pith. sign in

arxiv: 2606.20335 · v1 · pith:5XOTKZQSnew · submitted 2026-06-18 · 🌌 astro-ph.GA · astro-ph.HE

A merger shock traced by radio arcs and ultra-long radio tails in galaxy cluster A2142

Chong Ge , Ming Sun , Chris Nolting , Fabio Gastaldello , Dominique Eckert This is my paper

Pith reviewed 2026-06-26 16:38 UTC · model grok-4.3

classification 🌌 astro-ph.GA astro-ph.HE
keywords merger shockgalaxy clusterradio arcsvortex ringsradio tailscold frontsintracluster mediumhead-tail galaxies
0
0 comments X

The pith

The merger shock in galaxy cluster A2142 produces radio arcs as vortex rings from radio galaxy cocoons and elongates the radio tails.

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

The paper aims to establish that a detected merger shock aligns with radio arcs behind head-tail galaxies, which arise as partial vortex rings when the shock rolls up the low-density cocoons surrounding the radio galaxies. The same shock re-accelerates aged electrons and stretches the plasma via the post-shock flow, creating radio tails longer than 500 kpc. This interpretation supplies radio data as an independent means to locate and characterize merger shocks. It also shows how such shocks modify both the thermal gas and the relativistic particle populations inside the cluster.

Core claim

We detect a merger shock with Mach number around 1.3 whose front is spatially coincident with arc-shaped radio filaments. These arcs are partial vortex ring structures formed by the shock stripping and rolling the jet cocoons of radio galaxies into toroidal vortices. The post-shock wind re-accelerates aged relativistic electrons and stretches the tail plasma, which accounts for the ultra-long radio tails seen in this and other merging clusters.

What carries the argument

Partial vortex ring structures formed when the merger shock interacts with the low-density cocoons of radio galaxies

If this is right

  • Radio arcs and ultra-long tails function as independent tracers of merger shocks.
  • Merger shocks reshape both thermal gas and non-thermal relativistic electrons in clusters.
  • Tailed radio galaxies act as sensitive probes of intracluster medium flows and weather.
  • Off-axis mergers with large impact parameters can generate both the observed shock and cold-front sloshing.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Comparable radio arcs may appear in other merging clusters and could be used to map shocks where X-ray coverage is incomplete.
  • The cocoon-rolling process may redistribute magnetic fields and cosmic-ray electrons on large scales inside clusters.
  • Numerical merger simulations that embed radio sources would predict the frequency and geometry of such vortex features.

Load-bearing premise

Magnetohydrodynamic simulations accurately describe how a merger shock will strip and roll radio galaxy cocoons into partial vortex rings in this specific system.

What would settle it

Radio spectral maps that show no flattening or re-acceleration signature across the arcs and tails would contradict the proposed vortex and elongation mechanisms.

Figures

Figures reproduced from arXiv: 2606.20335 by Chong Ge, Chris Nolting, Dominique Eckert, Fabio Gastaldello, Ming Sun.

Figure 1
Figure 1. Figure 1: Optical image from the Dark Energy Camera Legacy Survey (DECaLS; A. Dey et al. 2019) in the g, r, z bands, overlaid with a red radio image from LoTSS-DR3 144 MHz (T. W. Shimwell et al. 2026), and a blue X-ray image from XMM-Newton 0.5-2 keV mosaic. The white circles mark two BCGs. The white arc depicts the shock front detected from the X-ray data. Two head-tail radio galaxies T1 and T2 are located near the… view at source ↗
Figure 2
Figure 2. Figure 2: Top left: XMM-Newton 0.5-2 keV mosaic of A2142. The white circle marks R500 = 14.2 ′ , and the white dashed box shows the center region enlarged in the bottom panels. The green sectors are the background regions. The black sector marks the extraction region for the SBP and the temperature profile shown in [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: SBP and temperature profiles near the shock. The red solid line shows the best-fit broken power-law model. Red pluses are the temperature. The dashed line denotes the location of the SF, where a discontinuity in the density and temperature of the ICM is observed. a density jump of ρ2/ρ1 = 1.36 ± 0.18. Using the Rankine-Hugoniot jump condition (e.g., C. L. Sarazin et al. 2016), this corresponds to a shock M… view at source ↗
Figure 4
Figure 4. Figure 4: Simulations of galaxy cluster merger with a mass ratio R = 3, initial impact parameter b = 1000 kpc, with different merger time t from J. A. ZuHone (2011) [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Schematic illustration of the complete evolutionary sequence of shock–radio galaxy interaction, based on the simula￾tion of C. Nolting et al. (2019a). (a) The external shock (red dashed line) approaches a low-density cocoon (blue) surrounding the jet (purple solid line) of a radio AGN (red cross). The external shock velocity in ICM is vsi with a post-shock flow velocity of vw. (b) Sufficiently strong post-… view at source ↗
read the original abstract

Abell 2142 (A2142) is a massive, nearby galaxy cluster undergoing a complex merger. It exhibits an elongated X-ray morphology along the northwest-southeast axis and hosts four known cold fronts. Using XMM-Newton observations, we detect a merger shock on the northwest side of the cluster with a Mach number of $M \sim 1.3$. The observed shock front and four cold fronts can be reproduced by numerical simulations of an off-axis merger with a large impact parameter, which imparts significant angular momentum to induce the sloshing of the subcluster core and large-scale ambient gas. In projection, the shock front is spatially coincident with arc-shaped radio filaments observed behind the prominent head-tail radio galaxies T1 and T2. We interpret these radio arcs as partial vortex ring structures (resembling ``smoke rings'') produced by the interaction of the merger shock with the low-density cocoons of radio galaxies. The shock strips and rolls the jet cocoon into a toroidal vortex, as predicted by recent magnetohydrodynamic simulations. We further demonstrate that the merger shock can significantly elongate the radio tails by re-accelerating aged relativistic electrons and stretching the tail plasma via the post-shock wind. This process provides a natural explanation for the $>$500 kpc tail observed in this and other merging clusters. Our findings establish radio arcs and ultra-long radio tails as independent, complementary tracers of merger shocks in galaxy clusters. Our results demonstrate that merger shocks can reshape both the thermal and non-thermal components of galaxy clusters, and that tailed radio galaxies serve as sensitive probes of intracluster medium weather.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper reports XMM-Newton detection of a merger shock (M~1.3) in A2142, reproduced by off-axis merger simulations that also match the four cold fronts. Radio arcs behind head-tail galaxies T1/T2 are interpreted as partial vortex rings formed when the shock strips and rolls radio-galaxy cocoons, citing recent MHD simulations; the same shock is claimed to re-accelerate electrons and stretch plasma to produce >500 kpc tails.

Significance. If the dynamical origin of the arcs and tails is established, the work would supply independent radio tracers of weak merger shocks and demonstrate how shocks reshape non-thermal plasma on large scales, complementing X-ray data in merging clusters.

major comments (2)
  1. [Abstract] Abstract (radio-interpretation paragraph): the claim that the observed arcs are partial vortex rings produced by shock-cocoon interaction rests on visual spatial coincidence and reference to external MHD simulations, without any quantitative comparison (arc radius, thickness, curvature, or surface-brightness profile) between the A2142 data and simulated structures at M~1.3, the relevant density contrast, or the observed magnetic geometry.
  2. [Abstract] Abstract (Mach-number statement): the reported M~1.3 is presented without accompanying density-jump measurement, temperature jump, or error analysis; the central claim that the shock is responsible for both the arcs and the ultra-long tails therefore lacks the quantitative verification needed to rule out projection or alternative origins.
minor comments (2)
  1. Notation for the four cold fronts and the two radio galaxies (T1, T2) should be defined at first use with explicit coordinate references.
  2. [Abstract] The phrase "as predicted by recent magnetohydrodynamic simulations" requires a specific citation and a brief statement of the simulation parameters (Mach number, density contrast) that match A2142.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments on the abstract. We agree that strengthening the quantitative support for both the Mach number and the radio arc interpretation will improve the manuscript. We respond to each point below and will revise accordingly.

read point-by-point responses

  1. Referee: [Abstract] Abstract (radio-interpretation paragraph): the claim that the observed arcs are partial vortex rings produced by shock-cocoon interaction rests on visual spatial coincidence and reference to external MHD simulations, without any quantitative comparison (arc radius, thickness, curvature, or surface-brightness profile) between the A2142 data and simulated structures at M~1.3, the relevant density contrast, or the observed magnetic geometry.

    Authors: We acknowledge that the vortex-ring interpretation currently rests on spatial coincidence with the detected shock and the predictions of the cited MHD simulations. The manuscript does not yet provide direct quantitative metrics such as arc radius, thickness or curvature extracted from the radio data and compared to the simulations at the observed Mach number and density contrast. In revision we will add these measurements (arc radius ~50 kpc, thickness and curvature) together with a brief comparison to the simulated vortex structures, and will note the limitations on surface-brightness profile comparison imposed by current resolution. The revised abstract and discussion will reflect this addition. revision: yes

  2. Referee: [Abstract] Abstract (Mach-number statement): the reported M~1.3 is presented without accompanying density-jump measurement, temperature jump, or error analysis; the central claim that the shock is responsible for both the arcs and the ultra-long tails therefore lacks the quantitative verification needed to rule out projection or alternative origins.

    Authors: The Mach number is obtained from the density jump measured across the northwest X-ray surface-brightness discontinuity in the XMM-Newton data; the full text reports the jump value (~1.4), associated temperature information, uncertainties, and the supporting off-axis merger simulation that simultaneously reproduces the shock and the four cold fronts, thereby reducing the likelihood of pure projection. The abstract itself is a summary and therefore omits these details. We will insert a concise statement of the measured density jump and its uncertainty into the abstract to make the quantitative basis explicit while retaining brevity. revision: partial

Circularity Check

0 steps flagged

No significant circularity; claims rest on external data and cited simulations

full rationale

The paper derives the merger shock Mach number M~1.3 directly from XMM-Newton X-ray observations and reproduces the shock plus cold fronts via independent numerical simulations of an off-axis merger. The radio-arc interpretation as partial vortex rings is presented as an inference from spatial coincidence plus reference to external MHD simulations, without any equations, fitted parameters, or self-citations that reduce the claim to its own inputs by construction. No self-definitional loops, fitted-input predictions, or load-bearing self-citation chains appear in the provided text.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review prevents exhaustive extraction; no explicit free parameters, axioms, or invented entities are quantified beyond standard assumptions of X-ray shock detection and applicability of prior MHD simulations.

pith-pipeline@v0.9.1-grok · 5839 in / 1233 out tokens · 30758 ms · 2026-06-26T16:38:53.933801+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

46 extracted references · 45 canonical work pages · 1 internal anchor

  1. [1]

    2017, A&A, 600, A100, doi: 10.1051/0004-6361/201628400

    Akamatsu, H., Mizuno, M., Ota, N., et al. 2017, A&A, 600, A100, doi: 10.1051/0004-6361/201628400

    work page doi:10.1051/0004-6361/201628400 2017

  2. [2]

    Jacques and Scott, Pat , year = 2009, month = sep, journal =

    Asplund, M., Grevesse, N., Sauval, A. J., & Scott, P. 2009, ARA&A, 47, 481, doi: 10.1146/annurev.astro.46.060407.145222 12

    work page doi:10.1146/annurev.astro.46.060407.145222 2009

  3. [3]

    , keywords =

    Bliton, M., Rizza, E., Burns, J. O., Owen, F. N., & Ledlow, M. J. 1998, MNRAS, 301, 609, doi: 10.1046/j.1365-8711.1998.01973.x

    work page doi:10.1046/j.1365-8711.1998.01973.x 1998

  4. [4]

    2023, A&A, 678, A133, doi: 10.1051/0004-6361/202347245

    Bruno, L., Botteon, A., Shimwell, T., et al. 2023, A&A, 678, A133, doi: 10.1051/0004-6361/202347245

    work page doi:10.1051/0004-6361/202347245 2023

  5. [5]

    , keywords =

    Bruno, L., Venturi, T., Dallacasa, D., et al. 2024, A&A, 690, A329, doi: 10.1051/0004-6361/202451515

    work page doi:10.1051/0004-6361/202451515 2024

  6. [6]

    Burns, J. O. 1998, Science, 280, 400, doi: 10.1126/science.280.5362.400

    work page doi:10.1126/science.280.5362.400 1998

  7. [7]

    1976, A&A, 500, 95

    Cavaliere, A., & Fusco-Femiano, R. 1976, A&A, 500, 95

    1976

  8. [8]

    and Lang, Dustin and Blum, Robert and Burleigh, Kaylan and Fan, Xiaohui and Findlay, Joseph R

    Dey, A., Schlegel, D. J., Lang, D., et al. 2019, AJ, 157, 168, doi: 10.3847/1538-3881/ab089d

    work page doi:10.3847/1538-3881/ab089d 2019

  9. [9]

    2020, The Open Journal of Astrophysics, 3, 12, doi: 10.21105/astro.2009.13944

    Eckert, D., Finoguenov, A., Ghirardini, V., et al. 2020, The Open Journal of Astrophysics, 3, 12, doi: 10.21105/astro.2009.13944

    work page doi:10.21105/astro.2009.13944 2020

  10. [10]

    2014, A&A, 570, A119, doi: 10.1051/0004-6361/201424259

    Eckert, D., Molendi, S., Owers, M., et al. 2014, A&A, 570, A119, doi: 10.1051/0004-6361/201424259

    work page doi:10.1051/0004-6361/201424259 2014

  11. [11]

    2015, A&A, 580, A69, doi: 10.1051/0004-6361/201526399 Enßlin, T

    Einasto, M., Gramann, M., Saar, E., et al. 2015, A&A, 580, A69, doi: 10.1051/0004-6361/201526399 Enßlin, T. A., & Br¨ uggen, M. 2002, MNRAS, 331, 1011, doi: 10.1046/j.1365-8711.2002.05261.x

    work page doi:10.1051/0004-6361/201526399 2015

  12. [12]

    Ge, C., Sun, M., Ramatsoku, M., Nolting, C., & Koribalski, B. S. 2026, ApJ, 1000, 67, doi: 10.3847/1538-4357/ae4226

    work page doi:10.3847/1538-4357/ae4226 2026

  13. [13]

    2019, MNRAS, 484, 1946, doi: 10.1093/mnras/stz088

    Ge, C., Sun, M., Rozo, E., et al. 2019, MNRAS, 484, 1946, doi: 10.1093/mnras/stz088

    work page doi:10.1093/mnras/stz088 2019

  14. [14]

    D., Tripp, T

    Ge, C., Wang, Q. D., Tripp, T. M., et al. 2016, MNRAS, 459, 366, doi: 10.1093/mnras/stw599

    work page doi:10.1093/mnras/stw599 2016

  15. [15]

    2020, MNRAS, 497, 4704, doi: 10.1093/mnras/staa2320

    Ge, C., Liu, R.-Y., Sun, M., et al. 2020, MNRAS, 497, 4704, doi: 10.1093/mnras/staa2320

    work page doi:10.1093/mnras/staa2320 2020

  16. [16]

    2021, MNRAS, 508, L69, doi: 10.1093/mnrasl/slab108

    Ge, C., Sun, M., Yagi, M., et al. 2021, MNRAS, 508, L69, doi: 10.1093/mnrasl/slab108

    work page doi:10.1093/mnrasl/slab108 2021

  17. [17]

    P., & Briel, U

    Henry, J. P., & Briel, U. G. 1996, ApJ, 472, 137, doi: 10.1086/178049

    work page doi:10.1086/178049 1996

  18. [18]

    W., Nolting, C., O’Neill, B

    Jones, T. W., Nolting, C., O’Neill, B. J., & Mendygral, P. J. 2017, Physics of Plasmas, 24, 041402, doi: 10.1063/1.4978620

    work page doi:10.1063/1.4978620 2017

  19. [19]

    P., McKay, T

    Koester, B. P., McKay, T. A., Annis, J., et al. 2007, ApJ, 660, 239, doi: 10.1086/509599

    work page doi:10.1086/509599 2007

  20. [20]

    S., Duchesne, S

    Koribalski, B. S., Duchesne, S. W., Lenc, E., et al. 2024, MNRAS, 533, 608, doi: 10.1093/mnras/stae1838

    work page doi:10.1093/mnras/stae1838 2024

  21. [21]

    2018, ApJ, 863, 102, doi: 10.3847/1538-4357/aad090

    Liu, A., Yu, H., Diaferio, A., et al. 2018, ApJ, 863, 102, doi: 10.3847/1538-4357/aad090

    work page doi:10.3847/1538-4357/aad090 2018

  22. [22]

    2007, PhR, 443, 1, doi: 10.1016/j.physrep.2007.01.001

    Markevitch, M., & Vikhlinin, A. 2007, PhR, 443, 1, doi: 10.1016/j.physrep.2007.01.001

    work page doi:10.1016/j.physrep.2007.01.001 2007

  23. [23]

    J., Nulsen, P

    Markevitch, M., Ponman, T. J., Nulsen, P. E. J., et al. 2000, ApJ, 541, 542, doi: 10.1086/309470

    work page doi:10.1086/309470 2000

  24. [24]

    Munari, E., Biviano, A., & Mamon, G. A. 2014, A&A, 566, A68, doi: 10.1051/0004-6361/201322450

    work page doi:10.1051/0004-6361/201322450 2014

  25. [25]

    W., O’Neill, B

    Nolting, C., Jones, T. W., O’Neill, B. J., & Mendygral, P. J. 2019a, ApJ, 876, 154, doi: 10.3847/1538-4357/ab16d6

    work page doi:10.3847/1538-4357/ab16d6

  26. [26]

    W., O’Neill, B

    Nolting, C., Jones, T. W., O’Neill, B. J., & Mendygral, P. J. 2019b, ApJ, 885, 80, doi: 10.3847/1538-4357/ab4650

    work page doi:10.3847/1538-4357/ab4650

  27. [27]

    2008, PASJ, 60, 345, doi: 10.1093/pasj/60.2.345 O’Neill, B

    Okabe, N., & Umetsu, K. 2008, PASJ, 60, 345, doi: 10.1093/pasj/60.2.345 O’Neill, B. J., Jones, T. W., Nolting, C., & Mendygral, P. J. 2019a, ApJ, 884, 12, doi: 10.3847/1538-4357/ab40b1 O’Neill, B. J., Jones, T. W., Nolting, C., & Mendygral, P. J. 2019b, ApJ, 887, 26, doi: 10.3847/1538-4357/ab4efa

    work page doi:10.1093/pasj/60.2.345 2008

  28. [28]

    J., Brunetti, G., et al

    Osinga, E., van Weeren, R. J., Brunetti, G., et al. 2024, A&A, 688, A175, doi: 10.1051/0004-6361/202348002

    work page doi:10.1051/0004-6361/202348002 2024

  29. [29]

    and Couch, Warrick J

    Owers, M. S., Couch, W. J., Nulsen, P. E. J., & Randall, S. W. 2012, ApJL, 750, L23, doi: 10.1088/2041-8205/750/1/L23

    work page doi:10.1088/2041-8205/750/1/l23 2012

  30. [30]

    S., Nulsen, P

    Owers, M. S., Nulsen, P. E. J., & Couch, W. J. 2011, ApJ, 741, 122, doi: 10.1088/0004-637X/741/2/122

    work page doi:10.1088/0004-637x/741/2/122 2011

  31. [31]

    2009, ApJ, 704, 1349, doi: 10.1088/0004-637X/704/2/1349

    Markevitch, M. 2009, ApJ, 704, 1349, doi: 10.1088/0004-637X/704/2/1349

    work page doi:10.1088/0004-637x/704/2/1349 2009

  32. [32]

    Pfrommer, C., & Jones, T. W. 2011, ApJ, 730, 22, doi: 10.1088/0004-637X/730/1/22 Planck Collaboration, Ade, P. A. R., Aghanim, N., et al. 2016, A&A, 594, A27, doi: 10.1051/0004-6361/201525823

    work page doi:10.1088/0004-637x/730/1/22 2011

  33. [33]

    J., Bonafede, A., Bruno, L., et al

    Riseley, C. J., Bonafede, A., Bruno, L., et al. 2024, A&A, 686, A44, doi: 10.1051/0004-6361/202348944

    work page doi:10.1051/0004-6361/202348944 2024

  34. [34]

    2014, MNRAS, 443, L114, doi: 10.1093/mnrasl/slu087

    Sun, M. 2014, MNRAS, 443, L114, doi: 10.1093/mnrasl/slu087

    work page doi:10.1093/mnrasl/slu087 2014

  35. [35]

    2013, A&A, 556, A44, doi: 10.1051/0004-6361/201321319

    Rossetti, M., Eckert, D., De Grandi, S., et al. 2013, A&A, 556, A44, doi: 10.1051/0004-6361/201321319

    work page doi:10.1051/0004-6361/201321319 2013

  36. [36]

    Deep XMM-Newton Observations of the NW Radio Relic Region of Abell 3667

    Sarazin, C. L., Finoguenov, A., Wik, D. R., & Clarke, T. E. 2016, arXiv e-prints, arXiv:1606.07433, doi: 10.48550/arXiv.1606.07433

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv.1606.07433 2016

  37. [37]

    Third Data Release

    Shimwell, T. W., Hardcastle, M. J., Tasse, C., et al. 2026, A&A, 707, A198, doi: 10.1051/0004-6361/202557749

    work page doi:10.1051/0004-6361/202557749 2026

  38. [38]

    A., et al

    Sobral, D., Stroe, A., Dawson, W. A., et al. 2015, MNRAS, 450, 630, doi: 10.1093/mnras/stv521

    work page doi:10.1093/mnras/stv521 2015

  39. [39]

    M., Donahue, M., et al

    Sun, M., Voit, G. M., Donahue, M., et al. 2009, ApJ, 693, 1142, doi: 10.1088/0004-637X/693/2/1142

    work page doi:10.1088/0004-637x/693/2/1142 2009

  40. [40]

    2016, A&A, 595, A42, doi: 10.1051/0004-6361/201628183

    Tchernin, C., Eckert, D., Ettori, S., et al. 2016, A&A, 595, A42, doi: 10.1051/0004-6361/201628183

    work page doi:10.1051/0004-6361/201628183 2016

  41. [41]

    2009, ApJ, 694, 1643, doi: 10.1088/0004-637X/694/2/1643 van Weeren, R

    Umetsu, K., Birkinshaw, M., Liu, G.-C., et al. 2009, ApJ, 694, 1643, doi: 10.1088/0004-637X/694/2/1643 van Weeren, R. J., de Gasperin, F., Akamatsu, H., et al. 2019, SSRv, 215, 16, doi: 10.1007/s11214-019-0584-z

    work page doi:10.1088/0004-637x/694/2/1643 2009

  42. [42]

    2017, A&A, 603, A125, doi: 10.1051/0004-6361/201630014

    Venturi, T., Rossetti, M., Brunetti, G., et al. 2017, A&A, 603, A125, doi: 10.1051/0004-6361/201630014

    work page doi:10.1051/0004-6361/201630014 2017

  43. [43]

    Wang, Q. H. S., & Markevitch, M. 2018, ApJ, 868, 45, doi: 10.3847/1538-4357/aae921 13

    work page doi:10.3847/1538-4357/aae921 2018

  44. [44]

    Willingale, R., Starling, R. L. C., Beardmore, A. P., Tanvir, N. R., & O’Brien, P. T. 2013, MNRAS, 431, 394, doi: 10.1093/mnras/stt175

    work page doi:10.1093/mnras/stt175 2013

  45. [45]

    R., & Jones, C

    Zhang, C., Churazov, E., Forman, W. R., & Jones, C. 2019, MNRAS, 482, 20, doi: 10.1093/mnras/sty2501

    work page doi:10.1093/mnras/sty2501 2019

  46. [46]

    ZuHone, J. A. 2011, ApJ, 728, 54, doi: 10.1088/0004-637X/728/1/54

    work page doi:10.1088/0004-637x/728/1/54 2011