11institutetext: Institute of Theoretical Astrophysics, University of Oslo,
P.O. Box 1029 Blindern, N-0315 Oslo, Norway 22institutetext: Rosseland Centre
for Solar Physics, University of Oslo, P.O. Box 1029 Blindern, N-0315 Oslo,
Norway
22email<EMAIL_ADDRESS>33institutetext: Departament Física,
Universitat de les Illes Balears, E-07122 Palma de Mallorca, Spain
44institutetext: Institute of Applied Computing & Community Code (IAC3), UIB,
Spain 55institutetext: LESIA, Observatoire de Paris, Université PSL, CNRS,
Sorbonne Université, Université de Paris, 5 place Janssen, 92290 Meudon
Principal Cedex, France 66institutetext: Centre for mathematical Plasma
Astrophysics, Dept. of Mathematics, KU Leuven, 3001 Leuven, Belgium
77institutetext: SUPA, School of Physics and Astronomy, University of Glasgow,
Glasgow G12 8QQ, UK 88institutetext: Instituto de Astrofísica de Canarias,
E-38200 La Laguna, Tenerife, Spain 99institutetext: Departamento de
Astrofísica, Universidad de La Laguna, E-38206 La Laguna, Tenerife, Spain
1010institutetext: Department of Physics, DSB Campus, Kumaun University,
Nainital – 263 001, India

# Interaction of solar jets with filaments: Triggering of large-amplitude
filament oscillations

Reetika Joshi 1122 Manuel Luna 3344 Brigitte Schmieder 556677 Fernando Moreno-
Insertis 8899 Ramesh Chandra 1010

###### Abstract

Context. Large-amplitude oscillations (LAOs) are often detected in filaments.
Using multiwavelength observations, their origin can be traced back to the
interaction with eruptions and jets.

Aims. We present two different case studies as observational evidence in
support of 2.5D MHD numerical experiments that show that the LAOs in the
filament channels can be initiated by solar jets.

Methods.  We use longitudinal magnetic field observations using the
Helioseismic Magnetic Imager to study the evolution of the filament channels.
The LAOs in the filaments are analysed using two techniques. The first one is
time-distance diagnostics with EUV and H$\alpha$ datasets. In the second
method, the oscillations in different parts of the filaments are examined
using Fourier analysis of the brightness variations of all pixels in H$\alpha$
observations.

Results. In the two studied events, we can identify a quadrupolar
configuration with an X-point at the top of the parasitic region suggestive of
a classical null-point. The X-point evolves into a flat structure suggestive
of a breakout current sheet. A reconnection flow emanates from this structure
leading to a jet that propagates along the filament channel. In both cases we
can identify the quiescent and eruptive phases of the jet. The triggered LAOs
have periods of around 70-80 minutes and are damped after a few oscillations.
The minimum magnetic field intensity inferred with seismology for the filament
turns out to be around 30 Gauss.

Conclusions. We conclude that the two case studies are consistent with the
recent numerical model of Luna & Moreno-Insertis (2021), in which the LAOs are
initiated by jets. The relationship between the onset of the jet and filament
oscillations is straight-forward for the first case and less for the second
case. In the second event, although there is some evidence, we cannot rule out
other possibilities such as activity unrelated to the null-point or changes in
the magnetic structure of the filament. Both jets are associated with very
weak flares which did not launch any EUV wave. Therefore the role of EUV waves
for triggering the filament oscillations can be eliminated for these two
cases.

###### Key Words.:

Sun: activity — Sun: filaments, prominences — Sun: flares — Sun: magnetic
fields — Sun: oscillations

##  1 Introduction

Solar filaments (or prominences) are clouds of dense and cool plasma hanging
in coronal heights (Labrosse et al., 2010; Mackay et al., 2010; Gibson, 2018)
and their origin is magnetic in nature. Occasionally the active as well as the
quiet filaments can oscillate. According to their amplitude, the oscillations
can be divided into two categories. If the amplitude velocity is larger than
10 km s-1 they are termed large-amplitude oscillations (LAOs); otherwise they
are known as small-amplitude oscillations. The oscillations are also grouped
according to the relative direction of their motion with respect to the
prominence magnetic field. When the motion is mainly in the assumed direction
of the field lines, the oscillations are called ‘longitudinal’; when
perpendicular to them, the oscillation is called ‘transverse’. In this paper
we consider only the longitudinal case by studying two large-amplitude
longitudinal oscillation (LALO) events.

For a long time now, oscillations in prominences/filaments have been observed.
In early observations they were called winking filaments, as they were moving
in and out of relatively narrow bandpasses (Hyder, 1966; Ramsey & Smith, 1966;
Vrsnak, 1993). However, the first clear detection of a LALO is recent. It was
reported by Jing et al. (2003) where the cold plasma of the prominence
oscillated along the filament spine. Afterward, more cases have been reported
(see e.g., Vršnak et al., 2007; Zhang et al., 2012; Luna & Karpen, 2012; Luna
et al., 2014, 2017). Observations show that LALOs have periods of a few tens
of minutes up to 160 minutes although they mostly have periods close to one
hour (Luna et al., 2018). Recently Luna et al. (2022b) have shown
theoretically that the period can never exceed 167 minutes. In these
oscillations the filament threads move along the dipped magnetic field lines.
Luna & Karpen (2012) proposed a so-called pendulum model where the restoring
force is mainly gravity projected along the field lines. The gas pressure
gradient also contributes although it is considerably smaller than the
gravitational force (Zhang et al., 2012; Luna et al., 2012). In the pendulum
model the period is given exclusively by the average radius of curvature of
the dipped field lines (see also Roberts, 2019). More studies based on 2D and
3D numerical simulations confirmed that the pendulum model describes quite
well the longitudinal oscillations (Luna et al., 2016; Zhou et al., 2018;
Zhang et al., 2019; Adrover-González & Terradas, 2020; Liakh et al., 2020,
2021).

The trigger for the LAOs is identified variously as Moreton or EUV waves (Eto
et al., 2002; Okamoto et al., 2004; Asai et al., 2012; Liu et al., 2012; Devi
et al., 2022), shock waves (Shen et al., 2014), filament eruptions (Isobe et
al., 2007; Chen et al., 2008), flares (Vršnak et al., 2007; Li & Zhang, 2012),
or jets (Luna et al., 2014; Zhang et al., 2017; Tan et al., 2023). These
active phenomena perturb the filaments, and produce significant displacements
with respect to the equilibrium configuration. In general, the displacements
are larger in LALOs than in the case of transverse oscillations (Schmieder et
al., 2013; Ofman et al., 2015). Jing et al. (2003) and Luna et al. (2017)
reported LALOs with velocity amplitudes on the order of 100 km s-1.

Nowadays it is unclear how the different energetic events can excite the
different polarizations of the LAOs. Only a few works have considered this
problem. Liakh et al. (2020) studied a flux-rope prominence and a very
energetic external disturbance. They found that both longitudinal and
transverse LAOs are excited. More recently, Luna & Moreno-Insertis (2021)
studied theoretically for the first time the interaction of a jet with a
prominence. They found that jets produce LALOs but also transverse
oscillations. These jets are thought to arise due to the rearrangement of the
magnetic field structure in the atmosphere caused either by magnetic flux
emergence from beneath the solar surface or due to driving process of the
footpoints of the field lines through photospheric flows, or due to the
induced stress in the the coronal magnetic field with a huge release of
magnetic energy as a jet or small flare (Joshi et al., 2021a, b; Joshi, 2022).
Whatever the precise magnetic configuration or evolutionary structure leading
to the jet eruptions, magnetic reconnection is well accepted to be present at
the core of this process for converting the stored magnetic energy to kinetic
energy of the jets (Joshi et al., 2020a, b; Schmieder et al., 2022; Schmieder,
2022). In their model, Luna & Moreno-Insertis (2021) explained that the jets
are produced in the sheared magnetic arcade near the footpoint of the filament
channel. After multiple reconnection processes, the jet flows towards this
filament channel and set the filament into oscillations, with amplitude larger
than 10 km s-1.

In this paper we present two different observational case-studies of such an
interaction between jet and filament, in which the jet initiates the
oscillations in the filament channel as suggested by Luna & Moreno-Insertis
(2021). The first event on February 5, 2015 concerns an active region (AR)
with a huge filament in its periphery. The AR was the site of repeated flux
emergence events and consequently small flares and jets. For this case, we
focus the study on one jet which hits one end of the filament and initiates
long time-period oscillations in the filament structure. The plasma material
was pushed along or in the flux rope containing the filament and LAOs were
observed. The second event was observed on January 1, 2014 and is chosen from
the catalog presented in Luna et al. (2018). It started with a few small scale
brightenings near one footpoint of the filament before the main jet, which
flew towards the filament channel and set it into oscillations. In the
conclusion we show the similarities between the observations and the model of
Luna & Moreno-Insertis (2021).

##  2 Description of the Observations and the Oscillation Analysis

Figure 1: Evolution of AR NOAA 12280 on February 3-5, 2015. Top panels: HMI
magnetograms, bottom panels: AIA 171 images. The emergence of magnetic bipoles
is clearly visible in the neighbourhood of the AR and near the jet base. Two
examples: the red circle in the top panels (a,b) indicates a new emerging
bipole on February 3; this was followed on February 5 by an another emerging
bipole marked by the blue oval (panel b). The green and red contours are the
HMI magnetic field contours of strength $\pm$ 100 Gauss respectively. The
images are aligned together at February 5, 2015 20:50 UT. The blue square is
the FOV of Fig. 3.

This study aims to give as complete a picture as possible of the interaction
of coronal jets with prominences using data from several ground-based and
space observatories. In addition, we also describe the technique to study and
parameterise the oscillations in the prominences after jet impact.

###  2.1 AIA, H$\alpha$, and HMI observations

For the study of these two cases, we use the high spatial and temporal
resolution EUV data from the Atmospheric Imaging Assembly (AIA, Lemen et al.,
2012) instrument on-board the Solar Dynamics Observatory (SDO, Pesnell et al.,
2012) satellite. AIA observes the full Sun in seven different UV and EUV
wavebands. The pixel size and cadence of this instrument are $0.6\arcsec$ and
$12$ s respectively. In order to increase the contrast of the images, we have
deconvolved the EUV data using the AIA point-spread function with the routine
_aia $\\_$deconvolve$\\_$richardsonlucy.pro_ available in solarsoft (Freeland
& Handy, 1998). All the AIA images are coaligned after correcting for the
solar rotation and are plotted in logarithmic intensity scale. To get the best
contrast for the filament and jet evolution, the multi-scale Gaussian
normalization processing technique (MGN: Morgan & Druckmüller, 2014) is
applied to the AIA images.

For the fulldisk observations of the Sun from ground-based telescopes, we use
the H$\alpha$ line-center photospheric data from the National Solar
Observatory/Global Oscillation Network Group (NSO/GONG). To cover the Sun for
the entire time of the day, there are six network telescopes situated all over
the globe (http://gong2.nso.edu). The pixel size and temporal resolution of
the H$\alpha$ data are $1$″and $1$ min, respectively. The filaments and their
motions are most easily observed and tracked in H$\alpha$. We use GONG’s
H$\alpha$ images to support the AIA EUV observations. H$\alpha$ images show
the dark filaments seen in absorption in sharp contrast to the bright
chromosphere around them.

In this study we use the longitudinal magnetic field to show the evolution of
the filament channels observed with the Helioseismic Magnetic Imager (HMI,
Schou et al., 2012) on-board SDO. HMI provides the photospheric magnetograms
with pixel size of $0.5\arcsec$ and a cadence of 45 s For both of the studied
events, we trace the magnetic history of the associated AR from previous few
hours till the start time of the jet filament interaction. Using the HMI
magnetic field contours over-plotted on the EUV images, we identify the
magnetic reconnection location near the jet base.

###  2.2 Oscillation analysis technique and prominence seismology

In the two events described in this work we have used the time-distance
diagram technique as in Luna et al. (2014, 2017). In the first event, we used
the GONG H$\alpha$ and the 171 Å SDO/AIA data (Sect. 3.3), whereas, in the
second event, we used 171 Å exclusively (Sect. 4.3).

We have selected the 171Å passband among all the AIA instrument filters
because this passband shows not only the absorption due to the presence of the
cool plasma prominence but also the prominence emission thought to be part of
the prominence-corona transition region (PCTR) at temperatures $>4\times
10^{5}$ K (Parenti et al., 2012). The PCTR is highly filamented, and thus the
171 Å band, with its combination of prominence absorption and emission, can
highlight fine structure allowing the tracking of the oscillations: when
laying an artificial “slit” that crosses the moving filament (as detailed in
Sect 3.3 and 4.3) and plotting the brightness along the artificial slit by
means of a time-distance diagram, clear oscillatory patterns become apparent.
Hereafter we will use the term slit instead of an artificial slit. Note that
when we use the term “slit” we refer to the path we use to measure the
intensity and not to the slit of a spectrograph. The oscillatory curves can
then be fitted to a damped sinusoidal curve of the form

$s(t)=s_{0}+A\,e^{-t/\tau}\sin\left(\frac{2\,\pi}{P}t+\varphi_{0}\right)\,,$
(1)

where $s$, $A$, $P$, $\tau$, and $\varphi_{0}$ are the coordinate along the
slit, amplitude, oscillation period, damping time, and the initial phase
respectively.

The study of oscillations with time-distance diagrams is restricted
exclusively to a small portion of the filament along which we have traced the
oscillations. However, as we will see, the jet reaches a large part of the
filament and makes it oscillate. So, to understand how the different parts of
the filament oscillate beyond what is captured by the slit, we will carry out
a Fourier analysis of the brightness variations of all pixels in the GONG
H$\alpha$ images, using the technique recently developed by Luna et al.
(2022a).

With this method we will see which regions oscillate and with which period.
However, with this technique we cannot extract the rest of the oscillation
parameters such as amplitude, damping time or direction of motion.

Luna & Karpen (2012) showed that the period of the longitudinal oscillations
is determined by the curvature of the dips that hold the plasma of the
prominence in the so-called pendulum model (see also Zhang et al., 2012). The
reason is that the dominant restoring force in the oscillation is gravity
projected along the field lines (Luna et al., 2012). Recently, Luna et al.
(2022b) have extended the pendulum model by considering that the gravity is
not uniform but changes its direction with the position over the solar
surface. This introduces important effects for periods larger than 60 minutes.
In addition, the authors have found that the periods of the longitudinal
oscillations cannot be longer than $P_{\odot}=$ 167 minutes.

They explained the relation between the period $P$ and the curvature of the
dips $R$, as

$\frac{R}{R_{\odot}}=\frac{\left(P/P_{\odot}\right)^{2}}{1-\left(P/P_{\odot}\right)^{2}}\,,$
(2)

where $R_{\odot}$ is the solar radius. The authors also determined a minimum
value of the magnetic field of the dipped lines in order to have magnetic
support of the cool mass. Using Eq. (27) from Luna et al. (2022b) we obtain

$B(\mathrm{Gauss})=\left(47\pm
24\right)\frac{P/P_{\odot}}{\sqrt{1-\left(P/P_{\odot}\right)^{2}}}\,.$ (3)

The term in the parenthesis is computed assuming a density range typical for
prominences of $\rho=2\times 10^{-11}-2\times
10^{-10}\mathrm{\leavevmode\nobreak\ kg\leavevmode\nobreak\ m^{-3}}$ (Parenti,
2014). We consider the prominence density to be the most important source of
uncertainty in the estimated magnetic field, because the uncertainties
associated with the fit are smaller than the above density range. In the
present work, we use these equations to compute the radius of curvature and
magnetic field.

##  3 Event 1: February 5, 2015

The jet-filament interaction on February 5, 2015 started with the ejection of
a solar jet parallel to the long filament near the AR 12280. This jet was
associated with a circular flare in the AR and it set the filament into
oscillations (see the attached animation AIA171_feb.mov).

Figure 2: Succession of flares in AR 12280 from February 2-5, 2015 registered
by GOES. The jet eruption presented here is associated with the GOES B7.8
class flare on February 5 at 20:52 UT. Figure 3: Zoom image of the jet base in
AIA 171 Å. The FOV for this figure is presented as the blue square in Fig. 1
(d). The null-point-like structure at the jet base is indicated with a white
arrow (panel a). The jet is initiated under the arcade (green arrow) following
a small filament eruption (red arrow). This small filament pushes the arcade
toward the null-point like structure which leads to the jet flows towards the
filament (white arrow in panel b-d) in the South-West. This flow is
bidirectional, as we observe the second branch, which flows toward the North,
is indicated with cyan arrows in panels (c-d). The null-point type structure
collapses into the breakout current sheet (BCS). The latter is marked using
yellow arrows in panels b-c-d. (See also the associated animation
%****␣OscillationJetFilament.tex␣Line␣275␣****AIA171_feb.mov).  Figure 4:
Filament and jet evolution for event 1 on February 5, 2015 observed in AIA 171
Å (top row), in AIA 304 Å (middle row), in H$\alpha$ (bottom row). The jet
ejects from a dome-like structure with a small filament eruption shown in
panel a. The jet flows towards the long filament through the BCS shown in
panel b, c, e, and f and a zoomed view is presented in Fig. 3. The long
filament is well observed in all these channels lying as a cool and dense
structure (pointed in panel (g)). This jet is associated with a GOES B7.8
circular flare shown in panel h.

###  3.1 Environment of the filament and jet

This event concerns active region NOAA AR 12280, which appeared on the solar
disk on February 2, 2015, and was located at S08 E17 (-282$\arcsec$,
-33$\arcsec$) on February 5 (Fig. 1). A succession of C-class X-ray flares,
related to several magnetic flux emergence events was registered by GOES
during its disk passage (see Fig. 2): on February 2 (C 1.7 class flare), on
February 3 (C 2.7 and C 1.5 class flares), on February 4 (C 2.7, C 1.5, C 3.0
flares) and a B7.8 class flare starting at 20:44 UT and peaked at 20:52 UT on
February 5 (https://www.spaceweatherlive.com/en/archive/2015/02/05/xray.html).
These flares were accompanied by recurrent jets. We concentrate our study on
the last event on February 5 at 20:44 UT.

The magnetic configuration of the AR consists of a complex polarity pattern
with a leading positive polarity (top panels of Fig. 1). Successive new
episodes of magnetic flux emergence were observed inside a remnant bipolar AR,
consequently increasing the complexity of AR 12280. We show two examples: on
February 3 there is a clear emerging bipole (red circle in panel a), and on
February 5 a second emerging flux event is indicated by a blue oval in panel
b. A large intermediate filament was located at the South-East of the AR along
an extended polarity inversion line (PIL). The bottom row of Fig. 1 shows the
AR in 171 Å for February 3 and February 5, 2015, where the filament is seen as
a dark structure (shown with the white arrow). The filament has one end
located over the AR near the origin of the jet. The jet initially pushes a
large part of the filament and we see periodic motions of the mass which moves
back and forth along the filament spine (see movie AIA171_feb.mov).

###  3.2 Generation and Evolution of the jet

The jet was associated with a circular flare and a bidirectional flow towards
the East and North directions. Fig. 3 shows a zoom view around the jet. The
figure contains deconvolved AIA 171 Å images; we use a black and white
representation to increase the contrast. In Fig 3a a dome- or arcade-shaped
structure overlying the emerging bipole can be clearly identified with an
‘X’-point configuration at its top, strongly suggestive of a null-point
structure (white arrow). A small filament (indicated by a red arrow in Fig.
3a) located under the magnetic arcade starts to erupt at 20:30 UT. During its
eruption, it encounters the null-point type configuration and produces its
collapse into a flat structure suggestive of a breakout current sheet (BCS)
(marked with yellow arrows in panels b through d). The configuration in panel
b (20:50 UT) roughly corresponds to the time when the jet flows reach the
filament; the succession of events leading to this configuration can be
studied in more detail by comparing, as done in Figure 4, the evolution in
three different filters (AIA 171 Å, AIA 304 Åand H$\alpha$, top, middle and
bottom rows) at times 20:40 UT, 20:44 UT and 20:50 UT, in the left, center and
right columns. The main reconnection flow issuing from the BCS leads to a
large jet that impinges onto the filament. This jet is apparent as a bright
spire issuing from the BCS in the AIA 171 and AIA 304 filters at 20:44 UT and
20:50 UT (Figure 4b, c, e and f). In the H$\alpha$ images (bottom row) the
filament is seen to roughly coincide in position with the hot jet; also, the
associated circular flare in the vicinity of the jet region is clearly visible
in those three panels. Going back to Fig. 3, we can see some additional
consequences of the jet ejection at times a little later than those shown in
Fig. 4: in particular, we can see that, apart from the main reconnection flow
leading to the large jet, there is a secondary flow issuing from the BCS and
oriented in the North direction, as marked with cyan arrows in panels (b)
through (d) of the figure.

The main jet moving towards the filament sets it into oscillations. To study
the propagation of the main jet and the filament oscillations, time-distance
diagrams are used (Fig 5). The slit used for the diagrams is shown in panel
(a) on the background of an AIA 171 Åimage; The choice of this non-straight
slit is such that its orientation follows the jet flow and direction of the
plasma oscillations of the prominence. To match the general direction of the
flow, distances along the slit are measured starting at the end nearest to the
AR. Leaving the analysis of the oscillations to Sec 3.3, we here focus (Fig.
5b) on the flows apparent in the time distance diagram in the region of the
slit nearest to the BCS, or, more precisely in the $150$″ starting at the top-
right of the slit. In the figure, we can see a complex structure with lots of
bright paths. The slope of the bright paths is proportional to the flow
velocity. The dashed lines indicate the trajectory of two such paths, one
toward the beginning and the other toward the end of the jet ejection; the
first one starts at 20:48 UT and has a projected speed of about $220$ km s-1
while the second starts at 21:08 UT and has a projected speed of about $90$ km
s-1. From those values, and from direct inspection of the inclination of the
tracks in the figure, we gather that the jet, which always follows the same
trajectory, decreases its velocity (and most probably also its kinetic energy
flux) as time advances.

Figure 5: Panel (a): Filament seen in absorption in AIA 171 Å on February 5,
2015, with the artificial slit used to construct the time-distance diagrams
(panels b-d) shown as a white contour. (Panel b) time-distance diagram for the
AIA171 image along the topmost $150$ ″of the slit; panel (b) in Fig. 3, taken
at time 20:50 UT. Panels c and d contain the time-distance diagrams for the
brightness in along the curved slit, clearly showing the oscillatory patterns
analyzed in the paper. The white tracks in panels c and d show one of the fits
obtained for the oscillation which has period $77$ min, velocity amplitude
$33$ $\mathrm{km\,s^{-1}}$ and damping time $\tau=196$ min. The black vertical
stripes in panels (b), (c) and (d) are data gaps.

###  3.3 Filament oscillations

To study the oscillations caused by the impact of the jet, the time-distance
diagram introduced just above has to be extended to the full length of the
slit and to a much longer time interval than shown in Fig 5(b). The diagram
used is shown in panel 5(c), with the white box marking the limited domain
used in panel 5(b).

The jet flows reach the filament at 20:50 UT as we have already seen in Sect.
3.2. The interaction produces a displacement of the prominence plasma along
the slit. During the first $50$ minutes we see bright and dark features moving
along the slit. We could say that this is the triggering phase where the jet
flow interacts with the filament plasma. This plasma moves until it reaches
maximum elongation at 21:20 UT approximately. Between this time and 02:00 UT a
clear oscillatory pattern can be identified in panel (c). However, the
movement of the prominence plasma is very complex with several specially
prominent oscillation paths visible: the plasma probably oscillates at various
levels with different periods and directions. Due to the difficulty of
tracking the movement of a single path we also use the H$\alpha$ data. Figure
5(d) shows the H$\alpha$ diagram constructed with the same slit. We can see
that H$\alpha$ shows a bulk motion of the plasma that is consistent with an
oscillation. We define a curve in the centre of the dark band and then fit the
oscillation using Eq. (1). The resulting fit is plotted in both panels (c) and
(d). The fit is very good in the H$\alpha$ diagram. In contrast, in AIA 171 Å
the curve does not match so well any of the paths in the diagram. The adjusted
period is 77$\pm$2 minutes, however in AIA 171 Å it seems that the period of
the different threads ranges up to 120 minutes.

The variation with height of the oscillation period is known from a
theoretical point of view (Luna et al., 2016). A similar behaviour was found
by Raes et al. (2017). They pointed out that this effect could produce the
false impression of vertically propagating waves. They called these apparent
waves superslow modes.

Beyond February 6, 02:00 UT the oscillation disappears, as the filament
configuration changes and the oscillation moves out of the slit. The rest of
the oscillation parameters from the fit are the velocity amplitude of $33\pm
5$ $\mathrm{km\,s^{-1}}$ and the damping time $\tau=196\pm 74$ minutes. The
ratio between the damping time and the oscillation period is $\tau/P=2.5$,
which indicates that the oscillation damping is relatively strong. Luna et al.
(2018) found typical ratios $\tau/P=1.25$ for LAOs indicating strong damping
of this kind of motions. Using Eq. (2), for a period of 77 minutes we obtain a
radius of the dips $R=188$ Mm. In addition, with Eq. (3) we can also obtain a
lower limit for the magnetic field intensity in the range $B=12-37$ Gauss.

As, we have just seen, the oscillations in the filament are quite complex with
several periodicities involved. Moreover, the analysis of the oscillations
using a single slit is limited to a small area of the filament. To make a more
complete study of what the periodicities are and which regions of the filament
oscillate after the impact of the jet, we applied a technique developed by
Luna et al. (2022a), as already mentioned in Sect. 2.2. The technique studies
the periodic fluctuations of every pixel of the H$\alpha$ images from the GONG
network. With the fast-Fourier transform the power spectral density (PSD) is
computed. To discriminate spurious fluctuations from the real oscillations, it
is required that the peak in the PSD be greater than several times the
background noise so that the confidence level is above 95%.

Figure 6: Time periods of the filament oscillations over a GONG H$\alpha$
image on February 5, 2015 using the technique developed by Luna et al.
(2022a). The color code shows the periods in minutes.

As shown in Fig. 6, the jet produces oscillations in a large part of the
filament. The periods range from $60$–$110$ minutes, which is in agreement
with the $77$ minutes obtained with time-distance method. It is interesting to
note that at the northern end a large area oscillates with periods around
$110$ minutes. The spatial distribution of periods may be associated with the
fact that we observe the oscillations along different field lines and these
have different curvatures in their dips. Using Eq. (2), from the period range
from 77-120 minutes, we obtain that the radius of the dip is in the range
$103$–$534$ Mm. Similarly, using Eq. (3) we obtain that the field strength in
the filament ranges between $9$ and $64$ Gauss.

###  3.4 Comparison with the theoretical model of Luna & Moreno-Insertis
(2021)

The observations presented in Sect. 3 bear remarkable similarities to what was
described in the theoretical model of Luna & Moreno-Insertis (2021). In their
model, the magnetic arcade associated with a bipolar parasitic region at the
flanks of the filament channel (FC) of a prominence was sheared at its
photospheric feet. The null point at the top of the parasitic region initially
has a classical X-point shape; through the photospheric shear, however, the
X-point evolves into a breakout current sheet (BCS) where reconnection takes
place; the change in the magnetic configuration and associated reconnection
lead to a succession of nonlinear waves or jets (Alfvénic front, sonic front,
eruptive jet) which propagate along the filament channel eventually impacting
the prominence. An important part of the basic features of that model seem to
be discernable in the observations. Starting with the null point and BCS, the
time series of events in AIA 171 Å(Fig. 3 and associated movie AIA171_feb.mov)
seem to show precisely this kind of configuration: in Fig. 3a the AIA 171
Åimage clearly delineates an X-point which then (panels b and c) evolves into
a flat BCS. In Fig. 7, we compare the electric current distribution at a
relevant time in the numerical model, with its characteristic flat top, to
Fig. 3b. There is a clear morphological and evolutionary similarity between
the AIA 171 Åbrightness patterns and the results of the model.

Figure 7: Similarity between the observation of event 1 on February 5, 2015
and the numerical model of Luna & Moreno-Insertis (2021). The left panel is
identical to panel b of Fig. 3; the right panel shows the electric current
distribution of the model of Luna & Moreno-Insertis (2021) (adapted from their
Fig. 4c). The flat breakout current sheet is marked in both panels by a yellow
arrow.

The nonlinear waves and jets arising in the model as a result of the
reconnection were produced in two stages; in the first one, an Alfvénic front
followed by a more standard sonic shock were launched from the BCS. These are
difficult to discern in the current observations. Then, in the second stage,
reconnection in a quasi-vertical current sheet starts below the BCS; a twisted
flux rope, resembling a mini-filament, is produced and hurled upward against
the BCS. There follows a violent eruptive jet which is launched along the
field lines of the filament channel and eventually impacts the prominence. In
the observations, we already mentioned the appearance of a small filament-like
structure which erupts below the magnetic arcade (marked with a red arrow in
Fig. 3) toward the BCS. More importantly, the major eruptive jet at
$\sim$20:50 UT, already discussed in Figs. 3b, c and d (also in the animation,
AIA171_feb.mov, and in Fig. 4) clearly originates in one of the sides of the
BCS and travels along the filament channel toward the filament. This matches
quite well the magnetic field and velocity patterns obtained in the numerical
model, as apparent in, e.g., Fig. 12 of Luna & Moreno-Insertis (2021), adapted
here with extra markers for easiness of comparison (see Fig. 8). The two
panels show the eruptive phase of the jet. In (a), the yellow rectangle
delimits the area where the near-vertical current sheet occurs during the
eruptive phase of the magnetic reconnection. The plasmoid originated in the
vertical current sheet moves upwards and merges with the overlying field. The
plasmoid moves with a high velocity as indicated by the almost vertical arrow
in the figure. This produces a large perturbation that generates flows that
propagate along the field lines that collide with the prominence (see Fig.
8(b)). In contrast to the model, the jet in the observations shows a
rotational motion along the filament channel with about one turn along the
entire length between the BCS and the filament; this leads to a misalignment
of about $30$ deg between some of the branches of the jet and the filament
spine. In the theoretical simulation, changes in field line orientation were
seen propagating along the FC, but no real rotation of the plasma around the
field lines of the FC could develop given the two-dimensional (more precisely
2.5D) nature of the model. Finally, in the numerical simulation the side of
the BCS opposite to the filament also had an outflow, albeit much weaker than
the main outflow and jets. This is apparent as a thin layer with velocity
arrows pointing upward and away from the BCS in Fig. 7. In the observation, as
pointed out in Section 3, there is also a collimated brightening issuing from
the BCS and pointing in the North direction (marked with cyan arrows in Figs.
3c and d). This is suggestive of the presence of a secondary outflow from the
reconnection site also in the actual observed configuration.

Figure 8: Interaction of the ejected plasma with a filament channel adapted
from Luna & Moreno-Insertis (2021). Both panels show the evolution of the jet
at $t=27$ (a) and $t=29.7$(b) minutes after the start of the numerical
simulation. The green contours are isolines of the density. Around x = 0 we
see the green contour of the filament suspended in dips of arcades of magnetic
field (indicated by a black arrow in (a)). Red and blue are the velocity flows
projected along the magnetic field lines. The vector field shows the flow
velocity. For a better visualisation, only vectors with a velocity greater
than 20 km s-1 are shown. To show the scale of the velocity vectors, a 50 km
s-1 arrow is shown on the right side of the panel (b).

##  4 Event 2: January 1, 2014

Figure 9: Evolution of magnetic field (top row) and filament channel in AIA
171 Å (bottom row) for event 2. The AR 11938 consists a big positive polarity
patch (P0’, P0, and P1) surrounded with negative polarities (N0, N1). The
different PILs (1, 2, 3) are shown in panel (b). The filament appears as dark
areas (panel (c-d)) and the bright thin loops are possibly arcades or magnetic
field lines of the filament structure. The jet flowing towards the filament
channel near the PIL2 is shown with arrow in panel (d). The dome and null-
point-like structure is enclosed by a blue circle. The green and red contours
in the bottom row are the HMI magnetic field contours of strength $\pm$ 50
Gauss respectively. All images are aligned together at January 1, 2014 at
15:56 UT. Blue rectangular box is the FOV for Fig. 13. Figure 10:  Filament
and jet evolution on January 1, 2014 (event 2) in AIA 171 Å (top row), AIA 304
Å (middle row), and H$\alpha$ (bottom row). The null-point-like structure is
shown with a white arrow in panel (a) at the top of the dome-like structure.
The jet propagation from this null-point towards the filament channel is shown
with black arrows (panel (b and e)). The cyan arrows in panel (c and f) show
the later brightening associated with the jet, which reinforces the
oscillations. The filament is very well observed in H$\alpha$ as a dark long
structure shown with black arrow in panel indicating the sinistral handedness
of the filament (g). The contours of the filament observed in H$\alpha$ are
over-plotted in AIA 171 and 304 Å channels (panels a,b,d). The black contours
in panel e and h are for the brightening at the jet base observed in H$\alpha$
overplotted in AIA 304 Å.

###  4.1 The host active region and the filament

On January 1, 2014, AR 11938 was located near disk center (S09W03). It
consists (Fig. 9a, b) of disperse polarities (P0-N0); new emerging magnetic
flux (EMF; P1-N1) had appeared on December 31, 2013. That emergence had
occurred in the middle of the positive polarity P0, causing it to split into
two main fragments; we call P0’ the fragment that is closer to N0. There are
several PILs in the active region (Fig. 9 b). PIL1 is between P0’ and N0, PIL3
between P1 and N1 in the oval of panel b. We followed the evolution of the
magnetic field for 12 hours before the eruption and observed the expansion of
P1-N1 as the flux emergence process advances; between them there are mixed
polarities probably indicating sea serpent lines which originate from the edge
of the sunspot and create moving magnetic features (MMF, Sainz Dalda & Bellot
Rubio, 2008). During this expansion a strong shear occurs between P0’ and
these mixed polarities. In panels c and d the coronal emission counterpart can
be seen through AIA 171 Åimages, with, superimposed, green and red contours
marking the HMI polarities. In panel d we can see a structure resembling a
dome surmounted by a null point or current sheet, probably associated with
(and resulting from) the strong photosperic shear mentioned just above
(enclosed with the blue circle).

The best identification between chromospheric, TR and coronal structures, and
the clearest view of the filament, can be gained by comparing simultaneous
H$\alpha$, AIA 304 Åand AIA 171 Åimages, as presented in Fig. 10. Looking at
the H$\alpha$ panels (bottom row), the filament is clearly visible in the
neighbourhood of NOAA AR 11938 and stretches mainly in the direction
SouthEast-NorthWest, with the southern tip touching the AR, which is also
where the bright jet activity described below takes place; the top part of the
filament is arched in the East-West direction. Both from Fig. 9c,d, and from
the AIA 171 Åand AIA 304 Åsnapshots of Fig. 10 (e.g., panel b and e), one sees
that the filament has one end in the vicinity of the dome. The magnetic
configuration near the dome appears to be quadrupolar again, like in the
February event described in Sec. 3, and thus of the type studied in the
theoretical model of Luna & Moreno-Insertis (2021). The filament is sinistral
according to the orientation of its lateral barbs in the H$\alpha$ images
(Figure 10 g,h,i).

Figure 11: Tracing of the oscillations in the filament for the first event on
January 1, 2014 observed with AIA 171 Å. Figure showing the filament seen in
absorption in AIA 171 Å. The artificial slit is shown as a white contour shown
in panel (a) to construct the time-distance diagram shown in panels (b) and
(c).  Figure 12: Time periods of the filament oscillations over a GONG
H$\alpha$ image on January 1, 2014 using the technique developed by Luna et
al. (2022a). The color code shows the periods in minutes.

###  4.2 Jet activity

To follow the jet propagation from its source towards the filament channel, we
analysed the AIA multi-wavelength observations in 171 and 304 Å shown in Fig.
10 (top and middle rows) and, in full for 171 Å, in an accompanying animation
(AIA171_jan.mov). Between 12:00 to 12:35 UT, we observe many small bright jets
with short lifetimes. They emanate from the null-point-like structure going
upward in the direction of the filament. In Fig. 10 (a) we can see the hot
plasma that has emanated from these jets as bright structures on the filament
following the magnetic field lines of the filament channel. Right after 12:40
UT a significant jet is observed: an intense brightening is seen around the
area of the null point and the jet is accompanied by apparently larger flows
than the previous cases (see the left black arrow in Figs. 10 b and 10 e),
which can also be seen over the filament (right black arrow in Fig. 10 (b)).
Prior to 13:20 UT, no clear association of the jets with filament oscillations
can be established. At 13:21 UT, however, an intense brightening (like a
burst) is observed around the null point. This brightening leads to a jet
propagating on the left-hand branch issuing from the null-point-like structure
more than in the direction of the filament (cyan arrow in Figs. 10 c and Fig.
10 f). Alternatively, this could be caused by activity unrelated to the null
point area. For example, at 13:22 UT at x=-40 and y=25 arcsecs, a brightening
occurs simultaneously with that of the null point. However, we do not observe
any flows impacting the filament from other regions.

Similarly to the previous event (Sec. 3.3 and 3.2), we can analyze the
velocity of the jet and the oscillatory pattern using the same curved slit for
both determinations, as shown in Fig. 11(a). Concentrating here on the jet
velocity, Fig. 11(b) shows the time-distance diagram for the AIA171 intensity
along the slit in the first $120$ minutes. The initial jet activity (say,
before 12:45 UT) is clearly seen in the form of bright features moving along
the slit. These early jets all have a similar velocity; using a bright feature
that starts at 12:42 UT, we obtain a speed of $\sim$ 120 km s-1, as indicated
with a dotted line on the left of the panel. Later, at 13:22 UT, we can
identify an almost vertical brightening stretching between
100$\arcsec$–150$\arcsec$ and followed by a more gradual arch-like collection
of brightenings all the way to the right end of the panel. The inclination of
the almost vertical brightening corresponds to a propagation velocity of about
$1000$ km s-1 [dashed line in Fig. 11(b)]. Continuing that dashed line toward
the origin of the slit one can see that it reaches the neighborhood of what
appears to be a counterpart of the semi vertical brightening near the
dome+null-point region. Still, it is not possible to find any causal
connection between the two brightenings: we cannot identify in any of the EUV
AIA channels anything propagating along the slit that could cause the filament
to brighten in the $100\arcsec$-$150\arcsec$ region of the slit as a result of
the activity near the null-point region. Going now to the arch-like
brightenings, we can clearly identify velocities between $40$ and $55$ km s-1
in the initial part of the arches. Looking further in time [Fig. 11(c)], one
sees that the arches are the initial part of oscillatory features in the
filament (to help the identification, the location of panel b is indicated in
panel c with a white rectangle). These are analyzed in the next section.

Figure 13:  Zoom view of the jet base region in 171Å maps as indicated with
the blue rectangular box in Fig. 9 (c). The three panels show three stages of
the temporal evolution of the jet. In (a) a X-point structure can be
identified in the central part. This structure evolves and acquires a BCS
H-type shape marked by the white arrow. Important flows are seen emanating
from the H structure. The inset in panel (b) shows the electric currents
distribution from the Luna & Moreno-Insertis (2021) model (adapted from their
Fig. 4b). The white curves are the magnetic field lines and the blue vectors
are the velocities of the plasma. Finally in (c) this structure disappears and
a brightening is seen around it. The cyan arrow in panel (c) shows the
brightening along the field lines associated with the eruptive phase.

###  4.3 Filament oscillations

We focus now on the oscillatory patterns that start at $\sim$ 13:20 UT
following the almost vertically propagating brightening just discussed and
last for more than 4 hours. In contrast to the February event, the
oscillations here are more clearly discernible with all the threads
oscillating more or less in phase. The oscillation can be distinguished until
18:00 UT. A fit to one of the oscillatory patterns gained through Eq. 1 can be
seen through the white curve on the panel, with the parameters of the fit
indicated on the top right. The period is $74\pm 1$ min, which is in agreement
with the results of the catalog by Luna et al. (2018); and, the damping time
is $165\pm 23$ minutes, which is almost in agreement with the catalog value of
$121\pm 15$ minutes when considering the error bars. Using Eq. (2) we obtain a
radius of curvature of the dipped field lines of $R=170$ Mm. Also, Eq. (3)
gives the minimum field value to support the cold plasma of the prominence
against gravity. With the periods obtained we find that the range of minimum
values of the field intensity $B_{min}=11-35$ Gauss. As mentioned in the
previous event, by studying the oscillations with a slit we can determine the
amplitude, period and damping time. However, the slit covers a restricted area
of the filament. Using the technique introduced by Luna et al. (2022a) for
this case, as we did for the February event of Sec. 3.3, we can see the main
oscillation periods in the whole filament (see Fig. 12).

It can be seen that almost the entire filament oscillates and that the periods
in the different regions range from 50–90 minutes but predominantly near
$80^{+10}_{-8}$ minutes. This value is in agreement with the value obtained
with the slit analysis. Using this range of periods we obtain a range of radii
of curvature $69-285$ Mm and a minimum field intensity of $7-46$ G.

###  4.4 Comparison of the observations to the theoretical model

Like for the jets discussed in Sec. 3.4, the Jan 1st event has some striking
similarities to the Luna & Moreno-Insertis (2021) model. The basic underlying
magnetic configuration of the model described in Sec. 3.4 is also present
here, namely an arcade associated with a bipolar parasitic zone at one end of
the FC surmounted by a null X-point. Three snapshots along the time evolution
that are particularly relevant for the comparison are shown in Fig. 13 using
AIA 171Å maps. In panel (a), taken from the map at $t=$ 12:03 UT, an arcade is
clearly seen at the southern end of the filament: going from the arcade
upwards, the remote connectivity of the magnetic field and its orientation
change abruptly at a point resembling an X-crossing: all of this indicates the
probable presence of a null point at the top of the arcade. Photospheric shear
at the feet of the arcade causes the null point to become a BCS where
reconnection takes place. In fact, at the later time shown in panel (b) ($t=$
12:31 UT), at the location of the null point one sees a structure with a clear
H-shape probably corresponding to the BCS. The flows emanating from it are
directed mainly toward the filament, but also in the opposite direction. From
the model, we expect this to correspond to the quiescent phase of the jet,
with continuous plasma flows emanating from the reconnection site. The
resemblance to the numerical model is remarkable, as can be gathered by
comparing the observed structure with that in the inset, adapted from the Luna
& Moreno-Insertis (2021) paper, which contains a color map of the module of
the electric current with velocity arrows superimposed. In the numerical
model, the reconnection in the BCS ceases later on, but, by then, the arcade
has become elongated in the vertical direction and an intense vertical current
sheet appears at its center; there follows reconnection across that current
sheet, and a violent jet is ejected along the filament channel. Panel (c),
taken from the AIA171 map at $t=$ 13:21 UT can correspond to this phase, with
a brightening along the field lines indicated by the cyan arrow. That
brightening could be associated with the eruptive phase, in which a plasmoid
or mini filament is ejected. The eruption as it is described in the model is
not really identifiable. However, these brightenings indicate that an
energetic process has taken place. As an additional indication of the violence
of the process, the oscillation of the filament starts right after this
brightening, as we have studied in Sect. 4.3.

##  5 Conclusion

This observational study has been inspired by the scenario recently proposed
by Luna & Moreno-Insertis (2021) for triggering the large-amplitude
oscillations (LAOs) in filaments. The authors propose that the LAOs may be
initiated by jets in a reconnection process in the magnetic structure of the
filament. We have been able to identify two case studies which show
similarities to the model. In both cases we analyse observational data to
understand how the oscillation starts and how the filament oscillates after
this perturbation. In the first case, occurring on February 5, 2015 the jet
perturbs a large portion of the H$\alpha$ filament that oscillates mainly with
a period of 74 min. The period detected in 171 Å is not so clearly defined, in
a range of periods of $70-110$ min., leading us to believe that the filament
is made by different structures at different altitudes. In the second case, on
January 1, 2014, a large portion of the H$\alpha$ filament is perturbed as
well, and the oscillations have a range of periods of $50-90$ min. In both
cases periods reaching 120 minutes are detected. These values for the period
are consistent with those of typical LAOs and with the results from the
catalog of Luna et al. (2018). We have applied prominence seismology using the
pendulum model by Luna et al. (2012, 2022b) allowing us to compute the
curvature of the dips in the flux rope containing the filament, and the
magnetic field strength. The latter has been estimated to be of the order of
30 Gauss in both filaments. These values are in agreement with direct
measurements from observations (Leroy et al., 1984; Levens et al., 2016,
2017). Both cases described in this work are intermediate filaments with one
end connected to active regions and the magnetic field can be rather large
(López Ariste & Aulanier, 2007; Díaz Baso et al., 2019). Luna et al. (2017)
and more recently Kucera et al. (2022) have shown that the seismological
predictions of the pendulum model work well and give similar results of the
field geometry and field strength as other techniques.

Both events have similarities to the Luna & Moreno-Insertis (2021) model. Both
show a quadrupolar structure with a parasitic bipole at one end of the
filament channel. On top of this parasitic polarity there is a classical
X-shaped structure in the AIA brightenings strongly resembling a null-point
configuration. In both cases the parasitic polarity is produced by magnetic
flux emergence. There is also a strong shear along the polarity inversion line
which may be responsible for disturbing the null point and producing the
magnetic reconnection that leads to the jet. A structure with the appearance
of a breakout current sheet can be identified which surprisingly resembles the
structures obtained in the Luna & Moreno-Insertis (2021) numerical
simulations.

In the first observed event (February 5, 2015), the formation of the BCS is
followed by the eruption of a mini filament. This indicates that both the
quiescent and eruptive phase of the jet occur almost at the same time, in
contrast to the model. This may be due to the fact that the magnetic shear
injection in the parasitic region is higher than in the model. In the model we
did not explore the possibility of increasing the injection rate, which will
be left for a future study. When the jet is launched, part of it goes more or
less directly to impact the dense material in the filament, but part of it
runs along the overarching field lines. An interpretation is that the filament
is sitting at the bottom of the main dips of a flux rope, but the field lines
above the filament are arched, perhaps also moderately twisted around the
filament as in Aulanier & Schmieder (2002).

In the second event (January 1, 2014), the breakout current sheet-like
structure is observed for a long time, which, as in the previous case, is in
agreement with the model. We identify this first phase as quiescent; the
emanating jet does not seem to impact the filament since it does not produce
oscillations. These flows probably travel along field lines of the filament
channel without threads. As seen in the numerical modelling, the initial
height of the null point relative to the filament determines how the different
phases of the jet impact the filament. After some time, a sudden brightening
around the parasitic zone is observed, which could be identified with the
eruptive phase of the jet. After this brightening, the filament starts to
oscillate with a large amplitude motion. However, we cannot identify any
plasma flow from the jet area to the filament. Perhaps, the plasma moves along
field lines that are partially hidden by the filament itself or by the
foreground emission of coronal structures. The triggering of the oscillations
in this second event could be caused by activity unrelated to the null point.
However, we did not observe plasma flows reaching the filament from other
regions. An alternative explanation could be that some disturbance (e.g.
reconnection) produces changes in the magnetic structure of the filament that
disturb its cold plasma.

Still, the direct impact of jets remains the most probable cause of the
filament oscillations in the first event. Further, interestingly, a preprint
published after submission of the present manuscript reports on another event
where filament oscillations are caused by jets, also showing clear bilateral
flows (Tan et al., 2023).

Nevertheless we conclude that the events presented here bear a clear
resemblance to those described in the model by Luna & Moreno-Insertis (2021).
A comprehensive study of the triggering processes of LAOs in filaments is
needed to better understand these processes. A numerical study is also needed
to investigate how the jet synthesis is affected by different parameters such
as boundary driving. It is also necessary to extend the study to three
dimensions.

###### Acknowledgements.

We acknowledge the anonymous referee for the valuable/constructive comments
and suggestions. This research has been supported by the European Research
Council through the Synergy Grant number 810218 (“The Whole Sun”,
ERC-2018-SyG) and by the Research Council of Norway through its Centres of
Excellence scheme, project number 262622. M.L. acknowledges support through
the Ramón y Cajal fellowship RYC2018-026129-I from the Spanish Ministry of
Science and Innovation, the Spanish National Research Agency (Agencia Estatal
de Investigación), the European Social Fund through Operational Program FSE
2014 of Employment, Education and Training and the Universitat de les Illes
Balears. This publication is part of the R+D+i project PID2020-112791GB-I00,
financed by MCIN/AEI/10.13039/501100011033. Funding by the Spanish Ministry of
Science, Innovation and Universities through project PG2018-095832-B-I00 is
also gratefully acknowledged.

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