Time-resolved Spectroscopy of the Polar EU Cancri in the Open Cluster Messier 67

0.39 MB·English

by  Kurtis A. Williams

Accepted for publicationin the Astronomical Journal
PreprinttypesetusingLATEXstyleemulateapjv.5/2/11
TIME-RESOLVED SPECTROSCOPY OF THE POLAR EU CANCRI IN THE OPEN CLUSTER MESSIER 67
Kurtis A. Williams
Department ofPhysics&Astronomy
TexasA&MUniversity–Commerce
P.O.Box3011,Commerce,TX,USA,75429
Steve B. Howell
3 NASAAmesResearchCenter
1 P.O.Box1,M/S244-30,MoffettField,CA94035
0
2 James Liebert and Paul S. Smith

n StewardObservatory
a UniversityofArizona,Tucson,AZ
J

5 Andrea Bellini
2
SpaceTelescopeScienceInstitute
3700SanMartinDrive,Baltimore,MD21218

]
R
Kate H. R. Rubin
S
. Max-Planck-Institutfu¨rAstronomie
h K¨onigstuhl17,69117Heidelberg,Germany
p and
-
o Michael Bolte
r UCO/LickObservatory
st UniversityofCalifornia
a 1156HighSt.,SantaCruz,CA,USA,95064
[ Accepted for publication in the Astronomical Journal

1 ABSTRACT
v
We present time-resolved spectroscopic and polarimetric observations of the AM Her system EU
6
Cnc. EU Cnc is located near the core of the old open cluster Messier 67; new proper motion mea-
3
surementsindicatethatEUCncis indeedamemberofthe starcluster,this systemthereforeis useful
9
to constrain the formation and evolution of magnetic cataclysmic variables. The spectra exhibit
5
two-component emission features with independent radial velocity variations as well as time-variable
.
1 cyclotron emission indicating a magnetic field strength of 41 MG. The period of the radial velocity
0 and cyclotronhump variationsare consistent with the previously-knownphotometric period, and the
3 spectroscopic flux variations are consistent in amplitude with previous photometric amplitude mea-
1
surements. Thesecondarystarisalsodetectedinthespectrum. Wealsopresentpolarimetricimaging
:
v measurements of EU Cnc that show a clear detection of polarization, and the degree of polarization
i drops below our detection threshold at phases when the cyclotronemission features are fading or not
X
evident. The combined data are all consistent with the interpretation that EU Cnc is a low-state
r polar in the cluster Messier 67. The mass function of the system gives an estimate of the accretor
a
mass of MWD ≥0.68M⊙ with MWD ≈0.83M⊙ for an average inclination. We are thus able to place
a lower limit on the progenitor mass of the accreting WD of ≥1.43M⊙.
Subject headings: white dwarfs – novae, cataclysmic variables – Stars: individual: EU Cnc – open
clusters and associations: individual: Messier 67 – Accretion, accretion disks
1. INTRODUCTION The identification of CVs in star clusters provides in-
teresting constraints on the formation and evolution of
Cataclysmicvariables(CVs)areinteractingbinarysys-
the interacting system. As all members of an cluster are
tems in which a white dwarf (WD) is accreting material
coeval, the total age of the system is known, as is the
from a low-mass companion star. If the WD has a suffi-
system’s distance and metallicity. Further, if the mass
ciently strong magnetic field, the formation of an accre-
and effective temperature of the white dwarf can be de-
tiondiskisinhibited,andmaterialaccretesdirectlyonto
termined, then a limit on the white dwarf’s progenitor
oneormoremagneticpolesofthewhitedwarf. Thesebi-
mass can be derived via the same methods used to con-
nariesareknownas AMHer systemsor polars,after the
structtheinitial-finalmassrelation(e.g.,Williams et al.
high fraction of polarized light detected in the systems.
2009). Because the white dwarf is likely re-heated to
[email protected] some extent by the ongoing accretion, the constraint on
2 Williams et al.
the progenitor mass would be strictly a lower limit. detected an X-ray source coincident with the optically-
CVs are quite common in globular clusters (e.g. variablesource; its very soft X-rayhardness ratio is typ-
Margon et al. 1981; Grindlay et al. 1995). The glob- ical for AM Her systems in the ROSAT bands. The AM
ular CV population tends to be centrally concen- Her nature of EU Cnc was confirmed by Pasquini et al.
trated (e.g. Grindlay et al. 1995, 2001). This result (1994), who obtained three 75-minute optical spectra of
is likely explained by the formation of tight binaries the source. These spectra exhibit cyclotron humps and
by stellar encounters in globular cluster cores (e.g. radial-velocity variable emission lines of H, He I, He II,
Podsiadlowskiet al. 2002; Pooley et al. 2003). As such, and Fe II. Under the assumption that EU Cnc is in the
globular cluster CVs are excellent tracers of a globular’s star cluster, Pasquini et al. (1994) conclude that the ab-
dynamichistory,buttheseCVsmaynotshedmuchlight soluteopticalmagnitudeandX-rayluminosityofEUCnc
on the formation and evolution of CVs in the galactic are typical for low-state AM Her systems.
field where stellar encounters are rare. SubsequentX-raystudiesbyBelloni et al.(1998)using
Openstarclustersmaythereforebe a moreusefullab- ROSATdetected100%modulationofthesoftX-rayflux
oratory for studying CV evolution. The stellar densities with a period equal to the optical period, indicative of
arefarlowerthaninglobularclusters,eveninthecluster accretiononto a single magnetic pole. Chandra observa-
core,anddynamicalsimulationssuggestthatCVforma- tions by van den Berg et al. (2004) detected hard X-ray
tion is not enhanced by the stellar encounters that do emissionfromEUCnc,againtypicalforAMHersystems
occur (Shara & Hurley 2002), though a small fractionof and likely due to shocks in the accretion flow.
openclusterCVsmaystillbeformedbystellarexchanges More recent time-series photometry from Nair et al.
(Shara & Hurley 2006). Open clusters also span a wide (2005) again detected high-amplitude optical modula-
rangeofages,metallicities,andstellarmasses,raisingthe tion, with V-magnitudes varying from 21.6 to 20.3 mag
potential to study how these parametersimpact CV for- atthesame2.09hrperiodofGilliland et al.(1991). The
mation and evolution more precisely than possible from variation amplitude was about 30% larger than in 1991,
studies of field CVs. with that difference likely due to different filters used in
Unfortunately, the number of CVs in open clusters is the two studies, V containing a large cyclotron modula-
small, and none are well-studied. In the ancient, dense, tion.
metal-richopenclusterNGC6791,twospectroscopically- Based on the body of work on EU Cnc, Nair et al.
confirmed CVs are known (Kaluzny et al. 1997; (2005) point out an interesting conundrum. The high-
Mochejska et al. 2003); de Marchi et al. (2007) identify amplitude optical variability is typical for AM Her sys-
a suspected third cluster CV based on photometric temsinahighaccretionstate,whiletheX-rayluminosity
properties and conclude that all three CVs are likely ofEUCnc,under the assumption it is a member of M67,
cluster members. One CV, EU Cnc, is known in the is typical of magnetic CVs in a low accretion state.
open cluster M67 and described in detail below. These In this paper, we present time-resolved spectroscopy
four objects are the only confirmed cluster member of EU Cnc obtained serendipitously with the 10-m Keck
CVs, and due to the large distances of the clusters telescope, as well as the first polarimetric measurements
[(m−M) =13.4 for NGC 6791 and (m−M) =9.97 of this system. After discussing the observed phe-
V V
for M67], spectroscopic studies of these CVs with the nomenology, we revisit the issue of EU Cnc’s cluster
same precisionand the same techniques (such as tomog- membership. We will show that the optical variability
raphy) as current field CV studies require significant is almost entirely due to cyclotron emission changing
time on 8 m-class telescopes and larger. throughout the orbit and that the optical spectrum is
Other candidate open cluster CVs have been sug- typicalofa lowaccretionstatepolar. We detectthe sec-
gested: Mochejska et al. (2004, 2006) identify a CV in ondary star in the spectrum and, along with the other
the field of the ∼2−3 Gyr-old open cluster NGC 2158, evidence, we show that EU Cnc is a member of the M67
though it may lie foreground to the cluster. One CV open cluster.
is identified photometrically in the field of the 3.5 Gyr-
oldclusterNGC6253,butnomembershipinformationis 2. TIME-RESOLVEDSPECTROSCOPY
available (de Marchi et al. 2010). The rich open cluster 2.1. Observations and Data Reduction
M37 (age ∼ 550 Myr) has two CV candidates identified
We targeted EU Cnc serendipitously as part of a pro-
photometrically by Hartman et al. (2008). Finally, an
gramtoobtainhighsignal-to-noisespectroscopyofWDs
X-ray source in the field of the cluster NGC 6819 (age
inMessier67. WeobtainedobservationsonUT2007Jan
∼ 2−2.4 Gyr) has properties consistent with CVs, but
19 with the low-resolutionimaging spectrometer (LRIS)
its true nature and cluster membership are unconfirmed
on the Keck I telescope (Oke et al. 1995; Steidel et al.
(Gosnell et al. 2012). The Hyades contains at least one
2004). Weobtainedsimultaneousspectrawithbothblue
pre-CV, V471 Tau (e.g Vauclair 1972), but no actively
and red sides of the spectrograph through a multiobject
accreting systems. slit mask with slitlet widths of 1′.′0. On the blue side,
1.1. EU Cancri we used the 400 lines mm−1 grism blazed at 3400˚A for
a resulting spectral resolution of ≈ 7˚A FWHM. On the
EU Cnc was detected as variable object in the field of
red side of the spectrograph, we used the D560 dichroic
the old open star cluster Messier 67 by Gilliland et al.
(1991), who identified it as a likely AM Her system and the 600 grooves mm−1 grating blazed at 7500˚A, for
based on the similarities of its light curve to that of a resulting spectral resolution of 4.8˚A FWHM. The to-
VV Pup. They determined EU Cnc has a photomet- talspectralcoveragerangedfrom7400˚Abluewardtothe
ric period of 2.091±0.002 hr with variations through a UV atmospheric cutoff.
CuSO (U band) filter of 0.6 mag. Belloni et al. (1993) The weather was nearly photometric through the en-
4
Spectroscopy of EU Cnc 3
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3600 4800 6000 7200 -120001200-120001200
Figure 1. Time-orderedspectroscopy ofEUCnc. Theleftpanelscontaintheentirespectrum;thegapatλ≈5650˚A isthegapbetween
theblueandredarmsofthespectrograph. Therightpanelscontainclose-upsoftheλ4686HeIIline(left)andHβ line(right);theradial
velocity variations and variable line asymmetries are clearly visible. Phase φ = 0 indicates the negative zero crossing of the narrow-line
component oftheemissionlines.
tireobservation,andseeingwasmoderateat0′.′9FWHM. attempted to minimize the effects of atmospheric dis-
Sevenexposures,eachoftwenty-minuteintegration,were persion by using a blue filter in the guider camera, but
taken over a ∼ 2.5 hr period, with two short breaks diminution ofthe UV lightis severeat higher airmasses.
for mask re-alignment. During the final exposure, the We reduced the data using the onedspec and twodspec
flux dropped dramatically for most stars, likely indicat- packages in IRAF. Overscan regions were used to de-
ing that the mask was slightly misaligned. termine and remove the amplifier bias. Flat-fielding on
Theseobservationsweretakenpriortothe installation the blue side data was accomplished using a piecewise-
of the LRIS atmospheric dispersion corrector, and due smoothresponsefunctionasdescribedinWilliams et al.
to constraints in slit mask design, the slitlets were ori- (2009)toeliminateringingduetoasharpinflectionpoint
ented nearly perpendicular to the parallactic angle. We in the flat field at ≈ 4200˚A. Cosmic rays were removed
4 Williams et al.
fromeachtwo-dimensionalspectrumusingtheL.A.Cos-
micLaplaciancosmicrayrejectionroutine(van Dokkum
2001). Wavelength solutions on the blue side were de-
rived from Hg, Cd, and Zn arclamp spectra; on the red
side, Ne and Ar arclamp spectra were used. These cal-
ibrations were obtained prior to the final mask realign-
ment.
Relative flux calibration was obtained using 1′′-wide
long-slit spectroscopy of the spectrophotometric stan-
dards G191-B2Band G138-31taken at parallactic angle
near the start of the night. No attempt was made to
obtain absolute spectrophotometric calibrations.
2.2. Spectral Phenomenology
The time-series spectra are shown in Figure 1. Qual-
itatively, the spectra appear fairly typical for AM Her-
typesystemsinalowaccretionstate,similartothoseob-
servedforHUAqr(Glenn et al.1994). Cyclotronhumps
are visible and variable in strength. Emission lines of H
andHeareobservedandhaveatleasttwocomponents,a
narrow(unresolved)componentandabroadcomponent.
Theemissionlineshavevariableradialvelocities,andthe
Figure 2. Radial velocity curve for EU Cnc (top panel) and a
radial velocities of the two line components are not in
G-type star in a neighboring slitlet (bottom panel). Filledcircles
phase. This type of emission line component behavior is (blue in the online color version)indicate relative radial velocities
often seen in polars, for example VV Pup (Mason et al. fromemissionlinesonthebluearmofthespectra;stars(redinthe
2008) whereby the narrow line component phases with onlineversion)indicatedatafromtheredarmofthespectrograph.
Thesolidcurve (magenta inthe onlineversion) isthe best-fitting
the motion of the secondary star (Mason et al. 2008;
sinewave.
Howell et al. 2008). The time scales for both the cy-
clotronhump variations and emission line variations ap-
peartobeconsistentwiththeknownphotometricperiod, described further below. The resulting radial velocities
though additional time-series spectra would be required (relative to the observations closest to zero phase) are
to provethese areidentical. We now quantify these phe- given in Table 1 and shown in Figure 2. The radial ve-
nomena. locities atφ≈0.59arelikely measuringdifferentmotion
We estimate the strength of the magnetic field us- than the other points, as the narrow component of the
ing the spacing of the cyclotron humps in the optical emission lines disappears during these observations.
spectra. The locations of the peaks are estimated by As a cross-check, we used the same method to deter-
fitting a 12th-order polynomial to the continuum, ex- mine the radial velocity of a G-type star targeted in a
cluding the obvious emission lines. We use equation 54 neighboringslitlet. Theradialvelocityofthisstarshould
from Wickramasinghe & Ferrario (2000) to get a mag- be constant over the set of observations, and although a
netic field strength of B ≈ 41 MG. We do not see Zee- slightpositivevelocityoffsetmayexist,itisoflowampli-
mansplithydrogenabsorptionlinesinthespectrumcor- tude compared with the variations observed in the CV.
responding to this magnetic field strength, but later we The phase and amplitude of the radial velocity varia-
willseethattheyarelikelyfilledinbytheredcontinuum tions were determined by fitting a function of the form
contribution of the secondary star.
v =Ksin[2π(φ−φ +0.5)]+v
rel 0 0
2.2.1. Radial Velocity
to the radial velocity data. The period was fixed to
Because these data were not obtained with the goal the known optical period of 2.091 hours, and the phase
of obtaining precision radial velocities, and because the shift φ , amplitude K, and the relative velocity zero-
0
flexureinthespectrographwassignificantoverthecourse point v were allowed to vary. The best-fit values are
0
of the observations, it was not possible to obtain abso- K = 340±20kms−1 and v = +43±37 km s−1. We
0
luteradialvelocities. Attemptstousenightskyemission emphasizethat this velocityzeropointis a velocityrela-
linesasvelocityzeropointsfailedduetothelackofnight tive to the spectra used as our zero velocity, which were
sky lines in data from the blue arm of the spectrograph, selectedsincetheyaretheclosestdatatoaphaseofzero.
where the majority of the CV’s emission lines were lo- Basedonthe detailed observationofnarrowline compo-
cated. nents in the polars VV Pup (Mason et al. 2008) and EF
Instead, relative radial velocities were obtained as fol- Eri (Howell et al. 2008), mapping to the motion of the
lows. First, the continuum was fit with a high-order secondarystar,thetypicalorbitalphase0.0usedforcat-
polynomial and removed from each spectrum. The ra- aclysmic variables would occur near phase 0.5 as shown
dial velocity of the narrow component of the emission in Figures 1 and 2. However, we do not have sufficient
lineswasdeterminedbyautocorrelationofeachspectrum datahere(e.g.,avelocitycurveofthephotosphereofthe
with that of an observation with an exposure midpoint secondarystar)tostatethisfactwithabsolutecertainty.
close to zero phase. This determination involved some Asthesevelocitiesarenotabsoluteradialvelocities,they
iterative bootstrapping with the radial velocity fitting cannotbe used for cluster membership determination or
Spectroscopy of EU Cnc 5
Table 1
RadialvelocitiesofEUCncandanunrelatedneighboringG-typestar
Obs. Midpt Phase Spectrograph vEUCnc,rel σ(vEUCnc,rel) v∗,rel σ(v∗,rel)
(MJD) Arm (kms−1) (kms−1) (kms−1) (kms−1)
54119.51236 0.682 Red 384.9 13.8 27.8 5.2
54119.52732 0.854 Red 183.0 23.2 9.4 20.8
54119.54231 0.026 Red 0.0 0.0 0.0 0.0
54119.56151 0.246 Red −288.7 27.6 1.5 46.9
54119.57651 0.418 Red −187.5 28.1 31.5 42.4
54119.59146 0.590 Red 201.4 25.6 23.8 44.3
54119.61542 0.865 Red 179.7 23.5 −5.9 71.1
54119.51239 0.682 Blue 458.5 17.9 36.3 11.8
54119.52689 0.849 Blue 248.3 27.5 29.3 18.8
54119.54145 0.016 Blue 0.0 0.0 0.0 0.0
54119.56153 0.246 Blue −297.7 30.5 9.7 19.9
54119.57613 0.414 Blue −158.2 24.9 22.9 21.2
54119.59067 0.581 Blue 285.7 33.6 10.5 22.7
54119.61545 0.865 Blue 223.2 35.2 22.6 25.0
Note. — Phaseφ=0indicatesthenegativezerocrossingofthenarrow-linecomponent oftheemissionlines;velocities arerelativeto
theexposurecloseesttoφ=0.
rejection.
Qualitatively, the sine curve is not a superb fit to the Table 2
TimeSeriesBroad-bandPhotometryofEUCnc
data, especially for phases between 0.5 and 1. We note
that, at these phases, the narrowcomponent of the lines
is relatively weak and the broad component strong. In MidpointObs. g∗,meas a,b gEUCnc,measa gEUCnc,corrc
(HJD) (mag) (mag) (mag)
fact, at phase φ = 0.59, the narrow component of the
lines is not visible. These velocity measurements are 2454120.01789 20.563 20.806 20.567
2454120.03239 20.676 21.601 21.249
likelynon-Keplerianstreamingmotion. However,theex-
2454120.04695 20.480 21.672 21.516
cellent fit for the points with phases between 0 and 0.5, 2454120.06703 20.703 21.266 20.887
where the emission lines are dominated by the narrow 2454120.08163 20.614 20.440 20.150
component, suggests that our fit amplitude and phase 2454120.09617 20.467 20.429 20.286
2454120.12095 21.147 21.706 20.883
shift are not unreasonable.
2.2.2. Photometric Variability a Measuredfluxfoldedthroughg filterresponse
b Instrumental magnitudeoftheneighboringKstar
As mentioned above, absolute spectrophotometry was c EUCncphotometrycorrectedtostandardsystem
not a goal of our observations; slit losses as a function
of wavelengthcould be significant and time-variable due
to both seeing and atmospheric dispersion effects. Even results are included in Table 2. The errors in this pho-
so, it would be instructive to compare photometry de- tometryareuncertain. Therandomerrorsduetophoton
rived from our spectroscopy with previous photometric shotnoise in the source and sky are small, ≤0.003 mag.
monitoringofthissystem. Wethereforecalculatebroad- However,systematic errorssuchas differential slit losses
bandphotometrybyfoldingour(relative)flux-calibrated likely dominate the photometric uncertainty. The mag-
spectrathroughfilterresponsefunctions. Duetothesig- nitude of the error in absolute photometry is at least
nificantlossofUVlightinthelaterexposures,werestrict 0.03mag (the errorin the broadbandphotometry of the
our analysis to the g-band. comparisonstar).
In order to correct for slit losses and variable atmo- We compare our derived photometry with the time-
spheric absorption, we perform the same calculation for series photometry of Nair et al. (2005). These published
a K-type star targeted in a different slitlet on the same data were taken in V; we convertedthese magnitudes to
mask (note that this is not the same star used for ra- g usingthePopulationItransformationequationsinTa-
dial velocity comparisons in §2.2.1). The star is located ble 4 of Jordi et al. (2006) and the B−V=0.41 color of
at α(J2000)=8h51m35s.46, δ(J2000)= 11◦50′19′.′1, and, EU Cnc from Gilliland et al. (1991). As these transfor-
in our photometry (Williams et al, in preparation), has mations are for single stars, and as the color of EU Cnc
g =20.324±0.032. ThisstaralsoappearsinSDSSDR7, is likely changing as a function of phase, we emphasize
with PSF magnitude g = 20.263± 0.038. Due to the that these transformations are meant to be illustrative
higher precision of our data, we adopt our photometry only. Since the ephemeris of EU Cnc is not sufficiently
for this star. well-determined to allow us to phase the data precisely,
For each exposure, the calibrated spectra of both EU we added an arbitrary phase shift to the published pho-
Cnc and the comparison star are folded through the g- tometry.
bandfilterresponsefunctionusingtheSynphotsynthetic The results of this comparison are shown in Figure
photometrypackageinSTSDAS.Allmagnitudesarecal- 3. With the exception of our observation at φ = 0.865,
culatedasABmagnitudes. Zero-pointoffsetsingarecal- ourcorrectedspectrophotometryandthepublishedtime-
culated from the comparison star; these offsets are then seriesphotometryagreeverywellinbothshapeandam-
applied to the calculated magnitudes for EU Cnc. The plitude.
6 Williams et al.
phase as the second exposure. The total flux is slightly
lowerandthereisnosignificantdetectionofpolarization
(v =−2.8±2.6); the final exposure is the faintest of the
four and has no significant polarization.
As these observations were taken 11 months after the
spectroscopy,andasthe ephemerisofEUCncisnotsuf-
ficientlywellknown,thespectroscopicphaseoftheseob-
servationscannotbecalculated–theaccumulateduncer-
taintyinphasegiventhe0.002hruncertaintyinthepho-
tometric period of Gilliland et al. (1991) is ≈7.5 cycles.
However, from the total counts in the polarimetry mea-
surements, we know that these observations were taken
on the declining portion of the light curve. We there-
fore calculate relative magnitudes from the total inten-
sitymeasurementsinTable3 andaddanarbitrarymag-
nitudezeropointandphaseshifttoplacethesepointsin
the folded light curve of Figure 3.
Fromthisexercise,weseethattherateofdeclineinthe
observedintensityagreeswiththatobservedinthetime-
series photometry of Nair et al. (2005) and in our spec-
trophotometry,indicatingthatthespectroscopicphaseof
the first polarimetric observations was φ ≈ 0.5 to 0.65.
Figure 3. ThelightcurveforEUCnc. Largefilledcirclesarethe Comparison with the time-series spectra in Figure 1
spectrophotometrydatafromthiswork;errorbarsarenotincluded shows that this corresponds to a phase when the cy-
but are likely at least 0.03 mag. Filled triangles with error bars
clotron humps are dominant in the spectrum; these
(redintheonlineversion)aredatafromNairetal.(2005),shifted
in phase by an arbitrary offset. Stars (blue inthe online version) humps then vanish by a phase φ = 0.85. This is con-
arespectropolarimetricdata form this work. Thelightcurves are sistentwiththestrongdegreeofpolarizationobservedin
qualitatively nearly identical between these data sets, suggesting thefirstexposure,andthe weaker/insignificantpolariza-
littlechange inthestate ofthe polarbetween early2004andlate
tion in the other polarimetry exposures.
2007.
In summary, we detect significant polarization from
EU Cnc at a phase likely corresponding to strong spec-
troscopic cyclotron emission features, and the degree of
2.3. Time-series Polarimetry
polarization decreased below our detection threshold at
CircularpolarimetryofEUCncwasobtainedwiththe phases when the cyclotron features were fading or not
SPOL spectropolarimeter (Schmidt et al. 1992) on the evident in the spectrum. This proves that the features
2.3-m Bok Telescope at Steward Observatory in 2007 are indeed cyclotronemission. From a semantic point of
December. The observations were taken in the imaging view, this detection of significant polarization also con-
mode of the instrument using a Hoya HA30+Y48 filter firmsthatwecanusethemoniker“polar”torefertoEU
combination, giving a broad bandpass of ≈ 4800−7000 Cnc.
˚A.Imageacquisitionanddatareductionfollowthosede-
scribed in Smith et al. (2002), but modified as appro- 3. DISCUSSION
priate for circularpolarimetry. A λ/4 waveplate is used
3.1. Cluster Membership
toconvertincidentcircularpolarizationtolinearandthe
Wollastonprismseparatesthelightintotwoorthogonally EU Cnc is projected ≈1.′7 away from the cluster cen-
polarizedbeams that are focused onto a CCD. Two sep- ter defined by Montgomery et al. (1993) (0.4 pc at the
arate reads of the CCD are made with the wave plate cluster distance), well within the observedcore radius of
rotated through four positions to determine the circular ≈4.′5(e.g.,Tinsley & King1976;Bonatto & Bica2003).
V Stokes parameter. Two consecutive 10-minute expo- However, this proximity alone is not sufficient evidence
sures (150 s per wave plate position) were obtained on of cluster membership.
each of two nights. The sky was clear during the ob- Bellini et al. (2010) present proper-motion data for
servations, but no attempt at absolute calibration was white dwarfs in M67, precise to V ≈ 26, obtained from
made because of the non-standard filter bandpass used. multiple-epoch imaging from the Canada-France-Hawaii
Photometric information was extracted using a circular Telescope and the Large Binocular Telescope. Figure 4
aperture of radius 6′′. shows the vector-point diagram of objects within 20′
The observing log and resulting circular polarization from the cluster center (right panel). The circle indi-
measurements(V/I =v)aregiveninTable3. Alsogiven cates the proper motion membership cut adopted by
are the background subtracted counts and the phase of Bellini et al. (2010); the error bars show the displace-
themidpointofeachobservationrelativetofirstexposure mentuncertaintyforEUCnc,solidlyinsidethemember-
onthefirstnightassumingaphotometricperiodof2.091 shipcircle. Inaddition,the proper-motionselectedcolor
h. There is a significant detection of polarization in the magnitude diagram (left panel) shows that EU Cnc lies
first exposure, with v = −12.7±1.8%. The degree of on the WD cooling sequence of M67.
polarization and the total flux both drop significantly Astrometry performed on EU Cnc and 3 encircling
in the second exposure (v = −6.3±2.3%). The third brighter known member stars, using the POSS I and II
exposure, taken two nights later, is at nearly the same platesaswellasadeep,0′.′4seeingimageobtainedbyus
Spectroscopy of EU Cnc 7
Table 3
PolarimetricObservationsofEUCnc
ObservationDate Obs.Time RelativePhasea Counts V/I σ(V/I)
(UT) (UT) (∆Φ) (ADU) (%) (%)
2007December14 10:28 ··· 74147 −12.7 1.8
2007December14 10:39 0.08 55485 −6.3 2.3
2007December16 08:41 0.10 48303 −2.8 2.6
2007December16 08:52 0.19 30698 4.6 4.0
a Phaserelativetofirstpolarimetricobservation
Figure 4. The proper-motion selected color-magnitude diagram
(CMD, left) for M67 and the vector point diagram (VPD, right)
forallstarsinthefieldasdeterminedbyBellinietal.(2010). The
cross(redintheonlineversion)intheCMDindicatesthelocation
of EU Cnc. The circle (blue in the online version) in the VPD
Figure 5. Red spectrum from phase 0.865 in Fig. 1 along with
indicates the selection criteria Bellini et al. used to select clus-
a scaled M5V spectrum taken from the Jacoby Atlas (star 57,
ter members; the error bars (red in the online version) show the
Jacobyetal.1984). TheM5Vstarisscaled1.4magnitudesfainter
location and uncertainty in the proper motion of EU Cnc. The
thanthestellarcontinuum,approximatingthelevelofcontribution
qualitative data are convincing that EU Cnc is a proper-motion
isprovidestotheredendofthespectrumofEUCnc.
memberofthecluster.
atthe KittPeakWIYN telescopein2007,showthatthe tical spectrum of EU Cnc (see the late phase red spec-
polar’s location relative to the other three stars changes tra in Fig. 1 and Fig. 5) by noting the TiO absorption
by 0′.′3±0′.′5 over the 60 year interval. This is a similar bands chopping into the spectrum at the characteristic
uncertaintyto that for eachofthe brighterstarsrelative locations near 6800˚A and 7100˚A. The shape and rela-
to each other. We therefore feel confident that EU Cnc tive amplitude of the TiO humps are a good match to a
is a member of the M67 star cluster. M5Vstarwhichis alsothe expected spectraltype of the
secondary star in EU Cnc (see below). Noting the dilu-
3.2. A low-state polar in M67 tion of the TiO bands compared to a single M5V star,
wedeterminethatthesecondarystarcontributes20-25%
Nair et al. (2005), suggest that the luminosity of EU
of the continuum redward of 6000˚A. This estimate sug-
Cnc is lower than other high state polars and fully con-
geststhattheM5Vsecondarystarwillhaveanapparent
sistent with the luminosity of low-state polars in globu-
magnitude near 22.5 and, for an its M =12.6, yields a
lar clusters; the distances to field magnetic CVs are too V
distance to EU Cnc of 832 pc, again the same as M67.
uncertain to allow for such a precise comparison. The
The M star continuum is also the likely cause of filling
spectra obtained in this study, as well as those prior,
in the Zeeman spilt Hα absorption components.
show the clear indications of a low state polar: a steep
Balmer decrement (compared to a flat decrement and
3.3. The masses of the white dwarf accretor and its
Balmer jump in emission in high states) and the separa-
progenitor star
blenarrowandbroademissionline components. Warner
(1999) examine the high-low state range of polars and AnadvantageoffindingamagneticCVinanopenstar
notes that the magnitude difference is typically near 3-4 clusteristhatnumerousconstraintscanbeplacedonthe
for a 2 hour polar. Additionally, low state polars have progenitor system. As EU Cnc is a member of Messier
absolute magnitudes near 11-12in V comparedwith 8-9 67, its initial metallicity and total evolutionary age are
in V when in a high state. If EU Cnc were in a high identical to the cluster’s characteristics. With some rea-
state with its observed apparent V magnitude, it would sonable assumptions, we can go one step further to con-
need to reside at a distance of near 3100 pc. However, strainthe white dwarf’s mass and cooling age,which we
in its low state and V ∼21, we find it to be at a distance can then use to constrain the white dwarf progenitor’s
of approximately 850 pc or the same distance as M67 mass. We describe these steps in detail below, but note
(Sarajedini et al. 2009). that this methodology has been used in numerous open
Additionally, we detect the secondary star in the op- cluster and field star studies to determine WD progen-
8 Williams et al.
itor masses (e.g. Liebert et al. 2005; Kalirai et al. 2008; age is subtracted from the cluster age to get the progen-
Catal´an et al. 2008; Williams et al. 2009; Dobbie et al. itor star’s nuclear lifetime; stellar evolutionary models
2012) are then used to infer the progenitor star mass.
WD masses are often determined through model at- The WD mass estimates are sufficiently high to con-
mosphere fits of the WD spectrum, but absorption lines clude that the WD has a carbon-oxygen core, indicat-
from the white dwarf photosphere are not convincingly ing that the common envelope phase for the progenitor
evidentinourdata,being filledinandmisshapedbythe system did not occur before helium ignition in the WD
emission. However, we note that Liebert & Stockman progenitor. Since the AGB phase of stellar evolution is
(1985) and Mason et al. (2008) determined that the relatively short compared to the WD cooling times and
“centerof mass”for the narrowemissionlines originates progenitornuclear lifetimes we estimate for this star,we
between L and the center of mass of the donor, that assume that any effect of the common envelope phase
1
is they approximate the center of mass of the secondary on the calculation of the progenitor nuclear lifetime is
star. Wethereforeassumethatthenarrowcomponentof minimal.
the emission lines originates from the center of mass of To estimate the effective temperature of the WD, we
the secondarystaranduse ourvelocityamplitude to de- assume that the minimum luminosity of the system is
termine the massfunction ofthe systemandto estimate due to solely to the combined light of the M5V sec-
the mass of the white dwarf, M . ondary and the WD photosphere, and we assume that
WD
The mass function f(M) of the system is the WD has not been heated by the ongoing accretion.
Under these assumptions, the WD has M = 12.5. We
(MWDsini)3 PK3(1−e2)3/2 then interpolate WD photometric evolutVionary tables
f(M)= = (1)
(M +M )2 2πG providedonlinebyP.Bergeron1andcomputedfromcolor
WD 2
and model calculations of Holberg & Bergeron (2006),
where M is the mass of the donor star. Assuming a
2 Kowalski& Saumon (2006), Tremblay et al. (2011), and
circular orbit (e = 0) with a period P = 2.091 hr and
Bergeronet al. (2011) to find the WD’s cooling age as a
the velocity amplitude K = 340 km s−1, from Eq. 1 we
function of mass at which its luminosity is equal to the
find f(M)=0.356M⊙. observedminimumluminosityoftheCV.Despitetheun-
Since we do not see eclipses, we can constrain the in-
certainty in the WD mass, the cooling age of the WD is
clination to be . 74◦ (e.g. Warner 1995). If we assume
relatively insensitive to its mass, at least over the range
MWD >>M2,wethereforefindthatMWD ≥0.40M⊙. If of 0.5M⊙ to 1.0M⊙, at logτcool = 8.86 to 8.95. If the
insteadwe assume anaveragevalue of<sin3i>=0.679 WD has experienced significant heating, or if the min-
(e.g. Trimble 1974), then we find MWD =0.52M⊙. imum luminosity is significantly contaminated by light
However, the mass of the donor star is not negli- from the accretion stream and/or the accretion column,
gible. Howell et al. (2001) present detailed evolution then its actual cooling age will be older than these cal-
models for the secondary stars in cataclysmic variables culations. This means that our derived progenitor mass
and note that for those systems with orbital periods is a lower limit on the WD’s actual progenitor mass.
below the period gap (< 2.5hr), the secondary stars We now calculate the WD progenitor mass. We adopt
follow the normal main sequence mass-radius relation- anageofM67of3.5Gyrto4.5Gyr,andaclustermetal-
ship. We therefore expect the mass of the secondary licity of ZM67 ≈Z⊙ and the calculated primordial value
star in EU Cnc to be M2 = 0.21M⊙ with a radius of of Z⊙ = 0.0142 (Grevesse et al. 2010). Since the lower
R2 =0.22R⊙. These value are roughly those of an M5V limit on the WD cooling age is well-constrained, we ob-
star. Adopting this mass for the secondary star, we find tain a fairly precise lower limit on the progenitor mass
MWD & 0.68M⊙ (since i . 74◦) and MWD = 0.83M⊙ of MWD,init = 1.43M⊙ ±0.07M⊙, with the majority of
for <sin3i>=0.679. theuncertaintyduetotheuncertaintyintheageofM67.
We note that these masses assume that our velocity For comparison,the currentmain sequence turnoff mass
amplitude is correct. As noted in §2.2.1, our value of (using the same models and inputs) is 1.35M⊙.
K assumes that our velocity amplitude is resolving the If we relax the assumption of no heating of the WD,
narrowcomponentoftheemissionlinesandthatthenar- thentheWD’scoolingage(timesinceitsemergencefrom
row lines trace the center of mass of the secondary star. the red giant progenitor) could be significantly longer;
Higherspectralresolutionswouldbenecessarytotestthe this would imply a larger progenitor mass. Therefore,
firstassumption,andsowedonothavegoodconstraints wecanonlyconstraintheWDprogenitormasscalculated
onthe errorsorourconfidence limits onthe white dwarf above to be a lower limit; i.e. MWD,init ≥1.43M⊙.
mass. However, the WD mass estimates are similar to
or higher than the spectroscopic masses of young mem- 4. CONCLUSIONS
ber WDs in M67 (M = 0.5M⊙ to 0.6M⊙, Williams et We have presented new observations of the polar EU
al. in preparation). Further, through a lucky coinci- Cnc. In particular, proper motion studies strongly indi-
dence, our ignorance of the WD mass does not signif- cate that this system is a bona-fide member of the old
icantly impact estimates of the WD’s progenitor mass. openstarclusterM67,whichprovidesstrongconstraints
Wethereforeproceed(perhapsquixotically)toconstrain on EU Cnc’s total age,metallicity, and progenitor mass.
the WD’s progenitor mass. Usingphase-resolvedopticalspectraandpolarimetry,we
To constrain the progenitor mass, we use the method- have shown that EU Cnc exhibits all the properties of a
ology of Williams et al. (2009). To summarize, we use low state polar. Both assumed “best fit” polar parame-
the effective temperature and mass of the WD to de- ters as well as standard values for the donor star lead to
termine its cooling age (the elapsed time since the WD
emerged from the AGB progenitor star). This cooling 1http://www.astro.umontreal.ca/~{}bergeron/CoolingModels
Spectroscopy of EU Cnc 9
conclusions that are consistent with the system’s mem- Hartman,J.D.,Gaudi,B.S.,Holman,M.J.,etal.2008,ApJ,
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2541
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tional Science Foundation awards AST-0397492 and X-rayBinaries,ed.D.Q.Lamb&J.Patterson, 151–177
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