technosignatures in parts of parameter space
that are mutually-derivable to an observer on Earth and a distant transmitter.
In this work, we used the L-band (1.1–1.9 GHz) receiver on the Robert C. Byrd
Green Bank Telescope (GBT) to perform the first technosignature search pre-
synchronized with exoplanet transits, covering 12 Kepler systems. We used the
Breakthrough Listen turboSETI pipeline to flag narrowband hits ($\sim$3 Hz)
using a maximum drift rate of $\pm$614.4 Hz/s and a signal-to-noise threshold
of 5 — the pipeline returned $\sim 3.4\times 10^{5}$ apparently-localized
features. Visual inspection by a team of citizen scientists ruled out 99.6% of
them. Further analysis found 2 signals-of-interest that warrant follow-up, but
no technosignatures. If the signals-of-interest are not re-detected in future
work, it will imply that the 12 targets in the search are not producing
transit-aligned signals from 1.1 – 1.9 GHz with transmitter powers $>$60 times
that of the former Arecibo radar. This search debuts a range of innovative
technosignature techniques: citizen science vetting of potential signals-of-
interest, a sensitivity-aware search out to extremely high drift rates, a more
flexible method of analyzing on-off cadences, and an extremely low signal-to-
noise threshold.

technosignatures — search for extraterrestrial intelligence — biosignatures —
astrobiology

††journal: The Astronomical Journal††facilities: GBT††software:  Astropy
(Astropy Collaboration et al., 2013, 2018), Numpy (Harris et al., 2020),
Matplotlib (Hunter, 2007), blimpy (Breakthrough Listen Collaboration, 2019;
Price et al., 2019), turboSETI (Enriquez & Price, 2019).

##  1 Introduction

A vast and still-growing part of our astronomical exploration is the search
for life elsewhere in the universe. Many programs look for such life on
exoplanets through their biosignatures, surface features (e.g., Coelho et al.,
2022), or atmospheric constituents (e.g., Thompson et al., 2022) that indicate
the presence of biological activity. Another complementary strategy is to look
for the technosignatures of technologically-capable life — Extraterrestrial
Agents (ETA)s, to use the terminology of Döbler & Raab (2021) — which may be
more abundant, long-lived, highly-detectable, and unambiguous than other
previously-described biosignatures (Wright et al., 2022).

The most popular technosignature search strategy to date is radio searches for
artificial emission (as pioneered by Drake, 1961), which has grown
exponentially in recent years, making use of cutting-edge computational
techniques and newly-developed hardware (e.g., Harp et al., 2018; Ma et al.,
2022). However, even with the renewed observational energy, the search space
remains mostly unexplored (Wright et al., 2018a). This provides an opportunity
for radio observation projects, large and small, to make an impact by filling
in unexplored regions of parameter space.

One suggestion on how to best navigate this huge parameter space is to use
“Schelling Points” (Schelling, 1960; Wright, 2020), to prioritize mutually-
derivable parts of parameter space which a transmitter and receiver can both
land upon without any prior communication. This allows for more efficient
traversal of parameter space — potentially leading to a technosignature
detection much sooner — and also can be more power efficient for the
transmitter, which can focus its energy in particular directions and times.
One application of this idea is to prioritize certain places and times
synchronized with an astronomical event (Pace & Walker, 1975). In some of
these synchronized strategies, the event is external to the transmitter and
receiver’s systems, i.e., a nearby supernova or nova (Tang, 1976; Lemarchand,
1994; Davenport et al., 2022). In another application, the synchronizing event
is some feature of the transmitter or receiver’s system, observable or
predictable by both parties (e.g., Corbet, 2003).

Here, we make use of exoplanetary transits as temporal Schelling points
(Kipping & Teachey, 2016): if an ETA transmitter on an exoplanet sends a
signal towards its anti-stellar point, the signal will necessarily arrive to
any observer along the line-of-sight at the same time as the exoplanet appears
to be at mid-transit. This provides a known time and place (during an
exoplanetary transit) for the observer to look for a signal. The transmitter
may be targeting a specific system that happens to lie within its ecliptic,
and thus sends a signal once each of its exoplanetary years. Conversely, the
transmitter may be constantly targeting its exoplanet’s anti-stellar point,
sending out a transmission which sweeps across its ecliptic. In the extreme
case, a tidally-locked planet hosting a single surface-locked transmitter
could be constantly sweeping the ecliptic via the anti-stellar point, perhaps
powered by energy collected photo-voltaically from the star-facing side of the
exoplanet. Observations at this special periodic epoch offer a way to sample
the large possibilities of repetition rates associated with periodic
transmissions (Wright et al., 2018b). Completely divorced from this Schelling
Point logic, ETAs may preferentially emit high-power microwave radiation in
their ecliptics (as we do in our solar system due to space communications),
making transiting systems potentially more favourable for detecting
unintentional artificial signals.

In this work, we perform the first radio technosignature search of exoplanet-
hosting stars, where observations were pre-synchronized with their transits.
This is a complementary approach to that performed by Franz et al. (2022),
which looked back into archival data to identify serendipitous observations
during transit. We also follow the growing tradition of conducting
technosignature work and obtaining novel astronomical results using a cohort-
based, academic course centered research model (Margot et al., 2021; Tusay et
al., 2022).

In Section 2, we describe how the targets were chosen. In Section 3 we discuss
the observing plan, the observation parameters, and the data format. We cover
the methods for the search, including the software, assumptions, and chosen
search parameters in Section 4. We discuss our findings and upper limits in
Section 5. Finally, we discuss and conclude in Section 6 and Section 7
respectively.

##  2 Target Selection

We first compiled a list of 540 exoplanets that transit during a 2-day
potential observing window as a function of distance, using ephemerides from
the NASA Exoplanet Archive (Figure 1; Akeson et al., 2013). Down-sampling from
this subset of transiting exoplanets, we selected planets discovered by the
Kepler mission due to their limited range of celestial coordinates. This
enabled us to minimize our slew times during the nodding sequence, and boost
the observing duty cycle. While there have been previous searches focused on
transiting exoplanets from the Kepler mission (Harp et al., 2016; Siemion et
al., 2013b), these have not prioritized observations during planetary
transits. As explained above, we consider the transit a temporal Schelling
point and hence aim to maximize the fraction of transit that we observed. To
further improve our observing efficiency, we decided to observe alternate
transiting planets as part of the on-off-on sequence used to identify Radio
Frequency Interference (RFI), and identified pairs of exoplanets in the Kepler
field that are transiting at similar times and are particularly close on-
sky111None of these pairs are close enough on the sky to potentially cause
source confusion, i.e., the angular distance between the targets $\gg$ GBT
beam diameter in L band.. . The properties of our 12 observed targets are
listed in Table 1, and their on-sky positions are visualized in Figure 2.

Figure 1: Confirmed transiting exoplanets in the Kepler field as observable from the Green Bank Telescope (GBT) during on March 25, 2018. The horizontal errorbars depict the transit duration, whereas the colour of the markers represent the stellar effective temperature. Points without visible errorbars have extremely well-defined transit midpoints. We did not include a habitability requirement in planet selection. Figure 2: A plot of all exoplanetary systems (blue stars) observed with the GBT for this project, overlaid on the Kepler field of view, which covers 115 square degrees on sky (Mullally et al., 2016). The name of each system as it appears in Table 4 is shown. Boyajian’s star (an off-source target) is also included for reference. Table 1: Stellar and planetary properties for the twelve transiting Kepler planets observed in this work. We use the properties from Morton et al. (2016) for all planets, except Kepler-446b which we pull from Muirhead et al. (2015). Target | RA | Dec | Distance | Radius | Period | $t_{0}$ | $T_{eq}$ | $T_{eff}$
---|---|---|---|---|---|---|---|---
| (J2000) | (J2000) | (pc) |  ($R_{\oplus}$) | (d) | (BJD - 2454000) | (K) | (K)
Kepler-446b | 18h49m0.05s | 44d55m15.96s | 120 |  1.5 $\pm$0.25 | 1.57 | 965.91 | 648 | 3464
Kepler-537b | 19h19m31.20s | 51d16m48.00s | 465 |  1.41${}^{+0.06}_{-0.04}$ | 3.25 | 1004.28 | 1181 | 5703
Kepler-723b | 18h59m19.32s | 44d39m29.30s | 965 |  12.19${}^{+1.58}_{-0.79}$ | 4.08 | 1002.64 | 1016 | 5655
Kepler-732c | 18h54m55.68s | 45d57m31.57s | 150 |  1.27${}^{+0.07}_{-0.1}$ | 0.89 | 967.54 | 893 | 3582
Kepler-738b | 19h10m16.73s | 46d34m4.30s | 992 |  2.5${}^{+0.2}_{-0.17}$ | 24.59 | 1006.70 | 530 | 5474
Kepler-842b | 19h29m16.80s | 49d38m60.00s | 552 |  1.6${}^{+0.08}_{-0.09}$ | 1.22 | 966.46 | 1252 | 4838
Kepler-992b | 18h57m43.20s | 47d38m24.00s | 268 |  1.62${}^{+0.04}_{-0.27}$ | 20.16 | 977.34 | 510 | 4975
Kepler-1039b | 19h53m16.80s | 45d18m36.00s | 324 |  1.46${}^{+0.09}_{-0.22}$ | 0.93 | 964.58 | 2080 | 4777
Kepler-1053b | 19h25m40.80s | 39d7m48.00s | 171 |  0.98${}^{+0.05}_{-0.04}$ | 2.41 | 965.43 | 953 | 4507
Kepler-1164b | 19h10m7.20s | 38d53m24.00s | 447 |  1.12${}^{+0.04}_{-0.07}$ | 3.98 | 966.62 | 936 | 5143
Kepler-1222b | 19h39m33.60s | 49d22m48.00s | 455 |  0.79 $\pm$0.06 | 1.92 | 965.47 | 1246 | 5083
Kepler-1332b | 19h24m7.20s | 43d54m36.00s | 465 |  1.37${}^{+0.09}_{-0.05}$ | 11.87 | 973.21 | 728 | 5523

##  3 Observations and Data

We pre-planned our observing sequence to ensure that we would hit each
exoplanet during its transit, using individual 5-minute observing blocks
spanning our 6 hour observing window on March 25, 2018 (starting at 11:00 UT);
we elected to use the standard Breakthrough Listen (BL) Green Bank Telescope
(GBT) integration of 5 minutes, and assumed a 2 minute overhead to account for
e.g., the slewing and settling of the telescope. Table 4 shows the log of
observations, including their relative temporal position to the target
exoplanet’s mid-transit point. We created individual GBT observing scripts for
each pair which toggled back-and-forth between the two targets until they were
replaced by the next target script. This sequence was adjusted dynamically
throughout the observing session to select targets closest to mid-transit, in
light of actual slew times and unanticipated observing overheads. For example,
we started our transit observations with Kepler-992b for scans 0010 and 0012,
the former of which spanned the transit midpoint. During these scans, we
observed Kepler-738b as our ‘off’ target. After covering the transit midpoint
for Kepler-992b, we switched to Kepler-1039b and Kepler-732c, which had the
next occurring transit midpoints. The total in-transit time for each planet in
the sample varied in duration from 0.65–3.9 hours (median: 1.8 hours), so the
5-minute scans covered approximately 5% of each transit.

We followed a similar logic through the rest of our observing window, where we
tried to observe targets for at least 2 scans each during transit;
furthermore, we prioritized observations of transit midpoints and tried to
minimize slew times. We bracketed our observing block with calibration
observations of quasar 3C 295 (scans 0006 and 0007) in the beginning, and
pulsar B0329+54 (scan 0059) at the end. Additionally, we obtained one scan
(scan 0009) of KIC 8462852, commonly known as Boyajian’s star (Boyajian et
al., 2018) before starting our transit sequence; it was a conveniently-located
off-source also targeted by BL laser technosignature searches using Lick
Observatory’s Automated Planet Finder telescope (Lipman et al., 2019).

Data were recorded using the L-band receiver (1.1–1.9 GHz) (Balser et al.,
2021) and the BL backend on the GBT, which in 2018222It is now capable of
digitizing up to 12 GHz of instantaneous bandwidth. was capable of digitizing
up to 6 GHz of instantaneous bandwidth in 2 polarizations at 8-bit resolution
— for more information, see MacMahon et al. (2018). The raw voltage data is
then channelized using the gpuspec code to produce three spectral SIGPROC
filterbank files containing Stokes I total power/frequency/time datacubes,
each file at a different time and spectral resolution (Lebofsky et al., 2019).
In the following analyses, we make use of the high spectral resolution data
product, with a frequency resolution of $\sim 3$ Hz and a time resolution of
$\sim 18$ s.

We performed data quality checks using the calibrator observations at the
beginning and end of the observing session. The pulsar B0329+54 was easily
visible in a prepfold plot (Ransom, 2011), providing a first-order
confirmation that the system was working as expected. In addition, it had an
expected Signal-to-Noise Ratio (S/N) of 9172 given our system parameters,
observing parameters, and its characteristics in the ATNF pulsar
database333https://www.atnf.csiro.au/research/pulsar/psrcat/, and was detected
at an S/N of 5306 (57.85%). Given that pulsars in general (and this pulsar in
particular) are not perfect flux calibrators (they exhibit variability in flux
over time due to scintillation, which was distinctly present in the scan),
this is entirely within the range of expected outcomes.

We also used the first 3C 295 scan as a continuum flux calibrator “on”-source,
and the following observation of Boyajian’s Star as an “off” source, to derive
a system temperature. Assuming a flux density of 22.22 Jy at 1408 MHz (as
measured by Ott et al., 1994), and a spectral index of $\alpha=-0.7$, as found
for the calibrator’s hotspots in a recent LOFAR observation (Bonnassieux et
al., 2022), we obtain an empirical system temperature measurement of
$T_{sys}=22.66$ K. The theoretical value given in the GBT Proposer’s Guide for
the L-band receiver is $T_{sys}\approx 20$ K, which is consistent with the
experimental results.

##  4 Search Methods and Data Reduction

BL has a well-established data pipeline for performing narrowband Search for
Extraterrestrial Intelligence (SETI) searches on high frequency resolution
filterbank files. This pipeline consists of import, plotting, and other
utility functions in the blimpy package (Breakthrough Listen Collaboration,
2019; Price et al., 2019), and a narrowband search code turboSETI (Enriquez &
Price, 2019) based on the de-dispersion algorithm of Taylor (1974) and adapted
for de-Doppler searches. These pipelines have frequently been used for SETI
searches in the recent literature (e.g., Siemion et al., 2013a; Smith et al.,
2021).

For this work, we ran turboSETI’s narrowband hit-finder with a maximum drift
rate of $\pm$ 614.4 Hz/s and a S/N threshold of 5. Both of these parameters
are unusual choices, for the reasons presented below.

A typical drift rate for radio SETI searches is $\sim\pm$10 Hz/s, within a
factor of a few (e.g., Sheikh et al., 2020; Franz et al., 2022). However,
Sheikh et al. (2019) showed that known exoplanetary systems could produce
drift rates up to $\pm$ 200 nHz (i.e., $\pm 200\times\nu$ Hz/s, where $\nu$ is
the observing frequency in GHz). The largest drift rates would be expected
from exoplanets with the largest radial accelerations relative to the receiver
on Earth, e.g., transiting exoplanets that are viewed edge-on. This work marks
the first time that a SETI survey has followed the 200 nHz recommendation, by
using a maximum drift rate of $\pm$614.4 Hz/s; this drift rate is sufficient
to capture drift rates of $\pm$200 nHz even at 1.9 GHz, the highest frequency
in these observations.

It should be noted that turboSETI, in its current configuration, does not
automatically account for the sensitivity loss sustained when incoherently-
dechirping past the “one-to-one point” $\nu_{\mathrm{1-to-1}}$, where a signal
drifts one frequency bin in every time bin (Sheikh et al., 2019). Here, we
implement the first of the two partial solutions to this problem described by
Margot et al. (2021). We search the original high spectral-resolution
filterbank file with a drift rate range from 0 to $\pm\nu_{\mathrm{1-to-1}}$
Hz/s, in steps of $\sim 0.01$ Hz/s. Then, we “scrunch” the file in frequency
by a factor of 2, halving the number of bins by summing every other bin with
its following neighbor. We then search again, using a new drift rate range of
$\pm\nu_{\mathrm{1-to-1}}$ to $\pm 2\times\nu_{\mathrm{1-to-1}}$ Hz/s (the new
one-to-one point in the new file), with a correspondingly doubled drift rate
step. We repeat this process until we have covered the entire desired drift
rate range, which requires a series of 12 scrunch-and-search iterations. It
should be noted that each frequency-scrunch, though it maximizes the S/N
within its range of drift rates, still causes an unavoidable $\sqrt{2}$ loss
in sensitivity due to the original dimensions of the incoherent sum that
produced the data product. The sensitivity losses are discussed further in
Section 5.4, and it should be noted that exact signal positions and drift
rates within the band may also cause irregularity in sensitivity with this
method.

Recent SETI searches have often chosen an S/N of 10 for their hit thresholds,
including Price et al. (2020) and (Margot et al., 2021). In narrowband radio
signal detection these limits are primarily dictated by the filtering
resources of the search, rather than any inherent statistical significance —
the environment is so contaminated by RFI that false alarm rates from other
common astronomical distributions, e.g., white noise or Gaussian statistics,
do not apply. In this work, we instead decided upon a lower S/N of 5, which
allows us to double the sensitivity of the search. It should be noted that
this causes an immense number of hits to pass the turboSETI filtering step, in
addition to the shorter BAB cadence described in the following section: we
managed this step with citizen science (Section 5.2), but also note its
difficulties (Section 6).

##  5 Results

We ran turboSETI’s hit-finding algorithm on every observation in Table 4. We
ignored the region from 1.20–1.34 GHz, which corresponds to the L-band “notch
filter”, which applies to the most RFI–contaminated region of the spectrum at
the GBT. This generated a total of $\sim$2.53 million hits. We then used
turboSETI’s event-finding capability to compare hits in each Kepler
observation (and Boyajian’s star) to hits in each of the observations directly
preceding and following it; this is the equivalent of an off-on-off or BAB
cadence. In rare cases where the same target was observed twice in a row to
realign the observations with the transit timeline (e.g., scans 0018 and 0019,
both targeting Kepler-738b), we used the next closest scan in the
preceding/following direction that was on a different target. This event-
finding process resulted in 338473 unique events. The frequency distribution
of the hits and events are shown in Figure 3.

Figure 3: A histogram showing the frequency distribution of the hits (lighter)
and events (darker) in a logarithmic (left) and a linear (right) scale. The
notch filter is responsible for the absence of hits between 1200–1340 MHz.
Three distinct frequency regions contain more than 100000 hits each: 1165–1185
MHz, 1375–1385 MHz, and 1570–1580 MHz. These three regions are discussed in
further detail in Section 5.1.

###  5.1 RFI-Heavy Bands

We find that three frequency ranges — 1165–1185 MHz, 1375–1385 MHz, and
1570–1580 MHz — contain the majority of the RFI in our observations: 5% of the
band (excluding notch filter) accounts for 56% of the hits. These ranges are
consistent with the interference-heavy regions discussed by Price et al.
(2020). Here, we briefly discuss each of these frequency ranges in turn, and
attempt to associate them with Federal Communications Commission (FCC)
frequency
allocations444https://transition.fcc.gov/oet/spectrum/table/fcctable.pdf.

Figure 4: a) An example of an event in the 1165–1185 MHz region, consistent
with GPS L5. This event is RFI, as it appears in multiple different targets in
consecutive observations. The dashed red line represents turboSETI’s best-fit
drift rate for the detected hit. b) An example of an event in the 1375–1385
MHz region. These events occur for only a fraction of the observation (here,
about 100 seconds) within a single scan — this makes it difficult to determine
whether they are impulsive RFI or whether they are true transient signals
localized on the sky. However, because we observe the same morphology of
signal in multiple targets, and because of the match to the GPS L3 downlink,
we can assign these events as RFI. c) An example of an event in the 1570–1580
MHz region. These events are similar to the example shown in subfigure b in
that they are degenerate between transient and localized signals; this is a
common challenge for single-dish technosignature searches. The same signals
were identified in multiple targets, however, indicating that they are indeed
RFI — likely the GPS L1 downlink.

1165–1185 MHz: There is an FCC frequency allocation for aeronautical
radionavigation and radionavigation-satellite (including space-to-Earth)
transmissions between 1164–1215 MHz, covering this observed interference
region in Figure 3. The distinct peak from 1165–1185 MHz is consistent with
the GPS L5 downlink555https://www.nist.gov/pml/time-and-frequency-
division/popular-links/time-frequency-z/time-and-frequency-z-g. An example of
an event in this region that passed turboSETI’s thresholds is shown in Figure
4a.

1375–1385 MHz: This narrow region of the spectrum is occupied by the GPS L3
downlink band, which provides communications links for the U.S. Nuclear
Detonation Detection System. An example of an event in this region that passed
turboSETI’s thresholds is shown in Figure 4b.

1570–1580 MHz: Once again, this interferer falls within an FCC allocation
dedicated to aeronautical radionavigation and radionavigation-satellite
(including space-to-Earth) transmissions; in this case, however, the
allocation is much wider (1559 MHz–1610 MHz) than the region where we see the
majority of interference. An example of an event in this region that passed
turboSETI’s thresholds is shown in Figure 4c. Given the frequency range, and
the presence of other GPS downlinks within the dataset, these hits can likely
be attributed to the GPS L1 downlink centered at 1575 MHz.

Finally, we detected a series of swooping signals (changing from high drift
rate, to low drift rate, to high again) between 1616–1626.5 MHz that also
passed turboSETI’s event filtering. These signals account for the event spike
above 1600 MHz in the right panel of Figure 3. An example is shown in Figure
4d. We attribute these signals to the Iridium satellite constellation’s L-band
downlink666https://apollosat.com/iridium-satellite-frequency-bands, and note
that these signals have passed turboSETI event filters in multiple GBT L-band
SETI observations (e.g., Enriquez et al., 2017; Tusay et al., 2022).

###  5.2 Filtering By Citizen Scientists

At this stage, with $>340,000$ events, most radio technosignature campaigns
would make a change to the event thresholds to get them to a number suitable
for visual inspection by a single researcher. For example, the S/N could be
raised from 5 to 10 (leaving only $92,000$ events), or even 25 (leaving only
$26,000$ events), or the drift rate could be further reduced. However, making
these changes would lower our sensitivity. For this campaign, we decided
instead to apply the power of crowdsourcing via a limited citizen science
project.

We created .pdf files containing 1000 plots each, making them accessible via
cloud services such as Box and Google Drive, and developed an hour-long
lecture and interactive quiz to train volunteers. Six undergraduate volunteers
from the Penn State Pulsar Search Collaboratory (PSPSC) club777An affiliate of
the Pulsar Search Collaboratory project described by Blumer et al. (2020) and
others. looked through output plots such as those shown in Figure 4, and
flagged any signal that appeared in only the on-source middle panel. Due to
the COVID–19 pandemic, the PSPSC members only completed approximately 20% of
the sample in the Fall 2020 semester — additional volunteers were recruited
from the lead author’s professional network to assist with signal filtering.

In the end, 13 citizen scientists (named in the Acknowledgements) flagged
approximately 0.4% ($\sim 1600$ signals) of the dataset for further analysis,
reducing the number of interesting events to a few thousand. It should be
noted that this number is approximate: some signals were identified multiple
times at different drift rates (see Section 6), and clusters of plots with
repeating signals (such as those in Figure 4a) were grouped as a single
phenomenon. Due to the size of the dataset compared to the number of
volunteers, we did not have the resources to send the same data to multiple
recipients, as is done in projects such as
Zooniverse888https://www.zooniverse.org/. To ensure quality in flagging, the
majority of the work was done in collaborative “hack sessions” with multiple
participants on the same call, so plots-of-interest or borderline cases could
be discussed and viewed by multiple participants simultaneously. The citizen
scientists’ effort meant that the filtered dataset was now at a manageable
size for visual inspection by the authors, all while maintaining the extremely
sensitive S/N 5 threshold.

###  5.3 Filtering Events with Context

Each of these plots, in isolation, had the characteristics of a localized
signal on the sky (only present in the on-source observation). However,
following the technosignature verification framework of Sheikh et al. (2021),
these signals should also be analyzed in the context of similar, nearby
signals. We grouped the remaining few thousand plots by frequency and
morphology. Then, we checked to see if identical signals appear in two
different targets (indicating that they are not local to either) or if we see
a near-identical signal within a set that is definitely interference (the way
that blc1 was eventually disproved by Sheikh et al., 2021). With this
strategy, we reduced the pool of signals-of-interest to 479. The frequencies,
drift rates, and S/Ns of these 479 signals are shown in the context of the
overall hits and events in Figures 5, 6, and 7 respectively.

Figure 5: A histogram showing the frequency distribution of the hits (light
gray), events (light purple), and signals-of-interest (purple). The signals-
of-interest are distributed relatively evenly throughout the spectrum. Note
the gap from 1.20–1.34 GHz due to the GBT L-band receiver’s notch filter.
Figure 6: A histogram showing the drift rate distribution of the hits (light
gray), events (light orange), and signals-of-interest (orange). The signals-
of-interest are found only at low absolute drift rates. Figure 7: A histogram
showing the S/N distribution of the hits (light gray), events (light green),
and signals-of-interest (green). The signals-of-interest are primarily faint.
There are also 5 hits with S/N $>10000$ which are not shown on this plot for
readability.

It is, however, possible that the 479 signals-of-interest have disqualifying
features elsewhere in the observing session; for example, a sub-threshold
repetition of the signal on a non-adjacent scan would not be picked up in the
previous filtering step. Therefore, as a final verification, we plotted each
of the remaining 479 plots in the context of the entire session of
observations (all 52 observations in Table 4), to produce stacked waterfall
plots with extreme aspect ratios. We eliminate a signal-of-interest from our
list if it is a continuation or repetition of signals in other targets at any
time during the morning of observations: this is a similar strategy to that
applied in Section 5.2 but now across the largest possible time baseline.

This process eliminated all but 2 signals-of-interest: one in a scan of
Kepler-1332b and one in a scan of Kepler-842b. Neither of these signals are
actually narrowband, but they were bright enough to be detected by turboSETI
and we did not want to restrict ourselves to only the signal morphologies we
expected, if we serendipitously found a signal with a different morphology.
Interestingly, both the detection in Kepler-1332b (during scan 0031) and the
detection in Kepler-842b (during scan 0056) were during their respective
transit midpoints. The waterfall plots are shown in Figures 8 and 9, and the
signal properties are summarized in Table 2.

Figure 8: The signal-of-interest detected in Kepler-1332b. Figure 9: A portion of the signal-of-interest detected in Kepler-842b. This signal-of-interest spans 1040–1438 MHz, so this is not the full signal, but rather a narrow bandwidth example of one of the “hits” on this signal generated by turboSETI. Target | Scan | MJD of Scan | Frequency | Transit Phase | Signal Type
---|---|---|---|---|---
Kepler-1332b | 0031 | 58202.59350 | 1749.4209 MHz | Transit Midpoint | Pulse
Kepler-842b | 0056 | 58202.69226 | 1040–1438 MHz | Transit Midpoint | Broadband Pulse
Table 2: Properties of the two interesting signals-of-interest reported in
this study.

We are close to the limit of what we can deduce from this dataset for these
two signals-of-interest. With the information we have, it is impossible to
exclude these signals as being due to RFI. Therefore, we recommend a follow-up
observation of these two systems in L-band, during transit, with a different
instrument. We are planning to do this with the newly-refurbished Allen
Telescope Array (ATA) (e.g., Farah et al., 2021). These signals-of-interest do
not merit the scrutiny of blc1 (Sheikh et al., 2021) because they only appear
in a single 18 second integration; while this may be expected for synchronized
transmitters which only send a signal at mid-transit, it also makes the
standards-of-evidence higher (no proof of signal localized on sky, no drift
rate measurement, etc.), requiring reobservation as the next step before more
detailed analyses.

###  5.4 Upper Limits

We calculate technosignature upper limits following the method of Price et al.
(2020). The minimum detectable flux density, $F_{\mathrm{min}}$ for a
narrowband signal is given by:

$F_{\mathrm{min}}=\textrm{S/N}_{\mathrm{min}}\frac{2k_{B}T_{\mathrm{sys}}}{A_{\mathrm{eff}}}\sqrt{\frac{\delta\nu}{n_{\mathrm{pol}}t_{\mathrm{obs}}}}$
(1)

Here, $\textrm{S/N}_{\mathrm{min}}$ is the signal-to-noise threshold, $k_{B}$
is the Boltzmann constant, $T_{\mathrm{sys}}$ is the system temperature,
$A_{\mathrm{eff}}$ is the effective collecting area of the telescope,
$\delta\nu$ is the frequency channel width, and $n_{\mathrm{pol}}$ is the
number of polarizations. We make the same assumption as Price et al. (2020):
that the transmitting signal is the same width as the frequency channel
$\delta\nu$, so no additional constant factor is needed to downweight
$F_{\mathrm{min}}$.

With an $\textrm{S/N}_{\mathrm{min}}$ of 5, a $T_{\mathrm{sys}}$ of 20 K, an
$A_{\mathrm{eff}}$ of 5655 m2 (equivalent to using an effective diameter of
100m for the GBT, with an L-band aperture efficiency of 0.72), a $\delta\nu$
of 3 Hz, an $n_{\mathrm{pol}}$ of 2 and a $t_{\mathrm{obs}}$ of 300 seconds,
we calculate an $F_{\mathrm{min}}$ of 3.45 $\times$ 10-26 W/m2, equivalent to
1.15 Jy. This is consistent with other BL searches at L-band with the GBT
(e.g., Enriquez et al., 2017; Price et al., 2020), but with extra sensitivity
due to the low signal-to-noise threshold.

The population of Kepler exoplanets is relatively distant, with all of the
targets in this study falling between 150–992 pc. The Equivalent Isotropic
Radiated Power (EIRP) is calculated as:

$EIRP_{\mathrm{min}}=4\pi d^{2}F_{\mathrm{min}}$ (2)

where $d$ is the distance to the furthest target in the survey. Using 992 pc,
we get a survey-wide EIRPmin of 406 TW, or $\sim 20\times$ the EIRP of the
Arecibo radar. The two targets that showed signals-of-interest, Kepler-1332b
and Kepler-842b, are located closer, at 465 pc and 552 pc respectively. This
leads to target-specific EIRPs of 89 TW and 125 TW, or $4.5$–$6.3\times$ the
EIRP of Arecibo.

Finally, one can also express an upper limit in the form of a fraction of the
8-dimensional “haystack”, as described by Wright et al. (2018a). Using the
same minimum and maximum axis bounds as described in that work, we calculate a
total haystack fraction of $4.42\times 10^{-20}$ covered by this search,
comparable to Project Phoenix searches with Parkes and Arecibo (e.g., Backus
et al., 2002).

##  6 Discussion

This search represents the lowest S/N ever chosen for a Breakthrough Listen
affiliated project on the GBT. However, caution is advised if following our
procedure. We found that lowering the S/N to 5 made turboSETI’s temporal on-
off filtering much less effective. The lower S/N magnified the likelihood of
e.g., a bright pixel in the “on” target causing a hit to be flagged as an
event. It may be more effective to recoup sensitivity in other parts of the
signal processing chain, rather than as a threshold in turboSETI. This may be
especially relevant for high drift rate signals (using methods such as boxcar
convolution, e.g., Adámek & Armour, 2020).

In addition, vetting $\sim 3.4\times 10^{5}$ events involved a large amount of
work, even considering the citizen science approach. Using a single on-source
with two off-sources produces a degeneracy between intermittent RFI and sky-
localized signals in a single-dish telescope, compounding the issue. We
recommend that future searches invest in a better understanding of their RFI
environment and try to algorithmically filter further before performing visual
classification.

One approach is to better characterize the frequencies, drift rates, and
morphologies of common interference sources, and only down-select signals that
are not particularly consistent with those properties. Another approach is to
use employ spatial filtering with a multi-beam receiver (such as the GBT’s
K-band Focal Plane Array) or an interferometer (such as the Allen Telescope
Array (ATA)).

$\dot{\nu}_{\mathrm{max}}$ (Hz/s) | Sensitivity Loss Factor | Number of Hits in Bin [% of total] | Number of Events in Bin [% of total]
---|---|---|---
0.15 | $1$ | 1838435 [53.1%] | 228741 [54.7%]
0.3 | $1.4$ | 1216882 [35.1%] | 129808 [31.0%]
0.6 | $2$ | 376107 [10.9%] | 46390 [11.1%]
1.2 | $2.8$ | 21999 [0.64%] | 7569 [1.81%]
2.4 | $5.7$ | 5549 [0.16%] | 3232 [0.77%]
4.8 | $8$ | 2607 [0.08%] | 1514 [0.36%]
9.6 | $11.3$ | 816 [0.02%] | 441 [0.11%]
19.2 | $16$ | 251 [$<0.01$%] | 134 [0.03%]
38.4 | $22.6$ | 139 [$<0.01$%] | 68 [0.02%]
76.8 | $32$ | 172 [$<0.01$%] | 90 [0.02%]
153.6 | $45.3$ | 125 [$<0.01$%] | 71 [0.02%]
307.2 | $64$ | 83 [$<0.01$%] | 54 [0.01%]
614.4 | $90.5$ | 0 [$<0.01$%] | 0 [$<0.01$%]
Table 3: Maximum drift rates (absolute value), the corresponding multiplier
for reduction in sensitivity, and the number of hits affected by that
reduction. The reason for the sensitivity reduction is described in Section 4.
99% of hits and 97% of events that we detected suffer a sensitivity loss of 2
or less. We can also consider the implied population of high-drift hits that
we did not detect, due to the sensitivity loss. However, the number of high-
drift rates is so many orders-of-magnitude below the low-drift hits, that we
do not expect the number of “missed” hits to meaningfully affect the total
number. This implies that the sensitivity loss at high-drift rates should not
greatly affect the conclusions of our survey. Note that this logic assumes
that high-drift hits are not preferentially likely to be caused by an ETA.

Also, as Margot et al. (2021) has mentioned, the turboSETI pipeline does not
optimize for signals with high drift rates by default, such that signals
suffer from drift-smearing across frequency bins, lowering the sensitivity.
However, we can recover as much sensitivity as is physically possible (in an
incoherent data product) by performing stepped frequency scrunching. The
remaining sensitivity loss factors for this data, and how many signals were
affected by those factors, are shown in Table 3. While we recommend that other
turboSETI users also perform frequency scrunching if their searches cover
applicably high drift rates, we note that each scrunched data product must be
searched separately. This means that bright-enough hits will be detected
redundantly multiple times, at multiple drift rates, as the hits from each
scrunched data product are produced independently. This provides a strong
motivation to integrate drift-rate-stepped scrunching into turboSETI in a more
robust way.

Another way to address high-drift signals is to coherently correct the raw
voltage data to an accelerating reference frame or fiducial drift rate (e.g.,
$\pm$100 Hz/s) before the creation of the reduced and channelized data
products (as done in pulsar de-dispersion, e.g., Sobey et al., 2022). For
signals at the chosen drift rate, there will be no sensitivity loss, and
signals that are nearby in drift rate space can be searched for incoherently
(with the same sensitivity loss considerations as discussed above), broadening
the applicability of the technique. However, note that for lower loss
tolerances at any given drift rate, the problem gets computationally heavier —
to minimize loss, it is necessary to dedisperse and save the entire array at
every drift rate of interest.

This search, synchronized with planetary transits, is part of a class of
search strategies aligned in time with particular astronomical events, as
discussed in Section 1. For any such search strategy, we expect that the
transmitter will likely not be transmitting continuously, but instead will
only transmit at particular times, potentially with short durations.
Therefore, searches for these kinds of signals benefit from observing with
arrays that can do simultaneous off- and on-sources with multiple beams,
instead of single-dish single-pixel instruments like the GBT at L-band.

The short transmission times also make synchronization strategies more energy-
efficient for the transmitter, similar to the argument made by Gray (2020).
Assume that the energy required to transmit for a full exoplanetary orbit is
$E$. For the exoplanets in our sample, transmitting only during transit (as
seen by a single receiver, in this case Earth), costs only 1–10% of $E$. If
the transmitter instead only signalled during the 5 minutes around the mid-
transit point (corresponding to the length of one of the observations in this
campaign), the energy cost would be 0.1–0.01% of $E$. Another strategy to
improve energy efficiency could be to use a transmitter with a very large
effective area, leading to an extremely narrow beam. In this strategy, the
tiny beam size would cause a short flash right at mid-transit as seen from
Earth. Having such a tiny angular beam size only works well if the observer
knows exactly when to expect the signal, so it pairs well with transit
synchronization. To an order-of-magnitude, using exoplanetary properties
consistent with our 12 exoplanet sample, we can imagine a continuously-
emitting transmitter with an effective area equivalent to an exoplanet’s
projected area. Before, we assumed the effective area would be the same as
that of the GBT, so the new effective area is now a billion times larger. This
factor propagates, leading to such a small beamsize that a transmitted signal
would be visible for a few milliseconds at mid-transit, and could be sent with
a transmitter six orders-of-magnitude less powerful than Arecibo was. This
paper does not account for an optimization this extreme, but it could be an
interesting avenue for more specialized searches in the future.

##  7 Conclusion

In this work, we describe the first radio technosignature search that pre-
planned observations to synchronize with exoplanets during their transits, in
a survey of a dozen exoplanets in the Kepler field. Using 6 hours of L-band
(1.1–1.9 GHz) data taken with the BL bankend on the GBT, we performed a SETI
search using the narrowband signal search code turboSETI. We chose a maximum
drift rate of $\pm$614.4 Hz/s — the first modern radio technosignature project
to encompass such extreme drift rates — in order to account for the full range
of drifts that could be produced from known exoplanetary systems. We also
chose a low S/N of 5. With these parameters, the algorithms flagged $\sim
2.53\times 10^{6}$ hits, which were then temporally filtered with an on-off
method into $3.4\times 10^{5}$ events. Many of these events could be
attributed to GPS satellite downlinks.

Thirteen citizen scientists volunteered their time to assist the science team
with the further filtering of the turboSETI events. From this process, the
list of signals-of-interest was reduced to a few thousand signals that
appeared to be either transient or sky-localized. We further removed signals
that appeared in multiple targets, or that were identical to signals proven to
be RFI, reducing the pool further to 479 signals-of-interest. Upon
investigating these 479 signals in the context of the entire observing
session, we determined that only two remained as signals-of-interest: one at
1749 MHz in Kepler-1332b, and the other from 1040-1438 MHz in Kepler-842b.

These signals do not rise to the level of even “candidate” technosignature
signals because there is no proof that they are spatially isolated (and they
are consistent with anthropogenic RFI), and so do not warrant follow-up with
the rigor described in (Sheikh et al., 2021). Reobservation of these targets
during transits, with a multibeam instrument such as the ATA, will conclude
the experiment and, if nothing is found, complete the null result we report
here. We hope that the “new ground” that we have broken in radio
technosignature parameter space will be extended by more synchronized SETI
searches in the future, across many more instruments and teams.

ETA

    Extraterrestrial Agents
GBT

    Green Bank Telescope
BL

    Breakthrough Listen
RFI

    Radio Frequency Interference
S/N

    Signal-to-Noise Ratio
SETI

    Search for Extraterrestrial Intelligence
FCC

    Federal Communications Commission
GPS

    Global Positioning System
PSPSC

    Penn State Pulsar Search Collaboratory
EIRP

    Equivalent Isotropic Radiated Power
ATA

    Allen Telescope Array

This work would not have been possible without the following citizen
scientists: Killian Cook, Anish Doshi, Gus Eberlein, Rhett Gentile, Jordan
Hanner, Shara Hussain, Matthew LaFountain, Yika Luo, Cole Penkunas, Livia
Seifert, Nate Smith, Valeria Ventura, and James Wu. This material is based
upon work supported by the Green Bank Observatory which is a major facility
funded by the National Science Foundation operated by Associated Universities,
Inc. We acknowledge Ron Maddalena for GBT observing and scientific assistance.
S.Z.S. acknowledges that this material is based upon work supported by the
National Science Foundation MPS-Ascend Postdoctoral Research Fellowship under
Grant No. 2138147NSF. CIC acknowledges support by NASA Headquarters under the
NASA Earth and Space Science Fellowship Program through grant 80NSSC18K1114
and the Pennsylvania State University’s Bunton-Waller program. C.G.
acknowledges the support of the Pennsylvania State University, the Penn State
Eberly College of Science and Department of Astronomy & Astrophysics, the
Center for Exoplanets and Habitable Worlds and the Center for Astrostatistics.
This paper is a result of the class project for the 2020 graduate course in
SETI at Penn State. We acknowledge Alan Reyes for participation in the class
project. The Pennsylvania State University campuses are located on the
original homelands of the Erie, Haudenosaunee (Seneca, Cayuga, Onondaga,
Oneida, Mohawk, and Tuscarora), Lenape (Delaware Nation, Delaware Tribe,
Stockbridge-Munsee), Shawnee (Absentee, Eastern, and Oklahoma), Susquehannock,
and Wahzhazhe (Osage) Nations. As a land grant institution, we acknowledge and
honor the traditional caretakers of these lands and strive to understand and
model their responsible stewardship. We also acknowledge the longer history of
these lands and our place in that history. Breakthrough Listen is managed by
the Breakthrough Initiatives, sponsored by the Breakthrough Prize Foundation.
The Center for Exoplanets and Habitable Worlds and the Penn State
Extraterrestrial Intelligence Center are supported by the Penn State and the
Eberly College of Science. This research made use of
Astropy,999http://www.astropy.org a community-developed core Python package
for Astronomy (Astropy Collaboration et al., 2013, 2018). This research has
made use of NASA’s Astrophysics Data System Bibliographic Services.

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##  Appendix A Observation Log

Table 4: The observation log from this project’s Green Bank Telescope observations. The scan ID number is shown in the first column, the target is shown in the second column, the transit synchronization is shown in the third column, and any additional notes are shown in the fourth column. Scan IDs are mostly consecutive, but missing ID numbers indicate scans which did not take data. Targets prefixed with a “K” indicate a “Kepler” system, with the letter suffix indicating which planet in the system was predicted to be transiting during our observing window. The relationship of the observation time to the transit time is indicated by letters: I-M indicates an observation which occurred between a transit’s ingress and midpoint, M indicates an observation which contained the transit midpoint, and M-E indicates an observation which occurred between a transit’s midpoint and egress (blank entries occurred outside of transit). Scan 0051 is missing a node of data (about 1/8th of the bandwidth) due to faulty data collection, encompassing frequencies from 1.25–1.30 GHz (entirely within the notch filter). Scan ID | Target | Relation to Transit | Notes | Scan ID | Target | Relation to Transit | Notes
---|---|---|---|---|---|---|---
0006 | 3C295 | non-planet obs. | Quasar | 0033 | K723b | I-M |
0007 | 3C295 | non-planet obs. | Quasar | 0034 | K1164b | M-E |
0009 | Boyajian’s Star | non-planet obs. | Off-source | 0035 | K723b | M-E |
0010 | K992b | M |  | 0036 | K537b | M |
0011 | K738b | I-M |  | 0037 | K723b | I-M |
0012 | K992b | M-E |  | 0038 | K537b | M-E |
0013 | K738b | I-M |  | 0039 | K723b | I-M |
0014 | K1039b | M |  | 0040 | K537b | M-E |
0015 | K1039b | M-E |  | 0041 | K723b | I-M |
0016 | K732c | M |  | 0042 | K723b | M |
0017 | K1039b | M-E |  | 0043 | K1332b |  |
0018 | K738b | M |  | 0044 | K723b | M-E |
0019 | K738b | M-E |  | 0045 | K1332b |  |
0020 | K732c | M-E |  | 0046 | K723b | M-E |
0021 | K1164b | I-M |  | 0048 | K723b | M-E |
0022 | K732c |  |  | 0049 | K446b | I-M |
0023 | K1164b | I-M |  | 0050 | K723b | M-E |
0024 | K732c |  |  | 0051 | K446b | I-M | missing node
0025 | K1164b | I-M |  | 0052 | K446b | M |
0026 | K1053b | M |  | 0053 | K1222b | I-M |
0027 | K738b | M-E |  | 0054 | K1222b | M |
0028 | K1164b | M |  | 0055 | K842b | I-M |
0029 | K1053b | M-E |  | 0056 | K842b | M |
0030 | K738b | M-E |  | 0057 | K723b | M-E |
0031 | K1332b | M |  | 0058 | K723b | M-E |
0032 | K1164b | M-E |  | 0059 | B0329+54 | non-planet obs. | Pulsar

##  Appendix B Mid-resolution plots for the two signals-of-interest

Figure 10: The signal-of-interest in Kepler-1332b data shown in the high
frequency-resolution data (left) and the mid-resolution data (right). The
regions of data shown are related as indicated by the white-dashed rectangles,
with the right plot zoomed-out in frequency and zoomed-in in time. The signal-
of-interest is actually composed of two short ($<$1 second) pulses. Figure 11:
The signal-of-interest in Kepler-842b data shown in the high frequency-
resolution data (left) and the mid-resolution data (right). The regions of
data shown are related as indicated by the white-dashed rectangles, with the
right plot zoomed-out in frequency and zoomed-in in time. The signal-of-
interest has a distinctive, periodic structure in frequency and is present
across the bandwidth. This behaviour is characteristic of RFI.

  *[ETA]: Extraterrestrial Agents
  *[RFI]: Radio Frequency Interference
  *[BL]: Breakthrough Listen
  *[GBT]: Green Bank Telescope
  *[S/N]: Signal-to-Noise Ratio
  *[SETI]: Search for Extraterrestrial Intelligence
  *[FCC]: Federal Communications Commission
  *[GPS]: Global Positioning System
  *[PSPSC]: Penn State Pulsar Search Collaboratory
  *[EIRP]: Equivalent Isotropic Radiated Power
  *[ATA]: Allen Telescope Array