Figure 1.2. Sequences of photoionization models for spherical, uniform nebulae ionized by stars of various effective temperatures. Thin curve: ionization parameter U = 10-2, He/H = 0.1. Thicker curve: U = 10-3, He/H = 0.1. Thickest curve: U = 10-2, He/H = 0.15. For simplicity, the models were run with a black-body central star.

A few properties, illustrated by the models shown in Figure 1.2, are worth noting.

• He I A5876/Hp measures T* only in a small range of temperatures (T* < 40 kK for our models with a black-body central star as seen in Figure 1.2a, this limit being of course different for realistic stellar atmospheres).

• Owing to the competition between H0 and He+ to absorb photons with energies above 54.4 eV, He II A4686/HP saturates at T* > 150 kK and depends on U at T* > 100 kK (Figure 1.2b).

• He II A4686/HP is independent of He/H (Figure 1.2b), while He II A4686/He I A5876 depends on He/H (Figure 1.2c). Indeed, He II A4686 is a counter of photons, as long as the He++ Stromgren sphere is smaller than the H+ Stromgren sphere.

• The temperatures in the H0 and He+ zones are not equal (Figure 1.2f).

T* from the observed ionization structure. Since the ionization structure of a nebula depends on T*, one can think of using the line ratios of two successive ions to infer T* (e.g. Kunze et al. 1996). However, in such an approach, the effect of the ionization parameter must be considered as well.

To alleviate this problem, Vilchez & Pagel (1988) introduced a "radiation softness parameter", which they defined as

and expected to be independent of U to a first approximation. This, however, was not sufficient for an accurate determination of T* (or even for ranking the effective temperatures of different objects).

Morisset (2004) constructed a grid of photoionization models with various values of U (at various metallicities) to allow a proper estimate of T*. The grid was constructed using the WM-BASIC model atmospheres of Pauldrach et al. (2001).

T* from energy-balance methods. This method was first proposed by Stoy (1933). It makes use of the fact that the heating rate of a nebula is a function of the effective temperature. Since, in thermal equilibrium, the heating rate is compensated for by the cooling rate, a measure of the cooling rate allows one to estimate T*. Most of the cooling is done through collisionally excited lines. Therefore, an estimation of T* can be obtained from the formula

Pottasch & Preite-Martinez (1983) proposed a calibration of this method for planetary nebulae.

A similar argument led Stasinska (1980) to propose a diagram to estimate the average effective temperature of the ionizing stars of giant H II regions. This diagram plots the value of [O Ill] A4363/5007 as a function of the metallicity O/H, for photoionization models corresponding to various values of T*.

1.3.4 Determining the star-formation rate The star-formation rate is an important quantity to measure in galaxies. It can be obtained in many ways: from the ultraviolet continuum, far-infrared continuum, radio continuum, recombination lines and forbidden lines. The latter two are sensitive to the most recent star formation (less than a few Myr ago, which is the lifetime of the mostmassive stars). Note that, while the luminosity in a line measures the absolute value of the recent star-formation rate, the equivalent width of the line measures the ratio of the present to past star-formation rate. Any technique must be calibrated using simulations of stellar populations in which the basic parameters are the stellar initial mass function, the star-formation history and the metallicity. These simulations are based on libraries of stellar evolutionary tracks and of stellar atmospheres. Kennicutt (1998) and Schaerer (2000) give exhaustive reviews on the question. Here, we simply mention a few issues regarding the estimation of star-formation rates using emission lines.

Determining the star-formation rate using Hp or Ha. As with any determination of a physical parameter using Hp, the basic assumption is that all the Lyman-continuum photons are absorbed by the gas. Also, the effect of extinction arising from intervening dust must be properly accounted for (see Kewley et al. 2002). As shown by Schaerer (2000), the derived star-formation rate strongly depends on the choice of stellar initial mass function and upper stellar mass limit.

Determining the star-formation rate using [O ii] A3727. It may seem strange to use such a line to measure the star-formation rate, instead of simply using Ha. In addition to the provisos on Ha, the [OII] A3727 obviously must depend on the metallicity and the ionization parameter. The main reason for attempting to use the [OII] A3727 line in spite of this is that it can be observed in the optical range at larger red-shifts than can Ha and Hp. However, it is an observational fact that the [OII] A3727/Hp ratio strongly varies among emission-line galaxies, even discounting objects containing an active nucleus (see Figure 1.3). Therefore, the use of [OII] A3727 as a star-formation-rate indicator is extremely risky.

Figure 1.3. Diagrams using data on galaxies from the Sloan Digital Sky Survey (taken from Stasinska 2006) to show how strongly the [O Il] A3727/H|3 ratio varies among normal star-forming galaxies (left), galaxies containing an active nucleus (right) and hybrid galaxies (middle).

1.3.5 How can one distinguish normal galaxies from AGN hosts?

After the discovery of spiral galaxies with a very bright nucleus emitting strong and broad (several thousands of km s_1) emission lines (Seyfert 1941), it became clear that these galactic nucleif were the locus of violent, non-stellar activity (Burbidge et al. 1963, Osterbrock & Parker 1965), perhaps of the same nature as found in quasars. Heckman

(1980) performed a spectroscopic survey of the nuclei of a complete sample of 90 galaxies, and found that low-ionization nuclear emission-line regions (LINERs) were quite common and seemed to be the scaled-down version of Seyfert nuclei. Baldwin et al.

(1981) were the first to propose spectroscopic diagnostics based on emission-line ratios to distinguish normal star-forming galaxies from AGNs. The most famous is the [O Ill] A5007/H|3 versus [NII] A6584/Ha diagram, often referred to as the BPT diagram (for Baldwin, Phillips & Terlevich). The physics underlying such a diagram is that photons from AGNs are harder than those from the massive stars that power HII regions. Therefore, they induce more heating, implying that optical collisionally excited lines will be brighter with respect to recombination lines than in the case of ionization by massive stars only. Veilleux & Osterbrock (1987) proposed additional diagrams: [O Ill] A5007/H|3 versus [SII] A6725/Ha and [O Ill] A5007/h|3 versus [O I] A6300/Ha. As had previously been found by McCall et al. (1985), giant HII regions form a very narrow sequence in these diagrams.

It was a great surprise, after the first thousands of galaxy spectra from the Sloan Digital Sky Survey (SDSS) (York et al. 2000) had been released, to find that a proper subtraction of the stellar continuum in galaxies (Kauffmann et al. 2003) allowed one to see a second sequence in the BPT diagram, in the direction opposite to that of the star-forming sequence. Thus, emission-line galaxies in the BPT diagrams are distributed in two wings, which look like the wings of a flying seagull (see Figure 1.4).

Just a few years before, Kewley et al. (2001) had constructed a grid of photoionization models in order to determine a theoretical upper limit to the ionization by massive stars in the BPT diagram. This upper limit, later referred to as the "Kewley line", proved well to the right of the star-forming wing from the SDSS. Kauffmann et al. (2003) shifted this line to the left to define an empirical limit between normal star-forming galaxies and AGN hosts (the "Kauffmann" line). Stasinska et al. (2006) found this limit to be still too "generous", and proposed a more-restrictive one, based on a grid of photoionization f The term Seyfert galaxy was used for the first time by de Vaucouleurs (1960).

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