Alkali Line Proﬁles in Degenerate Dwarfs

Alkali Line Profiles in Degenerate Dwarfs

Derek HomeierInstitut für Astrophysik Göttingen

PHOENIX Collaborators: France Allard (CRAL, ENS Lyon/IAP)

Nicole Allard (IAP) Christine Johnas, Peter Hauschildt (Hamburger Sternwarte)

Derek Homeier Alkali Lines in Degenerate Dwarfs VIth SCSLSA 12 June 2007

Ultracool Dwarfs

28 Jul 2005 12:16 AR AR251-AA43-06.tex XMLPublishSM(2004/02/24) P1: KUV

L AND T DWARFS 207

Figure 3 A sequence of mid-M through late-T spectra between 0.95 and 2.3 µm. Featureidentifications within the H- and K-band windows are marked. The feature-rich J-band spec-tra are shown on an expanded scale in Figure 4. Spectra have been displaced vertically byhalf integral units to ease intercomparison. These spectra come from the Brown Dwarf Spec-troscopic Survey archive (http://www.astro.ucla.edu/∼mclean/BDSSarchive/) and are fromMcLean et al. (2003).

have shown that optical L dwarf types usually map well into a near-infraredsequence.

There are, however, exceptions. Figure 3, which is a replotting of the spectralsequence shown in figure 3 of McLean et al. (2003), illustrates this point. Thespectral types here are based on the optical classifications of these objects, andthis leads to an ordering that lacks the “movie frame” consistency of the opticalspectral sequence in Figure 2. If we consider only the sequence of J-band spectra inFigure 4, however, we see a much smoother ordering. This is perhaps not surprisingbecause J-band wavelengths are not far from the optical wavelengths at which theordering was established and thus sample similar atmospheric physics. Lookingindividually at the H- and K-band spectra of Figure 3, we see larger discrepanciesin the ordering. Specifically, the shape of the H-band peak near 1.65 µm does notchange smoothly from L2 through L8. The slope (color) of the spectrum from Jthrough K also varies non-monotonically, with the spectrum of the L6 not fitting the

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Ultracool Dwarfs

• Extremely reddened optical/near-IR spectrum of late L and T dwarfs ➙ dust or other opacity source?

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(Sub-)stellar atmosphere modelling

• independent Variables (minimal):

• effektive temperature Teff

• surface gravity g(r) = GM/r2

• mass M or radius R or luminosity L = 4 π R2 σ Teff

4

FieldRadiation

TemperatureCorrection

END

SYNTHETIC SPECTRUM

OUTPUT

Pressure

INPUT

Stratification

lineopacity

continuumopacity

molecular bandopacity

NO

Converged?YES

ITERATION


(Sub-)stellar atmosphere modelling

• Radiative transfer solution provides thermal structure to determine

• gas phase physics (ionisation/occupation ratios)

• chemistry (partial pressures, condensation)


BD Models — Cloud Opacity

• Dust clouds need to be sustained by turbulent mixing.

• Visible clouds have to be supported by convective overshoot.

• Cloud layer recedes from the photosphere in T dwarfs.

• Atomic and molecular lines becoming more important.

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1600K/4.50


Brown Dwarfs — Line Absorption

•Most atoms in ground state, little contribution at longer wavelengths

• Spectral energy distribution shi/s toward IR

• Importance of molecular bands dependent on

• Line strengths ➙ gf, abundances, chemistry

• Line shapes

• Line numbers

• Line distribution

• Bands with complex spectra (polyatomic molecules) produce strongest blanketing effects.


Ultracool Atmosphere Models

• Coming and going of dust clouds explains the M-L-T spectra (Allard et al. 2001)

• Molecules: 3500-2500 K

• Dust: 2500-1500 K

• CH4: 1500-500 K


T Dwarfs — Dust-free atmospheres

• No visible dust ➙ Massive alkali line broadening responsible for optical/near-IR absorption

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T Dwarfs — Alkali lines• Depletion of metals due to condensation and sedimentation

• Alkali resonance lines still strong in deep atmosphere layers

• Powerful probe of atmosphere at very different optical depths!

1e-30

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0.0001 0.001 0.01 0.1 1 10

P/P

gas

!1.2

NaK

RbCs

CrHFeH


Alkali line profiles

• Impact and single-perturber approximations with accurate inter-atomic potentials (Allard et al. 2005, 2007)

6 N. F. Allard et al.: Impact broadening of alkali lines in brown dwarfs

Table 4. Half width (10−20cm−1/cm−3) of alkali resonance lines perturbed by H2 collisions

Alkali-H2 Transition 500 K 1000 K 1500 K 2000 K 2500 K 3000 K

Li 2s 2S1/2-2p 2P1/2 1.94 2.22 2.46 2.66 2.83 2.99

2s 2S1/2-2p 2P3/2 1.63 2.1 2.45 2.77 2.98 3.24

Van der Waals 2.08 2.55 2.89 3.15 3.36 3.55

Na 3s 2S1/2-3p 2P1/2 1.46 1.86 2.16 2.42 2.63 2.8

3s 2S1/2-3p 2P3/2 1.96 2.49 2.94 3.24 3.59 3.87

Van der Waals 2.24 2.75 3.11 3.39 3.63 3.83

K 4s 2S1/2-4p 2P1/2 1.55 1.96 2.48 2.53 2.76 2.97

4s 2S1/2-4p 2P3/2 2.33 2.94 3.49 3.90 4.27 4.51

Van der Waals 2.32 2.86 3.23 3.52 3.76 3.98

4 6 8 10 12 14 16 18 20R(Å)

-50

-40

-30

-20

-10

0

10

!V

(cm

-1 )

Li-He Na-HeK-HeLi-He Van der WaalsNa-He Van der WaalsK-He Van der Waals

Fig. 3. Difference ∆V of upper and lower state potentials forthe D1 lines of alkali-He systems.

Allard, N. F., & Kielkopf, J. F. 1982, Rev. Mod. Phys., 54,1103

Allard, N. F., & Biraud, Y. G. 1983, J. Physique, 44, 935Allard, N. F., Royer, A., Kielkopf, J. F., & Feautrier, N. 1999,

Phys. Rev. A, 60, 1021Allard, N. F., Allard, F., Hauschildt, P. H., Kielkopf, J. F., &

Machin, L. 2003, A&A 411, L473-L476Allard, N. F., Allard, F.,& Kielkopf, J. F. 2005, A&A, 440,

1195Allard, N. F., & Spiegelman, F. 2006, in press in A&ABaranger, M. 1958a, Phys. Rev., 111, 481Baranger, M. 1958b, Phys. Rev., 111, 494Burrows, A., Marley, M. S., & Sharp, C. M. 2000, ApJ, 531,

438Chatham, R. H., Gallagher, A., & Lewis, E.L. 1980, J. Phys.

B, 13, L7Cohen, J. S., & Schneider, B. 1974, J. Chem. Phys., 61, 3230

2 3 4 5 6 7 8R(Å)

-4000

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0

1000

2000

3000

4000

5000

!V

(cm

-1 )

B 2" # X Li-He

A 2$

3/2 # X Li-He

B 2" # X Na-He

A 2$

3/2 # X Na-He

B 2" # X K-He

A 2$

3/2 # X K-He

K-He Van der WaalsLi-He Van der WaalsNa-He Van der Waals

Fig. 4. Difference ∆V of upper and lower state potentials forthe transitions contributing to the D2 lines of alkali-He sys-tems.

Deleage, J. P., Kunth, D., Testor, G., Rostas, F., & Roueff, E.1973, J. Phys. B, 6, 1892

Hauschildt, P. H., & Baron, E. 1999, JCAM, 109, 41Hindmarsh, W. R., Petford, A. D., & Smith, G. 1967, Proc.

Roy. Soc. A 207, 296Kielkopf, J. 1976, J. Phys. B, 9, L547Kielkopf, J. 1980, J. Phys. B, 13, 3813Kirkpatrick, J. .D., Reid, I. N., Liebert, J., Cutri, R. N., Nelson,

B., Beichman, C. A., Dahn, C. C., Monet, D. G., Gizia,J. .E., Skrutskie, M. F. 1999, ApJ, 519, 802

Lortet, M. C., & Roueff, E. 1969, A&A, 3, 462Lwin, N., McCartan, D. G., & Lewis, E. L. 1976, J. Phys. B,

9, L161Lwin, N., & McCartan, D. G. 1978, J. Phys. B, 1, 3841McCartan, D. G., & Farr, J. M. 1976, J. Phys. B 9, 985Pascale, J., & Vandeplanque, J. 1974, J. Chem. Phys. 64, 2278Pascale, J. 1983, Phys. Rev. A, 28, 632


T Dwarfs - Alkali lines• Broadening by He and H2 (several geometries)

• Far wings shape spectrum over several µm!

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D1 layer 40 010D1 layer 40 110D1 layer 40 101D1 layer 40 011D1 layer 40 111D1 layer 40 000

D1 layer 40 all2MASS 0415

convolved profs. v2 800K/5.00/-0.0wide profiles co-add. 800K/5.00/-0.0

wide profiles conv. 800K/5.00/-0.0

Profiles from Allard, Allard, Hauschildt, Kielkopf & Machin (2003, 2007)


A Unified Set of Model AtmospheresM-L-T-(Y?)-dwarfs

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Na I

K I

H2O

H2O

H2OH2O

CH4

CH4

CH4

CH4

NH3

CO

CO

VO

TiO

FeH

d = 5pc

V R I Z J H K L’ M’


Alkali line profiles

• Interaction potentials show local minimum ➙ quasi-molecular resonance in the blue wing

N. F. Allard et al.: Theoretical profiles of alkali lines for brown dwarfs 1197

(a) VΣΠ(R). (b) ∆V(R).

Fig. 2. The fine structure splitting !ω compared to the variation of VΣΠ(R), the splitting between the |Σ〉 and |Π〉 states, and ∆V(R) for theA2Σ − X2Σ transition as a function of the internuclear distance R. The potential energies are tabulated by Pascale (1983).

in its ground 1S0 state. The interaction for the lower state of thesystem is then spherically symmetric about the alkali. We con-sider the system to be composed of a radiating alkali atom A incollision with an atom or molecule B, separated from A by thedistance R. In the case of an alkali-H2 collision, B is situated atthe center of mass of H2.

To describe the collision, we introduce two referenceframes with common origin at the center of mass of atom A,as illustrated in Fig. 1. A fixed-frame Oxyz is for atomic rep-resentation with the quantization axis Oz perpendicular to thecollision plane. A rotating frame OXYZ is for molecular repre-sentation, the internuclear axis being the quantization axis. Thepassage from the fixed to the rotating frame is described by theEuler angles (φ, π2 ,

π2 ).

We adopt the physical model of Nikitin (1965), in whichwe consider an alkali atom composed of a core and an ex-cited p electron. The presence of the perturber at a distance R isequivalent to an induced electric dipole at distance R. The prob-lem reduces to a one-electron problem in which the radiatorHamiltonian is divided into HA, the electrostatic Hamiltonian,and HSO, the spin-orbit coupling of the alkali. The total elec-tronic Hamiltonian can be written

H = HA + HB + V + HSO· (16)

HA and HB are the electrostatic Hamiltonians of the separatedsystems A and B. V is the electrostatic interaction of A and B.

In the semi-classical treatment, the problem reduces to thesolution of the time-dependent Schrödinger equation:

HΨ(t) = i!∂Ψ(t)∂t· (17)

The spin-orbit Hamiltonian HSO is diagonal in the |J,m〉 or|J,M〉 representation, while V, symmetric about the internu-clear axis, is diagonal in a molecular basis |ΛML〉 where Λ =|ML|. Taking into account the symmetry in a reflection throughany plane containing the internuclear axis, we may be expand|ΛML〉 as

|ΛML;±〉 =∑

i

aΛi(|Li ML〉(±)(−1)ML |Li − ML〉

). (18)

Although it is impossible to diagonalize the total Hamiltonianin either the atomic or the molecular basis, it is possible to usea basis which minimizes the off-diagonal elements and dropthem. The system may then be described by a Hund’s case(Nikitin 1965; Masnou-Seeuws & McCarroll 1974).

2.3. Case of alkalis with small fine structure

We will now restrict our study to the case of the light alkaliswhich present a small fine structure: Li, Na, and K.

For large R, HSO # V, and the orbital angular momentumL of the electron is coupled with its spin S . The Hamiltonian isdiagonal in the |J,M〉 representation. We may define the fine-structure splitting !ω by the relation

!ω =⟨

2P 32|HSO |2P 3

2

⟩−⟨

2P 12|HSO|2P 1

2

⟩. (19)

Values of !ω corresponding to Li, Na, K, are respectively equalto 0.334, 17.19, and 57.7 cm−1. When R is small, V # HSO,and L is coupled with the electric field along the internuclearaxis. The eigenstates are then the molecular |Σ〉 and |Π〉 states.Denoting by VΣΠ the difference between the eigenvalues of Vfor the same asymptotic excited atomic state, we have

VΣΠ = 〈Σ|V|Σ〉 − 〈Π|V|Π〉. (20)

Figure 2a displays VΣΠ(R), the variation of the splitting be-tween |Σ〉 and |Π〉 states as a function of the internuclear dis-tance R compared to the fine structure splitting considered tobe independent of R. Here we show the cases of Li, Na, K per-turbed by He. Similar results are obtained for these alkalis per-turbed by H2.

The shape of the line wing is sensitive to ∆V(R), the differ-ence between the ground and excited state interaction potential.When ∆V(R) for a given transition goes through an extremum,a relatively wider range of interatomic distances contribute tothe same spectral frequency, resulting in an enhancement, orsatellite, in the line wing (Allard 1978).

Figure 2b shows the B2Σ − X2Σ potential energy differ-ences which exhibit a maximum and may lead to the formationof satellites on the resonance lines. The maxima in ∆V(R) in


Absorption in the blue wing of KI

• CaH “resurgence” - a molecular band returning or a new absorption feature?

6400 6500 6600 6700 6800 6900 7000 7100 7200

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DENIS J0255-4700

HaC HaC OiTIiL

IrS


Alkali lines - quasi-molecular satellites!

• New profiles by Allard, Spiegelmann & Kielkopf 2007

6000 6500 7000 7500 8000 8500 9000 9500 10000

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Challenges - Alkali chemistry

• Depletion of refractory species depends on complex chemical reaction network and mixing properties

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ZElemental abundances for 800K: old (--) vs. new (-) Settl

CaNaK


Challenges - Alkali chemistry

• Modelling of condensation still important in late T dwarfs!

• Gas density in line-forming region exceeds 1020 cm-3

➙ single-perturber approximation no longer valid in wings

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Alkali lines in White Dwarfs

• Strong V absorption in metal-rich cool white dwarfs

• Evidence for extremely pressure-broadened Na lines

0

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H-models log $g$ = 8.0, [M/H]=-3.5, [Na,K/H]=-1.5

K I

Li INa I

Ca I

CaH

MgH

WD 2356-2093400K3600K3800K

Oppenheimer et al. 2001, Salim et al. 2004(obs.) Homeier et al. EuroWD 06


Alkali lines in White Dwarfs

• 2 ultra-cool white dwarfs with strong Na absorption

• Hydrogen- or Helium-dominated atmosphere?

0

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H-models log $g$ = 8.0, [M/H]=-3.5, [Na,K/H]=-1.5

K I

Li INa I

Ca I

CaH

MgH

SDSS J1330+64353400K3600K3800K

Harris et al. 2003(obs.)Homeier et al. EuroWD 06


FT Expansion breaks down at high density

• Standard density expansion to 3rd or even 7th order only carries a fraction of the line strength!

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FT Expansion breaks down at high density

• Better treatment of far wings by direct calculation required for densest objects!

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Conclusions• Atmosphere models have made great progress towards

understanding substellar objects

• Condensation and depletion of dust species explains the properties of L dwarfs and the transition from L to T

• Line absorption paramount to correctly model T dwarfs

• Few, massively broadened alkali resonance lines shape large regions of brown dwarf spectra

• Next generation of line profiles needed to model atmospheres of still denser objects ➙ Y dwarfs, metal-rich white dwarfs

Thanks for your attention & Thanks to the organisers!

Alkali Line Proﬁles in Degenerate Dwarfs

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