The Magnetic White Dwarfs – open issues

Lilia Ferrario

Mathematical Sciences Institute The Australian National University

Grw+70o 8247 (Kuiper 1934)

2

•  First MWD discovered (Kuiper 1934).

•  Spectrum nearly featureless except for “Minkowski bands” (1938).

•  Strongly circularly polarised spectrum (Kemp 1970).

•  Computations of H transitions in strong magnetic fields in mid-80s revealed that features of Grw+70o8247 are due to Zeeman shifted H lines in 100− 320MG.

(Wickramasinghe & Ferrario 1988)

Grw+70o 8247

Field determination in MWDs:Zeeman

3

•  These are the calculations that allowed the spectrum of Grw+70o8247 to be understood.

•  Wavelengths and oscillator strengths of H published by LSU (Henry & O'Connell 1984,1985) and Tuebingen (Rosner et al. 1984; Wunner et al. 1985) groups.

•  Components of H lines whose wavelengths vary slowly with B (stationary components) are not smeared by field spread (a factor of two for a dipole).

•  Some H and He transitions still unavailable. (β= B/4.7×109G)

Wunner et al. (1985)

Zeeman modelling: peculiar objects •  Feige 7 is a He-rich rotating MWD with

bands of H-rich material. This is probably due to the effects of the magnetic field on convective mixing.

•  GD356 has Zeeman triplets in emission. Possible interpretation: iron core of a planet moving through the WD magnetosphere - electrical currents are generated, which heat the atmosphere of the WD near its magnetic poles (like Io-Jupiter interaction). Rotation period was predicted and later found by Brinkworth (2004, 115 minutes). Wickramasinghe et al (2010) placed a stringent upper limit of 12MJ for the mass of such planet.

4

Achilleos & Wickramasinghe (1992)

Li, Ferrario & Wickramasinghe (1998)

Outstanding Issues on Zeeman modelling

•  Continuum is quantised into Landau levels.

•  Lamb & Sutherland (1974) used simple prescriptions for the bound - free opacity of hydrogenic atoms (a bound free edge will split into 3 edges separated by Larmor ωL)

•  First calculations of bound-free absorption cross sections for H were conducted by Merani, et al.(1995) and show how complex resonances develop in the Landau continua.

5

•  Inclusion of these opacities in model atmospheres (Jordan & Merani 1995) has shown no significant improvements.

Accreting Magnetic White Dwarfs

6

RKM.com.au

Field determination in Accreting WDs: Cyclotron lines

7

VV Puppis, Mason et al (2007)

Position of nth harmonic in a field is given by:

λn =10, 710n

108

B!

"#

$

%& A

Accretion in VV Puppis occurs near both magnetic poles of field strength B=31 MG and B=56 MG à Offset dipole.

5 6 7

Magnetic Field Distribution

8

Magnetic White Dwarfs

Fig. 8 Distributions of magneticfield strength in polars (blue line)and IPs (red line) compared tothat of single magnetic WDs(black line). This figure has beenprepared using the data inTables 1, 2, and 3 (this work)

From time-resolved polarimetry (e.g. Potter et al. 2004) and spectropolarimetry (e.g.Beuermann et al. 2007) detailed information on the complexity (quadrupole or even mul-tipoles) of magnetic field topology in these systems can be obtained (see also Sect. 3.3).However, in systems with ages ! 1 Gyr a substantial decay of multipole components couldbe expected and thus short period MCVs may not have complex fields (Beuermann et al.2007). Magnetic field strengths have been measured or estimated for ∼86 WDs in binaries(see Tables 2 and 3 for a complete list of known systems as of December 2014). Usingthe main pole magnetic field strength, Fig. 8 depicts the magnetic field distribution of po-lars compared to that of single MWDs listed in Table 1 with the latter having fields in therange 0.1–1000 MG. The polars clearly populate a more restricted range of field strengths,7–230 MG, with a mean value of 38 MG.

Fields strengths above 230 MG, which are detected in single magnetic WDs, are notfound in polars and there is no clear explanation for this yet. High magnetic field polars couldbe difficult to identify due to selection effects because these systems would be highly inter-mittent soft X-ray sources such as AR UMa. Hameury et al. (1989) explained the paucityof very high field polars in terms of their very short lifetimes due to efficient loss of angu-lar momentum via magnetic braking mechanism. However, it appears more likely that thestrong fields in polars may decrease the efficiency of magnetic braking, which would resultin a slower evolution of their orbital periods and in lower accretion luminosities (Li andWickramasinghe 1998; Webbink and Wickramasinghe 2002; Araujo-Betancor et al. 2005a).On the other hand, if the magnetic field is generated during the CE phase, then the highestfields could only be produced when the two stars merge to give rise to an isolated MWD(see Sect. 6 and the chapter on the origin of magnetic fields in this book).

The lowest surface averaged magnetic field strength measured in a polar is 7 MG inV2301 Oph which was modelled by Ferrario et al. (1995) with a dipolar field of 12 MGoffset by 20 % from the centre of the WD. The lack of lower field synchronous systemscould be explained if the asynchronous IPs represent the low field tail of the magnetic fieldstrength distribution in MCVs. However this is difficult to prove, because the absence of

•  Distributions of magnetic field strength in isolated MWDs, accreting polars (blue line) and IPs (red line).

•  Field distribution below a few MG in isolated MWDs is unknown.

Ferrario, de Martino & Gaensicke (2015)

Origin of magnetic fields in white dwarfs

•  I will discuss now possible scenarios for the origin of magnetic fields in the high field magnetic white dwarfs (HFMWDs).

9

Magnetic Flux in the most magnetic stars

10

The magnetic flux for the most magnetic MS stars (squares), MWDs (circles), high field radio pulsars (triangles) and magnetars (stars)

Magnetic field distribution of the MWDs compared to that of the NS when the WD radii are shrunk to those typical of NS (Ferrario et al. 2010).

Fossil Field Model

•  Magnetic Fields present in the ISM become frozen into stars at formation.

•  Magnetic flux is conserved as the star evolves. •  Ap/Bp stars are the progenitors of the High Field

Magnetic White Dwarfs (HFMWDs, Wickramasinghe & Ferrario 2005).

Thus Ø There should be the same fraction of HFMWDs in

Binary Stars as in Single Stars.

11

HFMWDs in Binaries

•  Magnetic White Dwarfs ought to occur as often in detached binary stars as single stars.

•  The Sloan Digital Sky Survey has identified thousands WD+M star detached spectroscopic binaries (e.g. Rebassa-Mansergas et al. 2012, 2013).

•  None of these WDs has B > a few MG which could be seen by Zeeman Splitting.

•  The sample of WDs within 20 pc (Holberg et al. 2008) has shown that 19.6 (+/-4.5)% have MS companions.

•  Thus,14-24% of the ~300 MWDs (~40-70 WDs) should have such companions. There is none.

12

Logical Conclusion

The origin of high magnetic fields in white dwarfs is intimately related to their duplicity (Tout et al. 2008).

13

RKM.com.au

Field Generation During CE Evolution (Tout et al. 2008)

14

•  Spiralling cores in Common Envelope create differential rotation.

•  Dynamo generates field from differential rotation. The closer the cores get before the envelope is ejected the stronger the fields.

Ø Strongest fields arise when stars merge.

Ø Next strongest fields in systems that emerge from the CE about to transfer mass (MCVs).

Ø Systems that emerge widely separated do not have high fields.

Merger scenario

15

•  Nordhaus et al. (2011): a low-mass star would be tidally disrupted by its proto-WD companion during CE to form an accretion disc. In this disc seed fields would be amplified through turbulence and shear and then advected on to the object that will become a MWD.

•  García-Berro et al. (2012): a hot and differentially rotating convective corona would form around the more massive star.

•  Wickramasinghe, Tout & Ferrario (2014): the fields are generated by an Ω dynamo within the CE of a binary system where a weak seed poloidal field would wind up by differential rotation.

•  The merger scenario could explain: Ø MWDs have higher masses than non-magnetic WDs. Ø Planetary system could form from disks. The disruption of

small planets could explain population of metallic MWDs.

Dynamo Evolution (Wickramasinghe, Tout, Ferrario 2014)

16

ζ = η =EMag

Eth

∝B

•  Dynamo generates B from differential rotation ΔΩ

•  Toroidal and poloidal fields are unstable on their own (Braithwaite 2009, Reisenegger 2009). Poloidal stabilizes toroidal and viceversa, limiting field growth.

•  Poloidal and toroidal fields reach a stable configuration.

0 ≤ ΔΩ≤Ωcrit =1τ dyn

=GMR3

•  Final poloidal field proportional to initial ΔΩ.

17

Population Synthesis: Mass Distribution (Briggs et al. 2015)

•  HFMWDs: mean mass ~0.78 M¤ (c.f. ~0.66M¤ for non-Magnetic WDs, Tremblay et al. 2013).

•  Best fit to incidence of magnetism among WDs (10-15%) and mass distribution requires α<0.3

Magnetic Field Evolution

18

Free Ohmic decay time L = length scale over which B changes σ = electrical conductivity. Simplest estimates with L ≈R and σ equal to the values expected in the fully degenerate cores of WDs yield tohm ∼ 2−6x1011 yrs.

tohm ≈4πσLc2

2

Lack of evidence for the evolution of field strength with Teff is consistent with these long decay time scales.

Ferrario, de Martino & Gaensicke (2015)

Magnetic Double Degenerates

•  These systems are important because they could be: 1.  Progenitors of Supernovae of Type Ia 2.  Progenitors of MSPs (without invoking pulsar

recycling) if WD has a low field (Hurley et al. 2010, Ferrario & Wickramasinghe 2008)

3.  High field DD mergers are the possible progenitors of high field pulsars and magnetars (EUVE0317-854 is a missed high field pulsar).

19

Magnetic DDs (Rolland and Bergeron 2015)

20

Best fits to the observations of 10 MWDs suspected to be in unresolved binary systems

Synthetic spectra obtained assuming the presence of an unresolved DC WD (left), a normal DA star (middle), or another DAH star (right). Both stars have Teff=6000 K and log g= 8. Contribution of unresolved companion, in percentage, is given in each panel.

Effective Temperatures of MWDs

21

Ferrario, de Martino & Gaensicke (2015)

•  The cumulative distribution function of MWD effective temperatures is smooth implying that the birthrate of MWDs has not changed over time (but note that this sample is dominated by SDSS objects).

•  Is there a higher incidence of magnetism among cool WDs than among hot WDs?

Conclusions

•  No HFMWD with B ≥3MG has been found in a detached binary system.

•  HFMWDs could originate from systems that merge during the CE phase.

•  The absence of pre-MCVs indicate most MWDs may have formed via interaction in the CE phase. MCVs emerge from CE just before mass transfer begins.

•  Magnetic DDs can be detected more easily than non magnetics DDs.

•  Presence of planets around MWDs may place unique signatures in their spectra.

22

Discussion points •  Do magnetic fields influence the hydrostatic equilibrium of the

atmosphere? It is generally assumed that the magnetic field in the atmosphere is force-free maintained by currents in the interior of the WD (see poster by Peterson & Dexheimer). However… Landstreet (1987) argued that Ohmic decay of a fossil field would lead to a decay-induced force that would drive a meridional motion perpendicular to field lines and affect the magneto-hydrodynamic structure of the WD atmosphere.

•  Do magnetic fields confine the motions of the stellar material along the direction of the field lines, thus inhibiting convection across field lines (see poster by Fusillo & Tremblay)?

•  What is the origin of magnetic fields? Only a small fraction of stars exhibit strong, large scale magnetic fields.

•  Polarised radiation transfer in non-LTE line core of H for model computation.

23

•  Metal pollution in WDs (due to the presence of elements like Ca, Mg, Cr, Na, Fe, and Ti) is caused by accretion from a circumstellar debris disc formed by the disruption of asteroids or small rocky planets. Cool WDs that only show metal lines are classified as DZ. In magnitude-limited samples, the incidence of magnetism among cool DZ WDs is nearly 14% which is very high considering that it is only around 4% among DA white dwarfs (Kawka & Vennes 2014, see poster by Hollands, et al.).

•  It should be possible to use stationary components that are insensitive to field structure to estimate gravities from line profiles in MWDs. However, this must await a full theory of Stark broadening in the presence of crossed electric and magnetic fields.

24

Discussion points