Low-acceleration space-time scale invariant dynamics (SID, Milgrom 2009a) predicts two fundamental correlations known from observational galactic dynamics: the baryonic Tully-Fisher relation (BTFR) and a correlation between the observed mass discrepa
ncy and acceleration (MDA) in the low acceleration regime for disc galaxies. SID corresponds to the deep MOdified Newtonian Dynamics (MOND) limit. The MDA data emerging in cold/warm dark matter (C/WDM) cosmological simulations disagree significantly with the tight MDA correlation of the observed galaxies. Therefore, the most modern simulated disc galaxies, which are delicately selected to have a quiet merging history in a standard dark-matter-cosmological model, still do not represent the correct rotation curves. Also, the observed tight correlation contradicts the postulated stochastic formation of galaxies in low-mass DM halos. Moreover, we find that SID predicts a baryonic to apparent virial halo (dark matter) mass relation which agrees well with the correlation deduced observationally assuming Newtonian dynamics to be valid, while the baryonic to halo mass relation predicted from CDM models does not. The distribution of the observed ratios of dark-matter halo masses to baryonic masses may be empirical evidence for the external field effect, which is predicted in SID as a consequence of the forces acting between two galaxies depending on the position and mass of a third galaxy. Applying the external field effect, we predict the masses of galaxies in the proximity of the dwarf galaxies in the Miller et al. sample. Classical non-relativistic gravitational dynamics is thus best described as being Milgromian, rather than Newtonian.
(Abridged) The existence of exotic dark matter particles outside the standard model of particle physics constitutes a central hypothesis of the current standard model of cosmology (SMoC). Using a wide range of observational data I outline why this hy
pothesis cannot be correct for the real Universe. Assuming the SMoC to hold, (i) the two types of dwarf galaxies, the primordial dwarfs with dark matter and the tidal dwarf galaxies without dark matter, ought to present clear observational differences. But there is no observational evidence for two separate families of dwarfs, neither in terms of their location relative to the baryonic Tully-Fisher relation nor in terms of their radius--mass relation. And, the arrangements in rotating disk-of-satellites, in particular around the Milky Way and Andromeda, has been found to be only consistent with most if not all dwarf satellite galaxies being tidal dwarf galaxies. The highly symmetric structure of the entire Local Group too is inconsistent with its galaxies stemming from a stochastic merger-driven hierarchical buildup over cosmic time. (ii) Dynamical friction on the expansive and massive dark matter halos is not evident in the data. Taking the various lines of evidence together, the hypothesis that dynamically relevant exotic dark matter exists needs to be firmly rejected.
We construct an idealized universe for didactic purposes. This universe is assumed to consist of absolute Euclidean space and to be filled with a classical medium which allows for sound waves. A known solution to the wave equation describing the dyna
mics of the medium is a standing spherical wave. Although this is a problem of classical mechanics, we demonstrate that the Lorentz transformation is required to generate a moving solution from the stationary one. Both solutions are here collectively referred to as spherons. These spherons exhibit properties which have analogues in the physical description of matter with rest mass, among them de Broglie like phase waves and at the same time relativistic effects such as contraction and a speed limit. This leads to a theory of special relativity by assuming the point of view of an observer made of such spheronic matter. The argument made here may thus be useful as a visualisation or didactic approach to the real universe, in which matter has wave-like properties and obeys the laws of special relativity.
It has been claimed in the recent literature that a non-trivial relation between the mass of the most-massive star, mmax, in a star cluster and its embedded star cluster mass (the mmax-Mecl relation) is falsified by observations of the most-massive s
tars and the Halpha luminosity of young star clusters in the starburst dwarf galaxy NGC 4214. Here it is shown by comparing the NGC 4214 results with observations from the Milky Way that NGC 4214 agrees very well with the predictions of the the mmax-Mecl relation and the integrated galactic stellar initial mass function (IGIMF) theory and that this difference in conclusions is based on a high degree of degeneracy between expectations from random sampling and those from the mmax-Mecl relation, but are also due to interpreting mmax as a truncation mass in a randomly sampled IMF. Additional analysis of galaxies with lower SFRs than those currently presented in the literature will be required to break this degeneracy.
It is widely accepted that the distribution function of the masses of young star clusters is universal and can be purely interpreted as a probability density distribution function with a constant upper mass limit. As a result of this picture the mass
es of the most-massive objects are exclusively determined by the size of the sample. Here we show, with very high confidence, that the masses of the most-massive young star clusters in M33 decrease with increasing galactocentric radius in contradiction to the expectations from a model of a randomly sampled constant cluster mass function with a constant upper mass limit. Pure stochastic star formation is thereby ruled out. We use this example to elucidate how naive analysis of data can lead to unphysical conclusions.
Observational studies are showing that the galaxy-wide stellar initial mass function are top-heavy in galaxies with high star-formation rates (SFRs). Calculating the integrated galactic stellar initial mass function (IGIMF) as a function of the SFR o
f a galaxy, it follows that galaxies which have or which formed with SFRs > 10 Msol yr^-1 would have a top-heavy IGIMF in excellent consistency with the observations. Consequently and in agreement with observations, elliptical galaxies would have higher M/L ratios as a result of the overabundance of stellar remnants compared to a stellar population that formed with an invariant canonical stellar initial mass function (IMF). For the Milky Way, the IGIMF yields very good agreement with the disk- and the bulge-IMF determinations. Our conclusions are that purely stochastic descriptions of star formation on the scales of a pc and above are falsified. Instead, star formation follows the laws, stated here as axioms, which define the IGIMF theory. We also find evidence that the power-law index beta of the embedded cluster mass function decreases with increasing SFR. We propose further tests of the IGIMF theory through counting massive stars in dwarf galaxies.
Previous studies of globular cluster (GC) systems show that there appears to be a universal specific GC formation efficiency $eta$ which relates the total mass of GCs to the virial mass of host dark matter halos, $M_{vir}$ (Georgiev et al 2010, Spitl
er & Forbes2009). In this paper, the specific frequency, $S_N$, and specific GC formation efficiency, $eta$, are derived as functions of $M_{vir}$ in Milgromian dynamics, i.e., in modified Newtonian dynamics (MOND). In Milgromian dynamics, for the galaxies with GCs, the mass of the GC system, $M_{GC}$, is a two-component function of $M_{vir}$ instead of a simple linear relation. An observer in a Milgromian universe, who interprets this universe as being Newtonian/Einsteinian, will incorrectly infer a universal constant fraction between the mass of the GC system and a (false) dark matter halo of the baryonic galaxy. In contrast to a universal constant of $eta$, in a Milgromian universe, for galaxies with $M_{vir} <= 10^{12}msun$, $eta$ decreases with the increase of $M_{vir}$, while for massive galaxies with $M_{vir}>10^{12}msun$, $eta$ increases with the increase of $M_{vir}$.
We introduce a new method to measure the dispersion of mmax values of star clusters and show that the observed sample of mmax is inconsistent with random sampling from an universal stellar initial mass function (IMF) at a 99.9% confidence level. The
scatter seen in the mmax-Mecl data can be mainly (76%) understood as being the result of observational uncertainties only. The scatter of mmax values at a given Mecl are consistent with mostly measurement uncertainties such that the true (physical) scatter may be very small. Additionally, new data on the local star-formation regions Taurus-Auriga and L1641 in Orion make stochastically formed stellar populations rather unlikely. The data are however consistent with the local IGIMF (integrated galactic stellar initial mass function) theory according to which a stellar population is a sum of individual star-forming events each of which is described by well defined physical laws. Randomly sampled IMFs and henceforth scale-free star formation seems to be in contradiction to observed reality.
Cosmological models that invoke warm or cold dark matter can not explain observed regularities in the properties of dwarf galaxies, their highly anisotropic spatial distributions, nor the correlation between observed mass discrepancies and accelerati
on. These problems with the standard model of cosmology have deep implications, in particular in combination with the observation that the data are excellently described by Modified Newtonian Dynamics (MOND). MOND is a classical dynamics theory which explains the mass discrepancies in galactic systems, and in the universe at large, without invoking dark entities. MOND introduces a new universal constant of nature with the dimensions of acceleration, a0, such that the pre-MONDian dynamics is valid for accelerations a >> a0, and the deep MONDian regime is obtained for a << a0, where space-time scale invariance is invoked. Remaining challenges for MOND are (i) explaining fully the observed mass discrepancies in galaxy clusters, and (ii) the development of a relativistic theory of MOND that will satisfactorily account for cosmology. The universal constant a0 turns out to have an intriguing connection with cosmology: bar a0 == 2 pi a0 approx c H_0 approx c^2(Lambda/3)^{1/2}. This may point to a deep connection between cosmology and internal dynamics of local systems.
The current knowledge on the stellar IMF is documented. It appears to become top-heavy when the star-formation rate density surpasses about 0.1Msun/(yr pc^3) on a pc scale and it may become increasingly bottom-heavy with increasing metallicity and in
increasingly massive early-type galaxies. It declines quite steeply below about 0.07Msun with brown dwarfs (BDs) and very low mass stars having their own IMF. The most massive star of mass mmax formed in an embedded cluster with stellar mass Mecl correlates strongly with Mecl being a result of gravitation-driven but resource-limited growth and fragmentation induced starvation. There is no convincing evidence whatsoever that massive stars do form in isolation. Various methods of discretising a stellar population are introduced: optimal sampling leads to a mass distribution that perfectly represents the exact form of the desired IMF and the mmax-to-Mecl relation, while random sampling results in statistical variations of the shape of the IMF. The observed mmax-to-Mecl correlation and the small spread of IMF power-law indices together suggest that optimally sampling the IMF may be the more realistic description of star formation than random sampling from a universal IMF with a constant upper mass limit. Composite populations on galaxy scales, which are formed from many pc scale star formation events, need to be described by the integrated galactic IMF. This IGIMF varies systematically from top-light to top-heavy in dependence of galaxy type and star formation rate, with dramatic implications for theories of galaxy formation and evolution.
