Harvard Astronomy 201b

ARTICLE: Molecular Rings around Insterstellar Bubbles and the Thickness of Star-Forming Clouds

Read the Paper by C.N. Beaumont and J.P. Williams (2010)

Summary by Li Zeng

1. Introduction

Christopher Beaumont and Jonathan Williams in this recent paper proposed a new ring-like three-dimensional structure of bubbles, based on their analysis of the data from James Clerk Maxwell Telescope’s observations and Spitzer’s observations of the J=3-2 line of CO in 43 bubbles. In the past, people had come up with ideas of spherical morphology of the bubbles. However, the authors in this paper provided evidence showing that the cold gas lies in a ring, not a sphere, around the bubbles indicating that the parent molecular clouds are flattened with a typical thickness of a few parsecs.

Chris and Jonathan also mapped the J=4-3 lines of HCO+ in 7 bubbles in particular to find that the column densities inferred from the CO and HCO+ line intensities are below that necessary for “collect and collapse” models for induced star formation. Thus they hypothesized that the flattened molecular clouds are NOT greatly compressed by the expanding shock fronts produced by the central star because of the central stars’ rapid breakout from their molecular confines, which may hinder further formation of new stars.

The bubbles are produced by intensive UV radiations and stellar winds from newly borne massive stars within the molecular clouds.

The data in this paper are mostly from the James Clerk Maxwell Telescope (JCMT), Spitzer Galactic Legacy Infrared Mid-Plane Survey Extraordinaire (GLIMPSE), and Very Large Array (VLA).

2. Background

(1) Bubbles

Very massive stars of the spectral classes O or B can emit very energetic radiation, especially UV radiation, which is able to ionize the neutral hydrogen (H I) in the vicinity of the star and turn them into ionized hydrogen (H II). Strömgren sphere is a simple static isotropic model trying to describe this scenario.

The boundary separating the H I and H II regions is known as an ionization front.

The following is a simple illustration of Strömgren sphere:

Fig.1: Strömgren sphere (Image Credit: http://www.astro.cornell.edu/)

In the meantime, material outflow or winds from hot stars could push against surrounding ISM and form shocks. These are the so-called Stellar-wind Bubbles.

If the surrounding ISM is uniform and the stellar wind is isotropic, then one would expect a spherical shape of the Stellar-wind Bubbles. However, this is not necessarily true in reality, as shown by Beaumont & Williams 2010, due to many reasons including the complex topology of ISM, the asymmetry and anisotropy in the stellar winds, etc.

The following diagram from Beaumont & Williams 2010 shows the observed structure of 2 bubbles under various wavelengths:

Bubble figure

Fig.2: These are two examples of many bubbles in Chris' dataset. The figures on the left show the peak intensity of the CO and, when observed, HCO+ emission. The center figure show Spitzer 8 micron emission in blue, and VLA 20 cm emission in red. The figures on the right show the first moment (flux) of the CO emission. The rings shown are N36 (top) and N45 (bottom). (Image Credit: Beaumont & Williams 2010)


(2) JCMT

JCMT, the James Clerk Maxwell Telescope is a 15-meter diameter submillimeter telescope, the largest telescope of this kind in the world. It is located at an altitude of 4092 m, near the summit of Mauna Kea in Hawaii.

Here is a picture of JCMT:

Fig.3: JCMT (Image Credit: http://outreach.jach.hawaii.edu)

A heterodyne receiver called HARP was commissioned and accepted by the JCMT in April 2007.

The 4×4 element array uses SIS detectors, and is the first sub-millimetre spectral imaging system on the JCMT. HARP provides 3-dimensional imaging capability with high sensitivity at 325-375 GHz and affords significantly improved productivity in terms of speed of mapping. Under typical atmospheric conditions on Mauna Kea, the HARP array can map 345 GHz line emission to a noise level of T = 0.3 K at a rate of 100 arcmin^2 per hour (Beaumont & Williams 2010).

The following diagram shows 3-D representation of HARP on JCMT:

Fig.4: HARP on JCMT (Image Credit: Smith et al. 2008)

For details of HARP, please see this reference: (Smith et al. 2008).

In this paper, the authors presented the HARP observations of the J=3—>2 CO line of 43 bubbles in the (Churchwell et al. 2006) catalog. The data revealed the 3-D structure of the bubbles and their interaction with the ambient molecular cloud. The authors also observed the J=4—>3 HCO+ line of 7 bubbles in particular to determine the amount of dense gas in their surroundings.

(3) GLIMPSE

GLIMPSE, the Galactic Legacy Infrared Mid-Plane Survey Extraordinaire, is an infrared survey of the inner Milky Way galaxy using the Spitzer Space Telescope. The GLIMPSE survey spans 130 degrees in longitude (65 degrees on either side of the center of the Galaxy), and 2-4 degrees in latitude. Since we are located around 8 kpc away from the center of the galaxy, this range encompasses a big fraction the volume of our galaxy.

The following logo cartoon shows roughly the range GLIMPSE covered:

GLIMPSE Logo

Fig.5: GLIMPSE Logo (Image Credit: GLIMPSE)

It consists of approximately 444,000 images taken at 4 separate wavelengths (3.6 µm, 4.5 µm, 5.8 µm and 8 µm) using the Infrared Array Camera (IRAC). (Ref.: GLIMPSE)

The significance of this survey is that in optical wavelength, we could only see 5% of the way through the Galaxy on average, due to the huge dust extinction towards the center of our galaxy. However, in the infrared wavelength, not only the dust particles are less opaque, but the heated dust particles also emit infrared radiation, giving away their distribution inside our galaxy.

The GLIMPSE survey have 100 times the sensitivity and over 10 times the resolution of previous infrared surveys.

(4) VLA MAGPIS Survey

The Very Large Array (VLA) consists of 27 radio antennas in a Y-shaped configuration on the Plains of San Agustin fifty miles west of Socorro, New Mexico. Each antenna is 25 meters in diameter. The data from the antennas is combined electronically to give the resolution of an antenna 36km across, with the sensitivity of a dish 130 meters in diameter.

The following is a picture of VLA:

Fig.6: VLA (Image Credit: http://apod.nasa.gov/apod/ap000530.html)

MAGPIS, the Multi-Array Galactic Plane Imaging Survey, are patches of the sky near the Galactic Plane that have been imaged at high resolution by Very Large Array (VLA) at 6 and 20 cm wavelengths.

(5) CO and HCO+

CO is the most abundant molecule with a low-energy transition in the ISM. Because the moment of inertia of CO is much larger than that of H2, the rotational levels of CO are much more closely spaced than those of H2, and therefore there are many more allowed rotation-vibration levels. (Bruce Draine)

The J = 3—>2 transition of CO is an excellent tracer of the cool, 20–50 K, moderately dense, nH2 ∼ 10^(3–4) cm^(−3), gas around the bubbles. The emission from this line traces the ambient molecular cloud around the bubble shells, and is very strong at their interface.

HCO+ is moderately abundant but has strong emission in gas with densities nH2 > 10^4 cm^(−3). Therefore it is a useful tracer for dense star-forming regions and potentially pre-stellar gas.

3. Results

3.1 Molecular Rings

The CO J=3—>2 line is readily excited by collisions in molecular clouds, and very easily becomes optically thick. Because of the CO’s opacity, the JCMT data cubes show the surfaces (in position-velocity space) of molecular clouds (as shown in Fig.2). The filamentary structures in these data illustrate the inhomogeneity of molecular clouds on parsec-scales.

There are in total 3 different lines of evidence suggesting that the molecular data are inconsistent with spherical shell morphology. Thus a ring-shaped morphology should be adopted.

(1) Contrast ratio between the bubble shells and bubble interiors

If we assume the bubble is a spherical shell and what we observe is a 2-D projection of this spherical shell, then in the simplest case of optically thin emission, the integrated intensity scales linearly with the line-of-sight path length through the shell, l, as a function of impact parameter b, given as follows (Beaumont & Williams 2010):

where the bubble has an inner radius R and thickness ∆R.

The following figure (Fig. 7) illustrates the geometry of a simple spherical shell model:

Fig. 7: An illustration of a simple thin spherical shell (Image by Li Zeng)

However, the observed CO intensity is inconsistent with the model of spherical shell, rather, it supports a ring shell model.

The most striking feature of the CO data is the rarity of emission toward the center of the bubbles (comparing the observed profiles (color lines) with various optically thin spherical shell models (black lines), as shown in Fig. 8).

Fig.8: Plot of the azimuthally averaged radial profile of four rings, compared to profiles for optically thin spherical shells. The data are inconsistent with these profiles, which have overly thin outer edges or low edge-to-center contrast ratios. This strongly disfavors the spherical shell model for bubble morphologies, and suggests instead that these bubbles lack fronts and backs.

Fig. 8 illustrates that the contrast ratio between the CO shells (they peak around 0.8~1 normalized radius) and interiors (near 0 radius) is problematically high. To reproduce such high contrasts, very thin shells must be invoked. However, the shell thicknesses are resolved in several of the larger objects in the authors’ sample, so as to rule out the very thin shell hypothesis. Furthermore, as mentioned above, treating the CO emission as optically thin is an unrealistic assumption, and its opacity makes the lack of emission interior to bubble shells even harder to reconcile to a spherical shell morphology.

(2) Intensity of emission surrounding the bubbles

Intensity of emission surrounding bubbles provides the second line of evidence against the spherical shell hypothesisMost of the objects in the authors’ sample are found to lie interior to, or on the edge of, regions of extended molecular emission. If bubbles are embedded in molecular material, then these clouds should contribute foreground and background emission inside bubble shells. However, the CO interiors of many bubbles are actually darker than their immediate exteriors (see, e.g., N21, N22, N29, N49, N74, N80). The authors (Beaumont & Williams 2010) notes that even the 8 μm emission occasionally displays this signature (bubbles from this study include N90, N94 and, to a lesser extent, N36 and N37).

(3) Radial velocity structure of the bubbles

An expanding spherical shell (as illustrated in Fig. 7) would manifest itself as a connected, coherent structure in a data cube. A data cube is a 3-dimensional array of values. In our case, the x and y coordinates encode position information which is just the projection of the 3-D cloud onto our 2-D viewing plane, while the 3rd coordinate z encodes the radial velocity information along our line-of-sight.

Specifically, as one steps through velocity space (which is the z-direction in the data cube), a sphere would appear as a blueshifted point (the bubble front) expanding into a ring (the midsection), and then contracting back to a redshifted point (the back). This is shown is the following diagram (Fig. 9):

Fig.9: illustration of bubble radial velocity concept (Image by Li Zeng)

A channel map for bubble N29 is displayed in Fig.10. The occasional filamentary structures seen interior to bubbles do not display the systematic velocity shifts as expected, but are instead moving at roughly the same radial velocity as the edges. These filaments are either unaffiliated foreground or background structures (consistent with the observation that they are absent from the Spitzer data), or they imply that the expansion of these regions has stalled.

Fig.10: Radial velocity profile of bubble N29. The radial velocity at each slice is listed in km s^(−1) in the upper right corner. An ellipse is drawn in for reference, to mark the approximate boundary of the interior. Note that the bubble interior is largely devoid of emission. The few structures that do appear inside the shell (for example, at a radial velocity of 37.6 km s^(−1) are not red- or blueshifted, as would be expected if N29 was an expanding sphere. Note also that the extended emission to the north of the bubble does not extend into the interior of N29. This points to an absence of ambient molecular material in front of or behind the bubble.

Based on all the evidence presented above, the authors suggested that the most natural interpretation to draw from the observations is that the fronts and backs of bubbles are missing. What we observse are equivalent to only the bubble midsection. A corollary is that the molecular clouds in which bubbles are embedded are oblate with thicknesses of a few parsecs, comparable to typical ring diameters (Fig.11). The authors further inferred that based on the ring morphology of the bubble that the expanding bubbles break out of the cloud along this axis so we see a ring of CO emission, approximately circular if the flattened axis is along our line of sight, otherwise elliptical. If viewed edge-on, the bubbles would not be identifiable as such either in our images or those from Spitzer, but might perhaps be classified as filamentary structures or Infrared Dark Clouds.

Fig.11: Schematic of an interstellar ring, where a central group of O and B stars clears out a cavity in a flattened molecular cloud. The top panel shows a face on view of an approximately circular cavity of diameter a few parsecs. None, or very little, CO emission is seen toward the cavity, whereas the molecular cloud extends for tens of parsecs in the plane of the sky. The authors interpret their finding as indicating that clouds have line-of-sight depths of a few parsecs, and that bubbles rapidly break out of their host clouds (illustrated in the lower panel). In this scenario, the interaction region between the star and cloud is smaller than it would be than for a more homogeneous cloud geometry.

3.2 Two Mechanisms Driving the Ring’s Expansion

There are in general two mechanisms driving the ring’s expansion, which would lead to different results in estimating the thickness of the molecular cloud.

(1) Scenario #1:

If the central O, B stars powering the bubble produce stellar winds strong enough, then the bubble expansion is driven by direct momentum transfer from the stellar wind into the ambient ISM material (Castor et al. 1975). In this scenario, the ring’s expansion would continue after it breaches the flattened cloud, and the observed ring diameter places an upper limit on the thickness of the molecular cloud.

(2) Scenario #2:

If the stars power an H II region but do not have powerful winds, then a shock from the pressure-driven expansion of the HII region surrounds the stellar wind shock front (Freyer et al. 2003). Rings in this case trace the boundary of the H II shock and, once the bubble breaches the cloud top and bottom, the pressure would drop and expansion would stop. In this case, the ring diameter is roughly equal to the cloud thickness.

It turn out both classes of bubbles are present in the sample presented in Chris’ paper (Beaumont & Williams 2010) .

3.3 Distance and Size Estimation of the Rings

The distance to a ring is determined by Galactic kinematics.

The following is a diagram illustrating our sun’s location in the Milky Way and the setup of Galactic Coordinate (Fig.12):

Fig.12: Milky Way and Galactic Coordinate (Notice in the diagram, the galactocentric distance is given as 7.7 kpc, which is different from 8.8 kpc as used in Chris' paper (Beaumont & Williams 2010))

For simplicity, let’s assume that the cloud lies in the Galactic plane (b=0) and is located at a given Galactic longitude l. There are actually two locations along the line-of-sight direction which could produce the same line-of-sight radial velocity: position A and position B as illustrated in Fig.13.

Fig.13: Galactic Kinematics (Image by Li Zeng)

The relations between various quantities in Fig.13 are described by the following equations from (Brand & Blitz 1993):


Equation (1) above gives the line-of-sight radial velocity as a function of galactocentric distances and the circular rotational velocities of the object (cloud) and the Sun, and the galactic longitude and latitude of that object.

Equation (2) gives relation between the galactocentric distance of the object and its heliocentric distance. It is simply the Law-of-cosine.

In Fig.13, Position A is called the Near Kinematic Distance. Position B is called the Far Kinematic Distance. The authors followed the same argument as in (Churchwell et al. 2006) that the bubbles are more likely located at their near kinematic distances, since interstellar extinction and confusion with other diffuse emission structures would tend to obscure objects on the far side of the Galactic disk.

So in this paper, the authors simply took all the distances as the Near Kinematic Distances, but of course this is NOT necessarily true in reality.

The authors took a galactic rotation model of (Brand & Blitz 1993), for R⊙ = 8.8 kpc and V⊙ = 275 km s^−1 (Reid et al. 2009), as inputs in their calculation of the distances to the rings.

Once the distance is determined, the actual physical size of a bubble could be easily calculated by multiplying the angular diameter with the distance.

4. Conclusion

The authors have presented new CO J=3–>2 maps of 43 Spitzer identified bubbles in the Galactic plane. These maps point toward a new interpretation for bubble morphology – namely, that the shock fronts driven by massive stars tend to create rings instead of spherical shells. The authors suggested that this morphology naturally arises because the host molecular clouds are oblate, even sheet-like, with thicknesses of a few parsecs, and width10 pc. Such a morphology implies that expanding shock fronts are poorly bound by molecular gas, and that cloud compression by these shocks may be limited. This idea is borne out by observations in HCO+, which show dense gas to be confined to small regions of bubble shells.

5. Acknowledgement

I would like to give Thanks to Christopher Beaumont and Alyssa Goodman for their gracious help in Ay201b ISM class. Through the process of reviewing this paper by (Beaumont & Williams 2010), I learned a great deal about bubble structures and galactic kinematics.

6. Reference

Molecular Rings Around Interstellar Bubbles and the Thickness of Star-Forming Clouds, Beaumont, Christopher N.; Williams, Jonathan P., The Astrophysical Journal, Volume 709, Issue 2, pp. 791-800 (2010). 

Interstellar bubbles, Castor, J., McCray, R., & Weaver, R. 1975, ApJ, 200, L107

Massive Stars and the Energy Balance of the Interstellar Medium. I. The Impact of an Isolated 60 solar-mass Star, Freyer, T., Hensler, G., & Yorke, H. W. 2003, ApJ, 594, 888

The Velocity Field of the Outer Galaxy, Brand, J., & Blitz, L. 1993, A&A, 275, 67

TRIGONOMETRIC PARALLAXES OF MASSIVE STAR-FORMING REGIONS. VI. GALACTIC STRUCTURE, FUNDAMENTAL PARAMETERS, AND NONCIRCULAR MOTIONS, Reid, M. J., et al. 2009, ApJ, 700, 137

Physics of the Interstellar and Intergalactic Medium by Bruce T. Draine.

http://www.vla.nrao.edu/

http://www.astro.wisc.edu/sirtf/

http://www.jach.hawaii.edu/JCMT/

http://outreach.jach.hawaii.edu

http://www.ifa.hawaii.edu/~beaumont/

http://www.ifa.hawaii.edu/~jpw/

HARP: a submillimetre heterodyne array receiver operating on the James Clerk Maxwell Telescope, Smith H. et al, Proceedings of the SPIE, Volume 7020, pp. 70200Z-70200Z-15 (2008). 

http://www.astro.cornell.edu/academics/courses/astro2201/stromgren_sphere.htm

The Bubbling Galactic Disk, Churchwell, E., et al. 2006, ApJ, 649, 759

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