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M on.N ot.R .A stron.Soc.000,1{16 (2008) Printed 23 June 2013 (M N LATEX style � le v2.2)

Strati�cation and Isotope Separation in C P Stars?

C.R.Cowley1,yS.Hubrig2,and J.F.Gonz�alez31D epartm entofA stronom y,U niversity ofM ichigan,Ann Arbor,M I 48109-1042,U SA2European Southern O bservatory,Casilla 19001,Santiago 19,Chile3Com plejo A stron�om ico ElLeoncito,Casilla 467,5400 San Juan,Argentina

A ccepted .R eceived ;in originalform

A B ST R A C T

W einvestigatetheelem entaland isotopicstrati�cation in theatm ospheresofselected

chem ically peculiar (CP) stars ofthe upper m ain sequence.Recon�guration ofthe

UVES spectrograph in 2004 hasm adeitpossibleto exam ineallthreelinesofthe Ca

iiinfrared triplet.M uch ofthe m aterialanalyzed wasobtained in 2008.

W e support the claim ofRyabchikova,K ochukhov & Bagnulo (RK B) that the

calcium isotopes have distinct strati�cation pro�les for the stars 10 Aql,HR 1217,

and HD 122970,with theheavy isotopeconcentrated toward thehigherlayers.Better

observationsare needed to learn the extentto which 40Ca dom inatesin the deepest

layersofallorm ostCP starsthatshow thepresenceof48Ca.Thereislittle evidence

for 40Ca in the spectra ofsom e HgM n stars,and the infrared tripletin the m agnetic

starHD 101065 iswell�tby pure 48Ca.In HR 5623 (HD 133792)and HD 217522 it

islikely thatthe heavy isotope dom inates,though m odels are possible where thisis

notthe case.

W hile elem entalstrati�cation is surely needed in m any cases,we point out the

im portanceofincludingadjustm entsin theassum ed Te� and log(g)values,in attem pts

to m odelstrati�cation.W e recom m end em phasis on pro�les ofthe strongest lines,

wherethe in uence ofstrati�cation ism ostevident.

Isotopicm ixtures,involving the4 stablecalcium nuclideswith m assesbetween 40

and 48 areplausible,butarenotem phasized.

K ey w ords: stars:atm ospheres{stars:chem ically peculiar{stars: m agnetic �elds

{stars:abundances {stars:individual: HR 1217 {stars:individual: HR 1800 {

stars:individual:HD 101065 {stars:individual:HD 122970 {stars:individual:HR 5623

{stars:individual: HR 7143 {stars:individual: 10 Aql {stars:individual: HR 7245 {

stars:individual:HD 217522

1 R A T IO N A LE A N D IN T R O D U C T IO N

Thecurrentstudy wasundertaken to solidify ourknowledge

ofchem icaland isotopic strati�cation ofcalcium in chem -

ically peculiar (CP) stars ofthe upper m ain sequence.W e

hope such knowledge willlead to an im proved understand-

ing of the com plex physicalprocesses taking place in the

atm ospheresofthese stars.

Previouswork (cf.Cowley and Hubrig 2005,henceforth

PaperI)hasdem onstrated clearly the presence ofrare iso-

topes ofcalcium in stars as di�erent as the �eld HZB star

Feige86 (Te� = 16430K )and Przybylski’sstar(HD 101065,

Te� = 6600K ).

? Based on observationsobtained atthe European Southern O b-

servatory,Paranaland La Silla,Chile (ESO program m es 65.L-

0316(a),68.D -0254(A ),076.D -0169(A ) and 081.D -0498(A ).

y E-m ail:cowley@ um ich.ed

LinesoftheCaiiinfrared triplet(IRT)haveeasily m ea-

surableisotopeshifts,very nearly 0.20 �A between48Ca and

40Caforallthreelines(N�ortersh�auser,etal.1998).Thelarge

shiftsarise because ofthe unusualnature ofthe 3d orbitals

ofthe ground term ofthe IRT;they have collapsed below

the 4p subshell.O therCa iilines show farsm aller isotopic

shifts,ofthe orderofm illiangstrom s.

In a few cases,e.g.the HgM n star HR 7143 (Castelli

and Hubrig 2004),the isotope-sensitive lines appear both

sym m etrical,and shifted entirely to the wavelengthsofthe

rare isotope,48Ca.This isotope com prises only som e 0.2%

ofterrestrialcalcium .

Ryabchikova(2005)and hercoworkers�nd thatin roAp

stars the cores ofthe pro�les indicate48Ca,but the wings

are arguably produced by the com m on isotope40Ca.

Ifonly thecoresoftheisotope-sensitivelinesareshifted,

theobservationsm ay bereproduced by a m odelwith a thin

layer of the rare heavy calcium isotope. In this case, the

2 C.R.Cowley,S.Hubrig,and J.F.Gonz�alez

relative am ountofthe exotic species,in term sofa colum n

density above opticaldepth unity,could be quite sm all{far

sm aller than ifthe bulk ofthe line absorption were due to48Ca.Itisim portantto know which,ifeither,ofthese sce-

nariosisdom inant.

W e have exam ined severalline pro�les in som e detail

forseven stars.The following discussion isbased on several

possible m odels,with and withoutstrati�cation.In the for-

m ercase,wecom puted pro�lesbased on both elem entaland

elem entalplusisotopic strati�cation.Autom ated aswellas

trialand errorm ethodswereused.D etailsofallm odelsand

techniques considered would not be appropriate here.W e

presentan eclectic resum �e.Speci�c details are available on

requestfrom CRC.

2 ELEM EN TA L ST R A T IFIC A T IO N

It is generally accepted that the outer layers of CP stars

are chem ically di�erentiated from their bulk com position.

The m echanism responsible for this separation (M ichaud

1970)iscapableofproducing di�erentiation within thepho-

tosphere,or line-form ing regions ofthese stars.Such sepa-

ration isnow widely referred to asstrati�cation (cf.D woret-

sky 2004).Early indicationsofthe need forvertical,chem -

icalor density structures that depart from a classicalone-

dim ensional,chem ically hom ogeneousatm osphericstructure

weredescribed by Babcock (1958),and analyzed in som ede-

tailin a seriesofpapersby Babel(cf.Babel1994).

Them oststriking indicationsofstrati�cation arein the

cores ofthe Ca iiresonance lines,particularly the K -line.

Babel (1992) proposed a wind m odelwith an abundance

pro�le thatreproduced the sharp,deep coresofthe H-and

K -lines(see hisFig.4).

Cowley,Hubrig & K am p (2006)presented a shortatlas

ofK -line cores in CP and norm alstars.They also showed

(cf.theirx6)thatan ad hocm odi�cation ofthetem perature

distribution would also givecoressim ilartothoseillustrated

in theirpaper.A sharp drop in theoverallatm osphericden-

sity in a chem ically hom ogeneous atm osphere would also

produce sharp K -line cores.However,work by Ryabchikova

and hercollaborators(e.g.Ryabchikova,K ochukhov & Bag-

nulo 2008, henceforth, RK B) show di�erent strati�cation

patterns for di�erent elem ents, that exclude m odels with

chem icalhom ogeneity.

LeBlanc& M onin (2004)discusscalculationssom ewhat

sim ilarto thoseofBabel,though withouta wind.They also

obtain strati�cation pro�les sim ilar to those which repro-

duce observations.

2.1 M odeling elem entalstrati�cation

There are no m odels of stellar atm ospheres with elem en-

talstrati�cation builtin from �rstprinciples,and m ostre-

searchers have used an em piricalapproach.W hile Babel’s

work focused on the strong Ca IIK -line,subsequentstrati-

�cation studieshaveem ploy variouslines,ofm orethan one

ionization stage.Strong and weak lineswereused,including

the IRT lines.

K ochukhov,etal.(2006,henceforth K TR)derivestrati-

�cation param etersby a \regularized solution ofthevertical

inversion problem " (VIP).They apply the technique to the

m agneticCP starHR 5623 (HD 133792).Thesophistication

ofthem ethod notwithstanding,VIP lacked asigni�cantgen-

erality in practice.K TR �rst �xed Te� ,log(g),�t = 0,and

v � sin(i) = 0,and used them to derive calculated spectra.

Thesefundam entalparam etersalsoa�ectthebasicobserved

m inuscalculated valuesused toobtain thestrati�cation pro-

�les.Thus,an errorin Te� orlog(g)could be re ected in er-

roneousstrati�cation param eters.In principle,thedi�erence

between observed and calculated spectrum should consider

allrelevant param eters including those speci�cally describ-

ing the strati�cation.

W ediscussthem odelforHR 5623 below,and conclude

thatthe m odelparam etersare noteasy to �x forthisstar.

Ryabchikova,Leone,and K ochukhov (2005)and subse-

quentpapersby these workersdescribe the code D DAFIT,

which is based on a lim ited set of4 param eters describing

the strati�cation.

Both D DAFIT and the VIP m ethod derive strati�ca-

tion pro�les from a com parison ofthe observed and calcu-

lated spectra.Ifapplied to any single line pro�le,D DAFIT

would be sim ilar to our m ethod (cf. g(x) and g48(x) be-

low).D DAFIT doesassum e a sharp boundary between do-

m ains with di�erentisotopic com positions,while our func-

tionssm ooth overtheseboundaries.D DAFIT autom atically

adjusts its param eters to achieve an optim um �t with the

help ofa Levenberg-M arquardtroutine (K ochukhov 2007).

In two previouspapers(Cowley,etal.2007,henceforth,

PaperII,Cowley & Hubrig 2008,henceforth PaperIII),we

used strati�cation pro�lesforcalcium based on an analytical

function,g(x),and fourparam eters,a,b,d,and in an obvi-

ousnotation,the abundance Ca=N tot in the deepestphoto-

sphere:

g(x)= b+ (1� b)

»

1

2�1

2erf(

p

(ajx + dj2)

–

: (1)

Here,x = log(�5000); the abundance at any depth,x,is

g(x)� Ca=Ntot.The negative sign is taken for x < � d (see

Fig.1).

W eused Atlas9 m odels,asim plem ented and described

by Sbordone et al. (2004) to obtain T(�5000). Pressures,

opacities,and linepro�leswereobtained with M ichigan soft-

ware described in previouspublications.

W ehaveused both a trial-and-errorm ethod and a least

squaresm inim ization based on the (downhill)sim plex rou-

tine UM PO L from the IM SL (1998)library.

2.2 Strong vs.w eak lines as strati�cation

indicators

In this work,we have tried to avoid weak lines,preferring

the strong lines ofCa ii,either the K -line,or lines ofthe

IRT.In som e stars,the resonance lines of Sr iishow the

characteristicsofstrati�cation (PaperIII).

Strong lineshave severaladvantagesoverweakerones.

First,the e�ects ofstrati�cation are m uch larger,as m ay

be seen by com paring Figs.7 and 9 of Paper III for the

strong Ca iilines��3933 and 8542 with the Fig.14,where

wewereatsom epainsto show thee�ectofstrati�cation on

the subordinate Sriiline,�4162.

M uch ofthe discrepancy between observed and calcu-

lated weak and interm ediate-strength lines is in the line

Strati�cation and Isotopic Separation in CP Stars 3

depths.Line depthshave subtle dependenceson m any fac-

tors,instrum ental,m odeldependent(Te� ,m icroturbulence,

v � sin(i),etc.),and atom ic (gf-values,dam ping,hfs).O ne

m ay readily get a �t for any individualline depth by ad-

justing one or m ore ofthese param eters.By contrast,the

observed pro�lesofstrongerlinesarelesssubjectto pertur-

bationsby noise,blends,and the instrum entalpro�les.W e

know ofno reasonable adjustm entofparam etersthatcould

reconcile the observed,anom alous cores with those calcu-

lated for the strong Ca iiK -line using a classical m odel.

However, the generally-accepted strati�cation m odels can

�tthese strong-line pro�les.

3 ISO T O P IC ST R A T IFIC A T IO N

Ithasbeen known fordecadesthatisotopicanom aliesoccur

in the atm ospheres ofCP stars (see the review by Cowley,

Hubrig,and Castelli,2008).

Theseanom alies,likethechem icalpeculiarities,arenot

believed to re ectthebulk com positionsofthestars.W hile

itisassum ed thattheisotopicseparationsarecaused by the

sam e kinds offorces that give rise to the overallchem ical

peculiarities,detailed explanationsofthe anom aliesrem ain

to be worked out.

In a few cases,the isotope separation m echanism has

been so e�cient that the m aterial rem aining in the line-

form ing regions is virtually isotopically pure.A canonical

case has been m ercury in � Lupi,which is som e 99% -pure204

Hg.Pro�tt,et al.(1999) give references and an exten-

sive discussion.Variouse�ortshave been m ade to establish

strati�cation ofm ercury.Theeven-A isotopesofm ercuryare

wellseparated in wavelength in certain sharp-lined spectra

(cf.W oolfand Lam bert1999),butwe know ofno convinc-

ing studies showing di�erent form ation strata for m ercury

isotopes.

In thecaseofstarsshowing anom alously strong linesof3He,Bohlender(2005)hasconcluded thatthelighterisotope

is in layers above those with the norm alisotope4He.He

�nds that the Stark widths are system atically sm aller for

the lighter isotope, indicating that it is form ed in higher

regionsofthe atm osphereswith lowergaspressures.

3.1 M odeling isotopic strati�cation

Ryabchikova(2005)and hercoworkersused m odelswith the

heaviest isotopes (48Ca and/or

46Ca) concentrated above

log(�5000)� � 1:3.The com m on40Ca dom inatesthedeeper

layers.In thedeepestlayers,theCa/H-ratio can exceed the

solarvalueby m orethan two ordersofm agnitude(HR 5105,

HR 7575).

W e avoid an abrupt transition in the isotopic m ix by

introducing a second function,g48(x),to sim ulate a layer

rich in theheavyisotope(orisotopes).Again,x = log(�5000).

Thisfunction placesthe centerofa cloud ofexotic calcium

at a depth x = � d0.The function g48(x) is de�ned to be

unity for x = � q � d0.O n either side ofthis dom ain,the

function declines rapidly to zero.By an appropriate choice

ofparam eters,the upperboundary ofthe cloud can be put

abovethehighestlayersin theatm osphere,asillustrated in

Fig.1.

Figure 1. Strati� cation functions g(x) (solid) and g48(x)

(dashed), where x = �5000. R elevant param eters for the plots

are in Tab 3 for �8542.N ote the m inim um ofg(x) is not zero,

butdeterm ined by the param eter b.Both b and g48(x)are setto

zero forvalues ofx sm allerthan 10� 8.

g48 = 1:0� erf(a0x2q); (2)

with

xq = jx + d0j� q; (3)

Fig.1 showsa casewith theheavy isotope ise�ectively

restricted to layersabove log(�5000)ca.� 0.8.

The sim plex �tstend to push the centroid ofthe cloud

very high in the m odel. This tendency had already been

noted by Ryabchikova(2005).Additionalstudy ofthisprob-

lem requires a hyperextended atm osphere including non-

LTE,which we leave forfuture work.

3.2 C olum n densities

In a strati�ed atm osphere there is no single Ca=N tot ratio.

Asa substitute one m ay considerintegralcolum n densities,

forsom e \equivalent" colum n length,H .W e adoptthe fol-

lowing,som ewhatarbitrary de�nition.

< N C aH > =

Z

�� (m ax)

�� (m in)

N C a exp(� 1:5� ��)d��

��: (4)

The integrals are taken from the sm allest opticaldepth of

ourm odelsto the largest,orfrom log(�5000 = � 5:4 to 1.4.

The N C a-values are calculated with the help of the

m odel atm osphere, and the relevant strati�cation pro�le,

g(x)org48(x).W ith thisde�nition,we can show thatvery

di�erentcolum n densities of48Ca arise in the m odels with

and withoutisotopic strati�cation.

A related colum n density isthatofallm assiveparticles.

In an obviousnotation,

< N totH > =

Z

�� (m ax)

�� (m in)

Pg � Pe

kTexp(� 1:5� ��)

d��

��: (5)

From theserelations,wem ay m akerough intercom par-

isonsofelem entalabundancesin strati�ed and unstrati�ed

atm ospheres.

4 C.R.Cowley,S.Hubrig,and J.F.Gonz�alez

Table 1.R ecent log(gf)-values forCa iiIRT

� [�A ] VA LD Brage etal. M BB

8498 � 1.416 � 1.369 � 1.366

8542 � 0.463 � 0.410 � 0.412

8662 � 0.723 � 0.679 � 0.675

3.3 V ariable log(gf)’s

In orderto allow forvariablerelativeabundancesofindivid-

ualcalcium isotopes,we often adjusted the log(gf) values

for the IRT lines independently.Since the line absorption

coe�cient involves the product of the abundance and os-

cillator strength,increasing the f- or gf-value for a given

line isequivalentto increasing the abundance forthatline.

The elem entaland atom ic data inputto the calculation in-

cludesa provisional(note the prim e)ratio Ca0=N tot,where

N tot = (Pg � Pe)=(kT),(m assive particles).W hen a good

line �tisachieved,theprovisionalCa0=N tot isthe optim um

abundance ratio for that particular line, provided the as-

sum ed gf-value is also the adopted one.Ifthe gf-value dif-

fersfrom thatadopted,the abundance thatcorrespondsto

a line �tm ustbe m odi�ed.Logarithm ically,

log(Ca=N tot)adopted = log(Ca0=N tot)provisional

+ log(gf)used � log(gf)adopted (6)

In thiswork wehaveonly assum ed thepresenceof40Ca and

48Ca.In som e cases,better �ts to the observations could

have been obtained by including interm ediate isotopes,but

thishasnotbeen done forthe presentstudy.

Forreference,Tab 1 listsvaluesoflog(gf)from VALD ,

M el�endez,Bautista,and Badnell(2007,M BB),and Brage

et al.(1993,Tab.IV,Col.3).Convenience m otivated our

adoption ofVALD values,although they are probably less

accurate than those ofM BB orBrage etal.

4 T H E O B SERVA T IO N A L B A SIS FO R

SEPA R A T IO N O F40C A ,

48C A ,A N D

P ER H A P S O T H ER C A ISO T O P ES

M ostoftherelevantobservationalm aterialforisotopicstrat-

i�cation ofheavy calcium has been obtained with the UV-

VisualEchelle Spectrograph (UVES) at UT2 ofthe VLT.

The instrum entand spectra have been described elsewhere

(cf.Castelliand Hubrig2004).O bserversm ay startfrom the

sam e raw observations,and getspectra thatcan be signi�-

cantly di�erentbecauseoftheway them aterialisprocessed.

Thisseem stobecritically truein theregion oftheCaiiIRT,

and isillustrated in Fig.2.

Epochs ofthe spectra illustrated here are given in the

�gurecaptions.M any wereobtained in Augustof2008,and

reduced especially forthepresentstudy by FG .Therem ain-

der were reduced with pipeline program s current for their

epoch.

A relatively sm allnum berofstars are suitable for the

study ofisotopic separation in calcium .First,the large iso-

topicshiftsoccuronly fortheIRT lines.Second,avery sm all

fraction ofCP starsshow the largestshifts,asm ay be seen

in Figs.1 and 2 ofPaperII.Tab.2 lists the CP starswith

Figure 2.Three reductionsofthe line �8498 ofthe IRT.A llare

based on U V ES spectra taken on 8 O ctober 2001 of10 A ql.The

verticallines are at the positions for 40Ca (8498.02),and 48Ca

(8498.22).In order ofincreasing depth at the latter wavelength,

the reductions were m ade (1)forthe ESO archive,

http://archive.eso.org/eso/eso archive adp.htm l U V ES Pipeline

3.9.0 (dotted:blue in online version,gray in b/w),(2) for SH in

2006 with U V ES Pipeline 2.9.0 and m ildly Fourier � ltered (thin

solid line:red onlineversion,darkergray in b/w),and (3)reduced

by FG using IR A F in 2008 (thick:black).N either(1)nor(3)were

Fourier � ltered,but allthree spectra were recti� ed as described

in Paper IIIx3.

thelargestaveraged shiftsfrom PaperII.Forthesestars,the

averagem easured shiftof��8498 and 8662 (aswellas8542,

when available) is> 0:15 �A.The seven roAp starswere all

included in the study by RK B.Note that HgM n stars are

am ong those with the largestshifts.

4.1 W avelengths,isotopes,and strati�cation

m odels

The plots in Papers I and II show unequivocally that the

wavelength shifts of all three lines of the IRT are highly

correlated.However,the shifts are signi�cantly di�erentin

the spectra of(m agnetic) CP2 stars (Preston 1974).M ea-

surem entsofpublished and recently obtained spectra show

thatshifts for the �8662 are 0.06 �A larger on the average,

than for�8498.Averageshiftsfor�8542 aresim ilarto those

for �8498,though in im portantindividualcases (10 Aql,

Equ),the shifts increase from the shortest to the longest

wavelength line.

W eestim ated (PaperII)thatany individualwavelength

m easurem ent m ight be uncertain by up to 0.05 �A.These

uncertainties could be due to a variety ofcauses,such as

proxim ity to ordergaps,the asym m etry ofthe line pro�les,

or to blends.W hatever their cause,shifts of the order of

0.06 �A are easily m easurable,and readily detected in our

�gures.

Atpresent,we adm itthatsigni�cantdi�erencesin the

wavelength shifts of IRT lines exist in individualspectra.

Theircause hasnotyetbeen resolved.

Strati�cation and Isotopic Separation in CP Stars 5

Table 2.CP starswith large IRT wavelength shifts

H D N um ber O ther Type A verage Shift

designation

24712 H R 1217 roA p 0.16

65949 m ercury 0.15

101065 Przybylski’s roA p 0.20

122970 roA p 0.16

133792 H R 5623 roA p 0.18

134214 roA p 0.18

175640 H R 7143 H gM n 0.20

176232 10 A ql roA p 0.18

178065 H R 7245 H gM n 0.16

217522 roA p 0.20

Figure 3.Single order U V ES spectrum (8 O ctober 2001) of10

A qlnear �8498.The dashed line m arksthe position ofP17.The

thick verticalline (actually two virtually unresolved lines)m arks

the wavelengths of40Ca and 48Ca.The centroid ofP16 isshown

by the verticalline furthestto the right,neara blend oftwo SiI

lines.

4.2 Isotopic strati�cation:di�erent core and w ing

shifts

Traditionaldetections ofisotopic m ixtures or anom alies in

stellar atm ospheres have been based prim arily on wave-

length shifts. RK B present plots showing that the m ean

wavelengths ofthe wings and cores ofIRT lines show dif-

ferentshifts.

These �ndings are illustrated in their �gures 6 and 7,

which include four of the stars of Tab.2.Their Figure 6

is ofthe �8498-line ofthe sharp-lined spectrum of10 Aql;

�gure 6b shows that a calculation assum ing a 50-50% m ix

of40Ca and 46Ca+ 48Ca havea wing thatisdeeperthan the

observed red wing.The core hasa m inim um at8498.20 �A,

which would correspond to pure48Ca.They conclude the

heavy isotope(s)dom inate only in the upperm ostlayers.

These workersnote the di�culty in establishing an ac-

curate observationalpro�le in Section 2 oftheirpaper.W e

entirely concur(cf.Fig.2).Theirprocedurereplacesa poor,

observed P16 pro�leby a theoreticalone.However,in order

to rem ovethe awed pro�le,itisnecessary to disentangleit

from theCa iiline,and thisisnotstraightforward.O necan

seethisfrom Fig.3,which showstheunrecti�ed pro�leofa

single orderfor10 Aql,asreduced by FG .

W e �rst discuss cases where the evidence for isotopic

8660 8665

Figure 4. Calculated (black) and observed spectra (gray with

dots,red in online version)ofIRT lines�8662 (above),and 8498

(below) in H R 1217. The U V ES spectrum (14 M arch 2001) is

from the U V ESPO P archive.The calculations are intended only

to show the m atch ofthe line wings with an assum ption ofpure40Ca.The two verticallines m ark the rest wavelengths for 40Ca

(left)and 48Ca (right).Theobserved red wing of�8662 isstrongly

a� ected by the order break,and we have m oved it to vertically.

Clearly lines centered at the position ofthe verticallines to the

right(48Ca)would not� tthe observed wings.

strati�cation isstrong,and then turn to starsforwhich the

indication ofsuch separation ism arginalorabsent.

5 H R 1217 (H D 24712)

HR 1217 is the best case that we have exam ined for iso-

topic separation.RK B’s Figure 7 shows observationaland

calculated �ts for the interm ediate-strength line,�8662 as

wellas �8498.Their best �t is shown to be the one with

high layersdom inated by heavy calcium {isotopic strati�ca-

tion.In Paper II,we reported shifts of0.17 and 0.15 (re-

spectively)forthesetwo linecores.O urm easurem entswere

from a UVESPO P archive spectrum (Bagnulo,etal.2003),

notfrom the sam e instrum entasused by RK B.

W e con�rm from the UVESPO P spectrum that both

linesarereadily �twith theheavierisotope,48Ca,providing

theshifted core.Fig.4 isbased on theUVESPO P spectrum ,

and showsthatthewingsofboth the�8498 and �8662 lines

agree with a pro�le calculated with40Ca only.

6 T H E C A II IR T IN 10 A Q L

The 10 Aqlm odelused below has Te� = 7650K ,log(g) =

4:0,and with solarabundancesreplaced by appropriate av-

erages (e.g.forneutralsand ions) from Ryabchikova,etal.

(2000).

New m easurem ents ofthe wavelengths ofthe cores of

6 C.R.Cowley,S.Hubrig,and J.F.Gonz�alez

Table 3.Param etersfor10 A ql� ts with (iso-strat)and without

(uniform ) isotopic strati� cation.The trialand error (t& e) solu-

tion wasalso m adewith a uniform isotopicratio.A bundancesare

in the rowslabeled log(Ca0=N tot).These valuesare m ultiplied by

g(x)org48(x)respectively in the pro� le calculation.

�8498 �8542

Param . uniform t& e iso-strat uniform iso-strat

a 4.28 4.0 2.23 4.289 2.0

log(b) � 4.72 � 4.19 � 6:00 � 5.133 � 6.30

d 0.4376 0.4 0.110 0.1936 0.0

log(Ca0=N tot) � 3.75 � 4.19 � 3.25 � 3.03 � 3.30

log(gf40) � 1.458 � 1.90 � 1.416 � 1.362 � 0.463

log(gf48) � 1.416 � 1.416 � 5.67 � 0.463 � 4.800

a0 0.949 0.5

d0 5.00 5.0

q 0.185 0.2

the IRT lines were obtained from UVES spectra obtained

on 4 August2008.W e obtained shiftsof+ 0.17,+ 0.19,and

+ 0.20�A ,for��8498,8542,and 8662,respectively.Them ea-

sured shifts reported in Paper II were + 0.14,and + 0.22�A

for��8498 and 8662.Thedi�erencesareconsistentwith our

errorestim atesform easurem entsofasym m etricalfeatures.

6.1 T he �8498 line

The �8498 line is the weakest ofthe IRT.Fig.5 (upper)

shows the result of an autom atic (sim plex) calculation of

the�8498 region,using thestrati�cation and abundancepa-

ram etersforg(x)given in the second colum n ofTab.3.For

theupperand m iddleplots,weassum ed no variation in iso-

topic abundances with depth.In the deepest layers ofthe

atm osphere,where g(x)isunity,the value log(Ca0=N tot)is

the relative abundance provided the oscillator strength is

theoneaccepted.IfweaccepttheVALD value,-1.416,then

log(48Ca=N tot)= � 3:75.The abundance forthe m ore com -

m on isotope is sm aller by 0.04 dex,because a sm aller os-

cillator strength was required to �t the part ofthe feature

dom inated by40Ca.Adding the isotopes,we get � 3.47 for

log[(40Ca+ 48 Ca)=N tot].

The center plot of Fig.5 results from trialand error

(t& e)adjustm entsoftheparam etersto geta better�tnear

the position ofthe48Ca core at 8498.22 �A.It is arguable

whether an im provem ent has been achieved, but the to-

talcalcium in the deeper layers,log[(40Ca+

48Ca)=N tot]=

� 4.07.

The param eters in the 4th colum n produced the �t

shown in the bottom plot ofFig.5.This was also a trial

and error�t,butadjusted from a sim plex solution.Theau-

tom ated result pushed the48Ca cloud so high that only a

\sliver" ofa region rem ained with theheavy isotope.Under

theseconditions,we did notbelieve thecolum n density cal-

culation was realistic.Note thatthe d-param eterofg(x)is

quitesm all,and thisrequiresa relatively high Ca/N tot ratio

in the deepestlayers.

Thereisno question thatthe�tfor�8498 isbetterwith

the m odelthat assum es isotopic strati�cation,as claim ed

by RK B.W eshallm akean overallassessm entafterthetwo

strongerIRT lines,and theCa iiK -linehavebeen discussed.

Figure 5. The �8498 line in 10 A ql (U V ES 4 A ugust 2008).

O bserved spectra are dark gray (red online)with points,calcula-

tions in black.Verticallines m ark the wavelengths for 40Ca and48Ca.The upperand m iddle plotsare fora uniform isotopic m ix

through atm osphere,but elem entalstrati� cation.Lower plot as-

sum es isotopic and elem entalstrati� cation.R elevant param eters

forthe � tare in Tab3.

6.2 T he �8542 line

Neither ofthe stronger IRT lines were exam ined in RK B’s

study.The �8542 line is the strongest,and was generally

unavailable on UVES spectra priorto Novem ber2004.The

intrinsic strength of �8542 is nearly 9 tim es greater than

thatof�8498.O nethereforeexpectsto seebetter-developed

wings.This should give an increased chance ofdetecting a

wavelength shift| between coreand wings| ifthecoreispri-

m arily dueto theheavy isotope while the wingsare form ed

deep,where the lightisotope dom inates.

The upperpartofFig.6 showsan autom atic (sim plex)

�t(black)to the observed pro�le,assum ing only elem ental

strati�cation.The constant48Ca/

40Ca ratio is about 6 to

1.Notethegreaterstrength ofthecalculated red wing,and

com pare the wing with the observed (dark gray with dots)

and pro�leforpure40Ca (thick lightergray).Thisbehavior

wasnoted by Ryabchikova and hercoworkers(e.g.RK B)as

an indication thatthewing wasform ed by a norm al(m ostly40Ca)m ixture.

The lower calculation (black)assum es the48Ca isin a

high cloud,with param eters (g48(x))given in Tab.3.Trial

and errorim provem entswerem adeafteran autom atic�tto

obtain the pro�le shown.

Ifwecom paretheupperand lowerpartsofFig.6,wesee

the sam e generalfeaturesasshown in Fig.5 forthe weaker

line,�8498.W ithoutisotopic strati�cation,one cannot get

enough absorption in thevioletwing withoutexceeding the

observed m inim um atthecentroid oftheabsorption for40Ca

(leftverticallinesin Figs.5and 6.Theisotopically strati�ed

m odelcan accom plish thisbecauseitreducestheam ountof

Strati�cation and Isotopic Separation in CP Stars 7

Figure 6.The �8542 line in 10 A ql(U V ES 4 A ugust2008).The

upper� gure:elem entalstrati� cation;lower� gure:elem entaland

isotopic strati� cation. Coding as in Fig.5.The thick gray line

(green in online version)isfora pro� le with pure40Ca;contrast

the behavior of the wings for the pro� les.R elevant param eters

forthe � t are in Tab3.

40Ca in the upperatm osphere,where the core ofthe line is

form ed.

Theparam etersforthetwo linesin Tab.3 in colum ns5

and 6 forthetwo linesdi�ersom ewhatforthestrati�cation

(g(x),and g48(x)).Itdi�culttojudgehow m eaningfulthese

di�erencesare.Colum n densitiesm ay be m ore m eaningful.

W e discussspeci�c resultsin x6.4.

6.3 T he �8662 line

The �8662 line (not shown) is intrinsically som e 55% as

strong as �8542.It can be �t with param eters sim ilar to

those in Tab.3 for the other two IRT lines.The �t in the

near,violet wing is com plicated by a strong Fe I line,at

8661.90 �A.Ifwe adjust the iron abundance,or the appro-

priate gf-value for that feature,a �t using only elem ental

strati�cation shows the sam e generalfeatures as the other

lines ofthe IRT.Som e absorption is m issing in the violet

wing,and the red wing istoo deep.

For the present,we conclude isotopic strati�cation is

the sim plestway to explain the IRT pro�lesin 10 Aql.

6.4 T he C a iiK -line in 10 A ql;overallcolum n

densities

Fig.7 shows our �t to the Ca iiK -line in 10 Aqlinclud-

ing a close up ofthe �t in the core.Relevantstrati�cation

param etersare given in the caption.

Tab.4 com paresthe colum n density ofthe K -line with

those forthe IRT.

W e know ofno previous work that has assem bled col-

um n densitiesforstrati�ed atm ospheres.Thus,we have no

Figure 7. Ca ii K -line � ts in 10 A ql. O bservation: gray (red

online;U V ES 8 O ctober2001),calculation:black.Both plotsare

centered at 3933:00 �A The K -line core (3933:66 �A ) is therefore

noticeably displaced in the lower � gure,which shows the inner

part of the � t. The strati� cation param eters are a = 2:2, b =

3:0� 10� 6,d = 0:1,and Ca=N tot = 2:0� 10� 4.

Table 4.Logarithm ic colum n densities forCa IIlinesin 10 A ql.

Isotopen� 8498 8542 8662 K -line

Elem entalstrat.only

48 18.93 19.34 18.85

40 18.90 18.44 18.07

40+ 48 19.22 19.40 18.92 18.93

Elem ental+ isotopic strat.

48 14.39 14.46 13.38

40 19.17 19.02 19.29

40+ 48 19.17 19.02 19.29 18.93

basis for judging how wellthe values for features allaris-

ing from Ca iishould agreewith oneanother.Thetotalsfor

thecalculationswith elem entalstrati�cation only di�erby a

m axim um of0.48 dex,ora factorofabout3.W hen isotopic

strati�cation isadded,them axim um spread isonly slightly

less,0.36 dex ora factorof2.3.

7 H D 122970

Handlerand Paunzen (1999)discovered the roAp nature of

HD 122970.Itwasam ong theobjectsstudied forelem ental

and isotopic strati�cation by Ryabchikova (2005).In Paper

I,we gave shifts for ��8498 and 8662 of0.13 and 0.19 �A,

respectively.New m easurem entsofallthree IRT lineshave

been m adebased on spectra obtained in August2008.They

yield thefollowing shifts:0.15,0.18,and 0.19 �A for��8498,

8542, and 8662 respectively. D i�erences for the m easure-

8 C.R.Cowley,S.Hubrig,and J.F.Gonz�alez

Figure 8. The strongest IRT line, �8542 line in H D 122970

without (top, and center) and with (below) isotopic strati� ca-

tion (U V ES 3 A ugust 2008).Param eters forthe � ts are given in

Tab.5.The upper� twasdone using the sim plex code.The cen-

ter plot is a trialand error (t& e) � t,starting from the sim plex

param eters.Thelowerplotisan unm odi� ed sim plex solution (see

text).

Table 5.Param eters of�8542 � ts for H D 122970 with uniform

and isotopic strati� cation. Cols. 2 and 3 refer to the top and

center plots ofFig.8.Col.4 gives param eters for the lower plot

ofthat � gure.

Param . uniform uniform iso-strat

sim plex t& e sim plex

a 6.361 6.300 7.342

log(b) � 3.455 -3.301 � 4.302

d 0.562 0.562 0.752

log(Ca/N tot) � 4.947 � 4.824 � 5.213

log(gf40) � 0.708 � 1.400 � 0.316

log(gf48) � 0.460 � 0.460 � 0.460

a0 1.500

d0 6.488

q 0.009

m ents in com m on are 0.02 and 0.00 �A,in good agreem ent

forbroad,asym m etricallines.Thetendency to m easurethe

weakerlineofthetripletata sm allershiftthan thestronger

linesisrepeated in the rem easurem ent.

Fig.8 shows �ts oftheoreticalspectra to the new ob-

servations,specially reduced by FG .O urm odelisbased on

the param etersofRyabchikova etal.(2000).

To m akea judgem enton whetherisotopicstrati�cation

is indicated,com pare the center and lower plots ofFig.8.

Clearly,thelower�tisbetter.In them iddleplotweseethe

e�ect pointed out by RK B for the weaker �8498 line.The

red wing is below the observations,while the violet wing

is above.This is explained by the hypothesisofa constant

isotopic ratio,which m akestoo great a contribution to the

red wing from the48Ca.

A better �t is shown in the lower part of the �gure,

where the wings are prim arily due to40Ca.The e�ect is

notlarge,butit is consistent with the e�ectshown in sev-

eralpapersby Ryabchikovaand coworkers,which dealtonly

with theweaker�8498 line.Thisconsistency arguesagainst

the possibility that the im proved �t is sim ply due to the

additionalparam etersofthe isotopically strati�ed m odel.

W ith isotopic strati�cation, the sim plex calculation

putsthem axim um oftheg48 function above thetop layerof

ourm odel[log(�5000)= � 5:4].W ediscussed a sim ilarresult

in x6.1 for �8498 in 10 Aql.The e�ect was already noted

by Ryabchikova (2005).W ehavenoted theneed fora study

including a hyperextended atm osphere (cf.x8.1),and non-

LTE.W e�nd thatan equally good �ttotheobserved pro�le

m ay be m ade ifwe m odify the sim plex param etersslightly,

as we discussed in x6.1.In particular, we used a0= 6:0,

d0 = 5:0,and q = 0:009.W e get an excellent �t,when we

also m ultiply the g48(x)by 0.01.

W ith the latter param eters,we �nd a colum n density

log(48CaH) = 14:38, and log(40CaH) = 18:26. This rela-

tively very low colum n density for48Cashould becontrasted

with the value thatfollowsfrom the param etersofthe uni-

form trialand error solution:18.33.Here,m ost ofthe cal-

cium is assum ed to be in the heavy isotope,and the total

colum n density isessentially the sam e asfor40Ca with the

isotopically strati�ed m odel.

The logarithm ofthe totalcolum n density ofm assive

particlesis23.97,so theoveralllog(Ca=N tot)valueis� 5.64,

close to the corresponding solarvalue,� 5.65.

8 G A M M A EQ U

Frequent statem ents m ay be found in the literature ofCP

stars that Equ and 10 Aqlhave very sim ilar spectra (cf.

W ol� 1983,Ryabchikova,et al.2000).Probably,the idea

goes back to a com m ent by Bidelm an (rem ark to CRC),

whosecarefulintercom parisonsofhigh resolution spectra of

CP starsin the 1960’swere (and are)both highly regarded

and wellknown tothosewhostudythespectraofthesestars.

Because ofits close association with 10 Aql,we include

Equ in thepresentstudy,even though theaverageIRT shifts

(0.13�A)are notquite large enough for itto be included in

Tab.2.Subsequentwork hasshown thatneitherthe abun-

dancesnorthespectra are identical,though thespectra are

m uch m ore like one another than to m any other coolCP

stars(cf.� CrB,HR 7575).

In PaperII,we�tthe�8542lineoftheIRT.Thatcalcu-

lation was m ade without the currentre�nem entsthattake

Paschen con uence into account (cf.Paper III,Appendix

A).Theadditionalcontinuousopacity from \dissolved" up-

perlevelsaccountsfora di�erencein linedepth oftheorder

of 0.05 of the continuum ,in the line wings.Additionally,

the e�ective oscillator strength ofP15 is reduced,because

som e ofthe line opacity isnow (quasi-)continuousopacity.

Thiscould accountforthe di�erence ofa factorof4 in the

Ca0=N tot values shown in Tab.6.W hile no adjustm ent to

the 10 Aqlcontinuum wasm ade forthe speci�c purpose of

�tting the IRT lines,we m ust adm it that the uncertainty

Strati�cation and Isotopic Separation in CP Stars 9

Figure 9. The �8542 line in Equ (U V ES spectrum from 18

Septem ber 2005).Param eters for g(x) are given in Tab.6.They

apply to the upper and center plots.The lower plot is an auto-

m ated � t assum ing isotopic strati� cation.The solid black line is

the calculation.The observed spectrum is the thin line in dark

gray (red in online version).The broad,light gray line (green in

online version)showsa � tassum ing allofthe calcium is40Ca.

Table 6.Param eters ofthe �8542 � tin Equ

�8542 Current Paper II

work Fig.7

Ca’/N tot 1:2� 10� 4 3:0� 10� 5

log(gf)40 � 0.46 � 0.46

log(gf)48 � 0.36 notused

a 6.7 6.7

b 1:5� 10� 5 10� 4

d 0.75 1.0

in placem entofthecontinuum isofthe orderofseveralper

cent.

Fitsto the �8498 line are shown in Fig.10.The strat-

i�cation param eters and value of Ca0=N tot are som ewhat

di�erent from those used for the �8542 line.A calculation

using the sam e param eters �ts reasonably wellin the core

and far wings,but is m uch too strong in the near wings.

O ptim um param etersare given in the �gure.

The third line of the IRT, �8662, is well �t by the

sam e strati�cation param eters as the stronger �8542 line,

but with Ca0=N tot = 3:0 � 10� 4, and log(gf)40 = � 1:00,

and log(gf)48 = � 0:72.The di�erences m ay not be signif-

icant. W hen we �t the IRT lines in Paper III,we found

the sam e strati�cation �t the two stronger lines,while the

weaker�8498 line,required signi�cantly di�erentstrati�ca-

tion param eters.

Note the good �ts for the red wings in the upper two

plotsforboth Figs.9and 10.Itdoesnotappearnecessary to

Figure 10.The �8498 line in Equ (U V ES spectrum from 18

Septem ber 2005).Param etersforg(x),which apply to the upper

two plots are:Ca0=N tot = 7:0 � 10� 4,a = 6:7,b = 2:5 � 10� 6,

d = 0:30,log(gf)40 = � 1:12,log(gf)48 = � 1:32.The lower plot

isan autom ated � tassum ing isotopic strati� cation.Colorcoding

asin Fig.9.

invokeisotopic strati�cation to accountfortheIRT pro�les

in Equ.

8.1 T he C a iiK -line in Equ

In Paper II,we noted (x7.4) that the sam e param eter set

that�tthe�8542 linealso \accountsquitewellfortheCa ii

K -line pro�le." Thissituation m ustbe reexam ined because

ofthe current use ofextra opacity from dissolved Paschen

lines.W e�nd thatslightly m odi�ed param eters(cf.Tab.6,

Col.2)provideagood �ttotheK -line:Ca=N tot = 9:0� 10� 5,

and d = 0:65.The a,and b param etersare the sam e.

Ryabchikova,et al.(2002,RPK ) exam ined the Ca ii

K -line in Equ in a study that em ployed a hyperex-

tended atm osphere,to log(�5000) = � 10.Since the center

ofthe K -line saturatesin the �rstdepth ofouratm osphere

[log(�5000)= � 5:4],such an extension would beappropriate.

W e have experim ented with sim ilar m odels,and �nd they

give essentially the sam e pro�lesto the one currently used,

provided thetem peraturesareappropriately adjusted atthe

shallowest depths.Since such atm ospheres are poorly con-

strained by radiative equilibrium in LTE,we use ourstan-

dard m odelhere.

Fig.11showsa�ttotheK -linein Equ,with acloseup

ofthe core.The param eters are indicated in the caption.

An equally good �t m ay results from param eters,chosen

to approxim ate those shown for calcium in RPK ’s Fig.3.

The two strati�cations and relevant param eters are given

in Fig.12.The �lled starsindicate the strati�cation pro�le

used by RPK ,which deviatesatthehighestlayersfrom the

approxim ation.

10 C.R.Cowley,S.Hubrig,and J.F.Gonz�alez

Figure 11.The Ca iiK -line in Equ (U V ES spectrum from 18

Septem ber 2005).Param eters forg(x)are:Ca=N tot = 9:0� 10� 5,

a = 6:7,b = 1:5 � 10� 5,d = 0:65,log(gf)= � 0:100.The central

partofthe pro� le isdisplayed in the lower partofthe � gure.

Figure 12.Strati� cation pro� les leading to good � ts for Ca ii

K -line in Equ (U V ES 18 Septem ber 2005).Param eters forthe

thicker,black curve are given in the caption to Fig.11.The gray

curve(red in onlineversion)isforthefunction g(x),and used fora

� tindistinguishable from thatshown in the lowerpartofFig11.

The param eters were Ca=N tot = 5:0 � 10� 5,log(gf) = � 0:100,

a = 30:0,b= 2:0� 10� 4,d = 0:9.See text forthe m eaning ofthe

� lled stars.

9 STA R S W IT H W EA K ER C A LC IU M LIN ES:

D O M IN A N T48C A

9.1 H gM n stars

SeveralCP starswith large isotopic shiftshaveratherweak

Ca iiand/orIRT lines{certainly relative to HR 1217.RK B

do notdiscussany oftheHgM n stars,which also show vary-

ing isotope shifts.Severalexam plesare shown in Fig.13

O nly HR 7143 (HD 175640) shows the fullshift cor-

responding to48Ca. This star was exam ined for elem en-

talstrati�cation by Castelliand Hubrig (2004) and Thiam

Figure 13.The strongest IRT line,�8542 in 4 H gM n stars.A r-

bitrary verticaldisplacem ents ofroughly norm alized spectra are

m ade fordisplay purposes.The stars,along with the datesofthe

U V ES exposuresare from top down:H D 29647 (5 A ugust2008),

H R 1800 (19 Septem ber 2005),H R 7245 (18 O ctober 2005),and

H R 7143 (20 Septem ber 2005).The verticallines m ark the posi-

tions ofpure 40Ca and pure 48Ca.

et al. (2008), who reported som e evidence for strati�ca-

tion from m etallic lines.Elem entalstrati�cation is gener-

ally accepted for em ission lines com m on in the red and

infrared of HgM n and related stars (Sigut 2001).The K -

line of Ca ii shows signi�cant wings, and m ight indi-

cate strati�cation if it were present. However, Castelli’s

web site shows an excellent �t with a non-strati�ed

m odel: http://wwwuser.oats.ts.astro.it.castelli/hd175640/

p3930-3936.gif

Theslopeofthe\edge" oftheHR 1800 pro�leissteeper

on the red side than on the blue.This shape is com m on

am ong theCP2 stars,asillustrated elsewhere in thispaper.

Presum ably,the m ore shallow violet slope is caused by an

adm ixtureof40Ca.Additionalwork isneeded to investigate

the question ofisotopic m ixtures.The pro�lesofHD 29647

and HR 7245could arguably beprim arily dueto 46Ca,which

has a shift of0.16 �A relative to40Ca.Contributions from

lighteraswellasheavierisotopesm ightbe required.

O ne cannot rule out the possibility that the48Ca is

in a high, strati�ed layer. If this were the case, and the

low photospheric abundance ofcalcium were assum ed very

high, the relative percentage of heavy calcium above the

photosphere could be m uch sm aller than it would appear

from a naive exam ination ofthe pro�le (see rem arksbelow

forthe IRT pro�lesin HR 5623).

Two other HgM n stars in Table A1 ofPaper II show

large isotopic shifts:HR 6520 (HD 158704) and HR 6759

(HD 165473).

9.2 C P 2 stars w ith w eaker IR T lines

Tab. 2 contains CP2 stars with large isotope shifts (ca.

0.2 �A) but m oderate or weak IRT lines: HR 5623 (HD

133792), Przybylski’s star (HD 101065), and HD 217522.

W e discussthem in thisorder.HR 5623 wasthe subjectof

the intensive study ofK TR,which introduced the vertical

inversion technique.Thelattertwo starshavem inorabsorp-

tion atbestthatcould be attributable to40Ca.

Strati�cation and Isotopic Separation in CP Stars 11

Figure 14.The �8498 line in H R 5623 (U V ES spectra 19 M arch

2006). Vertical lines m ark the wavelengths for 40Ca and 48Ca.

W hile the heavier isotope dom inates the absorption,it does not

necessarily dom inate the num ber of Ca ions above the photo-

sphere (x3.2,x10.4).

10 H R 5623 (H D 133792)

W e devote specialattention to HR 5623 because the weak-

est IRT line,�8498 has dom inant absorption at the posi-

tion for48Ca,with a signi�cantly sm allercontribution from

40Ca.Thisisshown in Fig.14.Itthusseem ed possible that

theabundancepro�leforcalcium in HR 5623 approxim ated

that in stars like HR 7143 (HD 175640),where there is no

obviousindication ofabsorption from the lighterisotope at

all.Absorption from the strongerline ofthe �8498 blend is

roughly double that ofthe weaker com ponent,presum ably

due to40Ca,so we m ightconclude the relative num bersof

the isotopes\above the photosphere" wasroughly 2 to 1 in

favor of48Ca.W hen absorption from the lighter isotope is

entirely m issing,there is no way strati�cation can lead to

any conclusion other than 48Ca dom inates.It m ight seem

thatisalso thecasewhen the40Ca contribution isrelatively

weak;strati�cation would not signi�cantly change the ap-

parent dom inance ofheavy calcium .However,we shallsee

thatthisisnotnecessarily the case (x10.4).

The work by K TR and RK B on this star is based on

UVES spectra taken on 26 February 2002.Additionalspec-

tra wereobtained on 27 January 2005,afterrecon�guration

of the instrum ent which m ove the order gaps away from

the IRT lines.IRT shifts from Paper IIwere + 0.18 �A for

both ��8498 and 8662.The new m easurem entsyield shifts

of+ 0.19,+ 0.20,and + 0.20 �A for ��8498,8542,and 8662

respectively.

10.1 E�ective tem perature and gravity

K TR �xed Te� = 9400K , and log(g) = 3:7 prior to car-

rying out their verticalinversion calculations. The m odel

param eters were based on Str�om gren and H� photom etry,

and the M oon & D woretsky (1985) calibration as im ple-

m ented by Rogers(1995,TEM PLO G G ).Signi�cantly,they

adopted a reddening E (B � V ) = 0:09,which they state

\...follows from the reddening m aps by Lucke (1978) and

high-resolution dustm apsby Schlegel,Finkbeiner& D avis

(1998)." Additionally,they �tH� and H� pro�les.

The assum ed excess,E (B � V )= 0:09,followsdirectly

from a standard absorption and reddening law (seeEq.3.66

ofBinney and M erri�eld 1998),and the Hipparcosparallax

of 5.87 m as.Ifthe color excess is correct it supports the

assum ed tem perature of9400K .

There is reason to suspect the e�ective tem perature

m ay be severalhundred degreescooler.A code kindly pro-

vided to CRC by B.Sm alley (private com m unication),but

based on theM oon-D woretsky (M oon 1984)work gives8960

or8900K ,depending on whetherthereduction isdonewith

Class 5 (A0-A3 III-V),or Class 6 (A3-F0 III-V).The red-

deningsE (b� y),are � 0.001 and + 0.032 respectively.

W em ay m akean estim ateofthereddeningfrom thein-

terstellarsodium lines,with the help ofthe work ofM unari

and Zwitter(1997).Theequivalentwidth oftheNaD 1 isline

di�cultto m easureprecisely,becauseitispartially blended

with thestellarline.W eestim ate 96 m �A.From M unariand

Zwitter’sFigure1,oneseesthatthisequivalentwidth would

correspond toE (B � V )valuesranging from 0.00 toperhaps

0.10.Theseauthorsalso providean em pirical�tto therela-

tion between E (B � V )and theequivalentwidthsofNa D 1

aswellasK I�7699.W e�ta quadraticto the�rst5 values

oftheir Table 2,and obtain E (B � V ) = 0:026 from the

Na line.The K I feature is arguably present.W e estim ate

an equivalentwidth of6.7 m �A ,which would correspond to

E (B � V )= 0:020.

Paunzen, Schnell, and M aitzen (2006) give the ex-

cess in the G eneva system as E (B 2 � V 1) = 0:63 �

E (B � V ). W ith this reddening, the G eneva colors

(www.unige.ch/sciences/astro/an) give Te� = 8952K and

log(g) = 3:32, according to a code kindly supplied by P.

North (cf.K unzli,et al.1997).This assum es a m etallicity

([Fe/H]) of+ 1,and a reduction grid chosen autom atically

by the code.

A spectroscopic determ ination ofTe� and log(g) m ay

be m ade from the equilibrium ofFe iand iifollowing the

m ethod ofPaperIII,butusing 4 tem peratures,8400,8900,

9400,and 9900K ,and 3 gravities,log(g)= 3:2,3.7,and 4.2.

The m odels assum ed abundances taken from K TR when

available,otherwise using solar values.A reasonable com -

prom ise for the m icroturbulence is 1 km s� 1.The num er-

ous slopes oflog(Fe=N tot) vs.log(W �) are then som etim es

slightly positive,som etim esslightly negative.

Calculationswerem adeusingan unstrati�ed m odeland

onestrati�ed m odelwith param etersapproxim atingthepro-

�le for iron ofK TR,but using a larger jum p:a = 20;b =

1:0� 10� 4;d = 0:95.Thelargerjum p wasused becauseK TR

found a less than 1 dex jum p.W e wanted to see the e�ect

ofa strongerstrati�cation.

Thecalculationsprovidecom binationsofTe� and log(g)

forwhich theFeiand iigivethesam eabundances.Tem per-

atureswith equalabundancesfrom thetwo stagesofioniza-

tion are given in Tab 7 forthree surface gravities.

The G eneva photom etry and iron equilibrium agree on

a low tem perature and surface gravity,and no iron strati-

�cation.Atleast som e im plem entations ofStr�om gren pho-

tom etry concur.A value oflog(g) as low as 3.2 would be

unusual(cf.Hubrig,North,Sch�oller& M athys2007).

Unfortunately,theBalm erlinesdo notclarify them at-

ter.W hile K TR support their choice of tem perature and

gravity by exam ining H� and H�,we �nd these pro�lesare

�t com parably wellwith Te� = 8900K ,and log(g) = 3:2.

An exam ple is illustrated in Fig.15,based on theoretical

12 C.R.Cowley,S.Hubrig,and J.F.Gonz�alez

Table 7. Te� {log(g) pairs with Fe i and Fe ii in equilibrium .

Calculations with and without strati� cation (\strat," see text).

Corresponding log(Fe=N tot)are given in colum ns 3 and 5.

log(g) N o Strat A bund Strat A bund

3.2 8914 -3.67 9143 -2.59

3.7 9490 -3.41 9653 -2.34

4.2 9834 -3.21 9916 -2.30

Figure 15.The FO R S1 spectrum ofH (dark gray with points)

in H R 5623.Thelightgray plotwasm adeassum ing Te� = 9400K ,

and log(g)= 3:7.The black curve was m ade using Te� = 8900K ,

and log(g)= 3:2.The � ts are com parable in quality.

pro�les ofStehl�e & Hutcheon (1999).The stellar observa-

tionsare oflow resolution from FO RS1 (Appenzeller1998)

which have som e advantage over the UVES for broad fea-

tures.However,wehavealso exam ined recti�ed H� and H

pro�lesfrom UVES spectra,and reach sim ilarconclusions.

10.2 Paschen lines

In principle,the Paschen linesm ightalso resolve the am bi-

guity in tem perature and surface gravity.The situation is

hardly betterthan with the low Balm er lines.O fthe three

Paschen linesnearthe IRT,two are signi�cantly in uenced

by the series convergence.In our calculations P13 (�8662)

isnotstrongly a�ected.W e also m ade calculations forP11

(�8862)and P12 (�8750).AllPaschen pro�lesused Lem ke’s

(1997) tables,because the newer Stehl�e and Hutcheon cal-

culations do not go to large enough values ofN e for high

seriesm em bers.W hile series convergence isnota problem ,

photom etry and norm alization probably is.Calculated pro-

�les for neither ofthe favored m odels,gave good �ts.W e

suggestm uch ofthedi�culty m ay liewith theobservations,

and note thatthe2006 UVES spectrum wasnotre-reduced

by FG .

Fig.16shows�tsofcalculated P12linestotheraw 2006

spectrum ,countsvs.wavelength m odi�ed only by:shifting

the wavelength scale fora radialvelocity of9.3 km s� 1,and

dividing thecountsby 2746.The�tcertainly appearsto fa-

vor the lower-tem perature m odel,but better observational

m aterialisneeded.The\raw" P12 pro�ledi�ered only sub-

tly from the norm alized and Fourier �ltered version that

wetypically use.Howeverthesm alldi�erenceswereenough

Figure 16.The H R 5623 U V ES spectrum (19 M arch 2006) of

P12 (dark gray with points, blue in online version). The light

gray curve (green online)wascalculated assum ing Te� = 9400K ,

and log(g) = 3:7.The black curve was calculated using Te� =

8900K ,and log(g) = 3:2.The overall� t is better for the lower

tem perature,forboth coreand wings.N o attem pthasbeen m ade

to reconcile the atom ic line spectrum with the observations.

that none ofthe calculated P12 pro�les gave a good �t.It

seem s that our (CRC) best e�orts at norm alization actu-

ally degraded the pro�le ofthis and perhaps other broad

features.

10.3 C alcium

W e see little basis in the IRT pro�les alone for assum ing

that calcium is isotopically strati�ed in the atm osphere of

HR 5623.Thisisclearfrom RK B’sFig.8 (upperm ostplot),

aswellasFig.17.Indeed,theevidenceforany strati�cation

ofcalcium at allis not strong.This is shown in the lower

plot ofour �gure,as wellas Tab.9.Reasonable �ts to all

three IRT pro�les m ay be obtained with any one ofthree

contending strati�cation assum ptions:none,elem ental,and

isotopic.

To show therelativeinsensitivity oftheseweak linesto

m odelassum ptions,weshow the�8498 �tto an isotopically

strati�ed m odel,the �8542 �t with elem ental,but not iso-

topic strati�cation,and the �8662 �twith no strati�cation.

Fits ofallthree lines with any ofthe three m odelassum p-

tionsclosely resem ble those shown in the �gure.

None ofthe IRT lines show an indication ofdisplaced

wings that would indicate a40Ca-dom inated deep photo-

sphere (cf.Fig. 4).Sm all verticaladjustm ents of the ob-

served Paschen wings were necessary to achieve the �ts

shown for the upper plots.W e have already noted photo-

m etric uncertaintiesin thisregion.

The di�culty in extracting a strati�cation pro�le for

calcium iswellillustrated in K TR’sFigure 9.O fthe seven

lines used,four are only m arginally above the levelofthe

noise.Usefulinform ation is probably contained in the Ca

K -line,butthere are di�cultieswith Ca i�4227,and Ca ii

�3159.The form er is badly blended with Cr I,while m uch

ofthediscrepancy illustrated forthelatterm ay be resolved

by taking a coolerm odel.Additionally,therearecontinuum

problem sin the region ofthisline.

RK B used a di�erent,butpartially overlapping,setof

Caiand iilinesfrom K TR,and obtained som ewhatdi�erent

Strati�cation and Isotopic Separation in CP Stars 13

8497 8500

8541 8543

0.6

Figure 17.TheIRT in H R 5623 (U V ES spectra 19 M arch 2006).

The calculated pro� les (solid black);observations are dark gray

(red online) with dots.The light gray pro� le for �8542 is calcu-

lated with 40Ca only.There is no indication, as in Fig.4 that

pure (or dom inant) 40Ca would give a better � tin the red wing.

A djustm ents (see text) have been m ade to the Paschen slopesto

� tthe appropriate Paschen calculations (see text).

Table 8. A bundances and g(x) param eters for approxim ations

to K TR and R K B strati� cation pro� les.

Param eter K TR R K B

a 6.0 30

b 1:29� 10� 4 3:16� 10� 3

d 0.0 0.6

strati�cation param eters.W ehaveapproxim ated them with

ourg(x)function with param etersgiven in Tab.8.

O nly the Ca iiK -line pro�le approaches the strength

needed to see strati�cation from the line shape alone.Even

for the K -line,the case for strati�cation is m arginal. At-

tem pts to derive the strati�cation from the pro�le should

also considercontributionsfrom an interstellarcom ponent.

K TR claim ed aCaoverabundanceof1.4dexin thedeep

photosphere(see theirx6).Assum ing a solarlog(Ca=N tot =

� 5:73,K TR’s assum ption for this value would be � 4.32.

Thisshould be com pared to RK B’svalue (see theirTab.4)

log(Ca=N tot)lo = � 5:6,which is in better agreem ent with

ourvalues(cf.Tab.9),depending on the assum ed m odel.

Little inform ation is available from Ca i.M ost ofthe

lines are very weak or badly blended.O nly the resonance

line,�4227 isofm odeststrength (ca.32 m �A).W ecalculate

abundances for this line,assum ing that it is blended with

Cr i�4226.75,and that the chrom ium abundance is �xed

atCr=N tot = 1:76� 10� 4.Sim ilarly,we adopted a m easured

225m �A for the K -line,and com puted abundances from it,

including blends with Cr and Fe I,which m ade only sm all

di�erences in the resulting abundances. Results for three

Table 9. Logarithm ic abundances (log(Ca/N tot) from 32 m �A

�4227,and 225 m �A K -line.Foreach m odel,theupperabundance

id forCa iand thelowerforCa iiColum nsm arked \di� " are(Ca

i� Ca ii).The lastthree rowsgive abundances that yield � ts to

the IRT lines,but only for the 8900K ,log(g) = 3:2 m odels.In

the case ofthe strati� ed m odel,the abundances referto the deep

photosphere.

Te� (K ) log(g) strat di� no strat di�

9400 3.7 � 5:41 � 6:49

� 6:02 0.61 � 7:19 0.70

8900 3.7 � 6:46 � 7:74

� 6:52 0.06 � 7:50 � 0.24

8900 3.2 � 5:92 � 7:31

� 6:32 0.40 � 7:58 0.27

�(T8900/logg= 3.2) strat no strat

8498 � 5.80 � 8.21

8542 � 5.54 � 7.94

8662 � 5.30 � 7.82

m odels,with and withoutthe RK B strati�cation are given

in Tab.9.

Thebestagreem entbetween theK -lineand Ca I�4227

is for a strati�ed m odelwith the tem perature-log(g) pair

(8900K {3.7).Agreem entispoorestatthehigh tem perature.

D eep photosphericabundancesagreereasonably wellam ong

the IRT lines;lesswellwith the K -line and �4227.

10.4 C olum n densities in H R 5623

W ecalculated colum n densitiesfor�tsto the�8498 pro�le,

shown in Figs.14 and 17.W e get a good �t (not shown)

usingelem ental(butnotisotopic)strati�cation,with param -

etersthe sam e asin colum n 3 ofTab.8,butwith Ca0=N tot

sm allerby afactorof0.6.Thisleadstoalogarithm iccolum n

density for48Ca of16.51 (cgs)and 16.00 for

40Ca.

An equally good �t(Fig.17)was m ade with both ele-

m entaland isotopic strati�cation.In thiscase,theassum ed

param eters for g(x) were sim ilar, though not identicalto

those for elem entalstrati�cation alone:a = 30,d = 0:8,

b= 3:16� 10� 10

.TheCa0=N tot valuedeep in thephotosphere

wassetto 5� 10� 6| thiswasessentially all

40Ca.Thisg(x)

essentially setallofthe lightisotope to zero abundance for

layershigherthan x = � 1:5.Theparam etersofg48(x)were

a0= 6,d

0= 4,and q = 3.These set the abundance of

48Ca to zero below x = 0:5.By x = � 1,the 48Ca=N tot had

reached itsm axim um value of4:12� 10� 9.

W ith isotopic strati�cation,even though the 48Ca fea-

ture isstronger,the colum n density ism uch lower.W e �nd

a logarithm ic colum n density for48Ca of14.77,while that

for 40Ca is17.22,a di�erence of2.45 dex.

By colum n density, the relative fraction of48Ca is

sm aller,though of the sam e m agnitude,as the terrestrial

fraction.Thissurprising resultwasnoted in x7.Ithappens

becausethecoreregionsofthelinesaturatevery high in the

atm osphere,and its signi�cance was pointed out by RK B.

Asfar as the core is concerned,the atm osphere below this

pointisinvisible,and to som e extent,irrelevant.

The two possible structures exam ined here surely re-

quire very di�erenttheoreticalscenarios.

14 C.R.Cowley,S.Hubrig,and J.F.Gonz�alez

Table 10.Independentm easurem entsofthe wavelengths ofIRT

lines in H D 101065.Entries are shifts [�A ]from the assum ed ter-

restrialwavelengths at8498.02,8542.09,and 8662.14 �A

Spectrum 8498 8542 8662

U V ES/2002 0.19 0.19

FERO S/2000 0.16 0.18

U V ES/2006 0.21 0.18 0.20

Figure 18.The �8662 line in H D 101065 (U V ES spectrum 14

January 2006). Vertical adjustm ents of 3% have been m ade to

achieve a � t to the wings ofP13.Calculations are in black,ob-

servations dark gray with dots (red online). Strati� cation pa-

ram eters are: a = 6:7, b = 4:0 � 10� 4, d = 0:0. W e used

log(Ca’/N tot) = � 6:20,and �t = 2 km s� 1.The ratio of 48Ca

to 40Ca is 31.6.The light gray curve was calculated with only40Ca.

11 P R ZY B Y LSK I’S STA R

The IRT lines in Przybylski’s star appear to have the full

shiftthatwould correspond to48Ca.W avelengthsfrom Pa-

perII,and new m easurem entsfrom UVES spectra obtained

on 1 Jan.2006 are shown in Tab.10.It surely seem s that48Ca dom inates.

W ehavenotsucceeded in �nding a strati�cation pro�le

that willreconcile the deep photospheric abundances from

the IRT,the Ca iiK -line,and Ca ilines.Nevertheless,the

agreem entam ong these featuresissom ewhat betterwith a

provisionalstrati�cation than withoutone.Theparam eters

are given in Fig.18 for�8662.

W enow addressthequestion ofwhethertheheavy cal-

cium dom inates the photosphere,or ifit occurs in a high

cloud above a photosphere with prim arily 40Ca.W e apply

the sam e test as used for HR 1217 and HR 5623,and see

ifthe wings ofthe IRT lines are better �t with a shifted

or unshifted theoreticalpro�les.W e do this for the �8662

line (Fig.18).There isno indication thata pure40Ca com -

position would yield a better�tto thewings.Com pare this

situation with thatillustrated forHR 1217 (Fig.4).Thefail-

ure ofpure40Ca to account for the wings ofthe strongest

IRT line,�8542,is sim ilar,butthe photom etry in the P15

wingsisnotgood.

The weakest of the IRT lines shows a slight Zeem an

splitting.Itiscalculated in Fig.19 assum ing pure48Ca,and

a transverse�eld of2.9 kG .TheZeem an codewasdescribed

in PaperIII.Paschen convergence wasnotincluded in this

Figure 19.The �8498 line in H D 101065 (U V ES spectrum 14

January 2006).Verticaladjustm ents of-2% have been m ade to

achieve a � tto the wingsofP16.Calculationsarein black,obser-

vations dark gray with dots (red online).Strati� cation param e-

tersareasin Fig.18.Pure 48Ca wasassum ed.Seetextforfurther

discussion.

calculation,butthe e�ectisvery sm all,because ofthe low

tem peratureofHD 101065.Theobserved pro�lewaslowered

by 2% to �tthe farP16 wings.

The cause ofthe broad localm inim um on either side

ofthe �8498 line is not known.It is unlikely to be due to

wings,since the stronger �8662 (Fig.18) and �8542 (not

shown)do nothaveextensivewings.Theabundanceneeded

for the �t shown was nearly 0.7 dex larger than needed to

�tthe two strongerIRT lines.Itisunclearhow m eaningful

this is,since the function g(x) changes from 5:2 � 10� 4

to

0.500 between log(�5000)= � 1:0 and 0.0.

W e see little basis in Fig.19 for assum ing any contri-

bution of40Ca to the pro�le.

12 H D 217522

HD 217522 isa roAp stardiscussed by Hubrig etal.(2002)

asa possible \twin" ofPrzybylski’sstar.G elbm ann (1998)

showed thatthe staris both iron de�cient,and atthe cool

end oftheCP starsequence.Heargued thatthisisageneral

trend am ong roAp stars.

M easurem ents on the cores of the IRT lines in HD

217522 show the full0.20 �A shiftof48Ca.The lines them -

selvesarestrongerthan in Przybylski’sstarbutdo notshow

welldeveloped wings.PaperIIreported shiftsof+ 0.18 and

+ 0.21 �A,for ��8498 and 8662.New m easurem ents ofthe

spectrum obtained on 4 August2008 yield shifts of+ 0.20,

+ 0.21,and + 0.22 �A,for ��8498,8542,and 8662,respec-

tively.

The IRT can be �t equally well{arguably{with either

an isotopic strati�cation,or a strati�cation m odelwith a

constant 48Ca/40Ca ratio that is 10-20 to one.W e prefer

thelatterbecausefeweradjustableparam etersarerequired.

Fig.20 showsa �tofthestrongestline,�8542.A calculation

with pure 40Ca is shown in light gray (green online).W e

obtain quitesim ilar�tsforthe��8498 and 8662 lines,with

sim ilar though not identical strati�cation and abundance

param eters.The plot resem bles Fig.18,where there is no

indication thatthe wingsofthe stellarfeature would be �t

betterwith pure40Ca.Com pareFigs.19and 20with Fig.4.

Strati�cation and Isotopic Separation in CP Stars 15

Figure 20. The �8542 line in H D 217522 (U V ES spectrum 4

A ugust2008).Strati� cation param eters(a = 20:0,b= 1:0� 10� 4,

d = 0:1)and the calcium abundance were chosen to m atch those

used by R K B,Ca0=N tot = 1:58 � 10� 5.The abundance applies

to 48Ca. A constant abundance ratio of 34.7 was assum ed for48Ca/40Ca.The light gray curve (green online) was m ade with

pure 40Ca.

The sam e strati�cation pro�le and abundance �ts the

Ca iiK -line reasonably well.

13 D ISC U SSIO N

Thepro�lesofstrong linesin CP starscannotbe�tby clas-

sicalm odelsthatassum euniform elem enttohydrogen ratios

throughoutthephotosphere.W esupporttheassum ption of

strati�cation toreconcilethediscrepancieswith observation,

em ployed by otherworkers.These attem ptsare notyeten-

tirely satisfactory because som ewhatdi�erentstrati�cation

m odelsare som etim es needed forlinesofthe sam e elem ent

orion.

Ideally,one m ay determ ine the strati�cation param e-

tersdirectly by com parison with the observations.Thusfar

workershavechosen am odel,and then attributed deviations

ofobservations from calculations to strati�cation.Possible

errorsin theassum ed m odelshould befolded in to thispro-

cedure.Such errors clearly in uence the relative strengths

ofneutralsand ions,aswellaslinesofa given specieswith

di�erent strengths and excitation.W e discussed one rele-

vantexam ple,HR 5623 (HD 133792),where we believe the

tem perature wassigni�cantly overestim ated.

W e investigated RK B’sbold hypothesisthatfractiona-

tion ofthecalcium isotopescould beobserved in CP2 stars.

W e support this claim for HR 1217,using di�erent obser-

vationalm aterialfrom their paper.W e con�rm that good

casesforsuch fractionation can bem adefor10 Aqland HD

122970.

O nem ightargue thatoptim um �tswith isotopic strat-

i�cation are only m arginally betterthan the optim um ones

without it.Certainly the additionalparam eters and m odel

exibility of the isotopic strati�cation would be expected

to give an im proved �t.However,the �ts without isotopic

strati�cation show a consistentpattern in a num berofstars,

including m ost studied by RK B.The calculated red wings

are too strong,indicating too m uch48Ca in the deeper at-

m osphere.

RK B wrote (x6):

A sim ple interpretation of the anom aly observed in the Ca ii

8498 �A linecoreisto suggestthattheheavy isotopesarestrongly

enhanced and even dom inantthroughouttheatm ospheresofsom e

m agnetic A p stars. H owever, our m agnetic spectrum synthesis

calculations dem onstrate thatthis hypothesis isincorrect.

The plots in Papers Iand IIshow that the IRT shifts

varyfrom sm allam ountstonearly thefullam ountsfor48Ca.

O nly a few starsshow thefullshifts.O fthese,HR 7143,an

HgM n star(Castelliand Hubrig 2004),and two roAp stars,

HD 101065 and HD 217522 show little or no indication of

thelighterisotope.In HR 5623,onem ay constructa m odel

where48Ca is not dom inant,though the m ost straightfor-

ward interpretation oftheobservationsisthatitis.In som e

HgM n stars,the sym m etricalpro�lesm ay suggestdom ina-

tion by isotopesofinterm ediate m ass.

The overallpicture ofisotope variationsiscom plex.

14 A C K N O W LED G EM EN T S

W ethank D rs.P.North and B.Sm alley forcom putercodes,

and J.R.Fuhr ofNIST for advice on oscillator strengths.

This research has m ade use ofthe SIM BAD database,op-

erated atCD S,Strasbourg,France.W e gratefully acknowl-

edgetheuseofESO archivaldata,including theUVESPO P

data base.O urcalculationshave m ade extensive use ofthe

VALD atom icdata base(K upka,etal.1999).W eappreciate

the help ofL.Sbordone and P.Bonifacio with im plem enta-

tion oftheir version ofAtlas 9.Thanks are also due to M .

Netopilforhelp during observationsin Augustof2008.

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