Rayleigh scattering in CP stars - magnetic17.physics.muni.cz · 1 stellar atmosphere calculation...

Rayleigh scattering in CP stars

J. Fi²ák12,supervisor: J. Kubát2,

in collaboration with: J. Krti£ka1 & D. Munzar1

1Masarykova Univerzita, P°írodov¥decká fakulta, Brno2Astronomický Ústav, Akademie v¥d, Ond°ejov

31.08.2017, Czech Republic, BrnoStars with a stable magnetic eld

from pre-main sequence to compact remnants

Motivation

Rayleigh scattering

Cross section → absorption coefficient

Computing of spectra

Results

Motivation

Radiative processes in the stellar atmospheres

What is inuence of these processes on the stellar spectra?

often included processes

bound-bound processes (line absorption and emission)bound-free processes (ionization and recombination)free-free absorption and emissionscattering on free electrons

often neglected processes

scattering on bound electrons (Rayleigh, Raman sc.)Auger ionizationautoionization, dielectronic recombination

Jakub Fi²ák et al. (P.F.MU & AV R) Rayleigh scattering 31.08.2017, Brno 3 / 23

Motivation

Why to study these processes?

-0.06

-0.04

-0.02

0

0.02

0.04

0.06 7800 8000 8200 8400 8600 8800 9000 9200

∆H

p [

ma

g]

JD − 2 440 000

possible solution to some openproblemsHD 191612 (Krti£ka 2016)

dierent importance of processesin dierent types of atmospheres

main sequence starsCP starswhite dwarfsWolf-Rayet starscentral stars of planetarynebulae

described by interesting physics(atomic physics, quantum eldtheory,. . . )


Motivation







Motivation


HD 37776, Khokhlova, et al. 2000






Motivation







Motivation

Rayleigh scattering



Results

Rayleigh scattering

Rayleigh scattering

Initial state

Bound state

Bound state

Basic description

interaction of photon withbound electron

1 absorption of photon & electronis excited to unstable state

2 emission deexcitation to theoriginal state & creation ofscattered photon


Rayleigh scattering

Rayleigh scatteringCross section

scattered photon ks

1

HED

atomic interstate

HEDphoton

k

atom in the state 1

ks

1 HEDL HED

k

1

Kramers-Heisenberg formula for Rayleigh scattering

dσ

dΩ=

e4ν4

4c4ε20 h2

∣∣∣∣∣∑j

(εksD1jεkDj1

νj −ν+

εkD1jεksDj1

νj + ν

)∣∣∣∣∣2

.


Rayleigh scattering

Rayleigh scatteringCross section

after some calculations we get from Kramers-Heisenberg formula

σ = K ω4 8

3π

∣∣∣∣∣∑j

∣∣∣⟨n0, l0 ∣∣∣R∣∣∣n, l⟩∣∣∣2 2νj

ν2j −ν2

∣∣∣∣∣2

.

dipole matrix element∣∣∣⟨n0, l0 ∣∣∣R∣∣∣n, l⟩∣∣∣2

n,n0 principal quantum numberl , l0 azimuthal quantum number

|n, l > divides into two parts

bound statescontinuum states, Lee & Kim 2004


Rayleigh scattering

Getting cross sectionExact analytical calculation

possible only for hydrogen and hydrogen-like ions

low frequency expansion

σ = a1ν4 +a2ν

6 + · · ·+anν4+2n + . . .


Rayleigh scattering

Getting cross sectionExact analytical calculation

possible only for hydrogen and hydrogen-like ions

low frequency expansion

σH I(ν)cm2 = 7.18×10−87 ·ν4 +1.96×10−117 ·ν6 +4.27×10−148 ·ν8

σHe II(ν)cm2 = 2.80×10−89 ·ν4 +4.79×10−121 ·ν6 +6.52×10−153 ·ν8

1.0e-38

1.0e-36

1.0e-34

1.0e-32

1.0e-30

1.0e-28

1.0e-26

1.0e-24

0 6x1014

1.2x1015

1.8x1015

2.4x1015

cro

ss s

ectio

n [

cm

2]

frequency [Hz]

H IHe II

free electrons


Rayleigh scattering

Getting cross section

Colgan et al. 2016

1.0×10−30

1.0×10−29

1.0×10−28

1.0×10−27

1.0×10−26

1.0×10−25

1.0×10−24

1.0×10−23

1.0×10−22

6×1014

1.2×1015

1.8×1015

2.4×1015

3×1015

cro

ss s

ectio

n [

cm

2]

frequency [Hz]

carbonnitrogenoxygen


Motivation

Rayleigh scattering



Results

Computation of models

The calculation procedure

1 stellar atmosphere calculation

from a scratch using the TLUSTY codeusing existing model from a grid if it was available online

2 synthetic spectrum calculation with and without Rayleigh scatteringincluded

3 convolution with the Gaussian function

4 comparison of two convolved spectra




1 stellar atmosphere calculationfrom a scratch using the TLUSTY codeusing existing model from a grid if it was available online


3 convolution with the Gaussian function4 comparison of two convolved spectra

0.0e+00

6.0e+08

1.2e+09

1.8e+09

1000 1500 2000

F [

erg

/cm

2/s

/Hz]

λ [Å]Jakub Fi²ák et al. (P.F.MU & AV R) Rayleigh scattering 31.08.2017, Brno 12 / 23







(H ∗g)(λ ) =1√2πσ

∫dλ′ H(λ

′)exp

(−(λ −λ ′)2

2σ2

)4 comparison of two convolved spectra







0.0e+00

6.0e+08

1.2e+09

1.8e+09

1000 1500 2000 2500 3000

F [

erg

/cm

2/s

/Hz]

λ [Å]Jakub Fi²ák et al. (P.F.MU & AV R) Rayleigh scattering 31.08.2017, Brno 12 / 23







4 comparison of two convolved spectra

∆m =−2.5 log HRS

HNO

HRS ux with Rayleigh scattering includedHNO ux without Rayleigh scattering included







1.0×10−4

2.0×10−4

3.0×10−4

4.0×10−4

5.0×10−4

6.0×10−4

1000 1200 1400 1600 1800 2000

∆m

[m

ag

]

λ [Å]

Teff = 21000 K



Parameters of models

B-type stars

helium rich B-type stars

helium rich white dwarfs

helium rich white subdwarfs

used existing model grid (Lanz, & Hubeny 2007)assumption NLTEeective temperature (15 30) kKlog(g) [cgs] 4helium abundance N(He)/N(H) = 0.1heavy elements abundance from Grevesse et al. 1998




B-type stars




input models computed using the TLUSTY codeassumption NLTEeective temperature (19 30) kKlog(g) [cgs] 4helium abundance N(He)/N(H) = 10heavy elements abundance from Grevesse et al. 1998




B-type stars




input models computed using the TLUSTY codeassumption NLTEeective temperature (16 30) kKlog(g) [cgs] 8helium abundance N(He)/N(H) = 10heavy elements abundances from Grevesse et al. 1998




B-type stars




input models computed using the TLUSTY codeassumption NLTEeective temperature (10 30) kKlog(g) [cgs] 5.5helium abundance N(He)/N(H) = 10heavy elements abundance from Grevesse et al. 1998


Motivation

Rayleigh scattering



Results

Results

B-type starsRayleigh scattering by He I & He II

0.0×10+0

2.0×10−5

4.0×10−5

6.0×10−5

8.0×10−5

1.0×10−4

1.2×10−4

1.4×10−4

1.6×10−4

1000 1200 1400 1600 1800 2000

∆m

[m

ag

]

λ [Å]

19000 K21000 K23000 K

0.0×10+0

2.0×10−5

4.0×10−5

6.0×10−5

8.0×10−5

1.0×10−4

1000 1200 1400 1600 1800 2000

∆m

[m

ag

]

λ [Å]

25000 K27000 K29000 K


Results

Helium rich B-type starsRayleigh scattering by He II

1.0×10−4

2.0×10−4

3.0×10−4

4.0×10−4

5.0×10−4

6.0×10−4

1000 1200 1400 1600 1800 2000

∆m

[m

ag

]

λ [Å]

21000 K24000 K

Rayleigh scattering by He IIA&A Fi²ák, et al. 2016

used low-frequency limit of thecross section for Hydrogen-likeatoms

Rayleigh scattering by He IIcauses only small changes

Rayleigh scattering by He I couldbe more signicant


Results

Helium rich B-type starsRayleigh scattering by He II

1.0×10−4

2.0×10−4

3.0×10−4

4.0×10−4

5.0×10−4

6.0×10−4

1000 1200 1400 1600 1800 2000

∆m

[m

ag

]

λ [Å]

27000 K30000 K

Rayleigh scattering by He IIA&A Fi²ák, et al. 2016

used low-frequency limit of thecross section for Hydrogen-likeatoms

Rayleigh scattering by He IIcauses only small changes

Rayleigh scattering by He I couldbe more signicant


Results

Helium rich B-type starsRayleigh scattering by He I & He II

0.0×10+0

5.0×10−4

1.0×10−3

1.5×10−3

2.0×10−3

1000 1200 1400 1600 1800 2000

∆m

[m

ag

]

λ [Å]

19000 K21000 K23000 K

0.0×10+0

1.0×10−4

2.0×10−4

3.0×10−4

4.0×10−4

5.0×10−4

6.0×10−4

1000 1200 1400 1600 1800 2000

∆m

[m

ag

]

λ [Å]

27000 K25000 K29000 K


Results

Helium rich B-type starsRayleigh scattering by He I, C I, N I, O I

−8.0×10−3

−6.0×10−3

−4.0×10−3

−2.0×10−3

0.0×10+0

2.0×10−3

4.0×10−3

1000 2000 3000 4000 5000

∆m

[m

ag

]

λ [Å]

20000 K22000 K

−1.0×10−5

0.0×10+0

1.0×10−5

2.0×10−5

3.0×10−5

4.0×10−5

5.0×10−5

6.0×10−5

7.0×10−5

8.0×10−5

1000 2000 3000 4000 5000

∆m

[m

ag

]

λ [Å]

25000 K27000 K29000 K


Results

Helium white dwarfsRayleigh scattering by He I

−1.2×10−3

−1.0×10−3

−8.0×10−4

−6.0×10−4

−4.0×10−4

−2.0×10−4

0.0×10+0

2.0×10−4

1500 2000 2500 3000 3500 4000

∆m

[m

ag

]

λ [Å]

16000 K18000 K22000 K

0.0×10+0

5.0×10−6

1.0×10−5

1.5×10−5

2.0×10−5

2.5×10−5

3.0×10−5

3.5×10−5

4.0×10−5

1500 2000 2500 3000 3500 4000

∆m

[m

ag

]

λ [Å]

24000 K26000 K28000 K


Results

Helium white subdwarfsRayleigh scattering by He I

0.0×10+0

5.0×10−5

1.0×10−4

1.5×10−4

2.0×10−4

2.5×10−4

1200 1600 2000 2400 2800

∆m

[m

ag

]

λ [Å]

21000 K23000 K25000 K

0.0×10+0

1.0×10−6

2.0×10−6

3.0×10−6

4.0×10−6

5.0×10−6

6.0×10−6

7.0×10−6

8.0×10−6

9.0×10−6

1.0×10−5

1200 1600 2000 2400 2800

∆m

[m

ag

]

λ [Å]

27000 K29000 K


Results

Conclusions

we computed several series of models of stellar atmospheres

we computed synthetic spectra from these models with and withoutRayleigh scattering included

largest dierences ∆m ∼ 10−3mag in the case of Rayleigh scatteringby He I for helium B-type stars


Results

Future work

calulate cross section or scattering coecient from absorptioncoecient by other ions

calculate other synthetic spectra for heavier elements (Si, Fe, . . . )using SYNSPEC

include Rayleigh scattering into the code we are currently developing

in collaboration with Brankica Kubátová and Markus KromerMonte Carlo code for NLTE radiative transfer in stellar winds


Thank you for your attention.

Rayleigh scattering in CP stars - magnetic17.physics.muni.cz · 1 stellar atmosphere calculation...

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