The primordial abundance of 4He: evidence for non-standard big bang nucleosynthesis

1.1 MB·English

by  Y. I. Izotov

Draftversion January25,2010
PreprinttypesetusingLATEXstyleemulateapjv.11/10/09
THE PRIMORDIAL ABUNDANCE OF 4HE: EVIDENCE FOR NON-STANDARD BIG BANG
NUCLEOSYNTHESIS
Yuri I. Izotov
MainAstronomicalObservatory,UkrainianNationalAcademyofSciences, 27Zabolotnohostr.,Kyiv03680, Ukraine
Trinh X. Thuan
AstronomyDepartment, UniversityofVirginia,P.O.Box400325, Charlottesville,VA22904-4325
0
Draft version January 25, 2010
1
0
ABSTRACT
2
WepresentanewdeterminationoftheprimordialheliummassfractionYp,basedon93spectraof86
n low-metallicityextragalacticH iiregions,andtakinginto accountthe latestdevelopmentsconcerning
a
systematic effects. These include collisional and fluorescent enhancements of He i recombination
J
lines, underlying He i stellar absorption lines, collisional and fluorescent excitation of hydrogen lines
5 and temperature and ionization structure of the H ii region. Using Monte Carlo methods to solve
2
simultaneouslyfortheabovesystematiceffects,wefindthebestvaluetobeY =0.2565±0.0010(stat.)
p
± 0.0050(syst.). This value is higher at the 2σ level than the value given by Standard Big Bang
]
O Nucleosynthesis (SBBN), implying deviations from it. The effective number of light neutrino species
N is equal to 3.68+0.80 (2σ) and 3.80+0.80 (2σ) for a neutron lifetime τ equal to 885.4 ± 0.9 s and
C ν −0.70 −0.70 n
878.5 ± 0.8 s, respectively, i.e. it is larger than the experimental value of 2.993±0.011.
.
h Subject headings: galaxies: abundances — galaxies: irregular — galaxies: ISM — ISM: abundances
p
-
o 1. INTRODUCTION have used this technique to derive the primordial He
r
t The determination of the primordial 4He (hereafter massfractionYp,withsomewhatdifferentresults. Inthe
s most recent study Izotov et al. (2007) based on a large
a He) abundance and of some other light elements such
sample of 93 spectra of 86 low-metallicity extragalac-
[ as D, 3He and 7Li, plays an important role in testing
tic H ii regions (hereafter the HeBCD sample) derived
cosmologicalmodels. In the standardtheory ofbig bang
1 Y = 0.2472 ± 0.0012 and Y = 0.2516 ± 0.0011, us-
nucleosynthesis (SBBN), given the number of light neu- p p
v ingBenjamin et al.(1999,2002)andPorter et al.(2005)
trino species, the abundances of these light elements de-
0 He i emissivities, respectively. On the other hand,
pend only on one cosmological parameter, the baryon-
4 Peimbert et al. (2007) obtained Y = 0.2477 ± 0.0029
to-photon number ratio η. p
4 based on a sample of 5 H ii regions, Porter et al. (2005)
Because of the strong dependence of its abundance on
4 He i emissivities, and adopting non-zero temperature
1. ηD,/dHeumteeraiusumrehmaesnbtsecionmdeatmhpeebdarLyyoαmestyesrteomfschaopicpee.aTr htoe fluctuations. Fukugita & Kawasaki (2006) derived Yp =
0 0.250 ± 0.004 for a sample of 31 H ii regions studied by
converge to a mean primordial value log D/H = −4.56
0 Izotov & Thuan(2004), adopting Benjamin et al.(1999,
± 0.04, corresponding to a baryon mass fraction Ω h2
1 b 2002) He i emissivities.
= 0.0213 ± 0.001 (Pettini et al. 2008). This estimate of
: It is generally believed that the accuracy of the de-
v Ω h2 is in excellent agreement with the value of 0.02273
b termination of the primordial He abundance is limited
i ± 0.00062 obtained by Dunkley et al. (2009) from anal-
X presently, not so much by statistical uncertainties, but
ysis of five years of observations with the Wilkinson Mi-
by our ability to account for systematic errors and bi-
r
crowaveAnisotropy Probe (WMAP).
a ases. There are many known effects we need to correct
AlthoughHeisnotasensitivebaryometer(Yp depends for to transform the observed He i line intensities into a
only logarithmically on the baryon density), its primor-
He abundance. These effects are: (1) reddening, (2) un-
dialabundancedependsmuchmoresensitivelythanthat derlyingstellarabsorptionintheHeilines,(3)collisional
ofDonthe expansionrateofthe Universeandonapos- excitation of the He i lines which make their intensities
sible lepton asymmetry in the early universe (Steigman
deviatefromtheirrecombinationvalues,(4)fluorescence
2006, 2007). Thus, accurate measurements of the pri- oftheHeilineswhichalsomaketheirintensitiesdeviate
mordial abundance of He are required to check the con-
from their recombination values, (5) collisional and (6)
sistency of SBBN.
fluorescentexcitationofthe Hlines,(7)the temperature
However, to detect small deviations from SBBN and structure of the H ii region and (8) its ionization struc-
make cosmological inferences, Y has to be determined
p ture. All these correctionsare ata levelof a few percent
to a level of accuracy of less than a few percent. The
except for effect (3) that can be much higher, exceeding
primordialabundanceofHe can, inprinciple, be derived 10%inthecaseoftheHeiλ5876emissionlineinhotand
accurately from observations of the He and H emission dense H ii regions. Most of these effects were analyzed
lines from low-metallicity H ii regions. Several groups
and taken into account by Izotov et al. (2007) for their
HeBCD sample.
[email protected]
We present here a new determination of the primor-
[email protected]
2
dial He abundance. A new study is warranted because (Press et al.1992)whichtakesintoaccountthe errorsin
there are several recent new developments that allow both Y and O/H for each object.
moreaccurateestimatesofsomeofthesystematiceffects
mentioned above. Thus, Gonz´alez Delgado et al. (2005) 2.2. A Monte Carlo algorithm for determining the best
havecalculatedevolutionarystellarpopulationsynthesis value of y+
models with high spectral resolution, so that equivalent
FollowingIzotov et al.(2007),weusethefivestrongest
widths of H i and He i absorptionlines for different ages
He i λ3889, λ4471, λ5876, λ6678 and λ7065 emission
ofsinglestellarpopulationsandforawiderangeofmetal-
linestoderivetheelectronnumberdensityN (He+)and
licitiesarenowavailable. Furthermore,Luridiana(2009) e
the optical depth τ(λ3889). The He i λ3889 and λ7065
has estimated the collisional enhancement of hydrogen
linesplayanimportantrolebecausetheyareparticularly
Balmer lines, while Luridiana et al. (2009) have consid-
sensitive to both quantities. Since the He i λ3889 line is
eredthe fluorescentexcitationofBalmerlinesingaseous
blended with the H8 λ3889 line, we have subtracted the
nebulae(theircaseD).Weincorporateallthesenewcal-
latter, assuming its intensity to be equal to 0.107 I(Hβ)
culations in our new determination of the primordialHe
(Aller 1984).
abundance.
The derived y+ abundances depend also on a num-
In §2, we briefly discuss the method used to derive He
ber of other parameters: the fraction ∆I(Hα)/I(Hα)
abundances in individual objects and the primordial He
of the Hα emission line flux due to collisional
abundance from the total sample. In §3, we derive the
excitation, the electron number density N (He+),
best value for Y and the linear regressionslope dY/dZ. e
p the electron temperature T (He+), the equivalent
Thecosmologicalimplicationsofournewresultsaredis- e
widths EW (λ3889), EW (λ4471), EW (λ5876),
cussed in §4. We summarize our conclusions in §5. abs abs abs
EW (λ6678)andEW (λ7065)ofHe istellar absorp-
abs abs
2. THEMETHOD tion lines, and the optical depth τ(λ3889) of the He i
λ3889 emission line. To determine the best weighted
2.1. Linear regressions meanvalueofy+,weusetheMonteCarloprocedurede-
As in our previous work (see Izotov et al. 2007, and scribedin Izotov et al. (2007), randomly varying eachof
references therein), we determine the primordial He the above parameters within a specified range.
mass fraction Y by fitting the data points in the Y Additionally, in those cases when the nebular He ii
p
– O/H plane with a linear regression line of the form λ4686 emission line was detected, we have added to y+
(Peimbert & Torres-Peimbert 1974, 1976; Pagel et al. theabundanceofdoublyionizedheliumy2+ ≡He2+/H+
1992) (Izotov et al. 2007).
dY
Y =Yp+ (O/H), (1) 2.3. Parameter set for the He abundance determination
d(O/H)
For the determination of He abundance, we adopt He
where i emissivities from Porter et al. (2005) and take into ac-
4y(1−Z)
Y = (2) count the following systematic effects: 1) reddening; 2)
1+4y the temperature structure of the H ii region, i.e. the
temperature difference between T (He+) and T (O iii);
is the He mass fraction, Z is the heavy element mass e e
4) underlying stellar He i absorption; 4) collisional and
fraction, y = (y+ + y2+)×ICF(He++He2+) is the He
fluorescentexcitation ofHe i lines; 5) collisionaland flu-
abundance, y+ ≡ He+/H+ and y2+ ≡ He2+/H+ are re-
orescent excitation of hydrogen lines; and 6) the ioniza-
spectively the abundances of singly and doubly ionized
tion structure of the H ii region. Most of these effects
He, and ICF(He++He2+) is the ionization correction
wereanalyzedbyIzotov et al.(2007)(seealsoreferences
factor for He.
therein).
The slope of the Y – O/H linear regression can be
We define the following set of parameters:
written as:
1. The reddening law of Whitford (1958) is adopted.
dY dY dY Izotov et al. (2007) have shown that He abundances are
=12 =18.2 , (3)
not sensitive to the particular reddening law adopted.
d(O/H) dO dZ
For example, use of the Cardelli et al. (1989) reddening
where O and Z are respectively the mass fractions of curve results in He and other element abundances simi-
oxygen and heavy elements. lartothoseobtainedwiththeWhitford(1958)reddening
We also take into account the depletion of oxygen on law. TheextinctioncoefficientC(Hβ)isderivedfromthe
dust grains. Izotov et al. (2006) demonstrated that the observed hydrogen Balmer decrement, after correcting
Ne/O abundance ratio for low-metallicity BCDs is not the Hα, Hβ, Hγ and Hδ line fluxes for the effects of col-
constant, but increases with increasing oxygen abun- lisional and fluorescent excitation. Finally, all emission
dance. This effect is small, with ∆logNe/O = 0.1 when lines are corrected for reddening, adopting the derived
the oxygen abundance changes from 12+logO/H = 7.0 C(Hβ).
to 8.6. We attribute such a change to oxygen depletion, 2. The electron temperature of the He+ zone is varied
and correct the oxygen abundance for it, using the log inthe range T (He+) = (0.95 – 1.0)×T (O iii). We have
e e
Ne/O versus oxygen abundance regressionline found by chosen this range following the work of Guseva et al.
Izotov et al. (2006), and assuming that depletion is ab- (2006) and Guseva et al. (2007) who have derived the
sent in galaxies with 12+logO/H= 7.0. electron temperature in the H+ zone from the Balmer
To derive the parameters of the Y versus O/H lin- and Paschen discontinuities in the spectra of more than
ear regressions, we use the maximum-likelihood method 100 H ii regions, and showed that T (H+) differs from
e
3
T (O iii) by not more than 5%. We also assume that second (Fig. 1b), they have been derived by adopt-
e
T (He+) = T (H+) because the H+ and He+ zones in ing the temperature T (O iii) derived from the [O iii]
e e e
our objects are nearly coincident. λ4363/(λ4959+λ5007)line flux ratio.
3. Oxygen abundances are calculated by considering The primordial values obtained from the two regres-
two possible values of the electrontemperature: 1)T = sionsinFig. 1, Y =0.2565±0.0010andY =0.2560±
e p p
T (He+) and 2) T = T (O iii). 0.0011,are very similar but are significantly higher than
e e e
4. N (He+)andτ(λ3889)arevariedrespectivelyinthe thevalue Y =0.2516±0.0011obtainedbyIzotov et al.
e p
ranges10– 450cm−3 and0–5,typicalforextragalactic (2007) for the same galaxy sample. The 2% difference
H ii regions. is due to the inclusion of the correction for fluorescent
5. ThefractionofHαemissionduetocollisionalexcita- excitation of H lines, the correction for a larger correc-
tion is varied in the range 0% – 5%, in accordance with tion for collisional excitation to the Hβ flux and larger
Stasin´ska & Izotov (2001) and Luridiana (2009). The adopted equivalent widths of the stellar He i 5876, 6678
fraction of Hβ, Hγ and Hδ emission due to collisional and7065absorptionlines. WeadoptthevalueofYpfrom
excitation is adopted to be 60% that of the Hα emis- Fig. 1a, where both O/H and Y are calculated with the
sion,inaccordancewith Luridiana(2009). We note that same temperature Te = Te(He+).
Izotov et al.(2007)underestimatedthatfractionforHβ, Wehavevariedtherangesofsomeparameterstostudy
adopting a value of only 1/3, and neglected altogether how the value of Yp is affected by these variations. We
to correct the Hγ and Hδ emission lines for collisional have found that varying the fraction of fluorescent exci-
excitation. tationofthe hydrogenlinesbetween0%and2%,and/or
6. Luridiana et al. (2009) have shown that the frac- setting Te(He+) = Te(O iii) or changing Te(He+) in
tion of Hβ emission due to fluorescent excitation by the the range (0.9 – 1.0)× Te(O iii) (instead of making it
far-UV non-ionizing stellar continuum could be as high change between 0.95 and 1.0 × Te(O iii)), result in a
as 2%, and somewhat lower for the Hα emission (their change of Yp between 0.254 and 0.258. Additionally,
case D). We have adopted the conservative value of 1% adding a systematic error of 1% caused by uncertain-
for the fraction of Hα, Hβ, Hγ and Hδ emission due to ties in the He i emissivities (Porter et al. 2009), gives
fluorescent excitation, since a similar effect could affect Yp=0.2565±0.0010(stat.) ±0.0050(syst.),where“stat”
the He i emission lines and partly compensate the effect and “syst” refer to statistical and systematic errors, re-
for the Balmer H lines (the He abundance is calculated spectively. Thus, the value of Yp derived in this paper,
relative to that of H). is 3.3% greater than the value of 0.2482 obtained from
7. The equivalent width of the He i λ4471 absorp- the 3yr WMAP data, assuming SBBN (Spergel et al.
tion line is chosen to be EWabs(λ4471) = 0.4˚A, fol- 2007). However, it is consistent with the Yp = 0.25+−00..1007
lowing Izotov et al. (2007) and Gonz´alez Delgado et al. obtained by Ichikawa et al. (2008) from the available
(2005). The equivalent widths of the other ab- WMAP, ACBAR, CBI, and BOOMERANG data [actu-
sorption lines are fixed according to the ratios ally,thepeakvalueintheirone-dimensionalmarginalized
EWabs(λ3889) / EWabs(λ4471) = 1.0, EWabs(λ5876) distribution of Yp (their Fig.3) is equal to 0.254].
/ EWabs(λ4471) = 0.8, EWabs(λ6678) / EWabs(λ4471) Using Eq. 3, we derive from the Y – O/H linear re-
= 0.4 and EWabs(λ7065) / EWabs(λ4471) = 0.4. The gression (Fig. 1a) the slopes dY/dO = 2.46±0.45(stat.)
EWabs(λ5876) / EWabs(λ4471) and EWabs(λ6678) / and dY/dZ = 1.62±0.29(stat.). These slopes are shal-
EWabs(λ4471) ratios were set equal to the values pre- lower than the ones of 4.33±0.75 and 2.85±0.49 derived
dicted for these ratios by a Starburst99 (Leitherer et al. by Izotov et al. (2007).
1999) instantaneous burst model with an age 3-4 Myr
andaheavyelementmassfractionZ =0.001–0.004,0.8 4. DEVIATIONSFROMSBBN
and0.4respectively. Thesevaluesaresignificantlyhigher
We now use our derived value of the primordial He
than the corresponding ratios of 0.3 and 0.1 adopted
abundance along with the observed primordial abun-
by Izotov et al. (2007). We note that the value cho-
dances of other light elements to check the consistency
sen for the EW (λ5876) / EW (λ4471) ratio is also
abs abs of SBBN. Deviations from the standard rate of Hubble
consistentwiththeonegivenbyGonz´alez Delgado et al.
expansion in the early Universe can be caused by an ex-
(2005). Since the outputhigh-resolutionspectrainStar-
tra contribution to the total energy density, for example
burst99 are calculated only for wavelengths ≤ 7000˚A,
by additional flavors of neutrinos. The total number of
we do not have a prediction for the EW (λ7065) /
abs different species of weakly interacting light relativistic
EW (λ4471) ratio. We set it to be equal to 0.4, the
abs particles can be conveniently be parameterized by N ,
ν
value of the EW (λ6678) / EW (λ4471) ratio.
abs abs the “effective number of light neutrino species”.
8. The He ionization correction factor To perform the study, we use the statistical χ2 tech-
ICF(He++He++) is adopted from Izotov et al. (2007).
nique,withthecodedescribedbyFiorentini et al.(1998)
3. THEPRIMORDIALHEMASSFRACTIONYP ANDTHE and Lisi et al. (1999). This code allows to analyze the
SLOPEDY/DZ constraints that the measured He, D and 7Li abun-
TwoY –O/HlinearregressionsfortheHeBCDgalaxy dances put on η and Nν. For the primordial D abun-
sample of Izotov et al. (2007), with the above set of pa- dance,weusethevalueobtainedbyPettini et al.(2008).
rameters, are shown in Fig. 1. The two regression lines As for 7Li, its value derived from observations of low-
differ in the way oxygen abundances have been calcu- metallicity halo stars (Asplund et al. 2006) is ∼ 5 times
lated. For the first regression line (Fig. 1a), oxygen lower than the one obtained from the WMAP analysis
abundances have been derived by setting the tempera- (Dunkley et al. 2009). Because mechanisms that may
ture of the O++ zone equal to T (He+), while for the leadtoareductionofthe7Liprimordialabundance,such
e
4
as diffusion or rotationally induced mixing, are not well half as large in the first case as compared to the latter
understoodandwedonotknowhowtocorrectforthem, case.
we have adopted the value of the primordial abundance
of 7Li abundance as derived from the 5yr WMAP data 5. SUMMARYANDCONCLUSIONS
ofDunkley et al.(2009). Thepredictedprimordialabun-
Wepresenthereanewdeterminationoftheprimordial
dances of light elements depend on the adopted neutron
helium mass fraction Y by linear regressions of a sam-
life-time τ . We haveconsideredtwovalues,the oldone, p
n ple of 93 spectra of 86 low-metallicity extragalactic H ii
τ = 885.4 ± 0.9 s (Arzumanov et al. 2000), and the
n regions.
newone,τ =878.5±0.8s(Serebrov et al.2005,2008).
n InthisnewdeterminationofY ,wehavetakenintoac-
With the old value of τ and our best value of the pri- p
n count the latest developments concerning several known
mordial He abundance, Y = 0.2565± 0.0010(stat.) ±
p systematic effects. We have used Monte Carlo methods
0.0050(syst.), the minimum χ2 (= 0.640524) is ob-
min to solve simultaneously for the effects of collisional and
tained when η = 6.47 and N = 3.68. The value of
10 ν fluorescentenhancements of He i recombinationlines, of
η is in agreement with η = 6.23±0.17 derived from
10 10 collisional and fluorescent excitation of hydrogen emis-
the WMAP data (Dunkley et al. 2009). If instead the
sionlines, of underlyingstellar He i absorption,of possi-
new value of τn is adopted with the same value of Yp, ble temperature differences between the He+ and [O iii]
then the minimum χ2min (= 0.619816) is obtained when zones, and of the ionization correction factor ICF(He+
η10 =6.51andNν =3.80. Wenotethatη10 andNν only + He2+).
slightlydependonthevalueofthe7Liabundance. They
We have obtained the following results:
aredecreasedby3%and2%,respectively,iftheobserved 1. Our best value is Y = 0.2565 ± 0.0010(stat.) ±
7Li abundance by Asplund et al. (2006) is adopted. p
0.0050(syst.),or3.3%largerthanthevalue derivedfrom
The joint fit of η and N is shown in Figures 2a and
ν the microwave background radiation fluctuation mea-
2b for the two values of τ . The 1σ (χ2 – χ2 = 1.0)
n min surements assuming SBBN. In order to bring this high
and 2σ (χ2 – χ2min = 2.71) deviations are shown respec- value of Yp into agreement with the deuterium and 5yr
tively by the thin and thick solid lines. We find the WMAPmeasurements,anequivalentnumberofneutrino
equivalent number of light neutrino species to be in the flavors in the range 3.68 – 3.80, depending on the life-
range Nν = 3.68+−00..8700 (2σ) (Fig. 2a) in the first case, time of the neutron, is required. This is higher than the
and N = 3.80+0.80 (2σ) (Fig. 2b) in the second case. canonical value of 3 and implies the existence of devia-
ν −0.70
tions from SBBN.
Both of these values are only marginally consistent (at
the2σ level)withthe experimentalvalueof2.993±0.011 2. The dY/dZ slope derived from the Y – O/H linear
regression is equal to 1.62 ± 0.29(stat.), shallower than
(Caso et al. 1998) shown by the dashed line, implying
the previous determination by Izotov et al. (2007).
deviationsfromSBBN.Wenotethat,althoughbothval-
ues are consistent with N = 4.4 ± 1.5 derived from
ν
the analysisof5yrWMAP observations(Komatsu et al.
Y.I.I. thanks the staff of the Astronomy Department
2009),theprimordialheliumabundancesetstightercon-
at the University of Virginia and of the Max Planck In-
straints on the effective number of neutrino species than
stitute for Radioastronomy in Bonn, Germany for warm
theCMBdata,theerrorbarsofN beingapproximately
ν
REFERENCES
Aller,L.H.1984,PhysicsofThermalGaseousNebulae Komatsu,E.,etal.2009, ApJS,180,330
(Dordrecht: Reidel) Leitherer,C.,Schaerer,D.,Goldader,J.D.,etal.1999,ApJS,
Arzumanov,S.,Bondarenko,L.,Chernyavsky, S.,etal.2000, 123,3
PhysicsLetters B483,15 Lisi,E.,Sarkar,S.,&Villante,F.L.1999,Phys.Rev.D,59,
Asplund,M.,Lambert,D.L.,Nissen,P.E.,Primas,F.,&Smith, 123520
V.V.2006, ApJ,644,229 Luridiana,V.2009,Ap&SS,324,361
Benjamin,R.A.,Skillman,E.D.,&Smits,D.P.1999,ApJ,514, Luridiana,V.,Sim´on-D´ıaz,S.,Cervin˜o,M.,etal.2009,ApJ,691,
307 1712
Benjamin,R.A.,Skillman,E.D.,&Smits,D.P.2002,ApJ,569, Pagel,B.E.J.,Simonson,E.A.,Terlevich,R.J.,&Edmunds,M.
288 G.1992,MNRAS,255,325
Cardelli,J.A.,Clayton,G.C.,&Mathis,J.S.1989,ApJ,345, Peimbert,M.,&Torres-Peimbert,S.1974,ApJ,193,327
245 Peimbert,M.,&Torres-Peimbert,S.1976,ApJ,203,581
Caso,C.,etal.(ParticleDataGroup)1998, Eur.J.Phys.,C3,1 Peimbert,M.,Luridiana,V.,&Peimbert,A.2007,ApJ,666,636
Dunkley,J.,etal.2009,ApJS,180,306 Pettini,M.,Zych,B.J.,Murphy,M.T.,Lewis,A.,Steidel,C.C.
Fiorentini,G.,Lisi,E.,Sarkar,S.,&Villante,F.L.1998, 2008,MNRAS,391,1499
Phys.Rev.D,58,063506 Porter,R.L.,Bauman,R.P.,Ferland,G.J.,&MacAdam,K.B.
Fukugita,M.,&Kawasaki,M.2006, ApJ,646,691 2005,ApJ,622,L73
Gonz´alezDelgado,R.M.,Cervin˜o,M.,Martins,L.P.,Leitherer, Porter,R.L.,Ferland,G.J.,MacAdam,K.B.,&Storey,P.J.
C.,&Hauschildt,P.H.2005,MNRAS,357,945 2009,MNRAS,393,L36
Guseva,N.G.,Izotov, Y.I.,&Thuan,T.X.2006, ApJ,644,890 Press,W.H.,Teukolsky, S.A.,Vetterling,W.T.,&Flannery,B.
Guseva,N.G.,Izotov, Y.I.,Papaderos,P.,&Fricke,K.J.2007, P.,1992,NumericalRecipes inC,TheArtofScientific
A&A,464,885 Computing/SecondEdition/,CambrigeUniversityPress
Ichikawa, K.,Sekiguchi,T.,&Takahashi, T.2008,Phys.Rev.D, Serebrov,A.P.,Varlamov,V.E.,Kharitonov,A.G.,etal.2005,
78,043509 PhysicsLettersB605,72
Izotov, Y.I.,&Thuan,T.X.2004,ApJ,602,200 Serebrov,A.P.,Varlamov,V.E.,Kharitonov,A.G.,etal.2008,
Izotov, Y.I.,Stasin´ska,G.,Meynet, G.,Guseva,N.G.,&Thuan, Phys.Rev.C78,035505
T.X.2006, A&A,448,955 Spergel,D.N.,Bean,R.,Dor´e,O.,etal.2007, ApJS,170,377
Izotov, Y.I.,Thuan,T.X.,&Stasin´ska,G.2007,ApJ,662,15 Stasin´ska,G.,&Izotov, Y.I.2001,A&A,378,817
5
Fig.1.— Linear regressions of the helium mass fraction Y vs. oxygen abundance for H ii regions in the HeBCD sample. The Ys are
derivedwiththeHeiemissivitiesfromPorteretal.(2005). TheelectrontemperatureTe(He+)isvariedintherange(0.95–1)×Te(Oiii).
Theoxygenabundance isderivedadoptinganelectrontemperatureequaltoTe(He+)ina)andtoTe(Oiii)inb).
Fig. 2.— a) Joint fits to the baryon-to-photon number ratio, η10, and the equivalent number of light neutrino species Nν, using a χ2
analysis with the code developed by Fiorentinietal. (1998). and Lisietal. (1999). The value of the primordial He abundance has been
set to Yp = 0.2565 (this paper), that of (D/H)p is taken fromPettini etal. (2008)and that of (7Li/H)p from5yr WMAP measurements
Dunkleyetal. (2009). A neutron lifetime τn = 885.4 ± 0.9s from Arzumanovetal. (2000) has been adopted. Thin and thick solid lines
represent respectively 1σ and 2σ deviations. The experimental value Nν = 2.993 (Casoetal. 1998) is shown by the dashed line. b) The
sameasin(a),butwithaneutronlifetimeτn =878.5±0.8s(Serebrovetal.2005,2008).
Steigman,G.2006,Int.J.Mod.Phys.E,15,1 Whitford,A.E.1958,AJ,63,201
Steigman,G.2007,AnnualReviewofNuclearandParticle
Science, 57,463