Modeling of Galactic Foreground Polarization with Velocity Gradients
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Modeling of Galactic Foreground Polarization with Velocity Gradients
Yue Hu
1, 2 and A. Lazarian Department of Physics, University of Wisconsin-Madison, Madison, WI 53706, USA Department of Astronomy, University of Wisconsin-Madison, Madison, WI 53706, USA
ABSTRACTThe detection of primordial B-mode polarization is still challenging due to the relatively low ampli-tude compared to the galactic foregrounds. To remove the contribution from the foreground, a com-prehensive picture of the galactic magnetic field is indispensable. The Velocity Gradient Technique(VGT) is promising in tracing magnetic fields based on the modern understanding of the magneto-hydrodynamic turbulence. In this work, we apply VGT to an H I region containing an intermediatevelocity cloud and a local velocity cloud, which are distinguishable in position-position-velocity space.We show that VGT gives an excellent agreement with the Planck polarization and stellar polarization.We confirm the advantages of VGT in constructing the 3D galactic magnetic field. Keywords:
Interstellar medium (847); Interstellar magnetic fields (845); Interstellar dynamics (839)THE VELOCITY GRADIENTS TECHNIQUEAs an output of modern MHD turbulence theories, theVelocity Gradients Technique (VGT) has already beendeveloped as a new method to trace the magnetic fields(Lazarian & Yuen 2018a). VGT drives the revolution-ary understanding of the galactic magnetic fields. Forinstance, Hu et al. (2020a) and Lu et al. (2020) utilizeVGT and the H I emission line to predict the foregrounddust polarization. The ratio of the E- and B-modes cal-culated from VGT is BB/EE ≈ ± [email protected], alazarian@facstaff.wisc.edu claim that everything possible to be obtained with RHTis available with VGT.Lazarian & Pogosyan (2000) predicted the intensityfluctuations in PPV cubes could arise due to turbulentvelocities along the LOS, which is called the velocitycaustics effect. Based on this theory, Lazarian & Yuen(2018a) proposed that velocity gradients in thin velocitychannels can trace the POS magnetic field. Here we alsoemploy this concept and extract the velocity gradientfrom all thin channels. A detailed recipe can be foundin Hu et al. (2018, 2020a,b)As a separate development, Clark et al. (2014) obser-vationally found the alignment of filaments in the chan-nel maps with the magnetic field. This empirical align-ment was argued in Clark et al. (2019) to be related tothe two-phase nature of H I , while the role of velocitycaustics was totally ignored. The empirical way of trac-ing filaments, i.e., the RHT-technique, was used to tracethe magnetic field and to predict the dust polarizationusing H I emission (Clark et al. 2015; Clark & Hensley2019).Compared to empirical RHT, VGT is based on thefoundations routed in the anisotropic properties of MHDturbulence and the theory of turbulent reconnection.The ability of VGT in tracing magnetic fields does notdepend on the media being one or two-phase, which wasdemonstrated numerically in Hu et al. (2019c) and byapplication to molecular clouds (Hu et al. 2019a,b).Due to the existence of two interpretations, the na-ture of fluctuations in channel maps became a subject a r X i v : . [ a s t r o - ph . GA ] J u l Hu & Lazarian
Figure 1. Right : the morphology of the magnetic fields inferred from Planck polarization (top left) and VGT (top rightand bottom).
Left: the spectral line used for the calculation and also the histogram of the relative angle between the Planckpolarization and VGT. The yellow segments indicate the direction of stellar polarization. The radius of dashed circles is ≈ . ◦ for visulization purpose. . of debates. The arguments in favor of them being puredensity features are provided in Clark et al. (2019). Thecounter-arguments stressing the role of velocity fluctu-ations are provided by Yuen et al. (2019), who appealsto two decades of theoretically and numerically studies.The velocity caustics effect must inevitably present inthe thin velocity channel maps, as a natural effect ofnon-linear spectroscopic mapping.In terms of the foreground polarization, Hu et al.(2020a) and Lu et al. (2020) demonstrated that VGThas better performance compared to RTH. In addition,VGT, as predicted in Lazarian et al. (2018a), can pro-vide the distribution of media magnetization of the me-dia, as demonstrated e.g. in Hu et al. (2019a).RESULTSWe use the H I emission line from the HI4PI surveywith spectral resolution ∆ v = 1.49 km/s (HI4PI Collab-oration et al. 2016). We apply VGT to all thin channels of the H I emission in the velocity range of -75 < v <
25 km/s. Here we rotate the resulting gradients by 90 ◦ to indicate the magnetic field orientation ψ . The re-sult is shown in Fig. 1. We make comparisons with thePlanck 353 GHz polarized dust signal data (Planck Col-laboration et al. 2018a). The relative orientation be-tween ψ and φ is quantified by the Alignment Measure(AM). AM = 1 means a perfect alignment case. Here,the resulting AM is 0.83. Also, we plot the normalizedhistogram of the relative angle between ψ and φ (seeFig. 1). The histogram is close to a Gaussian distribu-tion with the standard deviation σ ≈ . ◦ . Therefore,we can conclude that VGT gives an excellent agreementwith Planck.In addition, we apply VGT to the IVC and LVC iden-tified by Panopoulou et al. (2019) centering on ( l , b )= (104.08 ◦ , 22.31 ◦ ). In particular, Panopoulou et al.(2019) find the LVC locates at a distance of 346 - 393pc associated with H I emission in the velocity range odeling of Galactic Foreground Polarization with Velocity Gradients < v < -1.2 km/s. As for the IVC, it locatesat a distance of 1250 - 2140 pc and -55 < v < -41km/s. The H I emission within these velocity rangesare used for the calculation, respectively for IVC andLVC. The resulting magnetic field morphology is shownin Fig. 1. Here we make comparison with the stellarpolarization centered on ( l , b ) = (103.90 ◦ , 21.97 ◦ ) and( l , b ) = (104.08 ◦ , 22.31 ◦ ) associated with these clouds.The measured mean magnetic field from stellar polar-ization over a 0.16 ◦ circle is (cid:104) φ ∗ (cid:105) = 106 ± ◦ for IVC and (cid:104) φ ∗ (cid:105) = 42.6 ± ◦ for IVC (Panopoulou et al. 2019). Wecompute the mean magnetic field orientation inferredfrom VGT over the same region. We find (cid:104) ψ (cid:105) = 106.3 ◦ for the IVC and (cid:104) ψ (cid:105) = 43.5 ◦ for the LVC, which agreewith the results of stellar polarization, as well as Clark& Hensley (2019), where the authors got (cid:104) ψ RHT (cid:105)
IV C = 111.6 ◦ and (cid:104) ψ RHT (cid:105)
LV C = 42.6 ◦ . However, the out-put of RHT depends on three parameters as inputs: asmoothing kernel diameter, window diameter, and inten-sity threshold (Clark et al. 2014, 2015). In this sense,VGT is parameter-free and provides more statistical in-formation, making our estimates of polarization morerobust. Compared to RHT, VGT is able to trace mag-netization (Hu et al. 2019a) with additional advantageslisted in Lu et al. (2020).ACKNOWLEDGMENTSY.H. and A.L. acknowledges the support of the NASATCAN 144AAG1967, the NSF grant AST 1715754, and1816234.REFERENCES. However, the out-put of RHT depends on three parameters as inputs: asmoothing kernel diameter, window diameter, and inten-sity threshold (Clark et al. 2014, 2015). In this sense,VGT is parameter-free and provides more statistical in-formation, making our estimates of polarization morerobust. Compared to RHT, VGT is able to trace mag-netization (Hu et al. 2019a) with additional advantageslisted in Lu et al. (2020).ACKNOWLEDGMENTSY.H. and A.L. acknowledges the support of the NASATCAN 144AAG1967, the NSF grant AST 1715754, and1816234.REFERENCES