pith. machine review for the scientific record. sign in

arxiv: 2605.04173 · v1 · submitted 2026-05-05 · 🌌 astro-ph.SR · astro-ph.EP

Recognition: 2 theorem links

Orbital motion and dynamical mass of the complex periodic variable binary system 2MASS J05082729-2101444

A. Quirrenbach, A. Reiners, 'A. S\'anchez-Monge, A. Schweitzer, D. Montes, D. Vigan\`o, E. Ilin, F. Murgas, G. N. Ortiz-Le\'on, I. Ribas, J. A. Caballero, J. C. Morales, J. I. Vico Linares, J. M. Girart, M., M. P\'erez-Torres, M. Zechmeister, `O. Morata, P. J. Amado, R. Zapatero Osorio, S. Curiel, S. Kaur, Th. Henning, V. J. S. B\'ejar, Y. Shan

Authors on Pith no claims yet

Pith reviewed 2026-05-08 18:01 UTC · model grok-4.3

classification 🌌 astro-ph.SR astro-ph.EP
keywords M-dwarf binarydynamical massVLBA interferometryorbital parametersradio emissionradial velocitiesGaia parallaxevolutionary models
0
0 comments X

The pith

Combined radio astrometry, radial velocities, and imaging yield a dynamical mass of 0.459 solar masses for the eccentric M-dwarf binary 2M0508-21.

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

The authors combine three epochs of VLBA radio observations at 4.85 GHz with 119 radial velocity measurements spanning 8.1 years and one adaptive optics relative position to determine the orbital motion. This fit produces an eccentric orbit with period 2.19 years and angular semimajor axis 26.964 mas. Applying the Gaia parallax converts the angular size to a physical semimajor axis of 1.3 au and gives a total dynamical mass of 0.459 solar masses through Kepler's third law. The two components show similar levels of quiescent radio emission without flares or strong circular polarization.

Core claim

The combined fit of VLBA astrometric positions, radial velocity curves, and adaptive optics imaging shows that 2M0508-21 is an M-dwarf binary with an eccentric orbit of period 2.19 years and total dynamical mass 0.459 ± 0.007 solar masses assuming the Gaia parallax. Both stars are resolved as radio sources with comparable flux densities and emission properties consistent with a gyro-synchrotron origin.

What carries the argument

The joint orbital solution to VLBA radio positions, spectroscopic radial velocities, and one adaptive optics relative astrometric point, which fixes the angular semimajor axis before conversion to physical units via the Gaia distance and application of Kepler's third law.

If this is right

  • The measured mass exceeds the value predicted by luminosity and theoretical evolutionary models for the system's age and brightness.
  • Both components produce persistent quiescent radio emission at similar levels without detected flares or strong polarization.
  • Additional VLBA epochs would allow separation of the individual stellar masses rather than only the total.
  • The system provides a dynamical benchmark near the substellar boundary for testing models of young low-mass objects.

Where Pith is reading between the lines

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

  • A confirmed mass excess could indicate that current evolutionary tracks underestimate radii or effective temperatures for young M-dwarfs.
  • The multi-epoch radio plus velocity fitting method can be extended to other radio-detected young binaries to enlarge the sample of dynamical masses.
  • Verification of the radio emission mechanism would link magnetic activity levels to orbital separation in close pre-main-sequence pairs.

Load-bearing premise

The Gaia parallax value is taken as exact when converting the measured angular semimajor axis into a physical separation for the mass calculation.

What would settle it

An independent parallax or linear size measurement that differs by more than a few percent from the Gaia value would shift the derived total mass outside the stated 0.007 solar mass uncertainty.

Figures

Figures reproduced from arXiv: 2605.04173 by A. Quirrenbach, A. Reiners, 'A. S\'anchez-Monge, A. Schweitzer, D. Montes, D. Vigan\`o, E. Ilin, F. Murgas, G. N. Ortiz-Le\'on, I. Ribas, J. A. Caballero, J. C. Morales, J. I. Vico Linares, J. M. Girart, M., M. P\'erez-Torres, M. Zechmeister, `O. Morata, P. J. Amado, R. Zapatero Osorio, S. Curiel, S. Kaur, Th. Henning, V. J. S. B\'ejar, Y. Shan.

Figure 1
Figure 1. Figure 1: Intensity and Stokes V maps of 2M0508–21AB. In each image, 2M0508–21A is on the left and 2M0508–21B on the right. view at source ↗
Figure 2
Figure 2. Figure 2: Combined fitted solution. The top panel shows the fit view at source ↗
Figure 3
Figure 3. Figure 3: Upper panels: Radio light curves of left circularly polarized (LCP) and right circularly polarized (RCP) emission, computed view at source ↗
Figure 4
Figure 4. Figure 4: Measured flux density of all known radio observations of J0508 view at source ↗
Figure 5
Figure 5. Figure 5: Luminosity vs. age diagram. The luminosity of individual view at source ↗
read the original abstract

We uses very long baseline interferometry to constrain the orbit of the binary system 2MASS J05082729-2101444. We observed the system with the VLBA in three epochs at a frequency of 4.85 GHz, which provides an angular resolution of about 3 mas. We combined the three radio astrometric observations, 119 RVs (60 VIS and 59 NIR) obtained with the CARMENES high-resolution spectrograph over a period of 8.1 years, and a relative astrometric measurement of an archival H-band Keck NIRC adaptive optics image to fit the orbital motion of the binary system. The VLBA observations resolved the binary system and show emission from both stellar components, with similar flux density levels (0.34-0.67 mJy) and showing slight temporal flux variations. The emission appears quiescent, with no significant circular polarization, and with no flare events. We obtained a fit of the orbital motion of this binary system, which has an eccentric orbit (e = 0.71) with an orbital period of 2.19 yr and a semimajor axis of 26.964 mas (1.3 au). The VLBA observations made it possible to resolve the binary system and identify both stars as radio-loud sources. The combined fit shows that 2M0508-21 is an M-dwarf binary with a total dynamical mass of $0.459\pm0.007$ M$_{\odot}$, assuming Gaia parallax. This mass is slightly larger than those estimated from the luminosity and theoretical evolutionary models. The upper limit of the circular polarization at 4.85 GHz ($\lesssim$10\%), the persistence of the quiescent emission, and the relatively low brightness temperatures are consistent with a gyro-synchrotron or synchrotron origin for the radio emission. Further VLBA observations are needed to obtain the individual masses of the stars, as well as to verify Gaia's parallax of the system. A complete characterization of the system will help improve evolutionary models for young objects at the substellar boundary.

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

1 major / 1 minor

Summary. The manuscript reports VLBA radio observations combined with CARMENES radial velocities and Keck AO astrometry to determine the orbital parameters of the binary 2MASS J05082729-2101444. The fit yields an eccentric orbit (e = 0.71) with a period of 2.19 years and angular semimajor axis of 26.964 mas. Using the Gaia parallax, they derive a total dynamical mass of 0.459 ± 0.007 M⊙ for this M-dwarf binary and analyze the radio emission as likely gyro-synchrotron or synchrotron in origin.

Significance. If the central mass result holds after proper error propagation, the paper offers a dynamical mass measurement for a young low-mass binary near the substellar boundary, which is useful for calibrating evolutionary models. The multi-technique approach (VLBA resolving both components, long-baseline RV, and AO) provides a robust orbit solution and is a strength of the work. The radio emission analysis adds context on stellar activity.

major comments (1)
  1. Abstract: The total dynamical mass is reported as 0.459±0.007 M⊙ with an uncertainty that appears to reflect only the orbital fit parameters. However, the physical scale is set by the Gaia parallax, and mass scales as the cube of distance, so the parallax uncertainty must be included in the error budget. The abstract notes the need to 'verify Gaia's parallax', indicating it should not be treated as exact for the quoted precision.
minor comments (1)
  1. Abstract: Typo: 'We uses very long baseline interferometry' should read 'We use very long baseline interferometry'.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the positive assessment of our work and the recommendation for minor revision. We address the single major comment below.

read point-by-point responses

  1. Referee: Abstract: The total dynamical mass is reported as 0.459±0.007 M⊙ with an uncertainty that appears to reflect only the orbital fit parameters. However, the physical scale is set by the Gaia parallax, and mass scales as the cube of distance, so the parallax uncertainty must be included in the error budget. The abstract notes the need to 'verify Gaia's parallax', indicating it should not be treated as exact for the quoted precision.

    Authors: We agree that the quoted uncertainty of ±0.007 M⊙ corresponds to the formal errors from the orbital fit parameters (primarily the angular semimajor axis of 26.964 mas together with the period and eccentricity), while the Gaia parallax is adopted to convert the angular scale to a physical mass. Because total mass scales as distance cubed, the relative parallax uncertainty must be propagated (multiplied by three) and added in quadrature to obtain the full error budget. In the revised manuscript we will update the abstract to state the mass explicitly as derived from the orbital solution assuming the Gaia parallax, and we will include the Gaia parallax contribution in the reported uncertainty. This change will be reflected in both the abstract and the relevant section of the main text without altering the central value. revision: yes

Circularity Check

0 steps flagged

No significant circularity in dynamical mass derivation

full rationale

The paper derives the total dynamical mass by fitting a joint orbital model to VLBA astrometric positions, 119 radial velocities, and one AO relative position, obtaining an angular semimajor axis of 26.964 mas and period 2.19 yr. Kepler's third law is then applied after scaling the angular size to physical units with an external Gaia parallax. This chain uses independent observational inputs and standard dynamics; no fitted quantity is redefined in terms of the output mass, no prediction is statistically forced by a prior fit, and no self-citation supplies a uniqueness theorem or ansatz for the central result. The paper explicitly flags the parallax assumption and requests future verification, confirming the derivation remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on standard two-body Keplerian motion and an external distance; no new particles, forces, or ad-hoc constants are introduced.

axioms (1)
  • standard math The relative motion of the two stars obeys Keplerian two-body dynamics
    Invoked to fit the combined VLBA positions, radial velocities, and AO measurement into a single orbit solution.

pith-pipeline@v0.9.0 · 5845 in / 1292 out tokens · 101603 ms · 2026-05-08T18:01:58.081059+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

77 extracted references · 1 canonical work pages

  1. [1]

    M., Sip˝ocz, B

    Astropy Collaboration, Price-Whelan, A. M., Sip˝ocz, B. M., et al. 2018, AJ, 156, 123 Astropy Collaboration, Robitaille, T. P., Tollerud, E. J., et al. 2013, A&A, 558, A33

    2018

  2. [2]

    2023, A&A, 674, A32

    Babusiaux, C., Fabricius, C., Khanna, S., et al. 2023, A&A, 674, A32

    2023

  3. [3]

    2015, A&A, 577, A42

    Baraffe, I., Homeier, D., Allard, F., & Chabrier, G. 2015, A&A, 577, A42

    2015

  4. [4]

    2002, ApJ, 572, 503

    Berger, E. 2002, ApJ, 572, 503

    2002

  5. [5]

    2006, ApJ, 648, 629

    Berger, E. 2006, ApJ, 648, 629

    2006

  6. [6]

    M., et al

    Berger, E., Ball, S., Becker, K. M., et al. 2001, Nature, 410, 338

    2001

  7. [7]

    Binks, A. S. & Jeffries, R. D. 2016, MNRAS, 455, 3345

    2016

  8. [8]

    R., Vedantham, H

    Bloot, S., Callingham, J. R., Vedantham, H. K., et al. 2024, A&A, 682, A170

    2024

  9. [9]

    Bouma, L. G. & Jardine, M. M. 2025, ApJ, 988, L3

    2025

  10. [10]

    G., Jayaraman, R., Rappaport, S., et al

    Bouma, L. G., Jayaraman, R., Rappaport, S., et al. 2024, AJ, 167, 38

    2024

  11. [11]

    J., Melis, C., Todd, J., et al

    Burgasser, A. J., Melis, C., Todd, J., et al. 2015, AJ, 150, 180

    2015

  12. [12]

    A., Guàrdia, J., López del Fresno, M., et al

    Caballero, J. A., Guàrdia, J., López del Fresno, M., et al. 2016, in Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, V ol. 9910, Observatory Operations: Strategies, Processes, and Systems VI, ed. A. B. Peck, R. L. Seaman, & C. R. Benn, 99100E

    2016

  13. [13]

    2022, A&A, 666, A16

    Calissendorff, P., Janson, M., Rodet, L., et al. 2022, A&A, 666, A16

    2022

  14. [14]

    R., Pope, B

    Callingham, J. R., Pope, B. J. S., Kavanagh, R. D., et al. 2024, Nature Astronomy, 8, 1359

    2024

  15. [15]

    R., Tasse, C., Keers, R., et al

    Callingham, J. R., Tasse, C., Keers, R., et al. 2025, Nature, 647, 603

    2025

  16. [16]

    R., Vedantham, H

    Callingham, J. R., Vedantham, H. K., Shimwell, T. W., et al. 2021, Nat.As, 5, 1233

    2021

  17. [17]

    Clark, B. G. 1980, A&A, 89, 377

    1980

  18. [18]

    B., Guirado, J

    Climent, J. B., Guirado, J. C., Pérez-Torres, M., Marcaide, J. M., & Peña- Moñino, L. 2023, Science, 381, 1120

    2023

  19. [19]

    N., Mioduszewski, A

    Curiel, S., Ortiz-León, G. N., Mioduszewski, A. J., & Arenas-Martinez, A. B. 2024, ApJ, 967, 112

    2024

  20. [20]

    N., Mioduszewski, A

    Curiel, S., Ortiz-León, G. N., Mioduszewski, A. J., & Sanchez-Bermudez, J. 2022, AJ, 164, 93

    2022

  21. [21]

    N., Mioduszewski, A

    Curiel, S., Ortiz-León, G. N., Mioduszewski, A. J., & Torres, R. M. 2020, AJ, 160, 97

    2020

  22. [22]

    N., Pritchard, J., Murphy, T., et al

    Driessen, L. N., Pritchard, J., Murphy, T., et al. 2024, PASA, 41, e084

    2024

  23. [23]

    Dulk, G. A. 1985, ARA&A, 23, 169

    1985

  24. [24]

    J., Forbrich, J., Rizzuto, A., et al

    Dupuy, T. J., Forbrich, J., Rizzuto, A., et al. 2016, ApJ, 827, 23

    2016

  25. [25]

    2016, The Journal of Open Source Software, 1, 24

    Foreman-Mackey, D. 2016, The Journal of Open Source Software, 1, 24

    2016

  26. [26]

    W., Lang, D., & Goodman, J

    Foreman-Mackey, D., Hogg, D. W., Lang, D., & Goodman, J. 2013, PASP, 125, 306 Gaia Collaboration, Brown, A. G. A., Vallenari, A., et al. 2021, A&A, 649 Gaia Collaboration, Vallenari, A., Brown, A. G. A., et al. 2023, A&A, 674, A1

    2013

  27. [27]

    Greisen, E. W. 2003, in Astrophysics and Space Science Library, V ol. 285, In- formation Handling in Astronomy - Historical Vistas, ed. A. Heck, 109 Günther, M. N., Berardo, D. A., Ducrot, E., et al. 2022, AJ, 163, 144

    2003

  28. [28]

    Hunter, J. D. 2007, Computing in Science and Engineering, 9, 90

    2007

  29. [29]

    M., Hallinan, G., Pineda, J

    Kao, M. M., Hallinan, G., Pineda, J. S., et al. 2016, ApJ, 818, 24

    2016

  30. [30]

    M., Hallinan, G., Pineda, J

    Kao, M. M., Hallinan, G., Pineda, J. S., Stevenson, D., & Burgasser, A. 2018, ApJS, 237, 25

    2018

  31. [31]

    M., Mioduszewski, A

    Kao, M. M., Mioduszewski, A. J., Villadsen, J., & Shkolnik, E. L. 2023, Nature, 619, 272

    2023

  32. [32]

    Kaur, S., Viganò, D., Béjar, V . J. S., et al. 2024, A&A, 691, L17

    2024

  33. [33]

    M., Béjar, V

    Kaur, S., Viganò, D., Girart, J. M., Béjar, V . J. S., & et al. 2026, in prep

    2026

  34. [34]

    2025, A&A, 701, A69

    Kaur, S., Viganò, D., Villadsen, J., et al. 2025, A&A, 701, A69

    2025

  35. [35]

    L., Ireland, M

    Kraus, A. L., Ireland, M. J., Hillenbrand, L. A., & Martinache, F. 2012, ApJ, 745, 19

    2012

  36. [36]

    A., et al

    Launhardt, R., Loinard, L., Dzib, S. A., et al. 2022, ApJ, 931, 43

    2022

  37. [37]

    2021, MNRAS, 507, 1979

    Leto, P., Trigilio, C., Krtiˇcka, J., et al. 2021, MNRAS, 507, 1979

    2021

  38. [38]

    F., D’Alessio, P., Rodríguez, M

    Loinard, L., Rodríguez, L. F., D’Alessio, P., Rodríguez, M. I., & González, R. F. 2007, ApJ, 657, 916

    2007

  39. [39]

    2016, MNRAS, 457, 1224

    Lynch, C., Murphy, T., Ravi, V ., et al. 2016, MNRAS, 457, 1224

    2016

  40. [40]

    Melrose, D. B. & Dulk, G. A. 1982, ApJ, 259, 844

    1982

  41. [41]

    Miret-Roig, N., Galli, P. A. B., Brandner, W., et al. 2020, A&A, 642, A179

    2020

  42. [42]

    2020, lmfit/lmfit-py 1.0.1 Ortiz-León, G

    Newville, M., Otten, R., Nelson, A., et al. 2020, lmfit/lmfit-py 1.0.1 Ortiz-León, G. N., Loinard, L., Kounkel, M. A., et al. 2017, ApJ, 834, 141

    2020

  43. [43]

    Parsamyan, E. S. 1995, Astrophysics, 38, 206

    1995

  44. [44]

    S., Hallinan, G., & Kao, M

    Pineda, J. S., Hallinan, G., & Kao, M. M. 2017, ApJ, 846, 75

    2017

  45. [45]

    2024, MNRAS, 529, 1258

    Pritchard, J., Murphy, T., Heald, G., et al. 2024, MNRAS, 529, 1258

    2024

  46. [46]

    2021, MNRAS, 502, 5438

    Pritchard, J., Murphy, T., Zic, A., et al. 2021, MNRAS, 502, 5438

    2021

  47. [47]

    J., Caballero, J

    Quirrenbach, A., Amado, P. J., Caballero, J. A., et al. 2016, in Society of Photo- Optical Instrumentation Engineers (SPIE) Conference Series, V ol. 9908, Ground-based and Airborne Instrumentation for Astronomy VI, ed. C. J

    2016

  48. [48]

    J., Caballero, J

    Quirrenbach, A., Amado, P. J., Caballero, J. A., et al. 2014, in Society of Photo- Optical Instrumentation Engineers (SPIE) Conference Series, V ol. 9147, Ground-based and Airborne Instrumentation for Astronomy V , ed. S. K. Ram- say, I. S. McLean, & H. Takami, 91471F

    2014

  49. [49]

    J., Ribas, I., et al

    Quirrenbach, A., Amado, P. J., Ribas, I., et al. 2018, in Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, V ol. 10702, Ground- based and Airborne Instrumentation for Astronomy VII, ed. C. J. Evans, L. Simard, & H. Takami, 107020W

    2018

  50. [50]

    M., Stauffer, J

    Rebull, L. M., Stauffer, J. R., Cody, A. M., et al. 2018, AJ, 155, 196

    2018

  51. [51]

    M., Stauffer, J

    Rebull, L. M., Stauffer, J. R., Hillenbrand, L. A., et al. 2022, AJ, 164, 80

    2022

  52. [52]

    E., & Harvin, J

    Riaz, B., Gizis, J. E., & Harvin, J. 2006, AJ, 132, 866

    2006

  53. [53]

    2018, A&A, 618, A23

    Rodet, L., Bonnefoy, M., Durkan, S., et al. 2018, A&A, 618, A23

    2018

  54. [54]

    2023, ApJ, 951, L43

    Rose, K., Pritchard, J., Murphy, T., et al. 2023, ApJ, 951, L43

    2023

  55. [55]

    & Wolszczan, A

    Route, M. & Wolszczan, A. 2012, ApJ, 747, L22

    2012

  56. [56]

    & Wolszczan, A

    Route, M. & Wolszczan, A. 2013, ApJ, 773, 18

    2013

  57. [57]

    & Wolszczan, A

    Route, M. & Wolszczan, A. 2016, ApJ, 821, L21

    2016

  58. [58]

    Sanderson, H., Jardine, M., Collier Cameron, A., Morin, J., & Donati, J. F. 2023, MNRAS, 518, 4734

    2023

  59. [59]

    C., Shkolnik, E

    Schneider, A. C., Shkolnik, E. L., Allers, K. N., et al. 2019, AJ, 157, 234

    2019

  60. [60]

    Seaquist, E. R. 1993, Reports on Progress in Physics, 56, 1145

    1993

  61. [61]

    C., Bowler, B

    Shan, Y ., Yee, J. C., Bowler, B. P., et al. 2017, ApJ, 846, 93

    2017

  62. [62]

    Somers, G., Cao, L., & Pinsonneault, M. H. 2020, ApJ, 891, 29

    2020

  63. [63]

    2017, AJ, 153, 152

    Stauffer, J., Collier Cameron, A., Jardine, M., et al. 2017, AJ, 153, 152

    2017

  64. [64]

    M., Jardine, M., et al

    Stauffer, J., Rebull, L. M., Jardine, M., et al. 2021, AJ, 161, 60

    2021

  65. [65]

    M., Loinard, L., Mioduszewski, A

    Torres, R. M., Loinard, L., Mioduszewski, A. J., & Rodríguez, L. F. 2007, ApJ, 671, 1813

    2007

  66. [66]

    Treumann, R. A. 2006, A&A Rev., 13, 229

    2006

  67. [67]

    2018, A&A, 609, A117 Van Der Walt, S., Colbert, S

    Trifonov, T., Kürster, M., Zechmeister, M., et al. 2018, A&A, 609, A117 Van Der Walt, S., Colbert, S. C., & Varoquaux, G. 2011, Computing in Science and Engineering, 13, 22 Article number, page 10 Curiel et al.: Orbital motion and dynamical mass of a young binary system van Lieshout, R. & Rappaport, S. A. 2018, in Handbook of Exoplanets, ed. H. J. Deeg & ...

    2018

  68. [68]

    K., Callingham, J

    Vedantham, H. K., Callingham, J. R., Shimwell, T. W., et al. 2020, Nature As- tronomy, 4, 577

    2020

  69. [69]

    E., et al

    Virtanen, P., Gommers, R., Oliphant, T. E., et al. 2020, Nature Methods, 17, 261

    2020

  70. [70]

    Waugh, R. F. P. & Jardine, M. M. 2022, MNRAS, 514, 5465

    2022

  71. [71]

    Williams, P. K. G. & Berger, E. 2015, ApJ, 808, 189

    2015

  72. [72]

    Williams, P. K. G., Berger, E., & Zauderer, B. A. 2013, ApJ, 767, L30

    2013

  73. [73]

    Williams, P. K. G., Gizis, J. E., & Berger, E. 2017, ApJ, 834, 117

    2017

  74. [74]

    Yiu, T. W. H., Vedantham, H. K., Callingham, J. R., & Günther, M. N. 2024, A&A, 684, A3

    2024

  75. [75]

    Zarka, P. 1998, J. Geophys. Res., 103, 20159

    1998

  76. [76]

    J., et al

    Zechmeister, M., Reiners, A., Amado, P. J., et al. 2018, A&A, 609, A12

    2018

  77. [77]

    2023, ApJ, 953, 65 Article number, page 11 A&A proofs:manuscript no

    Zhang, J., Tian, H., Zarka, P., et al. 2023, ApJ, 953, 65 Article number, page 11 A&A proofs:manuscript no. aa59905-26 Appendix A: Corner plot of the combined fit rvsys = 0.8893+0.0092 0.0092 7.50 7.65 7.80 7.95 K K = 7.7117+0.0748 0.0731 800.2 800.8 801.4 802.0 802.6 P P = 801.4040+0.2972 0.2947 4.5 5.0 5.5 6.0 6.5 T0 T0 = 5.5862+0.2308 0.2323 0.705 0.71...

    work page arXiv 2023