Magnetic fields in molecular clouds: Limitations of the analysis of Zeeman observations

Context. Observations of Zeeman split spectral lines represent an important approach to derive the structure and strength of magnetic fields in molecular clouds. In contrast to the uncertainty of the spectral line observation itself, the uncertainty of the analysis method to derive the magnetic field strength from these observations is not been well characterized so far. Aims. We investigate the impact of several physical quantities on the uncertainty of the analysis method, which is used to derive the line-of-sight (LOS) magnetic field strength from Zeeman split spectral lines. Methods. We simulate the Zeeman splitting of the 1665 MHz OH line with the 3D radiative transfer (RT) extension ZRAD. This extension is based on the line RT code Mol3D (Ober et al. 2015) and has been developed for the POLArized RadIation Simulator POLARIS (Reissl et al. 2016). Results. Observations of the OH Zeeman effect in typical molecular clouds are not significantly affected by the uncertainty of the analysis method. We derived an approximation to quantify the range of parameters in which the analysis method works sufficiently accurate and provide factors to convert our results to other spectral lines and species as well. We applied these conversion factors to CN and found that observations of the CN Zeeman effect in typical molecular clouds are neither significantly affected by the uncertainty of the analysis method. In addition, we found that the density has almost no impact on the uncertainty of the analysis method, unless it reaches values higher than those typically found in molecular clouds. Furthermore, the uncertainty of the analysis method increases, if both the gas velocity and the magnetic field show significant variations along the line-of-sight. However, this increase should be small in Zeeman observations of most molecular clouds considering typical velocities of ~1 km/s.Comment: 9 pages, 6 figure

Tracing planet-induced structures in circumstellar disks using molecular lines

Circumstellar disks are considered to be the birthplace of planets. Specific structures like spiral arms, gaps, and cavities are characteristic indicators of planet-disk interaction. Investigating these structures can provide insights into the growth of protoplanets and the physical properties of the disk. We investigate the feasibility of using molecular lines to trace planet-induced structures in circumstellar disks. Based on 3D hydrodynamic simulations of planet-disk interactions, we perform self-consistent temperature calculations and produce N-LTE molecular line velocity-channel maps and spectra of these disks using our new N-LTE line radiative transfer code Mol3D. Subsequently, we simulate ALMA observations using the CASA simulator. We consider two nearly face-on inclinations, 5 disk masses, 7 disk radii, and 2 different typical pre-main-sequence host stars (T Tauri, Herbig Ae). We calculate up to 141 individual velocity-channel maps for five molecules/isotopoloques in a total of 32 rotational transitions to investigate the frequency dependence of the structures indicated above. We find that the majority of protoplanetary disks in our parameter space could be detected in the molecular lines considered. However, unlike the continuum case, gap detection is not straightforward in lines. For example, gaps are not seen in symmetric rings but are masked by the pattern caused by the global (Keplerian) velocity field. We identify specific regions in the velocity-channel maps that are characteristic of planet-induced structures. Simulations of high angular resolution molecular line observations demonstrate the potential of ALMA to provide complementary information about the planet-disk interaction as compared to continuum observations. In particular, the detection of planet-induced gaps is possible under certain conditions.(abridged)Comment: 19 pages, 19 figures, accepted for publication in A&

The effect of a nucleating agent on lamellar growth in melt-crystallizing polyethylene oxide

The effects of a (non co-crystallizing) nucleating agent on secondary nucleation rate and final lamellar thickness in isothermally melt-crystallizing polyethylene oxide are considered. SAXS reveals that lamellae formed in nucleated samples are thinner than in the pure samples crystallized at the same undercoolings. These results are in quantitative agreement with growth rate data obtained by calorimetry, and are interpreted as the effect of a local decrease of the basal surface tension, determined mainly by the nucleant molecules diffused out of the regions being about to crystallize. Quantitative agreement with a simple lattice model allows for some interpretation of the mechanism.Comment: submitted to Journal of Applied Physics (first version on 22 Apr 2002

All Pain, Whose Gain? A Fifty-State Analysis of the Independent State Legislature Doctrine for Redistricting

The “Independent State Legislature” (ISL) doctrine has recently been offered as a reinterpretation of legislative control over federal elections and may upend decades of election law precedent. Based on Article I of the U.S. Constitution, the ISL doctrine holds that such authority of state legislatures potentially overrides state constitutions, as well as state courts, citizen initiatives, and even the governor. The original political goals of the ISL doctrine were the 2000 and 2016 Presidential elections. The doctrine has recently come before the Supreme Court in Moore v. Harper, a case concerning redistricting, and could open the door to increased gerrymandering of U.S. congressional districts. Here we analyze the practical consequences in all fifty states. We find that such a change in redistricting law would be highly asymmetric to the major political parties, giving considerable advantage to Democrats because it would undo an existing propensity for reform or judicial intervention in Democratic-leaning and swing states. This asymmetry raises questions of the desirability of introducing the ISL to questions of redistricting