Flare Rise Research Articles

Properties of PSR J1023+0038 Based on Kepler, TESS, and FAST

The pulsar system PSR J1023+0038 is a very interesting binary with radio millisecond pulsar and low-mass X-ray binary transitions, which depend on the stellar accretion process. We have used Kepler light curves with 1 minute cadence and TESS light curves with 2 minute cadence to study the flare properties of PSR J1023+0038. We detected 516 flare events in the K2 data and 84 flare events in the TESS survey data. We determined the flare rise and delay times, the flare durations and amplitudes, and flare energies. We obtained a value of the power-law index of 0.359 ± 0.023 between the flare energies and decay times, which is similar to the theoretically predicted value of 1/3. This in turn indicates that PSR J1023+0038 might be exhibiting physical mechanisms described by magnetic reconnection theory. Using the maximum likelihood estimation method, we also calculated the power-law index of the cumulative flare frequency distribution, finding 1.87 ± 0.27 for the Kepler data and 1.74 ± 0.29 for the TESS data. Meanwhile, we reduced six FAST observations of PSR J1023+0038 from 2019–2021 using a standard pulsar search procedure. We report that we detected a prompt signal with a period compatible with that found in previous observations of PSR J1023+0038. However, there are several reasons (statistical, excess DM, pulse shape, etc.) as to why the association is not likely.

Delayed Development of Cool Plasmas in X-Ray Flares from the Young Sun-like Star κ 1 Ceti

The Neutron star Interior Composition Explorer (NICER) X-ray observatory observed two powerful X-ray flares equivalent to superflares from the nearby young solar-like star κ 1 Ceti in 2019. NICER follows each flare from the onset through the early decay, collecting over 30 counts s−1 near the peak, enabling a detailed spectral variation study of the flare rise. The flare in September varies quickly in ∼800 s, while the flare in December has a few times longer timescale. In both flares, the hard-band (2–4 keV) light curves show typical stellar X-ray flare variations with a rapid rise and slow decay, while the soft X-ray light curves, especially of the September flare, have prolonged flat peaks. The time-resolved spectra require two temperature plasma components at kT ∼0.3–1 and ∼2–4 keV. Both components vary similarly, but the cool component lags by ∼200 s with a four to six times smaller emission measure (EM) compared to the hot component. A comparison with hydrodynamic flare loop simulations indicates that the cool component originates from X-ray plasma near the magnetic loop footpoints that mainly cools via thermal conduction. The time lag represents the travel time of the evaporated gas through the entire flare loop. The cool component has a several times smaller EM than its simulated counterpart, suggesting a suppression of conductive cooling, possibly by the expansion of the loop cross-sectional area or turbulent fluctuations. The cool component’s time lag and EM ratio provide important constraints on the flare loop geometry.

The Response of Black Hole Spark Gaps to External Changes: A Production Mechanism of Rapid TeV Flares?

Abstract We study the response of a starved Kerr black hole magnetosphere to abrupt changes in the intensity of disk emission and in the global magnetospheric current, by means of one-dimensional general relativistic particle-in-cell simulations. Such changes likely arise from the intermittency of the accretion process. We find that in cases where the pair-production opacity contributed by the soft disk photons is modest, as in, e.g., M87, such changes can give rise to delayed, strong teraelectronvolt (TeV) flares, dominated by curvature emission of particles accelerated in the gap. The flare rise time, and the delay between the external variation and the onset of the flare emitted from the outer gap boundary, are of the order of the light-crossing time of the gap. The rapid, large-amplitude TeV flares observed in M87, and perhaps, other active galactic nuclei may be produced by such a mechanism.

Characteristic time of stellar flares on Sun-like stars

ABSTRACT Using the short-cadence data (1-min interval) of the Kepler space telescope, we conducted a statistical analysis for the characteristic time of stellar flares on Sun-like stars (SLS). Akin to solar flares, stellar flares show rise and decay light-curve profiles, which reflect the two distinct phases (rise phase and decay phase) of the flare process. We derived characteristic times of the two phases for stellar flares of SLS, resulting in a median rise time of about 5.9 min and a median decay time of 22.6 min. It is found that both the rise time and the decay time of the stellar flares follow a lognormal distribution. The peak positions of the lognormal distributions for flare rise time and decay time are 3.5 min and 14.8 min, respectively. These time values for stellar flares are similar to the time-scale of solar flares, which supports the idea that stellar flares and solar flares have the same physical mechanism. The statistical results obtained in this work for SLS can be a benchmark of flare characteristic times when comparing with other types of stars.

Statistical and Observational Research on Solar Flare EUV Spectra and Geometrical Features

Abstract We performed statistical analysis on the flare emission data to examine parameters related to the flare extreme-ultraviolet (EUV) spectra. This study used the data from the Geostationary Operational Environmental Satellite X-ray Sensors to determine the fundamental flare parameters. The relationship between soft X-ray data and EUV emission data observed by the Extreme Ultraviolet Variability Experiment on board the Solar Dynamics Observatory (SDO) MEGS-A was investigated for 50 events. The results showed the hotter Fe line emissions have strong correlation with soft X-ray data in many cases. However, our statistical study revealed that EUV flare peak flux of Fe xv, Fe xvi and He ii lines have weak correlation with soft X-ray peak flux. In EUV line light curves, there was time difference in peak time, however the tendency to reach the peak in order from the hotter line to cooler line was not so clear. These results indicate that the temporal evolution of EUV emission can be roughly explained by soft X-ray data. However, the time changes of temperature and density distributions in the flare loop must be needed for accurate reproduction. Moreover, we compared the geometrical features of solar flares observed by the Atmospheric Imaging Assembly on board the SDO with the fundamental flare parameters for 32 events. The ribbon distance strongly correlated with both soft X-ray flare rise and decay times. This results indicate that the geometrical feature is essential parameter for predicting flare emission duration.

The Kinematic Evolution of Erupting Structures in Confined Solar Flares

Abstract In this Letter, we study the kinematic properties of ascending hot blobs associated with confined flares. Taking advantage of high-cadence extreme-ultraviolet images provided by the Atmospheric Imaging Assembly on board the Solar Dynamics Observatory, we find that for the 26 events selected here, the hot blobs are first impulsively accelerated outward, but then quickly slow down to motionlessness. Their velocity evolution is basically synchronous with the temporal variation of the Geostationary Operational Environmental Satellite soft X-ray flux of the associated flares, except that the velocity peak precedes the soft X-ray peak by minutes. Moreover, the duration of the acceleration phase of the erupting blobs is moderately correlated with that of the flare rise phase. For nine of the 26 cases, the erupting blobs even appear minutes prior to the onset of the associated flares. Our results show that a fraction of confined flares also involve the eruption of a magnetic flux rope, which sometimes is formed and heated prior to the flare onset. We suggest that the initiation and development of these confined flares are similar to that of eruptive ones, and the main difference may lie in the background field constraint, which is stronger for the former than for the latter.

A Solar Magnetic-fan Flaring Arch Heated by Nonthermal Particles and Hot Plasma from an X-Ray Jet Eruption

Abstract We have investigated an M1.3 limb flare, which develops as a magnetic loop/arch that fans out from an X-ray jet. Using Hinode/EIS, we found that the temperature increases with height to a value of over 107 K at the loop top during the flare. The measured Doppler velocity (redshifts of 100–500 km s−1) and the nonthermal velocity (≥100 km s−1) from Fe xxiv also increase with loop height. The electron density increases from 0.3 × 109 cm−3 early in the flare rise to 1.3 × 109 cm−3 after the flare peak. The 3D structure of the loop derived with Solar TErrestrial RElations Observatory/EUV Imager indicates that the strong redshift in the loop-top region is due to upflowing plasma originating from the jet. Both hard X-ray and soft X-ray emission from the Reuven Ramaty High Energy Solar Spectroscopic Imager were only seen as footpoint brightenings during the impulsive phase of the flare, then, soft X-ray emission moved to the loop top in the decay phase. Based on the temperature and density measurements and theoretical cooling models, the temperature evolution of the flare arch is consistent with impulsive heating during the jet eruption followed by conductive cooling via evaporation and minor prolonged heating in the top of the fan loop. Investigating the magnetic field topology and squashing factor map from Solar Dynamics Observatory/HMI, we conclude that the observed magnetic-fan flaring arch is mostly heated from low atmospheric reconnection accompanying the jet ejection, instead of from reconnection above the arch as expected in the standard flare model.

On the Possible Mechanism of GLE Initiation

Abstract With the goal of understanding the initiations of solar energetic particle (SEP) (MeV) and ground-level enhancement (GLE) (GeV) particles, we have studied relative timings at approximately the Sun between temporal evolutions of the particles and some electromagnetic radiation components representing flares and shocks. Results show that GLE onsets appear after flare prompt onsets and m-type II onsets, while the GLE-associated SEP onsets appear before the flare prompt onsets and m-type II onsets, thus specifying that the GLE-associated SEPs originate over the flare initial phases and get accelerated intensively over the flare prompt phases associated with coronal shocks. The flare initial phase is found always earlier than the coronal mass ejection (CME) initial phase, further justifying that the MeV particles are initiated particularly by the flare initial phases and are accelerated to GeV energetic by flare prompt phases associated with the coronal shocks. On the contrary, most of the non-GLE-SEP onsets appear well after the flare prompt onsets and m-type II onsets, demonstrating that the non-GLE-SEPs mostly generate over the most intense part of the flare rise phases associated with the coronal shocks. In another development, the relative timings of flare prompt onset and peak times to the m- and DH-type II onsets show that usually the m-type II bursts commence before the flare peaks and DH-type II bursts commence after the flare peaks, signifying that the coronal shocks manifested in m-type II bursts operate over the flare main acceleration phases, while the coronal shocks manifested in DH-type II bursts operate over the flare decay and/or CME propagation phases, thereby suggesting that the evolution of the particles accelerated at the flare main acceleration phases can be prolonged by the shocks associated with the CME propagation phases.

Geometry, Kinematics, and Heliospheric Impact of a Large CME-driven Shock in 2017 September

Abstract A powerful coronal mass ejection (CME) occurred on 2017 September 10 near the end of the declining phase of the historically weak solar cycle 24. We obtain new insights concerning the geometry and kinematics of CME-driven shocks in relation to their heliospheric impacts from the optimal, multispacecraft observations of the eruption. The shock, which together with the CME driver can be tracked from the early stage to the outer corona, shows a large oblate structure produced by the vast expansion of the ejecta. The expansion speeds of the shock along the radial and lateral directions are much larger than the translational speed of the shock center, all of which increase during the flare rise phase, peak slightly after the flare maximum and then decrease. The near simultaneous arrival of the CME-driven shock at the Earth and Mars, which are separated by 156.°6 in longitude, is consistent with the dominance of expansion over translation observed near the Sun. The shock decayed and failed to reach STEREO A around the backward direction. Comparison between ENLIL MHD simulations and the multipoint in situ measurements indicates that the shock expansion near the Sun is crucial for determining the arrival or nonarrival and space weather impact at certain heliospheric locations. The large shock geometry and kinematics have to be taken into account and properly treated for accurate predictions of the arrival time and space weather impact of CMEs.

Ground-based detection of G star superflares with NGTS

We present high cadence detections of two superflares from a bright G8 star (V = 11.56) with the Next Generation Transit Survey (NGTS). We improve upon previous superflare detections by resolving the flare rise and peak, allowing us to fit a solar flare inspired model without the need for arbitrary break points between rise and decay. Our data also enables us to identify substructure in the flares. From changing starspot modulation in the NGTS data we detect a stellar rotation period of 59 hours, along with evidence for differential rotation. We combine this rotation period with the observed \textit{ROSAT} X-ray flux to determine that the star's X-ray activity is saturated. We calculate the flare bolometric energies as $5.4^{+0.8}_{-0.7}\times10^{34}$ and $2.6^{+0.4}_{-0.3}\times10^{34}$ erg and compare our detections with G star superflares detected in the \textit{Kepler} survey. We find our main flare to be one of the largest amplitude superflares detected from a bright G star. With energies more than 100 times greater than the Carrington event, our flare detections demonstrate the role that ground-based instruments such as NGTS can have in assessing the habitability of Earth-like exoplanets, particularly in the era of \textit{PLATO}.

Dynamic Spectral Imaging of Decimetric Fiber Bursts in an Eruptive Solar Flare

Abstract Fiber bursts are a type of fine structure that is often superposed on type IV radio continuum emission during solar flares. Although studied for many decades, its physical exciter, emission mechanism, and association with the flare energy release remain unclear, partly due to the lack of simultaneous imaging observations. We report the first dynamic spectroscopic imaging observations of decimetric fiber bursts, which occurred during the rise phase of a long-duration eruptive flare on 2012 March 3, as obtained by the Karl G. Jansky Very Large Array in 1–2 GHz. Our results show that the fiber sources are located near and above one footpoint of the flare loops. The fiber source and the background continuum source are found to be co-spatial and share the same morphology. It is likely that they are associated with nonthermal electrons trapped in the converging magnetic fields near the footpoint, as supported by a persistent coronal hard X-ray source present during the flare rise phase. We analyze three groups of fiber bursts in detail with dynamic imaging spectroscopy and obtain their mean frequency-dependent centroid trajectories in projection. By using a barometric density model and magnetic field based on a potential field extrapolation, we further reconstruct the 3D source trajectories of fiber bursts, for comparison with expectations from the whistler wave model and two MHD-based models. We conclude that the observed fiber burst properties are consistent with an exciter moving at the propagation velocity expected for whistler waves, or models that posit similar exciter velocities.

The 26 December 2001 Solar Eruptive Event Responsible for GLE63: III. CME, Shock Waves, and Energetic Particles

The SOL2001-12-26 moderate solar eruptive event (GOES importance M7.1, microwaves up to 4000 sfu at 9.4 GHz, CME speed 1446 km/s) produced strong fluxes of solar energetic particles and ground-level enhancement of cosmic-ray intensity (GLE63). To find a possible reason for the atypically high proton outcome of this event, we study multi-wavelength images and dynamic radio spectra and quantitatively reconcile the findings with each other. An additional eruption probably occurred in the same active region about half an hour before the main eruption. The latter produced two blast-wave-like shocks during the impulsive phase. The two shock waves eventually merged around the radial direction into a single shock traced up to $25R_\odot$ as a halo ahead of the expanding CME body, in agreement with an interplanetary Type II event recorded by the Radio and Plasma Wave Investigation (WAVES) experiment on the Wind spacecraft. The shape and kinematics of the halo indicate an intermediate regime of the shock between the blast wave and bow shock at these distances. The results show that i) the shock wave appeared during the flare rise and could accelerate particles earlier than usually assumed; ii) the particle event could be amplified by the preceding eruption, which stretched closed structures above the developing CME, facilitated its lift-off and escape of flare-accelerated particles, enabled a higher CME speed and stronger shock ahead; iii) escape of flare-accelerated particles could be additionally facilitated by reconnection of the flux rope, where they were trapped, with a large coronal hole; iv) the first eruption supplied a rich seed population accelerated by a trailing shock wave.

Extending the ‘energetic scaling of relativistic jets from black hole systems’ to include γ-ray-loud X-ray binaries

We show that the jet power Pj and geometrically corrected γ-ray luminosity Lγ for the X-ray binaries (XRBs) Cygnus X-1, Cygnus X-3, and V404 Cygni, and γ-ray upper limits for GRS 1915+105 and GX339-4, follow the universal scaling for the energetics of relativistic jets from black hole (BH) systems found by Nemmen et al. for blazars and GRBs. The observed peak γ-ray luminosity for XRBs is geometrically corrected, and the minimum jet power is estimated from the peak flux density of radio flares and the flare rise time. The Lγ–Pj correlation holds across ∼17 orders of magnitude. The correlation suggests a jet origin for the high-energy emission from XRBs, and indicates a common mechanism or efficiency for the high-energy emission 0.1–100 GeV from all relativistic BH systems.

Ultraluminous X-ray bursts in two ultracompact companions to nearby elliptical galaxies

A flaring X-ray source was found near the galaxy NGC 4697 (ref. 1). Two brief flares were seen, separated by four years. During each flare, the flux increased by a factor of 90 on a timescale of about one minute. There is no associated optical source at the position of the flares, but if the source was at the distance of NGC 4697, then the luminosities of the flares were greater than 1039 erg per second. Here we report the results of a search of archival X-ray data for 70 nearby galaxies looking for similar flares. We found two ultraluminous flaring sources in globular clusters or ultracompact dwarf companions of parent elliptical galaxies. One source flared once to a peak luminosity of 9 × 1040 erg per second; the other flared five times to 1040 erg per second. The rise times of all of the flares were less than one minute, and the flares then decayed over about an hour. When not flaring, the sources appear to be normal accreting neutron-star or black-hole X-ray binaries, but they are located in old stellar populations, unlike the magnetars, anomalous X-ray pulsars or soft γ repeaters that have repetitive flares of similar luminosities.

Observations of bubbles in natural seep flares at MC 118 and GC 600 using in situ quantitative imaging

AbstractThis paper reports the results of quantitative imaging using a stereoscopic, high‐speed camera system at two natural gas seep sites in the northern Gulf of Mexico during the Gulf Integrated Spill Research G07 cruise in July 2014. The cruise was conducted on the E/V Nautilus using the ROV Hercules for in situ observation of the seeps as surrogates for the behavior of hydrocarbon bubbles in subsea blowouts. The seeps originated between 890 and 1190 m depth in Mississippi Canyon block 118 and Green Canyon block 600. The imaging system provided qualitative assessment of bubble behavior (e.g., breakup and coalescence) and verified the formation of clathrate hydrate skins on all bubbles above 1.3 m altitude. Quantitative image analysis yielded the bubble size distributions, rise velocity, total gas flux, and void fraction, with most measurements conducted from the seafloor to an altitude of 200 m. Bubble size distributions fit well to lognormal distributions, with median bubble sizes between 3 and 4.5 mm. Measurements of rise velocity fluctuated between two ranges: fast‐rising bubbles following helical‐type trajectories and bubbles rising about 40% slower following a zig‐zag pattern. Rise speed was uncorrelated with hydrate formation, and bubbles following both speeds were observed at both sites. Ship‐mounted multibeam sonar provided the flare rise heights, which corresponded closely with the boundary of the hydrate stability zone for the measured gas compositions. The evolution of bubble size with height agreed well with mass transfer rates predicted by equations for dirty bubbles.

ENERGY PARTITIONS AND EVOLUTION IN A PURELY THERMAL SOLAR FLARE

This paper presents a solely thermal flare, which we detected in the microwave range from the thermal gyro- and free-free emission it produced. An advantage of analyzing thermal gyro emission is its unique ability to precisely yield the magnetic field in the radiating volume. When combined with observationally-deduced plasma density and temperature, these magnetic field measurements offer a straightforward way of tracking evolution of the magnetic and thermal energies in the flare. For the event described here, the magnetic energy density in the radio-emitting volume declines over the flare rise phase, then stays roughly constant during the extended peak phase, but recovers to the original level over the decay phase. At the stage where the magnetic energy density decreases, the thermal energy density increases; however, this increase is insufficient, by roughly an order of magnitude, to compensate for the magnetic energy decrease. When the magnetic energy release is over, the source parameters come back to nearly their original values. We discuss possible scenarios to explain this behavior.

An Updated View of Solar Eruptive Flares and the Development of Shocks and CMEs: History of the 2006 December 13 GLE-Productive Extreme Event

Abstract An extreme 2006 December 13 event marked the onset of the Hinode era, being the last major flare in the solar cycle 23 observed with NoRH and NoRP. The event produced a fast CME, strong shock, and a big particle event responsible for GLE70. We endeavor to clarify the relations between the eruptions, shock wave, and flare, and to shed light on a debate over the origin of energetic protons. One concept relates it to flare processes. Another one associates the acceleration of ions with a bow shock driven by a CME at (2-4)R⊙. The latter scenario is favored by a delayed particle release time after the flare. However, our previous studies have established that a shock wave is typically excited by an impulsively erupting magnetic rope (future CME core) during the flare rise, while the outer CME surface evolves from an arcade whose expansion is driven from inside. Observations of the 2006 December 13 event reveal two shocks following each other, whose excitation scenario contradicts the delayed CME-driven bowshock hypothesis. Actually, the shocks developed much earlier, and could accelerate protons still before the flare peak. Then, the two shocks merged into a single stronger one, and only decelerated and dampened long afterwards.

MULTI-WAVELENGTH OBSERVATIONS OF SOLAR FLARES WITH A CONSTRAINED PEAK X-RAY FLUX

We present an analysis of soft X-ray (SXR) and extreme-ultraviolet (EUV) observations of solar flares with an approximate C8 Geostationary Operational Environmental Satellite (GOES) class. Our constraint on peak GOES SXR flux allows for the investigation of correlations between various flare parameters. We show that the duration of the decay phase of a flare is proportional to the duration of its rise phase. Additionally, we show significant correlations between the radiation emitted in the flare rise and decay phases. These results suggest that the total radiated energy of a given flare is proportional to the energy radiated during the rise phase alone. This partitioning of radiated energy between the rise and decay phases is observed in both SXR and EUV wavelengths. Though observations from the EUV Variability Experiment show significant variation in the behavior of individual EUV spectral lines during different C8 events, this work suggests that broadband EUV emission is well constrained. Furthermore, GOES and Atmospheric Imaging Assembly data allow us to determine several thermal parameters (e.g., temperature, volume, density, and emission measure) for the flares within our sample. Analysis of these parameters demonstrate that, within this constrained GOES class, the longer duration solar flares are cooler events with larger volumes capable of emitting vast amounts of radiation. The shortest C8 flares are typically the hottest events, smaller in physical size, and have lower associated total energies. These relationships are directly comparable with several scaling laws and flare loop models.

Locating the -ray emission region of the flat spectrum radio quasar PKS 1510-089

I present a study of the high-energy gamma-ray properties of the flat spectrum radio quasar, PKS 1510-089, based on 3.75 years of observations with the Large Area Telescope (LAT) detector on-board the Fermi gamma-ray Space Telescope. Throughout the observing period, the 0.1 GeV < E < 300 GeV gamma-ray flux was highly variable, undergoing several flaring events where the daily flux exceeded 10^{-5} photons cm^{-2} s^{-1} on 3 separate occasions. The increased photon statistics of these large flares allowed the observations to be re-analysed in 6 and 3 hour intervals, revealing flux doubling timescales as small as 1.3\pm0.12 hours during the flare rise time, and flux halving timescales of 1.21\pm0.15 hours during the flare decay. These are the smallest variability timescales measured to date at MeV-GeV energies for the Flat Spectrum Radio Quasar class of Active Galactic Nuclei. The >10^{-5} photons cm^{-2} s^{-1} flare events were also studied in more detail in an attempt to uncover evidence for the location of PKS 1510-089's gamma-ray emission region. In particular, two approaches were used: (i) searching for an energy dependence to the cooling timescales, and (ii) searching for evidence of a spectral cut-off. Furthermore, an analysis of the highest photon events within the 3.75 year data set finds PKS 1510-089 to be a source of >20 GeV gamma-rays at the 13.5\sigma confidence level; a observational property which is difficult to explain in the traditional view that gamma-ray emission from Active Galactic Nuclei originates from the base of the relativistic jet. The combined results of these two approaches, along with the confirmation of >20 GeV photon flux from PKS 1510-089, suggest the presence of multiple gamma-ray emission regions being located in both the broad line region and molecular torus region of PKS 1510-089.

THE RELATIONSHIP BETWEEN X-RAY LUMINOSITY AND MAJOR FLARE LAUNCHING IN GRS 1915+105

We perform the most detailed analysis to date of the X-ray state of the Galactic black hole candidate GRS 1915+105 just prior to (0 to 4 hours) and during the brief (1 to 7 hour) ejection of major (superluminal) radio flares. A very strong model independent correlation is found between the 1.2 keV - 12 keV X-ray flux 0 to 4 hours before flare ejections with the peak optically thin 2.3 GHz emission of the flares. This suggests a direct physical connection between the energy in the ejection and the luminosity of the accretion flow preceding the ejection. In order to quantify this concept, we develop techniques to estimate the intrinsic (unabsorbed) X-ray luminosity, $L_{\mathrm{intrinsic}}$, from RXTE ASM data and to implement known methods to estimate the time averaged power required to launch the radio emitting plasmoids, $Q$ (sometimes called jet power). We find that the distribution of intrinsic luminosity from 1.2 keV - 50 keV, $L_{\mathrm{intrinsic}}(1.2 - 50)$, is systematically elevated just before ejections compared to arbitrary times when there are no major ejections. The estimated $Q$ is strongly correlated with $L_{\mathrm{intrinsic}}(1.2 - 50)$ 0 to 4 hours before the ejection, the increase in $L_{\mathrm{intrinsic}}(1.2 - 50)$ in the hours preceding the ejection and the time averaged $L_{\mathrm{intrinsic}}(1.2 - 50)$ during the flare rise. Furthermore, the total time averaged power during the ejection ($Q$ + the time average of $L_{\mathrm{intrinsic}}(1.2 - 50)$ during ejection) is strongly correlated with $L_{\mathrm{intrinsic}}(1.2 - 50)$ just before launch with near equality if the distance to the source is $ \approx 10.5$ kpc.