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Register a new userMagnetic Field Uniformity Across the GF 9-2 YSO, L1082C Dense Core, and GF 9 Filamentary Dark Cloud
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The orientation of the magnetic field (B-field) in the filamentary dark cloud GF 9 was traced from the periphery of the cloud into the L1082C dense core that contains the low-mass, low-luminosity Class 0 young stellar object (YSO) GF 9-2 (IRAS 20503+6006). This was done using SOFIA HAWC+ dust thermal emission polarimetry (TEP) at 216 um in combination with Mimir near-infrared background starlight polarimetry (BSP) conducted at H-band (1.6 um) and K-band (2.2 um). These observations were augmented with published I-band (0.77 um) BSP and Planck 850 um TEP to probe B-field orientations with offset from the YSO in a range spanning 6000 AU to 3 pc. No strong B-field orientation change with offset was found, indicating remarkable uniformity of the B-field from the cloud edge to the YSO environs. This finding disagrees with weak-field models of cloud core and YSO formation. The continuity of inferred B-field orientations for both TEP and BSP probes is strong evidence that both are sampling a common B-field that uniformly threads the cloud, core, and YSO region. Bayesian analysis of Gaia DR2 stars matched to the Mimir BSP stars finds a distance to GF 9 of 270 +/- 10 pc. No strong wavelength dependence of B-field orientation angle was found, contrary to previous claims.
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New visible polarization data combined with existing IR and FIR polarization data are used to study how the magnetic field threading the filamentary molecular cloud GF 9 connects to larger structures in its general environment. We find that when both visible and NIR polarization data are plotted as a function of extinction, there is no evidence for a plateau or a saturation effect in the polarization at Av ~ 1.3 as seen in dark clouds in Taurus. This lack of saturation effect suggests that even in the denser parts of GF 9 we are still probing the magnetic field. The visible polarization is smooth and has a well-defined orientation. The IR data are also well defined but with a different direction, and the FIR data in the core region are well defined and with yet another direction, but are randomly distributed in the filament region. On the scale of a few times the mean radial dimension of the molecular cloud, it is as if the magnetic field were `blind to the spatial distribution of the filaments while on smaller scales within the cloud, in the core region near the IRAS point source PSC 20503+6006, polarimetry shows a rotation of the magnetic field lines in these denser phases. Hence, in spite of the fact that the spatial resolution is not the same in the visible/NIR and in the FIR data, all the data put together indicate that the field direction changes with the spatial scale. Finally, the Chandrasekhar and Fermi method is used to evaluate the magnetic field strength, indicating that the core region is approximately magnetically critical. A global interpretation of the results is that in the core region an original poloidal field could have been twisted by a rotating elongated (core+envelope) structure. There is no evidence for turbulence and ambipolar diffusion does not seem to be effective at the present time.
In this work we describe an efficient implementation of a hierarchy of algorithms for the decomposition of dense matrices over the field with two elements (GF(2)). Matrix decomposition is an essential building block for solving dense systems of linear and non-linear equations and thus much research has been devoted to improve the asymptotic complexity of such algorithms. In this work we discuss an implementation of both well-known and improved algorithms in the M4RI library. The focus of our discussion is on a new variant of the M4RI algorithm - denoted MMPF in this work -- which allows for considerable performance gains in practice when compared to the previously fastest implementation. We provide performance figures on x86_64 CPUs to demonstrate the viability of our approach.
We describe an efficient implementation of a hierarchy of algorithms for multiplication of dense matrices over the field with two elements (GF(2)). In particular we present our implementation -- in the M4RI library -- of Strassen-Winograd matrix multiplication and the Method of the Four Russians multiplication (M4RM) and compare it against other available implementations. Good performance is demonstrated on on AMDs Opteron and particulary good performance on Intels Core 2 Duo. The open-source M4RI library is available stand-alone as well as part of the Sage mathematics software. In machine terms, addition in GF(2) is logical-XOR, and multiplication is logical-AND, thus a machine word of 64-bits allows one to operate on 64 elements of GF(2) in parallel: at most one CPU cycle for 64 parallel additions or multiplications. As such, element-wise operations over GF(2) are relatively cheap. In fact, in this paper, we conclude that the actual bottlenecks are memory reads and writes and issues of data locality. We present our empirical findings in relation to minimizing these and give an analysis thereof.
This paper gives new methods of constructing {it symmetric self-dual codes} over a finite field $GF(q)$ where $q$ is a power of an odd prime. These methods are motivated by the well-known Pless symmetry codes and quadratic double circulant codes. Using these methods, we construct an amount of symmetric self-dual codes over $GF(11)$, $GF(19)$, and $GF(23)$ of every length less than 42. We also find 153 {it new} self-dual codes up to equivalence: they are $[32, 16, 12]$, $[36, 18, 13]$, and $[40, 20,14]$ codes over $GF(11)$, $[36, 18, 14]$ and $[40, 20, 15]$ codes over $GF(19)$, and $[32, 16, 12]$, $[36, 18, 14]$, and $[40, 20, 15]$ codes over $GF(23)$. They all have new parameters with respect to self-dual codes. Consequently, we improve bounds on the highest minimum distance of self-dual codes, which have not been significantly updated for almost two decades.
LDN 1157, is one of the several clouds situated in the cloud complex, LDN 1147/1158, represents a coma-shaped morphology with a well-collimated bipolar outflow emanating from a Class 0 protostar, LDN 1157-mm. The main goals of this work are (a) to map the inter-cloud magnetic field (ICMF) geometry of the region surrounding LDN 1157 to investigate its relationship with the cloud morphology, with the outflow direction and with the core magnetic field (CMF) geometry inferred from the mm- and sub-mm polarization results from the literature, and (b) to investigate the kinematic structure of the cloud. We carried out R-band polarization observations of the stars projected on the cloud to map the pc-scale magnetic field geometry and made spectroscopic observations of the entire cloud in 12CO, C18O and N2H+ (J=1-0) lines to investigate its kinematic structure. We obtained a distance of 340$pm$3 pc to the LDN 1147/1158, complex based on the Gaia DR2 parallaxes and proper motion values of the three YSOs associated with the complex. A single filament of $sim1.2$ pc in length and $sim0.09$ pc in width is found to run all along the coma-shaped cloud. Based on the relationships between the ICMF, CMF, filament orientations, outflow direction, and the presence of an hour-glass morphology of the magnetic field, it is likely that the magnetic field had played an important role in the star formation process in LDN 1157. Combining the proper motions of the YSOs and the radial velocity of LDN 1147/1158 and another complex LDN 1172/1174 which is situated $sim2$dgr~east of it, we found that both the complexes are moving collectively toward the Galactic plane. The filamentary morphology of the east-west segment of LDN 1157 may have formed as a result of mass lost by ablation due to the interaction of the moving cloud with the ambient interstellar medium.
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