Harvard Astronomy 201b

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H II Region Line Diagnostics

In Uncategorized on May 5, 2011 at 6:37 pm

Intro/References: I will discuss the five main diagnostics from line ratios and continuum fluxes for H II regions that can be applied to other photoionized emission regions including active galactic nuclei, planetary nebulae, and any other emission line sources such as Wolf-Rayet stars, etc.  For a more detailed description of photoionization modeling, statistical mechanics /  thermodynamics, and quantum mechanics, please see Chapter 18 of Draine, this link (from which the summary and figures below are based), and the all-time best reference AGN2 : Astrophysics of Gaseous Nebulae and Active Galactic Nuclei 2nd Ed. by Osterbrock and Ferland.

Motivation: Line ratios and relative continuum fluxes of photoionized emission regions can give much physical insight regarding the properties of the nebula and its vicinity including the amount and type of dust extinction along the line of sight, the number density, temperature, physical radius / volume, mass, and metallicity of the gas, and even the temperature of the ionizing source.  These indicators may also give further clues as to the surrounding environment, including and certainly not limited to the star formation rate and history, metallicity and mass of the host stellar population / galaxy / AGN, and depletion rates and abundances of the dust and gas.

(1) Dust Extinction and Reddening from Balmer Decrement

Photoionization of hydrogen is fairly well understood as it relies on already quantified atomic properties such as the photoionization cross-section, the recombination rate, the cascade matrix toward lower energies after recombination, oscillator strengths / Einstein A coefficients of the various transitions, etc.  Consider the following table of theoretical emission line strengths jn’n from various Balmer transitions (relative to Hβ):

where Case A and Case B represent the limits of two idealized situations so that actual H II regions must lie between these two extremes.  Namely, Case A assumes the optically thin limit where hydrogen emission from all energy levels (Lyman, Balmer, etc.) can escape the H II region unabsorbed while Case B assumes all transitions more energetic than Lyα are absorbed and re-radiatved via Lyα and longer wavelengths.  This is why the Hα emission line strength is greater in Case B.  Nevertheless, the line ratios between Hβ and Hγ , for example, only vary by ~10% despite the temperature changing by a factor of two and not knowing in which optical depth regime the H II region exists.  Thus, this Balmer decrement of decreasing relative line strengths toward more energetic transitions is fairly insensitive to temperature and number densities across the parameter space of H II regions.

If the actual line strengths of an H II region are measured and since we know the theoretical Balmer decrement, we can infer the amount of dust reddening toward the H II region.  If only two Balmer lines are measured, the amount of dust reddening along with a theoretical dust extinction curve can give us a dereddened spectrum corrected for dust extinction.  Additional Balmer lines can be used to constrain the type and functional dependence on wavelength of the actual dust extinction.  This information has its own merit for inferring the dust properties along the line of sight and possibly dust properties in the vicinity of the H II region itself, but perhaps more important it gives us corrected emission line strength ratios which can be used for other diagnostics (see below).

(2) Electron Number Density and Temperature from Forbidden Lines

The forbidden transitions of [OIII] and [S II] can serve as excellent diagnostics of both temperature and density of the gas.  Theoretically, observations of [OII] and [NII] can also constrain these properties but in reality the transitions of [OII] are too closely spaced to be resolved while the [NII] lines are typically contaminated by Hα.  Consider the energy diagrams of [OIII] and [S II] below, where you can see all the important listed transitions are forbidden due to violation of one or more of the selection rules of quantum mechanics: ΔL = ±2 (such as transitioning from a D state to S state or vice versa),   ΔJ = ±2 (which is intrinsically tied to ΔL), and/or no change in parity πf = π(both initial and final states in these cases have even parity).  Obviously, these transitions are only forbidden to electric dipole radiation, and do occur in nature when densities are sufficiently low such that timescales of collisional deexcitation are longer than the lifetime before spontaneous decay via these forbidden transitions.

Now consider the relative population of ions in the various electronic configurations and the measured transitions that arise from these upper energy levels. For example in [OIII], the ratio of the λ4363 to either or the sum of the λ4959, λ5007 intensities can allow you to infer the relative populations of the 1Sto 1Dstates.  Considering the energies between the two levels are widely spaced, the relative population will be almost completely dictated by the temperature of the gas, so the ratio of these [OIII] line intensities can be used to infer the temperature of the gas with only a slight dependence on number density.  Conversely, the upper energy levels that give rise to the λ6716 and λ6731 transitions in [S II] are closely spaced in terms of energy so that the relative population will be controlled by collisional excitation / deexcitation between the two levels which depends significantly on the electron density.  Thus, the relative intensities of these two transitions can be used to infer the number density of electrons.  Combining observations of both pairs of transitions can further refine the precision of electron density and temperature via detailed photoionization modeling that relies on thermodynamic and quantum mechanical properties such as Boltzmann, Saha, Einstein A coefficients, collisional strengths and cross sections, and incident radiation.

(3) Mass and Radius from Hβ Flux

Once the temperature and density of the gas can be ascertained, other physical properties can be modeled from atomic physics such as the recombination rate αB, the subsequent probability of then cascading via Hβ emission PHβ so that the total volumetric rate of Hβ emission is αHβ = αP, and thus finally the emissivity of Hβ emission εHβ = αHβ . (Historically, Hβ is used instead of Hα because it is in the green part of the optical spectrum where the sensitivity of photographic film peaks and since Hα is typically contaminated on either side by transitions of [N II] in real HII regions.)  The functional fit of Hβ emissivity is given by:

which then gives the following relationship between Hβ luminosity, flux, and emissivity:

Since nis known from the forbidden transitions, εHβ is calculated based on the gas temperature also inferred from the forbidden transitions, the total FHβ can be measured and corrected for dust extinction according to the Balmer decrement, and the ratio of radius to distance R/d can be measured by the angle the HII region subtends on the sky, then the absolute values of d and R can be calculated.  Once the radius of and distance to the HII region are known, the mass of ionized hydrogen within the HII region is simply given by:

where as stated we already know the specified parameters on the right hand side.

(4) Zanstra Temperature of Ionizing Source from Continuum Flux

Using a simple Stromgren sphere analysis, the temperature of the central ionizing star can be inferred from the ratio of continuum flux (e.g. in the visual V filter) to line flux (e.g. Hβ) in a manner that is independent of the distance to the ionizing source and HII region.  The actual relation is the following inequality:

because we must make the assumption that we are in the optically thick regime, i.e. Case B, where all ionizing photons are absorbed within the HII region and reradiated at longer wavelengths. In the equation, f is the fraction of the flux of photons that are capable of ionizing hydrogen, and can be simply modeled while simultaneously fitting the temperature of the ionizing source T*.  So to infer the temperature of the star, you must measure the broadband continuum V magnitude and know the response of the V filter with respect to frequency.  You must also estimate the emissivity which you have already measured from the ratios of forbidden lines.  Nevertheless, in all these input parameters you never had to assume the distance to the HII region, so the Zanstra temperature of the ionizing source is distance independent.

(5) Metallicity / Abundances from Line Ratios

By comparing line ratios from ions of different elements, the metallicity / chemical abundances of the gas can be estimated.  Granted, there is an implicit correction for excitation and ionization, but empirical observations have shown that there is a measured correspondence between certain line ratios and metallicities.  For example, the R23 ratio defined by:

has been found empirically to have the following dependence on the oxygen to hydrogen abundance:

Note that the relationship is double valued because of ionization and excitation effects.  Nevertheless, observations of line ratios of other various ions can help constrain the abundances.  Moreover, detailed photoionization modeling relying on the observed ratios of line intensities of the same ion can be used to derive the actual corrections for excitation and ionization.

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The Orion Bar

In Uncategorized on May 1, 2011 at 1:43 am

1. Overview of the Orion Bar

The Hubble image below shows the Orion A complex, which harbors two large HII regions, M43 to the Northeast (top left) the brighter Orion Nebula (M42, center). The HII region within the Orion Nebula is carved out by the Trapezium cluster, which is extremely dense (stellar density of 560 pc-3 – compare that with our local density of ~1 pc-3) and dominated by four stars, the brightest of which, θ1 Ori C (spectral type O7V), produces ~80% of the ionizing photons. M43 is ionized primarily by a single star, NU Ori (spectral type B0.5).

HST optical image of the Orion Nebula (Credit: NASA, ESA, M. Robberto, and the Hubble Space Telescope Orion Treasury Project Team)

The Orion A complex has been useful in understanding HII regions because of its proximity to us (~414 ± 7 pc), which allows its structure to be studied with high spatial resolution. The HII region within the Orion Nebula has broken out of the molecular cloud, creating a champagne flow. M42 has a particularly bright photodissociation region (PDR), known as the Orion Bar, which is visible to the Southeast of the Trapezium stars.

HST optical image of M42, with the Orion bar visible as a bright ridge in the bottom left (Credit: NASA, C.R. O'Dell and S.K. Wong (Rice University))

The Orion Bar stands out as a bright ridge to the Southeast of the Trapezium cluster, but its prominence is actually a consequence of limb brightening, i.e. our peculiar viewing angle. The Orion Nebula is bounded on multiple sides by an ionization front, but we happen to see the bar edge-on, causing it to appear brighter.

2. Structure from Radio Continuum Observations

Dense, hot regions of ionized hydrogen are bright in the radio continuum, as scattering of electrons off of H+ ions produces free-free emission. Felli et al. (1993) (ADS Link) mapped the Orion A complex in the radio continuum using the VLA in several configurations. A particularly nice map of the free-free emission at 20 cm in the Orion Nebula HII region is given in their Fig. 3d, reproduced below:

Fig. 3d from Felli et al. (1993). The Orion Bar is particularly prominent in this radio continuum map of the HII region of the Orion Nebula (20 cm, 6.2" resolution). The positions of several bright stars, including the four brightest Trapezium stars, are marked. The contours range from 95.0 to 300.7 mJy/beam.

Felli et al. further demonstrate that the radio continuum emission correlates well with Hα emission, as we should expect. Bruce Draine (§28.2) calculates a maximum line-of-sight rms electron density of approximately 3200 cm-3 based on the Felli et al. (1993) peak emission measure (the integrated square of the electron density along the line of sight) of 5 × 10 cm-6 pc and an assumed diameter of 0.5 pc for the HII region. For an explanation of the emission measure, see this link or recall §5.3 of Rybicki & Lightman, which discusses free-free absorption. The basic idea is that the absorption coefficient due to free-free absorption is proportional to the product of the ion and electron densities. If the medium is neutral overall, then this is simply the square of the electron density, so the optical depth of an ionized cloud due to free-free absorption is proportional to the integrated square electron density.

3. Progression of Species in the Photodissociation Region

The chemistry and structure of the photodissociation region (PDR, also called the photon-dominated region) is dominated by the effects of the intense incident ultraviolet radiation from the O and B stars in the HII region. As the binding energy of the H2 molecule is lower than that of the electron in the hydrogen atom, HII regions are enveloped by a region of atomic hydrogen. In this region, the UV flux is great enough to photodissociate H2, but the recombination rate is high enough to keep the ionized fraction low. Deeper in the cloud (i.e. farther away from the HII region), the UV flux has been sufficiently attenuated, such that most hydrogen is bound in H2. The interface between the regions dominated by atomic hydrogen and fully ionized hydrogen is called the ionization front, while the boundary between the atomic hydrogen and the molecular hydrogen is called the dissociation front. Figure 31.2 of Draine’s ISM textbook, reproduced below, gives a diagrammatic sketch of the structure of a PDR:

The progression of species refers to the progression of chemical species that dominate as one travels away from the HII region and into the molecular cloud. The key variable which changes along this path is the intensity of the UV flux. This has several effects: the ionized medium at first gives way to neutral atomic species, and deeper into the cloud molecules such as H2, CO, O2 and PAHs (polycyclic aromatic hydrocarbons) become stable; the temperature drops as the incident radiation becomes more attenuated (with increasing optical depth since the ionization front); assuming pressure balance, the density of the gas must increase into the cloud as the temperature drops. The assumption of pressure equilibrium is not exact, however, as HI flows from the dissociation front towards the ionization front. As this flow becomes smaller, the assumption of pressure balance and steady-state become more accurate.

4. Comparison with Theoretical Models

Tielens et al. (1993) (ADS Link) compare the observed structure of the Orion Bar to theoretical models of what a photodissociation region should look like, in what is a short and eminently readable paper. The paper presents observations of the 1-0 S(1) H2 line, the J=1-0 CO rotational line, and the carbon-hydrogen stretching mode of PAHs. Both the H2 and CO lines are caused by decay of excited ro-vibrational states. They are thus dependent on the presence of UV radiation; as one travels deeper into the molecular cloud, the increasing attenuation of the UV flux suppresses the excitation of these excited states. Going in the opposite direction, towards the HII region, the density of molecular hydrogen and CO becomes lower, and the the 1-0 S(1) H2 and CO J=1-0 lines are no longer prominent. The regions in which the H2 and CO ro-vibrational lines are observed should thus be determined by the interplay between the density of these species and the strength of the UV flux. For more on the origin of ro-vibrational transitions in H2, see this link and the introductory paragraph of Laine et al. (2010) (Thanks to Tanmoy for discussions on this and for this last paper). Tielens et al. (1993) present a false-color picture showing the PAH, H2 and CO emission observed from the Orion Bar. The diagram has the same orientation as the picture of the above pictures of the Orion Bar, with the HII region to the upper right, and the molecular cloud to the bottom left. Thus, molecular hydrogen density and UV optical depth increase from the top right to the bottom left. The separation of the peaks of each type of emission is clearly visible:

Figure 1 from Tielens et al. (1993) showing PAH emission (blue), 1-0 S(1) H2 emission (green) and the CO J=1-0 transition (red).

Tielens et al. (1993) use the spatial separation between PAH 3.3 μm, H2 and CO line peaks to map UV penetration in the Orion Bar. By then assuming a hydrogen density to visual extinction ratio NH/Av = 1.9 × 1021 cm-2 mag-1 and an estimate of the viewing angle, they determine a gas density of 1-5 × 104 cm-3. The observed spatial distribution of these three emission mechanisms is compared to a PDR model, which treats the PDR as a homogenous slab of constant density 5 × 104 cm-3. The model takes into account chemical composition, energy balance, radiative transfer and line cooling. The modeled intensity of emission along a cut through the Orion Bar (rightward is deeper into the molecular cloud) is compared to observation:

The authors of the paper argue that the agreement between the modeled and observed emission features UV pumping as the mechanism driving excitation of CO and H2 ro-vibrational lines. As mentioned in the ESO link above, these lines are also observed in post-shock regions, where the gas has been collisionally excited. In order for the emission to be shock induced, however, the shock velocity would have to exceed 10 km/s, which would evaporate the bar on a timescale of 103 years. The authors also note that one weakness of their model is that it does not include clumping, which is likely to be important in the Orion Bar and traced by CO and CS maps. Finally, other molecular tracers, such as HCN, can be used to probe the denser regions of PDRs.

5. References

Draine, Bruce T., Physics of the Interstellar and Intergalactic Medium. Princeton, NJ: Princeton University Press, 2011.

Felli M., Churchwell E., Wilson T. L., Taylor G. B. 1993, A&AS 98, 137-164. (ADS Link)

Rybicki B.R., Lightman A.P, Radiative Processes in Astrophysics, 2nd Ed. Weinheim, Germany: Wiley-VCH Verlag, 2004.

Tielens A.G.G.M., Meixner M.M., van der Werf P.P., Bregman J., Tauber J.A., Stutzki J., Rank D. 1993, Science 262, 86-89. (ADS Link)

van der Werf P.P., Goss W.M. 1989, A&A 224, 209-224. (ADS Link)

van der Werf P.P., Stutzki J., Sternberg A., Krabbe A. 1996, A&A 313, 633-648. (ADS Link)