2025A&A...698A.167S

Query : 2025A&A...698A.167S

2025A&A...698A.167S - Astronomy and Astrophysics, volume 698A167 (2025/6-1)

The p-Laplacian as a framework for generalizing Newtonian gravity and Milgromian gravitation.

SCHERER D., PFLAMM-ALTENBURG J., KROUPA P. and GJERGO E.

Abstract (from CDS):

Context. The radial acceleration relation (RAR) follows from Milgromian gravitation (MoND) and velocity dispersion data of many dwarf spheroidal galaxies (dSphs) and galaxy clusters have been reported to be in tension with it.
Aims. We consider the generalized Poisson equation (GPE), expressed in terms of the p-Laplacian, which has been applied in electrodynamics, and investigate whether it can address these tensions.
Methods. From the GPE we derive a generalized RAR characterized by the p parameter from the p-Laplacian and a velocity dispersion formula for a Plummer model. We apply these models to Milky Way and Andromeda dSphs and HIFLUGS galaxy clusters and derive a p parameter for each dSph and galaxy cluster. We explore a relation of p to the mass density of the bound system, and alternatively a relation of p to the external field predicted from Newtonian gravity
Results. This ansatz allows the deviations of dSphs and galaxy clusters from the RAR without the need of introducing dark matter. Data points deviate from the Milgromian case, p = 3, with up to 5σ-confidence. Also, we find the model predicts velocity dispersions, each of which lies in the 1σ-range of their corresponding data point allowing the velocity dispersion to be predicted for early-type dwarf satellite galaxies from their baryonic density. The functional relation between the mass density of the bound system and p suggests p to increase with decreasing density. We find for the critical cosmological density p(ρcrit) = 12.27±0.39. This implies significantly different behaviour of gravitation on cosmological scales. Alternatively, the functional relation between p and the external Newtonian gravitational field suggests p to decrease with increasing field strength.
Conclusions. The GPE fits the RAR data of dSphs and galaxy clusters, reproduces the velocity dispersions of the dSphs, gives a prediction for the velocity dispersion of galaxy clusters from their baryonic density and may explain the non-linear behaviour of galaxies in regions beyond the Newtonian regime.

Abstract Copyright: © The Authors 2025

Journal keyword(s): gravitation - galaxies: clusters: general - galaxies: dwarf - galaxies: groups: general - galaxies: kinematics and dynamics - dark matter

Status at CDS : All or part of tables of objects will not be ingested in SIMBAD.

Simbad objects: 73

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Number of rows : 73
N Identifier Otype ICRS (J2000)
RA 		ICRS (J2000)
DEC 		Mag U Mag B Mag V Mag R Mag I Sp type #ref
1850 - 2026 		#notes
1 NAME Andromeda XX G 00 07 30.70 +35 07 56.4     18.2     ~ 77 0
2 And XIX G 00 19 32.10 +35 02 37.1     15.6     ~ 168 0
3 NAME Andromeda XXVI G 00 23 45.6 +47 54 58     17.3     ~ 76 0
4 NAME Cetus Dwarf Galaxy G 00 26 10.8 -11 03 14     13.2     ~ 257 0
5 NAME Andromeda XXV G 00 30 08.9 +46 51 07     14.8     ~ 120 0
6 NGC 147 GiG 00 33 12.120 +48 30 31.46   12.0 9.5     ~ 720 1
7 NAME Andromeda III G 00 35 33.8 +36 29 52     14.4     ~ 309 0
8 NAME Cassiopeia III G 00 35 59.4 +51 33 35           ~ 59 0
9 NAME Andromeda XXX G 00 36 34.90 +49 38 48.0           ~ 59 0
10 NAME Andromeda XVII G 00 37 07.0 +44 19 20     15.8     ~ 101 0
11 NAME Andromeda XXVII G 00 37 27.1 +45 23 13     16.7     ~ 82 0
12 NGC 185 Sy2 00 38 57.9400026024 +48 20 15.035874648   9.10 9.2     ~ 840 1
13 M 110 GiG 00 40 22.0572349992 +41 41 07.507220136   8.92 8.07     ~ 1370 1
14 ACO 85 ClG 00 41 36.21 -09 19 30.4           ~ 974 0
15 M 31 AGN 00 42 44.330 +41 16 07.50 4.86 4.36 3.44     ~ 13622 1
16 NAME Andromeda I G 00 45 39.8 +38 02 28   13.9 12.7     ~ 355 0
17 NAME Andromeda XI G 00 46 20.0 +33 48 05     17.5     ~ 130 0
18 NAME Andromeda XII G 00 47 27.0 +34 22 29     18.3     ~ 124 0
19 NAME Andromeda XIV G 00 51 35.0 +29 41 49     15.9     ~ 132 0
20 NAME Andromeda XIII G 00 51 51.0 +33 00 16     18.1     ~ 128 0
21 NAME Andromeda IX G 00 52 53.0 +43 11 45     16.3     ~ 176 1
22 NAME Pisces V G 00 59 29.8 +32 22 36     14.4     ~ 149 0
23 NAME Sculptor Dwarf Galaxy G 01 00 09.4 -33 42 32   9.79 8.6 8.81   ~ 1498 4
24 NAME Pisces I G 01 03 55.0 +21 53 06   16.18 14.3     ~ 404 0
25 NAME Andromeda X G 01 06 33.70 +44 48 15.8     16.6     ~ 125 1
26 NAME Andromeda V G 01 10 17.1 +47 37 41     15.3     ~ 215 0
27 NAME Andromeda XV G 01 14 18.7 +38 07 03     14.6     ~ 123 0
28 NAME Andromeda II G 01 16 29.8 +33 25 09     11.7     ~ 402 0
29 NAME Andromeda XXIV G 01 18 30.0 +46 21 58     16.3     ~ 64 0
30 NAME Andromeda XXII G 01 27 40.0 +28 05 25     18.0     ~ 95 0
31 NAME Andromeda XXIII G 01 29 21.8 +38 43 08     14.2     ~ 88 0
32 ACO 262 ClG 01 52 50.4 +36 08 46           ~ 727 1
33 NAME Segue 2 G 02 19 16.0 +20 10 31     15.2     ~ 299 0
34 MCG-06-07-001 G 02 39 59.3 -34 26 57   9.02 7.4     ~ 1894 1
35 NAME Hor I G 02 55 31.7 -54 07 08           ~ 169 0
36 NAME Andromeda XXXIII G 03 01 23.6 +40 59 18           ~ 43 0
37 NAME Reticulum II G 03 35 42.1 -54 02 57           ~ 375 0
38 ACO 3158 ClG 03 43 07.5 -53 38 09           ~ 327 0
39 ACO 496 ClG 04 33 40.8 -13 14 34           ~ 728 2
40 ESO 206-20A G 06 41 36.7 -50 57 58   22.14 11.0 19.47   ~ 1190 0
41 ACO 576 ClG 07 21 24.1 +55 44 20           ~ 312 1
42 NAME UMa II Galaxy G 08 51 30.0 +63 07 48     13.3     ~ 410 0
43 NAME Leo T G 09 34 53.4 +17 03 05     15.1     ~ 434 0
44 NAME Segue 1 G 10 07 03.2 +16 04 25     15.3     ~ 517 1
45 Z 64-73 G 10 08 28.12 +12 18 23.4   11.3 10.0     ~ 1284 1
46 NAME Sextans dSph LSB 10 13 02.9 -01 36 53   12 10.4     ~ 921 0
47 NAME UMa I Galaxy G 10 34 52.80 +51 55 12.0     14.4     ~ 355 1
48 NAME Willman 1 G 10 49 21.0 +51 03 00     15.2     ~ 345 0
49 Z 126-111 G 11 13 28.13 +22 09 10.1   12.9 12.0     ~ 899 0
50 NAME Leo V LSB 11 31 09.60 +02 13 12.0     16.0     ~ 234 0
51 NAME Leo IV LSB 11 32 57.0 -00 32 00     15.1     ~ 419 1
52 NAME Hydra II G 12 21 42.1 -31 59 07           ~ 118 0
53 NAME Coma Dwarf Galaxy G 12 26 59.0 +23 54 15     14.1     ~ 482 1
54 NAME CVn II dSph G 12 57 09.6 +34 19 12     16.1     ~ 287 2
55 NAME CVn I dSph G 13 28 03.5 +33 33 21     13.1     ~ 352 1
56 ACO 3571 ClG 13 47 32.4 -32 50 12           ~ 308 2
57 ACO 1795 ClG 13 48 47.4 +26 34 55           ~ 1330 0
58 NAME Bootes II G 13 58 00.0 +12 51 00     15.4     ~ 269 0
59 NAME Bootes Dwarf Spheroidal Galaxy G 14 00 00.0 +14 30 00     12.8     ~ 491 0
60 Z 318-18 G 15 09 08.0 +67 13 21   13.60 10.6     ~ 1459 0
61 ACO 2029 ClG 15 10 54.2 +05 44 23           ~ 1020 0
62 ACO 2142 ClG 15 58 26.5 +27 13 52           ~ 825 0
63 NAME Hercules Dwarf Galaxy G 16 31 02.0 +12 47 30     14.0     ~ 379 1
64 Z 300-12 G 17 20 14.335 +57 55 16.39   12.40 10.6     ~ 1428 1
65 NAME Andromeda XXVIII G 22 32 41.20 +31 12 58.2     15.6     ~ 88 0
66 NAME Tuc Galaxy G 22 41 49.6 -64 25 10   15.7 15.2     ~ 324 0
67 NAME Lacerta I G 22 58 16.3 +41 17 28           ~ 53 0
68 NAME Pisces II G 22 58 31.0 +05 57 09     16.3     ~ 283 0
69 ACO 2589 ClG 23 24 00.5 +16 49 29           ~ 327 1
70 NAME Andromeda VII GiG 23 26 31.0 +50 40 33   13.6 11.8     ~ 222 1
71 NAME Peg dSph GiG 23 51 46.3 +24 34 57   14.5 13.2     ~ 250 2
72 NAME Andromeda XXI G 23 54 47.7 +42 28 15     14.8     ~ 117 0
73 NAME Andromeda XXIX G 23 58 55.6 +30 45 20     16.0     ~ 61 0

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