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J. W. Moffat - One of the best experts on this subject based on the ideXlab platform.
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Rotational velocity Curves in the milky way as a test of modified gravity
Physical Review D, 2015Co-Authors: J. W. Moffat, Viktor T TothAbstract:Galaxy Rotation Curves determined observationally out to a radius well beyond the Galaxy cores can provide a critical test of modified gravity models without dark matter. The predicted Rotational velocity curve obtained from scalar-vector-tensor gravity is in excellent agreement with data for the Milky Way without a dark matter halo, with a mass of $5\ifmmode\times\else\texttimes\fi{}1{0}^{10}{M}_{\ensuremath{\bigodot}}$. The velocity Rotation curve predicted by modified Newtonian dynamics does not agree with the data.
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the mog weak field approximation and observational test of Galaxy Rotation Curves
Monthly Notices of the Royal Astronomical Society, 2013Co-Authors: J. W. Moffat, S RahvarAbstract:As an alternative to dark matter models, MOdified Gravity (MOG) theory can compensate for dark matter by a covariant modification of Einstein gravity. The theory introduces two additional scalar fields and one vector field. The aim is to explain the dynamics of astronomical systems based only on their baryonic matter. The effect of the vector field in the theory resembles a Lorentz force where each mass has a charge proportional to the inertial mass. In this work, we obtain the weak field approximation of MOG by perturbing the metric and the fields around Minkowski space-time. We derive an effective gravitational potential which yields the Newtonian attractive force plus a repulsive Yukawa force. This potential, in addition to the Newtonian gravitational constant, $G_N$, has two additional constant parameters $\alpha$ and $\mu$. We use the THINGS catalog of galaxies and fix the two parameters $\alpha$ and $\mu$ of the theory to be $\alpha =8.89 \pm 0.34$ and $\mu =0.04 \pm 0.004 {\rm kpc}^{-1}$. We then apply the effective potential with the fixed universal parameters to the Ursa-Major catalog of galaxies and obtain good fits to Galaxy Rotation curve data with an average value of $\bar{\chi^2} = 1.07 $. In the fitting process, only the stellar mass-to-light ratio $(M/L)$ of the galaxies is a free parameter. As predictions of MOG, our derived $M/L$ is shown to be correlated with the color of galaxies, and we fit the Tully-Fisher relation for galaxies. As an alternative to dark matter, introducing an effective weak field potential for MOG opens a new window to the astrophysical applications of the theory.
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scalar tensor vector gravity theory
Journal of Cosmology and Astroparticle Physics, 2006Co-Authors: J. W. MoffatAbstract:A covariant scalar–tensor–vector gravity theory is developed which allows the gravitational constant G, a vector field coupling ω and the vector field mass μ to vary with space and time. The equations of motion for a test particle lead to a modified gravitational acceleration law that can fit Galaxy Rotation Curves and cluster data without non-baryonic dark matter. The theory is consistent with solar system observational tests. The linear evolutions of the metric, vector field and scalar field perturbations and their consequences for the observations of the cosmic microwave background are investigated.
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Galaxy Rotation Curves without nonbaryonic dark matter
The Astrophysical Journal, 2006Co-Authors: Joel R Brownstein, J. W. MoffatAbstract:We apply the modified acceleration law obtained from Einstein gravity coupled to a massive skew-symmetric field Fμνλ to the problem of explaining Galaxy Rotation Curves without exotic dark matter. Our sample of galaxies includes low surface brightness (LSB) and high surface brightness (HSB) galaxies and an elliptical Galaxy. In those cases for which photometric data are available, a best fit via the single parameter (M/L)stars to the luminosity of the gaseous (H I plus He) and luminous stellar disks is obtained. In addition, a best fit to the Rotation Curves of galaxies is obtained in terms of a parametric mass distribution (independent of luminosity observations)—a two-parameter fit to the total galactic mass (or mass-to-light ratio M/L) and a core radius associated with a model of the Galaxy cores—using a nonlinear least-squares fitting routine including estimated errors. The fits are compared to those obtained using Milgrom's phenomenological MOND model and to the predictions of the Newtonian/Kepler acceleration law.
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Galaxy Rotation Curves without non baryonic dark matter
arXiv: Astrophysics, 2005Co-Authors: Joel R Brownstein, J. W. MoffatAbstract:We apply the modified acceleration law obtained from Einstein gravity coupled explaining Galaxy Rotation Curves without exotic dark matter. Our sample of galaxies includes low surface brightness (LSB) and high surface brightness (HSB) galaxies, and an elliptical Galaxy. In those cases where photometric data are available, a best fit via the single parameter (M/L)_{stars} to the luminosity of the gaseous (HI plus He) and luminous stellar disks is obtained. Additionally, a best fit to the Rotation Curves of galaxies is obtained in terms of a parametric mass distribution (independent of luminosity observations) -- a two parameter fit to the total galactic mass, (or mass-to-light ratio M/L), and a core radius associated with a model of the Galaxy cores using a nonlinear least-squares fitting routine including estimated errors. The fits are compared to those obtained using Milgrom's phenomenological MOND model and to the predictions of the Newtonian-Kepler acceleration law.
T P Singh - One of the best experts on this subject based on the ideXlab platform.
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Galaxy Rotation Curves from a fourth order gravity
Journal of Physics: Conference Series, 2014Co-Authors: P. Mishra, T P SinghAbstract:While the standard and most popular explanation for the flatness of Galaxy Rotation Curves is dark matter, one cannot at this stage rule out an explanation based on a modified law of gravitation, which agrees with Newtonian gravitation on the scale of the Solar system, but differs from it on larger length scales. Examples include Modfied Newtonian Dynamics (MOND) and Scalar-Tensor-Vector Gravity (STVG). Here, we have reported on a fourth order modification of the Poisson equation, which yields the same Yukawa type modification of Newtonian gravity as STVG, and which can explain flat Galaxy Rotation Curves for a large sample of galaxies, once specific values for two parameters have been chosen. We have speculated on two possible origins for this modified Poisson equation: First, a possible fourth order modification of general relativity, and second, quadrupole gravitational polarization induced on a Galaxy because of the pull of neighbouring galaxies.
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Galaxy Rotation Curves from a fourth order gravity
Journal of Physics: Conference Series, 2014Co-Authors: P. Mishra, T P SinghAbstract:While the standard and most popular explanation for the flatness of Galaxy Rotation Curves is dark matter, one cannot at this stage rule out an explanation based on a modified law of gravitation, which agrees with Newtonian gravitation on the scale of the solar system, but differs from it on larger length scales. Examples include Modfied Newtonian Dynamics [MOND] and Scalar-Tensor-Vector Gravity [STVG]. Here we report on a fourth order modification of the Poisson equation which yields the same Yukawa type modification of Newtonian gravity as STVG, and which can explain flat Galaxy Rotation Curves for a large sample of galaxies, once specific values for two parameters have been chosen. We speculate on two possible origins for this modified Poisson equation: first, a possible fourth order modification of general relativity, and second, quadrupole gravitational polarization induced on a Galaxy because of the pull of neighbouring galaxies.
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fourth order gravity scalar tensor vector gravity and Galaxy Rotation Curves
Physical Review D, 2013Co-Authors: P. Mishra, T P SinghAbstract:The Lambda-CDM model is the best fit to cosmological data, and to the observed galactic Rotation Curves. However, in the absence of a direct detection of dark matter one should explore theories such as MOND, and perhaps also modified gravity theories like fourth order gravity and Scalar-Tensor-Vector Gravity [STVG] as possible explanations for the non-Keplerian behaviour of Galaxy Rotation Curves. STVG has a modified law for gravitational acceleration which attempts to fit data by fixing two free parameters. We show that, remarkably, the biharmonic equation which we get in the weak field limit of the field equations in a fourth order gravity theory implies a modification of Newtonian acceleration which is precisely of the same repulsive Yukawa form as in the STVG theory, and the corrections could in principle be large enough to try and explain the observed Rotation Curves. We also explain how our model provides a first principles understanding of MOND. We also show that STVG and fourth order gravity predict an acceleration parameter $a_0$ whose value is of the same order as in MOND.
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modified gravity as a common cause for cosmic acceleration and flat Galaxy Rotation Curves
arXiv: General Relativity and Quantum Cosmology, 2012Co-Authors: P. Mishra, T P SinghAbstract:Flat Galaxy Rotation Curves and the accelerating Universe both imply the existence of a critical acceleration, which is of the same order of magnitude in both the cases, in spite of the galactic and cosmic length scales being vastly different. Yet, it is customary to explain galactic acceleration by invoking gravitationally bound dark matter, and cosmic acceleration by invoking a `repulsive` dark energy. Instead, might it not be the case that the flatness of Rotation Curves and the acceleration of the Universe have a common cause? In this essay we propose a modified theory of gravity. By applying the theory on galactic scales we demonstrate flat Rotation Curves without dark matter, and by applying it on cosmological scales we demonstrate cosmic acceleration without dark energy.
Alefe O F De Almeida - One of the best experts on this subject based on the ideXlab platform.
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Galaxy Rotation Curves in modified gravity models
Journal of Cosmology and Astroparticle Physics, 2018Co-Authors: Alefe O F De Almeida, Luca Amendola, Viviana NiroAbstract:In this work, we investigate the possibility that the Galaxy Rotation Curves can be explained in the framework of modified gravity models that introduce a Yukawa term in the gravitational potential. We include dark matter and assume that the fifth-force couples differently to dark matter and to baryons. We aim at constraining the modified gravity parameters β and λ, that is, the strength and the range of the Yukawa fifth force, respectively, using a set of 40 Galaxy Rotation Curves data from the SPARC catalogue. We include baryonic gas, disk and bulge components, along with a NFW halo of dark matter. Each Galaxy Rotation curve is modeled with three free parameters, beside the two global Yukawa parameter. We find that the inclusion of the Yukawa term improves the χ2 from 680.75 to 536.23 for 655 degrees of freedom. As global best-fit we obtain β = 0.34±0.04 and λ = 5.61±0.91kpc and a dark matter content on average 20% smaller than without the Yukawa term. The Bayesian evidence in favor of a NFW profile plus Yukawa term is higher than 8σ with respect to the standard gravity parametrization.
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Galaxy Rotation Curves in modified gravity models
arXiv: Astrophysics of Galaxies, 2018Co-Authors: Alefe O F De Almeida, Luca Amendola, Viviana NiroAbstract:In this work, we investigate the possibility that the Galaxy Rotation Curves can be explained in the framework of modified gravity models that introduce a Yukawa term in the gravitational potential. We include dark matter and assume that the fifth-force couples differently to dark matter and to baryons. We aim at constraining the modified gravity parameters $\beta$ and $\lambda$, that is, the strength and the range of the Yukawa fifth force, respectively, using a set of 40 Galaxy Rotation Curves data from the SPARC catalogue. We include baryonic gas, disk and bulge components, along with a NFW halo of dark matter. Each Galaxy Rotation curve is modeled with three free parameters, beside the two global Yukawa parameter. We find that the inclusion of the Yukawa term improves the $\chi^2$ from $680.75$ to $536.23$ for $655$ degrees of freedom. As global best-fit we obtain $\beta = 0.34\pm0.04$ and $\lambda = 5.61\pm0.91$kpc and a dark matter content on average 20\% smaller than without the Yukawa term. The Bayesian evidence in favor of a NFW profile plus Yukawa term is higher than 8$\sigma$ with respect to the standard gravity parametrization.
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a method for evaluating models that use Galaxy Rotation Curves to derive the density profiles
Monthly Notices of the Royal Astronomical Society, 2016Co-Authors: Alefe O F De Almeida, Oliver F Piattella, Davi C RodriguesAbstract:There are some approaches, either based on General Relativity (GR) or modified gravity, that use Galaxy Rotation Curves to derive the matter density of the corresponding Galaxy, and this procedure would either indicate a partial or a complete elimination of dark matter in galaxies. Here we review these approaches, clarify the difficulties on this inverted procedure, present a method for evaluating them, and use it to test two specific approaches that are based on GR: the Cooperstock-Tieu (CT) and the Balasin-Grumiller (BG) approaches. Using this new method, we find that neither of the tested approaches can satisfactorily fit the observational data without dark matter. The CT approach results can be significantly improved if some dark matter is considered, while for the BG approach no usual dark matter halo can improve its results.
Dilip G Banhatti - One of the best experts on this subject based on the ideXlab platform.
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newtonian mechanics gravity fully model disk Galaxy Rotation Curves without dark matter
IAUS, 2009Co-Authors: Dilip G BanhattiAbstract:EGRET gamma-ray archival data used with GALPROP software show two ringlike structures in Milky Way Plane which roughly tally with distribution of stars ([1] & references therein). To understand fully the implications of this and similar results on detailed structure and Rotation curve of especially Milky Way Disk as well as Rotation Curves of other galaxies as derived from spatially resolved spectroscopic data-cubes, a re-examination of the basis of the connection between mass density and Rotation curve is warranted. Kenneth F Nicholson’s approach [2], which uses only Newtonian dynamics & gravity, is presented. Assumptions. The following assumptions are made in this approach. 1. Axisymmetry (that is, azimuthal symmetry relative to the dominant structural axis) in the disk plane, taken to be the xy-plane and bilateral symmetry at every radius r in the normal direction, taken to be the z-direction. 2. The measured (that is reduced from the spatially resolved spectroscopic data cube) Rotation speeds are taken to be applicable at the central (disk) plane (z = 0). 3. A definite maximum radius rmax beyond which (circular) speeds are not specified. 4. Thickness (h) variation with radius (r) is estimated at 1.491 times that of stars as roughly measured from edge-on Galaxy images (like in Figure 1). This is specific to each Galaxy, unless it is not measurable. Then it is taken from some other similar Galaxy (after necessary normalization and scaling). The function h(r) also extends to rmax. All calculations and plots essentially apply only upto r = rmax. 5. Volume mass density rho = surface mass density / h [that is, rho(r) = SMD(r)/h(r)]. Figure 1. Examples of edge-on disk galaxies – NGC4565 from Jeff MacQuarrie’s homepage, NGC4013 from Hubble (only half the disk is shown), and M101 (Sombrero) from Hubble. ----------------------------------------------------------------------Method. The method consists of two parts – a forward part and a reverse part. The forward part computes the Rotation profile from a given mass distribution. The reverse part finds the mass distribution for a given Rotation profile. Equations and coding for the forward part are checked against simple analytical solutions, giving a high degree of confidence in its use. The reverse part is done by repeated trials and feedback corrections with the forward part, to adjust the mass distribution until errors between computed and measured Rotation speeds are all very small at each radius (that is, each ring out of upto 100 rings – as few as 4 or 5 rings being sometimes enough). To check the reverse part, a given mass distribution is used to find the Rotation profile with the forward part, and that profile is then used as inputs for the reverse part to check against the initially input mass distribution. Thus the same degree of confidence associated with the forward part carries over to the reverse part. Geometry and computational variables. Figure 2 and the following description of the computation is essentially reproduced from Kenneth F Nicholson’s paper arXiv:astroph/0309762v1, listed in [2], the other papers giving various other details and applications. --------------------------------------------------------------------------------------------------------------------An equivalent constant-density thickness is chosen for rings at a given radius to make the integration in z analytic. This results in a simple answer for the gravity effects of a fundamental segment of mass ddm = rho h S , where S = r dth dr. When computing is done, the equivalent thickness and density is used to find the correct local density distribution in z. Reverse Part The computing procedure used is: 1. input Galaxy dimensions, measured speeds at the outer edges of each ring, and arbitrary starting densities for each ring (usually just one density for all rings) 2. compute Rotation speeds at the outer edges of each ring using (3) 3. use speed errors to correct densities of the rings (i = 1 to Nr) errv = (vm−v) / vmax , f = 0.75 errv , if all errv < 1E−6 then go to 5 (4) limit abs(f) < 0.5 , rho(j) = (1+f) rho(j−1) for each cycle j where vm = measured speed and vmax = maximum measured speed 4. go to 2 for the next cycle 5. make results dimensionless for plots, print or plot results and quit. Results include total mass, volume, average density, average SMD, Kepler rim speed, maximum computed speed, and the plotted data: md, rhod, rSMDd, vd. Examples of graphical results. Figure 3. Linear scale plots for NGC3198 using Rotational speed data from [3]. ------------------------------------------------------------------------------------------------Figure 4. Lon (i.e., natural log) scale plots for NGC3198 using Rotational speed data from [3]. Please notice that, taken at face value, SMD plot here is inconsistent with that in Figure 3. --------------------------------------------------------------------------------------------The thickness as a function of radius for NGC3198 is taken to be of the same form as for Milky Way, from a computer-generated side view done by Bab(?)call & Soneira, as compiled by Bok [4]. Milky Way Rotational speeds, measured by Schmidt & Blitz, are also taken from Bok’s compilation [4]. Figure 5. Linear scale plots for Milky Way using data from [4]. ---------------------------------------------------------------------------Conclusions from the two examples. Newton's law needs no correction and no dark-matter halos are needed to find Galaxy mass distributions from Rotation profiles. Given reasonable estimates of Galaxy dimensions, including thickness, good values for the mass, SMD, and density distributions are easily found from the Rotation profiles. The total masses of galaxies found using dark-matter halos are far too high. Based on reasonable values for dimensions and their Rotation profiles, the best values for the total masses of the Milky Way and NGC3198 are 2.079E11 and 1.035E11 msuns respectively. Nicholson [2] presents results for three more examples. A brief summary of some of the parameters for all the five examples is reproduced below. Tabular summary from 5 fits The units are parsec for the first column, cubic parsec for the second, msuns for the third, msuns/square pc for the fourth & msun/cubic pc for the fifth. Outlook. Researchers interested in Rotation Curves need to answer certain questions afresh with an open mind. Instead of discounting Kenneth F Nicholson’s model just because it is different from the current fashion, it needs to be judged on its own merits. The model calculation needs only modest computing resources. Application to the vast Rotation curve and disk thickness data now available should therefore give valuable insights to at least classify galaxies in a sensible scheme. There are two other models available to deal with the data in an axisymmetric approximation [1, 5] which also need to be explored without bias from current practice in this area of research. One is a disk Galaxy simulation with 50000 particles and the other a matrix inversion calculation with 250000 particles. Comparison of these two and contrast with Nicholson’s method promise rich astrophysical dividends. References. [1] Dilip G. Banhatti 25 April 2008 Current Science 94(8) 960 + 986to95 : Spiral galaxies & dark matter + Disk Galaxy Rotation Curves and dark matter distribution (also astroph/0703430v7). [2] Kenneth F Nicholson arXiv: astro-ph/0309823 : Errors in equations for Galaxy Rotation speeds; 0309762v2 : Galactic mass distribution without dark matter or modified Newtonian mechanics; 0309762 : Galaxy statics without dark matter; 0303135v2 & v1 : Galaxy mass distributions from Rotation speeds by closed-loop convergence; 0101401 : Galaxy mass distributions for some extreme orbital speed profiles; 0006330 : Disk-Galaxy density distribution from orbital speeds using Newton’s law – Version 1.1; 0006140v2 & v1 : DiskGalaxy density distribution from orbital speeds using Newton’s law. [3] T S van Albada et al 1985 Astrophysical Journal 295 305to13: Distribution of dark matter in the spiral Galaxy NGC3198. [4] Bok, R(?).J., The Milky Way Galaxy, Scientific American, March 1981. [5] Dilip G Banhatti arXiv:0804.4163v2 [astro-ph] : Need for context-aware computing in astrophysics. Acknowledgments. I gratefully acknowledge University Grants Commission, New Delhi, India for support. I also thank my family members for comments & help. [Author’s email addresses: dilip.g.banhatti@gmail.com, banhatti@uni-muenster.de] Note added in proof: Kenneth F Nicholson's assumption 4 effectively assumes the same mass-to-light ratio over the full disk, upto its visible extent. The numerical evaluation of the integral transform between the Rotation curve and the surface mass distribution SMD(r) thus shows, for the five cases considered, that this works within Newtonian mechanics and gravity. In contrast, R H Sanders (0806.2585 16 June 2008 : From dark matter to MOND) uses a modified Newtonian mechanics towards the same end. Taken at face value, this seems to be a numerical paradox, if the same disk galaxies can be modelled both ways. It will be interesting to examine this contrast further. -------------------------------------------0x0----------------------------------------------------
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newtonian mechanics gravity fully model disk Galaxy Rotation Curves without dark matter
arXiv: Astrophysics, 2008Co-Authors: Dilip G BanhattiAbstract:EGRET gamma-ray archival data used with GALPROP software show two ringlike structures in Milky Way Plane which roughly tally with distribution of stars ([1] & references therein). To understand fully the implications of this and similar results on detailed structure and Rotation curve of especially Milky Way Disk as well as Rotation Curves of other galaxies as derived from spatially resolved spectroscopic data-cubes, a re-examination of the basis of the connection between mass density and Rotation curve is warranted. Kenneth F. Nicholson's approach [2], which uses only Newtonian dynamics & gravity, is presented.
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disk Galaxy Rotation Curves and dark matter distribution
arXiv: Astrophysics, 2007Co-Authors: Dilip G BanhattiAbstract:After explaining the motivation for this article, I briefly recapitulate the methods used to determine, somewhat coarsely, the Rotation Curves of our Milky Way Galaxy and other spiral galaxies, especially in their outer parts, and the results of applying these methods. Recent observations and models of the very inner central parts of galaxian Rotation Curves are only briefly described. I then present the essential Newtonian theory of (disk) Galaxy Rotation Curves. The next two sections present two numerical simulation schemes and brief results. Application of modified Newtonian dynamics to the outer parts of disk galaxies is then described. Finally, attempts to apply Einsteinian general relativity to the dynamics are summarized. The article ends with a summary and prospects for further work in this area.
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disk Galaxy Rotation Curves and dark matter distribution
Current Science, 2006Co-Authors: Dilip G BanhattiAbstract:After explaining the motivation for this article, we briefly recapitulate the methods used to determine the Rotation Curves of our Galaxy and other spiral galaxies in their outer parts, and the results of applying these methods. We then present the essential Newtonian theory of (disk) Galaxy Rotation Curves. The next two sections present two numerical simulation schemes and brief results. Finally, attempts to apply Einsteinian general relativity to the dynamics are described. The article ends with a summary and prospects for further work in this area. Recent observations and models of the very inner central parts of galaxian Rotation Curves are omitted, as also attempts to apply modified Newtonian dynamics to the outer parts. Motivation . Extensive radio observations determined the detailed Rotation curve of our Milky Way Galaxy as well as other (spiral) disk galaxies to be flat much beyond their extent as seen in the optical band. Assuming a balance between the gravitational and centrifugal forces within Newtonian mechanics, the orbital speed V is expected to fall with the galactocentric distance r as V 2 = GM/r beyond the physical extent of the Galaxy of mass M, G being the gravitational constant. The run of V against r, for distances less than the physical extent, then leads to the distribution M(r) of mass within radius r. The observation Vconstant for large enough r, upto the largest r, upto 100 kpc, thus shows that there is substantial amount of matter beyond even this largest distance. A spherically symmetric matter density �(r) ∝ 1/r 2 , characteristic of an isothermal sphere, leads to V = constant. Since this matter doesn't emit radiation, it is called dark matter. In general, the existence of dark matter is, by astrophysical definition, inferred solely from its gravitational effects. (Astro)particle physicists hope to change this by directly detecting dark matter particles. One often assumes an isothermal dark matter halo, although �(r) ∝ 1/r 2 is only one of many density profiles leading to V = constant, the others being disklike. For disklike mass distributions, in contrast to spherically symmetric ones, the circular speed at a given r is determined by matter distributed from 0 to r and also beyond r, as can be easily seen by applying Gauss' integral theorem (or law) to appropriately shaped closed volumes. Some textbooks make the error of integrating only upto r, leading to wrong results (Mera et al 2006).
P. Mishra - One of the best experts on this subject based on the ideXlab platform.
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Galaxy Rotation Curves from a fourth order gravity
Journal of Physics: Conference Series, 2014Co-Authors: P. Mishra, T P SinghAbstract:While the standard and most popular explanation for the flatness of Galaxy Rotation Curves is dark matter, one cannot at this stage rule out an explanation based on a modified law of gravitation, which agrees with Newtonian gravitation on the scale of the Solar system, but differs from it on larger length scales. Examples include Modfied Newtonian Dynamics (MOND) and Scalar-Tensor-Vector Gravity (STVG). Here, we have reported on a fourth order modification of the Poisson equation, which yields the same Yukawa type modification of Newtonian gravity as STVG, and which can explain flat Galaxy Rotation Curves for a large sample of galaxies, once specific values for two parameters have been chosen. We have speculated on two possible origins for this modified Poisson equation: First, a possible fourth order modification of general relativity, and second, quadrupole gravitational polarization induced on a Galaxy because of the pull of neighbouring galaxies.
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Galaxy Rotation Curves from a fourth order gravity
Journal of Physics: Conference Series, 2014Co-Authors: P. Mishra, T P SinghAbstract:While the standard and most popular explanation for the flatness of Galaxy Rotation Curves is dark matter, one cannot at this stage rule out an explanation based on a modified law of gravitation, which agrees with Newtonian gravitation on the scale of the solar system, but differs from it on larger length scales. Examples include Modfied Newtonian Dynamics [MOND] and Scalar-Tensor-Vector Gravity [STVG]. Here we report on a fourth order modification of the Poisson equation which yields the same Yukawa type modification of Newtonian gravity as STVG, and which can explain flat Galaxy Rotation Curves for a large sample of galaxies, once specific values for two parameters have been chosen. We speculate on two possible origins for this modified Poisson equation: first, a possible fourth order modification of general relativity, and second, quadrupole gravitational polarization induced on a Galaxy because of the pull of neighbouring galaxies.
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fourth order gravity scalar tensor vector gravity and Galaxy Rotation Curves
Physical Review D, 2013Co-Authors: P. Mishra, T P SinghAbstract:The Lambda-CDM model is the best fit to cosmological data, and to the observed galactic Rotation Curves. However, in the absence of a direct detection of dark matter one should explore theories such as MOND, and perhaps also modified gravity theories like fourth order gravity and Scalar-Tensor-Vector Gravity [STVG] as possible explanations for the non-Keplerian behaviour of Galaxy Rotation Curves. STVG has a modified law for gravitational acceleration which attempts to fit data by fixing two free parameters. We show that, remarkably, the biharmonic equation which we get in the weak field limit of the field equations in a fourth order gravity theory implies a modification of Newtonian acceleration which is precisely of the same repulsive Yukawa form as in the STVG theory, and the corrections could in principle be large enough to try and explain the observed Rotation Curves. We also explain how our model provides a first principles understanding of MOND. We also show that STVG and fourth order gravity predict an acceleration parameter $a_0$ whose value is of the same order as in MOND.
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modified gravity as a common cause for cosmic acceleration and flat Galaxy Rotation Curves
arXiv: General Relativity and Quantum Cosmology, 2012Co-Authors: P. Mishra, T P SinghAbstract:Flat Galaxy Rotation Curves and the accelerating Universe both imply the existence of a critical acceleration, which is of the same order of magnitude in both the cases, in spite of the galactic and cosmic length scales being vastly different. Yet, it is customary to explain galactic acceleration by invoking gravitationally bound dark matter, and cosmic acceleration by invoking a `repulsive` dark energy. Instead, might it not be the case that the flatness of Rotation Curves and the acceleration of the Universe have a common cause? In this essay we propose a modified theory of gravity. By applying the theory on galactic scales we demonstrate flat Rotation Curves without dark matter, and by applying it on cosmological scales we demonstrate cosmic acceleration without dark energy.
