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4. Discussion: Astrophysical Implications
4. Discussion: Astrophysical Implications
The inclusion of an additional term in the Law of Gravitation, at scales larger than tens of parsecs, involves the analysis and discussion of a plethora of astrophysical problems such as Angular Diameter Distance Distributions (4.1), The Virial Theorem (4.2), the Kepler's third law in globular clusters and rotation curves (4.3), the Arp controversy and gravitational redshift (4.4), the Jean length and mass (4.5), the gravitational lensings (4.6), the BAO and CMB-anisotropies (4.7) and the Pioneer anomaly (4.8). In each of them, observable predictions are made that will allow the proposed model to be verified and/or the solution to important and controversial questions in current astrophysics is shown.
Figure 6: Angular diameter distance in function of the redshift for different set of cosmological parameter. (Falcon 2021)
4.1 Angular Diameter distance
4.1 Angular Diameter distance
The mass and size of a galaxy (or general overdensity) is often defined in terms of the "virial mass" and "virial radius" the mass of a galaxy is often inferred by measuring the rotation velocity of its gas and stars, assuming circular Keplerian orbits. Using the virial theorem, the dispersion velocity σ can be used in a similar way.
4.2 The Virial Theorem
4.2 The Virial Theorem
Figure 7: Expected deviation of Kepler's third law in globular Clusters as function of the comoving distance to the Milky Way center. (Falcon 2021)
Figure 8 Relative intensity of the Force due to Yukawa's field as a function of comoving distance, in the 10-100 kpc range, for interstellar scale (left), and in the 1-10 Mpc range, for intra clusters of galaxies (right).(Falcon 2021)
4.3 Kepler’s third law in globular clusters and rotations curves
4.3 Kepler’s third law in globular clusters and rotations curves
The term of the Newtonian potential is greater than the term due to UYF for ranges less than 21.8 kpc, from which the latter becomes greater, as indicated in figure 4. In the Harrys Catalog (2010) there is at least a 10% of globular clusters with distances greater than the indicated limit value. Note that the dynamic relationship (54) and Fig. 7 can also be used to reinterpret the rotation curves of the MoND-Milgrom theories (Falcon 2013; Milgrom 1983) where the velocity dispersion increases monotonically with radial distance instead of the Keplerian behavior predicted by the inverse law of the square of the distance. In Fig. 8 (left), the comparison between Newtonian forces and that associated to the UYF term is shown on a logarithmic scale, for interstellar distance ranges. Both forces would be comparable in the 15-40 kpc intervals, being able to explain the missing mass in the rotation curves. In the range of distances greater than 50 kpc the Newtonian force is negligible compared to the inertia caused by the large-scale distribution of matter caused by the FIY force. On the other hand, in much greater distance ranges, for example for the interior of galaxy clusters, the force is proportional to the inverse of the comoving distance , as shown in Fig. 8 (right). The Newtonian force is thirty orders of magnitude smaller than FIY on this scale. The null value of FIY at r = 10Mpc is in agreement with the previous discussion about the graviton's rest mass (section 2). As said before, at cosmological distance scales the FIY force is repulsive and manifests itself as the cosmic acceleration (Dark Energy). In ranges of comoving distances, FIY is negligible and the gravitational force is prescribed by the law of the inverse square of the distance (Newtonian gravitation).
4.4 Arp Controversy and Gravitational redshift.
4.4 Arp Controversy and Gravitational redshift.
Beyond 10 Mpc the gravitational redshift remains constant in accordance with the previous assumption of the massive graviton. Then the maximum additional contribution (58) of the UYF to the redshift gravitational is 7.83 (x ≥10 Mpc) and zg increases by a factor until 88.3. This result is interesting to understand the problem of AGN at High-redshift and the nature of Quasars. Also in fig 6 (right), the variation (in logarithmic scale) of the gravitational redshift for different objects as a function of distance is shown, in particular the observation of White Dwarf's in the interior of the globular clusters could be a test for UYF . The extreme cases of high redshift are the SBH in center of galaxies, with event horizon of the order of a light-year and masses in order of the core-mass in M87 (Event Horizon Telescope Collaboration 2019). The figure 109 show the Gravitational redshift for compact objects, note that that in distance ranges of the order of one third of the range of gravity the gravitational redshift remains constant for any compact object considered, therefore, the observation of these objects outside the local group of galaxies will allow the cosmological redshifts to be calibrated. Observe that second term in (58) increase the Gravitational redshift until 7.83 and would help understand the problem of AGN at High-redshift and the nature of Quasars. An important result in (28) is that two galaxies an equal distance could be present redshift different, thus it´s solvent the Arp’s controversy (Arp, 2003).
Figure 9. Gravitational redshift vs. comoving distances, in compact objects. (own source).
Stephan's Quintet, by sample, is a visual grouping of five galaxies in the constellation Pegasus, with Redshifts Controversies: NGC 7320 indicates a small redshift (790 km/s) while the other four exhibit large redshifts (near 6,600 km/s).
4.5 Longitude and Mass of Jean
4.5 Longitude and Mass of Jean
In the formalism of the gravitational collapse of protogalactic clouds , the temporal evolution is considered through the gravitational amplification of density perturbation, that depend critically of the time needed for gravitational free-fall collapse (tg) in compared with the travel-time of acoustic waves (tS). The Jean’s length (lJ0) is the characteristic length for which pressure balances gravity; which in term of the density (r), temperature (Te) and hydrogen mass (mH) is (Jeans 1928):
Consider a uniform self-gravitating mass, with electronic temperature and effective density, constants. In the Newtonian Gravitation approach, the Jeans length (λ_J^0) remains constant for all r and therefore agglutination and / or fragmentation will be homogeneous. Figure 11 shows that, when considering a large-scale modification of Newtonian gravitation, through the potential UYF, the effective Jeans length (λJ) decreases for the mega parsec range, reaching a minimum of approximately half the Abell radius favoring the agglutination. The reason for this is that the gravitational potential now exerts a stress on the gas, between the center (where the term Newtonian r-2 dominates) and the periphery (where the term of the force due to UYF dominates) whose maximum is in order of Abell: 1.2 Mpc. As the Jeans Masses, is proportional to the cube of Jeans longitude, would be decrease very much. The Jeans mass is the critical mass above which gravity dominates, so if the Jeans Mass decreases then the gravity dominates, and so a perturbation will collapse even further when compressed, leading to run-away collapse in range of comoving distance of the megaparsec. We observe in Fig. 11 that the modification of the Newtonian gravitation on a large scale does not affect the Jeans length in ranges of comoving distance less than 100 kpc, even for densities as low as that of the intergalactic medium. Increasing the density of the number of particles tends to smooth the difference between the Jeans lengths with and without the large-scale correction for Newtonian gravity. For low densities, such as those in the intergalactic medium, the difference between the two models for Jean's length is significant. Being of the order of 40% less than lJ0 in the distance ranges of (0.5 to 2) Mpc, which coincides with the agglutination of hot gas observed in X-rays in galaxy clusters. In the previous discussion the free fall time is used, therefore it is implicitly assumed that the protostellar or protogalactic cloud has dimensions of the order of r in the gravitational potential (both in Newtonian and in UIY). Both lengths coincide when x << 1 Mpc, so no changes are expected in the fragmentation of protoplanetary or protostellar molecular clouds, for which r << 1kpc. However, the inclusion of UIY does modify, as seen in figure 11, the fragmentation of protogalactic clouds; according to the initial phenomenological description (figure 2) where the dynamics is prescribed differently for the different length scales
Instability in a cloud of gas in space due to fluctuations in the density of the gas, causing the matter in the cloud to clump together and lead to gravitational collapse. The Jeans mass is the mass that a spherical cloud of gas must have in order to contract under its own weight.. Jeans' length is the critical radius of a cloud where thermal energy, which causes the cloud to expand, is counteracted by gravity, which causes the cloud to collapse.
Fig.10. Jean's length corrected for potential UYF vs comoving distance in scale of the clusters of galaxies, for several number density (Falcon 2021).
4.6 Gravitational Lensing
4.6 Gravitational Lensing
The matter, through the bending of space in its gravitational field, alters the direction of light passing nearby. The effect is analogous to that produced by a lens.A gravitational lens is a distribution of matter (such as a cluster of galaxies) between a distant light source and an observer that is capable of bending the light from the source as the light travels toward the observer.Strong gravitational lensing can actually result in such strongly bent light that multiple images of the light-emitting galaxy are formed. Weak gravitational lensing results in galaxies appearing distorted, stretched or magnified.
4.7 BAO and CMB anisotropies
4.7 BAO and CMB anisotropies
The anisotropy of the cosmic microwave background (CMB) consists of the small temperature fluctuations in the blackbody radiation left over from the Big Bang. The average temperature of this radiation is 2.725 K as measured by the COBE satellite. The CMB anisotropies are the result from inhomogeneities in the distribution of matter at the epoch of recombination.
Baryonic acoustic oscillations (BAO) are fluctuations in the density of the visible baryonic matter (normal matter) of the universe, caused by acoustic density waves, before the decoupling of matter and radiation, where the perturbation of baryonic matter propagated as a wave. BAO are the result of a competition between gravitational potentials, which group the baryons, and Compton scattering between baryons and photons which causes a pressure that dissipates the baryonic matter. BAO can be considered as a damped harmonic oscillator forced . •Thus, baryonic matter propagates as a pressure wave on the photon-baryon fluid , emulating the propagation of a sound wave.
Radio-metric Doppler tracking data received from the Pioneer 10 and 11 spacecraft from heliocentric distances of 20 – 70 AU has consistently indicated the presence of a small, anomalous, blue-shifted frequency drift uniformly changing with a rate of 6 × 10–9 Hz/s. Ultimately, the drift was interpreted as a constant sunward deceleration of each particular spacecraft at the level of aP = (8.74 ± 1.33) × 10–10 m/s2. This apparent violation of the Newton’s gravitational inverse-square law has become known as
4.8 Pioneer Anomaly
4.8 Pioneer Anomaly
Another interesting controversy in recent years is that concerning to anomalous acceleration from de Pioneer 10/11 spacecraft when traveling through the outer reaches of the solar system. Indicated the presence of a drift of Doppler frequency, in blue-shift , small and anomalous, interpreted as a sunward acceleration of ap =(8.74±1.33)×10 10 m/s^2 (Anderson et al 1998, 2002). This signal has become known as the Pioneer anomaly; the nature of this anomaly is still being investigated (Toth 2009, Olsen 2007). Another possible interpretation of the Pioneer anomaly is to consider the bigravity, For example, if in addition Newtonian gravity, there is a counterpart of the UYF , as in (3) and U_0(M) , as before (section 2.1). Using (5) by average distance between 20 to 70 UA, i.e. , thus
We obtain ap ≈7.6 10-10 m/s2 in order of ap =(8.74±1.33)×10 10 m/s2 (Anderson et al 2002). This is certainly a very crude approximation but it`s easy to see in figure 2 that in the range of 20 to 40 UA the UYF varies very slowly and therefore its contribution to the acceleration is almost constant in this range of distance (very small compared with r0).
4.9 Merging of Galaxies
4.9 Merging of Galaxies
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