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Fig. 3. Schematic picture of the poloidal currents Jp (open arrows), the poloidal Poynting flux Sp (filledarrows), and the poloidal particle energy flux Fp near the equatorial plane (i.e., the inflow of the particlenegative energies; striped arrow) in the steady state in the northern hemisphere in the KS coordinates. The BHloses its rotational energy directly by Sp along the field lines threading the horizon (see Sects. 4 and 5) and byFp near the equatorial plane, which is associated with Sp along the field lines threading the equatorial plane inthe ergosphere (see Sect. 3).

For typical AGN jets, ℓgy is expected to be ∼ 10 orders of magnitude smaller than GM/c2 (cf. Ref.[47]), so that the distance that a particle travels until it achieves the asymptotic azimuthal velocity istiny compared to the size of the ergosphere. This justifies our calculations of the particle motion inthe fixed orthonormal basis with uniform electromagnetic fields, and the asymptotic velocities canbe interpreted as the local velocities of the test particles.

Since the current crossing region is bounded at r < res, the positively charged particles do notcross the last ergospheric field line and will gyrate around this field line. When they emerge fromthe ergosphere, they contribute to the current flowing outward along the last ergospheric field line(see Fig. 3). The particles outside the ergosphere generally have positive energies.

3.3. Comparison to the mechanical Penrose processWe argue that the BZ process for the ergospheric field lines threading the equatorial plane is similarto the mechanical Penrose process, in which the rotational energy of a BH is extracted as mechanicalenergy by making the BH absorb negative-energy particles [28,29]. For simplicity, let us considerthe positively and negatively charged particles in the geometrically thin current crossing region as aone-fluid. The energy equation for this fluid in the steady state is written as

∂r√

γ (−αT rp,t) = E · Jp < 0, (36)

where T νp,µ is the energy–momentum tensor of the fluid. The boundary condition at r = res is

T rp,t = 0. Therefore, the solutions of Eq. (36) should be Fr ≡ −αT r

p,t > 0 in the current crossingregion. Then one has −T r

p,t = −ρmUtU r > 0, where ρm and Uµ are the comoving mass densityand the four-velocity of the fluid, respectively. Since all the particles may have negative energy, it is

10/29

at Tohoku University on June 30, 2016

http://ptep.oxfordjournals.org/D

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dmWq;KH�/G-:flZi�<, ��5H/�GIE�/E=LkQaZjN�#@I@B84626 S. J. Tanaka, K. Toma and N. Tominaga

given σ w. In Section 3.2, we will see that κw and τ diss slightly changethe velocity profile through the cooling effect. In other words, thesetwo parameters change lr, syn and ηsyn (see also the discussion inSection 4.2). We also study dependence of the nebular flow profileson rTS in Section 3.3 as an interesting topic.

We take κw = 104 and rTS = 0.1 pc as fiducial values from the paststudies (e.g. Kennel & Coroniti 1984a,b). We vary τ diss from 10 yr(fast dissipation) to ∞ (no dissipation). For the wind magnetizationparameter σ w, we study three representative cases of σ w = 0.1, 10,and 103 and also σ w = 0.003, which corresponds to KC model. Notethat the cases of σ w = 1 do not show a special behaviour, and wedo not study the cases of σ w ≥ 104 for which the strong shock jumpcondition is not available (see equation A10). The values of τ conv

are derived for each combination of (σ w, κw, rTS, τ diss) in order toreproduce β(rPWN)c = 1500 km s−1.

3.1 Flow dynamics

Fig. 1 compares the flow dynamics for different dissipation time-scales τ diss. All three magnetization cases of σ w = 0.1 (red solid),10 (blue dashed), 103 (green dotted) are overplotted. The thin andthick lines correspond to the fast (τ diss =10 yr) and no (τ diss = ∞)dissipation models, respectively. rTS = 0.1 pc and κw = 104 arecommon in all these plots. For reference, we plot the profiles ofKC model including the synchrotron cooling effect (σ w = 0.003,κw = 104, rTS = 0.1 pc, and τ diss = τ conf = ∞). Note that thehorizontal axes are not the distance from the pulsar r but fromthe termination shock &r ≡ r − rTS. The used parameters aresummarized in Table 1.

The thin and thick lines are overlapped for the radial velocityu (r) (top panel), the total enthalpy density ϵ(r) (fourth panel), andthe toroidal magnetic field b̄2(r) (sixth panel) profiles of the nebularflow. These lines demonstrate that τ diss is not important for the flowvelocity profile. The derived conversion time-scales τ conv are alsoalmost independent of τ diss, and we conclude that the flow dynamicsis controlled mainly by τ conv and not by τ diss for a given σ w.

The difference between the thin and thick lines is apparent forthe profiles of the magnetization σ (r) (second panel), the enthalpydensity w (fifth panel), and the turbulent magnetic field δb2 (bottompanel). These differences caused by τ diss affect the radiative prop-erties, which will be discussed in the next Section 3.2. Note that wedo not need to reduce σ (r) in order to decelerate the flow (the thicklines in the second panel of Fig. 1).

For the cases of a high-σ w wind (σ w = 10 and 103), the velocityis still relativistic behind the termination shock u(rTS) ≈ √

σw > 1(equation A11), and as is evident from the third panel of Fig. 1,the conversion term ξ conv plays a role for gradual deceleration toa non-relativistic velocity by the flow getting to &r ∼ 0.2 pc. Af-ter conversion of the toroidal to turbulent magnetic field, the flowbehaves as the hydrodynamic post-shock flow of u ∝ r−2 becausethe turbulent magnetic field behaves as the relativistic gas (see Sec-tion 2.3). We also studied a low-σ w wind of σ w = 0.1, which isstill a much larger magnetization than KC model of σ w = 0.003.For the case of a low-σ w wind, we require a finite ξ conv but " 1 todecelerate the flow to 1500 km s−1.

For another measure of the velocity profiles, we tabulated theadvection time-scale tadv in Table 1. tadv is almost independent ofσ w, i.e. the velocity profiles at &r " 0.1 pc do not contribute totadv. Although, tadv is a bit smaller than the age of the Crab Nebula(tage ∼kyr) for all the cases including KC model, three-dimensionalturbulent flow structures beyond &r # 1 pc would resolve thisdiscrepancy in practice (e.g. Porth et al. 2014b).

Figure 1. The nebular flow profiles that satisfy vPWN = 1500 km s−1 areplotted. The horizontal axis is the distance from the termination shock&r = r − rTS. The adopted parameters are summarized in Table 1. τ diss is10 yr for the thin and ∞ for the thick lines, and σw is 103 (red solid lines), 10(blue dashed lines), and 0.1 (green dotted lines). For reference, KC modelwith the cooling effect is plotted in the black dot-dashed line.

MNRAS 478, 4622–4633 (2018)Downloaded from https://academic.oup.com/mnras/article-abstract/478/4/4622/5001888by Tohoku University Library useron 12 July 2018

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9. 李 宇珉 研究室:恒星物理学脈動変光星の理論的研究

近年、MOST, CoRoT, Kepler衛星などを使った観測により極めて質の高い データが大量に提供されるようになり、脈動変光星の研究はほとんど革命的 な変革を受けた。当研究室では、恒星脈動を使ってその内部構造を探る。

Chaplin & Miglio (2013)中性子星の固有振動や安定性の研究

中性子星は質量は太陽程度であるが、半径は10kmという極めてコンパクトな 天体である。回転や磁場や超流動など様々な物理の影響を考慮して、中性子星の 固有振動(脈動)の研究を行う。

Watts 2011

SGR 1900+14: Giant γ Flare

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G{}�����7S���hV�����7S���,�_�0M��<(v�hSa)���~���Ie�^�v�{7�x(«¤�©µ�<(v�{7S�fs)iu�Sa)�qm~{m���n�°�¨¢¯�Uu~�m��p�Qr+pwh���7S$;�ot�TL!,�" �+�p�whV����7S�U6�Y�EH�w�m�xi

TL!,p��Sa)��h���n�7Sq��|t)�v��m��ph�mn��hjlp�kN,�=m{P5¦¶£�hSpitzer��.]dq�#w{¦¶£�=m�EHw�m�xi��c7�������m�xiP5���w��h,3�7Sq��>��h8�`J[��TL!,�����h��Fx�n�Silicate(��`���7)q�sO�p��xiSilicateqO�p�yh�³®`�7(AlOx)��qO�p���l�hz��n�,3�,�7S�\mq�*<����p��m�EH�w�m�xi

x = 1 → forsterite, x = 0 → fayalite, 0 < x < 1 → olivine.

x = 1 → enstatite, x = 0 → ferrosilite, 0 < x < 1 → pyroxene.

Mg2xFe¹(1−º)SiO4 �²«µ(�µ±µD)MgxFe(1-x)SiO3 ª�´��µ(WD)

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