Kinetic Energy Of Random Motions Research Articles

Study of the Relation between the Spiral Arm Pitch Angle and the Kinetic Energy of Random Motions of the Host Spiral Galaxies, A

In this work, we report a relation between the kinetic energy of random motions of the corresponding host galaxies and spiral arm pitch angles (Mdynσ2- P), (M*σ2- P) where Mdyn is the bulge dynamical mass, M* is bulge stellar mass, and σ is the velocity dispersion of the host galaxy bulge. We measured the spiral arm pitch angle (P) for a sample of Spitzer/IRAC 3.6-μm images of 54 spiral galaxies, estimated by using a 2D Fast Fourier Transform decomposition technique (2DFFT). We selected a sample of nearly face-on spiral galaxies and used IRAF ellipse to determine the ellipticity and major-axis position angle in order to deproject the images to face-on, and using a 2D Fast Fourier Transform decomposition technique, we determined the spiral arm pitch angles. We estimated the kinetic energy of random motions of the corresponding host galaxies (Mdynσ, M*σ2) by using Mdyn, M*, and σ, where the stellar velocity dispersion (σ) of the bulge was taken from the literature. We determined the bulge dynamical mass (Mdyn) using the virial theorem, and the bulge stellar mass (M*) was estimated by using the bulge 3.6-μm luminosity with the appropriate stellar mass-to-light ratio (M/L).

DYNAMICS OF NON-STEADY SPIRAL ARMS IN DISK GALAXIES

In order to understand the physical mechanisms underlying non-steady stellar spiral arms in disk galaxies, we analyzed the growing and damping phases of their spiral arms using three-dimensional $N$-body simulations. We confirmed that the spiral arms are formed due to a swing amplification mechanism that reinforces density enhancement as a seeded wake. In the damping phase, the Coriolis force exerted on a portion of the arm surpasses the gravitational force that acts to shrink the portion. Consequently, the stars in the portion escape from the arm, and subsequently they form a new arm at a different location. The time-dependent nature of the spiral arms are originated in the continual repetition of this non-linear phenomenon. Since a spiral arm does not rigidly rotate, but follows the galactic differential rotation, the stars in the arm rotate at almost the same rate as the arm. In other words, every single position in the arm can be regarded as the co-rotation point. Due to interaction with their host arms, the energy and angular momentum of the stars change, thereby causing the radial migration of the stars. During this process, the kinetic energy of random motion (random energy) of the stars does not significantly increase, and the disk remains dynamically cold. Owing to this low degree of disk heating, the short-lived spiral arms can recurrently develop over many rotational periods. The resultant structure of the spiral arms in the $N$-body simulations is consistent with some observational nature of spiral galaxies. We conclude that the formation and structure of spiral arms in isolated disk galaxies can be reasonably understood by non-linear interactions between a spiral arm and its constituent stars.

The scaling relation between the mass of supermassive black holes and the kinetic energy of random motions of the host galaxies

Thanks to the angular resolution of modern telescopes and kinematic models, the existence of supermassive black holes (SMBHs) in the inner part of galaxies has been established on quite solid grounds. A possible correlation between the mass of SMBHs and the evolutionary state of their host galaxies is expected. Based on the recent 2D decomposition of mid-infrared Spiter/IRAC images of local galaxies with M_bh measurements, we investigated various scaling laws, studying what the best predictor of the mass of the central SMBHs is. We focused on the M_bh-M_G sigma^2 law, the relation between the mass of SMBHs and the kinetic energy of random motions of the corresponding host galaxies. In order to find the best fit for each of the scaling laws examined, we performed a least-squares regression of M_bh on x for the considered sample of galaxies, x being a whatever known parameter of the galaxy bulge. Our analysis shows that M_bh-M_G sigma^2 law fits the examined experimental data successfully as much as the other known scaling laws and shows a value of chi^2 better than the others, a result which is consistent with previous determinations. This means that a combination of sigma and M_G could be necessary to drive the correlations between M_bh and other bulge properties. This issue has been investigated by a careful analysis of the residuals of the various relations. In order to avoid rushed conclusions on galaxy activity and evolution, the indirect inferring of M_bh from the kinetic energy of random motions should be considered, especially when applied to higher redshift galaxies. This statement is suggested by a reanalysis of the SDSS data used to study the SMBH growth in the nearby Universe. Adopting the M_bh-M_G sigma^2 relation instead of the M_bh-sigma, a radio-quiet/radio-loud dichotomy appears in the SMBH mass distribution of the corresponding SDSS early-type AGN galaxies.

The SMBH mass versus M G σ 2 relation: a comparison between real data and numerical models

The relation between the mass of supermassive black holes located in the center of the host galaxies and the kinetic energy of random motions of the corresponding bulges can be reinterpreted as an age-temperature diagram for galaxies. This relation fits the experimental data better than the M_bh-M_G, M_bh-L_G, and M_bh-sigma laws. The validity of this statement has been confirmed by using three samples extracted from different catalogues of galaxies. In the framework of the LambdaCDM cosmology our relation has been compared with the predictions of two galaxy formation models based on the Millennium Simulation.

A HERTZSPRUNG-RUSSELL-LIKE DIAGRAM FOR GALAXIES: THEM•VERSUSMGσ2RELATION

We show that the relation between the mass of supermassive black holes located in the center of the host galaxies and the kinetic energy of random motions of the corresponding bulges is a useful tool to study the evolution of galaxies. In the form log[M_BH] = b + m log[M_G sigma^2/c^2], the best-fitting results for a sample of 64 galaxies of various morphological types are the slope m=0.80 and the normalization b=4.53. We note that, in analogy with the H-R diagram for stars, each morphological type of galaxy generally occupies a different area in the M_BH - (M_G sigma^2)/c^2 plane. In particular, we find elliptical galaxies in the upper part of the line of best fit, the lenticular galaxies in the middle part, and the late-type galaxies in the lower part, the mass of the central black hole giving an estimate of the age, whereas the kinetic energy of the stellar bulges is directly connected with the temperature of each galactic system. Finally, the values of the linear correlation coefficient, the intrinsic scatter, and the chi^2 obtained by using the M_BH - M_G sigma^2 relation are better than the corresponding ones obtained from the M_BH - sigma or M_BH - M_G relation.

IMPROVED TESTS ON THE RELATIONSHIP BETWEEN THE KINETIC ENERGY OF GALAXIES AND THE MASS OF THEIR CENTRAL BLACK HOLES

We support, with new fitting instruments and the analysis of more recent experimental data, the proposal of a relationship between the mass of a Supermassive Black Hole (SMBH) and the kinetic energy of random motions in the host elliptical galaxy. The first results obtained in a previous paper with 13 elliptical galaxies are now confirmed by the new data and an enlarged sample. We find MBH ∝ (MGσ2/c2)β with 0.8 ≤ β ≤ 1 depending on the different fitting methods and samples used. The meaningful case β = 1 is carefully analyzed. Furthermore, we test the robustness of our relationship, including in the sample also lenticular and spiral galaxies and we show that the result does not change. Finally, we find a stronger correlation between the mass of the galaxy and the corresponding velocity dispersion that allows us to connect our relationship to the MBH ∝ σα law. With respect to this law, our relationship has the advantage of having a smaller scatter.

IS THERE A RELATIONSHIP BETWEEN THE MASS OF A SMBH AND THE KINETIC ENERGY OF ITS HOST ELLIPTICAL GALAXY?

We use a restricted sample of elliptical galaxies, whose kinematical parameters inside the semi-major axis were calculated correcting for the effect of the integration of the light along the line of sight, in order to analyze a possible relationship between the mass of a supermassive black hole (SMBH) and the kinetic energy of random motions in the host galaxy. We find M BH ∝ (MG σ2)α with 0.87 ≤ α ≤ 1 depending on the different fitting methods and samples used. This result could be interpreted as a new fundamental relationship or as a new way to explain the old M BH - σ law. In fact, the relations of the velocity dispersion both with the mass of the SMBH (M BH ∝ σ4.12) and with the mass of the host galaxy (MG ∝ σ2.16) induce us to infer an almost direct proportionality: M BH ∝ MGσ2. A similar relationship is found for the total kinetic energy involving the rotation velocity too.

Central NGC 2146: A Firehose‐Type Bending Instability in the Disk of Newly Formed Stars?

As the observations of highly flattened galaxies, including the Milky Way, and gravitational N-body simulations show, the central parts of these systems at distances of, say, r < 0.5-0.7 kpc from the center rotate slowly, and their local circular velocities of regular rotation become less than (or comparable to) the residual (random) velocities. In such a thin, practically nonrotating, pressure-supported central disk, a typical star moves along the bending, perpendicular to the equatorial plane layer, under the action of two forces acting in opposite directions: the destabilizing centrifugal force, c, and the restoring gravitational attraction, g. Obviously, fierce instabilities of the buckling kind developing perpendicular to the plane may not be avoided if Fc > Fg. The latter condition is none other than the condition of the so-called firehose electromagnetic instability in collisionless plasmas. The source of free energy in the instability is the intrinsic anisotropy of a velocity dispersion ("temperature"). It seems reasonable that this is a natural mechanism for building a snake-shaped radio structure, which has recently been observed by Zhao and coworkers in the central region of the spiral starburst galaxy NGC 2146 with the Very Large Array at an angular resolution of 2''. In the current paper, in order to investigate the dynamics of the central region, N-body simulations of the firehose-type bending instability are presented for this galaxy. Use of concurrent computers has enabled us to make long simulation runs using a sufficiently large number of particles in the direct summation code, N ~ 20,000. In contrast to all previous N-body simulations of bending instabilities, we show how bending structures may be longer lived in real starburst galaxies than in the computer models. The simulations clearly confirm the qualitative picture and, moreover, are in fair quantitative agreement with the theory. A theoretical prediction is confirmed that the instability is driven by an excess of plane kinetic energy of random motions of stars, when the ratio of the dispersion of radial velocities of stars in the plane cr to the velocity dispersion in the perpendicular direction cz is large enough, cr ≳ 0.6cz, in other words, if the thickness of the stellar disk h ∝ cz is small enough. The extent to which our results on the stability of the disk can have a bearing on observable spiral galaxies with a high star formation rate in the central parts is discussed.

Evolution of random velocities of planetesimals in the course of accretion

The role of accretion in the random velocity evolution of planetesimals is examined. By combining the equation for velocity change caused by accretion and the coagulation equation for the mass distribution function, we derive an equation for random velocity evolution in the course of accretion, which is described in terms of eccentricity and inclination of planetesimal orbits in the framework of the Hill's approximations. We find that dissipation of random velocity due to accretion has the tendency to lead to equipartition of kinetic energy of random motion between planetesimals with different masses. We also compare the three effects on velocity evolution, that is, gas drag of the solar nebula, gravitational scattering, and accretion. At the Earth's orbit, all these three effects seem to contribute to velocity evolution at early stages of planetesimal accumulation. However, when the typical size of planetesimals becomes larger than 10 20 g, the effect of accretion on velocity evolution becomes less effective, and it is considered that planetesimals have certain equilibrium velocities determined by the balance between gravitational scattering and gas drag. At this, or at a slightly later stage, the onset of runaway growth of several protoplanets seems more probable.

Systems of colliding bodies in a gravitational field: Impact velocity, inelasticity and sizes distributions

We study numerically the dynamical evolution of a system of colliding bodies. Collisions are inelastic and the coefficient of rebound is a function of the impat velocity. Various functions are used. The system can reach an equilibrium state characterized by a finite thickness independently on the sense of variation of the functions. Within the frame of various distributions of the body sizes we observe a segregation rather than equipartition of the kinetic energy of random motions.

THE IONIC CENTRIFUGE AND FUSION NUCLEAR POWER

The Ionic Centrifuge is briefly described. The discharge in this device violates the usual miles of magnetohydrodynamics because of the high electric field parallel to the magnetic field in the space charge affected boundaries./sup 6,8/ The kinetic energy of random motion of the particles is proportional to the voltage which the main discharge holds at each point. By causing this voltage to rise to a high positive value and then drop to zero at the cylinder, the ions are not collected when their kinetic energy is high, but only at the cylinder where this kinetic energy is low again. The suitability of this arrangement for nuclear power converters is pointed out.