Burst Tails from SGR J1550-5418 Observed with Rossi X-ray Timing Explorer

We present the results of our extensive search using the Bayesian block method for long tails following short bursts from a magnetar, SGR J1550-5418, over all RXTE observations of the source. We identified four bursts with extended tails, most of which occurred during its 2009 burst active episode. The durations of tails range between ~13 s and over 3 ks, which are much longer than the typical duration of bursts. We performed detailed spectral and temporal analysis of the burst tails. We find that the spectra of three tails show a thermal nature with a trend of cooling throughout the tail. We compare the results of our investigations with the properties of four other extended tails detected from SGR 1900+14 and SGR 1806-20 and suggest a scenario for the origin of the tail in the framework of the magnetar model.Comment: 10 pages, 7 figures, 4 tables, accepted for publication in Ap

Variation of Spectral and Timing Properties in the Extended Burst Tails from the Magnetar 4U 0142+61

Extended emission episodes with intensity above the pre-burst level are observed following magnetar bursts from a number of soft gamma repeaters (SGRs) and anomalous X-ray pulsars (AXPs). Such extended tail emission were observed subsequent to two events detected from AXP 4U 0142+61. We investigated in detail the evolution of spectral and temporal properties during these two tail segments using RXTE/PCA observations, and report distinct variations both in the spectral and temporal behavior throughout the tails. In particular, sudden enhancement of pulsation amplitude in conjunction with bursts, and smooth decline of X-ray emission (cooling) during the tail were observed in both cases. We suggest that an inefficiently radiating trapped fireball formed during the burst, which can heat up the stellar surface, is able to explain the tail properties and its energetics. We also present the episodic detection of absorption and emission features during tails. One possible mechanism that has been proposed to give rise to such spectral lines is the proton/ion cyclotron resonance process which has been suggested to offer a valuable tool in probing the complex magnetic field of magnetars.Comment: 14 pages, 9 figures, 3 tables, accepted for publication in Ap

Numerical Renormalization Group Study of Quadrupole Kondo Effect with the Crystal-field Excited State

We have studied the quadrupolar Kondo effect for an impurity in cubic environment with taking account of a singlet excited state $\Gamma_1$, which models a $\mathrm{Pr}^{3+}$ ion with a non-Kramers double ground state $\Gamma_3$. We have used the numerical renormalization group approach and determined the phase diagram with varying quadrupole Kondo coupling $J$ and $\Gamma_1$ excitation energy $\Delta$. Two phases are found and identified as local Fermi liquid and non-Fermi liquid. This non-Fermi liquid phase is characteristic to the two-channel Kondo impurity, and a similar phase diagram has been also found in other extended quadrupole models. We have analyzed in detail the $J$-dependence of the Kondo temperature $T_K$ near the phase boundary $J_c (\Delta)$ and found a nice scaling behavior with an stretched exponential form $T_K \sim \delta J^{\alpha} \exp (-\mathrm{const.}/\sqrt{\delta J})$ where $\delta J \equiv J - J_c (\Delta)$. This differs from the standard scaling form and indicates that one needs to consider renormalization of multiple coupling constants

Broadband Spectral Investigations of SGR J1550-5418 Bursts

We present the results of our broadband spectral analysis of 42 SGR J1550-5418 bursts simultaneously detected with the Swift/X-ray Telescope (XRT) and the Fermi/Gamma-ray Burst Monitor (GBM), during the 2009 January active episode of the source. The unique spectral and temporal capabilities of the XRT Windowed Timing mode have allowed us to extend the GBM spectral coverage for these events down to the X-ray domain (0.5-10 keV). Our earlier analysis of the GBM data found that the SGR J1550-5418 burst spectra were described equally well with a Comptonized model or with two blackbody functions; the two models were statistically indistinguishable. Our new broadband (0.5 - 200 keV) spectral fits show that, on average, the burst spectra are better described with two blackbody functions than with the Comptonized model. Thus, our joint XRT/GBM analysis clearly shows for the first time that the SGR J1550-5418 burst spectra might naturally be expected to exhibit a more truly thermalized character, such as a two-blackbody or even a multi-blackbody signal. Using the Swift and RXTE timing ephemeris for SGR J1550-5418 we construct the distribution of the XRT burst counts with spin phase and find that it is not correlated with the persistent X-ray emission pulse phase from SGR J1550-5418. These results indicate that the burst emitting sites on the neutron star need not be co-located with hot spots emitting the bulk of the persistent X-ray emission. Finally, we show that there is a significant pulse phase dependence of the XRT burst counts, likely demonstrating that the surface magnetic field of SGR J1550-5418 is not uniform over the emission zone, since it is anticipated that regions with stronger surface magnetic field could trigger bursts more efficiently.Comment: accepted for publication in The Astrophysical Journa

A support system for solving problems of two-triangle congruence using "backward chaining"

We developed a system called DELTA that supports the students’ use of backward chaining (BC) to prove the congruence of two triangles. DELTA is designed as an interactive learning environment and supports the use of BC by providing hints and a function to automatically check the proofs inputted by the students. DELTA also has coloring, mark- ing, and highlighting functions to support students’ attempts to prove the congruence of two triangles. We evaluated the efficacy of DELTA with 36 students in the second grade of a junior high school in Japan. We found that (1) the mean number of problems, which the experimental group (EG) completely solved, was statistically higher than that of the control group on the post-test; (2) the EG effectively used the BC strategy to solve problems; and (3) the students’ attempt to use both the forward chaining strategy and the BC strategy led to solving the problems completely