Sulphur abundance determinations in star-forming regions-I: Ionization Correction Factor

0.49 MB·

by  O. L. Dors

Mon.Not.R.Astron.Soc.000,1–12(2011) Printed8January2016 (MNLATEXstylefilev2.2)
Sulphur abundance determinations in star-forming
regions-I: Ionization Correction Factor
6
1 O. L. Dors Jr.1⋆, E. P´erez-Montero2, G. F. H¨agele 3,4, M. V. Cardaci3,4,
0
A. C. Krabbe1
2
1 Universidade do Vale do Para´ıba, Av. Shishima Hifumi, 2911, Cep12244-000, S˜ao Jos´e dos Campos, SP, Brazil
n
2 Institutode Astrof´ısica de Andaluc´ıa (CSIC), PO Box 3004, E-18080 Granada, Spain
a
3 Institutode Astrof´ısica de La Plata (CONICET-UNLP), Argentina.
J
4 Facultad de Ciencias Astrono´micas y Geof´ısicas, Universidad Nacional de LaPlata, Paseo del Bosque s/n, 1900 La Plata, Argentina.
7

]
A Accepted- 2011April28.Received-2011February18.
G
. ABSTRACT
h
p
- Inthepresentworkweusedagridofphotoionizationmodelscombinedwithstellar
o
population synthesis models to derive reliable Ionization Correction Factors (ICFs)
r
t for the sulphur in star-forming regions. These models cover a large range of nebular
s
parameters and yielding ionic abundances in consonance with those derived through
a
[ optical and infrared observational data of star-forming regions. From our theoretical
ICFs, we suggested an α value of 3.27±0.01 in the classical Stasin´ska formulae. We

1 comparedthetotalsulphurabundanceinthegasphaseofalargesampleofobjectsby
v
using our Theoretical ICF and other approaches. In average, the differences between
0
the determinations via the use of the different ICFs considered are similar to the
2
uncertainties in the S/H estimations. Nevertheless, we noted that for some objects it
5
could reach up to about 0.3 dex for the low metallicity regime. Despite of the large
1
0 scatter of the points, we found a trend of S/O ratio to decrease with the metallicity,
. independently of the ICF used to compute the sulphur total abundance.
1
0 Key words: galaxies:general–galaxies:evolution–galaxies:abundances–galaxies:
6 formation– galaxies: ISM
1
:
v
i
X
1 INTRODUCTION where X+i is the ion whose ionic abundance can be calcu-
r
a lated from its observed emission-lines.
The knowledge of the abundance of heavy elements (e.g.
In particular, for sulphur, in the most of the cases the
O, S, N, Ne) in the gas phase of star-forming regions play
total abundance is calculated by a direct determination of
a key role in studies of stellar nucleosynthesis, initial mass
the abundance of the ions S+ and S2+, through the lines
function of stars and chemical evolution of galaxies.
[Sii]λλ6716,31 and [Siii]λλ9069, 9532 respectively, and by
To derive the total abundance of a given element (X)
usinganICFtocorrecttheunobservedS3+,whichproduces
in ionized nebulae, after to estimate the electron tempera-
forbidden lines at 10.51µm. In the pioneer work, Stasin´ska
ture and electron density of the gas phase, it is necessary
(1978a) proposed an ICF for the sulphurbased on both S+
to calculate the abundance of all its ionization stages (see
and S2+ ions and given by
Osterbrock1989).However,forthemajorityoftheelements
present in star-forming regions, only emission-lines of some O+ α −1/α
ionizationstagescanbemeasured.Inthesecases,theuseof ICF(S++S2+)= 1− 1− . (2)
(cid:20) (cid:18) O (cid:19) (cid:21)
Ionization Correction Factors (ICFs) is necessary to derive
the contribution of unobserved ions, as initially defined by
Along decades, the value of α have been largely discussed
Peimbert & Costero (1969)
in the literature. For example, Stasin´ska (1978a), using
X/H the photoionization models of Stasin´ska (1978b), which as-
ICF(X+i)= , (1)
X+i/H+ sume the Non Local Thermodynamic Equilibrium (NLTE)
stellar atmosphere models of Mihalas (1972), suggested
α = 3. French (1981), who used a sample of Hii re-
gions and planetary nebulae, derived α = 2. Garnett
⋆ E-mail:[email protected] (1989) combined spectroscopic data of Hii regions con-
2 Dors et al.
taining the [Siii]λλ9069, 9532 emission-lines (not consid- andinfrared linesand acomparison between S/Oand O/H
ered bymost of previousworks) with photoionization mod- abundances with prediction of chemical evolution models.
els assuming different stellar atmosphere models in or- Similar analysis was performed for the neon by Dors et al.
der to estimate an ICF for the sulphur. From this anal- (2013). The present paper is organized as follows. In Sec-
ysis, Garnett (1989) suggested that an intermediary α tion 2 the observational data used along the paper are pre-
value between 2 and 3 is correct. Vermeij & van der Hulst sented. In Section 3, we describe the photoionization mod-
(2002), using the optical and infrared spectroscopic data els used to derive ICFs for the sulphur, while methodology
of Vermeij et al. (2002), were able to derive directly an adoptedtoderivetheionicabundancesisgiveninSection4.
ICF for the sulphur and concluded that α = 3 is correct InSection5theresultscontainingtheICFsobtainedbyus-
for O+/O > 0.2, being their results less clear for higher ingphotoionizationmodelsandfromobservationalemission-
ionization stages (see also Dennefeld & Stasin´ska 1983; linesarepresented.Discussionandconclusionsregardingthe
Izotov et al. 1994; Thuan et al. 1995; Kwitter & Henry outcome are given in Sections 6 and 7, respectively.
2001;Kennicutt et al.2003;P´erez-Montero et al.2006).Di-
rect estimations for the sulphur ICF, such as the one per-
formed byVermeij& van derHulst(2002),requireinfrared
2 OBSERVATIONAL DATA
spectroscopic dataof Hiiregionsaswellasdirectmeasures
of electron temperatures, difficult for objects with low ion- We compiled from the literature emission-line intensities of
ization degrees (Bresolin et al. 2005). Thus, sulphur ICFs Hii regions and star-forming galaxies obtained in the opti-
have been mainly calculated by using photoionization mo- cal and infrared spectral ranges. These measurements were
dels, in which not comparison with observational data are used to obtain sulphur and oxygen ionic abundances in or-
performed. der to verify if our photoionization models are representa-
Other important subject is the relative abundance tive of real Hii regions, to check if thetheoretical ICFs are
between sulphur and oxygen, which has a direct impact compatiblewiththeonesderiveddirectlyfromobservations
on studies of stellar nucleosynthesis. These elements arise andinvestigatingtheS/O-O/Hrelation.Theselectioncrite-
from the nucleosynthesis in massive stars (Arnett 1978; rionfortheVisible-samplewasthedetectionoftheintensity
Woosley & Weaver 1995), however, there are two funda- lines [Oii]λλ3726+ 29 (hereafter refereed as [Oii]λ3727),
mental issues ill-defined: (a) The knowledge of the mass [Oiii]λλ4363, 5007, [Sii]λλ6717, 31 and [Siii]λ9069. In the
range of stars that dominates the production of these el- cases where the [Sii]λ6717 and λ6731 lines were not re-
ements. (b) If the initial mass function (IMF) of stars is solved, the sum of the intensity of these lines were consid-
universal. For decades, studies based on optical spectro- ered.Forsomeobjects(indicatedinTable5)thetheoretical
scopic data of star-forming regions have been used to solve relationI[Siii]λ9069=I[Siii]λ9532/2.5wasusedtoestimate
theseproblemsbut,notconclusiveresultswereobtained.For the emission line intensity of λ9069, since only the sum of
example, Garnett (1989), who derived sulphur abundances thesewas available.
for a sample of 13 extragalactic Hii regions, found a con- Since Hii regions and star-forming galaxies are indis-
stant S/O abundance over a range of O/H (generally used tinguishable in diagnostic diagrams (e.g. Dors et al. 2013),
as metallicity tracer), which suggests that either these ele- these objects were considered jointly in our analysis. To
ments are produced by massive stars within a similar mass eliminate objects with a secondary ionizing source, we use
range or by stars of different masses but with an univer- thecriterionproposedbyKewley et al.(2001)todistinguish
sal IMF (Henry& Worthey 1999). This result is supported objects ionized by massive stars from those containing an
by the majority of other works done in this direction (e.g. active galactic nucleus (AGN) and/or gas shock. Hence all
Berg et al. 2013; Guseva et al. 2011; P´erez-Montero et al. objects with
2006; Kennicuttet al. 2003). However, evidences of S/O
0.72
ranges with O/H werefound, for example, byV´ılchez et al. log[OIII]λ5007/Hβ < (3)
[log([SII]λλ6717+31/Hα)]−0.32
(1988)inthegalaxyM33andbyD´ıaz et al.(1991)inM51.
Moreover, due to large dispersion in S/O for a fixed value were selected. In Figure 1 the objects in our sample and a
of O/H (see e.g. H¨agele et al. 2012, 2008, 2006), the idea curverepresenting thecriterion above are shown.
that S/O does not range with the metallicity is somewhat IntheAppendix,Table5liststheobject identification,
uncertain (P´erez-Montero et al. 2006; Kehrig et al. 2006). optical emission-line intensities (relative to Hβ=100) and
In this paper, we employ a grid of photoionization mo- bibliographic references of the sample. We obtained optical
delsof Hiiregionsandalargesampleofopticalandinfrared data of 118 objects. All emission-line intensities were red-
spectroscopicdataofstar-formingregionswiththefollowing dening corrected by the authors of the original works from
goals: which we have taken the data. Dors et al. (2013) showed
1.ToderiveICFsfor thesulphurbased onaconsistent thateffectsofusingheterogeneousdatasample,suchasthe
comparison between ionic abundances predicted by pho- one used in this paper, do not yield any bias on the results
toionization model and calculated from observational data. of abundance estimations in the gas phase of star-forming
2.TocomparethediscrepancyinS/Habundancescom- regions.
puted byusing different ICFs. We also considered emission-line intensities of 143
3. To investigate the S/O-O/Hrelation in star-forming Hii galaxies of a sample of 310 galaxies considered by
regions considering different ICFs for the sulphur. Izotov et al.(2006a)andselectedfromtheSloanDigitalSky
This paper is the first (Paper I) of a series of three Survey(York et al.2000)DataRelease3.Weappliedasim-
works, where in the out-coming papers we will present a ilar selection criterion above but with small changes due to
comparison of S2+/H+ abundances obtained from optical the shorter wavelength spectral coverage of the Sloan data
Sulphur abundance determinations in star-forming regions 3
Kewley et al. (2005) presented adetailed analysis of theef-
fect of considering different aperture on determinations of
physical parameters of galaxies. They have found that sys-
tematicandrandomerrorsfromapertureeffectscanariseif
fibrescapturelessthan20percentofthegalaxylight.Most
of the star-forming regions in our sample can be treated as
point sources, and almost all the object extensions are ob-
served. Therefore, this effect seems to be negligible for our
sample of objects.
3 PHOTOIONIZATION MODELS
Webuiltagridofphotoionization models usingtheCloudy
code version 13.03 (Ferland et al. 2013) to estimate an ICF
for the sulphur. These models are similar to the ones pre-
sented by Dors et al. (2011) and in what follows the input
parameters are brieflydiscussed:
• Spectral Energy Distribution — The synthetic spec-
tra of stellar clusters with 1 Myr, built with the
STARBURST99(Leitherer et al.1999)assumingtheWM-
basic stellar atmosphere models by Pauldrach et al. (2001),
Figure1.log[OIII]λ5007/Hβvs.log([SII]λλ6717+31/Hα)diag- and the 1994 Geneva tracks with standard mass loss with
nosticdiagram.Solidline,takenfromKewleyetal.(2001),sepa-
metallicities Z =1.0,0.4,0.2,0.05Z⊙,were considered.
ratesobjectsionizedbymassivestarsfromthosecontainingactive • Ionization parameter – The ionization parameter U is
nuclei and/or shock-excited gas. Blacksquares represent theob-
defined as U =Q /4πR2nc, where Q is the number of
jectsinoursample.Opencirclesrepresentestimationspredicted ion in ion
hydrogenionizing photonsemitted persecond bytheioniz-
byourmodels(seeSect.3).
ingsource,R isthedistancefrom theionization sourceto
in
the inner surface of the ionized gas cloud (in cm), n is the
(when [Oii]λ3727 is observed [Siii]λ9069 is not, and vice particledensity(incm−3),andcisthespeedoflight.Weas-
versa, dependingon theobject redshift). Hence we selected sumedR =4pc,atypicalsize ofastellar clusterand also
in
the objects that present the [Siii]λ9069 emission lines and used by Stasin´ska & Izotov (2003) to model a large sample
[Oii]λ7325insteadof[Oii]λ3727.Theseobjectsarealsorep- of data of star-forming galaxies. The value n = 200cm−3
resented in Fig. 1 but are not listed in Table 5. was assumed in the models, a typical value of Hii regions
Concerning the IR-sample, the selection criterion was locatedindisksofisolatedgalaxies(e.g.Krabbe et al.2014).
the presence of the flux measurements of the emission-lines We considered the logQ ranging from 48 to 54 dex,
ion
Hi4.05 µm,[Siv]10.51µm and [Siii]18.71µm.Wecompiled with a step of 1.0 dex. From the computed sequence of
infrared data of 103 objects classified as being Hii regions modelsforthehypotheticalnebulae,wefoundlogU ranging
and nuclei of galaxies containing star-formation regions. from ∼ −1.5 to ∼ −4.0, typical values of Hii regions (e.g.
Only nine objects have both optical and IR data. In S´anchezet al. 2015; P´erez-Montero 2014; Rosa et al. 2014;
the Appendix, in Table 6, object identification, fluxes Freitas-Lemes et al. 2014; Dors et al. 2013; Bresolin et al.
of the emission-lines considered and bibliographic refer- 1999).
ences of the sample are listed. In some cases, indicated • Metallicity – The metallicity of the gas phase,
in Table 6, the Hi4.05 µm emission-line fluxes were Z, was linearly scaled to the solar metal composi-
computed from Hi12.37 µm or HI2.63 µm fluxes, assum- tion (AllendePrieto et al. 2001) and the values Z =
ing the theoretical ratios Hi4.051µm/Hi12.37µm=8.2 1.0,0.6,0.4,0.2,0.05Z⊙ were considered. In order to build
and HI4.051µm/HI2.63µm=1.74 taken from realistic models, the metallicity of the nebula was matched
Storey & Hummer (1995) for N = 100 cm−3 and with the closest available metallicity of the stellar atmo-
e
T =10000 K. sphere (see Dors et al. 2011 for a discussion about this
e
Fortheobjectswithemission-linemeasurementsatdif- methodology). For the nitrogen, we computed its abun-
ferentspatialpositions,indicatedintheTable6,theadopted dance from the relation between N/O and O/H given
fluxes were the sum (integrated) of the individual ones. by Vila-Costas & Edmunds (1993). Although the rela-
The purpose of this procedure is to avoid taking exclusive tion between N and O presents a high dispersion (e.g.
emission-lines from outer partsof Hiiregions intoaccount, P´erez-Montero & Contini 2009) this does not affect the re-
which the diffuse gas emission (e.g. Helmbold et al. 2005; sults of the present study, since we do not use nitrogen
Walterbos 1998) component can be important but it is not emission-lines. Since the relation between S/O and metal-
considered in ourphotoionization models. licity is uncertain (P´erez-Montero et al. 2006; Kehrig et al.
The aperture sizes in which the optical and infrared 2006),fivegridsofmodelswerebuiltwiththefollowing val-
data were taken for a same object can be different from ues of log(S/O): −1.31, −1.42 (solar value), −1.55 −1.72,
each other, yielding uncertainties in our results. In fact, and −2.12.
4 Dors et al.
The presence of internal dust was considered and the b (t)=−21.61+11.89/t+14.59·t ,
0 2
grain abundances of van Hoof et al. (2001) were linearly
b (t)=9.17−5.09/t−6.18·t , (6)
scaled with the oxygen abundance. The abundances of the 1 2
refractory elements Mg, Al, Ca, Fe, Ni and Na were de- being t definedby
2
pleted by a factor of 10, and Si by a factor of 2, rela-
tive to the adopted abundances of the gas phase in each
1.397
model. The resulting geometry was spherical in all mod- t2= 0.385+t−1. (7)
els. In total, 175 photoionization models were built. In 3
Fig.1,intensitiesofthelineratioslog([OIII]λ5007/Hβ)and For the cases where RS2 is unresolved, a value of Ne =
log([SII]λλ6717+31/Hα) predicted bythe models are also 200cm−3 was assumed.
plotted,whereitcanbeseenthatthemodelscoververywell TheO2+ andO+ abundanceswerecomputedfollowing
theregion occupied bythe observations. therelations:
O2+ I(5007)
12+log = log +6.3106
(cid:18) H+ (cid:19) (cid:20) I(Hβ) (cid:21)
4 DETERMINATION OF IONIC
1.2491
ABUNDANCES + −0.5816 × logt (8)
t 3
3
Using the observational data in Table 5, the ionic abun-
and
dances of O+, O2+, S+ and S2+ were computed using
O+ I(3727)
direct estimations of the electron temperatures (following 12+log = log +5.887
Dors et al.2013,thismethodwillbecalledtheVisible-lines (cid:18)H+(cid:19) (cid:20) I(Hβ) (cid:21)
method). We also used the observational data in Table 6 1.641
+ −0.543×logt +10−3.94n(,9)
to calculate the S2+ and S3+ ionic abundances through in- t 2 e
2
fraredemission-lines(thismethodwillbecalledtheIR-lines
where n =N /(104cm−3).
method). In what follows, a description of each method is e e
Concerning the SDSS data taken from Izotov et al.
given.
(2006a, not listed in Table5), for the objects with red-
shift z > 0.02 in which the [Siii]λ9069 was measured, the
4.1 Visible-lines method [Oii]λ3727 is out of the spectral range. Therefore, for this
dataset, the O+ abundance was computed using the fluxes
For the objects listed in Table 5, the electron tempera- of the [Oii]λ7320,λ7330 emission-lines and the expression
ture values and oxygen and sulphur ionic abundances were
also derived using thePyNeb code (Luridiana et al. 2015):
derived from the expressions obtained by P´erez-Montero
(2014) and by using the same atomic parameters used in
the version 13.03 of the Cloudy code and listed in Ta- O+ I(7320+7330)
12+log = log +7.21
ble 1. These parameters were included in the PyNeb code (cid:18)H+(cid:19) (cid:20) I(Hβ) (cid:21)
(Luridiana et al. 2015) to derive the oxygen and sulphur 2.511
+ −0.422×logt + (10)
abundances as a function of emission-line ratios and elec- t 2
2
trontemperature.Theseequationsarevalidfortheelectron 10−3.40n (1−10−3.44 × n ).
e e
temperature range 8000-25000 K and they are presented in
what follows. For the sulphur ionic abundances, the equations used
FortheobjectslistedinTable5,wecalculatedtheelec- are:
trontemperature(T )fromtheobservedline-intensityratio
e
RO3= (1.33×I[Oiii]λ5007)/I[Oiii]λ4363 for the high ion- S+ I(6717+6731)
ization zone (refereed as t ) using thefitted function: 12+log = log +5.423
3 (cid:18)H+(cid:19) (cid:20) I(Hβ) (cid:21)
t3 =0.7840−0.0001357×RO3+ 4R8O.434, (4) +0.t9241 −0.37logt2 (11)
with t in unitsof 104K. and
Adopting the same methodology of P´erez-Montero
(2014), the electron density (N ) was computed from the
ratio RS2 =[Sii]λ6716/λ6731 aend using the following ex- 12+log S2+ = log I(9069) +6.527
(cid:18)H+(cid:19) (cid:20) I(Hβ) (cid:21)
pression proposed by H¨agele et al. (2008)
0.661
Ne =103· RRS2··ab0((tt))++ba1((tt)), (5) + tS3 −0.527logtS3. (12)
S2 0 1
To derive the t temperature for the gas region
S3
with Ne in unitsof cm−3 and t in units of 104 K. where the S2+ is located, we used the relation (see
UsingtheappropriatefittingsandPyNebwithcollision P´erez-Montero & D´ıaz 2005)
strengths listed in Table 1, the coefficients of Eq. 5 can be
written in theform tS3=1.05× t3−0.08. (13)
a0(t)=16.054−7.79/t−11.32·t2, The electron temperature (t3), electron density and
ionic abundances calculated from the preceding equations
a1(t)=−22.66+11.08/t+16.02·t2, and using the optical data (Table 5) are listed in Table 7
Sulphur abundance determinations in star-forming regions 5
Table 1.Sources oftheatomicdataofsulphurandoxygen ions.
References
Ion Transitionprobabilities Collisionalstrengths
S+ Podobedova etal.(2009) Tayal &Zatsarinny(2010)
S2+ Podobedova etal.(2009) Tayal&Gupta(1999)
S3+ Johnsonetal.(1986) Tayal(2002)
O+ Zeippen(1982) Pradhanetal.(2006)
O2+ Storey&Zeippen(2000) Aggarwal&Keenan(1999)
in the Appendix. Typical errors of emission-line intensi-
ties are about 10-20 per cent and of electron tempera-
ture determinations ∼500 K, which yield an uncertainty in
ionic abundances of about 0.15 dex (see H¨agele et al. 2008;
Kennicutt et al.2003;Vermeij & van der Hulst2002).Here-
after,wewillassumethattheabundancesbasedonVisible-
lines method havean uncertaintyof 0.15 dex.
4.2 IR-lines method
In order to derive more precise ionic sulphur abundances,
wehavetakenintoaccount thetemperaturedependenceon
the emission coefficients to derive S2+ and S3+ abundances
frominfraredlines.WecomputedtheS2+andS3+ionicfrac-
tions from [Siii]18.71µm and [Siv]10.51µm emission-lines,
respectively, and considering theline HI4.05µm presented
inTable6.WeusedthecodePyNeb(Luridiana et al.2015)
and the atomic parameters presented in Table 1 to derive
theequations
S2+ I(18.71µm) Figure 2. Ionic abundances S+/(S+ +S2+) vs. O+/O. Black
12+log( ) = log +7.051 squares represent observational ionic determinations computed
H+ I(Hβ)
(cid:0) (cid:1) using the data from Table 5 and the Visible-lines method (see
0.053
− −0.634logt (14) Sect. 4.2). Open circles represent ionic abundances predicted by
te e ourmodels (see Sect. 3). Theerrorbarrepresents typical uncer-
taintiesasdefinedinSect4.1.
and
S3+ I(10.51µm)
12+log( ) = log +6.218 5 RESULTS
H+ I(Hβ)
(cid:0) (cid:1)
0.098 5.1 Theoretical-ICF
+ −0.252logt . (15)
t e
e
We derived a theoretical ICF for the sulphur based on the
Since it is not possible to calculate the electron tem- photoionizationmodelresultsdescribedinSect.3.Toverify
perature for most of the objects (∼90%) in our IR-sample how representative are our models of real Hii regions, in
(presented in Table 6), we assumed Te=10000K that im- Fig. 2, the ionic abundance ratio S+/(S+ + S2+) against
plies a certain amount of error. Variations of ±5000 K in the ionization degree O+/O calculated from the data from
the value of the electron temperature in Eqs. 14 and 15 Table 5 and using the Visible-lines method are compared
do the ionic abundance ranges by about ±0.1 dex. More- with those predicted by the models. The theoretical ionic
over, for these objects, we considered the theoretical rela- values considered are the ones weighted over the volume of
tion I(Hβ)/I(Hi4.05 µm)=12.87 assuming Ne=100 cm−3 thehypotheticalnebulae.Wecanseethatthemodelsoccupy
and Te=10000K (Osterbrock 1989). themostpartoftheregionwheretheobservationaldataare
Typical uncertainties in IR estimations are of the or- located and they reproduce thetendencyof S+/(S++S2+)
der of 0.1 dex and are caused, mainly, by the error in the increases with O+/O. However, there is a region occupied
emission-lines (Vermeij& van derHulst 2002). Hereafter, by observational data with [S+/(S+ + S2+)] & −1 and
we will assume that the ionic abundances calculated from (O+/O) & 0.2notcoveredbythemodels.Thisseemstobe
IR-linesmethod havean uncertainty of 0.10 dex. not crucial for the present analysis since similar ICFs can
6 Dors et al.
Figure 3.Such as Fig.2 butfor theIonic abundances S3+/H+ Figure4.IonizationCorrectionFactorforthesulphurvs.O+/O.
vs. S2+/H+ computed using the IR-sample (Table 6) and the Squares and triangles represent direct estimations (see Table 7)
IR-linesmethod(seeSect. 4.2). of the ICF taking into account the S2+ ionic abundance val-
ues estimated from the Visible-sample (Direc-Vis) and the IR-
sample(Direct-IR),respectively. Circlesrepresentestimationsof
be derived from both models and observations, as we are ourmodels.Curvesrepresentthe fittings totheEq.2:Solidline
presenting in this paper. showsthebestfitobtainedusingourmodelsanddashedanddot-
In Fig. 3, theS3+/H+ and S2+/H+ abundancescalcu- ted lines the ones obtained using the observational estimations,
latedusingtheIR-linesmethodandtheIR-sampleandthose as indicated. The α values of the best fits are indicated in the
legend. The error bars represent typical uncertainties as defined
predicted by the models are shown. Again, we can see that
inSect4.2.
themodels coverthe region occupied by theobservations.
Thepredictionsofthemodelswereusedtocomputean
ICF for the sulphurdefined by: of its sulphur ICF, these two values are named Direct-Vis
and Direct-IR ICFs.
S/H
ICF(S++S2+)= , (16) Theidentificationofthenineobjectsforwhichwaspos-
(S++S2+)/H+
sibletocomputetheICFbytheproceduredescribedabove,
where S/H is the ratio between the total sulphur and the theelectron temperature(t )and theionic abundanceva-
S3
hydrogen abundances. Assuming the expression suggested luesarelistedinTable7,whiletheO+/OratioandtheICF
by Stasin´ska (1978a) and presented in Eq. 2, we found α= values are presented in Table 3. For HubbleV and IZw36
3.27±0.01 from a fittingto our model results. were only possible to computethe S2+ ionic abundancevia
theIR-methodbecausethe[Siii]λ9069,λ9532emission-lines
are not available in the literature. These are the only two
5.2 Direct ICFs objects in thesubsamplethat donot fulfiltheselection cri-
terion to be in the Visible-sample but were included here
When emission-lines of the main ionization stages of
becausetheycontributetoabetterestimationoftheDirect-
an element are observed, it is possible to calculate the
IR sulphur ICF. The difference in the S2+ abundances cal-
total abundance of the element and thus, derive an
culated from Visible and IR lines methods has an average
ICF. Therefore, following the methodology presented by value of ∼0.15 dex, with the maximum value of ∼0.35 dex.
Vermeij & van der Hulst (2002) and P´erez-Montero et al.
Inthesubsequentpaperofthisseries,wewillusephotoion-
(2006), we used the Visible and IR samples and the equa-
ization models with abundance variations along the radius
tions presented in Section 4 to derive direct values for the
ofthehypotheticalnebulainordertoinvestigatethesource
sulphurICFforthecommonobjectsinbothsamplesassum-
of this discrepancy.1
ing
InFig. 4 thedirect sulphurICF valuesasafunction of
S++S2++S3+ O+/O are plotted together with the corresponding fittings.
ICF(S++S2+)= S++S2+ . (17) We found α = 2.76±0.22 when S2+ is computed by the
Thiswaspossibleonlyfornineobjects.TheS2+ canbe
estimated using the Visible data and/or using the IR data. 1 Similaranalysis but appliedforneon ionicabundances can be
Hence,foreachobject,wehavetwoindependentestimations foundinDorsetal.(2011).
Sulphur abundance determinations in star-forming regions 7
IR-methodand α=3.08±0.21 whentheVisible-method is S =ICF(S) × S++S2+, (18)
considered. We can note in Fig. 4 that the two fits for the H H+
estimations based onIRandVisiblemethods(redand blue using the S+ and S2+ ionic abundances estimated for the
lines) seem to be not satisfactory for O+/O . 0.2, i.e. for
objects in our Visible-sample via the Visible-lines method.
the regime of high excitation. Similar result was found by
Firstly, we compared the S/H abundances derived through
Vermeij & van der Hulst (2002). A larger number of direct the Theoretical ICF (α = 3.27±0.01), with those derived
ICF estimations for objects with high excitation is clearly usingtheDirect-VisICF(α=3.08±0.21)andtheDirect-IR
need to improvethe results for thisregime. ICF (α=2.76±0.22). In panels a of Fig. 5 these compar-
The error in the Direct-ICF value is due to the un-
isonsareshown.Inthisfigurewealsoplottedthedifferences
certainties ofionic abundancedeterminations(S+,S2+,O+,
(D) between the S/H total abundances estimations (panels
and O2+) and due to the discrepancy between the abun- b) and the O+/O ratio (panels c). It can be seen that the
dance of S2+ calculated via Visible and IR methods
Theoretical ICF yields S/H total abundances in excellent
(Dors et al. 2013;Vermeij & van der Hulst2002).Based on
agreementwiththosegivenbytheDirect-VisandDirect-IR
the results of Vermeij & vander Hulst (2002), we assumed ICFs, with an average difference < D >≈ 0.00 and disper-
anaverageerrorof0.2fortheDirect-ICFand0.15forO+/O,
sions of 0.005 dex and 0.01 dex respectively, independently
obtained from ionic estimations of Kennicuttet al. (2003). oftheionization degreethatissampledbytheO+/Oratio.
Theseuncertaintiesyieldanerrorinthetotalsulphurabun-
Secondly,wealsocomparetheS/Htotalabundancees-
dance of only ∼10%.
timations based on our Theoretical ICF with the ones ob-
tained using some ICFs proposed in the literature. In what
follows a brief description of theseICFs is presented.
6 DISCUSSION
• Kennicuttetal.ICF–Kennicuttet al.(2003)proposed
Intheirpioneerpaper,Peimbert & Costero(1969)obtained to use α = 2.5 for typical Hii regions. This is an average
photoelectric observations of the Hii regions Orion, M8 value obtained from the photoionization models grid calcu-
and M17 and suggested that the total abundance of the latedbyGarnett(1989).Thesameαvaluewasobtainedby
sulphur can be obtained by using an ICF defined by the P´erez-Montero et al. (2006) from optical and IR data.
ionic abundance ratio (O++O2+)/O+. This empirical ap- • Izotov et al. ICF– Izotov et al. (2006a) used a grid of
proachisbasedonthesimilarity betweentheionization po- photoionization models by Stasin´ska & Izotov (2003) built
tentials of S2+ and O+. During the next decades, sulphur assuming spectral energy distributions calculated with the
ICFs had been mainly derived from the analytical expres- Starburst99 (Leitherer et al. 1999) and stellar atmosphere
sionsuggested byStasin´ska(1978a),andtheαvalueofthis modelsbySmith et al.(2002)toderiveanexpressionforthe
original prescriptionhavebeenlargely discussed.Forexam- sulphurICF. These authors derived ICFs considering three
ple, data obtained with the Infrared Space Observatory by metallicityregimes:low[12+log(O/H) < 7.6],intermediate
Vermeij et al. (2002)became,possibly,thefirsttestforthe [7.6 < 12+log(O/H) < 8.2]andhigh[12+log(O/H) > 8.2],
α value, since direct estimations of sulphur ICFs were pos- which are given by:
sible. These authors showed that an α value equal to 2,
ICF(S) = 0.121x+0.511+0.161/x, low Z,
as suggested by French (1981), overpredicts the S3+ ionic
abundance, in concordance with the result previously ob- = 0.155x+0.849+0.062/x, inter. Z,
tained by Garnett (1989). From their observational data, = 0.178x+0.610+0.153/x high Z,
Vermeij & van der Hulst (2002) concluded that α = 3 is a
more reliable value, at least for O+/O>0.2. where x=O+/O.
Despite ICFs could be obtained from direct calcula- • Thuan et al. ICF– Thuan et al. (1995), who used the
tion of ionic abundances (Vermeij & van der Hulst 2002) results of photoionization models grid built by Stasin´ska
or even from ionization potential considerations (e.g. (1990) and NLTE atmosphere models by Mihalas (1972),
Peimbert & Costero 1969; French 1981), ICFs based on derived
grids of photoionization models of nebulae are more reli- −1
ICF= 0.013+x 5.10+x −12.78+x(14.77−6.11x) .
able because all ionization stages of a given ion as well as
severalphysicalprocesses(e.g.chargetransferreactions)are h (cid:2) (cid:0) (cid:1)(cid:3)i
• Kwitter & Henry ICF– Kwitter & Henry (2001) built
taken into account in the calculations (Stasin´ska 2002). In
a grid of photoionization models considering a blackbody
thepresent work, we built agrid of photoionization models
as the ionizing source in order to derive sulphur ICFs for
assuming a large range of nebular parameters (e.g. Z, U,
planetary nebulae that, in principle, it can beemployed for
S/O) and derived a theoretical sulphur ICF. Based on the
Hii regions. These authors proposed
agreementbetweenthemodelpredictionsanddataofalarge
sampleofobjects, wesuggested anαvalueof3.27±0.01in ICF(S)=e−0.017+(0.18β)−(0.11β2)+(0.072β3),
theStasin´skaformulae. Thisvalueissomewhat higherthan
theonederivedbyVermeij & van der Hulst(2002),butitis where β=log(O/O+).
in consonance with theone derived through direct ionic es- • Delgado-Inglada et al. ICF — Delgado-Inglada et al.
timations(α=3.08±0.21) basedmainlyontheVisible-line (2014) computed a large grid of photoionization models in
method (Direct-Vis ICF). ordertoderivenewformulaeforICFsofseveralelementsto
With the aim to compare the S/H total abundances be applied in studies of planetary nebulae. The expression
yieldedbytheuseofdifferentICFs, weconsidered therela- derived by these authors to calculate the total abundance
tion: S/H can beto write in the form
8 Dors et al.
Table 2.Electrontemperatures(tS3)andsulphurionicabundances estimatedfortheVisibleandIRsamples.
Object te(104K) log(S+/H+)Vis log(S2+/H+)Vis log(S2+/H+)IR log(S3+/H+)IR
N160A1 0.92 -6.24 -5.20 -5.31 -6.03
N160A2 0.88 -6.24 -5.18 -5.39 -6.22
N4A 0.94 -6.41 -5.27 -5.15 -5.93
N66 1.18 -6.53 -5.69 -5.72 -6.35
N157-B 1.29 -6.09 -5.49 -5.30 -6.57
N88-A 1.41 -6.87 -6.05 -6.40 -6.28
N81 1.26 -6.72 -5.81 -6.00 -6.62
HubbleVa 1.09 -6.68 — -5.58 -6.21
IZw36a 1.61 -6.90 — -5.81 -6.08
aSeetextforanexplanationabouttheinclusionofthesetwoparticularobjects.
Table 3.O+/Oionicabundances anddirectsulphurICFsestimationsusingtheVisible-linesandtheIR-linesmethods.
Object O+/O ICF
Vis IR
N160A1 0.256 1.13 1.17
N160A2 0.272 1.08 1.13
N4A 0.238 1.20 1.16
N66 0.192 1.20 1.20
N157-B 0.404 1.07 1.04
N88-A 0.126 1.60 1.98
N81 0.202 1.15 1.20
HubbleV 0.194 — 1.21
IZw36 0.120 — 1.49
Figure5.Panela:comparisonbetweentheS/HtotalabundancesobtainedfortheobjectsintheVisible-sampleapplyingtheTheoretical
ICF and, Direct-Vis (left plot) and Direct-IR (right plot) ICFs, as indicated. Panel b: differences between the estimations using the
consideredICFswiththeyaveragevalue(<D>)anditsdispersion(σ)indicated.Panelc:O+/Oratioforeachestimation.
Sulphur abundance determinations in star-forming regions 9
Figure 6.IdemFig.5fordifferentICFsfromtheliterature,asindicated.
S =ICF(S) × S++S2+ × O, of the ICF of Izotov et al. (2006a), there are clear system-
H O+ H atic differences between the values derived through the use
where of ourTheoretical ICF and from theotherICFs. Moreover,
difference in S/H abundances obtained from distinct ICFs
−0.02−0.03w−2.31w2+2.19w3
ICF(S)= , canbenotnegligible whenonlyanindividualobject iscon-
0.69+2.09w−2.69w2
sidered. In fact, we noted that it could reach up to about
and 0.3 dex for thelow metallicity regime (see Fig. 5).
w=O2+/O. Concerningtheratiobetweensulphurandoxygenabun-
dances, several studies have addressed the investigation
In Fig. 6 (panels a) a comparison between S/H total about the variation of S/O with O/H in individual galax-
abundance estimations based on our Theoretical ICF and ies(e.g.Croxall et al.2015;Berg et al.2013;Skillman et al.
those from the literature are shown. In this figure we also 2013; L´opez-Sa´nchez & Esteban 2009; Kennicutt et al.
show the difference (D) between these estimations (panels 2003; Vermeij & van derHulst 2002; Garnett et al. 1997;
b) and the O+/O ratio (panels c). Taking into account the Christensen et al. 1997; V´ılchez et al. 1988) or in a
typicalerrorsfoundintheS/Htotalabundanceestimations general context (e.g. Gusevaet al. 2011; H¨agele et al.
(see e.g. H¨agele et al. 2008) and the dispersion (σ) of the 2008, 2012; P´erez-Montero et al. 2006; Kehrig et al. 2006;
averagedifferences(<D>),itmightseemthatthedifferent Henry& Worthey 1999; Izotov et al. 1997). Most of these
S/Hestimations areinagreement. However,with exception results indicates that the ratio S/O appears to be constant
10 Dors et al.
Figure 7.IdemFig.5fortheICFproposedbyDelgado-Inglada etal.(2014)
withthemetallicity,whicharguesthateithertheseelements values and the number of objects used to calculate them
areproducedbymassivestarswithinasimilarmassrangeor are also listed in Table 8. Considering all the metallicity
bystarswithadistinctmassintervalbutbeingformedwith regimes together and all the considered ICFs we found an
anuniversalIMF(Henry& Worthey1999).However,when average<log(S/O)>=−1.72±0.03.Despitethedispersion,
a large sample of data is considered, the dispersion found when low, intermediate and high metallicities regimes are
is very large and the assumption of a constant S/O ratio is separately considered, we note a decrease in S/O when the
questionable(H¨agele et al.2008,2012;P´erez-Montero et al. metallicity increases. For low and high metallicity regimes
2006;Kehrig et al.2006).Therefore,withthegoalofstudy- we derived mean values of < log(S/O) > −1.53±0.05 and
ingtherelationoftheS/Oratiowiththemetallicity(traced −1.78±0.02, respectively. Similar results were also derived
bytheO/H abundance),we used thedata listed in Table 5 byD´ıaz et al.(1991),V´ılchez et al.(1988)forM51andM33
and all the ICFs considered in the present work to calcu- galaxies and by Shaveret al. (1983) for Milk Way.
late S/O and O/H ratios via the Visible-lines method. The
Direct-Vis ICF was not considered since its α value is very
similar to that of the Theoretical one. In Fig. 8 only the
7 CONCLUSIONS
estimations obtained from the Theoretical ICF is shown.
For estimations from other ICFs (not shown), similar re-
We built a grid of photoionization models combined with
sults were obtained. The solar values log(S/O)⊙ = −1.43 stellar population synthesis models to derive Ionization
and12+log(O/H)⊙ =8.69derivedusingthesulphurabun- Correction Factors (ICFs) for the sulphur. The reliability
dance from Grevesse & Sauval (1998) and the oxygen one
of these ICFs was obtained from the agreement between
fromAllendePrieto et al.(2001)arealsoindicated.Wecan
ionic abundances predict by the models and those calcu-
see in this figure that most of the objects present subsolar
lated through optical and infrared spectroscopic data of
S/O and O/H abundance ratios. Interestingly, for the ex-
star-forming regions with a very wide range in metallic-
tremelowmetallicityregime,someoftheobjectsreachvery
ity (7.0 . 12 + log(O/H) . 8.8) and ionization de-
highS/Oabundanceratios.Sincethedispersionishighand gree (0.1 . O+/O . 0.9). From our results, we suggest
thenumberofobjectsismuchlowerthanforthehighmetal- α=3.27±0.01tobeusedintheclassicalStasin´skaformula.
licty regime, more data are needed to confirm this result.
Thisαvalueisinconsonance with theonederivedfrom di-
Wealsoperformedafittothesedata,assumingalinear rectestimationsbasedonspectroscopicdataofasmallsam-
regressionwithouttakingintoaccounttheindividualerrors. ple of objects. A comparison of the S/H total abundance
In Table 8, the coefficients of the fittings, and the linear derivedby usfor theobjects in our visiblesample andcon-
regressions considering all ICFs are listed. We found that sidering different ICFs proposed in the literature was per-
the S/O ratio decreases with metallicity, yielding a mean formed.Although,inaverage, thedifferencesbetweenthese
slope ofabout −0.27 with all thefittedslopes in agreement determinations are similar to the uncertainties in the S/H
within the estimated errors. We also obtained the average estimations, we noted that it could reach up to about 0.3
values for log(S/O) estimated via the different ICFs and dexfor thelow metallicity regime. Finally, thehighest S/O
considering the three different metallicity regimes. These abundance ratios are derived for objects with extreme low