Modern challenges in stellar population synthesis C A U P

Transcription

1 Modern challenges in stellar population synthesis J a r l e B r i n c h m a n n C A U P

2 Overview Population synthesis - an overview The methods & ingredients Existing models - a brief overview Challenges as a function of wavelength The ionizing flux of hot stars The UV output of old stars The optical and non-solar abundance ratios The TP-AGB contribution in the red. Some further challenges & a summary Note: This will focus on UV-NIR stellar populations - see Granato s lecture for a more holistic view.

3 Some Buzzwords (Lick) Index: A measure of a feature in a spectrum, typically defined with a central band-pass with two bands around defining the continuum. Single Stellar Population (SSP): A set of stars all formed at the same time according to a given Initial Mass Function (IMF) and thereafter let to evolve. Horizontal Branch (HB): The stage in stellar evolution where stars have a helium burning core. [X/H] = Log X/H - Log (X/H) α-elements: Elements formed through triple-α reactions, they are copiously produced (relative to iron-peak elements) in core-collapse supernovae.

4 Why do we need population synthesis? Photometry Spectroscopy Redshift surveys Imaging surveys Empirical conclusions

5 Why do we need population synthesis? Photometry Spectroscopy Redshift surveys Imaging surveys What is the age? What is the mass? What was the SFH? Empirical conclusions

6 Why do we need population synthesis? Photometry Spectroscopy Redshift surveys Imaging surveys What is the age? What is the mass? What was the SFH? Empirical conclusions Population synthesis + Physical parameters

7 The workings t Fobs(λ, t) = f 0 SSP(λ, τ; Z,...) SFH(t-τ)dτ

8 The workings Fairly well known t Fobs(λ, t) = f 0 SSP(λ, τ; Z,...) SFH(t-τ)dτ

9 The workings Fairly well known t Fobs(λ, t) = f 0 SSP(λ, τ; Z,...) SFH(t-τ)dτ Of great interest!

10 The workings Fairly well known t Fobs(λ, t) = f 0 SSP(λ, τ; Z,...) SFH(t-τ)dτ Of great interest! Requirements for fssp: Stellar tracks/isochrones (perhaps special treatment for advanced stages) Observed stellar spectra Stellar atmosphere calculations

11 The workings Fairly well known t Fobs(λ, t) = f 0 SSP(λ, τ; Z,...) SFH(t-τ)dτ Of great interest! Requirements for fssp: Stellar tracks/isochrones (perhaps special treatment for advanced stages) Observed stellar spectra Stellar atmosphere calculations The implementation can be done in different ways, e.g. Maraston (1998) vs. Bruzual & Charlot (2003)

12 Some existing models Bruzual & Charlot (2003) [BC03] - Very widely used, comes with a set of useful programs to calculate properties. Soon: CB07 using MILES Starburst Probably the best treatment of massive stars - more flexibility than in BC03 but more complex as well Vazdekis models - vazdekis_models.html The first to produce high resolution SEDs, several improvements but more focused on older stellar populations. New version uses MILES PÉGASE - General package - previous versions have been low resolution but PÉGASE-HR uses Elodie. Includes chemical evolution directly. Maraston models - Extensively tested on GCs - good treatment of TP-AGB & HB. These are commonly used - but there are are many more!

13 Stellar evolution - a reminder 4 Tracks: Pietrinferni et al (2005) TP - AG B M=2.5 M Z=0.198 Y= Ea rly Core He burning AG B Log L/Lsun 3 RG t branch B Sub-Gian Core H burning (MS) 1 Changes between phases are typically due to changes in where energy is produced Log Teff The exact track followed for a particular star does depend on mass loss, He abundance, whether there are nearby companions, abundance patterns etc. so just specifying Z is not sufficient. Oh, and convective theory: Overshooting? But: Tracks do not provide an emitted spectrum...

14 From tracks to light An evolutionary tracks provides the physical & chemical conditions of a star, but to get a spectrum we need another ingredient.

15 From tracks to light An evolutionary tracks provides the physical & chemical conditions of a star, but to get a spectrum we need another ingredient. Theoretical approach: Theoretical atmosphere models abundances, Teff, g F(λ)

16 From tracks to light An evolutionary tracks provides the physical & chemical conditions of a star, but to get a spectrum we need another ingredient. Theoretical approach: Theoretical atmosphere models F(λ) abundances, Teff, g Semi-empirical approach (best): abundances, Teff, g s e Y Similar star observed? No Observed spectra F(λ) Theoretical atmosphere models

17 Resolution used to be a concern with models

18 Resolution used to be a concern with models - no longer Coelho et al (2007) IndoUS MILES Stelib HNGSL Pickles BaSeL Bruzual (2007)

19 Sampling of Stellar Parameters? Challenge 1 Metallicity distribution 100 One of the major uncertainties in pop. synthesis models is - and probably will continue to be for some time, the sampling of parameter space. Indo-US Stelib MILES This particularly means metallicity, age and chemical composition viewed together! [Fe/H] 0 1 Miles and Indo-US are noticeably better than Stelib.

20 Maraston (1998) MS SGB RGB HB E-AGB TP-AGB Different wavelengths are sensitive to different evolutionary stages, and this changes with time both the stellar evolutionary time and look-back time. To understand galaxies it is therefore important that all stages in stellar evolution are treated as accurately as possible.

21 Building up a galaxy from scratch Exponentially declining SFH with time-scale 6 Gyr. Balmer lines Models: Bruzual & Charlot (2003) for continuum. Charlot & Longhetti (2001) for emission lines.

22 Building up a galaxy from scratch Exponentially declining SFH with time-scale 6 Gyr. Models: Bruzual & Charlot (2003) for continuum. Charlot & Longhetti (2001) for emission lines.

23 Building up a galaxy from scratch Exponentially declining SFH with time-scale 6 Gyr. Normalised here D4000 windows

24 Building up a galaxy from scratch Exponentially declining SFH with time-scale 6 Gyr.

25 Mixed populations - teff Exponentially declining SFH with 6 Gyr time-scale

26 Challenge 2 Sources of Modelling Uncertainty Fitting models to data: Regardless of the details you will calculate something that is a quality of fit given the data. Let us call this P(Model Data). This should take into account the uncertainty estimates on your data unless they are equally uncertain. For Gaussian errors this gives (ignoring covariances):

27 Challenge 2 Sources of Modelling Uncertainty Fitting models to data: Regardless of the details you will calculate something that is a quality of fit given the data. Let us call this P(Model Data). This should take into account the uncertainty estimates on your data unless they are equally uncertain. For Gaussian errors this gives (ignoring covariances): χ2 = i (Fdata - Ymodel)2 error2

28 Challenge 2 Sources of Modelling Uncertainty Fitting models to data: Regardless of the details you will calculate something that is a quality of fit given the data. Let us call this P(Model Data). This should take into account the uncertainty estimates on your data unless they are equally uncertain. For Gaussian errors this gives (ignoring covariances): χ2 = i (Fdata - Ymodel)2 error2 In the rest of the lecture I ll talk about this.

29 Challenge 2 Sources of Modelling Uncertainty Fitting models to data: Regardless of the details you will calculate something that is a quality of fit given the data. Let us call this P(Model Data). This should take into account the uncertainty estimates on your data unless they are equally uncertain. For Gaussian errors this gives (ignoring covariances): χ2 = i (Fdata - Ymodel)2 error2 In the rest of the lecture I ll talk about this. So now, let us talk about this.

30 Sources of Modelling Uncertainty χ2 = i (Fdata - Ymodel)2 error2 Data - related uncertainty error = Poissonian arrival of photons + Detector etc.

31 Sources of Modelling Uncertainty χ2 = i (Fdata - Ymodel)2 error2 Data - related uncertainty error = Poissonian arrival of photons + Detector etc. + uncertainty in model predictions Normally the data-related uncertainty dominates, but that is not always the case. Without a good uncertainty estimate for data and models you cannot give accurate uncertainty estimates on your derived parameters!

32 Sources of Modelling Uncertainty Observational uncertainties in the empirical data (e.g. spectra) included in the models Uncertainties in atomic data Mismatch between observed stars and theoretical tracks (e.g. metallicity, age, Teff, log g) Numerical uncertainties in the model calculation (e.g. interpolation artefacts, numerical precision) Mismatch between single-parameter model and multi-parameter reality (cf. Kobulnicky, Kennicutt & Pisagno 1999)

33 Sources of Modelling Uncertainty Observational uncertainties in the empirical data (e.g. spectra) included in the models Uncertainties in atomic data Mismatch between observed stars and theoretical tracks (e.g. metallicity, age, Teff, log g) Numerical uncertainties in the model calculation (e.g. interpolation artefacts, numerical precision) Mismatch between single-parameter model and These uncertainties mustreality be understood for high S/N data. This multi-parameter (cf. Kobulnicky, Kennicutt is a major challenge1999) for the next generation of models. An & Pisagno alternative is to use observations to construct an empirical uncertainty estimate.

34 The Far-UV Young Massive Stars

35 Young stars & outflows At λ<1800å the stellar libraries are fewer and generally with low resolution. Very few direct tests of spectra at λ<912å. High redshift observations are typically fairly high resolution - helped by (1+z) stretching. Young, metal-rich stars are hard to find as are young stars with Z < ZSMC. This range contains a number of lines that mostly or exclusively originate in the ISM. Rotation recently realised to be of crucial importance in the evolution of these stars but not yet fully explored (e.g. Meynet & Maeder 2005) LMC & SMC have Z < Zsun or in stellar winds

36 Vázquez et al (2007) Rotation Geneva high mass loss tracks vrot=0 km/s vrot=300 km/s Combination of Starburst99 and Geneva tracks with rotation. Clear changes in important phases of stellar evolution - might lead to changes in total luminosity of a factor of 2 when dominated by young stars. But only preliminary results.

37 Importance Ionising Hydrogen Wolf-Rayet stars Supernova progenitors Ionisation of O+, Ne++, He etc. Constraints on the massive end of the Initial Mass Function. Constraints on stellar massloss at high redshift. Star formation rate estimators. Dopita et al (2006)

38 Does it matter? A short case-study He II 1640Å Shapley et al (2003) created a co-added spectrum of Lyman Break Galaxies and found a strong He II 1640Å line. Brinchmann, Pettini & Charlot (2007)

39 Does it matter? A short case-study Shapley et al (2003) created a co-added spectrum of Lyman Break Galaxies and found a strong He II 1640Å line. EW(He II 1640Å) ~ 1.3Å What causes the strong He II 1640 line in the spectrum of Lyman Break Galaxies? Pop III? Brinchmann, Pettini & Charlot (2007)

40 He II Ionization potential for He+: 54.4 ev - 228Å Only the most massive stars can therefore create He+/He++ zones. Most of the He II is created during the short-lived (few Myr) Wolf-Rayet stage of stellar evolution. Early models produced too weak He II emission to reproduce the observed EW (Shapley et al 2003). This led to the suggestion that there could be a contribution from Population III stars...

41 Model ingredients WR stars in the Milky-Way, LMC & SMC (model atmospheres not yet good enough) Crowther & Hadfield (2006) Log Luminosity (erg s!1) WN3!4 WN5!6 WN7!9 Binaries Also: F(1640) = 10 +/- 1 F(4686) (Early data gave ~7.9) 35.0 SMC Log EW (Å) + Add a model for stellar evolution at different metallicities + a Star Formation History

42 Agreement! Constant SFH With constant SFH a fixed value is reached and this is in good agreement with the observations. It might be a useful tool in the future for high-z WR studies.

43 The Near-UV Advanced stages of stellar evolution

44 Young stars In galaxies with on-going star formation, the UV is dominated by young stars. SFH: Exponential with T=6 Gyr Solar metallicity t=8 Gyr t=0.5 Gyr This wavelength region contains lines from a wide range of chemical elements & lines from energetic winds.

45 Young stars In galaxies with on-going star formation, the UV is dominated by young stars. SFH: Exponential with T=6 Gyr Solar metallicity t=8 Gyr Very important spectral range for wavelength This high redshift observations: region contains lines from a wide l=4500å (B-band) at range of chemical z=1: 2250Å elements & lines z=2: 1500Å from energetic z=3: 1250Å winds. t=0.5 Gyr So important to improve predictions & integrate with non-stellar processes.

46 Old (whatever that means) stellar systems do show UV emission: NGC 6681 (Globular cluster) Stars on the MS with Teff<8500K (A5) have very little emission at λ<1800å (Z~Zsun). Hotter (younger) stars do however, as do AGN. Blue: Far UV, Green: Near UV, red: optical (Brown et al 2001)

47 Older stars The morphology of the Horizontal Branch It is known that metallicity strongly influences the position of a star on the HB, but it is clear another parameter is required - the second parameter problem. O Connell (1999, ARA&A) EHB HB models: Teff These stages are hot and can be very important in old stellar systems without star formation - e.g. GCs. RHB He core H envelope

48 The UV-upturn in elliptical galaxies - UVX O Donnell (1999, ARA&A) 10 Many elliptical galaxies are found to have significant emission in the UV and with significant variation - much more than is seen in the optical. NGC 4649 (-3.0) 11 ml M Wavelength (Å) Large scatter: Additional ingredient needed relative to the optical spectrum. What is the origin? And can it be used to constrain the properties of the galaxies (Age, Z)?

49 Status about UVX Known not to be due to AGN or young population. The same optical spectrum can give rise to very different FUV properties. Old He-burning, low mass, stars are most likely. Extreme Horizontal Branch stars are the most popular candidates. But others have been suggested. EHB stars are sensitive to details of stellar models so the UVX can either be a good age indicator or a good constraint on stellar models. Difficult to say how well current models are doing but metallicity & time dependence should be crucial.

50 Metallicity & the UVX Does the UVX depend on metallicity? Burnstein et al (1988): Yes! 1 Galaxies (IUE) Clusters (ANS) Clusters (OAO) W Cen, M 79 (UIT) W Cen (15 - V) M3 But is this a metallicity tracer? Mg2 can vary significantly at constant metallicity. M Tuc Mg Rich et al (2005): No. UVX The metallicity dependence is not clear, but some dependence on Mg2 seems likely. 4 Donas et al (2006): Possibly/probably Mg2

51 Look-back time Dependence Ree et al (2007): Time-dependence of UV upturn for Brightest Cluster Galaxies in Abell clusters is consistent with model predictions. Main problem with this kind of study: Residual star formation & low-level AGN. These predictions are based on single-star evolution.

52 Model predictions - an example Donas et al (2006) Models: BC03 stochastic library from Salim et al (2005). The models work well, but the main FUV contribution comes from Post-AGB stars which are not the favoured counterparts based on direct imaging studies (which prefer EHB stars)

53 Model predictions Main models tailored for the UVX problem: Metal-poor: Old metal-poor population of hot subdwarfs. Require a substantial spread in metallicity. (Park & Lee 1997) Metal-rich: Metal-rich stars lose most or all of their envelope due to mass loss and requires tuning of mass-loss rate with metallicity (Mg?) as well as high age. (e.g. Yi, Demarque & Oemler 1997)

54 Model predictions Main models tailored for the UVX problem: The problem: Metal-poor: Old metal-poor population of hot subdwarfs. Require a Nonespread of these are very predictive. substantial in models metallicity. (Park & Lee 1997) They require matching to observations (e.g. Maraston et al 2003) and the metalmetal-rich: rich stars modellose (which workenvelope best) due to Metal-rich mostappears or all oftotheir offers explanation ofof why mass-loss mass loss andno requires tuning mass-loss rate with rates(mg?) are so as variable. metallicity well as high age. (e.g. Yi, Demarque & Oemler 1997) Possible missing ingredients: ΔY/ΔZ? Binary evolution? (Han et al 2007)

55 Binaries? Han, Podsiadlowski & Lynas-Gray (2007) Provide a physical model for strong mass loss and variation in this. Strong mass loss without substantial enrichment of the ISM? Binary fractions and distribution of separations poorly known and Z dependence even more so. Should be more explored!

56 Binaries? Han, Podsiadlowski & Lynas-Gray (2007) Provide a physical model for strong mass loss and variation in this. Strong mass loss without substantial enrichment of the ISM? Binary fractions and distribution of separations poorly known and Z dependence even more so. Should be more explored!

57 The Optical [α/fe]

58 Status At first glance in good shape.

59 Status At first glance in good shape.

60 Status At first glance in good shape. CB07 + Miles Data CB07 + Miles + Martins et al (2005)

61 Status At first glance in good shape. CB07 + Miles Data CB07 + Miles + Martins et al (2005)

62 Status At first glance in good shape.

63 Non-solar α/fe Determining the age of elliptical galaxies: Fe-sensitive indices: Mg-sensitive indices: Lower metallicites & higher ages Higher metallicites & lower ages Trager et al (2000) This inconsistency points to variations in Mg/Fe.

64 Model status Tripicco & Bell (1995) approach: Calculate the response of indices to changes in abundance around a particular isochrone & apply to existing models - requires the e.g. Trager et al (2000); Thomas et al (2003); use of fitting functions Tantalo et al (2007) Mixed approach: Calculate stellar atmospheres for different α/fe but use stellar tracks from scaled-solar calculations. e.g. Annibali et al (2007) Ab initio approach: Calculate stellar tracks and stellar atmospheres for different α/fe. e.g. Coelho et al (2007) with tracks from Weiss et al (2007) Major progress has been made over the last 6-7 years but work still remains to be carried out (consistency?) In particular the vast majority of work has focused on the Lick indices - a limited view of the world.

65 Model status Even models with similar methodology give disparate results: Trends roughly similar, but absolute values differ significantly... Possibly due to choice of tracks but this dependence is not fully understood.

66 Need consistent approach Coelho et al (2007) - tracks Weiss et al (2007) ΔY/ΔZ? Enrichment pattern probably not a major issue (but what about advanced phases?) [Fe/H] = -0.5 [α/fe] = 0.0 [α/fe] = 0.4

67 Identify features from data The data should have better S/N than the models for accurate comparison. Co-adding SDSS: 500,000 spectra -> ~1000 Result: Typical S/N per Å ~200 [ Å] Use Stellar mass & concentration as proxies for non-solar abundance ratios. Most other issues should not correlate with these quantities.

68 Stellar mass (& α/fe?) Concentration (& α/fe?)

69 Stellar mass (& α/fe?) Concentration (& α/fe?) Mg-indices

70 Define discrepancy: fobs(λ) - fbest fit(λ) d(λ) = fobs(λ) This region is known to be strongly sensitive to Mg/Fe variations. A similar approach allows identification of features with weak or strong α/fe dependency.

71 Using D4000 & HδA to estimate age & Z - α/fe effect? + Simple to use. + Narrow wavelength range required. - Noisy region in SDSS. - Models sensitive to calibration. - Some sensitivity to αenhancement. See Wild et al (2007) for an alternative (better) view using PCA.

72 Using D4000 & HδA to estimate age & Z - α/fe effect? + Simple to use. + Narrow wavelength range required. - Noisy region in SDSS. - Models sensitive to calibration. - Some sensitivity to αenhancement. Problematic region (young stars?) See Wild et al (2007) for an alternative (better) view using PCA.

73 Using D4000 & HδA to estimate age & Z - α/fe effect? + Simple to use. + Narrow wavelength range required. - Noisy region in SDSS. - Models sensitive to calibration. - Some sensitivity to αenhancement. Problematic region (young stars?) See Wild et al (2007) for an alternative (better) view using PCA. Significant offset?

74 Option m62, black-blue:miles+martins, red:stelib Could in part be due to stellar libraries. 10 But remember that the measurements are to some extent entangled with the stellar library used to carry out these measurements. 0 So are there other effects? Figure courtesy G. Bruzual

75 HδA bandpasses

76 See a discrepancy that increases with mass and with concentration. This turns out to match very well with the CN band head -> non-solar abundance ratios fit well. See: L. Prochaska et al (2007) for an in-depth discussion. HδA bandpasses

77 Issues... How does variations in α/fe affect stellar tracks? Advanced phases? Is it acceptable to vary α/fe only or do we need to treat Ca, C and other elements separately? What combination of information allows the best constraint on past SFH? [including α/fe would require a chemical evolution model] What are the effects on Balmer lines, and how do they compare with HB variations? At high Z the helium content becomes an important ingredient: ΔY/ΔZ

78 Into the Red The TP-AGB Phase

79 TP-AGB Stars Herwig (2005, ARA&A) Relatively short-lived & very luminous and cool phase. So gives a characteristic and strong contribution to longer wavelength light.

80 TP-AGB Stars Herwig (2005, ARA&A) TP-AGB Relatively short-lived & very luminous and cool phase. So gives a characteristic and strong contribution to longer wavelength light.

81 TP-AGB stars can become very luminous C stars and dominate the MIR light of a stellar population, particularly at low metallicity. They are very difficult to simulate from first principles so models covering large regions of parameter space use a synthetic approach with parameters calibrated by observations - typically C stars. The properties of the most extreme (TP-)AGB stars and AGB stars at low metallicity are not well known. Stellar atmospheres for these phases are less well developed and sensitive to dust treatment -> significant uncertainties in the relative contribution of NIR and MIR flux. The first TP-AGB stars in a population start to appear ~0.5Gyr after the star of star formation and provide >30% of the K-band light for several Gyrs after that. Age of the Universe at z=2: 3.2 Gyr.

82 The evolution of M/L - need for more K-band light? van der Wel et al (2005) z~1 E/S0 It appeared that the BC03 models under-predicted the K-band luminosity of these galaxies. But at t>5gyr TP-AGB stars do not dominate Kband light - what about younger systems? M/L from FP. Changes relative to z=0.

83 Estimating stellar masses. Maraston et al (2006, Fig 4 & 5 partial) As emphasised by Maraston et al (2006), rest-frame NIR photometry of star-forming galaxies is very sensitive to the TP-AGB treatment. This might cause substantial systematic uncertainties in mass estimates. If the TP-AGB luminosity is underestimated (as in the old BC03 models), the lack of red flux must be compensated by adding dust and increasing the age. Adding photometry uncritically is a bad idea - always ask: Will this improve my results?

84 Improving TP-AGB treatment Sparse grid of full calculations of TP-AGB stars Fitting formulae for evolutionary behaviour Dredge-up, Chemical composition, Pulsation mode Age-Z relation Compare with observations. Large grids of synthetic models Predict observational quantities Luminosity function of C-stars Life-times of C-stars (LMC, SMC) + SFH & Age-Metallicity relation See Marigo & Girardi (2007) for a detailed discussion.

85 Improving TP-AGB treatment See Marigo & Girardi (2007) for details.

86 Improved models CB BC Padova The effect of the new TP-AGB calibration by Marigo & Girardi (2007) on K-band light. 7 8 log t (yr) 9 10

87 But there is more!

88 Chemical evolution The metal content of a galaxy changes with time, and this ought to be taken into account. The problem? A large number of additional variables, infall, outflow etc. means that there are plenty of degeneracies to deal with - not to speak of spatial variation. And the detailed chemical output from supernovae and the variability is poorly known (well, unless you ask a modeller!) Crucial for understanding the MW. Ought to provide extra constraints on estimates of SFHs.

89 Chemical evolution Closed box model with Z=0.02 at t=5gyr 0.1 dex This becomes important for very high S/N spectra!

90 Chemical evolution Closed box model with Z=0.02 at t=5gyr 0.1 dex This becomes important for very high S/N spectra!

91 Chemical evolution Closed box model with Z=0.02 at t=5gyr Emission lines and stellar continuum are likely to trace difference metallicities. But higher or lower?

92 Emission Lines But even at low redshift there are significant effects when dealing with actively star forming systems. Redshift Emission lines trace different physics from stellar population synthesis so can often be treated separately. But sometimes they are crucial - for very high redshift galaxies and narrow band imaging surveys in particular.

93 Metal Free/Poor stars Stars with Z=0: Burn at higher temperatures because the CNO cycle cannot start without C. Are expected to have a considerably harder ionising spectrum that even Z=10-7 stars. Are thought to form with a very top-heavy IMF. Might be dominated by nebular continuum emission if the escape fraction is low (which it might not be c.f. Yoshida et al (2007). This area is still under development. The main challenges are to contrast models with observations - even at Z>0 this is still essential.

94 Metal-poor stars Tumlinson & Shull (2000) Schaerer (2003)

95 A Key Lesson Do not include an extra wavelength (band) just because you can! Just because a new instrument becomes available, does not mean that adding information from this will improve your results! You MUST check that the model predictions are reliable for what you need. But models can be improved so get the data (if you can!) and be critical & constructive!

96 Status & Issues Stellar rotation & evolutionary tracks? Binaries & HB morphology? Resolution - OK? Not yet fully exploited? TP-AGB - calibrated on LMC/SMC - metallicity variation uncertain - ab initio models not good enough. α/fe - progress, but not yet finished. Reverse use - use observations to constrain poorly known evolutionary phases. Resolved spectroscopy & separation of different stellar populations in velocity & chemical composition. Very low-z populations - empirical tests required. Uncertainty estimates on predictions?