Modeling of hydrogen Balmer lines for the diagnostic of magnetic white

dwarf atmospheres

J. Rosato, I. Hannachi, R. Stamm

Aix-Marseille Université, CNRS, PIIM, Marseille, France

12th SCSLSA conference – Vrdnik – June 4, 2019

Outline

1) Presentation of white dwarfs

2) Stark broadening calculations in WD atmosphere conditions

3) Zeeman effect in magnetized white dwarfs

White dwarfs: an overview

Source: Wikipedia

- WD are the end of the majority of stars (95 – 97%) with M < 10M⊙

- About 10% of WD have strong magnetic field

- They have a stratified structure- C, O core (99% M)- thin mantle of He (1% M)- envelope of H (< 0.01% M)

- They are classified by their dominant element in the atmosphere

- DA: strong hydrogen lines- DB: strong He I lines- DO: strong He II lines etc.

e.g. S. L. Shapiro and S. A. Teukolsky,Black Holes, White Dwarfs, and Neutron Stars

Example of white dwarf spectrum

4000 5000 6000 7000

0

20

40

60

80

100

120

H

HH

SDSS J165538.93+253345.99

Wavelength (Å)

Inte

nsity

(arb

. un

its)

Ha

Sloan Digital Sky Surveyhttp://www.sdss.org

Data from Belgrade Observatory (J. Kovačević-Dojčinović, M. S. Dimitrijević, L. Č. Popović)

Absorption lines in WD atmospheres

The outgoing radiation spectrum is obtained by solving the radiative transfer equation

nnnn Ids

dI (+ scattering)

Modeling the extinction coefficient

Free-free transitions: inverse bremsstrahlung, Rayleigh scattering, Thomson scattering

Bound-free transitions: photoionization

Bound-bound transitions: photoexcitation (atomic lines)

bbbfffnnnn

The bound-bound extinction coefficient

The depth of the absorption lines is determined by the bound-bound extinction coefficient

lu

lullubb NB

hnn f

n ,

4

u

l

atomic population

line shape

4000 5000 6000 7000

0

20

40

60

80

100

120

H

HH

SDSS J165538.93+253345.99

Wavelength (Å)

Inte

nsi

ty (

arb

. units)

Ha

Line broadening mechanisms

Wikipedia:“A spectral line extends over a range of frequencies, not a single frequency”

fn

n n

fn

Some causes of line broadening:- radiative decay (natural broadening)- Doppler effect (thermal motion of atoms)- collisions, Stark effect –d.E

Stark broadening in stellar atmosphere conditions

-4x10-4

-2x10-4 0 2x10

-44x10

-4

0

5x103

Doppler broadening Stark broadening

No

rma

lize

d lin

e s

ha

pe

Dw (eV)

Ha

Ne = 10

17 cm

-3

T = 1 eV

Stark broadening modeling

When emitting or absorbing a photon,an atom feels the presence of the charged particleslocated at vicinity

0

)()0(Re1

)( dtetddI tiw

w

A Stark broadened line is proportional to the Fourier transformof the atomic dipole autocorrelation function

d(t)

0.0 5.0x10-12

1.0x10-11

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

D

ipo

le a

uto

corr

ela

tio

n f

un

ctio

n

H Lyman a, simulation

N = 1017

cm-3, T = 1 eV

t (s)

Stark broadening modeling

Decrease time ~ 1/Dw1/2 “time of interest”

Calculation methods

Many models, formulas and codes have been developed:- quasistatic approximation (-d.E = cst)- kinetic theory- collision operators- stochastic processes (MMM, FFM)- fully numerical simulations

They are complementary to each other

Their validity can be assessed through comparisons to experimental spectra,and by cross-checking between codes(e.g. SLSP code comparison workshop, Vrdnik, last week)

Lyman aNe,i = 1019 cm-3

Te,i = 5 eV

Calculation methods

SLSP5 (last week)

Fitting an observed spectrum

-0.05 0.00 0.05-10

0

10

20

30

40

50 Observed spectrum Adjustment

-ln

(I/I

0)

Ha

Ne = 6x10

17 cm

-3

T = 1 eV

Dw (eV)

)/ln( 0IIf Beer-Lambert formula

A simplified atmosphere model: homogeneous medium

15

Zeeman effect: the energy levels and corresponding spectral lines are split

Influence of an external magnetic field on spectral lines

B

Zeeman effect in magnetic white dwarf spectra

4000 4500 5000 5500

20

40

60

H

H

SDSS J111010.50+600141.44

Inte

nsi

ty (

arb

. un

its)

(Å)

H

The separation between the components corresponds to B = 360 T

Data from Belgrade Observatory (J. Kovačević-Dojčinović, M. S. Dimitrijević, L. Č. Popović)

At very strong magnetic fields, the Zeeman triplet structure is no longer symmetrical

eee m

AeB

m

pAep

m 22)(

2

1 2222

quadratic Zeeman effect

Quadratic Zeeman effect

linear Zeeman effect

Quadratic Zeeman effect

-0.2 -0.1 0.0 0.1 0.2

0

20

40

60

N

orm

aliz

ed

lin

e s

ha

pe

Ha

Ne = 10

17 cm

-3

Te = T

i = 1 eV

B = 2000 T = 90°

Dw (eV)

Quadratic Zeeman effect

-0.4 -0.2 0.0 0.2 0.4

0

5

10

15

N

orm

aliz

ed

lin

e s

ha

pe

Dw (eV)

H

Ne = 10

17 cm

-3

Te = T

i = 1 eV

B = 2000 T = 90°

1.8 2.0 2.2 2.4 2.6 2.8

0

20

40

60

80

Lin

e s

ha

pe

(arb

. un

its)

Energy (eV)

Ha

H

Quadratic Zeeman effect

SDSS databaseB. Külebi et al., A&A 506, 1341 (2009)

Ha Zeeman components

Observation on magnetic white dwarf spectra

Summary

White dwarf spectra contain information on the plasma parameters

Accurate models are required for line broadening: Stark effect, Zeeman effect

Ongoing work: quadratic Zeeman effect