X-Ray Flares from Postmerger Millisecond Pulsars

B. Zhang; X. F. Wu; X. Y. Wang; Z. G. Dai

REVIEW

X-Ray Flares from Postmerger Millisecond Pulsars

Z. G. Dai, X. Y. Wang, X. F. Wu, B. Zhang

Astrophysics · Submitted 23 Feb 2006 · 33 references

Pith's verdict: A plausible but under-tested engine model for short-GRB X-ray flares: the surface field is fitted to the flare time, and the neglected MRI/turbulent transport leaves the differential-rotation engine exposed.

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arXiv IDastro-ph/0602525 (version 1)

Pith IDWKDOLJMS, Pith's permanent record of this paper and its review

CitationB. Zhang, X. F. Wu, X. Y. Wang, Z. G. Dai. "X-Ray Flares from Postmerger Millisecond Pulsars." arXiv:astro-ph/0602525 (2006). https://pith.science/paper/WKDOLJMS

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Editor's note

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Colleague — you should know this up front: this is a model paper, not a discovery paper. What's new is the specific claim that the ~100 s X-ray flares seen in two short GRBs can be produced by a differentially rotating, millisecond pulsar left over from a neutron star merger, with flares from buoyant magnetic toroids breaking through the surface and reconnecting. The winding/float-up mechanism is borrowed (Kluzniak & Ruderman 1998; Dai & Lu 1998), but the application to post-merger pulsars and to short-GRB flares is new. The paper also extends the idea to long GRBs.

It does well what an analytic model is supposed to do: it gives you explicit timescales for winding, buoyant rise, energy release, and outflow Lorentz factor, and it shows that a 100 s flare requires B_s ~ 5×10^10 G, a reasonable field for an old pulsar. Multiple flares and dimmer late flares come out naturally, and the stiff-EOS requirement is stated openly.

The soft spots are real. The surface field is essentially fitted to the flare time through Eq. (7), so the central t_flare ∝ B_s^{-1} relation is not independently tested; inserting that same B_s into the Lorentz-factor and flux predictions is a consistency check, not a predictive test. The toroid volume V_b/V* is also unconstrained, so the energy scale is adjustable. And the stress-test concern lands: the two-zone oscillator ignores MRI and turbulent angular momentum transport, which in a magnetized, differentially rotating fluid would plausibly erase ΔΩ on much shorter than 100 s. The paper does not justify why the only coupling is the large-scale magnetic torque. That is a genuine hole in the engine's assumed longevity, not a cosmetic issue.

On the citation side, the prior work is properly credited, and the authors do not oversell the EOS constraint.

Who is this for? The GRB and neutron star merger community. A thoughtful referee should press the MRI/transport question, but I would not desk reject it. It's a clear, honest contribution that frames an important alternative to the BH+torus picture. Send it to review.

Referee report

Significance

If the mechanism operates, it would remove a central difficulty for merger models of short GRBs by providing a natural, long-lived central engine with a concrete physical picture: magnetic winding, buoyancy, and reconnection produce multiple flares at 10^2 s with declining flux. The paper's analytic two-zone treatment is transparent, the order-of-magnitude estimates are internally consistent, and the model makes a sharp, parameter-free prediction for the Lorentz factor (Gamma ~ 160 for t_flare ~ 100 s) once the flare time is specified. The authors also connect their model to the observed properties of GRB 050724 and to long-GRB flares. These are genuine strengths. However, the central assumption that differential rotation survives for ~100 s is not defended against generic angular-momentum transport processes such as the magnetorotational instability, and the surface field B_s is calibrated from the same observed time that it is then used to predict, so the predictive status of the central relation needs to be stated more carefully.

Major objections (3)

[Section 2, Eqs. (1)-(7)] The model's central requirement that differential rotation survive until t_b ~ 100 s is not supported against the magnetorotational instability (MRI). In a magnetized, differentially rotating fluid, the MRI growth rate is of order Omega ~ 10^3 s^-1, far shorter than the model's windup time t_b; the paper includes only the large-scale magnetic torque (Eq. 2) and the dipole torque, and takes Delta-Omega to be approximately constant between t_b and tau (Eq. 6). If MRI or other turbulent angular-momentum transport erases Delta-Omega before B_phi reaches B_b, then Eq. (7) no longer gives the flare time and the observational anchor is lost. Please provide a quantitative estimate of the MRI growth/damping rate under the assumed neutron-star core conditions (field strength, stratification, conductivity), or identify a physical reason why the two-zone resonator is the only relevant channel coupling the core and shell.
[Eqs. (7) and (12)] The paper uses the observed flare time to set the surface field: for t_flare ~ 100 s it obtains B_s ~ 4.8 x 10^10 G, then inserts this value into Eq. (12) to derive Gamma_b,min ~ 160. Since B_s is not independently measured, the relation t_flare proportional to B_s^{-1} is a calibration rather than a prediction; the resulting consistency with typical pulsar fields is suggestive but does not independently test the windup relation. The paper should state this status explicitly and identify an observable consequence (e.g., a scaling between flare time, luminosity, and Lorentz factor, or a direct field estimate from spin-down or magnetar-like emission) that would falsify Eq. (7).
[Eq. (10)] The flare energy E_b = (B_b^2/8pi) V_b depends linearly on the unspecified volume ratio V_b/V_*. Because V_b/V_* is not derived from the model nor constrained by observations, the claim that the model 'self-consistently' explains the flare energetics is not fully substantiated. The authors should either provide a physically motivated estimate of the buoyant toroid's volume (e.g., from flux-tube geometry or buoyancy dynamics) or present the energy requirement as an upper limit and discuss what volume fraction is needed to match the observed flare fluences of GRB 050709 and GRB 050724.

Minor objections (5)

[Abstract] The first sentence contains a typo: 'short-dur ation' should be 'short-duration'.
[Eq. (7)] The notation 'Ps,0,ms s' after the numerical coefficient is confusing; please write the period as P_{s,0,ms} with values in milliseconds and keep the unit of time outside.
[Eq. (5)] Please clarify why epsilon = 0.3 is taken as 'typical'; the ratio of the surface dipole field to the interior radial field deserves a brief justification, and the sensitivity of tau and t_b to this parameter should be shown.
[Eqs. (5) and (7)] The statement that 't_b is substantially less than tau' should be quantified; for the fiducial parameters A0 = 1 and P_{s,0,ms} = 1, one finds t_b/tau ~ 0.2, which is sufficient for Delta-Omega to be nearly constant but not by a large order of magnitude, and the approximation degrades for A0 < 1 or P_s0 > 1 ms.
[Section on long GRBs] The sentence 'X-ray flares were observed in nearly a half of long Swift bursts' cites references 27 and 28, but the exact fraction and its uncertainty should be stated, and the comparison of temporal properties between long and short bursts should specify which properties (peak times, temporal indices) are being compared.

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The paper

The paper claims

X-ray flares about 100 seconds after short gamma-ray bursts can come from a differentially rotating millisecond pulsar formed in a neutron-star merger.

The reading

Short gamma-ray bursts are thought to come from mergers of neutron-star binaries, but the X-ray flares seen about 100 seconds after two such bursts seemed too late for the usual black-hole-plus-torus post-merger engine. This paper claims the merged remnant can instead be a differentially rotating, millisecond-period pulsar, and that the pulsar's interior poloidal magnetic field is wound into a strong toroidal field. When the toroidal field reaches roughly $10^{17}$ gauss it becomes buoyant, floats to the surface, and reconnects, releasing about $10^{51}$ erg per event; the cycle repeats to make multiple flares. The surface field needed to place the flares at $\sim 100$ s is about $5\times10^{10}$ gauss, typical of old neutron stars, so the model converts an apparent timing problem into a consequence of the remnant's spin and magnetism.

What carries the argument

The central object is a two-zone 'core–shell' model of the postmerger pulsar: the core and shell have moments of inertia $I_c$ and $I_s$ and angular velocities $\Omega_c$ and $\Omega_s$, and the differential angular velocity $\Delta\Omega=\Omega_c-\Omega_s$ winds the radial field $B_r$ into a toroidal field $B_\phi$ at the rate $B_r\Delta\Omega$. The magnetic torque $T_m=(2/3)R_c^3B_rB_\phi$ couples the two zones and opposes the differential rotation, while the buoyancy instability at $B_\phi\sim10^{17}$ gauss determines when the torus floats up and reconnects. These pieces set the winding time $t_b\simeq4.8\times10^4\,(\epsilon/0.3)\,B_{s,8}^{-1}A_0^{-1}P_{s,0,{\rm ms}}$ seconds and the explosion energy $E_b\sim1.6\times10^{51}(V_b/V_*)$ erg, so the observed flare time fixes the required surface magnetic field.

Extended reading notes

Core claim

The paper's central claim is that the post-merger object from a double neutron star merger can be a differentially rotating, millisecond-period pulsar rather than a promptly formed black hole, and that this pulsar's magnetic field is the engine behind late X-ray flares in short gamma-ray bursts. Differential rotation winds the radial field into a toroidal field at the rate $dB_\phi/dt=(\Delta\Omega)B_r$; when the toroidal field reaches the buoyancy threshold $B_b\sim10^{17}$ gauss, the torus floats to the surface in about 0.26 seconds and reconnects, releasing roughly $1.6\times10^{51}$ erg per event. Because the process repeats, the model produces multiple flares, and internal shocks between successive outflows make them softer and dimmer at later times. Matching the observed flare delay $t_{\rm flare}\sim100$ s requires a surface field $B_s\sim5\times10^{10}$ gauss, consistent with the field of an old neutron star. The model thus gives a self-consistent account of the energetics and the temporal and spectral behavior of the flares in the two short bursts.

Load-bearing premise

The load-bearing premise is that the merged remnant survives as a long-lived, differentially rotating neutron star with a surface field near $5\times10^{10}$ gauss; if the remnant collapses to a black hole within seconds, the winding–buoyancy–reconnection engine cannot produce the observed ~100-second flares.

Editorial extensions

If this is right

Short gamma-ray bursts with ~100-second X-ray flares no longer require a long-lived black-hole engine; a millisecond pulsar with a surface field of a few times $10^{10}$ gauss suffices.
Multiple flares arise naturally because each reconnection event resets the field, and the cycle repeats as long as differential rotation persists; later flares are dimmer and softer as the differential rotation weakens.
Events with weaker surface fields would show smooth X-ray afterglows without bright flares, while stronger fields would produce multi-peaked prompt emission.
The same mechanism can extend to long gamma-ray bursts if their central engines are moderately magnetized millisecond pulsars with fall-back accretion disks, making X-ray flares a common feature of both burst classes.
If correct, the ~100-second flare delay directly constrains the nuclear equation of state: it must be stiff enough for the remnant to avoid rapid collapse.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

Since each flare marks one winding–buoyancy–reconnection cycle, the lengthening intervals and dimming flux of later flares could be inverted to measure how fast the differential rotation decays, i.e., the interior magnetic braking timescale.
The same recurrent-flare engine should operate in any neutron star with strong interior differential rotation, so magnetar outbursts or post-glitch events with delayed X-ray flares at minutes to hours would be natural testbeds.
The model's ultrarelativistic flare ejecta, with minimum Lorentz factor around 160, could be probed by late-time radio or millimetre follow-up of nearby short bursts, where collisions with the low-density circumburst medium would produce observable emission.

Original abstract

Recent observations support the suggestion that short-duration gamma-ray bursts are produced by compact star mergers. The X-ray flares discovered in two short gamma-ray bursts last much longer than the previously proposed postmerger energy release time scales. Here we show that they can be produced by differentially rotating, millisecond pulsars after the mergers of binary neutron stars. The differential rotation leads to windup of interior poloidal magnetic fields and the resulting toroidal fields are strong enough to float up and break through the stellar surface. Magnetic reconnection--driven explosive events then occur, leading to multiple X-ray flares minutes after the original gamma-ray burst.

The compiled record

The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,223 input tokens.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.06 · human participants 0.02 · controlled comparison 0.06 · randomized assignment 0.01 · states quantitative result 0.07 · compares with prior results 0.84 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; show every role.

Recent observations support the suggestion that short-duration gamma-ray bursts are produced by compact star mergers. The X-ray flares discovered in two short gamma-ray bursts last much longer than the previously proposed postmerger energy release time scales. Here we show that they can be produced by differentially rotating, millisecond pulsars after the mergers of binary neutron stars. The differential rotation leads to windup of interior poloidal magnetic fields and the resulting toroidal fields are strong enough to float up and break through the stellar surface. Magnetic reconnection--driven explosive events then occur, leading to multiple X-ray flares minutes after the original gamma-ray burst.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	Recent observations support the suggestion that short-duration gamma-ray bursts are produced by compact star mergers.	background 1.00	0.05	0.03	hedged possibility 0.94
s1	The X-ray flares discovered in two short gamma-ray bursts last much longer than the previously proposed postmerger energy release time scales.	gap 0.57	0.50	0.05	asserted 1.00
s2	Here we show that they can be produced by differentially rotating, millisecond pulsars after the mergers of binary neutron stars.	contribution 0.79	0.86	0.87	asserted 0.89
s3	The differential rotation leads to windup of interior poloidal magnetic fields and the resulting toroidal fields are strong enough to float up and break through the stellar surface.	interpretation 0.56	0.59	0.09	asserted 1.00
s4	Magnetic reconnection--driven explosive events then occur, leading to multiple X-ray flares minutes after the original gamma-ray burst.	result 0.60	0.62	0.22	asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.97 · evidence from argument 0.74.

What was examined, and what was not

sources read

arXiv listing abstract v1

not examined

full text
figures and tables
references and citing sentences
relations to other papers

levels run

P abstract

not run

S sections
T body sentences
C citations
R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

References

Works cited (33)

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C. Kouveliotou et al., Astrophys. J. 413, L101 (1993)

View on Pith 1993
[2]

For a review, see B. Zhang, P. M´ esz´ aros,Int. J. Mod. Phys. A19, 2385 (2004)

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N. Gehrels et al., Nature 437, 851 (2005)

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J. S. Bloom et al., Astrophys. J. 638, 354 (2006)

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D. B. Fox et al., Nature 437, 845 (2005)

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J. S. Villasenor et al., Nature 437, 855 (2005)

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J. Hjorth et al., Nature 437, 859 (2005)

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S. D. Barthelmy et al., Nature 438, 994 (2005)

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E. Berger et al., Nature 438, 988 (2005)

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[10]

D. Eichler, M. Livio, T. Piran, D. N. Schramm, Nature 340, 126 (1989)

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R. Narayan, B. Paczy´ nski, T. Piran,Astrophys. J. 395, L83 (1992)

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R. Mochkovitch, M. Hernanz, J. Isern, X. Martin, Nature 361, 236 (1993)

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A. Panaitescu, Mon. Not. R. Astron. Soc., submitted (preprint available at http://arXiv.org/astro-ph/0511588). 8

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[14]

S. Rosswog, E. Ramirez-Ruiz, M. B. Davies, Mon. Not. R. Astron. Soc. 345, 1077 (2003)

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M. A. Aloy, H.-T. Janka, E. M¨ uller,Astron. Astrophys. 436, 273 (2005)

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M. B. Davies, A. Levan, A. King, Mon. Not. R. Astron. Soc. 356, 54 (2005)

View on Pith 2005
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The soft EOS at high densities models the interaction of n ucleons with a Reid soft-core potential, the moderately stiff EOS uses the two-body and th ree-body interactions, and the very stiff EOS models the nucleon interaction in terms of a mean scalar ﬁeld. The effects of these EOSs, uniform rotation, and differential r otation on the maximum mass of neu...

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D. J. Nice et al., Astrophys. J. 634, 1242 (2005)

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M. Shibata, K. Taniguchi, K. Ury ¯ u, Phys. Rev. D 71, 084021 (2005)

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W. Klu´ zniak, M. Ruderman,Astrophys. J. 505, L113 (1998)

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Z. G. Dai, T. Lu, Phys. Rev. Lett. 81, 4301 (1998)

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H. C. Spruit, Astron. Astrophys. 341, L1 (1999)

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P. Goldreich, A. Reisenegger, Astrophys. J. 395, 250 (1992)

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Y . Z. Fan, D. M. Wei,Mon. Not. R. Astron. Soc. 364, L42 (2005)

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B. Zhang et al., Astrophys. J., in press (preprint available at http://arXiv.org/astro-ph/0508321)

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To calculate the X-ray ﬂux, two spectral break frequenci es should be considered (2): the characteristic frequency νm and the cooling frequency νc. For typical parameters in our model, νm < ν c, implying the slow-cooling case. 9

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We thank P. F. Chen and M. D. Ding for helpful discussions a bout solar ﬂare models that have motivated us to consider X-ray ﬂare mechanisms and Y . F. Huang for valuable suggestions. This work is supported by the National NaturalScience Foundation of China (grant numbers: 10221001, 10233010, 10403002, and 1050301 2). B. Z. is supported by NASA (grant num...

View on Pith

Forward citations

Cited by 6 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Quasi-spherical fallback in binary neutron-star mergers: fuel and obstacle for extended emission
astro-ph.HE 2026-11 conditional novelty 6.0 of 10

A fallback-fed secondary jet, regulated by quasi-spherical fallback that both fuels and impedes it, can explain the extended emission in short gamma-ray bursts.
Evidence of self-organized criticality in the prompt emission of a bright gamma-ray burst
astro-ph.HE 2026-08 conditional novelty 6.0 of 10

The pulses in GRB 230307A show power-law distributions of duration, peak counts, and waiting time whose high-energy slopes are consistent with 3D self-organized criticality, the first such evidence in a single GRB's p...
Formation and Detectability of PSR J0653+0443-like Extremely Eccentric Binary Neutron Stars in the Milky Way
astro-ph.HE 2026-10 conditional novelty 5.0 of 10

Only about 0.6% of Milky Way binary neutron stars detectable by FAST should have orbital eccentricity above 0.99, so PSR J0653+0443 is rare but consistent with standard binary evolution.
Prospect for Detection of Strongly Lensed Multi-messenger Signals of Binary Neutron Star Mergers
astro-ph.HE 2026-07 conditional novelty 5.0 of 10

Future CE+ET detectors may detect lensed BNS kilonovae at ~0.5/yr via pointed follow-up of known galaxy lenses, while lensed sGRBs and afterglows remain rare or undetectable with current-generation facilities.
Optical observations of candidate host galaxies of eight fast X-ray transients
astro-ph.HE 2026-06 unverdicted novelty 4.0 of 10

Optical imaging and BAGPIPES SED fitting of eight FXTs yields candidate hosts consistent with WD-IMBH TDEs or BNS mergers for most events, with one reclassified as a Galactic flare and evidence for diverse origins.

Show 1 more citing papers

On the Duration of Gamma-Ray Bursts
astro-ph.HE 2024-12 conditional novelty 4.0 of 10

GRB duration is shaped by the progenitor, the central engine, the emitter, and geometry, so short versus long duration is not a reliable direct indicator of what exploded or merged.

How later papers used it

62 later papers cite it

Evidence: thin. 43 of the citing papers share no author with it, and 0 of those carry a confident label from Pith's citation classifier.

Pith read 6 of the 83 citing sentences, choosing only those whose citation markers point at this paper alone, and wrote the paraphrases from them. The summary, the counts, the evidence level, the links and the quotes come from code; the summary counts the papers listed below. A later paper is listed under a label when Pith's citation classifier gives one of its sentences that label at probability 0.8 or more (0.95 for support), Pith's reading finds that the citing paper itself did it, and a second check confirms the paraphrase against the sentence. This section lists uses only. It does not list criticism or disagreement, so their absence here says nothing about how the paper has been received. Papers that share an author with this one are listed apart, under "By the same authors". A quote is the citing authors' own sentence, shown when their paper's licence is CC BY, CC BY-SA or CC0. JSON

1 paper by the same authors is listed below: 1 used its data or values.

Uses its data or values 1 of 2 papers with this label · 1 by the same authors

By the same authors

Employed typical values for a normal neutron star in a neutron star-white dwarf merger, including a mass of 1.4 solar masses, a radius of 12 km, an initial period of 10 s, a surface field of 10^12 G, moments of inertia near 10^45 g cm^2, and an ellipticity of 0.3, from this paper.

Magnetars from Neutron Star--White Dwarf Mergers: Application to Fast Radio Bursts (2020) (same authors) · 0.80 · paraphrased: the licence does not allow quoting

How the literature uses it

12 arXiv papers cite this in 13 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 11 sentences without a confident label

Cites it as background 2 papers

The external origin of plateaus has been interpreted in terms of energy injection from a millisecond magnetar [ref] or a BH [ref] , into the surrounding environment.

GRB~250704B/EP250704a a Short Gamma-Ray Burst Powered by a Magnetar · Introduction · 0.84
Another possibility that has been suggested for powering the engine is the electromagnetic spindown emission from a highly magnetized NS (see, i.e., Refs. [ref] ), which survives for some time before collapsing to a BH or remains as a stable NS (if allowed by its mass [ref] ).

Binary Neutron Star Mergers and Short Gamma-Ray Bursts: Effects of Magnetic Field Orientation, Equation of State, and Mass Ratio · Short Gamma-Ray Bursts and Other Electromagnetic Signals · 0.94

Discussion

Disagree with the review, or know something it missed? Leave a comment, highlight any passage above to comment on it, or challenge this review formally.

[1] [1]

C. Kouveliotou et al., Astrophys. J. 413, L101 (1993)

View on Pith 1993

[2] [2]

For a review, see B. Zhang, P. M´ esz´ aros,Int. J. Mod. Phys. A19, 2385 (2004)

View on Pith 2004

[3] [3]

N. Gehrels et al., Nature 437, 851 (2005)

View on Pith 2005

[4] [4]

J. S. Bloom et al., Astrophys. J. 638, 354 (2006)

View on Pith 2006

[5] [5]

D. B. Fox et al., Nature 437, 845 (2005)

View on Pith 2005

[6] [6]

J. S. Villasenor et al., Nature 437, 855 (2005)

View on Pith 2005

[7] [7]

J. Hjorth et al., Nature 437, 859 (2005)

View on Pith 2005

[8] [8]

S. D. Barthelmy et al., Nature 438, 994 (2005)

View on Pith 2005

[9] [9]

E. Berger et al., Nature 438, 988 (2005)

View on Pith 2005

[10] [10]

D. Eichler, M. Livio, T. Piran, D. N. Schramm, Nature 340, 126 (1989)

View on Pith 1989

[11] [11]

R. Narayan, B. Paczy´ nski, T. Piran,Astrophys. J. 395, L83 (1992)

View on Pith 1992

[12] [12]

R. Mochkovitch, M. Hernanz, J. Isern, X. Martin, Nature 361, 236 (1993)

View on Pith 1993

[13] [13]

A. Panaitescu, Mon. Not. R. Astron. Soc., submitted (preprint available at http://arXiv.org/astro-ph/0511588). 8

View on Pith Pith review arXiv

[14] [14]

S. Rosswog, E. Ramirez-Ruiz, M. B. Davies, Mon. Not. R. Astron. Soc. 345, 1077 (2003)

View on Pith 2003

[15] [15]

M. A. Aloy, H.-T. Janka, E. M¨ uller,Astron. Astrophys. 436, 273 (2005)

View on Pith 2005

[16] [16]

M. B. Davies, A. Levan, A. King, Mon. Not. R. Astron. Soc. 356, 54 (2005)

View on Pith 2005

[17] [17]

The soft EOS at high densities models the interaction of n ucleons with a Reid soft-core potential, the moderately stiff EOS uses the two-body and th ree-body interactions, and the very stiff EOS models the nucleon interaction in terms of a mean scalar ﬁeld. The effects of these EOSs, uniform rotation, and differential r otation on the maximum mass of neu...

View on Pith

[18] [18]

D. J. Nice et al., Astrophys. J. 634, 1242 (2005)

View on Pith 2005

[19] [19]

M. Shibata, K. Taniguchi, K. Ury ¯ u, Phys. Rev. D 71, 084021 (2005)

View on Pith 2005

[20] [20]

W. Klu´ zniak, M. Ruderman,Astrophys. J. 505, L113 (1998)

View on Pith 1998

[21] [21]

Z. G. Dai, T. Lu, Phys. Rev. Lett. 81, 4301 (1998)

View on Pith 1998

[22] [22]

H. C. Spruit, Astron. Astrophys. 341, L1 (1999)

View on Pith 1999

[23] [23]

P. Goldreich, A. Reisenegger, Astrophys. J. 395, 250 (1992)

View on Pith 1992

[24] [24]

Y . Z. Fan, D. M. Wei,Mon. Not. R. Astron. Soc. 364, L42 (2005)

View on Pith 2005

[25] [25]

B. Zhang et al., Astrophys. J., in press (preprint available at http://arXiv.org/astro-ph/0508321)

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We thank P. F. Chen and M. D. Ding for helpful discussions a bout solar ﬂare models that have motivated us to consider X-ray ﬂare mechanisms and Y . F. Huang for valuable suggestions. This work is supported by the National NaturalScience Foundation of China (grant numbers: 10221001, 10233010, 10403002, and 1050301 2). B. Z. is supported by NASA (grant num...

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