2.1.2. Strong line or statistical methods
When the electron temperature cannot be determined, for example
because the observations do not cover the appropriate spectral range
or because temperature sensitive lines such as [O III]
4363 cannot be
observed, one has to go for statistical methods or "strong line
methods". These methods have first been introduced by
Pagel et al. (1979)
to derive metallicities in giant extragalactic H II
regions. They have since then being reconsidered and recalibrated by
many authors, among which
Skillman (1989),
McGaugh (1991,
1994),
Pilyugin (2000,
2001).
Pagel et al. (1979)
proposed to use the 4 strongest lines of O and H :
H,
H
, [O
II]
3727 and
[O III]
5007.
From Sect. 1, the main parameters
governing the relative intensities of the emission lines in a nebula are :
<T
>,
the mean effective
temperature of the ionization source, the gas density distribution
(parametrized by U in the case of homogeneous spheres), and the
metallicity, represented by O/H.
Luckily oxygen is at the same time the main coolant in nebulae, and
the element whose abundance is most straightforwardly related to the
chemical evolution of galaxies. The
spectra must be corrected for reddening, which is done by comparing
the observed H
/
H
ratio with
the case B recombination value at a typical Te and
assuming a reddening law (see Sect. 3.3).
Therefore two independent line ratios, [O II]
3727 /
H
and [O
III]
5007 /
H
, remain to
determine three quantities. Statistical methods rely on the assumption that
<T
>
(and possibly U) are closely linked to the metallicity, and that
it is the metallicity which drives the observed line ratios. Basing
on available photoionization model grids, Pagel et al.
showed that ([O II]
3727 + [O
III]
5007) /
H
, later called
O23, could be used as an indicator of O/H at metallicities
above half-solar.
Skillman (1989)
later argued that this ratio could also
be used in the low metallicity regime, in cases when the observations
did not have sufficient signal-to-noise to measure the [O
III]
4363 line intensity.
McGaugh (1994)
improved the method and proposed to use both [O III]
5007 /[O
II]
3727 and
O23 to
determine simultaneously O/H and U (his method should perhaps be
called the O23 + method). For the reasons explained above,
the same value of ([O II]
3727 + [O
III]
5007) /
H
can
correspond to either a high or
a low value of the metallicity. A useful discriminator is [N
II]
6584 / [O
II]
3727,
since it is an empirical fact that [N II]
6584 / [O
II]
3727 increases with O/H
(McGaugh 1994).
The expected accuracy of statistical methods is typically 0.2 - 0.3 dex, the method being particularly insensitive in the turnover region at O/H around 3 × 10-4.
On the low metallicity side, the method can easily be calibrated with
data on metal-poor extragalactic H II regions where the
[O III]
4363 line can be
measured. Recently,
Pilyugin (2000)
has done this using the large set of excellent quality observations of
blue compact galaxies by Izotov and coworkers
(actually, the strong line method proposed by Pilyugin differs
somewhat from the O23 method, but it relies on similar
principles). He showed that the method works extremely well at low
metallicities (with an accuracy of about 0.04 dex).
This is a priori surprising, since giant H II
regions are powered by clusters of stars that were formed almost
coevally. The most massive stars die gradually,
inducing a softening of the ionizing radiation
field on timescales of several Myr, which should affect the O23
ratio, as shown by
McGaugh (1991) or
Stasinska (1998).
As discussed by
Stasinska et
al. (2001),
data on H II regions in blue compact dwarf galaxies are
probably biased towards the most recent starbursts, and the dispersion in
<T
>
is not as large as could be expected a priori. Another possibility,
advocated by
Bresolin et al. (1999)
in their study of giant H II regions in
spiral galaxies is that some mechanism must disrupt the
H II regions after a few Myr. Of course, the
O23 method is expected of much lower accuracy when applied to
H II regions ionized
by only a few stars, since in that case the ionizing radiation field
varies strongly from object to object.
On the high metallicity side (O/H larger than about 5 ×
10-4), the situation is much more complex. In
this regime, there is so far no direct determination of O/H to allow a
calibration of the O23 method since the [O
III]
4363 line is too weak
to be measured (at least with 4 m class telescopes). The calibrations
rely purely on models but it is not
known how well these models represent real H II regions.
Besides, at these abundances, the [O II]
3727 and [O
III]
5007 line intensities
are extremely sensitive to any change in the nebular properties
(Oey & Kennicutt 1993,
Henry 1993,
Shields & Kennicutt
1995).
Note that the calibration proposed by
Pilyugin (2001)
of his related X23 method in
the high metallicity regime actually refers to O/H ratios that are
lower than 5 × 10-4.
Other methods have been proposed as substitutes to the O23
method. The S23 method, proposed by
Vílchez &
Esteban (1996) and
Díaz &
Pérez-Montero (2000)
relies on the same principles as the O23
method, but uses ([S II]
6716,
6731 + [S
III]
9069,
9532) /
H
(S23) instead of ([O II]
3727 +
[O III]
5007) /
H
.
One advantage over the O23 method is that the relevant line
ratios are less affected by reddening. Besides, the excitation levels
of the [S II]
6716,
6731 and [S
III]
9532 lines are lower
than those of the [O II]
3727 and
[O III]
5007 lines, so that
S23 increases with metallicity in a wider
range of metallicities than O23 (the turnover region for
S23 is expected at
O/H around 10-3). Unfortunately, [S III]
9532 is more difficult to
observe than [O III]
5007.
Oey & Shields
(2000)
argue that the S23
method is more sensitive to U than claimed by
Diaz & Perez-Montero
(2000).
This would require futher checks, but in any case, the S23
method could be refined into an S23 + method in the same way as
the O23 was refined into the O23 + method.
Stevenson et
al. (1993)
proposed to use [Ar III]
7136] / [S
III]
9532 as
an indicator of the electron temperature in metal-rich H
II regions,
and therefore of their metallicity. This method relies on the idea
that the Ar/S ratio is not expected to vary significantly from object
to object, and that the Ar++ and S++ zones should
be coextensive.
However, photoionization models show that, because of the strong
temperature gradients expected at high metallicity, this method could
lead to spurious results.
Alloin et al. (1979)
proposed to use [O III]
5007 / [N
II]
6584 as a statistical
metallicity indicator. While this line
ratio depends on an additional parameter, namely N/O, the accuracy of
this method turns out to be similar to that of statistical
methods mentioned above. More recently,
Storchi-Bergman et al. (1994),
van Zee et al. (1998) and
Denicolo et al. (2001)
advocated for the use of the [N II]
6584 /
H
ratio
(N2) as metallicity indicator. Similarly to [N II]
6584 /
[O III]
5007, this
ratio shows to be correlated with O/H over the entire range of
observed metallicities in giant H II regions. The reason
why, contrary to the O23
ratio, it increases with O/H even at high metallicity is due to a
conjunction of [N II]
6584 /
H
being less
dependent on
Te than O23, N/O being observed to increase
with O/H in giant H II regions (at high
metallicity at least) and U tending to decrease with metallicity.
The advantage of this ratio is that it is
independent of reddening and of flux calibration, and is only weakly
affected by underlying stellar absorption in the case of observations
encompassing old stellar populations. This makes it extremely
valuable for ranking metallicities of galaxies up to redshifts about 2.5.
As mentioned above, statistical methods for abundance determinations
assume that the nebulae under study form a one parameter family. This
is why they work reasonably well in giant H II
regions. They are not expected to
work in planetary nebulae, where the effective temperatures range
between 20000 K and 200000 K. Still, it has been shown
empirically that there is an upper envelope in the [O III]
5007 /
H
vs. O/H
relation
(Richer 1993),
probably corresponding to PNe with the
hottest central stars. The existence of such an envelope can be used
to obtain lower limits of O/H in PNe located in distant galaxies.