Determining the co-rotation radii of spiral galaxies using spiral arm pitch angle measurements at multiple wavelengths

ABSTRACT The spiral arms spanning disc galaxies are believed to be created by density waves that propagate through galactic discs. We present a novel method of finding the co-rotation radius where the spiral arm pattern speed matches the velocities of the stars within the disc. Our method uses an image-overlay technique, which involves tracing the arms of spiral galaxies on images observed in different wavelengths. Density wave theory predicts that spiral arms observed from different wavelengths show a phase crossing at the co-rotation radius. For the purpose of this study, 20 nearby galaxies were analysed in four different wavelengths with pitch angle measurements performed by two independent methods. We used optical wavelength images (B band 440 nm), two infrared wavelength images provided by Spitzer (3.6 and 8 μm) and ultraviolet images from GALEX (1350, 1750 Å). The results were compared and verified with other records found in the literature. We then found rotation curve data for six of our galaxies and used our co-rotation radii estimates to measure the time that would elapse between star formation and moving to their observed positions in the B-band spirals. The average time lapse for this motion was found to be ∼50 Myr. The success of this new method of finding the co-rotation radius confirms density wave theory in a very direct way.

The evolution of pitch angles of spiral arms

ABSTRACTIn spiral galaxies, the pitch angle, α, of the spiral arms is often proposed as a discriminator between theories for the formation of the spiral structure. In Lin–Shu density wave theory, α stays constant in time, being simply a property of the underlying galaxy. In other theories (e.g. tidal interaction, and self-gravity), it is expected that the arms wind up in time, so that to a first approximation $\cot \alpha \propto t$. For these theories, it would be expected that a sample of galaxies observed at random times should show a uniform distribution of $\cot \alpha$. We show that a recent set of measurements of spiral pitch angles (Yu & Ho) is broadly consistent with this expectation.

Impact of Domain Wall Pinning on the Dielectric Loss of Relaxor Ferroelectrics

Charge density wave theory is used to investigate the dependence of dielectric loss of relaxor ferroelectrics on temperature, frequency and concentration of impurities. The dielectric loss originates from the local pinning. The competition between the local and collective pinning leads to a peak in the curve of dielectric loss v.s. temperature as well as the curve of dielectric constant v.s. temperature. The peak temperature of dielectric constant TL, increases with increasing frequency and with decreasing concentration of impurities. The maximum dielectric loss is in proportion to TL and in inverse proportion to the barrier height. Our theoretical results agree qualitatively with the experimental results.