Internal Plateau Research Articles

The Yığma Tepe of Pergamon: stratigraphic construction of a monumental tumulus from seismic refraction measurements

AbstractThe monumental tumulus Yığma Tepe is an important part of the cityscape of the ancient city of Pergamon. The tumulus construction is estimated in the Hellenistic period, the internal structure and exact purpose have been unknown so far. Its height of 32 m and diameter of 158 m make the deep interior of the tumulus practically inaccessible for excavations. Therefore, we applied a combination of geophysical measurements and archaeological sondages to explore the structure of the Yığma Tepe. The investigations centre on P‐wave refraction soundings. They were carried out to clarify the stratigraphic structure and soil composition as a prerequisite for a better understanding of construction techniques, building history and soil deposition. Interactive seismic raytracing, traveltime tomography and visco‐elastic forward modelling were applied to derive a three‐dimensional seismic velocity model, which was validated by excavations and soil analysis, historical records and additional geoelectric measurements. Our results reveal that the tumulus is composed of three layers, each about 10 m thick, separated by first‐order seismic discontinuities which were locally verified. These layers form a stack of conical disks, the interfaces of which define two internal plateaus. The analysis of soil samples showed that the seismic velocity increase at the interfaces is likely to be caused by anthropogenic compaction applied to soils showing increased fractions of silt and clay. By combining topographic data with results from seismic and geoelectric sounding on the tumulus, the surrounding trench and the unaltered surrounding area, we show that the tumulus was built almost completely from the surrounding soils and that 17% of its original volume was displaced by destruction and erosion. Based on this mass balance the strongly destroyed and eroded original surface of the tumulus and its surrounding trench is reconstructed.

Voluntary femoro-tibial subluxations: a benign differential diagnosis in the snapping knee of a child.

Voluntary femoro-tibial subluxation is a rare entity predominantly found in pretoddlers. It presents as a dynamic phenomenon with uni- or bilateral audible snapping of the knee, often in a context of fatigue or irritation at the end of the day. The aim of the study was to observe the evolution and recovery in these patients. Ten children were included. Other causes of dislocating joints and pathologies with snapping of the lateral meniscus were excluded from this study. Six-week immobilisation with a splint at 70° of knee flexion was primarily recommended to all patients. The mean age at onset of symptoms was 10months. Forty percent of the patients presented with bilateral symptoms. Clinically, four patients were hyperlax. In all patients, subluxations could be reproduced passively by rotating the foot externally and advancing the internal tibial plateau anteriorly. Three of the patients were treated with a dorsal splint and experienced significantly less or cessation of symptoms. Two patients underwent surgery, one for a concomitant anterior cruciate ligament (ACL) rupture and meniscus tear that worsened the symptoms, another for concomitant patella dislocation and a meniscus tear. One patient's parents refused treatment and four patients experienced less symptoms at the time of consultation and were not immobilized. Except for the two patients undergoing surgeries, no sequelae were observed. In general, the symptoms got less frequent when the patient began to walk. Voluntary femoro-tibial subluxation in children is a rare and benign condition that often resolves spontaneously without sequelae. The risk of meniscus tear should, however, be considered if subluxations do not cease. IV.

Statistical Study of Gamma-Ray Bursts with a Plateau Phase in the X-Ray Afterglow

Abstract A plateau phase in the X-ray afterglow is observed in a significant fraction of gamma-ray bursts (GRBs). Previously, a correlation among three key parameters concerning the plateau phase is found to exist, i.e., the end time of the plateau phase in the GRB rest frame (T a ), the corresponding X-ray luminosity at the end time (L X) and the isotropic energy of the prompt GRB (E γ,iso). In this study, we systematically search through all the Swift GRBs with a plateau phase that occurred between 2005 May and 2018 August. We collect 174 GRBs, with redshifts available for all of them. For the whole sample, the correlation between L X, T a , and E γ,iso is confirmed, with the best-fit relation being . Such an updated three-parameter correlation still supports that the central leftover after GRBs is probably a millisecond magnetar. Note that short GRBs with durations less than 2 s in our sample also follow the same correlation, which hints that the merger production of two neutron stars could be a high-mass magnetar but not necessarily a black hole. Moreover, GRBs with an “internal” plateau (i.e., with a following decay index being generally smaller than −3) also obey this correlation. It further strengthens the idea that the internal plateau is due to the delayed collapse of a high-mass neutron star into a black hole. The updated three-parameter correlation indicates that GRBs with a plateau phase may act as a standard candle for cosmology study.

Dyson-Maleev theory of ferrimagnetic spin chain with bond alternation in longitudinal magnetic field

By using the method of Dyson–Maleev mean-field theory, we study the effect of bond alternation and longitudinal magnetic field in the model of ferrimagnetic spin chain. Based on the numerical results of self-consistent equations, properties of the excited spectrums, magnon internal energy, static susceptibility, magnetization plateau and specific heat are obtained with different bond alternation parameters δ and external magnetic field B. This method provides qualitative consistent results to describe the phase from ferrimagnetic state to bond altered state.

Fracture resistance of endodontically treated maxillary incisors restored with zirconia posts: effect of the internal plateau preparation

ABSTRACTWe report on a new approach to increase the fracture resistance of endodontically treated teeth. We propose a preparation of horizontal internal plateau (IP) in dentine and the use of retentive zirconia posts to achieve a more favourable load transmission. The aim of our work was to investigate the effect of the IP depth and the post diameter on the fracture resistance and the failure mode of maxillary central incisors. Seventy-two teeth were, divided into six groups of 12. IP 4 mm in diameter and 0, 1 or 2 mm in depth was prepared and zirconia posts of two diameters luted. Specimens were loaded until failure and fractures were classified as reparable or not. Two-way ANOVA, Tukey’s HSD test and Poisson regression were used for statistical analysis (α = 0.05). Significantly improved fracture resistance and predominantly favourable failure modes were found when 2-mm deep IP is prepared.

Signature of a Newborn Black Hole from the Collapse of a Supra-massive Millisecond Magnetar

Abstract An X-ray plateau followed by a steep decay (“internal plateau”) has been observed in both long and short gamma-ray burst (GRBs), implying that a millisecond magnetar operates in some GRBs. The sharp decay at the end of the plateau, marking the abrupt cessation of the magnetar’s central engine, has been considered the collapse of a supra-massive magnetar into a black hole (BH) when it spins down. If this “internal plateau” is indeed evidence of a magnetar central engine, the natural expectation in some candidates would be a signature from the newborn BH. In this work, we find that GRB 070110 is a particular case which shows a small X-ray bump following its “internal plateau.” We interpret the plateau as a spin-down supra-massive magnetar and the X-ray bump as fallback BH accretion. This indicates that a newborn BH is likely active in some GRBs. Therefore, GRB 070110-like events may provide further support to the magnetar central engine model and enable us to investigate the properties of the magnetar as well as the newborn BH.

Effects of pre-operative measurement of proximal tibia varus angle on the prediction for condylar twist angle in total knee arthroplasty

Objective To assess the effects of pre-operative measurement of proximal tibia varus angle (PTA) on predicting condylar twist angle (CTA) in total knee arthroplasty (TKA). Methods The CT-scan of lower limb was performed in sixty-one health female volunteers aged 31.5 (18-38) years with 160 (153-170) cm heights from March 2016 to August 2016. The PTA, medial proximal tibial angle (MPTA) and CTA were determined. The PTA was defined between a line perpendicular to the mechanical axis of the tibia and the tangent on the internal tibial plateau. The MPTA was the medial angle between the mechanical axis of the tibia and the tangent on the internal tibial plateau. The CTA was the angle between the sTEA and the posterior condylar line. The correlations between these parameters were analyzed statistically by linear regression. Results The PTA, MPTA and CTA parameters were conformed to the normal distribution. The PTA was 2.30°±1.86°, ranged from 1.40° to 6.50°. The MPTA was 87.7°±1.86°, ranged from 83.50° to 88.60°. The CTA was 3.4°±1.27°, ranged from 0.50° to 5.80°. The linear regression analysis showed a strong positive correlation between the CTA and PTA in health female knees (r=0.58, P=0.048), while negative correlation was found between the CTA and MPTA in health female knees (r=-0.58, P=0.048). There were fifty-two (85.2%) volunteers with PTA that was more than 2° and less than 4°. Six (9.8%) volunteers had PTA less than 2°, while three (4.9%) had PTA more than 4°. There were eight (13.1%) volunteers with CTA less than 3°. Forty-three (70.5%) volunteers had CTA more than 3° and less than 4°. CTA more than 4° was found in ten volunteers (16.4%). Based on these above results, two formulas were demonstrated for predicting the CTA: CTA=2.52+0.395PTA, CTA=38.06-0.390MPTA. Conclusion The CTA can be predicted by calculating the PTA by CT-scan and standard long-leg standing radiographs before TKA. Using the present method could reduce the risk of femur component malrotation and the flexion gap balancing during TKA. Key words: Arthroplasty, replacement, knee; Femur; Rotation; Tomography

What can we learn from “internal plateaus”? The peculiar afterglow of GRB 070110

Context: The origin of GRBs' prompt emission is highly debated. Proposed scenarios involve dissipation processes above or below the photosphere of an ultra-relativistic outflow. Aims: We search for observational features that would favour one scenario over the others by constraining the dissipation radius, the outflow magnetization or by indicating the presence of shocks. Bursts showing peculiarities can emphasize the role of a specific physical ingredient, which becomes more apparent under certain circumstances. Methods: We study GRB 070110, which exhibited several remarkable features during its early afterglow: a very flat plateau terminated by an extremely steep drop and immediately followed by a bump. We model the plateau as photospheric emission from a long lasting outflow of moderate Lorentz factor ($\Gamma\sim 20$) which lags behind an ultra-relativistic ($\Gamma> 100$) ejecta responsible for the prompt emission. We compute the dissipation of energy in the forward and reverse shocks resulting from this ejecta's deceleration by the external medium. Results: Photospheric emission from the long-lasting outflow can account for the plateau properties (luminosity and spectrum) assuming some dissipation takes place in the flow. The geometrical timescale at the photospheric radius is so short that the observed decline at the end of the plateau likely corresponds to the shut-down of the central engine. The following bump results from dissipated power in the reverse shock, which develops when the slower material catches up with the initially fast component, after it had been decelerated. Conclusions: Our interpretation suggests that the prompt phase resulted from dissipation above the photosphere while the plateau had a photospheric origin. If the bump is produced by the reverse shock, it implies an upper limit ($\sigma \lesssim 0.1$) on the magnetization of the slower material.

A Further Study of the of GRBs: Rest-frame Properties, External Plateau Contributions, and Multiple Parameter Analysis

Abstract Zhang et al. propose to redefine the true γ-ray burst (GRB) central engine activity duration, , by considering the contributions from the prompt γ-ray emission, X-ray flare, and internal plateau features. With a comprehensive study of a large sample of Swift GRBs, it is shown that the distribution in the observer frame consists of a bimodal feature, suggesting the existence of a new population of ultra-long GRBs. In this work, we make a series of further studies on : we update the Swift GRB sample up to 2016 June; we investigate the properties of distribution in the rest frame; we redefine by involving external plateau contributions; and we make a multiple parameter analysis to investigate whether the bursts within the ultra-long population are statistically different in the sense of other features besides the duration distribution. We find that for all situations, the distribution of requires two normal distributions in logarithmic space to provide a good fit both in the observer frame and in the rest frame. Considering the observational gap effect would not completely erase the bimodal distribution feature. However, the bursts within the ultra-long population may have no statistical difference in the sense of other features besides the duration term. We thus suggest that if the ultra-long population of GRBs indeed exists, their central engine and radiation mechanisms should be similar to those of the normal population, but they have a longer central engine activity timescale.

New Equations of State for Postmerger Supramassive Quark Stars

Abstract Binary neutron star (NS) mergers with their subsequent fast-rotating supramassive magnetars are one attractive interpretation for at least some short gamma-ray bursts (SGRBs), based on the internal plateau commonly observed in the early X-ray afterglow. The rapid decay phase in this scenario signifies the epoch when the star collapses to a black hole after it spins down, and could effectively shed light on the underlying unclear equation of state (EoS) of dense matter. In the present work, we compare the protomagnetar masses of the internal plateau sample from representative EoS models to that derived independently from the observed galactic NS–NS binary, aiming to contribute new compact star EoSs from SGRB observations. For this purpose, we employ various EoSs covering a wide range of maximum masses for both NSs and quark stars (QSs) and, at the same time, satisfying the recent observational constraints of the two massive pulsars for which the masses are precisely measured (around ). We first illustrate that how well the underlying EoS would reconcile with the current posterior mass distribution is largely determined by the static maximum mass of that EoS. We then construct three new postmerger QS EoSs (PMQS1, PMQS2, PMQS3), fully respecting the observed distribution. We also provide easy-to-use parameterizations for both the EoSs and the corresponding maximum gravitational masses of rotating stars. In addition, we calculate the fractions of postmerger products for each EoS, and discuss potential consequences for the magnetar-powered kilonova model.

Searching for Magnetar-powered Merger-novae from Short GRBS

Abstract The merger of a double neutron star (NS–NS) binary may result in a rapidly rotating massive NS with an extremely strong magnetic field (i.e., a millisecond magnetar). In this case, the magnetic spin-down of the NS remnant provides an additional source of sustained energy injection, which would continuously power the merger ejecta. The thermal emission from the merger ejecta would give rise to a bright optical “magnetar-powered merger-nova.” In this work, we carry out a complete search for magnetar-powered merger-nova from a Swift short gamma-ray burst sample. We focus on short GRBs with extended emission or internal plateau, which may signify the presence of magnetars as the central engine. We eventually find three candidates of magnetar-powered merger-nova from the late observations of GRB 050724, GRB 070714B, and GRB 061006. With standard parameter values, the magnetar remnant scenario could well interpret the multi-band data of all three bursts, including the extended emission and their late chromatic features in the optical and X-ray data. The peak luminosities of these merger-novae reach several times , more than one order of magnitude brighter than the traditional “kilo-novae” with peak luminosity of . Intense, multi-color, late-time observations of short GRBs are encouraged to identify more merger-novae in the future.

Monoarthritis of the knee revealing tabetic arthropathy.

53-year-old man presented with monoarthritis of the knee without fever evolving since 6 months associated with an inflammatory biological syndrome. The articular puncture brought back a sterile inflammatory fluid. The radiographs of the frontal knee (A) and profile knee (B) and CT of the knee (C, D) showed destruction of the internal femoral condyle with osteolysis of the medial border of the internal tibial plateau associated with multiple bone constructions with the presence of intra-articular fragments, intra-articular effusion and thickening of the synovium. The diagnosis of tabetic arthropathy in its hypertrophic form was retained following a 20-year history of syphilitic inoculation chancre, posterior radiculocordonal syndrome, imaging data and positive syphilitic serology (TPHA-VDRL) in the blood and cerebrospinal fluid. The patient was treated with penicillin G (24 million/day) for 15 days. Tabetic arthropathy is a type of neuropathic arthropathy that has become rare and unfamiliarity with the clinical presentation of this disease may lead to considerable delay in diagnosis. This disease means progressive painless joint destruction that is related to neurosensory deficits caused by syphilis. His diagnosis is difficult as its clinical presentation is not specific and differential diagnosis is wide ranging. Hence, his diagnosis requires clinical suspicion and an appropriate serological test.

Identification of a circular structure in eastern Pomerania (northern Poland) – a hypothesis of its origin

The possible existence of a circular structure in the Kościerzyna region (northern Poland) was suggested in two papers in the 1980s. The current studies were aimed at verifying this hypothesis. Analysis of a digital terrain model of the pre-Quaternary surface relief as well as of the present terrain revealed the existence of a large structure of ca. 50 km in diameter. Its geometry was established based on a model of the Neogene/Pliocene surface and identifiable lineaments. Its characteristic feature is the presence of rim-like forms, an internal plateau, and a “high” in the centre. The structure is estimated to date from before the Pleistocene. The circular structure has been reshaped by glacial erosion and accumulation, and is now buried under Quaternary deposits. The existence of the Kościerzyna circular structure was confirmed by conducted studies, but my hypothesis of an impact origin is still uncertain and needs to be confirmed by future research. Normal 0 21 false false false PL X-NONE X-NONE /* Style Definitions */ table.MsoNormalTable {mso-style-name:Standardowy; mso-tstyle-rowband-size:0; mso-tstyle-colband-size:0; mso-style-noshow:yes; mso-style-priority:99; mso-style-parent:; mso-padding-alt:0cm 5.4pt 0cm 5.4pt; mso-para-margin-top:0cm; mso-para-margin-right:0cm; mso-para-margin-bottom:10.0pt; mso-para-margin-left:0cm; line-height:115%; mso-pagination:widow-orphan; font-size:12.0pt; font-family:Arial,sans-serif; mso-bidi-font-family:CG Times 12pt; mso-fareast-language:EN-US;}

Internal x-ray plateau in short GRBs: Signature of supramassive fast-rotating quark stars?

A supramassive, strongly-magnetized millisecond neutron star (NS) has been proposed to be the candidate central engine of at least some short gamma-ray bursts (SGRBs), based on the "internal plateau" commonly observed in the early X-ray afterglow. While a previous analysis shows a qualitative consistency between this suggestion and the Swift SGRB data, the distribution of observed break time $t_b$ is much narrower than the distribution of the collapse time of supramassive NSs for the several NS equations-of-state (EoSs) investigated. In this paper, we study four recently-constructed "unified" NS EoSs, as well as three developed strange quark star (QS) EoSs within the new confinement density-dependent mass model. All the EoSs chosen here satisfy the recent observational constraints of the two massive pulsars whose masses are precisely measured. We construct sequences of rigidly rotating NS/QS configurations with increasing spinning frequency $f$, from non-rotating ($f = 0$) to the Keplerian frequency ($f = f_{\rm K}$), and provide convenient analytical parametrizations of the results. Assuming that the cosmological NS-NS merger systems have the same mass distribution as the Galactic NS-NS systems, we demonstrate that all except the BCPM NS EoS can reproduce the current $22\%$ supramassive NS/QS fraction constraint as derived from the SGRB data. We simultaneously simulate the observed quantities (the break time $t_b$, the break time luminosity $L_b$ and the total energy in the electromagnetic channel $E_{\rm total}$) of SGRBs, and find that while equally well reproducing other observational constraints, QS EoSs predict a much narrower $t_b$ distribution than that of the NS EoSs, better matching the data. We therefore suggest that the post-merger product of NS-NS mergers might be fast-rotating supramassive QSs rather than NSs.

The radiative efficiency of relativistic jet and wind: a case study of GRB 070110

A rapidly spinning, strongly magnetized neutron star is invoked as the central engine for some Gamma-ray bursts (GRBs), especially, the $"$internal plateau$"$ feature of X-ray afterglow. However, for these $"$internal plateau$"$ GRBs, how to produce their prompt emission remains an open question. Two different physical process have been proposed in the literature, (1) a new-born neutron star is surrounded by a hyper-accreting and neutrino cooling disk, the GRB jet can be powered by neutrino annihilation aligning the spin axis; (2) a differentially rotating millisecond pulsar was formed due to different angular velocity between the interior core and outer shell parts of the neutron star, which can power an episodic GRB jet. In this paper, by analyzing the data of one peculiar GRB 070110 (with internal plateau), we try to test which model being favored. By deriving the physical parameters of magnetar with observational data, the parameter regime for initial period ($P_{0\rm }$) and surface polar cap magnetic field ($B_{\rm p}$) of the central NS are $(0.96\sim 1.2 )~\rm ms$ and $(2.4\sim 3.7)\times 10^{14}~\rm G$, respectively. The radiative efficiency of prompt emission is about $\eta_{\gamma} \sim 6\%$. However, the radiative efficiency of internal plateau ($\eta_{\rm X}$) is larger than $31\%$ assuming the $M_{\rm NS}\sim1.4 M_{\odot}$ and $P_{0\rm }\sim1.2 ~\rm ms$. The clear difference between the radiation efficiencies of prompt emission and internal plateau implies that they maybe originated from different components (e.g. prompt emission from the relativistic jet powered by neutrino annihilation, while the internal plateau from the magnetic outflow wind).

MODELING THE MULTI-BAND AFTERGLOW OF GRB 130831A: EVIDENCE FOR A SPINNING-DOWN MAGNETAR DOMINATED BY GRAVITATIONAL WAVE LOSSES?

ABSTRACT The X-ray afterglow of GRB 130831A shows an “internal plateau” with a decay slope of ∼0.8, followed by a steep drop at around 105 s with a slope of ∼6. After the drop, the X-ray afterglow continues with a much shallower decay. The optical afterglow exhibits two segments of plateaus separated by a luminous optical flare, followed by a normal decay with a slope basically consistent with that of the late-time X-ray afterglow. The decay of the internal X-ray plateau is much steeper than what we expect in the simplest magnetar model. We propose a scenario in which the magnetar undergoes gravitational-wave-driven r-mode instability, and the spin-down is dominated by gravitational wave losses up to the end of the steep plateau, so that such a relatively steep plateau can be interpreted as the internal emission of the magnetar wind and the sharp drop can be produced when the magnetar collapses into a black hole. This scenario also predicts an initial X-ray plateau lasting for hundreds of seconds with an approximately constant flux which is compatible with observation. Assuming that the magnetar wind has a negligible contribution in the optical band, we interpret the optical afterglow as the forward shock emission by invoking the energy injection from a continuously refreshed shock following the prompt emission phase. It is shown that our model can basically describe the temporal evolution of the multi-band afterglow of GRB 130831A.

Comparative Microstrain Study of Internal Hexagon and Plateau Design of Short Implants Under Vertical Loading

To quantify microstrain development during axial loading using strain gauge analysis for short implants, varying the type of fixture-abutment joint and thread design. An internal hexagon implant (4 × 8 mm) and a plateau design implant (4 × 8 mm) were embedded on the center of 10 polyurethane blocks with dimensions of 190 × 30 × 12 mm. The respective abutments were screwed onto the implants. Four strain gauges (SGs) were bonded onto the surface of each block, and 4 vertical SGs were bonded onto the side of each block. Axial load of 30 kgf was applied for 10 seconds in the center of each implant. The data were analyzed statistically by analysis of variance for repeated measures and Tukey test (P < 0.05). The interaction between implant and region factors have been statistically significant (P = 0.0259). Tukey test revealed a difference on plateau's horizontal region. The cervical region presented higher microstrain values, when compared with the medium and apical regions of the implants. Within the purpose of the study, the type of fixture-abutment joint is a relevant factor to affect the amount of stress/strain in bone simulation. The microstrain development was concentrated on the cervical region of the implant.

THE MILLISECOND MAGNETAR CENTRAL ENGINE IN SHORT GRBs

One favored progenitor model for short duration gamma-ray bursts (SGRBs) is the coalescence of two neutron stars (NS-NS). One possible outcome of such a merger would be a rapidly spinning, strongly magnetized neutron star (known as a millisecond magnetar). These magnetars may be "supra-massive", implying they would collapse to black holes after losing centrifugal support due to magnetic dipole spindown. By systematically analyzing the BAT-XRT light curves of all short GRBs detected by {\em swift}, we test how well the data are consistent with this central engine model of short GRBs. We find that the so-called "extended emission" observed with BAT in some short GRBs are fundamentally the same component as the "internal X-ray plateau" as observed in many short GRBs, which is defined as a plateau in the lightcurve followed by a very rapid drop. Based on how likely a short GRB hosts a magnetar, we characterize the entire {\em Swift} short GRB sample into three categories: the "internal plateau" sample, the "external plateau" sample, and the "no plateau" sample. The derived magnetar surface magnetic field $B_{\rm p}$ and the initial spin period $P_0$ fall into the reasonable range. No GRBs in the internal plateau sample have the total energy exceeding the maximum energy budget of a millisecond magnetar. Assuming that the rapid fall time at the end of the internal plateau is the collapse time of a supra-massive magnetar to a black hole, and applying the measured mass distribution of NS-NS systems in our Galaxy, we constrain the neutron star equation of state (EOS). The data suggest that the NS equation of state is close to the GM1 model, which has a maximum non-rotating NS mass $M_{\rm TOV} \sim 2.37 M_\odot$.

REVISITING THE DISPERSION MEASURE OF FAST RADIO BURSTS ASSOCIATED WITH GAMMA-RAY BURST AFTERGLOWS

Some fast radio bursts (FRBs) are expected to be associated with the afterglow emission of gamma-ray bursts (GRBs), while a short-lived, supermassive neutron star (NS) forms during the GRBs. I investigate the possible contributions to the dispersion measure (DM) of the FRBs from the GRB ejecta and the wind blown from the precollapsing NS. On the one hand, sometimes an internal X-ray plateau afterglow could be produced by the NS wind, which indicates that a great number of electron-positron pairs are carried by the wind. If the pair-generation radius satisfies a somewhat rigorous condition, the relativistic and dense wind would contribute a high DM to the associated FRB, which can be comparable to and even exceed the DM contributed by the intergalactic medium. On the other hand, if the wind only carries a Goldreich-Julian particle flux, its DM contribution would become negligible; meanwhile, the internal plateau afterglow would not appear. Alternatively, the FRB should be associated with a GRB afterglow produced by the GRB external shock, i.e., an energy-injection-caused shallow-decay afterglow or a normal single-power-law afterglow if the impulsive energy release of the GRB is high enough. In the latter case, the DM contributed by the high-mass GRB ejecta could be substantially important, in particular, for an environment of main-sequence stellar wind. In summary, a careful assessment on the various DM contributors could be required for the cosmological application of the expected FRB-GRB association. The future DM measurements of GRB-associated FRBs could provide a constraint on the physics of NS winds.

HOW LONG DOES A BURST BURST?

Several gamma-ray bursts (GRBs) last much longer (~hours) in gamma-rays than typical long GRBs (~ minutes), and recently it was proposed that these "ultra-long GRBs" may form a distinct population, probably with a different (e.g. blue supergiant) progenitor than typical GRBs. However, Swift observations suggest that many GRBs have extended central engine activities manifested as flares and internal plateaus in X-rays. We perform a comprehensive study on a large sample of Swift GRBs with XRT observations to investigate GRB central engine activity duration and to determine whether ultra-long GRBs are unusual events. We define burst duration t_burst based on both gamma-ray and X-ray light curves rather than using gamma-ray observations alone. We find that t_burst can be reliably measured in 343 GRBs. Within this "good" sample, 21.9% GRBs have t_burst >=10^3 s and 11.5% GRBs have t_burst >=10^4 s. There is an apparent bimodal distribution of t_burst in this sample. However, when we consider an "undetermined" sample (304 GRBs) with t_burst possibly falling in the gap between GRB duration T_90 and the first X-ray observational time, as well as a selection effect against t_burst falling into the first Swift orbital "dead zone" due to observation constraints, the intrinsic underlying t_burst distribution is consistent with being a single component distribution. We found that the existing evidence for a separate ultra-long GRB population is inconclusive, and further multi-wavelength observations are needed to draw a firmer conclusion. We also discuss the theoretical implications of our results. In particular, the central engine activity duration of GRBs is generally much longer than the gamma-ray T90 duration and it does not even correlate with T90. It would be premature to make a direct connection between T90 and the size of the progenitor star.