# Posts Tagged pitch angle

## Recent Postings from pitch angle

### Galactic Spiral Arms by Swing Amplification

Based on the swing amplification model of Julian and Toomre (1966), we investigate the formation and structure of stellar spirals in disk galaxies. We calculate the pitch angle, wavelengths, and amplification factor of the most amplified mode. We also obtain the fitting formulae of these quantities as a function of the epicycle frequency and Toomre's $Q$. As the epicycle frequency increases, the pitch angle and radial wavelength increases, while the azimuthal wavelength decreases. The pitch angle and radial wavelength increases with $Q$, while the azimuthal wavelength weakly depends on $Q$. The amplification factor decreases with $Q$ rapidly. In order to confirm the swing amplification model, we perform local $N$-body simulations. The wavelengths and pitch angle by the swing amplification model are in good agreement with those by $N$-body simulations. The dependence of the amplification factor on the epicycle frequency in $N$-body simulations is generally consistent with that in the swing amplification model. Using these results, we estimate the number of spiral arms as a function of the shear rate. The number of spiral arms increases with the shear rate if the disk to halo mass ratio is fixed.

### Dynamics of Self-Gravity Wakes in Dense Planetary Rings I. Pitch Angle

We investigate the dynamics of self-gravity wakes in dense planetary rings. In particular, we examine how the pitch angle of self-gravity wakes depend on ring parameters using N-body simulations. We calculate the pitch angles using the two-dimensional autocorrelation function of the ring surface density. We obtain the pitch angles for the inner and outer parts of the autocorrelation function separately. We confirm that the pitch angles are 15 to 30 degrees for reasonable ring parameters, which are consistent with previous studies. We find that the inner pitch angle increases with the Saturnicentric distance, while it barely depends on the optical depth and the restitution coefficient of ring particles. The increase of the inner pitch angle with the Saturnicentric distance is consistent with the observations of the A ring. The outer pitch angle does not have the clear dependence on any ring parameters and is about 10 - 15 degrees. This value is consistent with the pitch angle of spiral arms in collisionless systems.

### Radiation reaction and the pitch angle changes for a charge undergoing synchrotron losses [Replacement]

In the derivation of synchrotron radiation formulas it has been assumed that the pitch angle of a charge remains constant during the radiation process. However from the radiation reaction formula, while the component of the velocity vector perpendicular to the magnetic field reduces in magnitude due to radiative losses, the parallel component does not undergo any change during radiation. Therefore there is a change in the ratio of the two components, implying a change in the pitch angle. We derive the exact formula for the change in energy of radiating electrons by taking into account the change of the pitch angle due to radiative losses. From this we derive the characteristic decay time of synchrotron electrons over which they turn from highly relativistic into mildly relativistic ones.

### The Structure of Spiral Shocks Excited by Planetary-mass Companions [Replacement]

Direct imaging observations have revealed spiral structures in protoplanetary disks. Previous studies have suggested that planet-induced spiral arms cannot explain some of these spiral patterns, due to the large pitch angle and high contrast of the spiral arms in observations. We have carried out three dimensional (3-D) hydrodynamical simulations to study spiral wakes/shocks excited by young planets. We find that, in contrast with linear theory, the pitch angle of spiral arms does depend on the planet mass, which can be explained by the non-linear density wave theory. A secondary (or even a tertiary) spiral arm, especially for inner arms, is also excited by a massive planet. With a more massive planet in the disk, the excited spiral arms have larger pitch angle and the separation between the primary and secondary arms in the azimuthal direction is also larger. We also find that although the arms in the outer disk do not exhibit much vertical motion, the inner arms have significant vertical motion, which boosts the density perturbation at the disk atmosphere. Combining hydrodynamical models with Monte-Carlo radiative transfer calculations, we find that the inner spiral arms are considerably more prominent in synthetic near-IR images using full 3-D hydrodynamical models than images based on 2-D models assuming vertical hydrostatic equilibrium, indicating the need to model observations with full 3-D hydrodynamics. Overall, companion-induced spiral arms not only pinpoint the companion's position but also provide three independent ways (pitch angle, separation between two arms, and contrast of arms) to constrain the companion's mass.

### Stellar Orbital Studies in Normal Spiral Galaxies II: Restrictions to Structural and Dynamical parameters on Spiral Arms

Making use of a set of detailed potential models for normal spiral galaxies, we analyze the disk stellar orbital dynamics as the structural and dynamical parameters of the spiral arms (mass, pattern speed and pitch angle) are gradually modified. With this comprehensive study of ordered and chaotic behavior, we constructed an assemblage of orbitally supported galactic models and plausible parameters for orbitally self-consistent spiral arms models. We find that, to maintain orbital support for the spiral arms, the spiral arm mass, M$_{sp}$, must decrease with the increase of the pitch angle, $i$; if $i$ is smaller than $\sim10\deg$, M$_{sp}$ can be as large as $\sim7\%$, $\sim6\%$, $\sim5\%$ of the disk mass, for Sa, Sb, and Sc galaxies, respectively. If $i$ increases up to $\sim25\deg$, the maximum M$_{sp}$ is $\sim1\%$ of the disk mass independently in this case of morphological type. For values larger than these limits, spiral arms would likely act as transient features. Regarding the limits posed by extreme chaotic behavior, we find a strong restriction on the maximum plausible values of spiral arms parameters on disk galaxies beyond which, chaotic behavior becomes pervasive. We find that for $i$ smaller than $\sim20\deg$, $\sim25\deg$, $\sim30\deg$, for Sa, Sb, and Sc galaxies, respectively, M$_{sp}$ can go up to $\sim10\%$, of the mass of the disk. If the corresponding $i$ is around $\sim40\deg$, $\sim45\deg$, $\sim50\deg$, M$_{sp}$ is $\sim1\%$, $\sim2\%$, $\sim3\%$ of the mass of the disk. Beyond these values, chaos dominates phase space, destroying the main periodic and the neighboring quasi-periodic orbits.

### Radial distributions of arm-gas offsets as an observational test of spiral theories

Theories of stellar spiral arms in disk galaxies can be grouped into two classes based on the longevity of a spiral arm. Although the quasi-stationary density wave theory supposes that spirals are rigidly-rotating, long-lived patterns, the dynamic spiral theory predicts that spirals are differentially-rotating, transient, recurrent patterns. In order to distinguish between the two spiral models from observations, we performed hydrodynamic simulations with steady and dynamic spiral models. Hydrodynamics simulations in steady spiral models demonstrated that the dust lane locations relative to the stellar spiral arms (hereafter, arm-gas offsets) depend on radius, regardless of the strength and pitch angle of the spiral and the model of the inter-stellar medium (ISM). In contrast, we found that the dynamic spiral models show no systematic radial dependence of the arm-gas offsets. The arm-gas offset radial profile method, together with the other test methods, will help us to distinguish between the two spiral models in observed spiral galaxies.

### Different studies of the global pitch angle of the Milky Way's spiral arms

There are many published values for the pitch angle of individual spiral arms, and their wide distribution (from -3 to -28 degrees) begs for various attempts for a single value. Each of the four statistical methods used here yields a mean pitch angle in a small range, between -12 and -14 degrees (table 7, figure 2). The final result of our meta-analysis yields a mean global pitch angle in the Milky Way's spiral arms of -13.1 degrees, plus or minus 0.6 degree.

### Asymmetric diffusion of cosmic rays

Cosmic ray propagation is diffusive because of pitch angle scattering by waves. We demonstrate that if the high-amplitude magnetohydrodynamic turbulence with $\tilde B/\langle B\rangle \sim 1$ is present on top of the mean field gradient, the diffusion becomes asymmetric. As an example, we consider the vertical transport of cosmic rays in our Galaxy propagating away from a point-like source. We solve this diffusion problem analytically using a one-dimensional Markov chain analysis. We obtained that the cosmic ray density markedly differs from the standard diffusion prediction and has a sizable effect on their distribution throughout the galaxy. The equation for the continuous limit is also derived, which shows limitations of the convection-diffusion equation.

### A Fundamental Plane of Spiral Structure in Disk Galaxies

Spiral structure is the most distinctive feature of disk galaxies and yet debate persists about which theory of spiral structure is the correct one. Many versions of the density wave theory demand that the pitch angle is uniquely determined by the distribution of mass in the bulge and disk of the galaxy. We present evidence that the tangent of the pitch angle of logarithmic spiral arms in disk galaxies correlates strongly with the density of neutral atomic hydrogen in the disk and with the central stellar bulge mass of the galaxy. These three quantities, when plotted against each other, form a planar relationship which, we argue should be fundamental to our understanding of spiral structure in disk galaxies. We further argue that any successful theory of spiral structure must be able to explain this relationship.

### A Fundamental Plane of Spiral Structure in Disk Galaxies [Replacement]

Spiral structure is the most distinctive feature of disk galaxies and yet debate persists about which theory of spiral structure is the correct one. Many versions of the density wave theory demand that the pitch angle is uniquely determined by the distribution of mass in the bulge and disk of the galaxy. We present evidence that the tangent of the pitch angle of logarithmic spiral arms in disk galaxies correlates strongly with the density of neutral atomic hydrogen in the disk and with the central stellar bulge mass of the galaxy. These three quantities, when plotted against each other, form a planar relationship which, we argue should be fundamental to our understanding of spiral structure in disk galaxies. We further argue that any successful theory of spiral structure must be able to explain this relationship.

### Galaxy Zoo: the dependence of the star formation-stellar mass relation on spiral disk morphology

We measure the stellar mass-star formation rate relation in star-forming disk galaxies at z<0.085, using Galaxy~Zoo morphologies to examine different populations of spirals as classified by their kiloparsec-scale structure. We examine the number of spiral arms, their relative pitch angle, and the presence of a galactic bar in the disk, and show that both the slope and dispersion of the M-SFR relation is constant when varying all the above parameters. We also show that mergers (both major and minor), which represent the strongest conditions for increases in star formation at a constant mass, only boost the SFR above the main relation by ~0.3 dex; this is significantly smaller than the increase seen in merging systems at z>1. Of the galaxies lying significantly above the M-SFR relation in the local Universe, more than 50% are mergers. We interpret this as evidence that the spiral arms, which are imperfect reflections of the galaxy's current gravitational potential, are either fully independent of the various quenching mechanisms or are completely overwhelmed by the combination of outflows and feedback. The arrangement of the star formation can be changed, but the system as a whole regulates itself even in the presence of strong dynamical forcing.

### The spatial, spectral and polarization properties of solar flare X-ray sources [Replacement]

X-rays are a valuable diagnostic tool for the study of high energy accelerated electrons. Bremsstrahlung X-rays produced by, and directly related to, high energy electrons accelerated during a flare, provide a powerful diagnostic tool for determining both the properties of the accelerated electron distribution, and of the flaring coronal and chromospheric plasmas. This thesis is specifically concerned with the study of spatial, spectral and polarization properties of solar flare X-ray sources via both modelling and X-ray observations using the Ramaty High Energy Solar Spectroscopic Imager (RHESSI). Firstly, a new model is presented, accounting for finite temperature, pitch angle scattering and initial pitch angle injection. This is developed to accurately infer the properties of the acceleration region from the observations of dense coronal X-ray sources. Moreover, examining how the spatial properties of dense coronal X-ray sources change in time, interesting trends in length, width, position, number density and thermal pressure are found and the possible causes for such changes are discussed. Further analysis of data in combination with the modelling of X-ray transport in the photosphere, allows changes in X-ray source positions and sizes due to the X-ray albedo effect to be deduced. Finally, it is shown, for the first time, how the presence of a photospheric X-ray albedo component produces a spatially resolvable polarization pattern across a hard X-ray (HXR) source. It is demonstrated how changes in the degree and direction of polarization across a single HXR source can be used to determine the anisotropy of the radiating electron distribution.

### The spatial, spectral and polarization properties of solar flare X-ray sources [Replacement]

X-rays are a valuable diagnostic tool for the study of high energy accelerated electrons. Bremsstrahlung X-rays produced by, and directly related to, high energy electrons accelerated during a flare, provide a powerful diagnostic tool for determining both the properties of the accelerated electron distribution, and of the flaring coronal and chromospheric plasmas. This thesis is specifically concerned with the study of spatial, spectral and polarization properties of solar flare X-ray sources via both modelling and X-ray observations using the Ramaty High Energy Solar Spectroscopic Imager (RHESSI). Firstly, a new model is presented, accounting for finite temperature, pitch angle scattering and initial pitch angle injection. This is developed to accurately infer the properties of the acceleration region from the observations of dense coronal X-ray sources. Moreover, examining how the spatial properties of dense coronal X-ray sources change in time, interesting trends in length, width, position, number density and thermal pressure are found and the possible causes for such changes are discussed. Further analysis of data in combination with the modelling of X-ray transport in the photosphere, allows changes in X-ray source positions and sizes due to the X-ray albedo effect to be deduced. Finally, it is shown, for the first time, how the presence of a photospheric X-ray albedo component produces a spatially resolvable polarization pattern across a hard X-ray (HXR) source. It is demonstrated how changes in the degree and direction of polarization across a single HXR source can be used to determine the anisotropy of the radiating electron distribution.

### The spatial, spectral and polarization properties of solar flare X-ray sources [Replacement]

X-rays are a valuable diagnostic tool for the study of high energy accelerated electrons. Bremsstrahlung X-rays produced by, and directly related to, high energy electrons accelerated during a flare, provide a powerful diagnostic tool for determining both the properties of the accelerated electron distribution, and of the flaring coronal and chromospheric plasmas. This thesis is specifically concerned with the study of spatial, spectral and polarization properties of solar flare X-ray sources via both modelling and X-ray observations using the Ramaty High Energy Solar Spectroscopic Imager (RHESSI). Firstly, a new model is presented, accounting for finite temperature, pitch angle scattering and initial pitch angle injection. This is developed to accurately infer the properties of the acceleration region from the observations of dense coronal X-ray sources. Moreover, examining how the spatial properties of dense coronal X-ray sources change in time, interesting trends in length, width, position, number density and thermal pressure are found and the possible causes for such changes are discussed. Further analysis of data in combination with the modelling of X-ray transport in the photosphere, allows changes in X-ray source positions and sizes due to the X-ray albedo effect to be deduced. Finally, it is shown, for the first time, how the presence of a photospheric X-ray albedo component produces a spatially resolvable polarization pattern across a hard X-ray (HXR) source. It is demonstrated how changes in the degree and direction of polarization across a single HXR source can be used to determine the anisotropy of the radiating electron distribution.

### The spatial, spectral and polarization properties of solar flare X-ray sources [Replacement]

X-rays are a valuable diagnostic tool for the study of high energy accelerated electrons. Bremsstrahlung X-rays produced by, and directly related to, high energy electrons accelerated during a flare, provide a powerful diagnostic tool for determining both the properties of the accelerated electron distribution, and of the flaring coronal and chromospheric plasmas. This thesis is specifically concerned with the study of spatial, spectral and polarization properties of solar flare X-ray sources via both modelling and X-ray observations using the Ramaty High Energy Solar Spectroscopic Imager (RHESSI). Firstly, a new model is presented, accounting for finite temperature, pitch angle scattering and initial pitch angle injection. This is developed to accurately infer the properties of the acceleration region from the observations of dense coronal X-ray sources. Moreover, examining how the spatial properties of dense coronal X-ray sources change in time, interesting trends in length, width, position, number density and thermal pressure are found and the possible causes for such changes are discussed. Further analysis of data in combination with the modelling of X-ray transport in the photosphere, allows changes in X-ray source positions and sizes due to the X-ray albedo effect to be deduced. Finally, it is shown, for the first time, how the presence of a photospheric X-ray albedo component produces a spatially resolvable polarization pattern across a hard X-ray (HXR) source. It is demonstrated how changes in the degree and direction of polarization across a single HXR source can be used to determine the anisotropy of the radiating electron distribution.

### The spatial, spectral and polarization properties of solar flare X-ray sources [Replacement]

X-rays are a valuable diagnostic tool for the study of high energy accelerated electrons. Bremsstrahlung X-rays produced by, and directly related to, high energy electrons accelerated during a flare, provide a powerful diagnostic tool for determining both the properties of the accelerated electron distribution, and of the flaring coronal and chromospheric plasmas. This thesis is specifically concerned with the study of spatial, spectral and polarization properties of solar flare X-ray sources via both modelling and X-ray observations using the Ramaty High Energy Solar Spectroscopic Imager (RHESSI). Firstly, a new model is presented, accounting for finite temperature, pitch angle scattering and initial pitch angle injection. This is developed to accurately infer the properties of the acceleration region from the observations of dense coronal X-ray sources. Moreover, examining how the spatial properties of dense coronal X-ray sources change in time, interesting trends in length, width, position, number density and thermal pressure are found and the possible causes for such changes are discussed. Further analysis of data in combination with the modelling of X-ray transport in the photosphere, allows changes in X-ray source positions and sizes due to the X-ray albedo effect to be deduced. Finally, it is shown, for the first time, how the presence of a photospheric X-ray albedo component produces a spatially resolvable polarization pattern across a hard X-ray (HXR) source. It is demonstrated how changes in the degree and direction of polarization across a single HXR source can be used to determine the anisotropy of the radiating electron distribution.

### The spatial, spectral and polarization properties of solar flare X-ray sources [Replacement]

X-rays are a valuable diagnostic tool for the study of high energy accelerated electrons. Bremsstrahlung X-rays produced by, and directly related to, high energy electrons accelerated during a flare, provide a powerful diagnostic tool for determining both the properties of the accelerated electron distribution, and of the flaring coronal and chromospheric plasmas. This thesis is specifically concerned with the study of spatial, spectral and polarization properties of solar flare X-ray sources via both modelling and X-ray observations using the Ramaty High Energy Solar Spectroscopic Imager (RHESSI). Firstly, a new model is presented, accounting for finite temperature, pitch angle scattering and initial pitch angle injection. This is developed to accurately infer the properties of the acceleration region from the observations of dense coronal X-ray sources. Moreover, examining how the spatial properties of dense coronal X-ray sources change in time, interesting trends in length, width, position, number density and thermal pressure are found and the possible causes for such changes are discussed. Further analysis of data in combination with the modelling of X-ray transport in the photosphere, allows changes in X-ray source positions and sizes due to the X-ray albedo effect to be deduced. Finally, it is shown, for the first time, how the presence of a photospheric X-ray albedo component produces a spatially resolvable polarization pattern across a hard X-ray (HXR) source. It is demonstrated how changes in the degree and direction of polarization across a single HXR source can be used to determine the anisotropy of the radiating electron distribution.

### The spatial, spectral and polarization properties of solar flare X-ray sources

X-rays are a valuable diagnostic tool for the study of high energy accelerated electrons. Bremsstrahlung X-rays produced by, and directly related to, high energy electrons accelerated during a flare, provide a powerful diagnostic tool for determining both the properties of the accelerated electron distribution, and of the flaring coronal and chromospheric plasmas. This thesis is specifically concerned with the study of spatial, spectral and polarization properties of solar flare X-ray sources via both modelling and X-ray observations using the Ramaty High Energy Solar Spectroscopic Imager (RHESSI). Firstly, a new model is presented, accounting for finite temperature, pitch angle scattering and initial pitch angle injection. This is developed to accurately infer the properties of the acceleration region from the observations of dense coronal X-ray sources. Moreover, examining how the spatial properties of dense coronal X-ray sources change in time, interesting trends in length, width, position, number density and thermal pressure are found and the possible causes for such changes are discussed. Further analysis of data in combination with the modelling of X-ray transport in the photosphere, allows changes in X-ray source positions and sizes due to the X-ray albedo effect to be deduced. Finally, it is shown, for the first time, how the presence of a photospheric X-ray albedo component produces a spatially resolvable polarization pattern across a hard X-ray (HXR) source. It is demonstrated how changes in the degree and direction of polarization across a single HXR source can be used to determine the anisotropy of the radiating electron distribution.

### Parallaxes of Star Forming Regions in the Outer Spiral Arm of the Milky Way

We report parallaxes and proper motions of three water maser sources in high-mass star-forming regions in the Outer Spiral Arm of the Milky Way. The observations were conducted with the Very Long Baseline Array as part of Bar and Spiral Structure Legacy Survey and double the number of such measurements in the literature. The Outer Arm has a pitch angle of 14.9 +/- 2.7 deg and a Galactocentric distance of 14.1 +/- 0.6 kpc toward the Galactic anticenter. The average motion of these sources toward the Galactic center is 10.7 +/- 2.1 km/s and we see no sign of a significant fall in the rotation curve out to 15 kpc from the Galactic center. The three-dimensional locations of these star-forming regions are consistent with a Galactic warp of several hundred parsecs from the plane.

### Back-tracing and flux reconstruction for solar events with PAMELA [Replacement]

The PAMELA satellite-borne experiment is providing first direct measurements of Solar Energetic Particles (SEPs) with energies from about 80 MeV to several GeV in near-Earth space. Its unique observational capabilities include the possibility of measuring the flux angular distribution and thus investigating possible anisotropies related to SEP events. This paper focuses on the analysis methods developed to estimate SEP energy spectra as a function of the particle asymptotic pitch angle. The crucial ingredient is provided by an accurate simulation of the asymptotic exposition of the PAMELA apparatus, based on a realistic reconstruction of particle trajectories in the Earth's magnetosphere.

### Back-tracing and flux reconstruction for solar events with PAMELA [Replacement]

The PAMELA satellite-borne experiment is providing first direct measurements of Solar Energetic Particles (SEPs) with energies from about 80 MeV to several GeV in near-Earth space. Its unique observational capabilities include the possibility of measuring the flux angular distribution and thus investigating possible anisotropies related to SEP events. This paper focuses on the analysis methods developed to estimate SEP energy spectra as a function of the particle asymptotic pitch angle. The crucial ingredient is provided by an accurate simulation of the asymptotic exposition of the PAMELA apparatus, based on a realistic reconstruction of particle trajectories in the Earth's magnetosphere. As case study, the results of the calculation for the May 17, 2012 event are reported.

### Back-tracing and flux reconstruction for solar events with PAMELA

The PAMELA satellite-borne experiment is providing first direct measurements of Solar Energetic Particles (SEPs) with energies from about 80 MeV to several GeV in near-Earth space. Its unique observational capabilities include the possibility of measuring the flux angular distribution and thus investigating possible anisotropies related to SEP events. This paper focuses on the analysis methods developed to estimate SEP energy spectra as a function of the particle asymptotic pitch angle. The crucial ingredient is provided by an accurate simulation of the asymptotic exposition of the PAMELA apparatus, based on a realistic reconstruction of particle trajectories in the Earth's magnetosphere.

### Back-tracing and flux reconstruction for solar events with PAMELA [Replacement]

The PAMELA satellite-borne experiment is providing first direct measurements of Solar Energetic Particles (SEPs) with energies from about 80 MeV to several GeV in near-Earth space. Its unique observational capabilities include the possibility of measuring the flux angular distribution and thus investigating possible anisotropies related to SEP events. This paper focuses on the analysis methods developed to estimate SEP energy spectra as a function of the particle asymptotic pitch angle. The crucial ingredient is provided by an accurate simulation of the asymptotic exposition of the PAMELA apparatus, based on a realistic reconstruction of particle trajectories in the Earth's magnetosphere.

### Characteristics of Spiral Arms in Late-type Galaxies

We have measured the positions of large numbers of H II regions in four nearly face-on, late-type, spiral galaxies: NGC 628 (M 74), NGC 1232, NGC 3184 and NGC 5194 (M 51). Fitting log-periodic spiral models to segments of each arm yields local estimates of spiral pitch angle and arm width. While pitch angles vary considerably along individual arms, among arms within a galaxy, and among galaxies, we find no systematic trend with galactocentric distance. We estimate the widths of the arm segments from the scatter in the distances of the H II regions from the spiral model. All major arms in these galaxies show spiral arm width increasing with distance from the galactic center, similar to the trend seen in the Milky Way. However, in the outer-most parts of the galaxies, where massive star formation declines, some arms reverse this trend and narrow. We find that spiral arms often appear to be composed of segments of ~5 kpc length, which join to form kinks and abrupt changes in pitch angle and arm width; these characteristics are consistent with properties seen in the large N-body simulations of D'Onghia, Vogelsberger and Hernquist (2013) and others.

### Compact formulae, dynamics and radiation of charged particles under synchro-curvature losses [Replacement]

We consider the fundamental problem of charged particles moving along and around a curved magnetic field line, revising the synchro-curvature radiation formulae introduced by Cheng and Zhang (1996). We provide more compact expressions to evaluate the spectrum emitted by a single particle, identifying the key parameter that controls the transition between the curvature-dominated and the synchrotron-dominated regime. This parameter depends on the local radius of curvature of the magnetic field line, the gyration radius, and the pitch angle. We numerically solve the equations of motion for the emitting particle by considering self-consistently the radiative losses, and provide the radiated spectrum produced by a particle when an electric acceleration is balanced by its radiative losses, as it is assumed to happen in the outer gaps of pulsar's magnetospheres. We compute the average spectrum radiated throughout the particle trajectory finding that the slope of the spectrum before the peak depends on the location and size of the emission region. We show how this effect could then lead to a variety of synchro-curvature spectra. Our results reinforce the idea that the purely synchrotron or curvature losses are, in general, inadequate to describe the radiative reaction on the particle motion, and the spectrum of emitted photons. Finally, we discuss the applicability of these calculations to different astrophysical scenarios.

### Polytropic models of filamentary interstellar clouds -II. Helical magnetic fields

We study the properties of magnetised cylindrical polytropes as models for interstellar filamentary clouds, extending the analysis presented in a companion paper (Toci & Galli 2014a). We formulate the general problem of magnetostatic equilibrium in the presence of a helical magnetic field, with the aim of determining the degree of support or compression resulting from the magnetisation of the cloud. We derive scale-free solutions appropriate to describe the properties of the envelopes of filaments at radii larger than the flat-density region. In these solutions, the polytropic exponent determines the radial profiles of the density and the magnetic field. The latter decreases with radius less steeply than the density, and field lines are helices twisted over cylindrical surfaces. A soft equation of state supports magnetic configurations that preferentially compress and confine the filament, whereas in the isothermal limit the field provides support. For each value of the polytropic exponent, the Lorentz force is directed outward or inward depending on whether the pitch angle is below or above some critical value which is a function of the polytropic exponent only.

### Constraining dark matter halo profiles and galaxy formation models using spiral arm morphology. II. Dark and stellar mass concentrations for 13 nearby face-on galaxies

We investigate the use of spiral arm pitch angles as a probe of disk galaxy mass profiles. We confirm our previous result that spiral arm pitch angles (P) are well correlated with the rate of shear (S) in disk galaxy rotation curves. We use this correlation to argue that imaging data alone can provide a powerful probe of galactic mass distributions out to large look-back times. We then use a sample of 13 galaxies, with Spitzer 3.6-$\mu$m imaging data and observed H$\alpha$ rotation curves, to demonstrate how an inferred shear rate coupled with a bulge-disk decomposition model and a Tully-Fisher-derived velocity normalization can be used to place constraints on a galaxy's baryon fraction and dark matter halo profile. Finally we show that there appears to be a trend (albeit a weak correlation) between spiral arm pitch angle and halo concentration. We discuss implications for the suggested link between supermassive black hole (SMBH) mass and dark halo concentration, using pitch angle as a proxy for SMBH mass.

### Pitch-angle scattering of energetic particles with adiabatic focusing

Understanding turbulent transport of charged particles in magnetized plasmas often requires a model for the description of random variations in the particle's pitch angle. The Fokker-Planck coefficient of pitch-angle scattering, which is used to describe scattering parallel to the mean magnetic field, is therefore of central importance. Whereas quasi-linear theory assumes a homogeneous mean magnetic field, such a condition is often not fulfilled, especially for high-energy particles. Here, a new derivation of the quasi-linear approach is given that is based on the unperturbed orbit found for an adiabatically focused mean magnetic field. The results show that, depending on the ratio of the focusing length and the particle's Larmor radius, the Fokker-Planck coefficient is significantly modified but agrees with the classical expression in the limit of a homogeneous mean magnetic field.

### The behavior of the pitch angle of spiral arms depending on optical wavelength

Based on integral field spectroscopy data from the CALIFA survey, we investigate the possible dependence of spiral arm pitch angle with optical wavelength. For three of the five studied objects, the pitch angle gradually increases at longer wavelengths. This is not the case for two objects where the pitch angle remains constant. This result is confirmed by the analysis of SDSS data. We discuss the possible physical mechanisms to explain this phenomenon, as well as the implications of the results.

### Analysis of the spiral structure in a simulated galaxy

We analyze the spiral structure that results in a numerical simulation of a galactic disk with stellar and gaseous components evolving in a potential that includes an axisymmetric halo and bulge. We perform a second simulation without the gas component to observe how it affects the spiral structure in the disk. To quantify this, we use a Fourier analysis and obtain values for the pitch angle and the velocity of the self-excited spiral pattern of the disk. The results show a tighter spiral in the simulation with gaseous component. The spiral structure is consistent with a superposition of waves, each with a constant pattern velocity in given radial ranges.

### A new method to estimate local pitch angles in spiral galaxies: Application to spiral arms and feathers in M81 and M51

We examine $8\mu$m IRAC images of the grand design two-arm spiral galaxies M81 and M51 using a new method whereby pitch angles are locally determined as a function of scale and position, in contrast to traditional Fourier transform spectral analyses which fit to average pitch angles for whole galaxies. The new analysis is based on a correlation between pieces of a galaxy in circular windows of $(\ln R, \theta)$ space and logarithmic spirals with various pitch angles. The diameter of the windows is varied to study different scales. The result is a best-fit pitch angle to the spiral structure as a function of position and scale, or a distribution function of pitch angles as a function of scale for a given galactic region or area. We apply the method to determine the distribution of pitch angles in the arm and interarm regions of these two galaxies. In the arms, the method reproduces the known pitch angles for the main spirals on a large scale, but also shows higher pitch angles on smaller scales resulting from dust feathers. For the interarms, there is a broad distribution of pitch angles representing the continuation and evolution of the spiral arm feathers as the flow moves into the interarm regions. Our method shows a multiplicity of spiral structures on different scales, as expected from gas flow processes in a gravitating, turbulent and shearing interstellar medium. We also present results for M81 using classical 1D and 2D Fourier transforms, together with a new correlation method, which shows good agreement with conventional 2D Fourier transforms.

### Self-similar expansion of solar coronal mass ejections: implications for Lorentz self-force driving

We examine the propagation of several CMEs with well-observed flux rope signatures in the field of view of the SECCHI coronagraphs aboard the STEREO satellites using the GCS fitting method of Thernisien, Vourlidas \& Howard (2009). We find that the manner in which they propagate is approximately self-similar; i.e., the ratio ($\kappa$) of the flux rope minor radius to its major radius remains approximately constant with time. We use this observation of self-similarity to draw conclusions regarding the local pitch angle ($\gamma$) of the flux rope magnetic field and the misalignment angle ($\chi$) between the current density ${\mathbf J}$ and the magnetic field ${\mathbf B}$. Our results suggest that the magnetic field and current configurations inside flux ropes deviate substantially from a force-free state in typical coronagraph fields of view, validating the idea of CMEs being driven by Lorentz self-forces.

### Pitch Angle of Galactic Spiral Arms

One of the key parameters that characterize spiral arms in disk galaxies is a pitch angle that measures the inclination of a spiral arm to the direction of galactic rotation. The pitch angle differs from galaxy to galaxy, which suggests that the rotation law of galactic disks determines it. In order to investigate the relation between the pitch angle of spiral arms and the shear rate of galactic differential rotation, we perform local $N$-body simulations of pure stellar disks. We find that the pitch angle increases with the epicycle frequency and decreases with the shear rate and obtain the fitting formula. This dependence is explained by the swing amplification mechanism.

### Spatial Confinement of the IBEX Ribbon: A Dominant Turbulence Mechanism

The narrow ribbon of enhanced energetic neutral atom flux observed by the Interstellar Boundary Explorer (IBEX) spacecraft has prompted numerous ideas to explain its structure and properties. One of these ideas is the "neutral solar wind" scenario, which identifies the source particles as pickup protons in the local interstellar medium originating in solar wind charge-exchange interactions. This scenario has been thought to require unrealistically weak pitch-angle scattering of the pickup protons to explain the narrow structure. Recently, Schwadron & McComas (2013) suggested that this structure could result from a spatial retention of the pickup protons, rather than from a restricted pitch-angle distribution. Here, we present a physically motivated, quantitative mechanism to produce such a spatial configuration. This mechanism is based on the "dominant turbulence" assumption, which can be applied where the production of new pickup protons is slow, and has been used to successfully explain the level of turbulent heating observed in the outer solar wind. This formalism predicts a pickup isotropization process which adds or subtracts energy from the ambient turbulent fluctuations, depending on the initial pitch angle of the pickup protons. We show that a simple model of this process can yield a ribbon structure in qualitative agreement with the observations. The results of this simple model are not yet quantitatively satisfactory, but we suggest several improvements which may reduce the quantitative discrepancy.

### The Transport of Cosmic Rays Across Magnetic Fieldlines [Replacement]

The long residence times and small anisotropies of cosmic rays suggest that they are well confined and well scattered by the Galactic magnetic field. Due to the disklike shape of the confinement volume, transport in the vertical direction, perpendicular to the mean Galactic magnetic field, is key to cosmic ray escape. It has long been recognized that this vertical transport depends both on the vertical component of the fieldlines themselves and on the extent to which the cosmic rays are tied to the fieldlines. In this paper we use magnetic fields with very simple spatial and temporal structure to isolate some important features of cross fieldline transport. We show that even simple magnetic nonuniformities combined with pitch angle scattering can enhance cross fieldline transport by several orders of magnitude, while pitch angle scattering is unnecessary for enhanced transport if the field is chaotic. Nevertheless, perpendicular transport is much less than parallel transport in all the cases we study. We apply the results to confinement of cosmic rays in the Fermi Bubbles.

### Pitch angle variations in spiral galaxies

We present a detailed photometric study and measurements of spiral arm pitch angles for a sample of 50 non-barred or weakly barred grand-design spiral galaxies selected from Sloan Digital Sky Survey. In order to find pitch angles, we used a new method based on the window Fourier analysis of their images. This method allows us not only to infer the average pitch angle, but to obtain its value as a function of galactocentric radius as well. Our main results are as follows: (1) Spiral arms of most galaxies cannot be described by a single value of the pitch angle. About 2/3 of galaxies demonstrate pitch angle variations exceeding 20%. In most galaxies in the sample their pitch angle decreases by increasing the distance from the centre. (2) Pitch angle variations correlate with the properties of galaxies - with the shape of the surface brightness distribution (envelope-type or truncated disc), and with the sign of stellar disc colour gradient. (3) More luminous and bright bulges produce more tightly wound spiral arms, that is in agreement with current models for spiral arms formation.

### EUV Non-thermal Line Broadening and High-energy particles during Solar Flares

We have studied the relationship between the location of EUV nonthermal broadening and high-energy particles during the large flares by using EUV imaging spectrometer onboard {\it Hinode}, Nobeyama Radio Polarimeter, Nobeyama Radioheliograph, and Atmospheric Imaging Assembly onboard {\it Solar Dynamic Observatory}. We have analyzed the five large flare events which contain thermal rich, intermediate, and thermal poor flares classified by the definition discussed in the paper. We found that, in the case of thermal rich flares, the nonthermal broadening of \ion{Fe}{24} occurred at the top of the flaring loop at the beginning of the flares. The source of the 17 GHz microwave is located at the footpoint of the flare loop. On the other hand, in the case of intermediate/thermal poor flares, the nonthermal broadening of \ion{Fe}{24} occurred at the footpoint of the flare loop at the beginning of the flares. The source of the 17 GHz microwave is located at the top of the flaring loop. We discussed the difference between thermal rich and intermediate/thermal poor flare based on the spatial information of nonthermal broadening, which may give a clue for the presence of turbulence playing an important role in the pitch angle scattering of the high-energy electron.

### Energetic particle cross-field propagation early in a solar event

Solar energetic particles (SEPs) have been observed to easily spread across heliographic longitudes, and the mechanisms responsible for this behaviour remain unclear. We use full-orbit simulations of a 10 MeV proton beam in a turbulent magnetic field to study to what extent the spread across the mean field can be described as diffusion early in a particle event. We compare the full-orbit code results to solutions of a Fokker-Planck equation including spatial and pitch angle diffusion, and of one including also propagation of the particles along random-walking magnetic field lines. We find that propagation of the particles along meandering field lines is the key process determining their cross-field spread at 1 AU at the beginning of the simulated event. The mean square displacement of the particles an hour after injection is an order of magnitude larger than that given by the diffusion model, indicating that models employing spatial cross-field diffusion cannot be used to describe early evolution of an SEP event. On the other hand, the diffusion of the particles from their initial field lines is negligible during the first 5 hours, which is consistent with the observations of SEP intensity dropouts. We conclude that modelling SEP events must take into account the particle propagation along meandering field lines for the first 20 hours of the event.

### Small-scale Gradients of Charged Particles in the Heliospheric Magnetic Field

Using numerical simulations of charged-particles propagating in the heliospheric magnetic field, we study small-scale gradients, or "dropouts", in the intensity of solar energetic particles seen at 1 AU. We use two turbulence models, the foot-point random motion model (Jokipii & Parker 1969; Giacalone et al. 2006) and two-component model (Matthaeus et al. 1990), to generate fluctuating magnetic fields similar to spacecraft observations at 1 AU. The turbulence models include a Kolmogorov-like magnetic field power spectrum containing a broad range of spatial scales from those that lead to large-scale field-line random walk to small scales leading to resonant pitch-angle scattering of energetic particles. We release energetic protons (20 keV - 10 MeV) from a spatially compact and instantaneous source. The trajectories of energetic charged particles in turbulent magnetic fields are numerically integrated. Spacecraft observations are mimicked by collecting particles in small windows when they pass the windows at a distance of 1 AU. We show that small-scale gradients in the intensity of energetic particles and velocity dispersions observed by spacecraft can be reproduced using the foot-point random motion model. However, no dropouts is seen in simulations using the two-component magnetic turbulence model. We also show that particle scattering in the solar wind magnetic field needs to be infrequent for intensity dropouts to form.

### Determination of Stochastic Acceleration Model Characteristics in Solar Flares [Replacement]

Following our recent paper (Petrosian & Chen 2010), we have developed an inversion method to determine the basic characteristics of the particle acceleration mechanism directly and non-parametrically from observations under the leaky box framework. In the above paper, we demonstrated this method for obtaining the energy dependence of the escape time. Here, by converting the Fokker-Planck equation to its integral form, we derive the energy dependences of the energy diffusion coefficient and direct acceleration rate for stochastic acceleration in terms of the accelerated and escaping particle spectra. Combining the regularized inversion method of Piana et al. 2007 and our procedure, we relate the acceleration characteristics in solar flares directly to the count visibility data from RHESSI. We determine the timescales for electron escape, pitch angle scattering, energy diffusion, and direct acceleration at the loop top acceleration region for two intense solar flares based on the regularized electron flux spectral images. The X3.9 class event shows dramatically different energy dependences for the acceleration and scattering timescales, while the M2.1 class event shows a milder difference. The M2.1 class event could be consistent with the stochastic acceleration model with a very steep turbulence spectrum. A likely explanation of the X3.9 class event could be that the escape of electrons from the acceleration region is not governed by a random walk process, but instead is affected by magnetic mirroring, in which the scattering time is proportional to the escape time and has an energy dependence similar to the energy diffusion time.

### Determination of Stochastic Acceleration Model Characteristics in Solar Flares

Abridged. Following our recent paper, we have developed an inversion method to determine the basic characteristics for the model of stochastic acceleration (SA) by plasma wave turbulence directly and non-parametrically from observations in the framework of the leaky box version of the Fokker-Planck kinetic equation. In particular, we show that by inverting the Fokker-Planck equation to its integral form, one can derive the energy diffusion coefficient and direct acceleration rate by turbulence in terms of the accelerated and escaping particle spectra. We apply the analytic formulas to solar flare suprathermal electrons, which produce HXR emission at the coronal loop top (LT) and two thick target footpoints. Using the spatially resolved electron spectra from regularized electron flux images, we determine the electron escape time (related to pitch angle scattering rate), and the energy diffusion coefficient at the LT accelerator. Results obtained from two intense RHESSI events indicate that the escape time increases with energy and the energy diffusion (acceleration) time and scattering time have dramatically different energy dependences. Such behaviors may be difficult to explain by existing SA modeling, and may indicate that a different acceleration mechanism is at work or imply a breakdown of the interpretation of the electron escape being a random walk process. The discrepant energy dependences can be alleviated somewhat by a much steeper than the Kolmogorov-type turbulence spectrum. A more likely explanation could be that the escape of electrons out of the LT acceleration region is governed by converging fields in a magnetic mirror geometry. The results demonstrate the critical importance of combined modeling of electron acceleration by plasma wave turbulence and the large scale magnetic field variations in a reconnection environment.

### Galactic Kinematics from a Sample of Young Massive Stars

Based on published sources, we have created a kinematic database on 220 massive (>10 solar masses) young Galactic star systems located within <3 kpc of the Sun. Out of them, approximately 100 objects are spectroscopic binary and multiple star systems whose components are massive OB stars; the remaining objects are massive Hipparcos B stars with parallax errors of no more than 10 percent. Based on the entire sample, we have constructed the Galactic rotation curve, determined the circular rotation velocity of the solar neighborhood around the Galactic center at Ro=8 kpc, Vo=259+-16 km/s, and obtained the following spiral density wave parameters: the amplitudes of the radial and azimuthal velocity perturbations f_R=-10.8+/-1.2 km/s, and f_\theta=7.9+/-1.3 km/s, respectively; the pitch angle for a two-armed spiral pattern i=-6.0+/-0.4 deg., with the wavelength of the spiral density wave near the Sun being 2.6+/-0.2 kpc; and the radial phase of the Sun in the spiral density wave -120+/-4 deg. We show that such peculiarities of the Gould Belt as the local expansion of the system, the velocity ellipsoid vertex deviation, and the significant additional rotation can be explained in terms of the density wave theory. All these effects decrease noticeably once the influence of the spiral density wave on the velocities of nearby stars has been taken into account. The influence of Gould Belt stars on the Galactic parameter estimates has also been revealed. Eliminating them from the kinematic equations has led to the following new values of the spiral density wave parameters: f_\theta=2.9+/-2.1 km/s and \chi_\odot=-104+/-6 deg.

### Cosmic Ray Parallel and Perpendicular Transport in Turbulent Magnetic Fields

A correct description of cosmic ray (CR) diffusion in turbulent plasma is essential for many astrophysical and heliospheric problems. This paper aims at presenting physical diffusion behavior of CRs in actual turbulent magnetic fields, model of which has been numerically tested. We perform test particle simulations in compressible magnetohydrodynamic (MHD) turbulence. We obtain scattering and spatial diffusion coefficients by tracing particle trajectories. We find no resonance gap for pitch-angle scattering at 90$^\circ$. Our result confirms the dominance of mirror interaction with compressible modes for most pitch angles as revealed by the nonlinear theory. For cross field transport, our results are consistent with normal diffusion predicted earlier for large scales. The diffusion behavior strongly depends on the Alfvenic Mach number and particle's parallel mean free path. We for the first time numerically derive the dependence of M_A^4 for perpendicular diffusion coefficient with respect to the mean magnetic field. We conclude that CR diffusion coefficients are anisotropic in sub-Alfvenic turbulence and spatially correlated to the local turbulence properties. On scales smaller than the injection scale, we find that CRs are superdiffusive. We emphasize the importance of our results in a wide range of astrophysical processes, including magnetic reconnection.

### Cosmic Ray Parallel and Perpendicular Transport in Turbulent Magnetic Fields [Replacement]

A correct description of cosmic ray (CR) diffusion in turbulent plasma is essential for many astrophysical and heliospheric problems. This paper aims at presenting physical diffusion behavior of CRs in actual turbulent magnetic fields, model of which has been numerically tested. We perform test particle simulations in compressible magnetohydrodynamic (MHD) turbulence. We obtain scattering and spatial diffusion coefficients by tracing particle trajectories. We find no resonance gap for pitch-angle scattering at 90$^\circ$. Our result confirms the dominance of mirror interaction with compressible modes for most pitch angles as revealed by the nonlinear theory. For cross field transport, our results are consistent with normal diffusion predicted earlier for large scales. The diffusion behavior strongly depends on the Alfvenic Mach number and particle's parallel mean free path. We for the first time numerically derive the dependence of M_A^4 for perpendicular diffusion coefficient with respect to the mean magnetic field. We conclude that CR diffusion coefficients are anisotropic in sub-Alfvenic turbulence and spatially correlated to the local turbulence properties. On scales smaller than the injection scale, we find that CRs are superdiffusive. We emphasize the importance of our results in a wide range of astrophysical processes, including magnetic reconnection.

### The Efficiency of Second-Order Fermi Acceleration by Weakly Compressible MHD Turbulence [Replacement]

We investigate the effects of pitch-angle scattering on the efficiency of particle heating and acceleration by MHD turbulence using phenomenological estimates and simulations of non-relativistic test particles interacting with strong, subsonic MHD turbulence. We include an imposed pitch-angle scattering rate, which is meant to approximate the effects of high frequency plasma waves and/or velocity space instabilities. We focus on plasma parameters similar to those found in the near-Earth solar wind, though most of our results are more broadly applicable. An important control parameter is the size of the particle mean free path lambda_{mfp} relative to the scale of the turbulent fluctuations L. For small scattering rates, particles interact quasi-resonantly with turbulent fluctuations in magnetic field strength. Scattering increases the long-term efficiency of this resonant heating by factors of a few-10, but the distribution function does not develop a significant non-thermal power-law tail. For higher scattering rates, the interaction between particles and turbulent fluctuations becomes non-resonant, governed by particles heating and cooling adiabatically as they encounter turbulent density fluctuations. Rapid pitch-angle scattering can produce a power-law tail in the proton distribution function but this requires fine-tuning of parameters. Moreover, in the near-Earth solar wind, a significant power-law tail cannot develop by this mechanism because the particle acceleration timescales are longer than the adiabatic cooling timescale set by the expansion of the solar wind. Our results thus imply that MHD-scale turbulent fluctuations are unlikely to be the origin of the v^{-5} tail in the proton distribution function observed in the solar wind.

### The Efficiency of Second-Order Fermi Acceleration by Weakly Compressible MHD Turbulence

We investigate the effects of pitch-angle scattering on the efficiency of particle heating and acceleration by MHD turbulence using phenomenological estimates and simulations of non-relativistic test particles interacting with strong, subsonic MHD turbulence. We include an imposed pitch-angle scattering rate, which is meant to approximate the effects of high frequency plasma waves and/or velocity space instabilities. We focus on plasma parameters similar to those found in the near-Earth solar wind, though most of our results are more broadly applicable. An important control parameter is the size of the particle mean free path lambda_{mfp} relative to the scale of the turbulent fluctuations L. For small scattering rates, particles interact quasi-resonantly with turbulent fluctuations in magnetic field strength. Scattering increases the long-term efficiency of this resonant heating by factors of a few-10, but the distribution function does not develop a significant non-thermal power-law tail. For higher scattering rates, the interaction between particles and turbulent fluctuations becomes non-resonant, governed by particles heating and cooling adiabatically as they encounter turbulent density fluctuations. Rapid pitch-angle scattering can produce a power-law tail in the proton distribution function but this requires fine-tuning of parameters. Moreover, in the near-Earth solar wind, a significant power-law tail cannot develop by this mechanism because the particle acceleration timescales are longer than the adiabatic cooling timescale set by the expansion of the solar wind. Our results thus imply that MHD-scale turbulent fluctuations are unlikely to be the origin of the v^{-5} tail in the proton distribution function observed in the solar wind.

### The Herschel Exploitation of Local Galaxy Andromeda (HELGA). IV. The distribution and properties of molecular cloud associations in M31

In this paper we present a catalogue of Giant Molecular Clouds (GMCs) in the Andromeda (M31) galaxy extracted from the Hershel Exploitation of Local Galaxy Andromeda (HELGA) dataset. GMCs are identified from the Herschel maps using a hierarchical source extraction algorithm. We present the results of this new catalogue and characterise the spatial distribution and spectral energy properties of its clouds based on the radial dust/gas properties found by Smith et al (2012). 236 GMCs in the mass range 10^4-10^7 M_sol are identified, their cumulative mass distribution is found to be proportional to M^-1.45 in agreement with earlier studies. The GMCs appear to follow the same cloud mass to L_CO correlation observed in the Milky Way. However, comparison between this catalogue and interferometry studies also shows that the GMCs are substructured below the Herschel resolution limit suggesting that we are observing associations of GMCs. Following Gordon et al. (2006), we study the spatial structure of M31 by splitting the observed structure into a set of spiral arms and offset rings. We fit radii of 10.5 and 15.5 kpc to the two most prominent rings. We then fit a logarithmic spiral with a pitch angle of \$8.9 deg to the GMCs not associated with either ring. Lastly, we comment upon the effects of deprojection on our results and investigate the effect different models for M31's inclination will have upon the projection of an unperturbed spiral arm system.