New Insights on the origin of Magnetic Fields in White Dwarfs

Dayal Wickramasinghe and Lilia FerrarioAustralian National University

Canberra

• The chemically peculiar Ap, Bp stars ( ~ 1.8 -5 Msun) are magnetic, and have ordered large scale fields, modelled as mainly dipolar with B >300 G. They constitute some 10 of A and B stars.

• Other stars in the same spectral range are non magnetic (Auriere et al (2006) – i.e they fail to show ordered large scale magnetic fields down to an observational limit of ~30G.

Magnetic Fields of A-B stars

300 G

• Many recent studies have shown that magnetism on the MS is much more widespread and not restricted to the chemically peculiar Ap, Bp stars.

• Observations of Orion and other massive starregions have shown that ~ 10-25 % are strongly magnetic (Donati et al. 2002)

• Hubrig et al. (2008) estimate that ~30% of early B and O type stars have longitudinal fields of 100- 300 G.

Magnetic Fields of early B and O stars

Magnetism in the Mid-Upper MS stars

There is growing evidence that the incidence of magnetism increases with increasing stellar mass through spectral type B to early O stars.

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Magnetic Flux : Φ = πR2B

Origin of Magnetic Fields in Mid-Early Type Stars

Two views on the origin of fields

Fields are relics of the previousphases of proto stellar evolution

Question: why are the observed fields large scale and ordered (mainly dipolar) and what does it say about their origin

Question: why are only some early type stars magnetic?

Fields generated by a contemporary dynamo operating in the convective core.

Can a small scale dynamo generated fields be transported outwards to produce the observed ordered large scale fields ?

Fossil Field Hypothesis Dynamo Hypothesis

Stability of Fields1950s-2000:Attempts to construct analytical models for equilibrium field structures in radiative stars led to the consideration of

• Stars with purely Toroidal Fields (Taylor 1973)

• Stars with purely Poloidal Fields (Markey and Taylor 1973, Wright 1973)

The structures were found to be subject to various MHD instabilities (e.g. non-axisymmetric perturbations of Poloidal fields)

Pendergast (1956): poloidal and toroidal fields were separately unstable, linked toroidal-poloidal field structures may be stable

Numerical MHD Models (2004 – current)

• Assume a stably stratified non-rotating radiative star

• Introduce a random initial field and follow its evolution allowing the fluid to adjust to the appropriate magnetic equilibrium (the field could be a remnant from a previous convective phase, or generated in a merger)

A surprising result emerged. All models evolved towards a stable linked poloidal-toroidal field structure on an Alfven time scale ( 10 yrs at 1 kilo Gauss for Ap stars) in the absence of dissipation.

- The main requirement appeared to be that the star is stably stratified!

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Ξ

Non axi-symmetric field distributiondeveloping on an Alfven time scale

Nearly axi-symmetric poloidal-toroidal field structuredeveloping on an Alfven time scale

BraithwaiteNordlund (2006),

Braithwaite (2008)

Subsequent evolution is expected to be on a diffusion time scale (mainly Ohmic~109 yrs ) and has only been approximately studied in the MHD calculations.

The toroidal fields are predicted to slowly rise and dissipate on this time scale and with it so would the poloidal field!

Ap, Bp stars are observed to have mainly dipolar fields (with a few exceptions) in agreement with the theoretical expectations providing strong support for the fossil field hypothesis.

So fields in magnetic A and B stars (and also O stars) have fields that are fossil from pre-main sequence.

Why are only some early type stars magnetic? -the late merger hypothesis-

• Observation show that stars form in high density turbulent regions, most of them in binary and multiple systems

• It is likely that among these stars, are failed binary systems, resulting from the merger of two young proto-stars with at least one component at the end of the Henyey track with a radiative envelope

• The merger drives strong differential rotation, resulting in a large scale dynamo field, which is then maintained in the radiative envelope.

• The hypothesis is in agreement with the observation that Ap stars tend not to be in close (P < 3 d) binaries.(Ferrario et al. 2009)

Dearth of objects ?

Magnetic White Dwarfs

Two groups:

High Field MWDs ~ 106 - 109 G (~14% ,Liebert et al. 2004) Low Field MWDs ~ 103 - 105 G (~16%, Jordan et al. 2006)

Different origins ?• bimodal field distribution• HFMWDs have a higher than average mass

LFMWDs

HFMWDs

0.59 .vs. 0.7 Msun

Pre WD core

Large scale stable linked poloidal-toroidal field structures, on an Alfven time scale (~ few days at 10 MG field for a WD) which thendecays on an Ohmic time scale

• Fossil fields • Fields from post MS dynamo•or from merger (see laer)

The Final State (regardless of origin)

Time scales of Ohmic decay of pure poloidal modes in WDs

(8-12) 109 yrs (Dipole) (4-6 ) 109 (Quadrupole) (e.g. Wendell, VanHorn and Sargent (1987), Cumming 2005)

If initially, the field is a mix of multipolar fields, the fieldsshould evolve to be mainly dipolar along the cooling sequence.But there are many examples of complex field structures• Dominant quadrupolar components and higher order

components (e.g. He 1045-0908 (Euchner et al. 2005)).

• combinations of off-centered dipole, quadrupole models.

At the moment, there are no field decay models of stable poloidal-toroidal field structures

Origin of magnetic fields in WDs The fossil (from the MS) field hypothesisHFMWDs evolve from the Ap, Bp stars with magnetic flux somehow conserved from the MS during stellar evolution (Wickramasinghe and Ferrario 2005, Tout, Wickramasinghe and Ferrario 2004)

• Need to postulate that magnetic flux is expelled fromconvective regions but maintained in radiative regions during stellar evolution (Tout, Wickramasinghe and Ferrario 2005). It is not clear from a theoretical point of view whether this is plausible. The fields may instead be destroyed when a region becomes convective, and re-generated by a dynamo mechanism.

Nevertheless, there are some interesting coincidenceswhich provide some support for this hypothesis:

B (Ap-Bp stars) ~ 300-30,000 G → B (WD) ~ 106 – 109 G

HFMWDs

Ap-Bp stars

(i) Magnetic flux correspondence

(ii) Birth Rates If one assumes that all known Ap, Bp stars, and 45% of stars with M> 4.5 M0 are magnetic, the observed incidence of magnetism of HFMWDs (15%) and the observed mass distribution of HFMWDs can be explained(Wickramasinghe and Ferrario 2005)- Recent observations of magnetism the MS makes this more likely

(iii) the slow rotation of HFMWDs?

Strongly Magnetic WDs ---P(rot) ~ 10 100 years

Slowly rotating group(High Field)

Stellar Evolution Calculations with Rotation and Magnetic Fields

Spruit (2002) proposed that a new type of dynamo may operate even in radiative regions of stars in the presence of differential rotation, which provides the energy source for the dynamo

Weak poloidal seed field + differential rotation

Toroidal ---- (instabilities)

Poloidal

The dynamo only operates in the weak field regime (Alfven crossing time across star >> Rotation period) but the fields generated have a dramatic effect in the transport of angular momentum during stellar evolution

• No magnetic fields: Stellar evolution calculations that allow for the transport of angular momentum only by hydro-dynamical effects spins down core to • P(rot) ~ 30 min

• With weak field Spruit (radiative) dynamoAM transport by magnetic torques spins down the stellar cores to even longer rotation periods P(rot) ~ 300 min

-still not enough to explain periods of a few days let alone 100 yrs

AM transport by weakmagnetic torques(dynamo generated by differential rotationIn radiative regions -Spruit(2005))

AM transport only by non-magnetic processes

HFMWDsSuijs et al. 2008

However, if there is strong coupling between core and envelope during evolution up the giant branch

P(rot) ~ 10-100 yrs (periods observed in a group of HFMWDs!)

Could it be that a fossil field above a certain threshold (well above where the Spruit radiative dynamo operates) can enforce near solid body rotation throughout post MS evolution, and survive through to the WD phase? Unfortunately there are no calculations of stellar evolution with fossil fields and rotation.

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Vrot ~ 40 km s-1 ( 5 solar mass MS star)

Prot ~ 100 40 km s-1

Vrot

⎛

⎝ ⎜

⎞

⎠ ⎟ yrs

Strongly Magnetic WDs ------------ P(rot) ~ 10 100 years ( a few exceptions 725 s (e.g. EUVE0317-853) – mergers?)

Slowly rotating group(High Field)

Mergers,Or MWDsspun up in binaries

The dynamo hypothesisAll memory of fields on the MS wiped out by stellar evolution. New fields are generated post-AGB by a dynamo mechanism, and get incorporated in the pre-WD stellar core. They evolve into large scale dynamically stable structures (linked toroidal-poloidal fields) on an Alfven time scale (~ few days at 10 MG field for a WD) (Braithwurst and Spruit 2005)

The above scenario is likely to be relevant to the LFMWDs. The vast majority of these would have evolved from stars with M<1.5 M0 , with any fossil flux likely destroyed during the Hayashi phase. They may develop weak fields during subsequent evolution by the above process.

This hypothesis has been driven by the curious observation first highlighted by Liebert et al. (2005)

HFMWDs don’t have M dwarf companions while non-magnetic WDs do (a 4 sigma result).

This led to the hypothesis that HFMWDs result from mergers during common envelope evolution that would normally lead to CVs (Tout et al. 2008)

Strong fields are generated in the differentially rotating envelope

--- if the common envelope is ejected at the point of merger, a rapidly spinning HFMWD is formed

---- otherwise, the HFMWD will spin down rapidly, and a slowly spinning HFMWD would be formed.

The Merger hypothesis for HFMWDs

• A fossil origin for the fields provides a natural explanation for the nearly dipolar poloidal fields seen in Ap/Bp/Op stars. The maximum magnetic flux may correspond to magnetic energies above which buoyancy effects destroy the field.

•Whether the fossil magnetic flux can survive through stellar evolution in the flux range

to explain the HFMWDs remains an open question. Currently there are no theoretical calculations of stellar evolution in this strong field regime.

Summary

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Φmin ≤ Φ ≤ Φmax (106 ≤ B(G) ≤109)

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Φmax ~ 1028Gcm2

• The vast majority of white dwarfs which have F star progenitors and start their MS lives with convective envelopes have no fossil field, and develop weak fields during subsequent evolution.

-small scale fields may be generated in the pre-WD convective core-larger scale fields by the Spruit dynamo in radiative regions and incorporated in pre-WD core

These evolve into a stable large scale poloidal- torroidal structure at the birth of the white dwarf (Braithwurst 2008) when the star becomes stably stratified. The vast majority of WDs will then have low fields (LFMWDs)

• It is possible that the HFMWDs come from a totally different mechanism, namely mergers during a common envelope evolution that would normally lead to the formation of Cataclysmic Variables.

Support for these hypotheses come from the lack of binaries with M dwarf companions and HFMWDs.

Conclusions Scenario A

Conclusions Scenario B