Element spots in Ap- and HgMn-stars from current-driven diffusion

0.09 MB·

by  Vadim Urpin

Astron.Nachr./AN325(2004)x,xxx–xxx
Element spots in Ap and Hg-Mn stars from current-driven diffusion
V. URPIN1,2
1)INAF,OsservatorioAstrofisicodiCatania,ViaS.Sofia78,95123Catania,Italy
2)A.F.IoffeInstituteofPhysicsandTechnology,194021St.Petersburg,Russia
6
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0 January26,2016
2

n
a
J
Abstract.Thestarsofthemiddlemainsequenceoftenhavespot-likechemicalstructuresattheirsurfaces.Weconsiderthe
5
2 diffusionprocesscausedbyelectriccurrentsthatcanleadtotheformationofsuchchemicalspots.Diffusionwasconsidered

using partial momentum equations derived by the Chapman-Enskog method. We argue that diffusion caused by electric
]
R currents can substantially change the surface chemistry of stars and form spotted chemical structures even in a relatively
S weakmagneticfield.TheconsideredmechanismcanberesponsibleforaformationofelementspotsinHg-MnandAp-stars.
.
h
(cid:13)c0000WILEY-VCHVerlagGmbH&Co.KGaA,Weinheim
p
-
o
r 1. Introduction cientlystrongtomagnetizeplasmaandmakediffusionanisotropic.
t
s AnisotropyofdiffusionischaracterizedbytheHallparame-
a Diffusion can lead to evolutionof atmosphericchemistry in ter,x =ω τ ,whereω = eB/m cisthegyrofrequency
[ Be e Be e
starsandbethereasonofchemicalpeculiarities.Thispartic- ofelectronsandτeistheirrelaxationtime.Ifthebackground
1 ularlyconcernsthestarsofthemiddlemainsequencethatof- plasmais hydrogen,thenτe = 3√me(kbT)3/2/4√2πe4nΛ
v tenhaverelativelyquiescentsurfacelayers.Manystarswith (see,e.g.,Spitzer1998)wherenandT arethenumberden-
6
peculiarchemicalabundancesshowlinevariationscausedby sityofelectronsandtheirtemperature,ΛistheCoulomblog-
9
elementspotsontheirsurface(see,e.g.,Pyper1969,Khokhlovaarithm.If x 1, theratesof diffusionalongandacrossthe
5
≥
6 1985,Silvesteretal.2012).Itwasthoughtthatchemicalspots magneticfieldaredifferentanddiffusioncanleadtoinhomo-
0 canonlyoccurinthepresenceofastrongmagneticfield.In- geneous element distributions. The condition x 1 yields
1. deed, some Ap stars show variations of both spectral lines thefollowingestimate ofthemagneticfieldthatm≥agnetizes
0 and magnetic field strength that can be related to rotation plasma
6 of chemical and magnetic spots. Often such stars have the
1 strongest concentration of heavy elements around the mag- B ≥Be =2.1×103n15T4−3/2Λ10 G, (1)
v: netic poles(see, e.g.,Havnes1975).Note thata reconstruc- where Λ10 = Λ/10, n15 = n/1015, and T4 = T/104K.
i tion ofthe stellar magneticgeometryfromobservationsisa Somestarswithchemicalspotshavesuchastrongmagnetic
X
verycomplexproblem.ThemagneticDopplerimagingcode fieldanddiffusioncanbeanisotropicthere.
r
a developed by Piskunov & Kochukhov(2002) makes it pos- In recent years, however, the discovery of chemical in-
sible to derive the magnetic map of a star self-consistently homogeneitiesin the so-called Hg-Mn stars has rised some
with the distribution of the chemical elements. The recon- doubts regarding their magnetic origin. The aspect of spot-
structionsshowthatthemagneticandchemicalmapsofstars likechemicalstructuresinHgMnstarswasdiscussedfirstby
can be very complex (Kochukhovet al. 2004a) and usually Hubrig& Mathys(1995).In contrastto Ap-stars, no strong
chemicalelementsdonotexhibitacorrelationwiththemag- madneticfield of kG orderhaseverbeen detectedin HgMn
neticgeometry.Thecalculateddistributionsdemonstratethe stars. For instance, Wade et al. (2004) find no longitudinal
complexity of diffusion in Ap-stars and show that chemical fieldabove50GinthebrightestHg-MnstarαAndwithchem-
distributionsare affected by a numberof poorlyunderstood icalspotsatthesurface.Theauthorsestablishanupperlimit
phenomenaandarenotdirectlyrelatedtothestrengthofthe of the globalfield at 300 G that is not sufficient to mag-
≈
magneticfield. netize plasma. Weak magnetic fields in the atmospheres of
Often, the chemical spots on the surface of stars are re- Hg-Mnstarshavebeendetectedbyanumberofauthors(see,
lated to anisotropic diffusion in the magnetic field. Indeed, e.g.,Hubrig&Castelli2001,Hubrigetal.2006,Makaganiuk
the magnetic field of Ap-stars (B 103 104 G) is suffi- etal.2011,2012).InarecentstudybyHubrigetal.(2012),
∼ −
(cid:13)c0000WILEY-VCHVerlagGmbH&Co.KGaA,Weinheim
1
thepreviousmeasumentsofthemagneticfieldhavebeenre- velocity is zero and only small diffusive velocities are non-
analysed and the presence of a weak longitudinal magnetic vanishing, the partial momentum equation for the species i
fieldupto60-80GhavebeenrevealedinseveralHgMnstars. canbewrittenas
The complex interrelations between the magnetic field and V
the chemical structures show how incomplete is our under- pi+Zieni E+ i B +Rie+RiH+Fi =0,(5)
−∇ (cid:18) c × (cid:19)
standingofdiffusionprocessesinstars.
whereZ isthechargenumberofthespeciesi,p ,andn are
Inthispaper,weconsideronemorediffusionmechanism i i i
itspartialpressureandnumberdensity,V isitsvelocity,and
thatcontributestoaformationofchemicalspotsinstars.This i
E isthe electric field. TheforceF is the externalforceon
mechanism is relevant to electric currents and has not been i
speciesi;instars,F isusuallydeterminedbygravitygand
studiedinstellarconditionsyet.Weconcentrateonthemain i
theradiationforce.TheforcesR andR arecausedbythe
qualitativefeaturesofthisprocessandcomparethediffusion ie iH
interactionofionsiwithelectronsandprotons,respectively.
rate caused by the presence of electric currentsand the rate
NotethatforcesR andR areinternalandtheirsumover
ofotherdiffusionprocesses.Weshowthatinteractionofthe ie iH
allplasmacomponentsis zeroinaccordancewithNewton’s
electric current with ions leads to diffusion in the direction
third law. Since diffusive velocities are typically small, we
perpendiculartothebothelectriccurrentandmagneticfield.
Suchdiffusioncanalterthesurfacechemicaldistributionsat neglectthetermsproportional(Vi·∇)V1inthemomentum
equation(5).
asubstantiallyweakermagneticfieldthanB .
e
Thes-andϕ-componentsofEq.(5)yield
d V
2. Basicequations (nikBT)+Zieni Es+ iϕB +Ries+RiHs =0,(6)
− ds (cid:18) c (cid:19)
V
Consider a cylindrical plasma configuration with the mag- Z en E isB +R +R =0.(7)
i i ϕ ieϕ iHϕ
(cid:18) − c (cid:19)
netic field parallel to the axis z, B = Be ; (s,ϕ,z) and
z
(es,eϕ,ez) are cylindrical coordinatesand the correspond- TheforceRie iscausedbyscatteringofionsionelectrons.
ingunitvectors.We assumethatthemagneticfielddepends Ifniissmallcomparedtothenumberdensityofprotons,Rie
onthecylindricalradiusalone,B =B(s).Then,theelectric isgivenby
currentis Z2n
R = i iR (8)
ie e
j = (c/4π)∂B/∂s. (2) − n
ϕ
−
where R is the force acting on the electron gas (see, e.g.,
e
Wesupposethatjϕ 0atlargesand,hence,B B0=const Urpin1981).Sincen n,R isdeterminedmainlybyscat-
→ → i e
at s . Note that B(s) can not be an arbitrary func- ≪
tering of electrons on protonsbut scattering on ions i gives
→ ∞
tionofsbecause,generally,themagneticconfigurationscan
a small contribution. Therefore, we can use for R the ex-
e
be unstable for some dependences of B(s) on s (see, e.g.,
pression for one componenthydrogenplasma calculated by
Tayler1973,Bonanno&Urpin2008a,bformoredetail).The
Braginskii(1965).Inourmodelofacylindricalplasmacon-
timescale of this instability is usually shorter than the diffi-
figuration,thisexpressionreads
siontimescaleand,therefore,aformationofchemicalstruc-
turesinsuchmagneticconfigurationsisunlikely. Re =−α⊥u+α∧b×u−β⊥uT∇T −β∧uTb×∇T, (9)
Weassumethatplasmaconsistsofelectronse,protonsp, whereu= j/enisthedifferencebetweenthemeanveloc-
−
andasmalladmixtureofheavyionsi.Thenumberdensityof itiesofelectronsandprotons,b = B/B,α ,α ,βuT,and
⊥ ∧ ⊥
speciesiissuchsmallthatitdoesnotinfluencedynamicsof βuT arecoefficientscalculatedbyBraginskii(1965).Thefirst
∧
plasma.Therefore,thisspeciescanbetreatedastestparticles twotermsonther.h.s.ofEq.(9)describethestandardfriction
that interacts only with electrons and backgroundhydrogen forcecausedbya relativemotionofthe electronandproton
plasma.Thehydrostaticequilibriumreads gases.Thelasttwotermsonther.h.s.ofEq.(9)representthe
so-calledthermoforcecausedbyatemperaturegradient.This
1
p+ρg+ j B =0, (3) partofR isresponsibleforthermodiffusion.
−∇ c × e
TakingintoaccountEq.(2),wehave
wherepandρarethepressureanddensity,respectively,g =
c dB
gez is gravity. Since the backgroundplasma is hydrogen, u= e . (10)
−p 2nk T wherek istheBoltzmannconstant.Integrating 4πen ds ϕ
B b
≈
thes-componentofEq.(3),weobtain Inthispaper,weconsiderdiffusiononlyinarelativelyweak
magnetic field that does not magnetize electrons, x 1.
n=n0 T0 1+ 1 1 , (4) Substituting Eq.(10) into Eq.(8) and using coefficient≪s α⊥,
(cid:18)T (cid:19)(cid:18) β0 − β(cid:19) α ,βuT,andβuT withtheaccuracyinlineartermsinx,we
∧ ⊥ ∧
whereβ =8πp0/B2;(p0,n0,T0,β0)arethevaluesof(p,n,T,βo)btain
atsT→he∞pa.rtial momentumequationsin fully ionized multi- Rieϕ =Zi2ni(cid:18)0.51mτeeu+0.81xkBddTs(cid:19), (11)
componentplasma has been consideredby a numberof au- m dT
R =Z2n 0.21x eu+0.71k . (12)
thors (see, e.g., Urpin (1981)). If the mean hydrodynamic ies i i(cid:18) τ B ds(cid:19)
e
2
TheforceR is thesum oftwo termsaswell, R = where c2 = k T/m and c2 = B2/4πm n. Eq.(22) de-
′ ′′ iH iH i B i A p
R +R that are proportionalto the relative velocityof scribes the drift of ions i under the combined influence of
iH iH
ionsiandprotonsandthetemperaturegradient,respectively. n , T,andj.
i
′ ∇ ∇
ThefrictionforceR canbeeasilycalculatedifA =m /m
′ iH i i p ≫
1. Inthiscase, R (V V )buttakingintoaccount
iH ∝ H − i
that the mean velocity of the background plasma is zero in
ThediffusivevelocitygivenbyEq.(22)differsfromthe
ourmodel,thefrictionforcecanberepresentedas(see,e.g.,
standard expression used in astrophysical calculations (see,
Urpin1981)
e.g.,Chapman&Cowling1970,Burgers1969)bythepres-
R′iH ≈ 0.42mτiniZi2(−Vi), (13) ethnactethoifsatetremrmis∝caduBse/ddbs.yIstcfaotltleorwinsgforofmheoavuyr cioonnssidoenraetlieocn-
i
where τ = 3√m (k T)3/2/4√2πe4nΛ and τ /Z2 is the trons. The classical works by Chapman & Cowling (1970)
i i B i i
and Burgers (1969) derive the atomic diffusion coefficients
timescaleofion-protonscattering;weassumethatCoulomb
from the Boltzmann equation but these coefficients are bet-
logarithmsarethesameforalltypesofscattering.
′′ tersuitedtodiffusioninneutralgasesorplasmawithalarge
Thethermalpartofthefrictionforce,R ,hasbeencal-
iH chargeof the backgroundions. The pointis thatthese stud-
culated by Urpin (1981). Since there is no diffusion in the
′′ ies neglect scattering of impurities on electrons in plasma,
z-direction, the expression for R with accuracy in linear
iH andtakeintoaccounttheirscatteringonlyonthebackground
termsinmagnetizationcanbewrittenas
ions. The latter is correct if the charge of backgroundions,
R′′ =Z2n k (1.71 T 3.43yb T), (14)
iH i i B ∇ − ×∇ Z0, is large,Z0 1. In stellar plasmas, however,the main
≫
where background ions are usually protons and, hence, Z0 = 1.
y = eBτp, τ = 3√mp(kBT)3/2. (15) Therefore, neglecting the contribution of electrons into ki-
mpc p 4√2πe4nΛ neticprocessesisunjustified.Thisfactwasfirstclearlyunder-
stoodbyBraginskii(1965)inhistheoryoftransportphenom-
′′
Then,thecylindricalcomponentsofR are
iH enainahigh-temperatureplasma.Thisresultcanbeclarified
R =Z2n miV +1.71k dT , (16) by simple qualitative estimates. Indeed, the momentum of
iHs i i(cid:18)− τ is B ds(cid:19) electronsis m c (c = k T/m isthethermalvelocity
i e e e B e
∼
m dT ofelectrons),andtherateopfmomentumtransferbyelectrons
RiHϕ =Zi2ni(cid:18)− τiiViϕ−3.43ykB ds(cid:19). (17) to impurities is ∼ meceνe ∼ mece/τe where νe is the fre-
quencyofelectroncollisions.Ontheotherhand,themomen-
The momentun equation for the species i (Eq.(5)) de-
tumofprotonsis m c wherec = k T/m isthether-
pendsoncylindricalcomponentsoftheelectricfield,Esand malvelocityofpr∼otonpsapnd,correpsponpdinBgly,theprateofmo-
E .Thesecomponentscanbedeterminedfromthemomen-
ϕ mentumtransferbyprotonsis m c ν m c /τ where
tumequationsofelectronsandprotons ∼ p p p ∼ p p p
ν is the frequency of proton collisions. Comparing these
u p
(nk T) en E+ B +R =0, (18) expressions, we obtain that the rates of momentum transfer
B e
−∇ − (cid:16) c × (cid:17) by electrons and protons are of the same order and, hence,
(nk T)+enE R +F =0. (19)
−∇ B − e p neglecting the electron contribution is unjustified in plasma
Taking into account the condition (3) and the friction force withZ0 1.However,ifthebackgroundplasmaconsistsof
Re (Eq.(9))calculatedbyBraginskii(1965),weobtainwith ionswith∼thechargeZ0 1,thenoneshouldreplaceτp by
accuracyinlineartermsinx therelaxationtimeofthe≫backgroundionsthatis τ /Z4.In
p 0
∼
uB 1 m u dT thiscase,therateofmomentumtransferbyionsturnsoutto
E = 0.21 e x+0.71k , (20)
s − 2c − e (cid:18) τe B ds(cid:19) be∼ Z04 timesgreaterthanthatbyelectrons.IfZ0 ≫1,the
electron contribution is small and can be neglected. There-
1 m u dT
Eϕ = 0.51 e +0.81xkB . (21) fore,theclassicaldiffusiontheoryisjustifiedinthiscase.
−e (cid:18) τ ds(cid:19)
e
Substituting Eqs.(11)-(12), (16)-(17), and (20)-(21) into
Eqs.(6) and (7), we arrive at the expression for a diffusion
velocity,V .Theradialcomponentofthisvelocityreads The fact that the consistent consideration of scattering
i
on electrons leads to diffusion of heavy ions with the ve-
V =V +V +V , (22)
is ni T B locity dB/ds is well known in plasma physics and was
where firstdis∝cussedbyVekshteinetal.(1975).Thisprocessplays
dlnn dlnT dlnB
V = D i, V =D , V =D ;(23) an important role in diffusion of impurities from the walls
ni − ds T T ds B B ds ofthedischargechamberanddiaphragmsinadenseplasma
Vni andVT arethevelocitiesofordinarydiffusionandther- in tokamaks (see, e.g., Vekshtein 1987 for review). Even a
modiffusion,respectively,VB isthediffusivevelocityassoci- smallfractionofimpurityionscanconsiderablyaffectthera-
atedwiththeelectriccurrent.Thediffusioncoefficientsare diation, electrical conductivity,and other plasma parameter.
D = 2.4c2iτi, D = 2,4c2iτi(2.42Z2 0.71Z 1), Unfortunaly,thiseffectisusuallyneglectedinstudiesofdif-
Z2 T Z2 i − i− fusioninstarsbutwewillshowthatitcanplayanimportant
i i
2.4c2τ role in a spot formation, particularly,in weakly magnetized
D = A i(0.21Z 0.71),(24)
B i stars.
A Z −
i i
3
3. Distributionofions inthepresence of spotwherethemagneticfieldisweakerthantheexternalfield
electric currents B0. The quantity (µ 1) can reach large negative values
−
and,therefore,dependence(31)onthemagneticfieldisvery
Considertheequilibriumdistributionofelementsinourmodel. sharp. A combined influence of both thermo- and current-
Inequilibrium,wehaveV =0andEq.(22)yields drivendiffusioncanresultinarathercomplicateddistribution
is
ofelements.
dlnn D dlnT D dlnB
i = T + B . (25)
ds D ds D ds
The second term on the r.h.s. is caused by the presence of 4. Conclusion
electric currents and describes the current-driven diffusion.
Note thatthistype ofdiffusionis drivenby theelectric cur- Wehaveconsidereddiffusionofelementsinthesurfacelay-
rentratherthananinhomogeneityofthemagneticfield.Oca- ers of stars under a combined influence of different diffu-
sionally,theconditionsdB/ds=0andj =0areequivalent sionmechanisms.Aspecialattentionwaspaidtothecurrent-
6 6
inoursimplifiedmodel.Equationofhydrostaticequilibrium drivendiffusionthathasnotbeendiscussedyetinthecontext
(3)yields ofchemicalspotsonstars. Thediffusionvelocitycausedby
d B dB electriccurrentcanbecomparableorhigherthanthevelocity
(nkBT)= . (26) ofthermodiffusion.Forinstance,ifelectronsarenotmagne-
ds −8π ds
tized (x < 1) the velocities of thermo- and current-driven
Substitutingexpression(26)intoEq.(25)andintegrating,we
diffusionscanbeestimatedas
obtain
ni = T ν n µ, (27) VT ∼ 5Lc2iτi, VB ∼ Ac2ALτi , (32)
ni0 (cid:18)T0(cid:19) (cid:18)n0(cid:19) whereL TandL arethielBengthscalesofT andB.Thecon-
T B
where dition V > V is satisfied if c 2c A1/2(L /L )1/2
ν =2Zi2+0.71Zi−1, or B T A ≫ i i B T
µ=−2Zi(0.21Zi−0.71), (28) B >2.6 102n1/2T1/2 LB 1/2 G, (33)
where ni0 is the value of ni at s . Denoting the local × 15 4 (cid:18)LT(cid:19)
→ ∞
abundance of the element i as γi = ni/n and taking into where n15 = n/1015cm−3 and T4 = T/104K. It appears
accountEq.(4),wehave that even a relatively weak magnetic field ( 10 100 G)
∼ −
ν µ−1 ν−µ+1 µ−1 canbethereasonofcurrent-drivendiffusionwiththevelocity
γ T n T 1 1
i = = 1+ ,(29) greaterthanthatofthermodiffusion.FromEq.(32),onecan
γi0 (cid:18)T0(cid:19)(cid:18)n0(cid:19) (cid:18)T0(cid:19) (cid:18) β0 − β(cid:19) estimatethevelocityofcurrent-drivendiffusionas
owfhieornesγiis0d=eternmi0i/nned0.bIytbtuortnhsthoeuttetmhaptetrhaetulroecaanldabmuangdnaentcice VB ∼1.1×10−4Ai−1/2B42n−152T43/2Λ10L−B110 cm/s, (34)
field. The dependence of γi on T is very sensitive to the whereΛ10 =Λ/10,B4 =B/104G,andLB10 =LB/1010cm.
charge number of ions. For example, if Zi = 1, the expo- ThevelocityVB turnsouttobesensitivetothefield(∝ B2)
nentinEq.(29)isν µ+1 = 1.71butitisaslargeas8.26 and,therefore,diffusionin a weakmagneticfield requiresa
−
ifZ =2.Therefore,evenasmallchangeinthetemperature longertimetoreachequilibrium.
i
canbethereasonofasignificantvariationinthelocalabun- Theconsideredmechanismcanformchemicalspotseven
danceofchemicalelements.Ifthemagneticfieldisconstant if the magnetic field is relatively weak whereas other diffu-
thenabundanceanomaliesaredeterminedbythethermodif- sion processes produce spots only if the magnetic field is
fusionalone.Inthiscase,wehave substantially stronger. For example, the radiative force and
γ T 2.42Zi2−0.71Zi gravity can generally be responsible for chemical inhomo-
i = . (30) geneities in stars (see, e.g., Vauclair et al. 1979, Michaud
γi0 (cid:18)T0(cid:19) et al. 1981). The radial diffusion velocity driven by these
Therefore, the regions with a higher temperature, T > T0, forcescanberelativelylarge,andthedistributionofimpuri-
should be overabundant by heavy elements but the regions tiesreachesaradialequilibriumonashorttimescale(Michaud
withalowertemperatureshouldbeunderabundant. 1970).Iftheradiativeandgravitationalforcesareofthesame
Local abundances are also flexible to the field strength orderofmagnitudethenthevelocityofradialdiffusioncanbe
and,particularly,thisconcernsveryheavyions.Ifvariations estimatedas
ofthetemperatureareneglidgibleandT T0,thenthedis- V gτ (35)
≈ r i
tributionofelementsisdeterminedbythecurrent-drivendif- ∼
(see Vauclair et al. 1979). This velocity is typically greater
fusionalone.Inthiscase,
than V in the surface layers of stars but the radial diffu-
γi = 1+ 1 1 µ−1. (31) sioncaBnnotformchemicalspotsif theradiativeforceandg
γi0 (cid:18) β0 − β(cid:19) havesphericalsymmetry.Departuresfromsphericitycanbe
Notethattheexponent(µ 1)isalwaysnegativeifZ 3 causedbythemagneticfieldsincethediffusionvelocityde-
i
and,hence,heavyelement−swithZ 3areindeficit(γ≥< pends on its direction and strength. For instance, the radial
i i
γi0)intheregionwithaweakmagne≥ticfield(B > B0)but, diffusionvelocitiesdifferbyatermoftheorderof
onthecontrary,suchelementsshouldbeoverabundantinthe ∆V V (ω τ /Z2)2 (36)
∼ r Bi i i
4
ifthemagneticfieldisparallelandperpendiculartogravity; Acknowledgements.TheauthorthankstheRussianAcademy
ω =eB/m cisthegyrofrequencyofimpurities(see,e.g., ofSciencesforfinancialsupportundertheprogrammeOFN-
Bi i
Vauclair et al. 1979, Alecian & Stift 2006). This difference 15.
in the radial velocities rather than V itself leads to forma-
r
tionofaspottedstructurebecausespotscannotbeformedif
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but the field is tangential, heavy ions drift basically in the Silvester,J.,Wade,G.A.,Kochukhov,O.,Bagnulo,S.,Folsom,C.P.,
tangentialdirectionandcanformchemicalspots. Hanes,D.2012.MNRAS,426,1003
Spitzer L. 1998. Physical Processes in the Interstellar Medium.
Themechanismconsideredcanoperateinvariousastro-
Wiley-VCH
physicalbodieswheretheelectriccurrentsarenon-vanishing.
Tayler,R.J.1973.MNRAS,161,365
Like other diffusion processes, the current-driven diffusion Urpin,V.1981.Ap&SS,79,11
canleadtoaformationofchemicalspotsifthestarhasrela- Urpin,V.,Geppert,U.,&Konenkov,D.1998.MNRAS,295,907
tivelyquiescentsurfacelayers.Thatisthecase,forexample, Vauclair,S.,Hardorp,J.,&Peterson,D.1979.ApJ,227,526
forwhitedwarfsandneutronstars.Manyneutronstarshave Vekshtein,G.,Riutov,D.,&Chebotaev,P.1975.SvJPP,1,220
Wade, G., Abecassis, M., Auriere, M., et al. 2004, in “Magnetic
strong magnetic fields and, most likely, topology of these
Stars”(eds.Yu.Glagolevskij,D.Kudryavtsev,andI.Romanyuk),
fieldsisverycomplexwithspot-likestructuresatthesurface
p.108-113.
(see,e.g.,Bonannoetal.2005,2006).Asitwasdiscussedin
this paper, such magnetic structures can be responsible for
the formation of a spot-like element distribution at the sur-
face.Suchchemicalstructurescanbeimportant,forinstance,
fortheemissionspectra,diffusivenuclearburning(Chang&
Bildsten2004,Brownetal.2002),etc.Evolutionofneutron
starsisverycomplicated,particularly,inbinarysystems(see,
e.g., Urpin et al. 1998) and, as a result, a surface chemistry
canbecomplicatedaswell.Diffusionprocessesmayplayan
importantroleinthischemistry(see,e.g.,Brownetal.2002,
Medin&Cumming2014)andcanbethereasonofchemical
sportsonthesurfaceofthesestars.