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High Field Magnetic White Dwarfs

High Field Magnetic White Dwarfs - Institute of Astronomy ... · PDF fileHigh Field Magnetic White Dwarfs ... B = 1 Tesla could produce a white dwarf of 107 m radius ... 117,000T 2

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Page 1: High Field Magnetic White Dwarfs - Institute of Astronomy ... · PDF fileHigh Field Magnetic White Dwarfs ... B = 1 Tesla could produce a white dwarf of 107 m radius ... 117,000T 2

High Field Magnetic White Dwarfs

Page 2: High Field Magnetic White Dwarfs - Institute of Astronomy ... · PDF fileHigh Field Magnetic White Dwarfs ... B = 1 Tesla could produce a white dwarf of 107 m radius ... 117,000T 2

High Field Magnetic White Dwarfs and phosphorus in silicon:

Spectroscopy of hydrogenic orbitals under extreme field

conditions

Ben Murdin, Matt Pang, Ellis Bowyer, Nicole Li, Konstantin Litvinenko, Steve

Clowes,

Advanced Technology Institute, University of Surrey

Hans Engelkamp

High Field Magnet Lab, Radboud University, Nijmegen

Sergey Pavlov, Heinz-Willem Hubers

Institute of Planetary Research, German Aerospace Centre, Berlin

Paul Murdin

Page 3: High Field Magnetic White Dwarfs - Institute of Astronomy ... · PDF fileHigh Field Magnetic White Dwarfs ... B = 1 Tesla could produce a white dwarf of 107 m radius ... 117,000T 2

Hydrogen-α in a magnetic field

• Photons are also

quantised with angular

momentum in units of

+ = right circular pol, s+

0 = linear polarisation, pz

- = left circular pol, s-

• So transitions must

change mL by DmL=-1,0,1

to conserve angular mtm

• There are 3 bunches of

transitions

• This is the Zeeman

effect n=1,L=0

n=3,L=2

n=2,L=1

Energy

B=0 B≠0

mL 2

1

0

-1

-2

1

0

-1

0

U = mBmLB

Ha

Page 4: High Field Magnetic White Dwarfs - Institute of Astronomy ... · PDF fileHigh Field Magnetic White Dwarfs ... B = 1 Tesla could produce a white dwarf of 107 m radius ... 117,000T 2

Zeeman splitting in a sunspot

National Optical Astronomy Observatories (NOAO) Bmax 0.4 T 1 T = 10,000 gauss

Page 5: High Field Magnetic White Dwarfs - Institute of Astronomy ... · PDF fileHigh Field Magnetic White Dwarfs ... B = 1 Tesla could produce a white dwarf of 107 m radius ... 117,000T 2

Magnetic Flux Compression in Lab

Field inside coil is “trapped”

Compress the coil, increase the

field

Page 6: High Field Magnetic White Dwarfs - Institute of Astronomy ... · PDF fileHigh Field Magnetic White Dwarfs ... B = 1 Tesla could produce a white dwarf of 107 m radius ... 117,000T 2

Generation of the highest magnetic fields Los Alamos National Laboratory (850 Tesla)

For greatest compression need a

powerful, uniform implosion, i.e. a

specially designed detonator – one

designed for an atomic weapon –

not many labs achieve the highest

fields (1,000 T)! The experiment is

brief and gets nowhere near the

astronomical extremes

Page 7: High Field Magnetic White Dwarfs - Institute of Astronomy ... · PDF fileHigh Field Magnetic White Dwarfs ... B = 1 Tesla could produce a white dwarf of 107 m radius ... 117,000T 2

Magnetic fields in White Dwarfs

• Stars are made of proton/electron plasma

– Highly conducting

• If flux is conserved during the collapse, then a nominal

star of radius 109 m and surface magnetic flux density

B = 1 Tesla could produce a white dwarf of 107 m radius

with a field of 10,000 T, unless dissipated somehow

• The first high magnetic field white dwarf was identified by

Roger Angel in 1972

– Grw +70 8247

– 24,000 T

H-γ shifted from

4341 to 4135A

Page 8: High Field Magnetic White Dwarfs - Institute of Astronomy ... · PDF fileHigh Field Magnetic White Dwarfs ... B = 1 Tesla could produce a white dwarf of 107 m radius ... 117,000T 2

Magnetic fields in White Dwarfs

• A large number with magnetic fields from 1 T

up to 100,000 T (1 G gauss) are now known

• Field value is obtained from theoretical calculations of

the Zeeman Effect in hydrogen, but no one has ever

done any lab (or bunker!) experiments above 1,000 T,

and theory is hard!

Page 9: High Field Magnetic White Dwarfs - Institute of Astronomy ... · PDF fileHigh Field Magnetic White Dwarfs ... B = 1 Tesla could produce a white dwarf of 107 m radius ... 117,000T 2

Parameterised high field Zeeman effect

• Low field Zeeman

energy

• Produces linear

energy shift of mLB

• Quadratic Zeeman

effect

• Becomes important at

high field, when B~B0

• Mixes states…..

Zero field Hamiltonian

responsible for Rydberg series

and spherical harmonics

H

ER=H0

ER+B

B0

.L+ 2B

B0

´r

a0

æ

èç

ö

ø÷

2

T000,117

242

12

23

0

B

Re EmeB

p

“Characteristic

field” “Binding

energy” “Bohr radius”

Page 10: High Field Magnetic White Dwarfs - Institute of Astronomy ... · PDF fileHigh Field Magnetic White Dwarfs ... B = 1 Tesla could produce a white dwarf of 107 m radius ... 117,000T 2

Spherical harmonics with

cylindrical perturbation by B • The quadratic Zeeman term produces mixing between states which

causes the wavefunction shapes to distort (1 au ~ 0.5Å)

2p- 6p-

B=0

B=B0

5f-2

z

y

160atomicunits

B B=B0=117,000 T

B=0

Page 11: High Field Magnetic White Dwarfs - Institute of Astronomy ... · PDF fileHigh Field Magnetic White Dwarfs ... B = 1 Tesla could produce a white dwarf of 107 m radius ... 117,000T 2

Zeeman effect at high fields in

the Lyman series of hydrogen

Record terrestrial B=2800 T Thickness of line is measure of line strength

(eV)

B=B0 117,000

left circular pol, s-

linear polarisation, pz

right circular pol, s+

Page 12: High Field Magnetic White Dwarfs - Institute of Astronomy ... · PDF fileHigh Field Magnetic White Dwarfs ... B = 1 Tesla could produce a white dwarf of 107 m radius ... 117,000T 2

WD Balmer

spectra • Hydrogen in magnetic

white dwarfs

• Spectra shifted up and

down to match calculated

H Balmer transitions

• Confusions:

– Other ions

– Paschen lines

– Broadening and relative

strengths • averaging over a range of

fields on the surface and

down through atmosphere

• Confirmation of theory

would be reassuring

Spectra from SDSS: K.M. Vanlandingham et al., Astron. J. 130, 734 (2005)

B=B0

117,000

Page 13: High Field Magnetic White Dwarfs - Institute of Astronomy ... · PDF fileHigh Field Magnetic White Dwarfs ... B = 1 Tesla could produce a white dwarf of 107 m radius ... 117,000T 2

A hydrogen-like atom in a silicon chip:

The Group 5 impurity

• P looks like

silicon with

– an extra +ve

charge in the ion

– & an extra

electron orbiting

Page 14: High Field Magnetic White Dwarfs - Institute of Astronomy ... · PDF fileHigh Field Magnetic White Dwarfs ... B = 1 Tesla could produce a white dwarf of 107 m radius ... 117,000T 2

Scaling from hydrogen to

phosphorus • The electron-ion attraction is screened by the

relative permittivity of silicon r

– extent to which Si concentrates electric lines of flux

• The electron mass is reduced to m*

– Newton’s law (F = mea) does not well describe an

electron moving in a solid material because of the

force created by other atoms

– “effective mass” is a concept that takes account of

departures and makes a law in the form of Newton’s

law work: F = m*a

Page 15: High Field Magnetic White Dwarfs - Institute of Astronomy ... · PDF fileHigh Field Magnetic White Dwarfs ... B = 1 Tesla could produce a white dwarf of 107 m radius ... 117,000T 2

Scaling from hydrogen to

phosphorus • Binding energy:

• Bohr radius

H Si:P

r 1 11.4

me or m* 1 0.19

ER 13.6 eV 0.020 eV

a0 0.056 nm 3.2 nm

ER =1

2

e2

4p

æ

èç

ö

ø÷

2

me

e2

a0 =4p 2

e2

e

me

Scale drawing of the 2p- wave

function on the crystal lattice

Page 16: High Field Magnetic White Dwarfs - Institute of Astronomy ... · PDF fileHigh Field Magnetic White Dwarfs ... B = 1 Tesla could produce a white dwarf of 107 m radius ... 117,000T 2

Scaling from hydrogen to

phosphorus • Characteristic field

H Si:P

r 1 11.4

me 1 0.19

ER 13.6 eV 0.020 eV

a0 0.056 nm 3.2 nm

B0 117,000 T 32 T

B0 =1

2

èç

ö

ø÷

3me

2

4pe( )2

Page 17: High Field Magnetic White Dwarfs - Institute of Astronomy ... · PDF fileHigh Field Magnetic White Dwarfs ... B = 1 Tesla could produce a white dwarf of 107 m radius ... 117,000T 2

The experiment • Magnet

– High Field Magnet Laboratory

• Radboud University, Nijmegen

• Netherlands Foundation for Fundamental Research

on Matter (FOM)

• a Large European Research Infrastructure

– Max Field: 33 Tesla

– Power: 17 MW

• vast generators and cooling system!

• Cryogenics

– Sample is helium cooled at 2.2K (so the

electron is bound)

• Spectroscopy

– Fourier Transform Interferometer with helium

cooled silicon bolometer as a detector

Page 18: High Field Magnetic White Dwarfs - Institute of Astronomy ... · PDF fileHigh Field Magnetic White Dwarfs ... B = 1 Tesla could produce a white dwarf of 107 m radius ... 117,000T 2

Donor

spectra:

comparison

of theory and

experiment

Magnetic f

ield

(B

0)

Magnetic f

ield

(T

)

Page 19: High Field Magnetic White Dwarfs - Institute of Astronomy ... · PDF fileHigh Field Magnetic White Dwarfs ... B = 1 Tesla could produce a white dwarf of 107 m radius ... 117,000T 2

Summary

• Through the use of a solid-state analogue we have

experimentally investigated the spectroscopy of

hydrogen in conditions appropriate to the surface of the

highest field magnetic white dwarfs, where the magnetic

energy is equal to the electric (binding) energy.

• The theory for the state energies and selection rules is

validated in this regime.

Page 20: High Field Magnetic White Dwarfs - Institute of Astronomy ... · PDF fileHigh Field Magnetic White Dwarfs ... B = 1 Tesla could produce a white dwarf of 107 m radius ... 117,000T 2

The future • Investigating solid-state analogues for the high-field

Zeeman effect for helium is immediately possible. The

theory of the Zeeman effect for helium is less well

established than for hydrogen. Other ions might be

possible.

• In doped silicon commonly available, the impurity atoms

are randomly distributed throughout the silicon lattice.

Through nano techniques, it is becoming possible to

place individual atoms of the donor impurity. In principle,

it should be possible to construct doped silicon with

phosphorus atoms side by side to simulate the hydrogen

molecule (or others). The theory of the high-field

Zeeman effect of H2 is very difficult indeed, so

experimental investigation would be pioneering