New Astronomy 22 (2013) 7–14

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New Astronomy

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Population types of cataclysmic variables in the solar neighbourhood

T. Ak a,⇑, S. Bilir a, T. Güver b, H. Çakmak a, S. Ak a

a _Istanbul University, Faculty of Sciences, Department of Astronomy and Space Sciences, University, 34119 _Istanbul, Turkeyb Sabancı University, Faculty of Engineering and Natural Sciences, Orhanlı–Tuzla, 34956 _Istanbul, Turkey

h i g h l i g h t s

" Galactic orbital parameters of cataclysmic variables (CVs) are calculated." About 6% of cataclysmic variables are thick disc stars." There is no halo CVs in the Solar vicinity." About 60% of the thick disc CVs have orbital periods shorter than 2.6 h." A kinematical age of 13 Gyr is obtained for the most probable thick disc CVs.

a r t i c l e i n f o

Article history:Received 17 October 2012Received in revised form 12 November 2012Accepted 22 November 2012Available online 29 November 2012Communicated by E.P.J. van den Heuvel

Keywords:97.80.Gm cataclysmic binaries98.10.+z Stellar dynamics and kinematics98.35.Pr solar neighbourhood

1384-1076/$ - see front matter � 2012 Elsevier B.V. Ahttp://dx.doi.org/10.1016/j.newast.2012.11.007

⇑ Corresponding author.E-mail address: tanselak@istanbul.edu.tr (T. Ak).

a b s t r a c t

The Galactic orbital parameters of 159 cataclysmic variables in the Solar neighbourhood are calculated,for the first time, to determine their population types using published kinematical parameters. Popula-tion analysis shows that about 6% of cataclysmic variables in the sample are members of the thick disccomponent of the Galaxy. This value is consistent with the fraction obtained from star count analysis.The rest of the systems in the sample are found to be in the thin disc component of the Galaxy. Our anal-ysis revealed no halo CVs in the Solar vicinity. About 60% of the thick disc CVs have orbital periods belowthe orbital period gap. This result is roughly consistent with the predictions of population synthesis mod-els developed for cataclysmic variables. A kinematical age of 13 Gyr is obtained using total space velocitydispersion of the most probable thick disc CVs which is consistent with the age of thick disc component ofthe Galaxy.

� 2012 Elsevier B.V. All rights reserved.

1. Introduction

Cataclysmic variables (CVs) are short-period interacting binarystars, consisting of a white dwarf primary and a low-mass latespectral type secondary star. The secondary star fills its Roche lobeand transfers matter to the primary via a gas stream and an accre-tion disc. Accretion disc formation is prevented in systems withstrongly magnetic white dwarfs in which mass accretion continuesthrough accretion columns. For a detailed review of observationalproperties of CVs, see Warner (1995).

Stehle et al. (1997) studied the long-term evolution of cataclys-mic variables as a function of the secondary star metallicity. Theyshowed that Pop II CVs with a low metallicity secondary star havea detached phase with a smaller orbital period width, a shorterminimum period (Paczynski, 1967) and a slightly higher masstransfer rate, resulting in shorter evolutionary timescales com-pared to CVs where the secondary star has a Solar chemical compo-

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sition. According to their population synthesis model, most Pop IICVs are expected to be found below the period gap (Verbunt andZwaan, 1981; Rappaport et al., 1982; Rappaport et al., 1983; Pac-zynski and Sienkiewicz, 1983; Spruit and Ritter, 1983; King,1988; Shao et al., 2012). Stehle et al. (1997) express that the highc velocities (systemic velocities or centre of mass velocities) ofsome systems found by van Paradijs et al. (1996) suggest these sys-tems to be Pop II CVs. However, most of these CVs are magneticsystems (DQ Her and AM Her stars), where the Doppler-shifts ofspectral lines originate mainly from the accretion stream. Conse-quently, the errors in the c velocities may be noticeably high. Still,finding magnetic systems below the period gap should not be asurprise as these systems concentrate towards shorter orbital peri-ods, with little evidence for a period gap (Warner, 1995). Interest-ingly, this narrow (or none) period gap is consistent with thepredictions from the study of Stehle et al. (1997). It should benoted that Ak et al. (2010) found magnetic systems to be much old-er than non-magnetic systems while they also emphasised doubtsabout the reliability of c velocities obtained from the observationsof magnetic systems.

8 T. Ak et al. / New Astronomy 22 (2013) 7–14

Some CVs have been suggested to be the members of old popula-tions in the Galaxy (Hawkins and Veron, 1987; Howell et al., 1987;Howell and Szkody, 1990; Drissen et al., 1994; Sheets et al., 2007;Uthas et al., 2011; Imamura and Tanabe, in press). Clearly, it is hardto detect thick disc and halo CVs if they are not outbursting systems.CVs in globular clusters could be detected from their outbursts,emission lines, X-rays or their blue colours. Low metallicity valuesextracted from spectra can be another indicator for thick disc andhalo CVs (Stehle et al., 1997). However, spectroscopic confirmationof these detections is difficult as they are very faint systems. For a de-tailed discussion on the detection of CVs in globular clusters, we re-fer to Knigge’s (in press) review and references therein.

A reasonable observable sample of Pop II CVs (thick disc and haloCVs) can only be found at vertical distances from the Galactic planez J 2 kpc (Stehle et al., 1997). However, the faintness of CVs restrictsmost of their photometric and spectroscopic studies to the Solar neigh-bourhood. Although some abundance anomalies in UV and IR werefound for CVs (Hamilton et al., 2011; Gänsicke et al., 2005), there areno reliable metallicity measurements for CVs. In the absence of metal-licity measurements, only kinematical and the dynamical methods areexpected to provide reliable results in the recognition of the thick discand halo CVs in the Solar neighbourhood. Although the development ofsensitive CCD cameras, spectrographs and larger size telescopes madeit possible to observe relatively faint CVs, we lack the necessary obser-vational information to understand the kinematical properties ofCVs in the Galactic scales.

In the next section we use the kinematical properties of 159 CVsin the solar neighbourhood to distinguish different Galactic popu-lations among them.

2. The data

2.1. Input parameters

The kinematical data used in this study are taken from Ak et al.,2010. The most important inputs used in their study are distances,c velocities and proper motions. The proper motions of CVs weremostly obtained from the NOMAD Catalogue (Zacharias et al.,2005). The types, equatorial coordinates and orbital periods ofCVs were mostly taken from Ritter and Kolb (2003, Edition 7.7)and Downes et al. (2001).

The distances were predicted using the PLCs relation of Ak et al.(2007). The PLCs relation is based on orbital period and Two Mi-cron All Sky Survey (2MASS, Skrutskie et al., 2006) JHKs photomet-ric data (Cutri et al., 2003). This relation is reliable and valid in theranges 0:032 < PðdÞ 6 0:454, �0:08 < ðJ � HÞ0 6 1:54;�0:03 <ðH � KsÞ0 6 0:56 and 2:0 < MJ < 11:7 mag. For a detailed descrip-tion of the method by the PLCs relation, we refer to Ak et al.’s(2007, 2008) studies. The distances obtained from this relation dif-fer in general less than 4% from those obtained from trigonometricparallaxes (Gariety and Ringwald, 2012).

The last important inputs used in Ak et al. (2010) are the radialvelocities which are used to calculate total space velocities. The ra-dial velocity with respect to the Sun comes from measurements ofDoppler-shifts in spectral lines. However, one has to take here intoaccount that CVs are binaries, and thus one has to determine theradial velocity of the centre of mass of the system. Ak et al.(2010) adopted the criteria defined by van Paradijs et al. (1996)when collecting c velocities from the literature and merged thesec velocities with those collected by van Paradijs et al. (1996). Ra-dial velocities, and consequently c velocities, derived from emis-sion lines are likely affected by the motion in the accretion discor the matter stream falling on the disc from the secondary. Thus,Ak et al. (2010) analyzed c velocities statistically and looked forpossible systematic errors in the c values obtained from emissionlines. They concluded that there is no substantial systematic differ-

ence between systemic velocities derived from emission andabsorption lines and that the observed c velocities can be reliablyused for statistical analysis (see Ak et al. (2010) for details).

From the celestial coordinates (a; d), proper motion components(la cos d;ld), systemic velocity (c) and the parallax (p), Ak et al.(2010) computed Galactic space velocities and their propagated er-rors with respect to the Sun using the algorithms and transforma-tion matrices of Johnson and Soderblom (1987). Although thesampled CVs are relatively nearby objects, Ak et al. (2010) appliedcorrections for differential Galactic rotation to space velocities asdescribed in Mihalas and Binney (1981). Ak et al. (2010) analyzedthe propagated errors of space velocities, with respect to LSR (LocalStandart of Rest), and refined their sample by removing systemswith a total space velocity error Serr > 30 km s�1. Although theycollected input data from the literature for 194 CVs, this analysesdecreased the number of usable systems in their sample to 159.In this study, the final sample of 159 CVs in Ak et al. (2010) is usedto calculate the Galactic orbital parameters of systems.

2.2. Calculation of galactic orbits

In order to determine possible Galactic orbits of CVs, we firstperform test-particle integration in a Milky Way potential whichconsists of a logarithmic halo of the form

UhaloðrÞ ¼ v20 ln 1þ r2

d2

� �; ð1Þ

with v0 ¼ 186 km s�1 and d = 12 kpc. The disc is represented by aMiyamoto–Nagai potential:

UdiscðR; zÞ ¼ �GMdffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

R2 þ ad þffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiz2 þ b2

d

q� �2s ; ð2Þ

with Md ¼ 1011M�; ad ¼ 6:5 kpc and bd ¼ 0:26 kpc. Finally, thebulge is modelled as a Hernquist potential,

UbulgeðrÞ ¼ �GMb

r þ c; ð3Þ

using Mb ¼ 3:4� 1010M� and c ¼ 0:7 kpc. The superposition ofthese components gives a good representation of the Milky Way.The circular speed at the Solar radius is taken �220 km s�1. Theorbital period of the LSR is PLSR ¼ 2:18� 108 years whileVc ¼ 222:5 km s�1 denotes the circular rotational velocity at the So-lar Galactocentric distance, R0 ¼ 8 kpc. The same formulae were al-ready used to determine the Galactic orbits of objects from differentclasses, e.g. Cos�kunoglu et al. (2012) and Bilir et al. (2012).

In order to analyse Galactic orbits of CVs, the mean radial Galac-tocentric distance (Rm) is taken into account as a function of thestellar population and the orbital shape. We consider the planarand vertical orbital eccentricities, ep and ev , respectively. Rm is de-fined as the arithmetic mean of the final perigalactic (Rp) and apo-galactic (Ra) distances, and zmax and zmin are the final maximum andminimum distances, respectively, to the Galactic plane whereas ep

and ev are defined as follows:

ep ¼Ra � Rp

Ra þ Rpð4Þ

and

ev ¼jzmaxj þ jzminj

Rm; ð5Þ

respectively, where Rm ¼ ðRa þ RpÞ=2 (Vidojevic and Ninkovic,2009). Due to z-excursions Rp and Ra can vary, however thisvariation is not more than 5%. Calculated orbital parameters ofthe 159 CVs are listed in Table 1. The columns of the table are

Table 1Calculated orbital parameters of CVs in the sample.

ID Star a (J2000.0) d (J2000.0) Rp Ra zmin zmax Jz ev ep

(hh:mm:ss) (�: 0: 00) (kpc) (kpc) (kpc) (kpc) (kpc km s�1)

1 AR And 01 45 03.27 +37 56 33.4 7.894 8.207 �0.124 0.124 1790.1 0.015 0.0192 LX And 02 19 44.09 +40 27 22.2 6.517 9.010 �0.150 0.150 1682.0 0.019 0.1613 PX And 00 30 05.81 +26 17 26.4 7.001 9.804 �0.492 0.491 1815.7 0.059 0.1674 RX And 01 04 35.54 +41 17 57.8 7.984 8.525 �0.128 0.128 1837.4 0.016 0.0335 V603 Aql 18 48 54.64 +00 35 02.9 7.442 7.957 �0.081 0.080 1706.0 0.011 0.0346 V1315 Aql 19 13 54.53 +12 18 03.2 7.574 10.974 �0.024 0.024 2018.9 0.003 0.1837 V1432 Aql 19 40 11.42 �10 25 25.8 7.463 10.199 �0.075 0.075 1934.1 0.008 0.1558 AE Aqr 20 40 09.16 �00 52 15.1 5.881 8.826 �0.090 0.089 1566.4 0.012 0.2009 HL Aqr 22 20 26.93 +02 00 53.4 7.613 9.427 �0.302 0.302 1878.0 0.035 0.10610 UU Aqr 22 09 05.76 �03 46 17.7 6.218 8.692 �0.413 0.415 1598.5 0.056 0.16611 VY Aqr 21 12 09.26 �08 49 36.8 6.804 7.995 �0.058 0.058 1626.8 0.008 0.08112 AT Ara 17 30 33.80 �46 05 58.9 7.596 8.195 �0.173 0.173 1749.8 0.022 0.03813 TT Ari 02 06 53.08 +15 17 41.8 7.794 8.624 �0.285 0.284 1819.6 0.035 0.05114 WX Ari 02 47 36.22 +10 35 37.7 5.898 8.670 �0.407 0.413 1547.8 0.056 0.19015 FS Aur 05 47 48.36 +28 35 11.1 7.089 9.574 �0.136 0.136 1820.4 0.016 0.14916 SS Aur 06 13 22.43 +47 44 25.4 7.515 9.428 �0.093 0.093 1869.7 0.011 0.11317 BY Cam 05 42 48.80 +60 51 31.4 7.300 19.534 �0.803 0.795 2444.0 0.060 0.45618 BZ Cam 06 29 33.96 +71 04 36.3 4.731 8.430 �0.648 0.651 1319.4 0.099 0.28119 LU Cam 05 58 17.89 +67 53 46.0 8.207 13.082 �0.800 0.801 2256.0 0.075 0.22920 Z Cam 08 25 13.20 +73 06 39.2 6.806 8.412 �0.166 0.166 1669.4 0.022 0.10621 OY Car 10 06 22.07 �70 14 04.6 6.876 8.140 �0.081 0.081 1652.2 0.011 0.08422 QU Car 11 05 42.49 �68 37 58.2 7.673 15.267 �0.060 0.060 2337.7 0.005 0.33123 AM Cas 02 26 23.38 +71 18 31.5 8.307 8.741 �0.130 0.130 1901.9 0.015 0.02524 HT Cas 01 10 13.13 +60 04 35.4 7.031 8.106 �0.028 0.028 1669.5 0.004 0.07125 V592 Cas 00 20 52.22 +55 42 16.3 8.137 11.534 �0.043 0.043 2154.0 0.004 0.17326 V436 Cen 11 14 00.05 �37 40 47.8 7.337 8.074 �0.047 0.047 1706.0 0.006 0.04827 V834 Cen 14 09 07.46 �45 17 17.1 7.330 7.956 �0.211 0.211 1688.8 0.028 0.04128 V1033 Cen 11 41 22.86 �64 10 14.4 6.688 7.972 �0.062 0.062 1608.6 0.008 0.08829 V1043 Cen 13 13 17.12 �32 59 12.3 7.784 12.400 �1.029 1.029 2130.3 0.102 0.22930 BO Cet 02 06 39.28 �02 03 42.5 7.376 10.077 �0.570 0.570 1893.7 0.065 0.15531 WW Cet 00 11 24.78 �11 28 43.1 7.990 9.523 �0.269 0.269 1940.8 0.031 0.08832 Z Cha 08 07 27.75 �76 32 00.7 7.895 10.700 �0.124 0.123 2042.8 0.013 0.15133 HL CMa 06 45 17.22 �16 51 34.7 8.120 8.859 �0.089 0.089 1892.4 0.010 0.04434 PU CMa 06 40 47.69 �24 23 13.9 8.037 11.775 �0.039 0.039 2158.6 0.004 0.18935 BG CMi 07 31 29.01 +09 56 23.1 8.133 10.111 �0.304 0.304 2014.9 0.033 0.10836 AK Cnc 08 55 21.18 +11 18 15.3 6.783 16.325 �2.261 2.255 2111.5 0.195 0.41337 AT Cnc 08 28 36.92 +25 20 03.0 8.368 10.054 �0.267 0.267 2046.1 0.029 0.09238 CC Cnc 08 36 19.15 +21 21 05.3 7.749 8.363 �0.165 0.166 1788.8 0.021 0.03839 DW Cnc 07 58 53.05 +16 16 45.2 7.683 8.855 �0.098 0.098 1834.9 0.012 0.07140 GY Cnc 09 09 50.55 +18 49 47.5 7.147 8.324 �0.293 0.293 1701.8 0.038 0.07641 GZ Cnc 09 15 51.68 +09 00 49.6 5.981 8.384 �0.625 0.628 1524.4 0.087 0.16742 YZ Cnc 08 10 56.65 +28 08 33.5 4.515 8.351 �0.237 0.237 1289.6 0.037 0.29843 TV Col 05 29 25.53 �32 49 03.9 5.038 8.844 �0.246 0.247 1419.5 0.036 0.27444 TX Col 05 43 20.17 �41 01 54.3 8.211 9.126 �0.316 0.317 1926.8 0.037 0.05345 GP Com 13 05 42.43 +18 01 04.0 7.396 8.778 �0.515 0.516 1773.0 0.064 0.08646 AP CrB 15 54 12.35 +27 21 52.4 7.911 9.536 �0.336 0.336 1928.8 0.039 0.09347 EM Cyg 19 38 40.12 +30 30 28.4 7.121 7.901 �0.089 0.089 1658.5 0.012 0.05248 SS Cyg 21 42 42.80 +43 35 09.9 6.211 9.859 �0.373 0.372 1697.4 0.046 0.22749 V503 Cyg 20 27 17.41 +43 41 22.5 6.778 10.928 �0.086 0.086 1883.9 0.010 0.23450 V751 Cyg 20 52 12.78 +44 19 26.1 7.847 9.034 �0.267 0.267 1871.1 0.032 0.07051 V1504 Cyg 19 28 56.47 +43 05 37.1 4.174 8.041 �0.067 0.066 1207.8 0.011 0.31752 CM Del 20 24 56.93 +17 17 54.4 7.347 9.264 �0.296 0.297 1824.4 0.036 0.11553 HR Del 20 42 20.35 +19 09 39.3 6.859 7.783 �0.160 0.161 1610.2 0.022 0.06354 AB Dra 19 49 06.58 +77 44 23.3 7.838 9.387 �0.204 0.205 1908.4 0.024 0.09055 DO Dra 11 43 38.49 +71 41 20.6 7.955 9.788 �0.120 0.120 1966.6 0.014 0.10356 EX Dra 18 04 14.24 +67 54 12.3 8.016 8.113 �0.425 0.425 1782.9 0.053 0.00657 AH Eri 04 22 38.11 �13 21 30.2 6.960 10.605 �0.474 0.475 1877.9 0.054 0.20858 AQ Eri 05 06 13.12 �04 08 07.3 5.913 8.384 �0.356 0.354 1526.5 0.050 0.17359 IR Gem 06 47 34.68 +28 06 22.3 6.593 8.189 �0.437 0.436 1605.6 0.059 0.10860 PQ Gem 07 51 17.39 +14 44 24.6 6.837 9.742 �0.419 0.429 1787.2 0.051 0.17561 U Gem 07 55 05.24 +22 00 05.1 6.493 8.595 �0.105 0.105 1641.1 0.014 0.13962 AH Her 16 44 10.01 +25 15 02.0 7.797 8.267 �0.251 0.251 1781.3 0.031 0.02963 AM Her 18 16 13.25 +49 52 04.9 7.800 7.989 �0.198 0.198 1751.4 0.025 0.01264 DQ Her 18 07 30.25 +45 51 32.6 7.564 8.053 �0.215 0.215 1729.2 0.028 0.03165 V795 Her 17 12 56.18 +33 31 19.3 7.263 10.614 �0.306 0.306 1933.9 0.034 0.18866 V1084 Her 16 43 45.70 +34 02 39.7 6.890 7.910 �0.225 0.225 1626.0 0.030 0.06967 EX Hya 12 52 24.40 �29 14 56.7 7.428 8.956 �0.092 0.092 1810.9 0.011 0.09368 LY Hya 13 31 53.86 �29 40 59.1 6.746 8.978 �0.313 0.313 1708.9 0.040 0.14269 V392 Hya 10 58 56.42 �29 14 40.8 7.936 8.978 �0.651 0.650 1858.5 0.077 0.06270 VW Hyi 04 09 11.39 �71 17 41.3 7.902 8.499 �0.144 0.145 1823.9 0.018 0.03671 WX Hyi 02 09 50.84 �63 18 39.9 7.914 8.510 �0.162 0.162 1825.8 0.020 0.03672 RZ Leo 11 37 22.27 +01 48 58.5 7.242 10.705 �0.402 0.425 1926.1 0.046 0.19373 T Leo 11 38 26.82 +03 22 07.0 5.150 8.047 �0.253 0.252 1378.2 0.038 0.220

(continued on next page)

T. Ak et al. / New Astronomy 22 (2013) 7–14 9

Table 1 (continued)

ID Star a (J2000.0) d (J2000.0) Rp Ra zmin zmax Jz ev ep

(hh:mm:ss) (�: 0: 00) (kpc) (kpc) (kpc) (kpc) (kpc km s�1)

74 X Leo 09 51 01.48 +11 52 31.4 7.083 8.226 �0.231 0.232 1684.9 0.030 0.07575 GW Lib 15 19 55.35 �25 00 24.5 7.760 8.073 �0.355 0.354 1750.5 0.045 0.02076 ST LMi 11 05 39.77 +25 06 28.5 7.082 8.066 �0.766 0.763 1641.9 0.101 0.06577 BH Lyn 08 22 36.05 +51 05 24.6 7.643 10.973 �0.501 0.502 2007.5 0.054 0.17978 BK Lyn 09 20 11.20 +33 56 42.3 8.131 11.304 �0.420 0.419 2123.8 0.043 0.16379 BP Lyn 09 03 08.89 +41 17 47.7 5.772 8.379 �0.336 0.336 1504.9 0.048 0.18480 CY Lyr 18 52 41.38 +26 45 31.5 7.005 7.955 �0.099 0.099 1649.1 0.013 0.06481 MV Lyr 19 07 16.29 +44 01 07.8 6.234 7.958 �0.188 0.189 1541.0 0.027 0.12282 AH Men 06 11 43.95 �81 49 22.7 7.916 11.080 �0.346 0.345 2073.8 0.036 0.16783 V426 Oph 18 07 51.69 +05 51 47.9 6.532 7.977 �0.039 0.039 1588.1 0.005 0.10084 V442 Oph 17 32 15.13 �16 15 22.1 5.892 7.645 �0.070 0.070 1462.6 0.010 0.13085 V2051 Oph 17 08 19.08 �25 48 31.7 7.612 7.920 �0.022 0.022 1723.4 0.003 0.02086 BI Ori 05 23 51.77 +01 00 30.6 8.481 10.850 �0.312 0.313 2137.1 0.032 0.12387 CN Ori 05 52 07.79 �05 25 00.5 7.702 8.291 �0.097 0.097 1776.4 0.012 0.03788 CZ Ori 06 16 43.23 +15 24 11.3 8.391 10.495 �0.299 0.298 2091.8 0.032 0.11189 V1159 Ori 05 28 59.57 �03 33 52.3 8.026 10.847 �0.873 0.873 2043.6 0.093 0.15090 V1193 Ori 05 16 26.67 �00 12 14.3 5.703 8.829 �0.402 0.395 1528.4 0.055 0.21591 BD Pav 18 43 11.92 �57 30 44.9 6.740 8.540 �0.405 0.399 1662.6 0.053 0.11892 V345 Pav 19 35 42.88 �59 08 22.4 6.891 7.764 �0.323 0.323 1606.8 0.044 0.06093 IP Peg 23 23 08.55 +18 24 59.3 7.684 12.528 �0.269 0.269 2155.7 0.027 0.24094 RU Peg 22 14 02.55 +12 42 11.3 7.624 9.551 �0.224 0.224 1894.2 0.026 0.11295 FO Per 04 08 34.98 +51 14 48.2 6.729 9.076 �0.224 0.224 1721.3 0.028 0.14996 KT Per 01 37 08.78 +50 57 20.3 5.366 8.907 �0.183 0.183 1484.1 0.026 0.24897 TZ Per 02 13 50.97 +58 22 52.3 8.227 10.513 �0.468 0.466 2063.7 0.050 0.12298 UV Per 02 10 08.30 +57 11 20.8 7.766 8.658 �0.564 0.565 1806.7 0.069 0.05499 AH Pic 05 57 12.65 �59 35 25.9 7.952 8.563 �0.646 0.647 1814.9 0.078 0.037100 TY PsA 22 49 39.90 �27 06 53.2 7.899 9.037 �0.162 0.162 1881.0 0.019 0.067101 AO Psc 22 55 17.99 �03 10 40.0 6.502 7.953 �0.297 0.296 1574.9 0.041 0.100102 EI Psc 23 29 54.21 +06 28 11.6 7.882 10.903 �0.287 0.286 2055.4 0.031 0.161103 TY Psc 01 25 39.35 +32 23 09.0 6.163 8.347 �0.180 0.179 1567.9 0.025 0.151104 BV Pup 07 49 05.26 �23 34 00.4 7.944 8.362 �0.097 0.097 1814.5 0.012 0.026105 CP Pup 08 11 46.06 �35 21 04.9 7.423 8.082 �0.047 0.047 1718.0 0.006 0.043106 VV Pup 08 15 06.80 �19 03 17.7 7.326 22.646 �0.541 0.531 2595.1 0.036 0.511107 V347 Pup 06 10 33.65 �48 44 25.4 6.991 8.370 �0.242 0.243 1688.8 0.032 0.090108 V348 Pup 07 12 32.91 �36 05 38.5 5.472 8.276 �0.200 0.199 1451.3 0.029 0.204109 VZ Pyx 08 59 19.84 �24 28 55.4 7.232 8.052 �0.038 0.038 1690.0 0.005 0.054110 BW Scl 23 53 00.86 �38 51 46.6 6.524 8.002 �0.085 0.085 1588.4 0.012 0.102111 V893 Sco 16 15 15.15 �28 37 30.1 5.559 7.912 �0.040 0.040 1436.8 0.006 0.175112 CT Ser 15 45 39.08 +14 22 31.8 5.256 8.628 �1.005 1.005 1407.0 0.145 0.243113 MR Ser 15 52 47.23 +18 56 27.6 7.402 8.069 �0.074 0.074 1714.1 0.010 0.043114 QW Ser 15 26 13.99 +08 18 02.2 6.910 8.484 �0.136 0.136 1690.2 0.018 0.102115 QZ Ser 15 56 54.47 +21 07 19.0 7.802 8.352 �0.122 0.122 1795.2 0.015 0.034116 RW Sex 10 19 56.62 �08 41 56.1 7.078 8.073 �0.230 0.230 1668.2 0.030 0.066117 SW Sex 10 15 09.39 �03 08 32.8 7.560 8.395 �0.398 0.393 1760.7 0.050 0.052118 VZ Sex 09 44 31.71 +03 58 05.6 6.479 8.331 �0.285 0.284 1609.3 0.038 0.125119 RZ Sge 20 03 18.47 +17 02 51.9 6.187 7.923 �0.252 0.252 1528.4 0.036 0.123120 WZ Sge 20 07 36.50 +17 42 14.8 5.199 8.265 �0.015 0.015 1407.8 0.002 0.228121 V1223 Sgr 18 55 02.31 �31 09 49.6 4.634 8.411 �0.132 0.131 1317.8 0.020 0.290122 V3885 Sgr 19 47 40.53 �42 00 26.4 7.378 8.160 �0.052 0.052 1720.8 0.007 0.050123 AI Tri 02 03 48.61 +29 59 25.8 5.350 9.486 �0.260 0.260 1525.5 0.035 0.279124 RW Tri 02 25 36.15 +28 05 50.9 5.940 8.253 �0.171 0.170 1524.5 0.024 0.163125 TW Tri 01 36 37.01 +32 00 39.9 7.547 8.291 �0.386 0.381 1746.9 0.048 0.047126 BZ UMa 08 53 44.17 +57 48 40.6 7.127 8.974 �0.063 0.063 1770.4 0.008 0.115127 CH UMa 10 07 00.57 +67 32 46.5 7.718 8.335 �0.356 0.357 1775.2 0.044 0.038128 CY UMa 10 56 57.00 +49 41 18.2 8.052 9.173 �0.178 0.178 1915.6 0.021 0.065129 DW UMa 10 33 52.84 +58 46 54.7 8.136 10.434 �0.698 0.700 2030.9 0.075 0.124130 EI UMa 08 38 22.00 +48 38 02.2 7.600 9.440 �0.739 0.739 1859.6 0.087 0.108131 IY UMa 10 43 56.73 +58 07 31.9 6.762 12.124 �1.393 1.393 1899.0 0.148 0.284132 LY Uma 10 48 18.01 +52 18 30.0 5.700 9.636 �0.545 0.545 1585.0 0.071 0.257133 SU UMa 08 12 28.26 +62 36 22.5 7.967 8.955 �0.324 0.324 1875.4 0.038 0.058134 SW UMa 08 36 42.76 +53 28 37.9 7.867 9.253 �0.172 0.172 1899.5 0.020 0.081135 UX UMa 13 36 40.96 +51 54 49.5 6.455 9.519 �0.371 0.371 1709.9 0.047 0.192136 CU Vel 08 58 33.03 �41 47 51.7 6.015 10.371 �0.104 0.105 1708.7 0.013 0.266137 IX Vel 08 15 18.97 �49 13 20.7 6.496 8.677 �0.366 0.367 1641.4 0.048 0.144138 HS Vir 13 43 38.44 �08 14 03.9 7.780 7.931 �0.432 0.432 1732.6 0.055 0.010139 TW Vir 11 45 21.16 �04 26 05.6 5.942 8.877 �0.395 0.374 1571.6 0.052 0.198140 QQ Vul 20 05 41.91 +22 39 58.7 7.805 8.070 �0.189 0.189 1761.7 0.024 0.017141 VW Vul 20 57 45.07 +25 30 25.7 7.783 8.872 �0.137 0.138 1849.2 0.017 0.065142 HS 0129+2933 01 31 59.86 +29 49 22.1 7.844 12.115 �0.912 0.908 2117.9 0.091 0.214143 HS 0229+8016 02 35 58.20 +80 29 44.2 7.952 10.225 �0.776 0.776 1978.9 0.085 0.125144 HS 0728+6738 07 33 41.42 +67 32 15.6 6.871 8.856 �0.218 0.219 1721.7 0.028 0.126145 HS 0922+1333 09 24 56.10 +13 20 52.0 7.454 12.285 �0.715 0.712 2081.8 0.072 0.245146 HS 2219+1824 22 21 44.80 +18 40 08.4 7.924 10.869 �0.074 0.074 2063.6 0.008 0.157147 J0130+6221 01 30 31.86 +62 21 32.5 7.281 8.780 �0.188 0.188 1770.7 0.023 0.093

10 T. Ak et al. / New Astronomy 22 (2013) 7–14

Table 1 (continued)

ID Star a (J2000.0) d (J2000.0) Rp Ra zmin zmax Jz ev ep

(hh:mm:ss) (�: 0: 00) (kpc) (kpc) (kpc) (kpc) (kpc km s�1)

148 J0518+2941 05 18 14.33 +29 41 13.0 8.425 9.200 �0.248 0.248 1964.1 0.028 0.044149 J0738+2855 07 38 17.73 +28 55 19.9 6.874 9.927 �0.612 0.611 1801.0 0.073 0.182150 J0809+3814 08 09 08.40 +38 14 06.1 7.699 10.069 �0.334 0.333 1950.8 0.038 0.133151 J0813+4528 08 13 21.93 +45 28 09.4 7.498 11.192 �1.771 1.767 1942.6 0.189 0.198152 J0924+0801 09 24 44.47 +08:01:51.0 6.924 9.091 �0.826 0.827 1721.0 0.103 0.135153 J1629+2635 16 29 36.53 +26:35:19.6 7.630 11.083 �1.046 1.044 1997.1 0.112 0.185154 J1702+3229 17 02 13.25 +32 29 54.3 7.503 10.750 �0.342 0.342 1982.0 0.038 0.178155 J1730+6247 17 30 08.38 +62 47 54.7 7.840 10.634 �0.938 0.936 1995.1 0.102 0.151156 J2050-0536 20 50 17.86 �05 36 26.9 7.481 16.702 �0.461 0.463 2373.4 0.038 0.381157 J2234+0041 22 34 39.94 +00 41 27.0 7.942 9.872 �0.273 0.272 1969.0 0.031 0.108158 J2303+0106 23 03 51.97 +01:06:51.2 7.966 10.591 �0.254 0.255 2040.9 0.027 0.142159 PG 0935+075 09 38 36.98 +07 14 55.1 6.188 8.919 �0.522 0.522 1612.3 0.069 0.181

T. Ak et al. / New Astronomy 22 (2013) 7–14 11

organized as follows: name, equatorial (a; d) coordinates, the finalperigalactic (Rp) and apogalactic (Ra) distances, the maximum(zmax) and minimum (zmin) distances to the Galactic plane, total orbi-tal angular momentum (Jz), and the planar (ep) and vertical (ev )orbital eccentricities. Apogalactic and perigalactic distances aredetermined from the averaged maximum and minimum galacto-centric distances of systems in the calculated Galactic orbits withinthe integration time of 3 Gyr, i.e. backwards in time over an intervalof 3 Gyr. This integration time is chosen to correspond to 12 or 15revolutions around the Galactic centre so that the averaged orbitalparameters can be determined reliably.

2.3. Determination of population types

In order to determine the population types of the CVs, we definesome dynamical and kinematical criteria. The criteria defined toselect thick disc or halo CVs are as following:

(1) The total space velocity (Vtot). Asar et al. (2012) showed thatstars with Vtot P100 km s�1 are thick disc or halo objects.

(2) The relative probability for thick disc to thin disc member-ship (TD=D). Bensby et al. (2003) and Bensby et al. (2005)proposed that the stars with TD=D > 1 are thick disc or haloobjects.

(3) The maximum distance from the Galactic plane (zmax). It iswell known that the thick disk is the dominant componentof the Galaxy between 1 and 5 kpc above the Galactic discwhile halo objects have zmax values larger than 5 kpc (Biliret al., 2008).

(4) Vertical orbital eccentricity (ev ). Bilir et al. (2012) concludedthat vertical eccentricities of Galactic orbits calculated forthe thick-disc and halo stars are larger than �0.1.

(5) Planar eccentricity of the Galactic orbit (ep). Using main-sequence stars, Pauli et al. (2003) found that stars with ep

J 0.3 belong to the thick disc.

Table 2Probable thick disc CVs in the sample. Remarks indicate the fulfilled criteria as defined in

Star Type Porb (hr) Criteria

(1) Vtot (km s�1) (2

J2050–0536 NL, AM 2.299 100.55 14VV Pup NL, AM 1.674 151.63 96BY Cam NL, AM 3.354 142.74 10CT Ser N 4.680 80.58 0.2V1043 Cen NL, AM 4.190 80.59 8.3J1629 + 2635 NL 2.033 72.11 2.5IY UMa DN, SU 1.774 114.73 70J0813 + 4528 DN, UG 6.936 78.34 0.5AK Cnc DN, SU 1.562 154.72 36

DN: dwarf novae, NL: nova-like stars, N: novae, SU: SU UMa type dwarf novae, UG: U G

TD=D is calculated using a purely kinematical approach de-scribed by Bensby et al. (2003). These probabilities were estimatedand listed by Ak et al. (2010). According to the criteria defined byBensby et al. (2003) the stars are selected from four differentTD=D intervals: TD=D < 0:1 (i.e. ‘‘high probability thin-disc stars’’);0:1 < TD=D < 1 (i.e. ‘‘low probability thin-disc stars’’);1 < TD=D < 10 (i.e. ‘‘low probability thick-disc stars’’) andTD=D > 10 (i.e. ‘‘high probability thick-disc stars’’). So, in this studya possible thick disc or halo CV is expected to fullfil at least two ofthese criteria.

Using the criteria defined above, we find that nine of 159 CVs in thesample belong to thick disc population. The rest of the sample consistsof thin disc systems. It is concluded that there are no halo CVs, as themaximum distances to the Galactic plane zmax of the CVs in the sampledo not exceed 5 kpc. Thick disc CVs found in this study are listed in Ta-ble 2 with their total space velocities (Vtot), with respect to LSR, types,orbital periods (Porb), and the maximum distances to the Galactic plane(zmax). The relative probability for the thick disc to thin disc member-ship (TD=D) is also listed in the Table 2. ep and ev are planar and verticaleccentricities of the Galactic orbits, respectively. In Figs. 1–3, nine thickdisc CVs are indicated in Vtot-ep; ep-ev and ep-Jz diagrams of the CV sam-ple in this study, respectively.

AK Cnc is the most probable thick disc CV in the sample. Thisobject fulfills all the criteria we defined above. IY UMa is alsoone of the strongest thick disc candidates of CVs. IY UMa accom-plishes four criteria but one: the planar eccentricity of its Galacticorbit is 0.284 which is very close to 0.3 (see, Fig. 3).VV Pup, BY Camand J2050-0536 accomplish three criteria: Vtot P 100km s�1, TD/D > 1 and ep J 0:3 for these CVs (see, Fig. 2). For J1629+2635 andV1043 Cen, we found TD=D > 1; zmax J 1 kpc and ev J 0.1. CTSer and J0813+4528 match with two criteria. We foundzmax J 1 kpc and ev J 0:1 for these two systems. AK Cnc, IY UMa,VV Pup, BY Cam and J2050-0536 were already suggested to bethick disc objects by Ak et al. (2010) using a pure kinematical ap-proach. Our results is consistent with this suggestion.

the text.

Remark

) TD=D (3) zmax (kpc) (4) ev (5) ep

.5 0.46 0.038 0.381 1, 2, 502 0.54 0.036 0.511 1, 2, 564 0.80 0.060 0.456 1, 2, 5

1.00 0.145 0.243 3, 41.03 0.102 0.229 2, 3, 41.04 0.112 0.184 2, 3, 41.39 0.148 0.284 1, 2, 3, 41.77 0.189 0.198 3, 4

015 2.26 0.195 0.413 1, 2, 3, 4, 5

em type dwarf novae, AM: AM Her (polars) type nova-like stars.

Fig. 1. Vtot-ep diagram for the CVs in the sample. Thick disc and thin disc objects areindicated with filled and empty circles, respectively. Dashed lines represent limitvalues of criteria defined in the text.

Fig. 2. ep-ev diagram for the CVs in the sample. Symbols and dashed lines are as inFig. 1.

Fig. 3. ep-Jz diagram for the CVs in the sample. Symbols are as in Fig. 1.

12 T. Ak et al. / New Astronomy 22 (2013) 7–14

3. Conclusion and discussions

In this study we calculated, for the first time, the Galactic orbitalparameters of a large number of CVs. We also determined theirpopulation types using these calculations and the kinematicalparameters as found by Ak et al. (2010).

Our analysis shows that almost all of the CVs in the sample arein the thin disc component of the Galaxy. Only nine CVs in the sam-ple are thick disc stars. These objects are listed in Table 2. These arethe CVs which cross the Galactic disc through their Galactic orbits.The Galactic orbits of these systems as projected onto X—Y andX—Z planes are shown in Fig. 4. Galactic orbits of the thick discCVs in Fig. 4 were calculated for an integration time of 3 Gyr, cor-responding to 12–15 revolutions around the Galactic centre. As themaximum distances from the Galactic plane (zmax) in Table 2 arenot larger than 5 kpc, we conclude that there are no halo objectsin the sample.

It is found that the fraction of thick disc CVs to thin disc CVs inthe sample is �6% which is in very good agreement with the frac-tion of Pop II field stars to Pop I field stars in the Solar neighbour-hood (Robin et al., 1996; Buser et al., 1999; Bilir et al., 2006). Thissuggests that our CV sample is complete for the Solar neighbour-hood. So, we conclude that statistical studies using this sample givereliable and self-consistent results.

Ak et al. (2010) found that the middle point of the period gap isat 2.62 h for the objects in the sample. An inspection of the thickdisc CVs in Table 2 reveals that �60% of thick disc CVs are locatedbelow the orbital period gap. According to the population synthesismodel of Stehle et al. (1997), most Pop II CVs are expected to befound below the period gap. We conclude that the calculated frac-tion of thick disc CVs below the period gap to the thick disc sys-tems above the period gap in this study is roughly consistentwith the theoretically expected fraction. It is also interesting tonote that �45% of thick disc CVs found in this study are magneticsystems (AM Her stars).

Some CVs have already been suggested to be the members ofold populations in the Galaxy. Objects proposed to be Pop II CVsin Howell et al. (1987), Drissen et al. (1994), Sheets et al. (2007),Uthas et al. (2011) and Imamura and Tanabe (in press) are not in-cluded in our sample. Howell and Szkody (1990) list 84 known orgood candidates for being halo CVs by selecting high Galactic lati-tude objects. Although 21 of them are included in our sample, onlyone of them (AK Cnc) is identified as a thick disc CV in this study. Itmust be emphasised that the Galactic latitude is not a reliable indi-cator for the population type of an object. Our analysis shows thatthe most probable thick disc CVs in Table 2 have high Galacticangular momentums, implying that they are in a population differ-ent than the thin disc (Fig. 3). As thick disc and halo objects haveeccentric orbits, they can pass through the Solar neighbourhoodduring their nuclear evolution. That is why the analysis of Galacticorbits is very important in the determination of population types.

The dispersion of the total space velocities is an indicator ofpopulation types, as the velocity dispersion of a group of objectsis related to their kinematical age. The total space velocities ofthe six systems with zmax J 1 kpc in Table 2 were taken from Aket al. (2010) and the dispersion of the total space velocities is

Fig. 4. Galactic orbits of the thick disc CVs found in this study projected onto X—Y and X—Z planes. Galactic orbits are calculated for an integration time of 3 Gyr.

T. Ak et al. / New Astronomy 22 (2013) 7–14 13

calculated as 101 km s�1. Using the equation given by Wielen(1977) and Wielen et al. (1992), the kinematical age of the six mostprobable thick disc CVs in the sample is calculated as 13 Gyr. Thisvalue is consistent with the age of the thick disc population in theGalaxy (Feltzing and Bensby, 2008).

Our study shows that there are thick disc CVs in the Solar neigh-bourhood. Our study also implies that halo CVs, if they are present,must be very rare in the vicinity of the Sun. Kinematical studies canreliably prove their presence. However, current c velocity mea-surements are mostly dubious. That is why we emphasise theimportance of radial velocity studies of CVs. Further observationaldata can help to find more thick disc or halo CVs. Specially, inves-tigations based on the data obtained from deep sky surveys couldhelp to find more Pop II CVs. Detailed observations of these sys-tems could give clues for their evolution.

Acknowledgments

Part of this work was supported by the Research Fund of theUniversity of Istanbul, Project Number: BYP-20366. We thank theanonymous referee for his/her comments and suggestions. This re-

search has made use of the SIMBAD database, operated at CDS,Strasbourg, France. This publication makes use of data productsfrom the Two Micron All Sky Survey, which is a joint project ofthe University of Massachusetts and the Infrared Processing andAnalysis Center/California Institute of Technology, funded by theNational Aeronautics and Space Administration and the NationalScience Foundation. This research has made use of the NASA/IPACExtragalactic Database (NED) which is operated by the Jet Propul-sion Laboratory, California Institute of Technology, under contractwith the National Aeronautics and Space Administration.

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