Pith. sign in

REVIEW 3 major objections 4 minor 1 cited by

Choked accretion onto a Schwarzschild black hole: A hydrodynamical jet-launching mechanism

T0 review · 3 major / 4 minor · reviewed 2026-08-14 · deepseek-v4-flash

Pith's one-line read The paper shows that a radially infalling flow onto a Schwarzschild black hole, when slightly denser at the equator than at the poles, accretes at a fixed Bondi–Michel rate and redirects all excess matter into a bipolar outflow.

desk verdict A genuine exact l=2 relativistic accretion solution worth refereeing, but the 'choked accretion' mechanism is largely encoded in the boundary data and the headline numerical comparison is just mass conservation. read the letter →

arxiv 1909.01527 v2 pith:32M5A6HG submitted 2019-09-04 astro-ph.HE

classification astro-ph.HE
keywords chokedaccretionBondiMichelblackholephysicsrelativistichydrodynamicsastrophysicaljetsstifffluidSchwarzschildspacetime
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper establishes a purely hydrodynamical jet-launching mechanism: when matter falls radially onto a Schwarzschild black hole with an equatorial overdensity and underdense poles, the flow cannot accrete faster than a fixed rate close to the Bondi–Michel value. Any excess flux is choked at a gravitational bottleneck and redirected along the polar axis as an outflow. The authors prove this exactly for an ultrarelativistic stiff fluid and show numerically that the same inflow-outflow morphology appears for general polytropic gases, with the accretion rate staying near the Michel value. If correct, the mechanism offers a way to launch jets without invoking magnetic fields or a spinning black hole.

What carries the argument

The central object is the quadrupolar velocity potential $\Phi=-e\left[t+2M\ln(1-2M/r)-A(3r^2-6Mr+2M^2)(3\cos^2\theta-1)\right]$, built from the general solution of the relativistic potential-flow wave equation in Schwarzschild spacetime. Regularity of the solution across the event horizon fixes the monopole term and thereby fixes the total accretion rate, while the quadrupole term redirects infalling streamlines toward the poles. The stagnation-point radius $S$ marks the dividing streamline: streamlines with $|\Psi|<1$ accrete and those with $|\Psi|>1$ escape, with ejection velocity and equatorial-to-polar density contrast related by explicit algebraic formulas.

What would settle it

Run a three-dimensional general-relativistic hydrodynamic simulation in which a rotating Keplerian disk feeds the inner boundary with a realistic angular-momentum profile; if the black hole accretes substantially faster than the Michel rate without producing a persistent polar outflow, or if the outflow disappears when the equatorial density contrast is removed with everything else unchanged, the choked-accretion claim would be falsified.

Watch

Extended reading notes

Core claim

For a stationary, axisymmetric, irrotational flow of a stiff fluid with equation of state $P=K\rho^2$, the paper constructs an exact solution around a Schwarzschild black hole using a quadrupolar $l=2$ perturbation of the velocity potential. The black hole then accretes at the fixed rate $\dot M=16\pi M^2\alpha_0\rho_0\Gamma_0$, which is close to the Michel rate, and the solution contains polar stagnation points that divide the flow into streamlines that fall into the hole and streamlines that escape as a bipolar outflow. The ejection rate satisfies $\dot M_{\rm ej}/\dot M_{\rm in}=1-1/\Lambda$, where $\Lambda$ grows with the injection rate, so the excess injected mass is expelled rather than accreted. Numerical simulations with a polytropic equation of state and a boundary density profile $\rho(\theta)=\rho_0(1-\delta\cos^2\theta)$ recover the same stable inflow-outflow configuration even for a density contrast as small as $\delta=0.1\%$, with the accretion rate remaining of order the Michel value.

Load-bearing premise

The mechanism's astrophysical relevance rests on the assumption that gas arriving at the inner edge of the disk has already lost essentially all its angular momentum, so the inflow is radial and irrotational, and that an equator-to-pole density contrast is established and maintained at the injection boundary.

Editorial extensions

If this is right

  • If the mass supply crossing the injection sphere exceeds the Bondi–Michel rate, the steady state is not higher accretion but a bipolar outflow, with the black hole still accreting at order $\dot M_{\rm M}$.
  • A very small equator-to-pole density contrast, of order $0.1\%$, suffices to switch the flow from spherical inflow to an inflow-outflow morphology.
  • The ejected fraction and ejection velocity increase monotonically with the injection rate and density contrast; in the analytic model the ejection velocity approaches the speed of light as the polar density contrast approaches unity.
  • The mechanism provides a jet-launching route that does not require magnetic fields or a rotating black hole, so it may operate in systems where magnetic or Kerr-related mechanisms are weak.
  • For ordinary plasmas the mechanism requires high inflow temperatures, and the paper estimates it is most applicable to relativistic electron-positron pair plasmas with temperatures above about $10^{11}$ K.

Reading between the lines

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

  • Because the choked rate is essentially the Michel rate, the model implies that time variability in the external mass supply maps almost one-to-one onto outflow variability, so stochastic feeding should produce flickering in the jet's mass flux before any magnetic collimation acts.
  • The same geometric idea could apply to other compact objects, where the horizon regularity condition would be replaced by a surface boundary condition; the paper confines its claims to black holes.
  • A full three-dimensional simulation with a realistic rotating disk would test whether the disk itself creates the required equatorial overdensity, turning the injection radius from an imposed boundary into an emergent property.
  • The relation $\dot M_{\rm ej}/\dot M_{\rm in}=1-1/\Lambda$ could be used as an observational diagnostic: measuring the jet-to-accretion mass ratio and the injection rate would locate the stagnation radius and effective density contrast in a real source.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 4 minor

Summary. This paper proposes a hydrodynamical 'choked accretion' mechanism for launching bipolar outflows from a Schwarzschild black hole. The analytic part constructs a stationary, axisymmetric, irrotational perfect-fluid solution with a stiff equation of state, taking a velocity potential composed of a monopole plus an l=2 quadrupole term (Eq. 2.13). The solution gives a horizon accretion rate Mdot = 16πM^2 α0 ρ0 Γ0 (Eq. 2.42) that is independent of the quadrupole amplitude, and a family of inflow-outflow configurations when the equatorial inflow speed V0 exceeds 6M^2/R^2 (Eq. 2.35). The authors define injection and ejection rates (Eqs. 2.49–2.50) and interpret the balance as a choked-accretion relation. They then perform axisymmetric general-relativistic hydrodynamic simulations with the aztekas code for polytropic equations of state, imposing an equatorial density contrast at the injection sphere while leaving the velocity components free. The simulations produce bipolar outflows with accretion rates of order the Michel rate, and the paper compares several flow diagnostics to the analytic model. Astrophysical applicability is discussed, with the authors noting that standard disk temperatures imply stagnation radii much larger than the inner disk and that the mechanism becomes relevant mainly for electron-positron plasmas at T > 10^11 K (Section 4.2).

Significance. If the mechanism operates as described, it offers a purely hydrodynamical route to bipolar outflows that does not rely on magnetic fields or black-hole spin, complementing the Blandford-Payne and Blandford-Znajek mechanisms. The exact analytic solution is a useful benchmark for relativistic hydrodynamics codes; the paper demonstrates convergence to 0.001% in the stiff-fluid benchmark (Fig. 6) and reports open-source code validation through shock-tube tests (Appendix B). The numerical exploration spans several polytropic indices, density contrasts, and sound speeds, and the qualitative inflow-outflow morphology appears robust across the parameter scan. The main limitations are the restrictive stiff-fluid assumption in the analytic model and the acknowledged absence of rotation, magnetic fields, and radiation transport; the paper's own Section 4.2 narrows the astrophysical applicability to pair-dominated plasmas with T > 10^11 K. These caveats are stated openly, which is a strength, but they should be weighed in the verdict.

major comments (3)
  1. [Section 4.1, Eq. (2.52), Fig. 14] The comparison in Fig. 14 is tautological and does not validate the choked-accretion model. Eq. (2.52) is simply Mdot_ej/Mdot_in = 1 − Mdot/Mdot_in, which follows directly from steady-state mass conservation and the definitions of the three rates. Any mass-conserving simulation will land on the analytic curve regardless of whether a choking mechanism is present. The 'very good agreement' claimed in Section 4.1 is therefore not evidence for the model. I recommend replacing Fig. 14 with a nontrivial comparison, such as the measured Mdot versus the Michel rate, or the predicted stagnation-point location as in Fig. 15, which is a genuine test.
  2. [Section 2.2, Eqs. (2.13), (2.33), (2.49)–(2.50)] The analytic model prescribes the outflow at the boundary rather than showing that an excess flux is dynamically redirected. The l=2 term in Eq. (2.13) is part of the assumed velocity potential, and the polar ejection velocity Vej in Eq. (2.33) is fixed by the same parameter V0 that sets the equatorial inflow. Eqs. (2.49)–(2.50) therefore describe a kinematic decomposition of a given steady-flow family, not an emergent choking of an independently specified injection rate. This does not invalidate the construction as an exact toy model, but the paper should be explicit that the 'choking' claim rests on the numerical simulations of Section 3, where the density contrast is imposed and the velocities are free. Alternatively, the authors could formulate a boundary-value problem in which Mdot_in is fixed and show that the steady solution has the outflow determined by the equations.
  3. [Section 3.2, Tables 3–6] The numerical evidence for flux saturation is stronger than the paper's presentation suggests, but it is not quantified. For fixed a0, the measured Mdot stays nearly constant while Mdot_in increases by up to a factor of six (e.g., Table 5, a0=0.6: Mdot_in from 52.6 to 318.9 while Mdot remains about 10.8), which is the key 'choked' behavior. The paper should present this explicitly, for example as a plot of Mdot/Mdot_M versus Mdot_in/Mdot_M, and give a quantitative range for the ratio Mdot/Mdot_M (0.98–1.67 across Tables 3–6) rather than stating only that it is 'of the order' of the Michel rate.
minor comments (4)
  1. [Section 2.5, Eq. (2.51)] The displayed equation has a typesetting issue: '8πρ 0' should be '8πρ0', and the square-root expression should be checked for readability.
  2. [Appendix A, Eq. (A.15)] The notation Mdot_M for the Michel rate is easily confused with the derivative of the black-hole mass; consider renaming it to, for example, Mdot_Michel for clarity.
  3. [Section 4.2] The paper's own discussion restricts the astrophysical applicability: for ordinary hydrogen plasmas the stagnation radius S is estimated to exceed 10^3–10^5 M, making the mechanism relevant only for pair-dominated plasmas at T > 10^11 K. This scope restriction should be stated more prominently, ideally in the abstract, so that readers do not overgeneralize the jet-launching claim.
  4. [Section 3.2, Eq. (3.5)] The sentence introducing Eq. (3.5) says that the density contrast δ is 'the same' as in Eq. (2.38), which is true at the pole, but the functional forms differ; a brief note that Eq. (3.5) is a first-order parametrization qualitatively matching the analytic profile would remove potential confusion.

Circularity Check

1 steps flagged · score 3.0 of 10

One comparison in the paper is a mass-conservation identity rather than a test of the choked-accretion mechanism; the central derivation is otherwise self-contained.

  1. self definitional [Sec. 2.5, Eq. (2.52); used in Sec. 4.1, Fig. 14]
    "Note in particular that from Eq. (2.50) we can write ˙Mej/ ˙Min = 1− ˙M/ ˙Min = 1− 1/Λ. (2.52) This simple functional dependence of the ratio of ejected to injected mass fluxes on the injection mass rate is shown in Figure 14 to compare the analytic model against the results of hydrodynamic numerical simulations."

    Equation (2.52) is just steady-state mass conservation restated: the net accretion rate is the injected rate minus the ejected rate, so the ejected/injected ratio is determined by Lambda independently of the choking mechanism. The numerical code is conservative, so any steady simulation with the same Mdot/Mdot_in will fall on this curve even if the outflow had a completely different origin. The agreement in Fig. 14 therefore validates conservation, not the choked-accretion prediction. The actual non-tautological results are Mdot close to Mdot_MM (Tables 1-6) and the bipolar morphology (Figs. 8-13), which do not reduce to this identity.

full rationale

The analytic model is constructed transparently from an assumed l=2 potential (Eq. 2.13), and the mass accretion rate (Eq. 2.42) follows from spherical-harmonic orthogonality; no parameter is fitted to the Michel rate. The polytropic simulations impose only a density contrast at the outer boundary and leave velocities free, so the bipolar outflow is emergent rather than prescribed. The Michel rate is an external benchmark, and the code is validated against independent shock-tube and analytic tests. The only notable circular element is the Figure 14 comparison, where the 'analytic' curve is the mass-conservation identity Eq. (2.52); this makes that particular validation tautological but does not undermine the central claim, which rests on the measured accretion rates and flow morphology. Self-citations to Hernandez et al. (2014) and Aguayo-Ortiz et al. (2019) provide context and the Newtonian limit but are not load-bearing for the relativistic derivation.

Assumptions & free parameters 5 free parameters · 7 assumptions · 0 invented entities

The central model is not data-driven; its parameters are imposed boundary conditions chosen to explore the mechanism. The analytic model uses V0, R, and the equation-of-state normalization; the numerical models add delta, a0, and gamma. The main physical axioms are the test-fluid limit, stationarity, axisymmetry, irrotational potential flow for the analytic part, the stiff equation of state for exact solubility, and the imposed equatorial overdensity, which is the symmetry-breaking premise of the whole paper. No new physical entities are introduced.

free parameters (5)
  • V0 = 0.16 for the R=10M benchmark; allowed interval 6M^2/R^2 < V0 < 1/2 + 6M^2/R^2
    Equatorial inflow speed at the injection sphere in the analytic model; chosen by hand as a boundary condition, controls whether polar outflow exists (Eqs. 2.21-2.35).
  • R (injection radius) = 10 M and 100 M
    Outer boundary radius in both analytic and numerical models; chosen by hand, sets the allowed V0 range and the morphology.
  • delta (density contrast) = 0.001 to 0.9
    Imposed polar density deficit at the injection sphere in numerical simulations (Eq. 3.5); chosen by hand, controls outflow strength.
  • a0 (equatorial sound speed) = 0.2, 0.4, 0.6, 0.8
    Imposed at the injection equator; chosen by hand, determines the polytropic pressure profile via Eq. 3.7 and strongly affects stagnation radius and ejection velocity.
  • gamma (adiabatic index) = 4/3, 3/2, 5/3, 2
    Chosen polytropic index for the numerical simulations; weak dependence of mass rates but changes the Michel normalization.
assumptions (7)
  • domain assumption The fluid is a test fluid in a fixed Schwarzschild background; its self-gravity is neglected.
    Used throughout; the metric is fixed with M=1 in the simulations (Section 3).
  • domain assumption The flow is stationary, axisymmetric, and symmetric about the equatorial plane.
    Section 2 introduction and numerical domain (r,theta) in [Racc,R] x [0,pi/2] with reflection boundaries.
  • domain assumption The analytic flow is irrotational, so hU_mu can be written as the gradient of a scalar potential.
    Section 2.1, around Eq. (2.9).
  • ad hoc to paper The analytic model uses a stiff equation of state P = K rho^2 with sound speed c, valid only for ultrarelativistic degenerate matter.
    Adopted for analytic tractability; the paper relaxes this assumption in the numerical section.
  • domain assumption The gas at the inner edge of the disk has lost essentially all angular momentum through viscosity before crossing the injection sphere.
    Section 1 and Section 2; the model ignores rotation in the fluid equations.
  • domain assumption An equatorial-to-polar density contrast is imposed and maintained at the injection sphere.
    Analytic model via the l=2 potential; numerical model via Eq. (3.5). This is the symmetry-breaking premise of the whole mechanism.
  • domain assumption For temperature estimates, the plasma is treated as an ideal gas with a given mean particle mass and polytropic index.
    Section 4.2, Eq. (4.2); used to derive the required temperatures for astrophysical applicability.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Choked accretion onto a Schwarzschild black hole: A hydrodynamical jet-launching mechanism." pith.science (2026). https://pith.science/paper/32M5A6HG

@misc{pith2026190901527,
  author       = {Pith},
  title        = {Pith review of: Choked accretion onto a Schwarzschild black hole: A hydrodynamical jet-launching mechanism},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/32M5A6HG}},
  note         = {Machine review of arXiv:1909.01527}
}
abstract

We present a novel, relativistic accretion model for accretion onto a Schwarzschild black hole. This consists of a purely hydrodynamical mechanism in which, by breaking spherical symmetry, a radially accreting flow transitions into an inflow-outflow configuration. The spherical symmetry is broken by considering that the accreted material is more concentrated on an equatorial belt, leaving the polar regions relatively under-dense. What we have found is a flux-limited accretion regime in which, for a sufficiently large accretion rate, the incoming material chokes at a gravitational bottleneck and the excess flux is redirected by the density gradient as a bipolar outflow. The threshold value at which the accreting material chokes is of the order of the mass accretion rate found in the spherically symmetric case studied by Bondi and Michel. We describe the choked accretion mechanism first in terms of a general relativistic, analytic toy model based on the assumption of an ultrarelativistic stiff fluid. We then relax this approximation and, by means of numerical simulations, show that this mechanism can operate also for general polytropic fluids. Interestingly, the qualitative inflow-outflow morphology obtained appears as a generic result of the proposed symmetry break, across analytic and numeric results covering both the Newtonian and relativistic regimes. The qualitative change in the resulting steady state flow configuration appears even for a very small equatorial to polar density contrast ($\sim 0.1\,\%$) in the accretion profile. Finally, we discuss the applicability of this model as a jet-launching mechanism in different astrophysical settings.

Figures

Figures reproduced from arXiv: 1909.01527 by the authors.

Figure 1
Figure 1. Schematic representation of the astrophysical setting under study: the inner region of an accretion disk-jet system around a central black hole. The analytic solution presented in this work constitutes a toy model of the inner engine behind a jet-launching process in which, through the action of hydrodynamical forces only, an accretion flow can be transformed into an inflow-outflow bipolar structure. Subsequent nume… view at source ↗
Figure 2
Figure 2. Streamlines of the accretion flow resulting from the velocity field in Eqs. (2.26) and (2.27). We have taken R = 10M as radius of the injection sphere while, from left to right, V0 = 0.06, 0.1, 0.56. Note that the first and third values of V0 correspond to the lower and upper limits in Eq. (2.35), respectively. The stagnation points in each case are shown as red crosses. The outer boundary of the model (r = R) as we… view at source ↗
Figure 3
Figure 3. Magnitude of the three-velocity V (Eq. 2.30) and density ρ (Eq. 2.36) of the analytic model for an ultrarelativ￾istic stiff fluid. Both quantities are shown as functions of the polar angle θ evaluated at the injection sphere for the par￾ticular case R = 10M and six different values of the velocity V0. In this case, from Eq. (2.32) we have that V0 is limited as V0 < 0.56 in order to guarantee that the whole solution … view at source ↗
Figures from the paper (11 more)
Figure 4
Figure 4. Figure 4: Example of the analytic model of choked accretion for the values R = 10M and V0 = 0.16. The figure shows isocontours of the fluid’s density as given by Eq. (2.36) (left panel) as well as the magnitude of the three-velocity as given by Eq. (2.30) (right panel). Note tha…
Figure 5
Figure 5. Figure 5: Dependence of different properties of the ana￾lytic model of choked accretion on the parameters R/M and M˙ in/M˙ M. From top to bottom, each panel shows: the loc￾ation of the stagnation point S, the maximum velocity at￾tained by the ejected material Vej (Eq. 2.31), and…
Figure 6
Figure 6. Figure 6: Benchmark test of aztekas with the analytic model of choked accretion described in Section 2. In this case we took R = 10M as radius of the injection sphere and V0 = 0.16 at the equator. The figure shows the time evolution of the relative error between the numerically …
Figure 7
Figure 7. Figure 7: Benchmark test of aztekas with the analytic model of choked accretion described in Section 2. In this case we took R = 10M as radius of the injection sphere and V0 = 0.16 at the equator. The left panel shows isocontour levels of the density field with the scale indicat…
Figure 8
Figure 8. Figure 8: Resulting steady state flow configuration for the numerical simulations for a polytropic fluid with γ = 4/3 accreting onto a Schwarzschild black hole. The value of the density contrast δ used in each case is indicated on the top-left corner of each panel, and increases…
Figure 9
Figure 9. Figure 9: Dependence of the different mass flux rates (in units of the corresponding Michel value M˙ M) on the poly￾tropic index γ [PITH_FULL_IMAGE:figures/full_fig_p014_9.png]
Figure 10
Figure 10. Figure 10: Dependence of the ratio M˙ in/M˙ M on the sound speed a0 as given at the equator of the injection sphere. Clearly this ratio is a monotonically increasing function of a0 with a steeper growth with increasing δ. 10 20 30 40 50 60 70 0.2 0.3 0.4 0.5 0.6 0.7 0.8 S/M a0 δ…
Figure 11
Figure 11. Figure 11: Dependence of the location of the stagnation point S on a0. Here we see that S is inversely proportional to both a0 and δ. Note that S shows a dependence on a0 that resembles the one followed by the critical radius rc on this same parameter. as more material is expell…
Figure 13
Figure 13. Figure 13: Resulting steady state configurations for a polytropic fluid with γ = 5/3 and δ = 0.5 %. The value of the sound speed a0 used in each case is indicated on the top-left corner of each panel. Also, as a0 increases the numerical data approaches the analytic model, for wh…
Figure 14
Figure 14. Figure 14: Ratio of ejected to injected mass rates M˙ ej/M˙ in as a function of the injection mass rate in units of the Michel value M˙ M. The injection radius is R = 100M. The different symbols correspond to the numerical results reported in Tables 3–6 for γ = 5/3 and sound spe…
Figure 15
Figure 15. Figure 15: Location of the stagnation point S as a function of the injection mass rate. The injection radius is R = 100M. The different symbols correspond to the numerical results reported in Tables 3–6 for γ = 5/3 and sound speeds as labeled. The solid line corresponds to the a…

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

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

  1. Choked accretion: from radial infall to bipolar outflows by breaking spherical symmetry

    astro-ph.HE 2019-09 conditional novelty 6.0 of 10

    Hydrodynamic simulations show that small axisymmetric density anisotropies cap the accretion rate onto a point mass at the Bondi value and eject the surplus in bipolar outflows.

Reference graph

Works this paper leans on

41 extracted references · 38 canonical work pages · cited by 1 Pith paper

  1. [1]

    P., Abbott R., Abbott T

    Abbott B. P., Abbott R., Abbott T. D., Acernese F., Ackley K., Adams C., Adams T., Addesso P., Adhikari R. X., Adya V. B., et al. 2017, Physical Review Letters, 119, 161101

  2. [2]

    Aguayo-Ortiz A., Mendoza S., Olvera D., 2018, PLoS ONE, 13, e0195494

  3. [3]

    Aguayo-Ortiz A., Tejeda E., Hernandez X., 2019, preprint (arXiv:1909.00884)

  4. [4]

    A., Hawley J

    Balbus S. A., Hawley J. F., 1991, Astrophysical Journal, 376, 214

  5. [5]

    A., Ib \'a \ n ez J

    Banyuls F., Font J. A., Ib \'a \ n ez J. M., Mart \' J. M., Miralles J. A., 1997, Astrophysical Journal, 476, 221

  6. [6]

    R., 2012, Active Galactic Nuclei

    Beckmann V., Shrader C. R., 2012, Active Galactic Nuclei

  7. [7]

    M., 1999, Monthly Notices of the Royal Astronomical Society, 305, 181

    Beloborodov A. M., 1999, Monthly Notices of the Royal Astronomical Society, 305, 181

  8. [8]

    S., Pidoprygora Y

    Beskin V. S., Pidoprygora Y. N., 1995, Soviet Journal of Experimental and Theoretical Physics, 80, 575

Show all 41 references
  1. [9]

    D., Payne D

    Blandford R. D., Payne D. G., 1982, Monthly Notices of the Royal Astronomical Society, 199, 883

  2. [10]

    D., Znajek R

    Blandford R. D., Znajek R. L., 1977, Monthly Notices of the Royal Astronomical Society, 179, 433

  3. [11]

    Bondi H., 1952, Monthly Notices of the Royal Astronomical Society, 112, 195+

  4. [12]

    N., Kennea J

    Burrows D. N., Kennea J. A., Ghisellini G., Mangano V., Zhang B., Page K. L., Eracleous M., Romano P., Sakamoto T., Falcone A. D., et al. 2011, Nature, 476, 421

  5. [13]

    Chaverra E., Sarbach O., 2015, Classical and Quantum Gravity, 32, 155006

  6. [14]

    M., Loska Z., Zycki P

    Czerny B., Niko ajuk M., R \'o \.z a \'n ska A., Dumont A. M., Loska Z., Zycki P. T., 2003, , 412, 317

  7. [15]

    Hartigan P., 2009, Astrophysics and Space Science Proceedings, 13, 317

  8. [16]

    F., Fendt C., Hardcastle M., Nokhrina E., Tchekhovskoy A., 2015, , 191, 441

    Hawley J. F., Fendt C., Hardcastle M., Nokhrina E., Tchekhovskoy A., 2015, , 191, 441

  9. [17]

    L., Rodr \' guez-Mota R

    Hernandez X., Rend \'o n P. L., Rodr \' guez-Mota R. G., Capella A., 2014, Revista Mexicana de Astronom\'ia y Astrof\'isica, 50, 23

  10. [18]

    P., 2017, , 55, 303

    Kaaret P., Feng H., Roberts T. P., 2017, , 55, 303

  11. [19]

    Liska M., Tchekhovskoy A., Ingram A., van der Klis M., 2019, Monthly Notices of the Royal Astronomical Society, 487, 550

  12. [20]

    L \'o pez-C \'a mara D., De Colle F., Moreno M \'e ndez E., 2019, Monthly Notices of the Royal Astronomical Society, 482, 3646

  13. [21]

    H., Ramirez-Ruiz E., 2010, Astrophysical Journal, 716, 1308

    L \'o pez-C \'a mara D., Lee W. H., Ramirez-Ruiz E., 2010, Astrophysical Journal, 716, 1308

  14. [22]

    C., 2006, Monthly Notices of the Royal Astronomical Society, 368, 1561

    McKinney J. C., 2006, Monthly Notices of the Royal Astronomical Society, 368, 1561

  15. [23]

    C., 1972, Astrophysics and Space Science, 15, 153

    Michel F. C., 1972, Astrophysics and Space Science, 15, 153

  16. [24]

    F., Rodr \' guez L

    Mirabel I. F., Rodr \' guez L. F., 1994, , 371, 46

  17. [25]

    Moncrief V., 1980, Astrophysical Journal, 235, 1038

  18. [26]

    30 of EAS Publications Series, A GPL Relativistic Hydrodynamical Code

    Olvera D., Mendoza S., 2008, in Oscoz A., Mediavilla E., Serra-Ricart M., eds, EAS Publications Series Vol. 30 of EAS Publications Series, A GPL Relativistic Hydrodynamical Code . pp 399--400

  19. [27]

    I., Shapiro S

    Petrich L. I., Shapiro S. L., Teukolsky S. A., 1988, Physical Review Letters, 60, 1781

  20. [28]

    Qian Q., Fendt C., Vourellis C., 2018, Astrophysical Journal, 859, 28

  21. [29]

    E., Boettcher M., Markoff S., Tavecchio F., 2017, , 207, 5

    Romero G. E., Boettcher M., Markoff S., Tavecchio F., 2017, , 207, 5

  22. [30]

    Semenov V., Dyadechkin S., Punsly B., 2004, Science, 305, 978

  23. [31]

    I., Sunyaev R

    Shakura N. I., Sunyaev R. A., 1973, Astronomy and Astrophysics, 24, 337

  24. [32]

    Shu C.-W., Osher S., 1988, Journal of Computational Physics, 77, 439

  25. [33]

    Siegert T., Diehl R., Greiner J., Krause M. G. H., Beloborodov A. M., Bel M. C., Guglielmetti F., Rodriguez J., Strong A. W., Zhang X., 2016, , 531, 341

  26. [34]

    M., van den Heuvel E

    Tauris T. M., van den Heuvel E. P. J., 2006, Formation and evolution of compact stellar X-ray sources . pp 623--665

  27. [35]

    A., Miller J

    Taylor P. A., Miller J. C., Podsiadlowski P., 2011, Monthly Notices of the Royal Astronomical Society, 410, 2385

  28. [36]

    Tejeda E., 2018, Revista Mexicana de Astronom\'ia y Astrof\'isica, 54, 171

  29. [37]

    Tejeda E., Aguayo-Ortiz A., 2019, Monthly Notices of the Royal Astronomical Society, 487, 3607

  30. [38]

    Wardle J. F. C., Homan D. C., Ojha R., Roberts D. H., 1998, , 395, 457

  31. [39]

    E., 1993, in American Astronomical Society Meeting Abstracts \#182 Vol

    Woosley S. E., 1993, in American Astronomical Society Meeting Abstracts \#182 Vol. 25 of Bulletin of the American Astronomical Society, Gamma-Ray Bursts from Stellar Collapse to a Black Hole? . p. 894

  32. [40]

    E., Bloom J

    Woosley S. E., Bloom J. S., 2006, Annual Review of Astronomy and Astrophysics, 44, 507

  33. [41]

    write newline

    " write newline "" before.all 'output.state := FUNCTION fin.entry write newline FUNCTION new.block output.state before.all = 'skip after.block 'output.state := if FUNCTION new.sentence output.state after.block = 'skip output.state before.all = 'skip after.sentence 'output.stat...

Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.