Simultaneous Horizontal and Vertical Oscillation of a Quiescent Filament Observed by CHASE and SDO

In this paper, we present the imaging and spectroscopic observations of the simultaneous horizontal and vertical large-amplitude oscillation of a quiescent filament triggered by an extreme-ultraviolet (EUV) wave on 2022 October 2. Particularly, the filament oscillation involved winking phenomenon in Hα images and horizontal motions in EUV images. Originally, a filament and its overlying loops across AR 13110 and 13113 erupted with a highly inclined direction, resulting in an X1.0 flare and a non-radial coronal mass ejection. The fast lateral expansion of loops excited an EUV wave and the corresponding Moreton wave propagating northward. Once the EUV wave front arrived at the quiescent filament, the filament began to oscillate coherently along the horizontal direction, and the “winking filament” appeared concurrently in Hα images. The horizontal oscillation involved an initial amplitude of ∼10.2 Mm and a velocity amplitude of ∼46.5 km s−1, lasting for ∼3 cycles with a period of ∼18.2 minutes and a damping time of ∼31.1 minutes. The maximum Doppler velocities of the oscillating filament are 18 km s−1 (redshift) and −24 km s−1 (blueshift), which were derived from the spectroscopic data provided by the Chinese Hα Solar Explorer/Hα Imaging Spectrograph. The three-dimensional velocity of the oscillation is determined to be ∼50 km s−1 at an angle of ∼50° to the local photosphere plane. Based on the wave–filament interaction, the minimum energy of the EUV wave is estimated to be 2.7 × 1020 J. Furthermore, this event provides evidence that Moreton waves should be excited by the highly inclined eruptions.


INTRODUCTION
The oscillatory phenomena in filaments are ubiquitous and complex dynamics, and have received more attention since the first systematic investigation performed Corresponding author: Jun Dai and Qingmin Zhang daijun@pmo.ac.cn, zhangqm@pmo.ac.cn by Hyder (1966).Nowadays, based on the observed velocity amplitude (Oliver & Ballester 2002;Ballester 2006), the oscillatory motions in filaments are classified into large-amplitude oscillations (LAOs, ≥20 km s −1 ) and small-amplitude oscillations (SAOs, ≤10 km s −1 ).Furthermore, the LAOs in filaments can be divided into two groups according to the direction, that is arXiv:2310.19228v1[astro-ph.SR] 30 Oct 2023 Dai et al. large-amplitude longitudinal oscillations (LALOs, Jing et al. 2003, 2006;Vršnak et al. 2007;Li & Zhang 2012;Zhang et al. 2012;Luna et al. 2014;Bi et al. 2014;Zhang et al. 2017bZhang et al. , 2020) ) where the filament material almost oscillate along its spine, and large-amplitude transverse oscillations (LATOs, e.g., Isobe et al. 2007;Pintér et al. 2008;Chen et al. 2008) where the filament considered as an long uniform cylinder oscillating perpendicular to its axis.According to the recent reviews (Oliver 2009;Tripathi et al. 2009;Arregui et al. 2018) and statistical study (Luna et al. 2018), both LATOs and LALOs are usually damping and lasting for several cycles, while the amplitudes and periods of LATOs are generally shorter than those of LALOs.Particularly, transverse and longitudinal oscillations can occur simultaneously in a filament or prominence (Pant et al. 2016;Wang et al. 2016;Zhang et al. 2017a;Luna & Moreno-Insertis 2021;Dai et al. 2021).
Generally, the LATOs are often triggered by Moreton waves (e.g., Eto et al. 2002;Liu et al. 2013) or extreme-ultraviolet (EUV) waves (Liu et al. 2012;Dai et al. 2012;Gosain & Foullon 2012;Shen et al. 2014aShen et al. , 2017;;Zhang & Ji 2018).The restoring force of the LATOs is mainly supplied by the magnetic tension force of the corresponding filament, and the energy loss or dissipative process is theoretically considered as the reasonable damping mechanism (Kleczek & Kuperus 1969).Specifically, when the LATOs are observed on the limb, the line-of-sight (LOS) and plane-of-sky (POS) motions correspond to the horizontal and vertical oscillations, while on the disk, the LOS and POS motions correspond to the nearly vertical and horizontal oscillations, respectively (Tripathi et al. 2009).The vertical oscillations are usually associated with a phenomenon known as "winking filament" which are frequently observed on the disk in the earlier research (Hyder 1966;Ramsey & Smith 1966).The winking filament are characterized with the alternative appearance and disappearance in Hα wings images, due to the velocity component along the line of sight resulting in the Doppler shift from the Hα center to the line wings (Eto et al. 2002;Okamoto et al. 2004).
The LOS velocity could be roughly derived from the simultaneous images in several wavelength channels close to the Hα line-center (e.g., ±0.4 Å or ±0.8 Å, Morimoto & Kurokawa 2003) and the value obtained in the previous studies ranged from 6 km s −1 to 50 km s −1 (Isobe & Tripathi 2006;Gilbert et al. 2008;Asai et al. 2012;Shen et al. 2014a).
As the prime triggering mechanism for the LATOs, EUV waves are globally propagating wavelike phenomena characterized with brightening wavefronts followed by extending coronal dimming, which were first detected in 195 Å (Moses et al. 1997;Thompson et al. 1998)  plasma (Vršnak et al. 2002;Vršnak & Cliver 2008).More recently, after investigating all the coronal-Moreton wave events over the past decade, Zheng et al. (2023) uncovered that Moreton waves are more likely to be excited by the highly inclined eruptions.
Benefiting from the high-cadence data provided by the Atmospheric Imaging Assembly (AIA; Lemen et al. 2012) on board the Solar Dynamics Observatory (SDO; Pesnell et al. 2012), an increasing number of EUV waves events containing both fast and slow components were reported (Chen & Wu 2011;White et al. 2012;Dai et al. 2012;Asai et al. 2012;Cheng et al. 2012;Kumar et al. 2013;Shen et al. 2013;Xue et al. 2013;Zong & Dai 2015;Liu et al. 2019).The hybrid wave theory (Chen et al. 2002) where the fast component was considered as the fast-mode MHD wave or shock wave (Thompson et al. 1998;Wang 2000;Wu et al. 2001) and the slow component was supposed as the apparent wave induced by the stretching of magnetic field lines, is thus well supported by the thermodynamic MHD simulation (Downs et al. 2012) and observations (Sun et al. 2022;Chen 2023).
Typically, the fast-component waves present outer sharp wavefronts and propagate with speed from ∼500 km s −1 to more than 1500 km s −1 , while the slow-component waves present inner diffuse wavefronts with speeds usually about one-third of the fast-component waves, sometimes even propagating slower than the coronal sound speed (Tripathi & Raouafi 2007;Thompson & Myers 2009;Zhukov et al. 2009).However, the physical nature of EUV waves is still under controversy and more details is available in recent reviews (Liu & Ofman 2014;Warmuth 2015;Chen 2016;Shen et al. 2020;Chen 2023).
On 2022 October 02, an X1.0 flare occurred in the active region (AR) 13110 and 13113, which was accompanied by an EUV wave ( In addition, soft X-ray (SXR) light curves of the flare in 0.5−4 Å and 1−8 Å were recorded by the GOES-16 spacecraft with a cadence of 2 s, and hard X-ray (HXR) fluxes at various energy bands (4-300 keV) were detected by the Gamma-ray Burst Monitor (GBM; Meegan et al. 2009) on board the Fermi spacecraft.The erupting filament across the two active regions and the related non-radial CME were also observed by the Extreme-UltraViolet Imager (EUVI; Wuelser et al. 2004) and the COR2 white-light coronagraph on board the Ahead Solar Terrestrial Relation Observatory (STEREO-A; Kaiser et al. 2008).The separation angle between STEREO-A and Earth was ∼17 • .

Models and Methods
The cloud model (Beckers 1964;Mein & Mein 1988;Chae 2014;Hong et al. 2014)  of solar rotation and instrument movement.Then, we recognize the filament region by larger line depth and lower intensity.At the filament region, we adopt the single cloud model to acquire the line-of-sight velocity of filament.For the other region without filament, the lineof-sight velocity is calculated by the moment analysis (Li et al. 2019;Yu et al. 2020).
The revised cone model is developed to track the 3D evolution of filament eruptions or CMEs and investigate the properties of the non-radial filament eruptions or CMEs, which require observations from at least two viewpoints (Zhang 2021(Zhang , 2022)).The revised cone model is based on the assumption that the shape of the eruptions or CMEs is the ice-cream cone, where the cone apex is located at the source regions and the cone base is spheric.The revised cone model is characterized by the matrix transforms between the heliocentric coordinate system (HCS), local coordinate system (LCS) and cone coordinate system (CCS) to determine the geometric parameters, such as the inclination angle θ 1 , ϕ 1 where t 0 , τ , c 0 , c 1 , and c 2 are free parameters.The onset of fast-rise phase is defined by setting the parameters as the point when the exponential velocity is equal to the linear velocity: The fitted curve is plotted with the blue solid line in    In order to investigate the horizontal motions of the filament, we select a straight slice (AB) perpendicular to the axis with a length of 36 ′′ in Figure 4(c), and the corresponding time-space diagrams in 171 Å are plotted in Figure 4(d1).It can be seen that the filament did not exhibit obvious oscillations from 20:00 UT to 20:23 UT.At ∼20:24 UT, when the EUV waves arrived, the filament began to deviate from the equilibrium position and moved coherently eastward.Then, the filament moved backward and oscillated with decaying amplitude for about three cycles.These phenomena indicate that the filament oscillation was triggered by the EUV wave, rather than the tornado phenomenon of the quiescent filament (Su et al. 2012;Panasenco et al. 2014).
To accurately determine the parameters of the filament oscillation, we fit the white curve in Figure 4(d1) using mpfit.proand the following exponentially decaying sine function: where A 0 is the initial amplitude, P is the period, τ is the damping time, ψ is the initial phase, and According to the prominence seismology applied to the winking filaments (Pintér et al. 2008;Shen et al. 2014b), the radial magnetic field strength of the quiescent filament can be expressed as the following equation (Hyder 1966) based on the measured parameters of the LATO: where B r is the radial component of the filament magnetic field, ρ = N H m H is the mass density in the filament (N H is the mean neutral hydrogen number density and m H is the mass of the hydrogen atom), r 0 is the scale height of the filament, P is the period, and τ is the damping time.If we set the value r 0 = 3 × 10 9 cm (Hyder 1966), using the observed value of P = 1092 s, τ = 1866 s, and taking the value of m H = 1.67 × 10 −24 g, N H = 3 × 10 11 cm −3 in the quiescent filaments (Heinzel et al. 2008), the radial component of the filament magnetic field is estimated to be about 6.5 Gauss, which is consistent with the values in previous studies (e.g., Shen et al. 2014b).

Energetics of Filament Oscillation and EUV wave
Since the transverse oscillation of the quiescent filament was triggered by the impact of EUV wave, the kinetic energy transferred from the EUV wave to the filament can be estimated based on their interaction.The mass of a filament can be estimated roughly using the following expression (Labrosse et al. 2010):  where V represents the volume of the filament plasma.
Typical range of N H in the quiescent filaments is 3 × 10 10 − 10 11 cm −3 at 6000−8000 K (Heinzel et al. 2008;Labrosse et al. 2010).In the current study, as showing the Figure 6, the apparent width and length of the oscillating filament are determined to be 4.5 Mm and 43.2 Mm, respectively.Assuming the geometry occupied by the filament plasma is a uniform cylinder, and considering that the filament is composed of thin threads with the filling factor of 0.1 (Lin et al. 2005;Martin et al. 2008;Lin et al. 2009), the total mass of the oscillating filament is estimated to be 3.5×10 12 −1.2×10 13g.Taking the 3D velocity (∼50 km s −1 ) of the oscillation and ensuring that the oscillation can be triggered in case of the maximum mass of the filament (Gilbert et al. 2008), the minimum energy transferred from the EUV wave to the filament is 1.5 × 10 19 J, which is actually the initial kinetic energy of the oscillating filament.As shown in the Figure 2(g), the propagation of the EUV wave is denoted by the partial longitude of the new solar coordinate system with an angle of ∼165 • , while the wavefilament interaction is marked by the sector F with an angle of ∼10 • .Assuming that the sectoral propagation of the EUV wave is isotropic, the area ratio between the filament and the EUV wave dome can be approximated as the angle ratio between the sector F and the propagating sector of the EUV wave.Thus, the minimum energy of the EUV wave is estimated to be 2.7 × 10 20 J. Furthermore, the minimum energy on the interaction between the EUV wave and coronal hole is estimated to be 1.8 × 10 20 J, since the velocity of the EUV wave was decelerated to one-third after the reflection.According to the prominence seismology, the radial magnetic field strength of the quiescent filament is determined to be ∼6.5 Gauss.Furthermore, the minimum energy of the EUV wave is estimated to be 2.7 × 10 20 J based on the wave-filament interaction.
The transverse (horizontal) and vertical oscillations of filaments have been widely reported and studied since 1930s (Hyder 1966;Tripathi et al. 2009;Arregui et al. 2018).When the oscillating filament are located far from the center of the solar disk, there are projection effects for both horizontal and vertical oscillations (Kleczek & Kuperus 1969), which can be removed by combining POS and LOS velocities.However, the simultaneous horizontal oscillation and winking phenomenon in a filament was rarely reported in previous studies.
To our knowledge, only Isobe & Tripathi (2006) and It should be noted that the maximum velocity of the Doppler redshift (18 km s −1 ) was slightly smaller than that of the blueshift (24 km s −1 ) during the first cycle of the filament oscillation.Excluding the calculation errors and the effect of the solar rotation, we suppose that since the initial displacement of the filament was greater than its height, the downward motion of the filament should be impeded by the chromospheric material and magnetic field below (see Figure 5), after being squeezed, the chromospheric material and magnetic field could provide gas and magnetic pressure gradient for the upward motion of the filament, while the resistance of the corona above can be negligible.
As we known, the direction of the filament oscillation is closely associated with the wave-filament interaction (Liu et al. 2013;Shen et al. 2014b) by Extreme-ultraviolet Imaging Telescope (EIT; Delaboudinière et al. 1995) on board the Solar and Heliospheric Observatory (SOHO; Domingo et al. 1995).Now it is generally accepted that EUV waves are driven by the lateral expansion of coronal mass ejections (CMEs) flank rather than the pressure pulse of flares (Biesecker et al. 2002; Cliver et al. 2005; Chen 2006; Patsourakos & Vourlidas 2012).Theoretically, Moreton waves (Moreton 1960; Moreton & Ramsey 1960) are excited by the downward enhanced pressure when the coronal EUV waves front sweep over the underlying chromospheric

Figure 1 .
Figure 1.The overview of the eruptions and the X1.0 flare in AR 13110 and 13113.Panel (a): SXR light curves of the X1.0 flare in 1-8 Å (red line) and 0.5-4 Å (blue line); Panel (b): HXR fluxes of the X1.0 flare at various energy bands (4-300 keV); Panels (c-e) give three EUV images in AIA 304 Å and 171 Å.Three yellow arrows point to erupting filament and loops, respectively; Panel (f) give an HMI LOS magnetogram with the magnetic field strengths in the range of -1200 and 1200 G; Panels (g-h) provide an Hα image observed by CHASE and a UV image in AIA 1600 Å. Panels (i1-i2): Time-distance diagrams of the slices S1 and S2 in AIA 171 Å.The blue diamonds outline the heights of the erupting filament and loops, and the blue solid lines represent the fitted curve using Equation (1).
and angular width ω.To construct the revised cone model, we select the images simultaneously observed by the STA/EUVI 195 Å and SDO/AIA 193 Å at 20:22 UT.
X1.0 flare and EruptionsIn Figure1, the top panels show the SXR (1-8 Å and 0.5-4 Å) and HXR (4-300 keV) fluxes of the X1.0 flare in AR 13110 and 13113, which peaked at ∼20:25 UT and ∼20:22 UT, respectively.It is worthy noting that the X1.0 flare was associated with eruptions of a filament and its overlying loops crossing AR 13110 and 13113, which are marked by three yellow arrows in Figure1(cd).From ∼20:05 UT to ∼20:22 UT, the overlying loops and the filament erupted successively, resulting in two roughly parallel flare ribbons denoted by yellow marks in Figure1(g-h).To investigate the kinematics of the eruptions, we select two long straight slices S1 and S2 with lengths of 97 Mm and 133 Mm in Figure 1(e) to construct the timespace diagrams in AIA 171 Å of Figure 1(i1-i2), since the eruptions were essentially in the same direction along S2 while the lateral expansion of loops moved along S1.As shown in Figure 1(i1-i2), the signals of the loops lateral expansion and eruptions pointed by yellow arrows can be clearly recognized.The height of Loop 1 lateral expansion along S1, as well as the heights of Loop 2 and filament eruptions along S2 can be obtained by outlining the edge in the diagrams.The height evolution in the plane-of-sky is characterized by a slow rise with a constant speed followed by an initial impulsive acceleration indicated by an apparent exponential increase.Hence, we fit h(t) using the function composed of a linear term and an exponential term as proposed by Cheng et al. (2013):

Figure 1 (
Figure 1(i1-i2).Precisely, loops started to rise slowly from ∼20:05 UT while their fast rise and lateral expansion started at ∼20:18 UT.The filament started to rise slowly from ∼20:10 UT and began to rise fast at ∼20:20 UT. 3.2.Triggering and Kinematics of EUV wave and Moreton wave Figure 2 presents the propagation of the Moreton wave in running difference images in Hα +0.4 Å and the EUV wave in base difference images in 193 Å. Combining the online animation of Figure2(d-e) and the fitted curve in Figure1(i1), it can be seen that the onset of the fast lateral expansion of loops was cotemporal with the first trace of the EUV wave at ∼20:18 UT, implying that the EUV wave was excited by the fast loops lateral expansion(Patsourakos & Vourlidas 2009;Patsourakos et al. 2010).Subsequently, the EUV wave propagated northward in a fan shape centered on the AR 13110 and its bright segment is pointed by yellow arrows in Figure2(de), while the simultaneous Moreton-wave dark front is pointed by white arrows in Figure2(a-b).What is noteworthy is that the bright segment was reflected at the

Figure 2 .Figure 3 .
Figure 2. Kinematics of EUV wave and Moreton wave.Panels (a-b): Running differences of Hα +0.4 Å images.Panel (c): An AIA 193 Å image.Panels (d,e,g) give three AIA 193 Å base-difference images.Panel (f): An HMI LOS magnetogram.Panel (h1-h2) provide time-distance diagrams along the sector E in panel (g) using the 193 Å and 211 Å base-difference images.The Moreton wave, the EUV wave and the oscillating filament are separately marked by white, yellow and blue arrows.The yellow contours in panels (c,d,f) mark the coronal hole.The white dotted lines in panel (g) partially display the longitude of the new solar coordinate system centered on the X1.0 flare, denoting the same sector as the EUV wave.The propagation of EUV wave through the oscillating filament is marked by sector F. The speeds of the propagating EUV wave are denoted by numbers in panels (h1-h2).The blue rectangle in panel (e) shows the FOV of Figure 4(a)-(c) and Figure 6(a).An animation of the unannotated SDO observations is available that covers ∼45 minutes starting at 20:10 UT and ending the same day at 20:55 UT, with a time cadence of 24 seconds.(An animation of this figure is available.)

Figure 4 .
Figure 4. Panels (a-b): Two Dopplergrams showing the velocities of the filament material along the LOS direction during the oscillation.Panel (c): An EUV image in AIA 171 Å of the filament before the oscillation.Panel (d1): Time-distance diagrams of the slice AB in AIA 171 Å.The white crosses outline the filament oscillation between 20:20 UT and 21:20 UT.Panel (d2): Extracted positions of the oscillating filament along the slice AB.The fitted curve is overlaid with black solid line.Corresponding parameters are labeled.regionsat a distance of ∼260 Mm.At ∼20:24 UT, the bright segment of the EUV wave swept over the quiescent filament, after which the winking phenomenon and the obvious horizontal oscillation of the filament was respectively detected in Hα and EUV images, indicating that the oscillation contained both POS and LOS velocity components at the same time.

Figure 3
Figure 3 presents the time sequence of Hα line-center (middle column), blue wing (left columns) and red wing (left columns) images to illustrate the upward and down- photosphere plane.

Figure 6 .
Figure 6.Panel (a): An Hα image in HIS 6562.82Å of the filament before the oscillation.The spine of the filament is marked by a dotted yellow line.Panel (b): Normalized intensity distribution along the line CD across the oscillating filament, which is fitted with a single-Gauss function.The full width at half maximum (FWHM) representing the width or LOS depth of the filament is labeled.

3. 5 .Figure 7 .
Figure 7. Panel (a): An STA/EUVI 195 Å image of the erupting filament and loops.Panels (b-c): The projections of the reconstructed cone are separately depicted by magenta and red dots, and overlaid on the simultaneous STA/EUVI 195 Å and AIA 193 Å base-difference images at 20:22 UT.Panels (d1-d2): Two snapshots of the white-light CME observed by STA/CRO2.The relative positions of the Sun, Earth and STEREO-A at 20:53 UT on 2022 October 02 are plotted in panel (d1).Panel (e): Height-time plot of the CME leading edges with red square symbols.The results of a linear fit is overlaid with a dashed line and the linear speed is labeled.kms −1 ) of the CME estimated from the STA/COR2 is approximately equal to its true speed.
Gilbert et al. (2008) reported the similar filament oscillations which involved both POS horizontal and LOS vertical motions, while the accurate 3D velocities were not determined due to the limitations of data.Although there was no winking filament observed(Isobe & Tripathi 2006), the Doppler velocities derived from two Hα wings (±0.8 Å) images was up to 50 km s −1 , which was obviously deviated from the observation.Likewise, based on a few available wavelengths (Hα and He I 10830 Å), the LOS velocity component was estimated to be 41 km s −1(Gilbert et al. 2008), which was also controversial since the Doppler velocity obtained by Jackiewicz & Balasubramaniam (2013) was only a few km s −1 in their reanalysis for the same event.Using the images in Hα line-center and six Hα wings (±0.5 Å, ±0.8 Å, ±1.2 Å), Shen et al. (2014a) obtained the accurate Doppler velocity ranging from 6 km s −1 to 14 km s −1 of a winking filament without horizontal motions.The above illustrates that the accuracy of Doppler velocities are determined by the data spectral resolution.Benefiting form the high-resolution spectral data provided by CHASE/HIS, the 3D velocity of the filament motion in this study have been derived from the unambiguous observation of the simultaneous horizontal and vertical oscillations, which almost completely eliminated the projection effect.
, while the direction of the coronal-Moreton wave is determined by the inclination of the corresponding eruption or CME.The inclination angles proposed by Zheng et al. (2023) were estimated by the lowest part of coronal wave fronts with respect to the solar radial direction.Correspondingly, the inclination angle in this work can be estimated by the lowest part of cone model with respect to the solar radial direction.Zheng et al. (2023) concluded that the bright segments of the EUV wavefronts and the simultaneous Moreton wave should be excited by the nonradial eruptions with inclination angles of 63 • −76 • .In this work, we found that the bright segment of the EUV wave was contemporal with the dark front of the Moreton wave.With the addition of angular width (ω/2), the inclination angle of the loops eruption in this event is determined to be 64 • northward, which reaches the value of the highly inclination.Thus, the inclination angle of the loops eruption here could be sufficient to excite the coronal-Moreton wave, which in turn triggered the simultaneous horizontal and vertical filament oscillation.