Perspective for Determining Surface Abundances and Physical Parameters

of Metal-Rich Stars

Yoichi Takeda(National Astronomical Observatory of Japan)

“The Metal-Rich Universe,” 2006 June 12-16 Los Cancajos, La Palma, Canary Island, Spain

Derivation of Stellar Physical Parameters

colors/spectraatmospheric parameters (Teff, log g, microturbulence, metallicity ([Fe/H]), elemental abundances (ε)

[model atmosphere theory, line-formation theory]SED modeling, spectrum modeling

photometric magnitudeparallax (e.g.Hipparcos) L (bolometric luminosity)

[stellar evolution theory]modeling of stellar interior/envelope and its time variation

age, mass, radius, …

bolometric correction

Reliable Modeling is Essential…

1. Determination of Stellar Atmospheric Parameters of

Metal-Rich Stars

Various determination methods for stellar atmospheric parameters, with emphasis on thespectroscopic approachNon-LTE overionization: theoretical expectation and observational suggestionHow is the assumption of LTE reliable?Check on the fiducial standard: Hyades stars

Various method for atmospheric Parameters• Teff (effective temperature)

– color (b-y, B-V, V-K)– Balmer line profile– excitation equilibrium (χ-independence of A: mostly Fe I)– line-depth ratio

• log g (surface gravity)– directly from M & R (estimated from evolutionary track)– ionization equilibrium [requirement of A(Fe I) = A(Fe II)]– wing-fitting of strong lines

• Microturblence (vt)– curve-of-growth matching (EW-independence of A:

mostly Fe I)

Spectroscopic Method is useful: all can be done based only on Fe I and Fe II lines measured from spectrum at hand

One concern for determination of Teff , log g, vt, & [Fe/H] via spectroscopic method

• Is (usually assumed) LTE valid for the line formation (especially for Fe I and Fe II)?

• Several recent studies report a possibility of significant departure from LTE Saha ionization equilibrium for late-type dwarfs, especially at Teff < 5000 K

• If this is real, appreciable errors in the resulting solutions may be expected …

Can we ever still rely on LTE? How much errors would be expected with this assumption?

Overionization: Imbalance of photo-ionization/-recombination at τ<1

Photo-ionization / recombination balance

b～R*/R ～ ∫(αB/hν)dν/ ∫(αJ/hν)dν

calculated for

(Teff = 5500 K, log g = 4.0) models of different [M/H]

Important factor affecting the UV photoionizing radiaton is “accumulating opacities due to numerous lines” treated with LTE pure absorption in most cases

With this assumption, lines act to thermalize the radiation field, NLTE overionization tends to become less significant at higher metallicity

Another factor determining the nature of overionization effect: Fraction of Fe I and Fe II in stellar atmospheres

“Trace” species is generally more affected by changes in the equilibrium condition

When Fe I 》 Fe II(e.g., K-M dwarfs), Fe I lines: robust FeII lines:strengthened

When Fe I 《 Fe II(e.g., F-G dwarfs), Fe I lines: weakened Fe II lines: robust

Note: The nature of high-excitation Fe I lines may conform to that of Fe II lines

The problem is “to which extent should we count for the non-LTE correction?”

Thevenin & Idiart(1999)

Non-LTE overionization has generally been considered as significant only for metal-poor stars, while LTE was regarded as comparatively much safer for metal-rich stars

However, Shuchukina et al.’s recent NLTE calculation (see the poster in this conference) suggests appreciable NLTE overionization corrections of ～0.2 dex for Fe I or Ti I lines even for G-K dwarfs of [Fe/H] >0

Inevitable uncertainties in NLTE calculations are collision crosssection(especially due to H I) and treatment of photoionizing UV radiation field

Validity/consistency should be checked by comparing the observations

Comparison of spectroscopic parameters with those from other methods (Takeda et al. 2005)

No serious discrepancy appears to exist …

160 Late-F to early-K stars at -0.7 < [Fe/H] < +0.4

Based on solar gf values [assuming A(FeI)=A(FeII) for the Sun]

Errors in spectroscopically established parameters?

Melendez & Ramirez (2005)

For metal-rich G and late-F dwarfs

Not so in Teff…

But appreciable underestimation in log g?

Use of experimental or theoretical gf values

Teff-Dependent Anomalous Ionization in Fe-group elements (Ti, V, Co)?

Bodhagee et al. (2003) Gilli et al. (2006)

Use of lines of neutral elements (except for Sc)

Differential analysis relative to the Sun

Co

Co V

V

TiTi

Mn

Mn CaCa

However, our [X/Fe] vs. Teff relations could not confirm such an apparent trend

Ti

V

Ca

Mn

Co

Similar differential analysis relative to the Sun

Takeda (2006)

160 Late-F to early-K stars at -0.7< [Fe/H]< +0.4

No significant trend appears to exist …

Actually, [X I/H] – [X II/H] scatters around zero (with almost no significant trend with Teff )

These results suggest that departure from LTE ionization equilibrium (if any exists) is not significant in a practical sense, at least in the Teffrange between 5000 K and 7000 K

Takeda (2006)

Hence, the situation is rather confusing in view of the diversity of results obtained by different groups…

A good touchstone: Hyades cluster

“True” stellar parameters are considered to be well established thanks to Hipparcos parallaxes and comparison with theoretical isochrones

De Bruijne et al. (2001)

Yong et al.’s (2004) results for Hyades G-K dwarfs (4000K < Teff< 6200K)

Teff: B-V and b-y colors

log g: from (Hipparcos L, Teff) with help of theoretical isochrones

vt: EW-independence of Fe I abundances

Appreciable discrepancy [A(FeI) < A(FeII)] at Teff < 5000K conspicuously increasing with a decrease in Teff

At 5000K < Teff, the difference is moderate & constant at 0.1-0.2 dex

Especially, Fe II lines can not be used with LTE any more at 5000K < Teff

This was confirmed by recent Schuler et al.’s (2006)analysis for Hyades G-K dwarfs/giants

However, the growth of discrepancy appears to be rather monotonic (becoming appreciable already at Teff ～5500K)

Fe II lines yield overestimated [Fe/H]

Giants are less problematic

(Again, they derived Teff from colors and log g from isochrones)

Activity-related non-LTE effect?Schuler et al. (2003)

O I 7773 triplet strength (quite sensitive to chromospherictemperature rise) remarkably increases with a lowering of Teff at Teff < 5000K

OH

O I 7773

[O I] 6300

Stellar activity may be the key to understanding the anomalous strength of O I 7773 (strengthened by T-rise) and FeII lines (strengthened by overionization) in K dwarfs

Departure is more pronounced and starts

earlier at ～5500 K

M34 (t～200Myr: youngerthan 700Myr of Hyades)

M34

If this speculation is correct, such an anomalous effect would be less significant in K dwarfs in old open clusters (e,g., M67)

If K dwarfs (Teff<5000K) unreliable, what about G stars?--Our analyses of Hyades G stars based on OAO data--

Study of atmospheric parameters and Fe abundances for Hyades dwarfs at 5000K < Teff < 6000K (use of 6000-7200A data) by two approaches:

1. Use of model atmospheres constructed with “actual” Teff and log g (de Bruijne et al.) and compare the resulting A(FeI) and A(FeII)

2. All atmospheric parameters are spectroscopically determined by using FeI and Fe II lines, and compared with “actual” parameters

Adoption of solar gf values derived on the assumption of A◎(FeI) = A◎(FeII) = 7.5

Results with “actual” Teff and log g of de Bruijne et al.

1. Qualitatively, there is surely a tendency of A(FeI) < A(FeII) as Yong et al. (2004) or Schuler et al. (2006) reported

2. But the typical difference is only <～0.1 dex and not very significant

3. Also, we can not observe any clear tendency of progressively increasing FeI-FeII discrepancytoward lower Teff

Spectroscopic Determination of Teff, log g, and vt

◎EW-independence of A(FeI) ◎χ-independence of A(FeI)

Hyades

G-K dwarfs

◎<A(FeI)> = <A(FeII)>

Differences between “actual” parameters and “spectroscopic” parameters

T(spec) tends to be higher than T(true) by ～0-200K

Difference between log g(spec) and log g(true) are within about ±0.2-0.3dex

Correlation between ΔT and Δlog g

Resulting abundances are consistent within <0.1dex

If content with this precision, why not invoke LTE?

Toward Ultimate Precision: Complete Differential Analysis

• A useful LTE-based method for high-precision differential abundance determination applicable to two similar (i.e., not very different) stars

• Formulated only by using differential parameter values (ΔTeff, Δlog g, Δvt, ΔAi) between two stars in the sense that the solutions of these (ΔTeff, Δlogg, Δvt) are solved with the requirements of – χ-independence of ΔAi– Requirement of ΔA(Fe I) = ΔA(Fe II)– EW-independence of ΔAi

• Errors in modeling (breakdown of LTE, 3D effect, etc.) are cancelled and sufficiently high precision of differential abundances is attained (even down to the order of ～0.01dex)(e.g., Laws & Gonzalez 2001, Takeda 2005, Melendez et al. 2006)

Application of complete differential technique to Sun-like G dwarfs of Hyades (|ΔTeff| < 250 K) relative to the Sun

Average of results for 16 stars:

[Fe/H] = +0.19 (σ=0.05)

Maybe intrinsic scatter within the cluster

Literature [Fe/H] of Hyades

our results

0.19 (±0.05)

Conventional definition of SMR stars ([Fe/H]SMR > 0.2) is just reasonable, which originally stemmed from [Fe/H]SMR > [Fe/H]Hyades

[Fe/H] of four Hyades giants and μLeo

Taken from Taylor’s (2001) table

γTau: [Fe/H] = +0.19

(4949K, 2.63, 1.36km/s)

δ1 Tau: [Fe/H] = +0.15

(4895K, 2.60, 1.32km/s)

εTau: [Fe/H] = +0.10

(4811K, 2.39, 1.52km/s)

θ1 Tau: [Fe/H] = +0.13

(4930K, 2.65, 1.33km/s)

μ Leo: [Fe/H] = +0.34

(4521K, 2.53, 1.36km/s)

μ Leo

Hyades giants Based on our spectroscopically determined parameters using Fe I and Fe II lines

2. Zero-Point Problem of [X/H]

[X/H] ≡ AX(☆) – AX(◎)Impact of 3D inhomogeneous atmosphere effect on the solar CNO abundancesThe discrepancy between Sun and early-type stars is removed?What are the metallicities of early-type stars

3D modeling of inhomogeneous stellar atmosphere

Asplund (2005)Metal-poor case (lowering of average <T(τ)> compared to 1D)

Metal-rich case (<T(τ)> is almost the same as 1D)

Important 3D impact: suggestion of downward revision of solar CNO abundances

By about ～0.2 dex lowered compared to what has been believed

Asplund et al. (2006)

Bewilderment of Solar Physicists• Such a downward revision of solar CNO by ～0.2 dex has

embarrassed solar astronomers, because the current standard solar model (which well explains observations of solar seismology or solar neutrinos) will be invalidated

• One possibility to maintain consistency even in the reductionof CNO is to keep the solar Ne-to-O ratio substantially higher(ANe/AO ～ 0.5) than the currently believed value (ANe/AO ～0.15) (Antia, Basu 2005; Bahcall et al. 2005)

• Active region X-ray data were analyzed to determine the ANe/AO ratio, but the results are rather confusing: while the confirmation of high scale (0.4) was once claimed for nearby solar-type stars (Drake, Testa 2005), successive studies for the Sun yielded essentially the standard low-scale ANe/AOratio of 0.15 (Schmelz et al. 2005; Young et al. 2005)

This problem seems still unsettled …

Anyway, this revision may solve the well-known CNO-discrepancy between Sun and young early-type stars

CNO in early B main-sequence stars Gies&Lambert (1992) and Kilian (1992)

Takeda & Hidai (1998)

Takeda & Honda (2005)

According to Asplund et al. (2004), the 3D correction for solar O I 6156-8 (χ= 10.7 eV) is appreciably large to be Δ= -0.15, in contrast to other high-excitation O I lines (|Δ|≦0.05,O I 7771-5, O I 8446, O I 9266), which may explain the discrepancy

Why such large variation of 3D correction among similar high-excitation O I lines?

However, subsolar in hot stars is not only CNO, but metallicity in general ?

Sadakane (1990)

Superficially normal late-B & A starsNiemczura’s (2003) study of B stars metallicity based on IUE spectra

While some other observations suggest near-solar metallicity of B stars

Gies and Lambert (1992)

Lyubimkov (2005)

[Mg/H] from Mg II 4481

Much more work on the metallicity ([Fe/H) of early-type stars (current composition of galactic gas) is needed, in comparison with the solar abundances

3. Effect of Physical Processes or Parameters on Stellar Evolutionary

Tracks of Metal-Rich Stars

Influence of solar CNO downward revisionEffect of envelope pollution due to accretionHow is the age estimation affected?

Influence of downward revision of solar CNO on evolutionary tracks

Suda (2006, private communication)

•Reduction of CNO brings increase of radius and lowering of Teff (shifting the track to the right)

•This effect becomes more appreciable for metal-rich tracks

Involvement of pollution with surface enrichment ?... may promising as planet-host stars are metal-rich, but a matter of debate

• The extent of overabundance Teff-dependent? (expected from the change of convection zone thickness)– No such tendency is observed (Pinsonneault et al. 2001, Santos et al.

2004, Cody, Sasselov 2005)– However, this might be circumvented by extra mixing process of

thermohaline convection in the presence of metallicity difference (Vauclair 2004)

• Difference in the enrichment degree between volatile and refractory elements?– Various reports so far, but recent studies suggest such a difference is

absent (e.g., Ecuivillon e al. 2005)• Abundance difference exists between components of

visual binaries?– Various reports so far, but no clear evidence has yet been established

(e.g., Desidera 2004)• Other sign of surface polution?

– Detection of Li6 isotope (HD 82943) may be counted as evidence that such process does take place (Isaraelian et al. 2003)

Effect of accreted matter on stars

Cody & Sasselov (2005)

Deepening of SCZ Increase of Radius Lowering of Teff

(Δz = +0.01 in the outer envelope) (Δz = 0.00, +0.005, +0.01, +0.015)

Evolution Track of Surface-Polluted Star

1.0 Msun

0.8 Msun

Z = 0.02Z = 0.04

Z = 0.02

Z = 0.03

z = 0.02 at interior z = 0.04 at SCZ

z = 0.02 at interior z = 0.03 at SCZ

If polluted track and standard homogeneous track with the same surface (enriched) metallicity (e.g., z=0.04) are compared with each other, the formersituates on the bluer side to the latter

Katsuta & Fujimoto (2006)

Do subdwarf-like metal-rich stars exist?

•Such a superficially metal-rich star caused by pollution would situate below (leftward) of the corresponding theoretical isochrones

•And thus its age is impossible to be determined with standard stellar evolutionary tracks

•If we could detect such a “subdwarf-like” metal-rich star, it would be a promising candidate for a pollution-enriched object

Schematic diagram

Positions of Metal-Rich F-G Stars

Red: planet-host starsBlue: non-planet-host stars

• Many metal-rich main-sequence stars appear to reasonably match the standard theoretical main-sequence

•Yet, a few “subdwarf-like” metal-rich stars candidates are seen, though they are all non-planet-host stars

•Anyway, surface abundance trend of these peculiar stars may be worth detailed reexamination

Pollution may take place, but unlikely to be the major cause of metal-enrichment

Age Estimation with the Surface Polluted Model

6.5 Gyr → 9.6 Gyr

Case of HD 80606b (assumed as a surface-polluted star)

Influence on the Age-Metallicity RelationCan the mistery of old metal-rich stars be explained?

Surface-polluted star evolution model suggests that the true age of superficially SMR star may be olderthan that obtained from standard homogeneous model

If an SMR stars is a pollution-enriched star, its age and metallicitywould be corrected in this direction

If the correction were in this direction, we could have reasonablly made it match the theoretical relation…

This might be realized by changing α(mixing length) and/or Y(Hecomposition), according to Katsuta & Fujimoto (2006) Age

[Fe/H]

Summary• Spectroscopic parameters of F-G-K stars with FeI/FeII lines

– For F-G stars with Teff higher than 5000K and K giants, the non-LTE effect is not so significant in spite of a marginal sign of overionization and LTE would still remain as a practically useful approximation.

– Meanwhile, LTE had better be avoided for K dwarfs with Teff<5000K because classical modeling is likely to break down (activity-related?) .

• Zero-point of [Fe/H]: Sun/hot-star connection– While recent downward revision of solar CNO based on 3D atmosphere

may resolve the discrepancy between Sun and early-type stars, it is still premature to regard it as being established.

– Attention should also be paid to the possibility of subsolar metallicity([Fe/H]) of hot stars.

• Effect of surface pollution on stellar evolution– A pullution-enriched star would appear as a "subdwarf-like" metal-rich

star locating lower-right of the standard (metal-rich) main sequence, though such candidates appear to be rather unusual (if any exists).

– The age of a polluted (supeficially) metal-rich star derived from standard metal-rich tracks would be underestimated