The cool magnetic DAZ white dwarf NLTT 10480Based on observations collected at the European Organisation for Astronomical Research in the Southern Hemisphere, Chile under programme ID 080.D-0521, 082.D-0750 and 086.D-0562.

The cool magnetic DAZ white dwarf NLTT 10480thanks: Based on observations collected at the European Organisation for Astronomical Research in the Southern Hemisphere, Chile under programme ID 080.D-0521, 082.D-0750 and 086.D-0562.

Adéla Kawka Astronomický ústav, Akademie věd České republiky, Fričova 298, CZ-251 65 Ondřejov, Czech Republic
11email: kawka,vennes@sunstel.asu.cas.cz
   Stéphane Vennes Astronomický ústav, Akademie věd České republiky, Fričova 298, CZ-251 65 Ondřejov, Czech Republic
11email: kawka,vennes@sunstel.asu.cas.cz
Received; accepted
Key Words.:
white dwarfs – stars: individual: NLTT 10480 – stars: atmospheres – stars: abundances

We have identified a new cool magnetic white dwarf in the New Luyten Two-Tenths (NLTT) catalogue. The high proper-motion star NLTT 10480 ( yr) shows weak Zeeman-split lines of calcium as well as characteristic H and Zeeman triplets. Using VLT X-shooter spectra, we measured a surface-averaged magnetic field  MG. The relative intensity of the and components of the calcium and hydrogen lines imply a high inclination (). The optical-to-infrared colour index and the Ca iCa ii ionization balance indicate a temperature between 4 900 and 5 200 K, while the Balmer line profiles favour a higher temperature of 5400 K. The discrepancy is potentially resolved by increasing the metallicity to solar, hence increasing the electron pressure. However, the measured calcium abundance and abundance upper limits for other elements (Na, Al, Si. and Fe) imply a low photospheric metallicity solar. Assuming diffusion steady-state, a calcium accretion rate of is required to sustain a calcium abundance of in the white dwarf atmosphere. We examine the implications of this discovery for the incidence of planetary debris and weak magnetic fields in cool white dwarf stars.

1 Introduction

NLTT 10480 (LHS 5070, LP 887-66) is a high proper-motion star (Luyten, 1979, 1980) that was also listed as a white dwarf candidate in Luyten’s white dwarf catalogue (Luyten, 1977). Using an optical-infrared reduced proper-motion diagram (Salim & Gould, 2002) and additional colourimetric criteria (Kawka et al., 2004b), we selected NLTT 10480 for spectroscopic observations to investigate stellar properties such as the effective temperature (), surface gravity (), chemical composition, and magnetic field strength, and to constrain its cooling age and mass.

The chemical composition of cool white dwarfs shows great diversity. Heavy elements, particularly calcium, are detected in close to a quarter of cool, hydrogen-rich (DA) white dwarfs, but with abundances well below solar (Zuckerman et al., 2003). The abundance of heavy elements decreases with white dwarf cooling ages mainly because of the increasing depth of the mixed convective layers in aging white dwarfs (Paquette et al., 1986; Koester, 2009). Few examples of very cool ( K) polluted white dwarfs (DAZ) are known, such as G 77-50 (WD 0322019, Hintzen & Strittmatter, 1974; Sion et al., 1990), which is also harbouring a weak magnetic field (Farihi et al., 2011). New high-dispersion and high signal-to-noise ratio spectroscopic observations of faint high proper-motion stars are likely to contribute new objects to the current sample.

Heavy elements in the atmosphere of cool white dwarfs are almost certainly accreted from their immediate environment. Kilic et al. (2006) and Farihi et al. (2009) reported infrared observations of a sample of cool white dwarfs contaminated with heavy elements, and the authors noted an infrared-excess incidence of 10-20%. This excess was attributed to debris discs of temperatures ranging from a few hundred degrees to over 1000 K. Some cool DAZ white dwarfs, such as G 17474 (WD 0245+541), do not show an infrared excess (Debes et al., 2007), and the presence of heavy elements in cool white dwarfs with ages in excess of several billion years suggests, instead, the effect of episodic accretion from small asteroids rather than from a stable debris disc (Jura, 2008). Therefore, the identification of new cool DAZ white dwarfs is of interest to constrain the phenomenon.

We present a first report on a programme aimed at identifying and characterizing new DAZ white dwarfs in the New Luyten Two-Tenths (NLTT) catalogue. Sect. 2 describes observations obtained at the European Southern Observatories (ESO) using the New Technology Telescope (3.6-m) and the Very Large Telescopes (VLTs). Sect. 3 presents our model atmosphere analysis including details of the model structures (Sect. 3.1), heavy element line opacities (Sect. 3.2), and Zeeman effect on line profiles (Sect. 3.3). We summarize and discuss some implications of our results in Sect. 4.

2 Observations

Instrument UT Date Range Note, .
VLT/FORS1 2007 Nov 1 3780-6180Å
NTT/EFOSC2 2008 Oct 23 3680-7400Å 14Å
VLT/X-shooter 2010 Dec 10 3000Å-2.5m
2011 Jan 10
2011 Jan 26
2011 Mar 3
Table 1: Log of spectroscopic observations

We first observed NLTT 10480 with the focal reducer and low-dispersion spectrograph (FORS1) attached to the 8m UT2 (Kueyen) at Paranal Observatory as part of our spectro-polarimetric survey of white dwarfs. The purpose of the survey was to search for white dwarfs with weak magnetic fields. We used the 600B grism combined with a slit-width of 1 arcsecond that provided a resolution of 6.0 Å. The spectra covered the range between 3780 and 6180 Å. The observations were conducted on UT 2007 Nov 1 and consisted of a sequence of two consecutive exposures with an exposure time of 1360 s each. In the first exposure the Wollaston prism is rotated to and it is followed by a second exposure with the Wollaston prism rotated to from which we extracted the flux and circular polarization spectra.

Since the FORS1 spectra did not include H, we obtained two additional low-dispersion spectra with the ESO Faint Object Spectrograph and Camera (EFOSC2) attached to the New Technology Telescope (NTT) at La Silla Observatory on UT 2008 Oct 23. We used Grism 11 which has 300 lines per mm and a blaze wavelength of 4000 Å. The slit-width was set to 1 arcsecond, which resulted in a spectral resolution of Å. The exposure time of each spectrum was 1500 seconds. Observations were carried out at the parallactic angle and were flux calibrated with the flux standard Feige 110.

Figure 1 compares the low-resolution spectrum of Ca II lines obtained with EFOSC2 to the higher resolution spectrum of FORS1. The flux and circular polarization spectra clearly show the components, proving NLTT 10480 to be magnetic.

Figure 1: Flux spectra of the Ca II H&K lines in NLTT 10480 obtained with EFOSC2 (top) and FORS1 (middle), and circular polarization (bottom) spectrum obtained with FORS1. The dotted lines mark the position of the components and the dashed lines mark the components (see Sect. 3.2.3).

Finally, we obtained a set of echelle spectra of NLTT 10480 with the X-shooter spectrograph attached to the UT2 (Kueyen) at Paranal Observatory. The spectra were obtained at four epochs (UT 2010 Dec 10, 2011 Jan 9 and 26, and March 3). The 2011 Mar 3 spectrum was of much poorer quality and was excluded from the analysis. The spectra were obtained with the slit-width set to 0.5, 0.9, and 0.6 arcsecond for the UVB, VIS, and NIR arms, respectively. This set-up delivered a resolving power of 9100 for UVB, 8800 for VIS, and 6200 for NIR. The exposure time for each exposure was 2400 seconds.

Table 1 summarizes our spectroscopic observations. The signal-to-noise ratio in the summed X-shooter spectrum is per binned-pixel at 4000Å, while it is in the summed FORS1 spectrum and in the summed EFOSC2 spectrum at the same wavelength.

We searched for photometric measurements using VizieR. The Two Micron All Sky Survey (2MASS) listed infrared magnitudes, but only the magnitude was of acceptable quality. We also used the acquisition images from the X-shooter observations to estimate a magnitude for NLTT 10480. We used 11 acquisition images of Feige 110 obtained between UT 2010 Dec 10 and 2011 Jan 1, and set the zero point. Next, we determined an average magnitude for NLTT 10480 using our five acquisition images. We employed the atmospheric extinction table of Patat et al. (2011). Table 2 lists the photometric measurements.

Band Measurement Reference
1
2
2
: 2
RA (J2000.0) 03 17 12.08 3
Dec (J2000.0) 29 11 34.33 3
() ( mas yr, 162) 3
( mas yr, 159) 4
( mas yr, 160) 5
\tablebib

(1) Johnson , this work; (2) 2MASS (Skrutskie et al., 2006); (3) Revised NLTT (Salim & Gould, 2003); (4) SPM Catalog 2.0 (Platais et al., 1998); (5) Liverpool-Edinburgh High Proper Motion Catalogue (Pokorny et al., 2004).

Table 2: Photometry and astrometry

The SPM Catalog provides a photographic magnitude (). However, due to large uncertainties in the SPM and other photographic magnitudes, these are not as useful as our magnitude and the 2MASS magnitudes. The 2MASS magnitude is unreliable and the magnitude is uncertain. The index loosely constrains the temperature in the range K, but the more precise index implies that NLTT 10480 is a cool white dwarf with K (see Table 3 and Sect. 3.1).

NLTT 10480 is also characterized by a large proper-motion of  yr (Table 2). The kinematical properties were determined using the proper-motion and the X-shooter radial velocity measurement (see Sect. 4).

3 Analysis

3.1 Model atmospheres and spectral syntheses

We calculated a grid of model atmospheres for cool hydrogen-rich white dwarfs. The models are in convective and radiative equilibrium with the total flux converged to better than 0.01% in all layers. The model grid covers the effective temperature range K in 100 K steps and the surface gravity range in steps of 0.25 dex. The adopted treatment of the convective energy transport and pressure ionization effects are described in Kawka & Vennes (2006), but further improvements to the models will be described in a forthcoming publication. All relevant species (H, H, H, H, H) are included in the statistical equilibrium equation. We employed the H partition function of Neale & Tennyson (1995). Electrons contributed by identifiable trace elements (e.g., calcium) are also included in the charge conservation equation, although the ionization of hydrogen atoms and molecules dominate the electron budget.

The model atmospheres include opacities caused by H bound-bound, bound-free and free-free transitions, H bound-free and free-free transitions, HH collision-induced absorption (CIA, Borysow et al., 1997, 2001), and the H-H and H-H collision-induced absorptions in the far Ly wing (see Kowalski & Saumon, 2006) using opacity tables from Rohrmann et al. (2011). Finally, the H and H Rayleigh scattering are included along with electron scattering.

Synthetic colours as well as detailed hydrogen and heavy element line profiles are computed using the model structures. Table 3 lists some photometric properties of the cool models. The colour indices at shorter wavelengths are effected by the Ly collision-induced absorptions. Allard et al. (2008) calculated new H line profiles including self-broadening effects and found a half-width at half maximum (HWHM) % larger than estimated by Ali & Griem (1965, 1966) and comparable to the calculations of Barklem et al. (2000a). We adopted the H HWHM from Allard et al. (2008) and the H, and H cross-sections and velocity parameters, converted into HWHM, from Barklem et al. (2000a). We describe the heavy element line profiles in the following section.

(cgs) (K) (mag) (mag)
7.5 4 900 0.826 1.570
5 100 0.733 1.460
5 300 0.658 1.360
5 500 0.602 1.270
5 700 0.556 1.188
8.0 4 900 0.858 1.562
5 100 0.760 1.453
5 300 0.677 1.351
5 500 0.611 1.260
5 700 0.559 1.178
8.5 4 900 0.887 1.550
5 100 0.790 1.446
5 300 0.701 1.344
5 500 0.627 1.251
5 700 0.568 1.167
Table 3: Selected synthetic colours

3.2 Neutral and ionized line profiles

3.2.1 Line broadening

The dominant broadening mechanism is collision with hydrogen atoms. We employed the coefficients of Barklem et al. (2000b), where the full-width at half-maximum (FWHM) of the Lorentzian profiles is given by

(1)

where for Ca i and for Ca ii H&K at K, and for Ca i and for Ca ii H&K. Although the adopted broadening parameters do not include the effect of hydrogen molecules, these provide 50% of the gas pressure in some layers. Following the approximate treatment of Kurucz & Avrett (1981), the broadening parameter , and, therefore, hydrogen molecules may contribute to the total line width. We found that neither Ca i or Ca ii equivalent widths are significantly affected in models at  K, but abundances inferred from Ca i may be underestimated by a factor of in models at 4 900 K.

3.2.2 Zeeman effect

Fundamentals of stellar line formation in the presence of a magnetic field are described by Unno (1956) and Martin & Wickramasinghe (1981), who also describe significant magneto-optical effects. In particular, Unno (1956) showed that the effect of field inclination with respect to to the line-of-sight on the relative intensity of and components reaches a maximum at an angle of 55. Moreover, Martin & Wickramasinghe (1981) showed that taking into account magneto-optical effects may enhance the depth of the components upon certain conditions.

Kemic (1975) studied the quadratic Zeeman effect for the Ca II H and K lines and showed that the linear Zeeman effect at fields of 15 MG is still dominant.

The Ca II H and K lines are the result of transitions between the ground state with , and the excited states with and , respectively, where is the total angular momentum, is the orbital angular momentum and is the spin angular momentum. The Ca I line is the result of transitions between the ground state with and the excited state with .

The levels are split by a magnetic field into components defined by the magnetic quantum number :

(2)

where is the wavelength in Å, is the magnetic field in MG, is the electron charge, is the electron rest mass and is the speed of light. The Landé factor and the magnetic quantum number of the upper and lower levels are given by and , respectively. Landé factors for calcium and other elements except iron were calculated assuming LS coupling:

(3)

For the 4S state of Ca II, the experimentally determined factor of 2.00225664 (Tommaseo et al., 2003) agrees with the theoretically calculated factor based on the LS coupling scheme. Similarly, for the 3p P state of Al I, the experimentally determined factor of (Martin et al., 1968) agrees with the LS coupling scheme calculated factor. For iron, the Landé factors were obtained from the Vienna Atomic Line Database (VALD)111http://vald.astro.univie.ac.at (Kupka et al., 2000)..

The permitted transitions are defined by , where defines the components and the components.

3.2.3 Opacity and line intensities

The relative intensities of the Zeeman components are computed following Condon & Shortley (1963). They found for the transitions where and ( components)

(4)

or where ( components)

(5)

Similarly, they found for transitions where and for the components

(6)

and for the components

(7)

Finally, for transitions where , the relative intensities are for the components

(8)

and for the components

(9)

Table 4 lists the total angular momenta, Landé factors, magnetic quantum numbers for the various transitions of calcium in a magnetic field of 0.513 MG. The relative intensities for the different components are also provided.

Figure 2: Linear Zeeman splitting of Ca II (H and K) (top), Ca I 4226 Å (bottom left), and H (bottom right) lines at  MG compared to the observed Zeeman splitting in the spectrum of NLTT 10480. The dotted lines indicate the components and dashed lines indicate the components.
Lower level Upper level Rel. Int.
(Å)
Ca ii3933.663
2 3927.482
3929.955
3932.427
3934.899
3937.371
3939.844
Ca ii3968.469
2 3963.436
3965.953
3970.985
3973.502
Ca i4226.728
0 4222.446
4226.728
4231.010
Table 4: Zeeman splitting at  MG (Ca i and Ca ii).

The observed relative intensities of the and components will also vary as a function of the angle between the magnetic field lines and the line of sight (Unno, 1956; Martin & Wickramasinghe, 1981). The monochromatic opacity of the components depends on the angle between the magnetic field axis and the line of sight:

(10)

Similarly, the monochromatic opacity of the components vary as

(11)

where the peak opacities and are given at and, as shown earlier, are calculated following Condon & Shortley (1963). For example, for hydrogen Balmer lines or Ca i4226 we have that

(12)

Figure 2 shows the observed linear Zeeman splitting of Ca II H&K, Ca I4226Å, and H lines obtained with the X-shooter spectrograph and the predicted line positions as a function of the magnetic field strength. Interestingly, the observed components for both Ca ii lines appear weaker than the components showing the effect of inclination of the field with respect to the line-of-sight. No significant variation in the line positions or intensities were noted between the three usable exposures.

Figure 3: Balmer lines (H to H) and best-fitting model ( K, ) showing prominent Zeeman-split H line (left panel), and (right panel) contours at 66, 90, and 99% confidence (dashed lines) in the (, ) plane. The measured calcium abundance from Ca ii lines () is drawn (full lines) as a function of the assumed temperature and surface gravity and labelled with the logarithm of the abundance. The thick line shows the range of temperature and surface gravity where the abundance measurements based on Ca i or Ca ii are consistent.

We fitted the ratio of the Ca II and line equivalent widths varying the inclination and determined . However, including magneto-optical effects would likely decrease the measured inclination.

3.3 Magnetic field and atmospheric parameters

We determined the averaged surface magnetic field of NLTT 10480 using H and the calcium lines. We first measured the centroids of the Zeeman components of Ca II, Ca I and H, where the spectrum was already adjusted to the solar system barycentre. We then fitted these lines to the predicted line positions by varying the magnetic field strength (assumed constant over the surface) and the velocity and by minimizing the . For calcium, we determined a surface-averaged magnetic field of  MG with a velocity of km s. Using H, we obtained  MG and km s. The measurements are consistent within 2 and taking the average we found and km s. Subtracting the gravitational redshift ( km s) of the white dwarf from the measured velocity results in the actual line of sight velocity of the star km s.

In principle, the effective temperature and surface gravity may be constrained simultaneously by fitting the Balmer line profiles. The strong H and weaker show the effect of Zeeman line splitting, while H is extremely weak. Figure 3 shows the best-fitting model to the Balmer lines that includes an approximate treatment of line opacities in a weak magnetic field. The 99% confidence contour corresponds to an uncertainty of 200 K in the temperature, and 0.5 dex in the logarithm of the surface gravity. The errors are statistical only and do not take into account possible systematic errors in the modelling of the line profiles.

3.3.1 Abundance of heavy elements

We determined the calcium abundance by fitting the Ca ii line profiles using minimization techniques where we varied the calcium abundance at each grid point in the () plane while fixing the magnetic field strength at 0.519 MG (Sect. 3.3). Figure 3 shows the resulting abundance map: the calcium abundance and its uncertainty depend on the adopted atmospheric parameters and .

Figure 4 shows best-fitting models to the calcium lines at () and at a lower temperature of 4 900 K (). The calcium abundance varies between (highest temperature) and (lowest temperature), but the calcium ionization balance favours a lower temperature than estimated with the Balmer lines (Fig. 3). The discrepancy is partially resolved by increasing the metallicity of the atmosphere. Using a set of heavy elements with low first-ionization potentials and higher solar abundances including C, N, and O, then Na to Si, and, finally, K to Cu, we found that a high metallicity of solar would restore the calcium ionization balance with an abundance of . However, a much lower abundance of heavy elements is present in the atmosphere of NLTT 10480.

Figure 5 shows the predicted location of the strongest lines of Fe I, Si I, Al I and Na I in the X-shooter spectrum. We calculated the position of the Zeeman-split lines for these elements assuming a magnetic field of 0.519 MG. For aluminium, some weak lines appear to match the predicted positions. However, the putative Al i3967.8532 component should be accompanied by stronger 3957.7353 and 3960.2458 components that are not clearly identified. Another possible identification for this feature is an interstellar Ca H line, although Ca K is not detected in the spectrum. Spectra with higher signal-to-noise ratios and better resolution are needed to clarify this identification.

We estimated sodium, aluminium, silicon and iron abundance upper limits using the spectral ranges covered in Figure 5. We found , and , while . The abundances relative to solar range from to times solar, or a few orders of magnitude below the level required to significantly increase the electron density and alter the calcium ionization balance.

Figure 4: X-shooter spectrum of the Ca i (bottom) and Ca ii (H & K: middle and top, respectively) lines and best-fitting models at () K and (thick lines), and K and (thin lines). The wavelength scale is normalized to , where  MG. Therefore, the line positions match the factors listed in Table 4 (vertical dashed lines). All models assume .
Figure 5: Spectra in the vicinity of the strongest Fe I (3734.8638, 3749.4851, and 3758.2330Å), Si I (3905.523 Å), Al I (3944.0060 and 3961.5200 Å), and Na I (5889.951 and 5895.924 Å) lines compared to the predicted Zeeman-split line positions assuming a magnetic field of 0.519 MG.

4 Summary and discussion

We found that the high proper-motion star NLTT 10480 is a rare example of cool white dwarfs with trace heavy elements and a weak magnetic field revealed in both the H circular polarization spectrum and Zeeman line-splitting. Other examples of this class of white dwarfs are the DZ white dwarfs LHS 2534 (Reid et al., 2001) and G 165-7 (Dufour et al., 2006), the DAZ white dwarfs G 77-50 (Farihi et al., 2011) and possibly LTT 8381 (Koester et al., 2009). Based on independent diagnostics (Table 5), we estimated a temperature of K and a surface gravity close to . However, we noted systematic differences in temperature measurements based on the calcium ionization ratio, the colour index, and the Balmer line profiles amounting to 400 K. The weaker Ca i lines favour a lower temperature than estimated using Balmer lines alone. The temperature measured with the colour index also favours a lower temperature. We found that increasing the heavy-element contribution to the electron density helps restore the calcium ionization balance, but we also found that the required abundance exceeds upper limits on the abundance of Na, Al, Si, and Fe by a few orders of magnitude. We are left with the possibility that subtle effects on line formation (broadening parameters, magnetic-optical, …) caused by the magnetic field may influence temperature measurements based on Balmer line profiles.

Although our modelling of the hydrogen line profiles takes into account the effect of inclination, we neglected the magneto-optical effects and only approximated the full solution of the radiative transfer equations that ought to include all Stokes parameters (see Martin & Wickramasinghe, 1981). The effect of this approximation on the determination of the stellar parameters using Balmer line profile fitting may well amount to a few hundred degrees.

Fortunately, because ionized calcium is the dominant species, the abundance of calcium based on Ca ii lines is not sensitive to temperature. On the other hand, as we have demonstrated, it does show a mild dependence on surface gravity because a higher electron pressure favours neutral calcium.

Parameter Measurement Note
 MG 1
km s 1
K 2
K 3
3
Abundance 4
4
4
4
4
pc 5
km s 6
222(1) Sect. 3.2; (2) , Sect. 2; (3) Balmer lines, Sect. 3.3; (4) Sect. 3.3.1; (5) Based on apparent and absolute magnitudes (Sect. 4); (6) Based on proper-motion and the estimated distance.
Table 5: Properties of NLTT 10480.

Adopting conservative error bars for the temperature and surface gravity we calculated an absolute magnitude using the mass-radius relations of Benvenuto & Althaus (1999). The distance modulus implies a photometric distance pc. The object is relatively old with a cooling age Gyr, but with an uncertain mass (). We determined the Galactic velocity vector (Table 5) using our distance estimate and radial velocity measurement (Sect. 3.3), and published proper-motion. We employed the algorithm of Johnson & Soderblom (1987). The kinematics imply membership to the old thin disk (Sion et al., 1988) consistent with the upper range of our age estimate.

The acquisition of broadband and photometry and of a parallax measurement should help determine the atmospheric parameters more precisely. The stellar radius, hence surface gravity measurement would be improved with a parallax measurement. Accordingly, the error on the calcium abundance measurement would be reduced. Accurate photometry would also allow us to investigate possible infrared excess and the presence of a debris disc.

The DAZ white dwarfs G 7750 and G 17474 are part of a survey including the coolest known DAZ white dwarfs (Zuckerman et al., 2003). In cool convective white dwarfs, heavy elements diffuse below the mixed convective layers, and their presence in white dwarf atmospheres is transitory. Koester & Wilken (2006) estimated the diffusion time-scale for various heavy elements. The accretion rate required to sustain a given mass fraction in the atmosphere is given by

(13)

where is the mass of the convection zone and the diffusion time-scale at the bottom of the convection zone, where diffusion is allowed to take place. The ratio is the ratio of the measured mass-fraction to the accreted mass fraction. Therefore, the mass accretion rate of any particular element is

(14)

Adopting, in the appropriate temperature range, a value for the slow-varying ratio to diffusion time scale of in units of  yr or in units of g s (Koester & Wilken, 2006), we estimated the mass accretion rate of calcium (in g s) to be

(15)

where , and and are the atomic weights. Assuming calcium is accreted as part of a solar-composition flow, the total mass accretion rate (including hydrogen) is g s or  yr.

Our measured error on the calcium abundance of dex translates into a similar error on the calculated accretion rate onto the white dwarf surface. The true error may well be much larger. Koester (2009) considers that the application of the mixing-length theory to the structure of convection zones may underestimate the mass of the mixed layers by orders of magnitude. The effect of “under”-shooting below the convection zone may affect diffusion time-scale estimates. Therefore, the precision claimed in measuring abundance of parent bodies may be over-estimated.

Farihi et al. (2011) propose that the model of Potter & Tout (2010)333See also Nordhaus et al. (2011) for the presence of a magnetic field in post-common envelope (CE) binaries could also be applied to CE episodes with planetary rather than stellar secondary components. Whether the magnetic field is acquired during such a process, or whether it is a fossil field cannot be ascertained for individual objects but rather from population studies (see, e.g., Kawka & Vennes, 2004a; Kawka et al., 2007; Wickramasinghe & Ferrario, 2005). In the case of NLTT 10480, which is old ( Gyr) with relatively short diffusion time-scales, the present-day metallicity is not linked to the CE event that potentially generated the magnetic field, but more likely to a recent accretion event.

A low incidence of planetary systems would imply a low incidence of weak magnetic fields ( MG). Current data indicate a low incidence of weak magnetic fields, and Kawka et al. (2007) found that 6 out of 53 local white dwarfs ( pc) observed with sufficient accuracy to unveil fields weaker than 1 MG were found to harbour such a low field. Moreover, Kawka & Vennes (2004a) found that low-field white dwarfs lack progenitors, a gap that could be filled with the CE-mechanism.

Early results from the Kepler survey also indicate a low incidence of very large planets in short-period orbits ( days, or AU) that are likely to trigger the field-generating CE events postulated by Farihi et al. (2011) based on the model of Potter & Tout (2010). Planets with sizes ranging from 8 to 32 () may occur within 0.25 AU of solar-type stars with a frequency of 1.3% (Howard et al., 2011). Borucki et al. (2011) quote a similar fraction for Jupiter-sized or larger planets within 0.2 AU based on the first data set from Kepler. Both studies noted a declining occurrence with increasing separation. Overall, large planets that are likely to participate in a CE phase may surround a few percents of white dwarf progenitors and generate, as observed, a similar percentage of low-field white dwarfs.

Acknowledgements.
S.V. and A.K. are supported by GA AV grant numbers IAA300030908 and IAA301630901, respectively, and by GA ČR grant number P209/10/0967. A.K. also acknowledges support from the Centre for Theoretical Astrophysics (LC06014). We thank the anonymous referee for several comments that improved the paper. This research has made use of the VizieR catalogue access tool, CDS, Strasbourg, France. This publication makes use of data products from the Two Micron All Sky Survey, which is a joint project of the University of Massachusetts and the Infrared Processing and Analysis Center/California Institute of Technology, funded by the National Aeronautics and Space Administration and the National Science Foundation.

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