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Teruaki Enoto

Publications and source records attributed to Teruaki Enoto.

At least 73 records · Page 4Linked to original sources

Analysis of Crab X-ray Polarization using Deeper IXPE Observations

We present Crab X-ray polarization measurements using IXPE data with a total exposure of 300ks, three times more than the initial 2022 discovery paper. Polarization is detected in three times more pulsar phase bins, revealing an S-shaped $+40^\circ$ polarization angle sweep in the main pulse and ${>}1σ$ departures from the OPTIMA optical polarization in both pulses, suggesting different radiation mechanisms or sites for the polarized emission at the two wavebands. Our polarization map of the inner nebula reveals a toroidal magnetic field, as seen in prior IXPE analyses. Along the southern jet, the magnetic field orientation relative to the jet axis changes from perpendicular to parallel and the polarization degree decreases by ${\sim}6\%$. These observations may be explained by kink instabilities along the jet or a collision with a dense, jet-deflecting medium at the tip. Using spectropolarimetric analysis, we find asymmetric polarization in the four quadrants of the inner nebula, as expected for a toroidal field geometry, and a spatial correlation between polarization degree and photon index.

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X-ray and multiwavelength polarization of Mrk 501 from 2022 to 2023

We present multiwavelength polarization measurements of the luminous blazar Mrk~501 over a 14-month period. The 2--8 keV X-ray polarization was measured with the Imaging X-ray Polarimetry Explorer (IXPE) with six 100-ks observations spanning from 2022 March to 2023 April. Each IXPE observation was accompanied by simultaneous X-ray data from NuSTAR, Swift/XRT, and/or XMM-Newton. Complementary optical-infrared polarization measurements were also available in the B, V, R, I, and J bands, as were radio polarization measurements from 4.85 GHz to 225.5 GHz. Among the first five IXPE observations, we did not find significant variability in the X-ray polarization degree and angle with IXPE. However, the most recent sixth observation found an elevated polarization degree at $>3σ$ above the average of the other five observations. The optical and radio measurements show no apparent correlations with the X-ray polarization properties. Throughout the six IXPE observations, the X-ray polarization degree remained higher than, or similar to, the R-band optical polarization degree, which remained higher than the radio value. This is consistent with the energy-stratified shock scenario proposed to explain the first two IXPE observations, in which the polarized X-ray, optical, and radio emission arises from different regions.

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An IXPE-Led X-ray Spectro-Polarimetric Campaign on the Soft State of Cygnus X-1: X-ray Polarimetric Evidence for Strong Gravitational Lensing

We present the first X-ray spectropolarimetric results for Cygnus X-1 in its soft state from a campaign of five IXPE observations conducted during 2023 May-June. Companion multiwavelength data during the campaign are likewise shown. The 2-8 keV X-rays exhibit a net polarization degree PD=1.99%+/-0.13% (68% confidence). The polarization signal is found to increase with energy across IXPE's 2-8 keV bandpass. The polarized X-rays exhibit an energy-independent polarization angle of PA=-25.7+/-1.8 deg. East of North (68% confidence). This is consistent with being aligned to Cyg X-1's AU-scale compact radio jet and its pc-scale radio lobes. In comparison to earlier hard-state observations, the soft state exhibits a factor of 2 lower polarization degree, but a similar trend with energy and a similar (also energy-independent) position angle. When scaling by the natural unit of the disk temperature, we find the appearance of a consistent trendline in the polarization degree between soft and hard states. Our favored polarimetric model indicates Cyg X-1's spin is likely high (a* above ~0.96). The substantial X-ray polarization in Cyg X-1's soft state is most readily explained as resulting from a large portion of X-rays emitted from the disk returning and reflecting off the disk surface, generating a high polarization degree and a polarization direction parallel to the black hole spin axis and radio jet. In IXPE's bandpass, the polarization signal is dominated by the returning reflection emission. This constitutes polarimetric evidence for strong gravitational lensing of X-rays close to the black hole.

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Probing the polarized emission from SMC X-1: the brightest X-ray pulsar observed by IXPE

Recent observations of X-ray pulsars (XRPs) performed by the Imaging X-ray Polarimetry Explorer (IXPE) have made it possible to investigate the intricate details of these objects in a new way, thanks to the added value of X-ray polarimetry. Here we present the results of the IXPE observations of SMC X-1, a member of the small group of XRPs displaying super-orbital variability. SMC X-1 was observed by IXPE three separate times during the high state of its super-orbital period. The observed luminosity in the 2-8 keV energy band of $L=2\times10^{38}$ erg/s makes SMC X-1 the brightest XRP ever observed by IXPE. We detect significant polarization in all three observations, with values of the phase-averaged polarization degree (PD) and polarization angle (PA) of $3.2\pm0.8$% and $97°\pm8°$ for Observation 1, $3.0\pm0.9$% and $90°\pm8°$ for Observation 2, and $5.5\pm1.1$% and $80°\pm6°$ for Observation 3, for the spectro-polarimetric analysis. The observed PD shows an increase over time with decreasing luminosity, while the PA decreases in decrements of 10°. The phase-resolved spectro-polarimetric analysis reveals significant detection of polarization in three out of seven phase bins, with the PD ranging between 2% and 10%, and a corresponding range in the PA from $\sim$70° to $\sim$100°. The pulse-phase resolved PD displays an apparent anti-correlation with the flux. Using the rotating vector model, we obtain constraints on the pulsar's geometrical properties for the individual observations. The position angle of the pulsar displays an evolution over time supporting the idea that we observe changes related to different super-orbital phases. Scattering in the wind of the precessing accretion disk may be responsible for the behavior of the polarimetric properties observed during the high-state of SMC X-1's super-orbital period.

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High-velocity blue-shifted Fe XXV He$α$ line during a superflare of the RS CVn-type star IM Peg

Monitor of All-sky X-ray Image (MAXI) detected a superflare, releasing $5\times 10^{37}$ erg in 2$-$10 keV, of the RS CVn-type star IM Peg at 10:41 UT on 2023 July 23 with its Gas Slit Camera (GSC; 2$-$30 keV). We conducted X-ray follow-up observations of the superflare with Neutron Star Interior Composition ExploreR (NICER; 0.2$-$12 keV) starting at 16:52 UT on July 23 until 06:00 UT on August 2. NICER X-ray spectra clearly showed emission lines of the Fe XXV He$α$ and Fe XXVI Ly$α$ for $\sim 1.5$ days since the MAXI detection. The Fe XXV He$α$ line was blue-shifted with its maximum Doppler velocity reaching $-2200 \pm 600$ $\mathrm{km \: s^{-1}}$, suggesting an upward-moving plasma during the flare, such as a coronal mass ejection (CME) and/or chromospheric evaporation. This is the first case that the Fe XXV He$α$ line is blue-shifted during a stellar flare and its velocity overwhelmingly exceeds the escape velocity of the star ($-230$ $\mathrm{km \: s^{-1}}$). One hour before the most pronounced blueshift detection, a signature of reheating the flare plasma was observed. We discuss the origin of the blueshift, a CME or high-velocity chromospheric evaporation.

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Discovery of a shock-compressed magnetic field in the north-western rim of the young supernova remnant RX J1713.7-3946 with X-ray polarimetry

Supernova remnants (SNRs) provide insights into cosmic-ray acceleration and magnetic field dynamics at shock fronts. Recent X-ray polarimetric measurements by the Imaging X-ray Polarimetry Explorer (IXPE) have revealed radial magnetic fields near particle acceleration sites in young SNRs, including Cassiopeia A, Tycho, and SN 1006. We present here the spatially-resolved IXPE X-ray polarimetric observation of the northwestern rim of SNR RX J1713.7-3946. For the first time, our analysis shows that the magnetic field in particle acceleration sites of this SNR is oriented tangentially with respect to the shock front. Because of the lack of precise Faraday-rotation measurements in the radio band, this was not possible before. The average measured polarization degree (PD) of the synchtrotron emission is 12.5 {\pm} 3.3%, lower than the one measured by IXPE in SN 1006, comparable to the Tycho one, but notably higher than the one in Cassiopeia A. On sub-parsec scales, localized patches within RX J1713.7-3946 display PD up to 41.5 {\pm} 9.5%. These results are compatible with a shock-compressed magnetic field. However, in order to explain the observed PD, either the presence of a radial net magnetic field upstream of the shock, or partial reisotropization of the turbulence downstream by radial magneto-hydrodynamical instabilities, can be invoked. From comparison of PD and magnetic field distribution with γ-rays and 12 CO data, our results provide new inputs in favor of a leptonic origin of the γ-ray emission.

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IXPE observation of PKS 2155-304 reveals the most highly polarized blazar

We report the X-ray polarization properties of the high-synchrotron-peaked (HSP) blazar PKS 2155$-$304 based on observations with the Imaging X-ray Polarimetry Explorer (IXPE). We observed the source between Oct 27 and Nov 7, 2023. We also conducted an extensive contemporaneous multiwavelength (MW) campaign. We find that during the first half ($T_1$) of the IXPE pointing, the source exhibited the highest X-ray polarization degree detected for an HSP blazar thus far, (30.7$\pm$2.0)%, which dropped to (15.3$\pm$2.1)% during the second half ($T_2$). The X-ray polarization angle remained stable during the IXPE pointing at 129.4$^\circ$$\pm$1.8$^\circ$ and 125.4$^\circ$$\pm$3.9$^\circ$ during $T_1$ and $T_2$, respectively. Meanwhile, the optical polarization degree remained stable during the IXPE pointing, with average host-galaxy-corrected values of (4.3$\pm$0.7)% and (3.8$\pm$0.9)% during the $T_1$ and $T_2$, respectively. During the IXPE pointing, the optical polarization angle changed achromatically from $\sim$140$^\circ$ to $\sim$90$^\circ$ and back to $\sim$130$^\circ$. Despite several attempts, we only detected (99.7% conf.) the radio polarization once (during $T_2$, at 225.5 GHz): with degree (1.7$\pm$0.4)% and angle 112.5$^\circ$$\pm$5.5$^\circ$. The direction of the broad pc-scale jet is rather ambiguous and has been found to point to the east and south at different epochs; however, on larger scales (> 1.5 pc) the jet points toward the southeast ($\sim$135$^\circ$), similar to all of the MW polarization angles. Moreover, the X-ray to optical polarization degree ratios of $\sim$7 and $\sim$4 during $T_1$ and $T_2$, respectively, are similar to previous IXPE results for several HSP blazars. These findings, combined with the lack of correlation of temporal variability between the MW polarization properties, agree with an energy-stratified shock-acceleration scenario in HSP blazars.

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X-ray Winds In Nearby-to-distant Galaxies (X-WING) - I: Legacy Surveys of Galaxies with Ultrafast Outflows and Warm Absorbers in $z \sim 0$-$4$

As an inaugural investigation under the X-ray Winds In Nearby-to-distant Galaxies (X-WING) program, we assembled a dataset comprising 132 active galactic nuclei (AGNs) spanning redshifts $z \sim 0$-$4$ characterized by blueshifted absorption lines indicative of X-ray winds. Through an exhaustive review of previous research, we compiled the outflow parameters for 573 X-ray winds, encompassing key attributes such as outflow velocities ($V_{\rm out}$), ionization parameters ($ξ$), and hydrogen column densities. By leveraging the parameters $V_{\rm out}$ and $ξ$, we systematically categorized the winds into three distinct groups: ultrafast outflows (UFOs), low-ionization parameter (low-IP) UFOs, and warm absorbers. Strikingly, a discernible absence of linear correlations in the outflow parameters, coupled with distributions approaching instrumental detection limits, was observed. Another notable finding was the identification of a velocity gap around $V_{\rm out} \sim 10,000~{\rm km~s^{-1}}$. This gap was particularly evident in the winds detected via absorption lines within the $\lesssim$2 keV band, indicating disparate origins for low-IP UFOs and warm absorbers. In cases involving Fe XXV/Fe XXVI lines, where the gap might be attributed to potential confusion between emission/absorption lines and the Fe K-edge, the possibility of UFOs and galactic-scale warm absorbers being disconnected is considered. An examination of the outflow and dust sublimation radii revealed a distinction: UFOs appear to consist of dust-free material, whereas warm absorbers likely comprise dusty gas. From 2024, the X-Ray Imaging and Spectroscopy Mission (XRISM) is poised to alleviate observational biases, providing insights into the authenticity of the identified gap, a pivotal question in comprehending AGN feedback from UFOs.

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Tracking the X-ray Polarization of the Black Hole Transient Swift J1727.8-1613 during a State Transition

We report on an observational campaign on the bright black hole X-ray binary Swift J1727.8$-$1613 centered around five observations by the Imaging X-ray Polarimetry Explorer (IXPE). These observations track for the first time the evolution of the X-ray polarization of a black hole X-ray binary across a hard to soft state transition. The 2--8 keV polarization degree decreased from $\sim$4\% to $\sim$3\% across the five observations, but the polarization angle remained oriented in the North-South direction throughout. Based on observations with the Australia Telescope Compact Array (ATCA), we find that the intrinsic 7.25 GHz radio polarization aligns with the X-ray polarization. Assuming the radio polarization aligns with the jet direction (which can be tested in the future with higher spatial resolution images of the jet), our results imply that the X-ray corona is extended in the disk plane, rather than along the jet axis, for the entire hard intermediate state. This in turn implies that the long ($\gtrsim$10 ms) soft lags that we measure with the Neutron star Interior Composition ExploreR (NICER) are dominated by processes other than pure light-crossing delays. Moreover, we find that the evolution of the soft lag amplitude with spectral state does not follow the trend seen for other sources, implying that Swift J1727.8$-$1613 is a member of a hitherto under-sampled sub-population.

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Discovery of the Free Precession in the Magnetar SGR 1806$-$20 with the ASCA GIS

Four X-ray data sets of the Soft Gamma Repeater SGR 1806-20, taken with the Gas Imaging Spectrometer (GIS) onboad ASCA, were analyzed. Three of them were acquired over 1993 October 9-20, whereas the last one in 1995 October. Epoch-folding analysis of the 2.8-12 keV signals confirmed the $\sim 7.6$ s pulses in these data, which Kouveliotou et al. (1998) reported as one of the earliest pulse detections from this object. In the 1995 observation, 3-12 keV pulses were phase modulated with a period of $T =16.4 \pm 0.4$ ks, and an amplitude of $\sim 1$ s. This makes a fourth example of the behavior observed from magnetars. Like in the previous three sources, the pulse-phase modulation of SGR 1806-20 disappeared at $\lesssim 2.5$ keV, where the soft X-ray component dominates. In the 1993 data sets, this periodic modulation was reconfirmed, and successfully phase-connected coherently across the 11 d interval. As a result, the modulation period was refined to $T =16.435 \pm 0.024$ ks. The implied high stability of the phenomenon strengthens its interpretation in terms of free precession of the neutron star, which is deformed to an asphericity of $\sim 10^{-4}$, presumably by the stress of toroidal magnetic fields reaching $\sim 10^{16}$ G. Toroidal fields of this level can be common among magnetars.

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Similarity to earthquakes again: periodic radio pulses of the magnetar SGR 1935+2154 are accompanied by aftershocks like fast radio bursts

It was recently discovered that the time correlations of repeating fast radio bursts (FRBs) are similar to earthquake aftershocks. Motivated by the association between FRBs and magnetars, here we report correlation function analyses in the time-energy space for the 563 periodic radio pulses and the 579 X-ray short bursts from the magnetar SGR 1935+2154, which is known to have generated FRBs. Although radio pulses are concentrated near the fixed phase of the rotational cycle, we find that when multiple pulses occur within a single cycle, their correlation properties (aftershock production probability, aftershock rate decaying in power of time, and more) are similar to those of extragalactic FRBs and earthquakes. A possible interpretation is that the radio pulses are produced by rupture of the neutron star crust, and the first pulse within one cycle is triggered by external force periodically exerted on the crust. The periodic external force may be from the interaction of the magnetosphere with material ejected in an outburst. For X-ray bursts, we found no significant correlation signal, though correlation on the same time scale as radio pulses may be hidden due to the long event duration. The aftershock similarity between the periodic radio pulsation and FRBs is surprising, given that the two are energetically very different, and therefore the energy sources would be different. This suggests that the essence of FRB-like phenomena is starquakes, regardless of the energy source, and it is important to search for FRB-like bursts from neutron stars with various properties or environments.

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X-ray Polarization of the Black Hole X-ray Binary 4U 1630-47 Challenges Standard Thin Accretion Disk Scenario

Large energy-dependent X-ray polarization degree is detected by the Imaging X-ray Polarimetry Explorer ({IXPE}) in the high-soft emission state of the black hole X-ray binary 4U 1630--47. The highly significant detection (at $\approx50σ$ confidence level) of an unexpectedly high polarization, rising from $\sim6\%$ at $2$ keV to $\sim10\%$ at $8$ keV, cannot be easily reconciled with standard models of thin accretion discs. In this work we compare the predictions of different theoretical models with the {IXPE} data and conclude that the observed polarization properties are compatible with a scenario in which matter accretes onto the black hole through a thin disc, covered by a partially-ionized atmosphere flowing away at mildly relativistic velocities.

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Pulsar-wind-nebula-powered Galactic center X-ray filament G0.13-0.11: Proof of the synchrotron nature by IXPE

We report the discovery of X-ray polarization from the X-ray-bright filament. G0.13-0.11 in the Galactic center (GC) region. This filament features a bright, hard X-ray source that is most plausibly a pulsar wind nebula (PWN) and an extended and structured diffuse component. Combining the polarization signal from IXPE with the imaging/spectroscopic data from Chandra, we find that X-ray emission of G0.13-0.11 is highly polarized PD=$57(\pm18)$% in the 3-6 keV band, while the polarization angle is PA=$21^\circ(\pm9^\circ)$. This high degree of polarization proves the synchrotron origin of the X-ray emission from G0.13-0.11. In turn, the measured polarization angle implies that the X-ray emission is polarized approximately perpendicular to a sequence of nonthermal radio filaments that may be part of the GC Radio Arc. The magnetic field on the order of $100\,{\rmμG}$ appears to be preferentially ordered along the filaments. The above field strength is the fiducial value that makes our model self-consistent, while the other conclusions are largely model independent.

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Rapid spin changes around a magnetar fast radio burst

Magnetars are neutron stars with extremely high magnetic fields that exhibit various X-ray phenomena such as sporadic sub-second bursts, long-term persistent flux enhancements, and variable rates of rotation period change. In 2020, a fast radio burst (FRB), akin to cosmological millisecond-duration radio bursts, was detected from the Galactic magnetar SGR 1935+2154, confirming the long-suspected association between some FRBs and magnetars. However, the mechanism for FRB generation in magnetars remains unclear. Here we report the X-ray discovery of an unprecedented double glitch in SGR 1935+2154 within a time interval of approximately nine hours, bracketing an FRB that occurred on October 14, 2022. Each glitch involved a significant increase in the magnetar's spin frequency, being among the largest abrupt changes in neutron star rotation ever observed. Between the glitches, the magnetar exhibited a rapid spin-down phase, accompanied by a profound increase and subsequent decline in its persistent X-ray emission and burst rate. We postulate that a strong, ephemeral, magnetospheric wind provides the torque that rapidly slows the star's rotation. The trigger for the first glitch couples the star's crust to its magnetosphere, enhances the various X-ray signals, and spawns the wind that alters magnetospheric conditions that might produce the FRB.

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First detection of polarization in X-rays for PSR B0540-69 and its nebula

We report on X-ray polarization measurements of the extra-galactic Crab-like PSR B0540-69 and its Pulsar Wind Nebula (PWN) in the Large Magellanic Cloud (LMC), using a ~850 ks Imaging X-ray Polarimetry Explorer (IXPE) exposure. The PWN is unresolved by IXPE. No statistically significant polarization is detected for the image-averaged data, giving a 99% confidence polarization upper limit (MDP99) of 5.3% in 2-8 keV energy range. However, a phase-resolved analysis detects polarization for both the nebula and pulsar in the 4-6 keV energy range. For the PWN defined as the off-pulse phases, the polarization degree (PD) of (24.5 ${\pm}$ 5.3)% and polarization angle (PA) of (78.1 ${\pm}$ 6.2)° is detected at 4.6$σ$ significance level, consistent with the PA observed in the optical band. In a single on-pulse window, a hint of polarization is measured at 3.8$σ$ with polarization degree of (50.0 ${\pm}$ 13.1)% and polarization angle of (6.2 ${\pm}$ 7.4)°. A 'simultaneous' PSR/PWN analysis finds two bins at the edges of the pulse exceeding 3$σ$ PD significance, with PD of (68 ${\pm}$ 20)% and (62 ${\pm}$ 20)%; intervening bins at 2-3$σ$ significance have lower PD, hinting at additional polarization structure.

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Highly Significant Detection of X-Ray Polarization from the Brightest Accreting Neutron Star Sco X-1

The Imaging X-ray Polarimetry Explorer (IXPE) measured with high significance the X-ray polarization of the brightest Z-source Scorpius X-1, resulting in the nominal 2-8 keV energy band in a polarization degree of 1.0(0.2)% and a polarization angle of 8(6)° at 90% of confidence level. This observation was strictly simultaneous with observations performed by NICER, NuSTAR, and Insight-HXMT, which allowed for a precise characterization of its broad-band spectrum from soft to hard X-rays. The source has been observed mainly in its soft state, with short periods of flaring. We also observed low-frequency quasi-periodic oscillations. From a spectro-polarimetric analysis, we associate a polarization to the accretion disk at <3.2% at 90% of confidence level, compatible with expectations for an electron-scattering dominated optically thick atmosphere at the Sco X-1 inclination of 44°; for the higher-energy Comptonized component, we obtain a polarization of 1.3(0.4)%, in agreement with expectations for a slab of Thomson optical depth of ~7 and an electron temperature of ~3 keV. A polarization rotation with respect to previous observations by OSO-8 and PolarLight, and also with respect to the radio-jet position angle, is observed. This result may indicate a variation of the polarization with the source state that can be related to relativistic precession or to a change in the corona geometry with the accretion flow.

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Detection of X-ray Polarization from the Blazar 1ES 1959+650 with the Imaging X-ray Polarimetry Explorer

Observations of linear polarization in the 2-8 keV energy range with the Imaging X-ray Polarimetry Explorer (IXPE) explore the magnetic field geometry and dynamics of the regions generating non-thermal radiation in relativistic jets of blazars. These jets, particularly in blazars whose spectral energy distribution peaks at X-ray energies, emit X-rays via synchrotron radiation from high-energy particles within the jet. IXPE observations of the X-ray selected BL Lac-type blazar 1ES 1959+650 in 2022 May 3-4 showed a significant linear polarization degree of $Π_\mathrm{x} = 8.0\% \pm 2.3\%$ at an electric-vector position angle $ψ_\mathrm{x} = 123^\circ \pm 8^\circ$. However, in 2022 June 9-12, only an upper limit of $Π_\mathrm{x} \leq 5.1\%$ could be derived (at the 99% confidence level). The degree of optical polarization at that time $Π_\mathrm{O} \sim 5\%$ is comparable to the X-ray measurement. We investigate possible scenarios for these findings, including temporal and geometrical depolarization effects. Unlike some other X-ray selected BL Lac objects, there is no significant chromatic dependence of the measured polarization in 1ES 1959+650, and its low X-ray polarization may be attributed to turbulence in the jet flow with dynamical timescales shorter than 1 day.

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Multiwavelength observation of an active M-dwarf star EV Lac and its stellar flare accompanied by a delayed prominence eruption

We conducted 4-night multiwavelength observations of an active M-dwarf star EV Lac on 2022 October 24$-$27 with simultaneous coverage of soft X-rays (NICER; 0.2$-$12 $\mathrm{keV}$, Swift XRT; 0.2$-$10 $\mathrm{keV}$), near-ultraviolet (Swift UVOT/UVW2; 1600$-$3500 Å), optical photometry (TESS; 6000$-$10000 Å), and optical spectroscopy (Nayuta/MALLS; 6350$-$6800 Å). During the campaign, we detected a flare starting at 12:28 UTC on October 25 with its white-light bolometric energy of $3.4 \times 10^{32}$ erg. At about 1 hour after this flare peak, our $\mathrm{Hα}$ spectrum showed a blue-shifted excess component at its corresponding velocity of $\sim 100 \: \mathrm{km \: s^{-1}}$. This may indicate that the prominence erupted with a 1-hour delay of the flare peak. Furthermore, the simultaneous 20-second cadence near-ultraviolet and white-light curves show gradual and rapid brightening behaviors during the rising phase at this flare. The ratio of flux in NUV to white light at the gradual brightening was $\sim 0.49$, which may suggest that the temperature of the blackbody is low ($< 9000 \: \mathrm{K}$) or the maximum energy flux of a nonthermal electron beam is less than $5\times10^{11} \: \mathrm{erg \: cm^{-2} \: s^{-1}}$. Our simultaneous observations of NUV and white-light flare raise the issue of a simple estimation of UV flux from optical continuum data by using a blackbody model.

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