Recovering the fundamental plane of galaxies by f(R)f(R) gravity

The fundamental plane (FP) of galaxies can be recovered in the framework of $f(R)$ gravity avoiding the issues related to dark matter to fit the observations. In particular, the power-law version $f(R)\propto R^n$, resulting from the existence of Noether symmetries for $f(R)$, is sufficient to implement the approach. In fact, relations between the FP parameters and the corrected Newtonian potential, coming from $R^n$, can be found and justified from a physical point of view. Specifically, we analyze the velocity distribution of elliptical galaxies and obtain that $r_c$, the scale-length depending on the gravitational system properties, is proportional to $r_e$, the galaxy effective radius. This fact points out that the gravitational corrections induced by $f(R)$ can lead photometry and dynamics of the system. Furthermore, the main byproduct of such an approach is that gravity could work in different ways depending on the scales of self-gravitating systems.Comment: 18 pages, 3 tables, 8 figures. Accepted for publication in Phys. Dark Univers

Addressing the missing matter problem in galaxies through a new fundamental gravitational radius

We demonstrate that the existence of a Noether symmetry in $f(R)$ theories of gravity gives rise to a further gravitational radius, besides the standard Schwarzschild one, determining the dynamics at galactic scales. By this feature, it is possible to explain the baryonic Tully-Fisher relation and the rotation curve of gas-rich galaxies without the dark matter hypothesis.Comment: 9 pages, 2 figures, to be published in JCA

Constraining Extended Gravity Models by S2 star orbits around the Galactic Centre

We investigate the possibility to explain theoretically the observed deviations of S2 star orbit around the Galactic Centre using gravitational potentials derived from modified gravity models in absence of dark matter. To this aim, an analytic fourth-order theory of gravity, non-minimally coupled with a massive scalar field is considered. Specifically, the interaction term is given by analytic functions $f(R)$ and $f(R,\phi)$ where $R$ is the Ricci scalar and $\phi$ is a scalar field whose meaning can be related to further gravitational degrees of freedom. We simulate the orbit of S2 star around the Galactic Centre in $f(R)$ (Yukawa-like) and $f(R,\phi)$ (Sanders-like) gravity potentials and compare it with NTT/VLT observations. Our simulations result in strong constraints on the range of gravity interaction. In the case of analytic functions $f(R)$, we are not able to obtain reliable constraints on the derivative constants $f_1$ and $f_2$, because the current observations of S2 star indicated that they may be highly mutually correlated. In the case of analytic functions $f(R,\phi)$, we are able to obtain reliable constraints on the derivative constants $f_0$, $f_R$, $f_{RR}$, $f_{\phi}$, $f_{\phi\phi}$ and $f_{\phi R}$. The approach we are proposing seems to be sufficiently reliable to constrain the modified gravity models from stellar orbits around Galactic Centre.Comment: 9 pages, 6 figure to appear in Phys. Rev.

Constraining the range of Yukawa gravity interaction from S2 star orbits

We consider possible signatures for Yukawa gravity within the Galactic Central Parsec, based on our analysis of the S2 star orbital precession around the massive compact dark object at the Galactic Centre, and on the comparisons between the simulated orbits in Yukawa gravity and two independent sets of observations. Our simulations resulted in strong constraints on the range of Yukawa interaction $\Lambda$ and showed that its most probable value in the case of S2 star is around 5000 - 7000 AU. At the same time, we were not able to obtain reliable constrains on the universal constant $\delta$ of Yukawa gravity, because the current observations of S2 star indicated that it may be highly correlated with parameter $\Lambda$ in the range $(0 <\delta < 1)$. For $\delta > 2$ they are not correlated. However, the same universal constant which was successfully applied to clusters of galaxies and rotation curves of spiral galaxies ($\delta=1/3$) also gives a satisfactory agreement with the observed orbital precession of the S2 star, and in that case the most probable value for the scale parameter is $\Lambda \approx 3000 \pm 1500$ AU. Also, the Yukawa gravity potential induces precession of S2 star orbit in the same direction as General Relativity for $\delta > 0$ and for $\delta < -1$, and in the opposite direction for $-1 <\delta < 0$. The future observations with advanced facilities, such as GRAVITY or/and European Extremely Large Telescope, are needed in order to verify these claims.Comment: 16 pages, 8 figures, accepted for publication in JCA

Constraints on RnR^n gravity from precession of orbits of S2-like stars

We study some possible observational signatures of $R^n$ gravity at Galactic scales and how these signatures could be used for constraining this type of $f(R)$ gravity. For that purpose, we performed two-body simulations in $R^n$ gravity potential and analyzed the obtained trajectories of S2-like stars around Galactic center, as well as resulting parameter space of $R^n$ gravity potential. Here, we discuss the constraints on the $R^n$ gravity which can be obtained from the observations of orbits of S2-like stars with the present and next generations of large telescopes. We make comparison between the theoretical results and observations. Our results show that the most probable value for the parameter $r_c$ in $R^n$ gravity potential in the case of S2-like stars is $\sim$100 AU, while the universal parameter $\beta$ is close to 0.01. Also, the $R^n$ gravity potential induces the precession of S2-like stars orbit in opposite direction with respect to General Relativity, therefore, such a behavior of orbits qualitatively is similar to a behavior of Newtonian orbits with a bulk distribution of matter (including a stellar cluster and dark matter distributions).Comment: 12 pages, 12 figures, accepted in Phys. Rev.

Controlling the onset of turbulence by streamwise traveling waves. Part 2. Direct numerical simulations

This work builds on and confirms the theoretical findings of Part 1 of this paper, Moarref & Jovanovi\'c (2010). We use direct numerical simulations of the Navier-Stokes equations to assess the efficacy of blowing and suction in the form of streamwise traveling waves for controlling the onset of turbulence in a channel flow. We highlight the effects of the modified base flow on the dynamics of velocity fluctuations and net power balance. Our simulations verify the theoretical predictions of Part 1 that the upstream traveling waves promote turbulence even when the uncontrolled flow stays laminar. On the other hand, the downstream traveling waves with parameters selected in Part 1 are capable of reducing the fluctuations' kinetic energy, thereby maintaining the laminar flow. In flows driven by a fixed pressure gradient, a positive net efficiency as large as 25 % relative to the uncontrolled turbulent flow can be achieved with downstream waves. Furthermore, we show that these waves can also relaminarize fully developed turbulent flows at low Reynolds numbers. We conclude that the theory developed in Part 1 for the linearized flow equations with uncertainty has considerable ability to predict full-scale phenomena.Comment: To appear in J. Fluid Mec

Line shifts in accretion disks - the case of Fe Kα\alpha

Here we present a short overview and main results of our investigations of several effects which can induce shifts in the broad Fe K$\alpha$ line emitted from relativistic accretion disks around single and binary supermassive black holes. We used numerical simulations based on ray-tracing method in the Kerr metric to study the role of classical Doppler shift, special relativistic transverse Doppler shift and Doppler beaming, general relativistic gravitational redshift, and perturbations of the disk emissivity in the formation of the observed Fe K$\alpha$ line profiles. Besides, we also investigated whether the observed line profiles from the binary systems of supermassive black holes could be affected by the Doppler shifts due to dynamics of such systems. The presented results demonstrate that all these effects could have a significant influence on the observed profiles of the broad Fe K$\alpha$ line emitted from relativistic accretion disks around single and binary supermassive black holes.Comment: 9 pages, 5 figures, 1 table. Accepted for publication in Astrophysics and Space Scienc

Constraints on RnR^n gravity from precession of orbits of S2-like stars: a case of a bulk distribution of mass

Here we investigate possible applications of observed stellar orbits around Galactic Center for constraining the R$^n$ gravity at Galactic scales. For that purpose, we simulated orbits of S2-like stars around the massive black hole at Galactic Center, and study the constraints on the R$^n$ gravity which could be obtained by the present and next generations of large telescopes. Our results show that R$^n$ gravity affects the simulated orbits in the qualitatively similar way as a bulk distribution of matter (including a stellar cluster and dark matter distributions) in Newton's gravity. In the cases where the density of extended mass is higher, the maximum allowed value of parameter $\beta$ in R$^n$ gravity is noticeably smaller, due to the fact that the both extended mass and $R^n$ gravity cause the retrograde orbital precession.Comment: 10 pages, 4 figures, accepted for publication in Advances in Space Researc

Masses and Mixing of cqqˉqˉc q \bar{q} \bar{q} Tetraquarks Using Glozman-Riska Hyperfine Interaction

In this paper we perform a detailed study of the masses and mixing of the single charmed scalar tetraquarks: $c q \bar{q} \bar{q}$. We also give a systematic analysis of these tetraquark states by weight diagrams, quantum numbers and flavor wave functions. Tetraquark masses are calculated using four different fits. The following SU(3)$_\mathrm{F}$ representations are discussed: $\bar{15}_\mathrm{S}$, $\bar{3}_\mathrm{S}$, $6_\mathrm{A}$ and $\bar{3}_\mathrm{A}$. We use the flavor-spin Glozman-Riska interaction Hamiltonian with SU(3) flavor symmetry breaking. There are 27 different tetraquarks composed of a charm quark $c$ and of the three light flavors $u, d, s$: 11 cryptoexotic (3 D$_\mathrm{s}^{+}$, 4 D$^{+}$, 4 D$^{0}$) and 16 explicit exotic states. We discuss D$_\mathrm{s}$ and its isospin partners in the same multiplet, as well as all the other four-quark states. Some explicit exotic states appear in the spectrum with the same masses as D$_\mathrm{s}^{+}$(2632) in $\bar{15}_\mathrm{S}$ and with the same masses as D$_\mathrm{s}^{+}$(2317) in $6_\mathrm{A}$ representation, which confirm the tetraquark nature of these states.Comment: 10 pages, 6 tables, 6 figures. Accepted for publication in Phys. Rev.

Masses of constituent quarks confined in open bottom hadrons

We apply color-spin and flavor-spin quark-quark interactions to the meson and baryon constituent quarks, and calculate constituent quark masses, as well as the coupling constants of these interactions. The main goal of this paper was to determine constituent quark masses from light and open bottom hadron masses, using the fitting method we have developed and clustering of hadron groups. We use color-spin Fermi-Breit (FB) and flavor-spin Glozman-Riska (GR) hyperfine interaction (HFI) to determine constituent quark masses (especially $b$ quark mass). Another aim was to discern between the FB and GR HFI because our previous findings had indicated that both interactions were satisfactory. Our improved fitting procedure of constituent quark masses showed that on average color-spin (Fermi-Breit) hyperfine interaction yields better fits. The method also shows the way how the constituent quark masses and the strength of the interaction constants appear in different hadron environments.Comment: 15 pages, 6 tables, 1 figure. Accepted for publication in Mod. Phys. Lett.