Lya physics and astrophysics

Since Lya, one of the strongest emission lines in the UV, plays an important role in searches for and studies of distant and primeval galaxies, we wish to discuss this line, the basic principles governing it, its diagnostics and possible difficulties, empirical findings etc. To the best of my knowledge few if any reviews or lectures summarizing these topics in a single text exist.

4.3.1 ISM emission and "escape"

All ionized regions, i.e. HII regions, the diffuse ISM and like regions in galaxies, emit numerous emission lines, including recombination lines from H, He and other atoms, and forbidden semi-forbidden and fine-structure metal lines resulting from de-excitations of these atoms; see the textbooks of Osterbrock & Ferland (2006) and Dopita & Sutherland (2003), and Chapter 1 in this volume. All galaxies with ongoing massive-star formation (somewhat loosely called "starbursts" hereafter) emitting intense UV radiation and an ionizing flux (i.e. energy at >13.6 eV) will thus "intrinsically", viz. at least in their HII regions, exhibit Lya emission.

From quite simple considerations one can find that the luminosity in a given H recombination line is proportional to the number of ionizing photons (i.e. Lyman-continuum photons), L(Lya, Ha, ...) = clQH, where QH is the Lyman-continuum flux in photons s_1 and ci a "constant" depending somewhat on the nebular temperature Te and the electron density ne. For hydrogen, about two thirds of the recombinations lead to the emission of a Lya photon, corresponding to the transition from level 2 to the ground state (Spitzer 1978; Osterbrock & Ferland 2006).

Furthermore the relative intensities of two different H recombination lines are known and relatively slowly varying functions of temperature and density, e.g. I(Lya)/I(Hn) = c(T,ne).

Already in the sixties it was recognized that Lya could be important in searches for primeval galaxies (e.g. Partidge & Peebles 1967). Indeed, at (very) low metallicities the Lya line is expected to be strong, if not dominant, for several reasons: there is an increasing ionizing flux from stellar populations; Lya can become the dominant cooling line when few metals are present; and one expects greater emissivity due to collisional excitation in a nebula with higher temperature. As a result up to —10% of the bolometric luminosity may be emitted in Lya, rendering the line potentially detectable out to the highest redshifts!

This prospect triggered various searches for distant Lya emitters, which remained, however, basically unsuccessful until the 1990s (see Section 4.4), for the reasons discussed below. In any case, it is interesting to note that most of the observational features predicted nowadays for Population III galaxies (Section 4.2.3) were predicted by early calculations, such as Partridge & Peebles' (1967), including of course the now-famous Lyman break (Section 4.4).

To anticipate it is useful to mention here the basics of the Lya escape problem. In short, even for very low column densities of NH i > 1013 cm~2 the Lya line is optically thick. Therefore radiation transfer within the galaxy determines the emergent line profile and the Lya "transmission"! Furthermore, dust may destroy Lya photons. Overall, the fate of Lya photons emitted in a galaxy can be one of the following: (1) scattering until escape, forming thus an extended Lya "halo"; (2) destruction by dust; or (3) destruction through two-photon emission. However, process (3) is possible only in the ionized region.

4.3.2 Lya: the observational problem As already mentioned, there were several unsuccessful searches for Lya emission from z — 2-3 "primordial" galaxies in the 1980s and 1990s (Pritchet 1994). Why these difficulties occurred could be understood from observations of nearby starbursts, which revealed one or two puzzles, namely a small number of Lya-emitting galaxies and/or lower-than-expected Lya emission. The second puzzle could, of course, in principle explain the first one. In particular UV spectra of nearby starbursts (Lya) taken with the IUE satellite and optical spectra (Ha, Hp) showed that (i) after extinction correction, the relative line intensity of e.g. I (Lya)/I (Hp) was much smaller than the expected case-B value and the Lya equivalent width W (Lya) smaller than expected from evolutionary synthesis models, and (ii) these findings do not depend on metallicity (e.g. Meier & Terlevich 1981; Hartmann et al. 1984; Deharveng et al. 1986).

Among the possible explanations put forward were (a) dust, which would destroy the Lya photons (Charlot & Fall 1993); (b) an inhomogeneous ISM geometry, not dust, as primary determining factor (Giavalisco et al. 1996); and (c) a short "duty cycle" of SF to explain the small number of Lya emitters. Also (d), Valls-Gabaud (1993) argued that with an appropriate, i.e. metallicity-dependent, extinction law (i) was no problem. Also, he stressed the importance of underlying stellar Lya absorption.

Dust as a sole explanation was rapidly ruled out by the observations of I Zw 18 and SBS 0335-052, the most-metal-poor starbursts known, which exhibit no Lya emission, actually having even a damped-Lya-absorption profile (Kunth et al. 1994; Thuan & Izotov 1997). However, we now know (from ISO and Spitzer observations) that these objects contain also non-negligible amounts of dust (Thuan et al. 1999; Wu et al. 2007), although it is not clear whether and how it is related to the line-emitting regions, in particular spatially. From the absence of correlations between different measurements of

Figure 4.3. Observations of the nearby Blue Compact Galaxy ESO 338-IG04 from Hayes et al. (2005). Left: Lya equivalent-width map. Regions of high equivalent width show up in dark colours. Particularly visible are the diffuse emission regions outside the starburst region. Much local structure can be seen, particularly around knot A (the main UV know) and the other bright continuum sources. Right: a false colour image showing [O Ill] in red, the UV continuum in green and the continuum-subtracted Lya image in blue.

Figure 4.3. Observations of the nearby Blue Compact Galaxy ESO 338-IG04 from Hayes et al. (2005). Left: Lya equivalent-width map. Regions of high equivalent width show up in dark colours. Particularly visible are the diffuse emission regions outside the starburst region. Much local structure can be seen, particularly around knot A (the main UV know) and the other bright continuum sources. Right: a false colour image showing [O Ill] in red, the UV continuum in green and the continuum-subtracted Lya image in blue.

extinction, Giavalisco et al. (1996) suggest that an inhomogeneous ISM geometry must be the primary determining factor, not dust. However, no quantification of this effect was presented or proposed. More detailed observations of local starbursts have since then provided important new pieces of information that we will now briefly summarize.

4.3.3 Lessons from local starbursts High-dispersion spectroscopy with the HST has shown the presence of neutral gas outflows in four starbursts with Lya in emission (P-Cygni profiles), whereas other starbursts with broad damped-Lya absorption do not exhibit velocity shifts between the ionized emitting gas and the neutral ISM traced by OI or Si II (Kunth et al. 1998). The metallici-ties of these objects range from 12 + log(O/H) ~ 8.0 to Solar; their extinction is EB-V ~ 0.1-0.55. From these observations Kunth et al. (1998) suggest that outflows and superwinds are the main determining factor for Lya escape.

Two- and three-dimensional studies of Lya emission and related properties in nearby starbursts have been carried out with the HST (UV) and integral-field spectroscopy (optical) to analyse at high spatial resolution the distribution and properties of the relevant components determining Lya, i.e. the young stellar populations, their UV slope (a measurement of the extinction), the ionized gas and the resulting Lya emission, absorption and local line profile (e.g. Mas-Hesse et al. 2003; Kunth et al. 2003; Hayes et al. 2005). In ESO 338-IG04 (Tol 1914-416), for example, diffuse Lya corresponding to about two thirds of the total flux observed in large apertures (e.g. the IUE) is observed, thus confirming the existence of a Lya resonant-scattering halo; see Figure 4.3 (Hayes et al. 2005). No clear spatial correlation between stellar ages and Lya is found. However, correlations between the Lya line kinematics and other kinematic tracers (NaID and Ha) are found.

Another interesting case is ESO 350-IG038, where Kunth et al. (2003) find two young star-forming knots (B and C) with similar, high extinction, one exhibiting Lya emission, the other not. Hence dust absorption cannot be the dominant mechanism here. From the observed Ha velocity field, Kunth et al. suggest that kinematics is primarily responsible for the observed differences between the two regions.

A "unifying" scenario to explain the observed diversity of Lya profiles in terms of an evolutionary sequence of starburst-driven supershells/superwind has been presented by Tenorio-Tagle et al. (1999) and confronted with local observations in the same paper and, in more depth, by Mas-Hesse et al. (2003).

In short we retain the following empirical results from nearby starbursts on Lya: W(Lya) and Lya/Hp are often smaller than the case-B prediction. No clear correlation of Lya with metallicity, dust and other parameters is found. Strong variations of Lya are observed within a galaxy. A Lya-scattering "halo" is observed. Starbursts have complex structure (super star clusters plus diffuse ISM), and outflows are ubiquitous. From the various observations it is clear that the formation of Lya is affected by (1) ISM kinematics, (2) ISM (H I) geometry and (3) dust. However, the precise order of importance remains unknown and may well vary among objects.

New, more-complete high-spatial-resolution observations are needed. In parallel quantitative modelling including known constraints (stars, emitting gas, H I, dust plus kinematics) with a three-dimensional radiation-transfer model remains to be done.

4.3.4 Lya radiation transfer 4.3.4.1 Basic line-formation processes and examples

To gain insight into the physical processes affecting Lya, to understand the variety of observed line profiles and their nature, and hence to develop quantitative diagnostics using Lya, it is important to understand the basics of Lya radiation transfer. To do so we rely on the recent paper by Verhamme et al. (2006), where more details and numerous references to earlier papers can be found. Among recent papers shedding new light on Lya radiation transfer we mention here the work of Hansen & Oh (2006) and Dijkstra et al. (2006ab).

The Lya line's optical depth can be written as

where T4 is the temperature in units of 104 K, NH the neutral-hydrogen column density and H(x, a) the Hjerting function describing the Voigt absorption profile. Here x describes the frequency shift in Doppler units, x = (v — v0)/AvD = -V/b, where the second equation gives the relation between x and a macroscopic velocity component V measured along the photon propagation (i.e. parallel to the light path and in the same direction). b is the usual Doppler parameter, b = Vth + VUrb. Equation (4.1) shows that Lya is very rapidly optically thick at line centre, i.e. even for modest column densities (Nh > 3 x 1013 cm-2). For NH = 1020 a very large number of scatterings (~107) is required for a photon to escape. However, velocity fields or an inhomogeneous medium can ease the escape (cf. below).

As is true for other lines, the scattering of photons in the Lya line is not a random walk: it corresponds to a walk in coupled spatial and frequency space, where transport is dominated by excursions to the line wings. In other words, photons propagate only over large distances allowing (long mean free path) them to escape when they are in the wings, where the opacity is lower. This already suffices to allow us to understand the formation of double-peak Lya line profiles in the case of Lya emission surrounded (or covered) by a static medium, as shown in Figure 4.4 (left): all photons initially emitted

Figure 4.4. Left: the predicted Lya line profile for a monochromatic source embedded in a static medium with various NH column densities. Note the characteristic symmetrical double-peak profile. The separation between the two peaks depends in particular on the total optical depth, i.e. on Nh. Right: the angle-averaged frequency-redistribution function for specific conditions (T and Voigt parameter a), shown as the probability distribution function for input frequencies x = 0 (line centre) to 4 ("wing"). Figures adapted from Verhamme et al. (2006).

Figure 4.4. Left: the predicted Lya line profile for a monochromatic source embedded in a static medium with various NH column densities. Note the characteristic symmetrical double-peak profile. The separation between the two peaks depends in particular on the total optical depth, i.e. on Nh. Right: the angle-averaged frequency-redistribution function for specific conditions (T and Voigt parameter a), shown as the probability distribution function for input frequencies x = 0 (line centre) to 4 ("wing"). Figures adapted from Verhamme et al. (2006).

at line centre (for illustration) are absorbed and "redistributed" to the wings, where they can escape. The higher the total optical depth, the larger the separation of the two peaks becomes. Asymmetries between the two peaks are of course introduced with shifts of the intrinsic emission frequency, or - equivalently - with an approaching/receding medium. These cases and many variations thereof are discussed in detail by Neufeld (1990).

In contrast to other scattering processes, Lya scattering is neither coherent nor isotropic. The frequency redistribution, e.g. described by the angle-averaged frequency-redistribution functions Rjj of Hummer (1962), is illustrated in Figure 4.4 (right). Schematically, for input frequencies xin close to the core the emergent photon has its frequency redistributed over the interval — \-x-ln, +xin]. Once photons are sufficiently far into the wing they are re-emitted at close to their input frequency, i.e. scattering is close to coherent in the comoving frame. This behaviour is fundamental to understanding e.g. the formation of the emergent line profile for expanding shells, which is illustrated in Figure 4.5. There detailed radiation-transfer calculations show that the peak of the asymmetric Lya profile is located approximately at the frequency Doppler-shifted by twice the expansion velocity resulting from photons from the back side of the shell (Verhamme et al. 2006). This mostly results from two facts. The first is the re-emission of the photons after their first scattering in the shell peaks at a Doppler shift of —vexp in the comoving reference frame of the shell, since the original Lya photon emitted at line centre (x = 0) is seen in the wing by the material in the shell (re-emission close to coherence). Secondly, in the external frame these photons have then frequencies between x — 0 and -2x(vexp). Now, the escape of the photons with the largest redshift being favoured, this will preferentially select photons from the back of the shell, thus creating a peak at -2x(vexp). The interplay between these different probabilities imprints the detailed line shape, as discussed in more detail in Verhamme et al. (2006). For a given geometry, e.g. an expanding shell appropriate to model outflows in starbursts, a wide variety of Lya profiles can be obtained, depending on the shell velocity and its temperature, the column density, the relative strength of the initial Lya emission with respect to the continuum

Astronomy Monochromatic Emission

Figure 4.5. Left: an emergent Lya profile from an expanding shell with central monochromatic source. The different shapes can be described with the number of backscatterings that photons undergo: bumps 1a and 2 are built up with photons that did not undergo any backscattering, the highest peak located at x = —2vexp/b (feature 1b) is composed of photons that undergo exactly one backscattering, and the red tail 1c is made of photons that undergo two or more backscatterings. See Verhamme et al. (2006) for more details. Right: the frequency distribution of the photons in the expanding shell after the first scattering. The solid curve contains all photons, whereas the dotted one represents the histogram of those photons which escaped after only one scattering. They form a bump around x ~ —2x(vexp), which explains the appearance of feature 1b. See the description in the text. Vexp = 300kms— 1, b = 40kms—1 and NHI = 2 x 1020cm-2. Adapted from Verhamme et al. (2006).

and the presence of dust; see Verhamme et al. (2006) for an overview. Let us now briefly discuss how dust affects the Lya radiation transfer.

4.3.4.2 Lya transfer with dust

A simple consideration of the probability of Lya photons interacting with dust, Pd = (nHaH(x) + ndad, shows that this event is quite unlikely, especially in the line core, where the Lya cross section exceeds that of dust, ad, by several orders of magnitude. Despite this, interactions with dust particles occur, especially in the wings, but also closer to line centre since the overall probability of a photon interacting with dust is increased by the large number of line scatterings occurring there. For this reason it is immediately clear that the destruction of Lya photons by dust depends also on the kinematics of the H I gas, where supposedly the dust is mixed in, although per se the interaction of UV photons with dust is independent of the gas kinematics.

The net result is a fairly efficient destruction of Lya photons by dust, as e.g. illustrated for static cases by Neufeld (1990) and for expanding shells by Verhamme et al. (2006). In the latter case the escape of Lya photons is typically reduced by a factor of ^2-4 with respect to a simple reduction by exp(—ra), where Ta is the dust-absorption optical depth. Finally it is also interesting to note that dust not only reduces the Lya emission (or the line's equivalent width), but also alters the line profile somewhat in a non-grey manner (Ahn 2004; Hansen & Oh 2006), since its effect depends on Lya scattering. See Verhamme et al. (2006) for illustrations.

4.3.4.3 Lya transfer: geometrical effects

Given the scattering nature of Lya, it is quite clear that the observed Lya properties of galaxies depend also in particular on geometry. By this we mean the intrinsic geometry of the object, i.e. the spatial location of the "initial" Lya emission in the HII gas, the distribution and kinematics of the scattering medium (namely the HI), but also the spatial region of this object which is ultimately observed. In other words the observed Lya-line properties (equivalent width and line profile) will in principle also vary if the observations provide an integrated spectrum of the entire galaxy or only a region thereof.

In an inhomogeneous ISM, UV-continuum and Lya-line photons will also propagate in different ways, since their transmission/reflection properties differ. Such cases were discussed e.g. by Neufeld (1991) and Hansen & Oh (2006), who show that this can lead to higher Lya equivalent widths.

In non-spherical cases, including for example galaxies with strong outflows and galactic winds with complex geometries and velocity structures, one may of course also expect significant orientation effects on the observed Lya line. Such cases remain largely to be investigated in realistic three-dimensional radiation-transfer simulations.

4.3.5 Lessons from Lyman-break galaxies Having already discussed relatively nearby starburst galaxies, where spatial information is available, it is of interest to examine the empirical findings related to Lya of more-distant spatially unresolved objects, the so-called Lyman-break galaxies (LBGs) discussed also in more detail in Section 4.4 and in Chapter 2 of this volume. These different categories of objects may help us understand in particular Lya emission and stellar populations in distant and primeval galaxies.

LBGs are galaxies with intense ongoing star formation, selected from their UV (restframe) emission. In 2003 approximately 1000 LBGs with spectroscopic redshifts were known, mostly ones studied by the group of Steidel (Shapley et al. 2003). Since then the number has grown, but this study remains the most comprehensive one on z ~ 3 LBGs. The rest-frame UV spectra of LBGs include stellar, interstellar and nebular lines testifying to the presence of massive stars. A diversity of Lya line profiles, ranging from emission, over P-Cygni to broad absorption-line profiles, and strengths is observed. Interstellar (IS) lines are found blueshifted with respect to the stellar lines (defining the object's redshift, when detected) by Av(abs — *) = —150 ± 60kms—1. A shift of A«(em — abs) ~ 450-650 km s—1 is also observed between the IS absorption lines and Lya. Finally Shapley et al. (2003) find several correlations relating the extinction, W(Lya), W(IS) and the star-formation rate (SFR), which have been understood poorly or not at all, at least until very recently; see Ferrara & Ricotti (2007) for a possible explanation.

From Lya radiation-transfer modelling discussed before, the observed shifts of stellar, IS and Lya lines are naturally understood if the geometry is that of a "global" expanding shell (Verhamme et al. 2006). The IS lines are then formed by absorption of the UV-continuum light from a central starburst in the shell along the line of sight towards the observer. Their blueshift with respect to the stars measures thus the expansion velocity vexp. One then obtains naturally A«(em — abs) ~ 3|Av(abs — *)| = 3vexp, since Lya originates from the back of the shell redshifted by 2vexp. This result indicates that large-scale, fairly symmetrical shell structures must be a good description of the outflows in LBGs.

What causes the variety of observed Lya line profiles and what does this tell us about these galaxies? Using the radiation-transfer code described in Verhamme et al. (2006) we have recently undertaken the first detailed modelling of typical LBGs at z ~ 3, in particular objects from the FORS Deep Field observed by Tapken et al. (2007) at a spectral resolution R ~ 2000, which is sufficient for one to do detailed line-profile fitting. Assuming the spherically expanding shell model motivated in particular by the correct velocity shifts just mentioned, the full variety of profiles can be reproduced for the observed values of vexp and extinction, and by varying NH and intrinsic Lya-line parameters (W and the FWHM).

Figure 4.6. Comparison of observed and modelled Lya line profiles of z ~ 3 LBGs with a variety of line-profile morphologies, from double-peaked, over P-Cygni, to broad absorption. See the discussion in the text. Adapted from Verhamme et al. (2007).

Three such examples are illustrated in Figure 4.6. Fitting the double-peak profile of FDF 4691 (left) is possible only with low velocities, i.e. conditions close to a static medium (cf. Figure 4.4). Such Lya profiles are relatively rare; other cases with such double-peak profiles include the Lya blob observed by Wilman et al. (2005) and interpreted by them as a "stalled" expanding shell, or even as a collapsing proto-galaxy (Dijkstra et al. 2006b). The profile of FDF 4454 (middle), which is quite typical of LBGs, indicates a typical expansion velocity of vexp — 220 km s-1 and a low extinction, compatible with its very blue UV slope. Finally, the profile of the lensed galaxy cB58 (right) from Pettini et al. (2000) is well reproduced with the observed expansion velocity and extinction (vexp — 255 km s 1, Eb-v — 0.3). The fits yield in particular constraints on the column density Nh and the intrinsic Lya-line parameters (W and the FWHM). This allows us to examine the use of Lya as a SFR indicator, to provide constraints on the SF history and age of these galaxies, and to shed new light on the observed correlations between Lya and other properties of LBGs (Verhamme et al. 2007). Understanding Lya in galaxies for which sufficient observations are available and that are located at various redshifts is of great interest also in order to learn how to exploit the more-limited information available for objects at higher z, including primeval galaxies (see Section 4.4).

4.3.6 Lya through the inter galactic medium Having discussed the properties of Lya-line formation and radiation-transfer effects in galaxies, we will now examine how the Lya profile is transformed/transmitted on its way to the observer, i.e. through the intergalactic medium (IGM).

In this situation we consider radiation from a distant background source passing through one or several "HI clouds". This geometry leads to a very simple case in which Lya photons are absorbed and then either scattered out of the line of sight or absorbed internally by dust. In other words no true radiation transfer needs to be computed, and the resulting Lya profile of the radiation emerging from the cloud is simply the input flux attenuated by a Voigt absorption profile characteristic of the cloud properties. For a given density and (radial) velocity - or equivalently redshift - distribution along the line of sight, the computation of the total attenuation and hence of the observed spectrum is thus straightforward.

The observational consequences for a distant source will thus be (1) the imprint of a number of (discrete) absorption components on top of the background source spectrum due to intervening H I clouds or filaments and (2) an alteration of the emergent observer

Hn Hi reionization z~6.5

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