V. Diagnostics of HII Regions

Transcription

1 1 AY30-HIIDiagnosis V. Diagnostics of HII Regions A. Motivations Primary means of studying the metallicity, SFR, density, extinction, temperature, etc. in star-forming galaxies For faint galaxies, emission lines may be the only aspects (beyond photometry) that are observable B. Primer on Saha Equation and Collisional Strengths (see RadProc notes) C. Hydrogenic Recombination Lines The relative strengths of the Balmer decrement (Hα/Hβ/Hγ) can be calculated theoretically The line ratios are nearly independent of T and n e Therefore, they are useful for inferring reddening because they are at widely separated wavelengths Furthermore, the flux of Hβ is useful for estimating other diagnostics of the HII Region Setup Let n n l equal the density of atoms in the n l level The statistical weights of these levels are Assume ε nl is independent of l Selection rule: l = ±1 Line emissivity j n n = 1 n 1 4π g l = l + 1 (1) n 1 g n = (l + 1) = n () l=0 l =0 l=l ±1 A n l nl is the spontaneous emission rate A n l nl = 4π ν 3 nn [ 8παa 0 Z 3c P = R = rψ is the normalized radial function 0 n n l A n l nlhν nn (3) ] max(l, l ) l + 1 P (n l, nl) (4) R n l (r)rr nl(r)dr (5)

2 AY30-HIIDiagnosis See Condon & Shortley or my AY04b notes for more Oscillator strength f nln l A n l nl = K K ε l + 1 nn l + 1 f nln l (6) ε nn = 1 n 1 n (7) K K = 1 α 5 mc = s 1 (8) The f-values are often tabulated Or emperically determined A values are also tabulated in Wiese et al., NBS 1966 Total decay rate from state nl A nl = n 1 n =n 0 l =l±1 A nln l (9) (a) Case A (n 0 = 1): This presumes all line transitions produced in the HII region escape. It is a good assumption for low mass HII regions but these are rare or, at the least, difficult to study. (b) Case B (n 0 = ): Assume all Lyman lines higher than Lyα are trapped and ultimately converted to Lyα and other lines. Reality generally lies between the two cases Lyman line cross-section (center of the line; we will derive this later) σ(lyn) = 3λ3 n1 8π ( mh πkt ) 1 A np,1s (10) At T K, τ(lyα) 10 4 Similarly, τ(lyβ) 10 3, τ(l8) 10, τ(l18) 10 The majority of interactions are scatterings Occasionally, however, the photon is converted to Hα, Hβ, etc. Cascade Matrix Means of calculating the population of various levels Consider steady state conditions (i.e. detailed balancing) Ignoring g l n e n p α nl(t ) + n n l A n l nl = n nl A nl (11) Averaging over l n e n p α n + n >n;l =l±1 n =n+1 n n A n n = n n A n (1)

3 3 AY30-HIIDiagnosis Definitions α n = α nl (13) l A n n = g l (n ) A n l nl (14) l l =l±1 n 1 A n = A nn (15) n =n 0 This assumes the population of l-levels is proportional to g l This is a good approximation for high n and l where both e and p collisions give nl n, l ± 1 Define P n n = probability that every entry into n is followed by a direct transition to n < n P n n = A n n A n (branching ratio) (16) Define C n n = probability that entry into n is followed by a transition to n < n by any route. Altogether C n,n = 1 (17) C n+1,n = P n+1,n (18) C n+,n = P n+,n+1 C n+1,n + P n+,n (19). (0) C n n = n p=n 1 Our equation for detailed balance becomes n n A n = n e n p P n pc pn (1) n =n α n C n n () One generally express the solution in terms of the departure coefficient b n n n n n (3) n n is given by the Boltzman equation (i.e. thermodynamic equilibrium) Using the Boltzman-Saha equation ( πmkt b n = h 3 ) 3 e I n/kt n A n α n C n n (4) n =n

4 4 AY30-HIIDiagnosis Note, there is no density dependence in the above equation An approximate solution to the Cascade matrix comes from Seaton He noted C gn C n as g He replaced the higher order terms of the sum by an integral α n C n n = n =n g 1 n =n Given these results, the emissivity becomes Table α n C n n + 1 α gc gn + 1 ( C gn + C n ) g α n d n (5) j n n = n n A n nhν n n/4π (6) = b n n n A n nhν n n/4π (7) Table 1: Seaton s Results (modern values) j n n Case A Case B T = 10 4 T = 10 4 T = 10 4 T = 10 4 Hα (86) 79 Hβ (100) 100 Hγ (47) 49.1 H (5.4) 6.3 H (1.6) 0.8 Case B values of Hα are much higher due to the trapping of Lyman lines Values in () are from Osterbrock (i.e. modern values) Note that all of the lines weaken together as T (α n T 1/ to T 3/ ) More accurate Balmer decrements Treat l explicitly Include collisional terms n e n p α nl (T ) + n =n+1 l =l±1 = n nl [ A nl + A n l nln n l + l =l±1 n e q nlnl + l =l±1 n e n nl q nl nl + n=n 0 l =l±1 n e q nln l ] n =n 0 l =l±1 n e n n l q n l nl α nl (T ) are determined using Milne s relation Define n 1 A nl = A nln l (8) n =n 0 l =l±1

5 5 AY30-HIIDiagnosis Collisions q nl nl±1 collisions are due to impacts by ions (Pengalley & Seaton 1964) q nl n±1l±1 collisions are due to electrons (Seraph 1964) See Osterbrock Tables 4.1 to 4.4 D. Effective Recombination Coefficient for Hβ: α Hβ Fig Define α Hβ = α B P Hβ (9) P Hβ is the probability of Hβ emission following recombination to higher excited levels Ignoring collisions P Hβ = n 1 n =4 l =0 α n l From Brocklehurst (ε Hβ α Hβ hν Hβ ): l =l±1 C n l nl l =l±1 A 4l,l A 4l (30) 0.11 (31) Table : Hβ recombination coefficient T α Hβ (cm 3 /s) ε Hβ (erg cm 3 / s) Functional fit α Hβ hν Hβ ( ) T (erg cm 3 /s) (3) 10 4 K

6 6 AY30-HIIDiagnosis Diagnostic of n e or M HII Measure F Hβ L Hβ F Hβ4πd 4 = ε Hβ 3 πr3 n e (33) If R/d is known, n e can be estimated If n e is known (e.g. [OII]), then M HII is inferred Zanstra s Method for finding T of the ionizing star (or the ionizing luminosity, φ) in an HII region M HII F Hβ4πd m p ε Hβ n e (34) (a) Observe the size of the HII region r HII. Global ionization equilibrium (e.g. the Stromgren radius) implies: r HII φ = α B n e4πr dr (35) 0 For an ionization bounded HII region, r HII = R S For r HII < R S, this is a density bounded region and φ is greater than the RHS of Equation 35. (b) Observe F Hβ F Hβ = 1 4πd hν Hβ r HII 0 α Hβ n e4πr dr If the nebula is nearly isothermal, then α Hβ = constant and α B = constant with radius In this case, the integral is trivial (c) Rearranging ( ) φ 4πd F Hβ αb (37) hν Hβ α Hβ (d) For a star (blackbody) φ(t ) = 15 π 4 ( ) L hν0 f hν 0 kt L = 4πR σt 4 Note, φ is a double-valued function of T (e) If the visible (V -band) flux is also known F V = 4πR 4πd = L σt πd (36) s 1 (38) πb ν (T )V ν dν (39) 0 πb ν V ν dν (40)

7 7 AY30-HIIDiagnosis V ν is the V -band filter (f) Rearrange the 3rd step F Hβ α Hβ α B hν Hβ φ 4πd = α Hβ α B hν Hβ 15 4πd π 4 L f (41) hν 0 (g) Divide step 5 by 6 F Hβ F V α Hβ 15 f hν Hβ α B π 4 hν 0 0 σt 4 πb ν (T )V ν dν (4) Gives a known function of T and T Solve for T, independent of L and d E. Forbidden Lines (Densty, Temperature) These states are generally excited by collisions Gas is optically thin to forbidden lines (no radiative transfer) Excited levels of forbidden lines are populated by collisions sensitive to n e or T Important diagnostics of density and temperature e.g. [OIII], [OII] [OIII] Configuration: 1s s p Two equivalent p electrons Allowed states: 1 S 0 ; 3 P 0,1, ; 1 D Other states are excluded by Pauli Relative energies: Hund s Rules (See RadProc notes) (a) Higher S Lower energy 3 P J has lowest energy (b) Higher L Lower energy 1 D has lower energy than 1 S 0 (c) Higher J Higher energy for less than half filled 3 P 0 has lower energy than 3 P 1, etc. Energy level diagram

8 8 AY30-HIIDiagnosis [O III] 1 S0! 4363! 31 1 D! 5007! P Wavelengths 1 S 0 1 D λ = 4363Å 1 D 3 P λ = 5007Å 1 D 3 P 1 λ = 4959Å 1 D 3 P 0 λ = 4931Å Transitions between any two of these states is forbidden No change in parity Parity of two p electrons is always even [OIII]: Temperature diagnostic Low density limit (n e < 10 5 cm 3 ) The low lying 3 P states have very nearly the same energy and are populated according to their statistical weights g J = (J + 1) Keys: Relative excitation of the upper levels is a function of T and not n e Every excitation is followed by spontaneous emission of a photon Excitation of 1 D level Followed by emission of λ 5007 or λ 4959 photon Relative probabilities A1 D, 3 P : A1 D, 3 P 1 3

9 9 AY30-HIIDiagnosis Excitation of 1 S level Emission of λ 4363 ( 1 D ) or λ 31 ( 3 P 1 ) photon Relative probabilities A1 S, 1 D : A1 S, 3 P 1 10 Emission of λ 4363 is followed by λ 5007 or λ 4959 photon (small contribution) Emission line strength (energy/s/volume) Consider 1 S 1 D j 4363 = [ rate 1 S is populated ] [ hν(4363) ] [ rate 1 S 1 D ] (43) Collisional excitation rate n3 P q3 P, 1 S = n3 P Ω( 3 P, 1 S) e hν(1 S, 3 P )/kt T 1 g3 P (44) Rate 1 S 1 D : Ratio of spontaneous emission coefficient Altogether A1 S, 1 D A1 S, 1 D + A1 S, 3 P 1 (45) j 4363 n3 P Ω( 3 P, 1 S) e hν(1 S, 3 P )/kt T 1 g3 P ν( 1 S, 1 D)A1 S, 1 D A1 S, 1 D + A1 S, 3 P 1 (46) Consider 1 D 3 P Convenient to consider the two channels together j j 5007 n3 P Ω( 3 P, 1 D) e hν(1 D, 3 P )/kt T 1 g3 P ν( 1 D, 3 P ) (47) where ν( 1 D, 3 P ) = ν(1 D, 3 P )A1 D, 3 P + ν( 1 D, 3 P 1 )A1 D, 3 P 1 A1 D, 3 P + A1 D, 3 P 1 (48) For higher accuracy, we should include the contribution of de-excitations from the 1 S 1 D transition But, these are small for T < 30000K Emission-line ratio j j 5007 = Ω(3 P, 1 D) A1 S, 1 D + A1 S, 3 P j 4363 Ω( 3 P, 1 S) A1 S, 1 D ν( 3 P, 1 D) ν( 1 S, 1 D) e E/kT (49) E = hν( 1 S, 1 D) The only physical dependence of the line ratio is temperature Excellent T diagnostic for low density regimes At higher n e, collisional de-excitation is important and 1 D is preferentially weakened.

10 10 AY30-HIIDiagnosis 1983MNRAS S Can correct equation (49) by a factor Useful expression (not quite exact) f = [See AGN] (50) j j 5007 j 4363 = 6.91 exp [ ( )/T ] (n e /T 1 ) A similar relation holds for [NII] lines, but these lines are less luminous than oxygen Since [OIII] is a major coolant of HII regions, we expect higher temperatures when the O abundance is lower. Indeed, T e is observed to increase with the distance from the center of the Galaxy Fig (Shaver et al. 1983) (51) [OII] Configuration Ground state: 1s s p 3 Three equivalent p electrons Add 1 equivalent p electron to the p states Allowed states: 4 S 3 ; P 1, 3 ; D 3, 5 Relative energies: Hund s Rules (a) Higher S Lower energy has lowest energy 4 S 3 (b) Higher L Lower energy are second D 3, 5 (c) Half full All bets are off P 1 D 3 is higher than D 5 is higher than 3 P 3

11 11 AY30-HIIDiagnosis Wavelengths 4 S 3 D 3 D 5 λ = 376Å λ = 379Å 4 S 3 Energy level diagram Transitions between any two of these states is forbidden No change in parity Parity of three p electrons is always odd [OII]: Density diagnostic Pair of emission lines with very nearly the same energy e E/kT 1 No significant T dependence, only n e Low density limit: Every collisional excitation is followed by a spontaneous emission j 379 Ω(4 S, D 5 j 376 Ω( 4 S, D 3 ) ν( 4 S, D 5 ) ) ν( 4 S, D 3 E kt for reasonable T e E/kT 1 ν( 4 S, D 5 )/ν( 4 S, D 3 ) 1 Useful relation: Therefore Ω(S L J, SLJ) = ) e E/kT (5) (J + 1) (S + 1)(L + 1) Ω(S L, SL) (53) Ω( 4 S, D 5 ) = 3 Ω(4 S, D 3 ) (54)

12 1 AY30-HIIDiagnosis And High density limit: Levels are Boltzmann populated j 379 j (n e 10 3 cm 3 ) (55) j 379 j 376 = g 379 g 376 A 379 A 376 = 0.3 (56) Transition between these two regimes occurs at the critical density n e = A q { cm 3 D cm 3 D 3 (57) AGN Fig 5.8 Real World F. Metallicity Often the observations of n e and T from different forbidden lines or other methods do not always agree Could be due to incorrect assumptions in the relative abundances More likely, the problem is that there are variations in the temperature that are not considered in one-zone models Piembert fluctuation method Definition and Notation Fraction of a gas/star/galaxy (by number or mass) that is made of metals Often assessed with a single element (e.g. O, Fe, C) And scaled against the Sun HII formalism: 1 + log (O/H) O/H is the number density of the particles (O/H) , but this keeps changing! Square-bracket notation: [O/H] = log(o/h) - log(o/h) Stellar dominated IGM, ISM Observations Local HII regions: Wealth of diagnostics we have been discussing and more Extragalactic: Often limited to the strongest lines observed at optical wavelengths Sensitivity of detectors and sky lines limit IR observations (improving) Things are progressing to the IR, however Lines

13 13 AY30-HIIDiagnosis Strong: [OII], Hβ, [OIII] λ4959, 5007, Hα, [NII] Weak: [OIII] λ4363, [SII] Key systematic observational error: Reddening Often use Hα/Hβ ratio and Case B assumption to estimate the reddening One generally has to assume an extinction law T e -Method Often considered the gold-standard of abundance estimates Literature (Lots) Shaver et al. 1983, MNRAS, 04, 53 Skillman Dopita et al. 006, ApJS, 167, 177 Basic procedure (a) Use specific lines to estimate T e and n e for the HII region (b) Construct an HII model based on these parameters (c) Solve for the metallicity based on the line fluxes of other lines (d) Iterate steps (a-c) as necessary Challenges Difficult to estimate T e : [OIII] λ4363 is very weak, especially in higher metallicity systems One must still make many simplifying assumptions about the HII region(s) How does one model a full galaxy of HII regions?! More advanced efforts Include extinction Include variable T e Include a range of stellar temperatures or a synthesis of multiple HII regions Fit for all lines together Empirical techniques Basic approach Measure O/H for a set of HII regions using the T e -method Search for correlations between O/H and strong emission lines Derive fitting formulas and proceed R 3 method :: Historical favorite Pagel et al. 1979, MNRAS, 189, 95 Definition R 3 = I [OII] λ I [OIII]λ459+λ5009 I Hβ (58)

14 14 AY30-HIIDiagnosis L.S. Pilyugin: On the oxygen abundance determination in H ii regions Empirical result (Pilyugin 000, A& A, 36, 35) sion will be presented in Sect. 3. ration L.S. Pilyugin: On the oxygen abundance determination in H ii regions 37 method and the R 3 method ances the X 3 (= log R 3 ) ver- Milky Way Galaxy H ii regions ii regions in spiral and irregular 3 calibrations after Edmunds & opita & Evans 1986, and Zaritucted, Fig. 1. The data for H ii re taken from (Izotov & Thuan 1997; Kobulnicky & Skillman t al. 1997; Skillman et al. 1994; lesias-paramo 1998). The data es were taken from (Esteban et ; Garnett et al. 1999; Gonzalez- Aller 1981; Pagel et al. 1980; iagram l. 1983; for Shields H ii regions & in Searle spiral and 1978; ire Esteban positions of1996; H ii regions Vilchez with 7.1 et al. These own by circles, lists (involving H ii regions with data own by triangles, H ii regions with 8.0 austive ones. In the case of lowa 7.1 large 1+log(O/H) set of data T e with 7.3 and recent H ii own by plusses. Solid lines are best fits ith /H) xygen T e 7.6. abundance Dashed lines with are lines the Twith e ere not included in our list. In i regions there are a few recent the selected oxygen subset abundance of H ii regions with result the etween X to include 3 = X in obs 3 X our list 3 and p all avail- 3, although some data were (1) 3 pations nofa pfew cases there are two inoxygen X = Xabundance obs X andin pthe = same p is 3 = 0 was adopted. The correations in different parts of the pe. present study is a search () for undance relation but not an inerties of individual 3 and X have been com- values of X galaxies, the ns from the selected subset. es oxygen (O/H) T abundance e versus observed in the X 3 same and Xas individual data points. Our 3 values for the selected subset of Kennicutt Fig. 4. The O/H et al. versus (000) X diagram that the the (Edmunds O/H versus & XPagel 3 diagram 1984) is proof oxygen 3 diagram is presented pre- /H versus X abundance, but an is the best fit to the O/H versus X3 hat it still results in an oxygen s the best fit to the O/H versus X 3 are he positioned mean at any between given correspondce po/h 3 values calibration are more close can to repro- zero logr 3. ough lated intersect and a new X 3 seem one to should be more be n of Fig. 4 shows that linear approxr the relations between O/H and X 3 ct Thus, the the linevalues intensities of X 3 and O/H X relafind f oxygen a best abundance fit R 3 using O/Hthe relation linear 3 have tshich to the oxygen data result abundances in the following were Fig. 1. The OH logr 3 diagram. The positions of H ii regions in spiral galaxies (circles) (the H ii regions in our Galaxy from Shaver et al (S83) are indicated by plusses) and in irregular galaxies Fig. (triangles) 3. The p 3 are versus shown X 3 together diagram for with H iioh regions Rin 3 spiral calibrations and irregular authors: galaxies Edmunds (points). & The Pagel positions 1984 of(ep), H ii regions McCall withet7.1 al of different (MRS), 1+log(O/H) Dopita & T Evans e are shown (DE), byand circles, Zaritsky H ii regions et al with 7.4 (ZKH). 1+log(O/H) T e 7.6 are shown by triangles, H ii regions with log(O/H) T e 8.1 are shown by plusses. Solid lines are best fitsnote: to positions Theofresults H ii regions are with double-valued!!! log(O/H) T e 7.3, H ii regions verified with in 7.4 the 1+log(O/H) One must have following additional T e simple 7.6, andway. H ii regions Let with us consider 8.0 knowledge to break the degeneracy the X 1+log(O/H) versus p T e 8.1. Dashed lines are lines with slope equal to 1. Functional and form X for 3 versus low metallicity p 3 diagrams, Figs., 3. (The following notations will be accepted here: R = I [OII]λ377+λ379 /I Hβ, X = logr, R 3 = I [OIII]λ4959+λ5007 /I Hβ, X 3 = logr 3, R 3 =R + R 3, X 3 = logr 3, p = X - X 3, and p 3 = X 3 - X 3.) If the value of R 3 is constant for H ii regions with similar oxygen abundances, then the H ii regions with similar oxygen abundances should lie along a straight line with a slope equal to 1 in the X versus p and X 3 versus p 3 diagrams. The positions of H ii regions with oxygen abundances logo/h+1 in the range from 7.1 to 7.3 are shown by circles, in the range interval from 7.4 to 7.6 are shown by triangles, and in the range interval from 8.0 to 8.1 are shown by plusses, Figs., 3. The linear best fits to corresponding data are presented by solid lines. Dashed lines are lines with a slope equal to 1. Inspection of Figs., 3 shows that the H ii regions with similar oxygen abundances lie indeed along a straight line, but a slope of this straight line is not equal Fig. 4. The oxygen abundances (O/H) T e versus observed X 3 and computed to 1. X and X 3 values for selected subset of galaxies with best definedthe oxygen fact abundances. that1 thethe + slope log(o/h) versus of the X R3 diagram best = 6.53 fitis differs presented from log R1 3 has (59) byfar-reaching triangles, the O/H implications: versus X3 diagram it means is presented that value by points, ofand logr 3 varies the O/H versus X 3 diagram is presented by plusses The solid line is the systematically best fit to the O/Hwith versuspx 3 and a quantity other than logr 3 should 3 relation, the dashed line is the best fit tobe theused O/H versus in oxygen X 3 relation. abundance determination. In order to verify the reality of this fact and to clearly recognize the consequences, the subset of selected H ii regions with best determined oxygen abundances through the T method has been considered. This

15 15 AY30-HIIDiagnosis L.S. Pilyugin: On the oxygen abundance determination in H ii regions Functional form for high metallicity Fig. 8. The oxygen abundances (O/H) T e versus observed X 3 (plusses) and computed X (triangles) and X 3 (circles) values for total set of H ii regions in spiral and irregular galaxies. The solid line is the adopted O/H X relation, the dashed line is the adopted O/H X 3 relation. Fig. 9. The differences between oxygen abundances d suggested p method and derived with the T e me and differences between oxygen abundances derived method and derived with the T e method (plusses) 1 + log(o/h) R3 = log R 3 (60) parameter p The solid line is the best fit log(o/h). the dashed line is the best fit log(o/h) R3 p re [NII], Hα, [OIII] methods solid line) in Fig. 7, the H ii regions with 0.05 > p 3 > 0.1 Literature are shown by plusses (and corresponding best fit is presented of the diagram. Using Eqs. (1) and () the values byalloin the long-dashed et al. 1979, line), A& the HAii regions 78, 00with p 3 > 0.05 are have been computed for all the H ii regions fro shown by triangles (and corresponding best fit is presented by Pettini & Pagel 004, MNRAS, 348, L59 lation. The oxygen abundances (O/H) T e versus the short-dashed line). The thick solid line in Fig. 7 is the general best fit, i.e. the best fit to all data (the same as in Fig. 4). (O/H) T e versus X is shown by triangles, the (O and versus computed X and X 3 values are shown Motivations Inspection Break the of Fig. R 7 shows that the H ii regions with different 3 degeneracy X 3 is presented by plusses, and (O/H) T e versu values of p 3 lie along different straight lines shifted relative by circles. The X 3 values are again positioned tostill each simpler other depending than the on the T e value method of p 3. According to the responding X and X 3 values. In the case of ox model Pushgrid toof higher McGaugh z (1991) this shifting is accounted for regions the values of p are usually closer to z by the variations in the geometrical factors. The general best fit N O/H index of p 3. Hence, the extrapolated intersect X seem X 3 (Eq. (3)) is very close to the best fit to the data for reliable than the extrapolated intersect X 3 and th HDefinition ii regions with 0.05 > p 3 > 0.1, Fig. 7. The H ii regions are more suitable for the oxygen abundance de with p 3 > 0.05 are shifted to the N right = log([nii]λ6583/hα) from the general best the oxygen-rich H ii regions. (61) The dispersions in X fit and as a consequence the (O/H) R3 values derived in these ues for a given oxygen abundance are significa HEmpirical ii regions with Eq. (3) are higher than (O/H) T e, Fig. 6. Conversely, the H ii regions with p 3 < 0.10 are shifted to the left For H ii regions with 1+log(O/H) T e > 8.1 oxygen-rich than for oxygen-poor H ii regions. from the general best fit in Fig. 7, and so the (O/H) R3 derived between O/H and X 3 and between O/H and X h for them from Eq. (3) are lower than (O/H) T e, Fig. 6. approximated by linear relationships. The adopt Thus, the above discussion of the subset of selected H ii tween O/H and X 3 (dashed line in Fig. 8) is regions with best determined oxygen abundances through the T e method suggests that i) the oxygen abundances derived 1 + log(o/h) R3 = X 3, with the R 3 method involve a systematic error caused by the failure to take into account the differences in physical conditions and the adopted relation between O/H and X in different H ii regions, ii) the physical conditions in H ii region Fig. 8) are well taken into account via the parameter p, and there is no systematic error in the oxygen abundances derived with the p 1 + log(o/h) P = X. method. We confirm the idea of McGaugh (1991) that the strong The differences log(o/h) P and log(o oxygen lines ([OII]λλ377, 379 and [OIII]λλ4959, 5007) contain the necessary information for determination of accurate abundances in low-metallicity H ii regions. McGaugh (1991) has found that all the models converge toward the same upper branch line, R 3 being relatively insensitive to geometrical factor and ionizing spectra in this region function of p are shown in Fig. 9. As in the ca metallicity H ii regions, the error in the value of dance derived with the R 3 method involve random error and a systematic error. However oxygen-rich H ii regions the systematic errors a large random errors. There is no systematic error

16 16 AY30-HIIDiagnosis L60 M. Pettini and B. E. J. Pagel Relation Figure 1. Oxygen abundance against the N index in extragalactic H II regions. The symbols have the following meanings. Filled squares (O/H) from photoionization models by Díaz et al. (1991 M 51) and Castellanos, Díaz & Terlevich (00a,b NGC 95 and NGC 1637). Crosses M 101 (Kennicutt, Bresolin & Garnett 003). Open triangles spiral 1 and+ irregular log(o/h) galaxies (Castellanos, = Díaz 0.57 & Terlevich N 00a; Garnett et al. 1997; (6) González-Delgado et al. 1994, 1995; Kobulnicky & Skillman 1996; Mathis, Chu & Peterson 1985; Pagel, Edmunds & Smith 1980; Pastoriza et al. 1993; Shaver et al [30 Dor and NGC 346]; O3N Skillmanindex et al. 003; Vílchez et al. 1988). Open squares blue compact galaxies (Campbell, Terlevich & Melnick 1986; Garnett 1990; Izotov, Thuan & Lipovetsky Definition 1994; Kniazev et al. 000; Kunth & Joubert 1985; Pagel et al. 199; Skillman & Kennicutt 1993; Skillman et al. 1994; Thuan, Izotov & Lipovetsky 1995; van Zee 000; Walsh & Roy 1989). Error bars in log (O/H) are only plotted when they are larger than the symbol to which they refer. The long-dashed line is the best-fitting linear relationship: 1 + log (O/H) = N. The short-dashed lines encompass 95 per cent of the measurements and correspond to a range in log (O/H) O3N = ± 0.41 = log relative { ([OIII]λ5007/Hβ)/([NII]λ6583/Hα) to this linear fit. The solid line is a cubic function of the} form 1 + log (63) (O/H) = N N N 3 which, however, gives only a slightly better fit to the data (95 per cent of the data points are within ±0.38 of this line). The [O III]/[N II] as an abundance indicator L61 dot-dash horizontal line shows the solar oxygen abundance 1 + log (O/H) = 8.66 (Allende-Prieto, Lambert & Asplund 001; Asplund et al. 004). Empirical lead to order of magnitude uncertainties in (O/H) in galaxies at z 3 (Pettini et al. 001). Edmunds & Köppen 000; Pettini et al. 00a). From the ground, Hα and [N II] can be followed all the way to redshift z.5 (the Partly to circumvent this latter problem, analogous limit of the K band). With thousands of galaxies now known at S 3 ([S II] + [S III])/Hβ (Vílchez & Esteban 1996; Christensen, z > 1 (Madgwick et al. 003; Steidel et al. 004; Abraham et al., in Petersen & Gammelgaard 1997; Díaz & Pérez-Montero 000) and S 34 ([S II] + [S III] + [S IV])/Hβ (Oey et al. 00) indices have been proposed. Although these sulphur-line based indices turn over at higher metallicities than R 3, the sulphur lines are weaker than their oxygen counterparts and their red and infrared rest wavelengths place them beyond the reach of ground-based observations at redshifts z 1.5. More promising are methods which involve [N II] and Hα. In this paper we reconsider the N index (N log{[n II] λ6583/hα}) recently discussed by Denicoló, Terlevich & Terlevich (00), and show how its accuracy can be further improved in the high abundance regime by comparison with [O III] λ5007/hβ. preparation), the N index offers the means to determine metallicities in a wholesale manner over look-back times which span most of the age of the Universe. It is thus worthwhile reconsidering its accuracy. Denicoló et al. (00) compiled an extensive sample of nearby extragalactic H II regions which could be used to calibrate N versus (O/H). We have revised their data base by: (i) including only H II regions with values of (O/H) determined either via the T e method or with detailed photoionization modelling, and excluding the untabulated estimates for H II regions from the catalogue of Terlevich et al. (1991), because for many of these (O/H) had been estimated from empirical (i.e. R 3 or S 3 ) indices; and (ii) updating it with recent measurements by Kennicutt et al. (003) for H II regions in M 101 and by Skillman et al. (003) for dwarf irregular galaxies in the Sculptor Group. Figure T. H EOxygen N Iabundance N D E X against the O3N index in extragalactic H II regions. The symbols have the same meaning as in Fig. 1. The long-dashed line is the best-fitting linear Relation relationship, 1 + log (O/H) = O3N, valid when The O3N total < sample, 1.9 The shown short-dashed in Fig. lines 1, encompass consists of per extragalactic cent of the measurements Followingwhich up onsatisfy earlier thiswork condition by and Storchi-Bergmann, correspond Calzetti & H II regions with well determined values of (O/H) and N. In all 1 + log(o/h) a range in = (O/H) 8.73 = ± 0.5. Kinney (1994) and by Raimann et al. (000), Denicoló et al. (00) but0.3 The six cases dot-dashed O3N horizontal line shows the (shown with filled symbols) (64) solar oxygen abundance 1 + log (O/H) = 8.66 (Allende-Prieto et al. 001; Asplund et al. 004). the oxygen abundance have focused attention again on the N index, pointing out its usefulness was determined with the T e method. References to the original in the search for low metallicity galaxies. The [N II]/Hα ratio works are given in the figure caption. It can be readily appreciated & Dopita 00). Forcing a linear fit to the sample, 1 we obtain a line Hα)}, but since then the O3N index has been comparatively neglected in nebular abundance studies. There is now a sufficient body is highly sensitive to the metallicity, as measured by the oxygen from Fig. 1 that, while N does indeed increase monotonically with of best fit according to the relation: abundance Because (O/H), HIIthrough emission a combination linesof two areeffects. produced As (O/H) by short-lived, log(o/h), a linear massive relationshipstars, is only antheir approximate representation of the data, which rather tend to lie along an S-shaped curve. In of high quality data to reassess its merits. We expect the inclusion 1 decreases + integrated log (O/H) below = 8.90 intensity solar, + there 0.57 isshould N a tendency scale for the with ionization the (1) to star-formation increase (either from hardness of the ionizing spectrum or from the particular, when (O/H) 8. ± 0., the value of N can span one of [O III] to rate be most inuseful a galaxy in the high metallicity regime where [N II] saturates but the strength of [O III] continues to decrease with shown ionization with the parameter, long-dashed or both), linedecreasing Fig. 1. Both the ratio the[nslope II]/[N andiii], the and, order of magnitude, from N 1.8 to N 0.8, whereas at solar increasing metallicity. intercept furthermore, are lower the (N/O) than the ratio values itself of decreases the fit at bythe Denicoló high-abundance et al. metallicity and beyond [N II] tends to saturate (Baldwin, Phillips & Fig. shows how O3N varies with (O/H) for the 137 extragalactic H II regions in our sample. Clearly this method is of little (00) end who because proposed of the 1 secondary + log (O/H) nature = 9.1 of+ nitrogen 0.73 N. (e.g. While Henry, Terlevich 1981) because it comes to dominate the cooling (Kewley use when O3N, but at lowerc values there appears to be a 004 RAS, MNRAS 348, L59 L63 G. Star Formation Rate (SFR) the formal statistical errors on the slope and intercept are small (0.03 and 0.04 respectively), of more interest is the dispersion of the points about the line of best fit in Fig. 1. Specifically, 95 per cent (68 per cent) of the measurements of log (O/H) lie within ± relatively tight, linear and steep relationship between O3N and log(o/h). A least-squares linear fit to the data in the range

17 17 AY30-HIIDiagnosis I will leave a proper treatment/discussion of this topic to other classes. Allow me to point you to Kennicutt 1998, ARA& A, 36, 189 as a starter