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Magnetic seismology of interstellar gas clouds: Unveiling a hidden dimension

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Science  11 May 2018:
Vol. 360, Issue 6389, pp. 635-638
DOI: 10.1126/science.aao1185

A vibrating molecular cloud in three dimensions

Molecular clouds are relatively dense assemblies of interstellar dust and gas (mostly molecular hydrogen) from which stars form. Determining the three-dimensional (3D) morphology of these clouds is difficult because we only see a 2D projection of them onto the sky. While examining far-infrared observations of the nearby Musca cloud, Tritsis and Tassis discovered that the cloud is vibrating with magnetohydrodynamic waves. The pattern of vibrations reveals the 3D structure and shows that Musca is a sheet seen edge-on, not a filament as previously assumed.

Science, this issue p. 635

Abstract

Stars and planets are formed inside dense interstellar molecular clouds by processes imprinted on the three-dimensional (3D) morphology of the clouds. Determining the 3D structure of interstellar clouds remains challenging because of projection effects and difficulties measuring the extent of the clouds along the line of sight. We report the detection of normal vibrational modes in the isolated interstellar cloud Musca, allowing determination of the 3D physical dimensions of the cloud. We found that Musca is vibrating globally, with the characteristic modes of a sheet viewed edge on, not the characteristics of a filament as previously supposed. We reconstructed the physical properties of Musca through 3D magnetohydrodynamic simulations, reproducing the observed normal modes and confirming a sheetlike morphology.

Astronomical objects are seen in two-dimensional projection on the plane of the sky. This is particularly problematic for studies of the interstellar medium (ISM), because the three-dimensional (3D) structure of interstellar clouds encodes information regarding the physical processes (such as magnetic forces, turbulence, and gravity) that dominate the formation of stars and planets. We seek a solution to this problem by searching for resonant magnetohydrodynamic (MHD) vibrations in an isolated interstellar cloud and by analyzing its normal modes. Normal modes have been used extensively to describe and analyze various systems in the physical sciences, from quantum mechanics and helioseismology to geophysics and structural biology. Normal modes have been observed in the ISM in two small pulsating condensations (Bok globules) located inside two molecular clouds (interstellar clouds dense enough to allow the formation of molecular hydrogen) (1, 2). Further applications have been limited because molecular clouds usually exhibit a complex morphology, including filamentary structures, as a result of turbulent mixing and shock interaction (3, 4).

Recent wide-field radio observations of molecular clouds (5) have unveiled the presence of well-ordered, quasi-periodically spaced elongations, termed striations, on the outskirts of clouds. The thermal dust continuum emission survey of nearby molecular clouds by the Herschel Space Observatory has shown that striations are a common feature of clouds (610), often associated with denser filaments (711) inside which stars are formed. Complementary polarimetric studies have revealed that striations are always well aligned with the cloud’s magnetic field projected onto the plane of the sky (5, 712).

From a theoretical perspective, the only viable mechanism for the formation of striations involves the excitation of fast magnetosonic waves (longitudinal magnetic pressure waves) (13). Compressible fast magnetosonic waves can be excited by nonlinear coupling with Alfvén waves (incompressible transverse waves along magnetic field lines) and/or perturbations created by self-gravity in an inhomogeneous medium. These magnetosonic waves compress the gas and form ordered structures parallel to magnetic field lines, in agreement with observations of striations (5, 712).

Once magnetosonic waves are excited, they can be reflected in regions of varying Alfvén speed (defined as Embedded Image, where B is the magnetic field and ρ is the density of the medium), setting up normal modes, just like vibrations in a resonating chamber. In regions where striations appear to be unassociated with denser structures (such as in H i clouds), this resonating chamber may be the result of external pressure confinement by a more diffuse, warmer medium. However, boundaries can also be naturally created, in the case of a contracting self-gravitating cloud, as a result of steep changes in density and magnetic field that in turn lead to sharp variations in the velocity of propagation of these waves (14). Any compressible fast magnetosonic waves excited during the formation of the cloud will then be trapped, thus resulting in striations in the vicinity of denser structures.

Fast magnetosonic waves traveling in both directions perpendicular to the magnetic field are coupled (13). By considering a rectangular box, we can express the spatial frequency k of each normal mode (n, m) asEmbedded Image(1)where the ordered component of the magnetic field is considered to be along the z axis and Lx and Ly are the lengths of the box along the x and y axes, respectively, with n and m being integers ranging from zero to infinity. By considering a rotation matrix, we can show that the spatial frequencies seen in the power spectra of cuts perpendicular to the long axis of striations are independent of the orientation of the cloud (14).

We analyzed these magnetohydrodynamic striations seen in Musca (designated G301.70-7.16), a molecular cloud located ~150 to 200 pc from Earth (15, 16). Because of its elongated and ordered morphology and its low column density (the integrated volume density along the line of sight), Musca is considered to be the prototype of a filamentary (cylindrical) molecular cloud (9, 1720) and is used as a comparison by many theoretical models. Musca has been mapped by Herschel as part of the Gould Belt Survey (9) and exhibits clear striations oriented perpendicularly to the main body of the cloud. We have reanalyzed the archival data (9); Fig. 1 shows the Herschel Spectral and Photometric Imaging Receiver 250-μm dust emission map of Musca. We have considered cuts perpendicular to the long axis of striations inside the green rectangle in Fig. 1 in order to study their spatial power spectra. We have verified that our selection does not introduce biases by considering cuts perpendicular to the long axis of the striations and studying their spatial power spectra in other regions as well (14).

Fig. 1 The Musca molecular cloud.

This Herschel 250-μm dust emission map of the Musca molecular cloud [with intensity expressed in megajanskies (MJy) per steradian] shows both striations and the dense elongated structure. The green rectangle marks the region where we have performed our normal-mode analysis, and the blue arrow shows the mean direction of the magnetic field projected onto the plane of the sky (9). Grid lines show equatorial coordinates.

The normalized power spectra from each cut and the distribution of the identified peaks are shown in Fig. 2, A and B, respectively. From Eq. 1 and the assumption that Lx is the largest dimension of the cloud, the smallest possible wave number is obtained for (n, m) = (1, 0). Thus, the first peak in Fig. 2B has to correspond to (n, m) = (1, 0), yielding Lx = 8.2 ± 0.3 pc. This value is consistent with the observed size of the cloud on the plane of the sky, which is variously reported to be from 6.5 to 7.85 pc when scaled to our adopted cloud distance of 150 pc (9, 18, 21). The second peak could correspond to either (n, m) = (0, 1) or, in the case of a cylindrical cloud with Embedded Image (and thus Embedded Image), to (n, m) = (2, 0). However, with Lx ~ 8 pc, the (n, m) = (2, 0) peak is expected at k ~ 0.8 (pc)−1, much higher than the actual location of the second peak. Thus, this second peak has to correspond to (n, m) = (0, 1). By inserting (n, m) = (0, 1) and the value of the second peak in Eq. 1, we deduce the hidden, line-of-sight dimension Ly to be 6.2 ± 0.2 pc, comparable to the largest dimension of the cloud. The other normal modes with their uncertainties determined through error propagation are predicted analytically by inserting these values for Lx and Ly into Eq. 1 and are overplotted in Fig. 2B. Therefore, Musca, previously considered to be a prototypical filamentary cloud, is instead a sheetlike structure seen edge on.

Fig. 2 Comparison of observed normal modes with the analytical solution.

(A) Normalized power spectra (black lines) of cuts through the observations perpendicular to the striations. Peaks we identified are marked with red dots. Fk, normalized spectral power density. (B) Distribution of peaks at different spatial frequencies. The red lines depict the values used to derive the dimensions of the cloud. The blue dashed lines show the rest of the normal modes [up to (n, m) = (2, 0)], predicted analytically from Eq. 1 given the cloud dimensions derived from the first two peaks. Shaded regions indicate the 1σ regions of the analytical predictions due to uncertainties in the determination of the locations of the first two peaks, propagated through Eq. 1. The bin size is comparable to the standard deviations of the points constituting the first two peaks. Npeaks, number of peaks.

In Fig. 2B, we plot all the normal modes up to (n, m) = (2, 2). We find good agreement between the predicted wave numbers and observations up to the first few modes, with n or m = 4 corresponding to physical scales of ~1.6 pc (fig. S1). However, the shape of the cloud is more complicated than an idealized rectangle, exhibiting higher-order structure on smaller scales, so the normal modes may be better modeled by a rectangle with rounded edges or an ellipse. Thus, Eq. 1 is an approximation that applies only to the normal modes with small spatial frequencies (i.e., large physical scales). At spatial frequencies higher than ~2 (pc)−1, the density of normal modes becomes so high that they cannot be identified in either the observations or the theoretical predictions (the uncertainties overlap for all predicted modes).

Through ideal (nondissipative) MHD simulations including self-gravity (14), we have constructed a 3D model of Musca, including the dense structure and striations in the low-density parts. In Fig. 3 we show the column density map from our simulation, which reproduces the observed dimensions of the cloud. A 3D representation of the volume density of the model of Musca is shown in Fig. 4. As intuitively expected from the normal-mode analysis of the observations, the shape of the cloud is that of a rectangle with rounded edges.

Fig. 3 Column density map of the model of the Musca molecular cloud.

The map is an edge-on view of the molecular gas column density from our MHD simulation of a sheetlike structure. The color bar shows the logarithm of the column density. The purple contour marks the region with N(H2) > 2 × 1021 cm−2, used to identify Musca’s main, dense filament (9). The magnetic field is along the z axis, and the time of the snapshot since the beginning of the simulation is ~2.7 million years.

Fig. 4 3D model of the Musca molecular cloud.

The model shows the logarithmic 3D volume density in our MHD simulation of the Musca cloud. Density isosurfaces are set at 90, 75, 70, and 55% of the logarithm of the maximum number density. Black lines represent the magnetic field.

The maximum column density in the simulation, from an edge-on view, is 1.9 × 1022 cm−2. For comparison, the maximum column density derived observationally from the dust emission maps (9) is ~1.6 × 1022 cm−2. The maximum volume number density in the simulation is ~2 × 103 cm−3, high enough for molecules to be collisionally excited and therefore observed via their rotational emission lines. Molecular line observations of the Musca molecular cloud are limited to CO, including several isotopologues, and NH3 (1720); the latter is observed only toward the densest core of Musca. The number densities required to excite CO and NH3 lines are ~102 and 103 cm−3, respectively (22), which are easily reached in our simulated model of the cloud. To reproduce the observed column density in any filamentlike geometry, in contrast to the sheetlike structure, the number density has to be ~5 × 104 cm−3 or higher (18). This value is well above the density threshold for star formation for clouds in the Gould Belt and a density threshold derived specifically for Musca (23). More evident star formation activity would be observed if Musca was a filament. Moreover, if the 3D shape of Musca was that of a filament, NH3 would be easily excited and observed throughout the ridge of the dense structure.

We used a suite of simulations of clouds of different shapes to validate our analysis and verify that Eq. 1 can be used to extract the correct cloud dimensions (14). In each of our simulations, the known dimensions of the clouds were recovered by the simulated normal-mode analysis. In contrast to the distribution of peaks seen in Fig. 2B, in cylindrical clouds (Embedded Image) the first few peaks at low spatial frequencies are all multiples of the first peak. The first few peaks for cylindrical clouds are due only to the largest dimension of the cloud, resulting in a sparser distribution of peaks than the sheet geometry (fig. S4). This is both quantitatively and qualitatively different from the distribution seen in the Musca data (Fig. 2), strengthening the case that the intrinsic shape of Musca is sheetlike. Sheetlike structures are common in turbulent clouds, as they may represent planarlike shocks from processes such as supernova explosions or expanding ionization regions or may result simply from accretion along magnetic field lines (4, 24, 25).

For decades, the determination of the 3D shapes of clouds has been pursued through statistical studies (2628), which do not provide information on a cloud-by-cloud basis. Other proposed methods (29, 30) rely on complex chemical and/or radiative processes and thus depend on numerous assumptions. With its 3D geometry now determined, Musca can be used to test theoretical models of interstellar clouds.

Supplementary Materials

www.sciencemag.org/content/360/6389/635/suppl/DC1

Materials and Methods

Figs. S1 to S4

References (3143)

References and Notes

  1. Materials and methods are available as supplementary materials.
Acknowledgments: We thank V. Pavlidou, G. Panopoulou, V. Charmandaris, N. Kylafis, A. Zezas, E. Economou, J. Andrews, S. Williams, P. Sell, D. Blinov, I. Liodakis, T. Mouschovias, and the three anonymous referees for comments that helped improve this paper. Funding: K.T. and A.T. acknowledge support by the Seventh Framework Programme through Marie Curie Career Integration grant PCIG-GA-2011-293531, “Onset of Star Formation: Connecting Theory and Observations.” A.T. acknowledges funding from the European Research Council (ERC) under the European Union’s Seventh Framework Programme (FP/2007-2013)/ERC grant agreement 617001. Usage of the Metropolis HPC Facility at the Crete Center for Quantum Complexity and Nanotechnology of the University of Crete, supported by the European Union Seventh Framework Programme (FP7-REGPOT-2012-2013-1) under grant agreement 316165, is acknowledged. Author contributions: A.T. performed the numerical simulations and the analysis of the observations and wrote the text. K.T. contributed to the interpretation of the results and the writing of the text. Competing interests: The authors declare no conflicts of interest. Data and materials availability: All observational data used in this research are from the Herschel Gould Belt Survey project and are publicly available at http://archives.esac.esa.int/hsa/whsa/#home (observation ID, 1342216012). All simulation outputs and setup files are available at https://doi.org/10.6084/m9.figshare.5950360. The FLASH software used in this work was developed in part by the Advanced Simulation and Computing Program of the National Nuclear Security Administration, U.S. Department of Energy, at the Flash Center for Computational Science at the University of Chicago and was obtained from http://flash.uchicago.edu/site/. The yt analysis toolkit is available at http://yt-project.org/#getyt, and Mayavi2 is available at https://github.com/enthought/mayavi.
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