Spectroscopy of Nine Cataclysmic Variable Stars

TL;DR

This study provides optical spectroscopy and orbital period measurements for nine cataclysmic variable stars, revealing interesting properties such as secondary star detection, high space velocity, and magnetic accretion features, contributing valuable data to CV research.

Contribution

The paper offers new orbital periods for nine CVs and detailed spectral analysis, including secondary star identification and magnetic accretion evidence, expanding the understanding of CV diversity.

Findings

BF Eri has a K3 secondary star and likely belongs to the halo population.

CZ Aql shows signs of magnetically-channeled accretion.

V1006 Cyg's period falls within the 2-3 hour gap in CV distribution.

Abstract

We present optical spectroscopy of nine cataclysmic binary stars, mostly dwarf novae, obtained primarily to determine orbital periods Porb. The stars and their periods are LX And, 0.1509743(5) d; CZ Aql, 0.2005(6) d; LU Cam, 0.1499686(4) d; GZ Cnc, 0.0881(4) d; V632 Cyg, 0.06377(8) d; V1006 Cyg, 0.09903(9) d; BF Eri, 0.2708804(4) d; BI Ori, 0.1915(5) d; and FO Per, for which Porb is either 0.1467(4) or 0.1719(5) d. Several of the stars proved to be especially interesting. In BF Eri, we detect the absorption spectrum of a secondary star of spectral type K3 +- 1 subclass, which leads to a distance estimate of approximately 1 kpc. However, BF Eri has a large proper motion (100 mas/yr), and we have a preliminary parallax measurement that confirms the large proper motion and yields only an upper limit for the parallax. BF Eri's space velocity is evidently large, and it appears to belong to the halo population. In CZ Aql, the emission lines have strong wings that move with large velocity amplitude, suggesting a magnetically-channeled accretion flow. The orbital period of V1006 Cyg places it squarely within the 2- to 3-hour "gap" in the distribution of cataclysmic binary orbital periods.

Figures

Tables

Table 1. Table 1: Stars Observed

Star	${\alpha }_{2000}$aaPositions measured from images taken at the 2.4m Hiltner telescope, using astrometric solutions from fits to USNO A2.0 (Monet et al., 1996) or UCAC 2 (Zacharias et al., 2004) stars. Uncertainties are of order 0.1 arcsec.	${\delta }_{2000}$	EpochbbThe date of the image used in the position measurement. The coordinate system (equator and equinox) is J2000 in all cases.	$V_{\mathrm{obs}}$ccSynthesized from spectra, as described in text.	maxddTaken from the GCVS (Kholopov et al., 1999). Photgraphic magnitudes flagged with ‘p’, visual with ‘v’.	min
	[hh:mm:ss]	[∘:′:$"$]		[mag.]	[mag.]	[mag.]
LX And	2:19:44.08	$+$40:27:22.3	2006.7	16.3	13.5p	16.4p
CZ Aql	19:19:58.21	$-$07:10:55.2	2003.4	15.4	13.p	15.p
LU Cam	5:58:17.86	$+$67:53:46.2	2002.0	16.3	14.v	$($16.v
GZ Cnc	9:15:51.68	$+$09:00:49.6	2000.3	15.4	13.1v	15.4v
V632 Cyg	21:36:04.22	$+$40:26:19.4	2000.5	17.9	12.6p	17.5p
V1006 Cyg	19:48:47.20	$+$57:09:22.8	2000.5	17.8	15.4p	17.0p
BF Eri	4:39:29.96	$-$04:35:59.5	2006.2	14.8	13.5p	15.5p
BI Ori	5:23:51.77	$+$01:00:30.6	2002.8	17.1	13.2p	16.7p
FO Per	4:08:34.98	$+$51:14:48.5	2004.0	17.1	11.8v	16.v

Table 2. Table 2: Journal of Observations

data	$N$	HA start	HA end	telescope
(UT)		[hh:mm]	[hh:mm]
LX And
2004 Jan 13	1	+2:35	+2:35	2.4m
2004 Mar 02	3	+3:45	+4:00	2.4m
2004 Nov 18	1	+0:29	+0:29	1.3m
2004 Nov 19	26	$-$3:36	+4:17	1.3m
2004 Nov 19	2	+2:31	+2:35	2.4m
2004 Nov 20	13	$-$3:17	+3:15	1.3m
2004 Nov 20	1	$-$1:23	$-$1:23	2.4m
2006 Jan 19	14	+1:31	+4:10	1.3m
2006 Jan 22	8	+3:31	+4:46	1.3m
2007 Jan 26	3	+1:36	+1:58	1.3m
2007 Jan 27	15	+0:58	+3:39	1.3m
CZ Aql
2005 Jul 02	3	+1:40	+2:04	1.3m
2005 Jul 04	48	$-$3:28	+3:17	1.3m
2005 Jul 05	13	$-$1:55	$-$0:06	1.3m
2005 Jul 06	12	$-$3:57	+2:28	1.3m
2005 Sep 03	2	+1:23	+1:32	1.3m
2005 Sep 07	2	$-$0:03	+0:05	1.3m
2005 Jun 28	2	$-$0:01	+0:04	2.4m
2006 Jun 18	2	+2:05	+2:10	2.4m
2006 Jun 19	2	+0:36	+0:40	2.4m
2006 Jun 23	3	$-$1:24	$-$1:12	2.4m
LU Cam
2002 Jan 22	2	$-$1:40	$-$1:19	2.4m
2002 Jan 23	8	$-$1:33	+2:31	2.4m
2002 Jan 24	25	$-$3:15	+5:47	2.4m
2002 Feb 18	2	+2:20	+2:28	2.4m
2002 Feb 19	2	+2:41	+2:50	2.4m
2002 Feb 20	4	$-$0:02	+3:43	2.4m
2002 Feb 22	1	+2:18	+2:18	2.4m
2004 Jan 16	2	+2:49	+2:53	2.4m
2004 Jan 17	1	+0:40	+0:40	2.4m
2004 Jan 19	1	$-$0:32	$-$0:32	2.4m
2004 Mar 02	1	+0:53	+0:53	2.4m
2004 Mar 07	6	+2:29	+3:14	2.4m
2004 Nov 19	4	+2:48	+3:27	2.4m
2005 Mar 21	1	+1:12	+1:12	2.4m
2005 Mar 22	2	+1:21	+1:30	2.4m
2005 Sep 09	1	$-$2:00	$-$2:00	2.4m
2005 Sep 12	1	$-$1:49	$-$1:49	2.4m
2006 Jan 09	2	+1:49	+1:55	2.4m
GZ Cnc
2000 Apr 07	2	+4:26	+4:32	2.4m
2000 Apr 08	1	+0:27	+0:27	2.4m
2000 Apr 10	5	$-$0:31	+4:32	2.4m
2000 Apr 11	15	+2:19	+4:22	2.4m
2001 Mar 24	2	+4:39	+4:49	2.4m
2001 Mar 25	21	$-$1:10	+3:10	2.4m
2001 Mar 26	20	$-$0:50	+4:27	2.4m
2001 Mar 27	2	$-$0:08	+0:01	2.4m
2001 Mar 28	3	+0:14	+0:25	2.4m
V632 Cyg
2005 Jul 07	2	+1:00	+1:16	1.3m
2005 Jul 08	10	$-$5:12	+0:33	1.3m
2005 Jul 09	18	$-$5:03	+1:09	1.3m
2005 Jul 10	18	$-$5:09	+1:07	1.3m
2005 Jul 11	3	+0:52	+1:19	1.3m
V1006 Cyg
2003 Jun 22	1	+1:06	+1:06	2.4m
2004 Jun 24	5	+0:52	+1:56	1.3m
2004 Jun 25	5	$-$1:43	+0:34	1.3m
2004 Jun 25	1	+4:06	+4:06	2.4m
2004 Jun 26	10	$-$4:25	+1:56	1.3m
2004 Jun 27	3	$-$3:00	$-$2:00	1.3m
2004 Jun 28	4	$-$2:25	+1:02	1.3m
2004 Jun 28	1	+0:28	+0:28	2.4m
2004 Jun 29	5	+0:55	+1:59	1.3m
2004 Jun 29	1	+4:07	+4:07	2.4m
2004 Jun 30	18	$-$4:39	+2:26	1.3m
2004 Jul 01	10	$-$3:58	+1:53	2.4m
2005 Jul 05	13	+0:58	+3:11	1.3m
2004 Jun 30	4	$-$3:41	+3:52	2.4m
2004 Jul 01	12	$-$4:07	+2:17	1.3m
2005 Jul 03	27	$-$3:57	+1:20	1.3m
2005 Jul 05	13	+0:58	+3:11	1.3m
BF Eri
2001 Dec 18	3	+2:35	+2:56	1.3m
2001 Dec 19	10	$-$3:06	+4:04	1.3m
2001 Dec 20	12	$-$3:49	+2:00	1.3m
2001 Dec 21	2	+3:04	+3:14	1.3m
2001 Dec 22	5	$-$3:13	$-$2:31	1.3m
2001 Dec 23	12	$-$3:18	+4:35	1.3m
2001 Dec 24	13	$-$3:17	+3:08	1.3m
2001 Dec 25	14	$-$2:20	+1:07	1.3m
2001 Dec 26	8	$-$2:10	+3:05	1.3m
2001 Dec 27	18	$-$2:39	+4:14	1.3m
2002 Jan 19	1	+1:27	+1:27	2.4m
2002 Jan 20	2	$-$1:33	+2:13	2.4m
2002 Jan 22	1	$-$2:02	$-$2:02	2.4m
2002 Feb 21	2	+1:26	+1:35	2.4m
2002 Feb 22	2	+0:40	+0:49	2.4m
2002 Oct 26	2	$-$0:11	+0:05	2.4m
2002 Oct 31	1	+3:21	+3:21	2.4m
2003 Feb 02	1	+0:04	+0:04	2.4m
2005 Sep 11	2	$-$0:57	$-$0:40	1.3m
2006 Mar 16	1	+1:56	+1:56	1.3m
2006 Mar 17	5	+2:15	+2:57	1.3m
2007 Jan 28	9	$-$1:46	$-$0:13	1.3m
BI Ori
2006 Jan 20	32	$-$2:54	+4:05	1.3m
2006 Jan 21	22	$-$2:47	+2:21	1.3m
2006 Jan 23	6	+1:03	+2:08	1.3m
FO Per
1995 Oct 09	9	$-$4:40	$-$3:26	2.4m
1995 Oct 10	5	$-$5:22	+1:26	2.4m
1996 Dec 19	14	+1:38	+4:03	1.3m
1996 Dec 20	5	+2:08	+3:43	1.3m
2001 Dec 18	9	$-$2:35	+4:36	1.3m
2004 Nov 18	1	$-$0:11	$-$0:11	1.3m
2004 Nov 19	9	+2:52	+5:08	1.3m
2004 Nov 19	2	+3:24	+2:48	2.4m
2004 Nov 20	20	$-$0:56	+5:10	1.3m
2006 Jan 10	12	$-$0:35	+2:35	1.3m
2006 Jan 10	1	+4:21	+4:21	2.4m
2006 Jan 11	18	$-$1:29	+2:41	1.3m
2006 Jan 11	1	$-$3:12	$-$3:12	2.4m
2006 Jan 12	4	$-$1:16	$-$0:36	1.3m
2006 Jan 13	10	+3:44	+5:37	1.3m
2006 Jan 16	11	$-$1:36	+1:00	1.3m

Table 3. Table 3: Spectral Features in Quiescence

	E.W.aaEmission equivalent widths are counted as positive.	Flux	FWHM bbFrom Gaussian fits.
Feature	(Å)	(10-16 erg cm-2 s1)	(Å)
LX And
H$\beta$	$45$	$690$	18
HeI $\lambda 4921$	$4$	$60$	25
HeI $\lambda 5015$	$3$	$50$	20
Fe $\lambda 5169$	$2$	$20$	14
HeI $\lambda 5876$	$11$	$120$	19
H$\alpha$	$54$	$560$	17
HeI $\lambda 6678$	$4$	$40$	19
CZ Aql
H$\beta$	$21$	$670$	18
HeI $\lambda 4921$	$1$	$40$	12
HeI $\lambda 5015$	$2$	$50$	13
HeI $\lambda 5876$	$7$	$160$	15
NaD	$-1$	$-16$	$\cdots$
H$\alpha$	$61$	$1250$	27
HeI $\lambda 6678$	$5$	$90$	16
LU Cam
H$\gamma$	$10$	$170$	12
HeI $\lambda 4471$	$2$	$30$	10
H$\beta$	$14$	$190$	12
HeI $\lambda 4921$	$1$	$20$	12
HeI $\lambda 5015$	$2$	$20$	13
Fe $\lambda 5169$	$1$	$10$	12
HeI $\lambda 5876$	$4$	$50$	12
H$\alpha$	$27$	$240$	13
HeI $\lambda 6678$	$3$	$20$	15
HeI $\lambda 7067$	$3$	$20$	$\cdots$
GZ Cnc
H$\gamma$	$26$	$940$	26
HeI $\lambda 4471$	$8$	$260$	28
HeII $\lambda 4686$	$5$	$140$	46
H$\beta$	$36$	$1040$	25
HeI $\lambda 4921$	$5$	$140$	26
HeI $\lambda 5015$	$4$	$100$	28
Fe $\lambda 5169$	$2$	$60$	26
HeI $\lambda 5876$	$9$	$200$	27
H$\alpha$	$38$	$790$	25
HeI $\lambda 6678$	$4$	$90$	31
HeI $\lambda 7067$	$3$	$60$	32
V632 Cyg
H$\beta$	$80$	$260$	24
HeI $\lambda 4921$	$6$	$20$	27
HeI $\lambda 5015$	$8$	$20$	26
Fe $\lambda 5169$	$5$	$10$	26
HeI $\lambda 5876$	$28$	$70$	27
H$\alpha$	$113$	$260$	27
HeI $\lambda 6678$	$15$	$30$	32
V1006 Cyg
H$\beta$	$74$	$250$	27
HeI $\lambda 4921$	$8$	$30$	30
HeI $\lambda 5015$	$8$	$20$	28
Fe $\lambda 5169$	$8$	$30$	28
HeI $\lambda 5876$	$26$	$70$	34
H$\alpha$	$108$	$250$	31
HeI $\lambda 6678$	$11$	$30$	38
BF Eri
HeII $\lambda 4686$	$6$	$240$	46
H$\beta$	$23$	$1060$	22
HeI $\lambda 5015$	$2$	$110$	29
HeI $\lambda 5876$	$5$	$240$	21
H$\alpha$	$27$	$1200$	22
HeI $\lambda 6678$	$3$	$120$	27
BI Ori
H$\beta$	$34$	$180$	32
HeI $\lambda 4921$	$6$	$30$	36
HeI $\lambda 5015$	$6$	$30$	43
Fe $\lambda 5169$	$5$	$30$	39
HeI $\lambda 5876$	$6$	$30$	31
H$\alpha$	$36$	$190$	31
FO Per
H$\beta$	$24$	$160$	9
HeI $\lambda 4921$	$2$	$20$	7
HeI $\lambda 5015$	$3$	$20$	7
Fe $\lambda 5169$	$2$	$10$	7
HeI $\lambda 5876$	$5$	$30$	7
H$\alpha$	$29$	$170$	9
HeI $\lambda 6678$	$2$	$10$	9

Table 4. Table 4: Radial Velocities

Star	time aaHeliocentric Julian date of mid-integration, minus 2400000.	$v_{\mathrm{abs}}$	${\sigma }_{v_{\mathrm{abs}}}$	$v_{\mathrm{emn}}$	${\sigma }_{v_{\mathrm{emn}}}$
		(km s-1)	(km s-1)	(km s-1)	(km s-1)
LX And	53017.7061	$\cdots$	$\cdots$	$-$44	$-$11
LX And	53066.6160	$\cdots$	$\cdots$	$-$57	$-$8
LX And	53066.6208	$\cdots$	$\cdots$	$-$37	$-$8
LX And	53066.6263	$\cdots$	$\cdots$	$-$77	$-$7

Table 5. Table 5: Fits to Radial Velocities

Star	AlgorithmaaCode for the convolution function used to derive emission line velocities; D = derivative of a Gaussian, G2 = double-Gaussian function (see text). For the D algorithm the number that follows gives the line full-width at half-maximum, in Å, for which the function is optimized; for the G2 algorithm the two numbers are respectively the separation of the two Gaussians and their individual FWHMa, again in Å.	$T_0$bbHeliocentric Julian Date minus 2400000. The epoch is chosen to be near the center of the time interval covered by the data, and within one cycle of an actual observation.	$P$	$K$	$\gamma$	$N$	$\sigma$ccRoot-mean-square residual of the fit.
			(d)	(km s-1)	(km s-1)		(km s-1)
LX And	G2,21,7	53754.6861(12)	0.1509743(5)	81(4)	$-48\left(3\right)$	87	15
CZ Aql	G2,18,8	53557.880(2)	0.2005(6)ddThe period determination in this case is complicated by unknown numbers of cycles between observing runs; the uncertainty given here is an estimate based on fits to individual runs. Only certain values within the period range given here are allowed; see text for details.	193(15)	$5\left(10\right)$	89	61
LU Cam	D,15	52327.7421(14)	0.1499686(4)	57(4)	$44\left(3\right)$	66	14
GZ Cnc	G2,15,9	51992.8928(13)	0.0881(4)ddThe period determination in this case is complicated by unknown numbers of cycles between observing runs; the uncertainty given here is an estimate based on fits to individual runs. Only certain values within the period range given here are allowed; see text for details.	79(7)	$22\left(5\right)$	71	26
V632 Cyg	D,28	53560.9746(13)	0.06377(8)	62(8)	$-49\left(5\right)$	51	28
V1006 Cyg	G2,20,9	53187.9091(16)	0.09904(9)ddThe period determination in this case is complicated by unknown numbers of cycles between observing runs; the uncertainty given here is an estimate based on fits to individual runs. Only certain values within the period range given here are allowed; see text for details.	89(8)	$-11\left(6\right)$	120	44
BF Eri emission	G2,21,7	52574.0027(18)	0.2708801(6)	109(5)	$-91\left(3\right)$	126	24
BF Eri absorption	$\cdots$	52573.8632(9)	0.2708805(4)	182(4)	$-72\left(3\right)$	117	20
BF Eri mean:	$\cdots$	$\cdots$	0.2708804(4)	$\cdots$	$\cdots$	$\cdots$
BI Ori	53756.541(3)	G2,35,9	0.1915(5)	131(13)	$24\left(9\right)$	60	44
FO Per (shorter)	D,11	52261.872(3)	0.1467(4)ddThe period determination in this case is complicated by unknown numbers of cycles between observing runs; the uncertainty given here is an estimate based on fits to individual runs. Only certain values within the period range given here are allowed; see text for details.	27(3)	$-49\left(2\right)$	131	17
FO Per (longer)	D,11	52261.893(3)	0.1719(5)ddThe period determination in this case is complicated by unknown numbers of cycles between observing runs; the uncertainty given here is an estimate based on fits to individual runs. Only certain values within the period range given here are allowed; see text for details.	27(3)	$-45\left(2\right)$	131	17

Equations

$$P_{\mathrm{orb}}=(t_2-t_1)/n.$$

Full text

Several of the stars proved to be especially interesting. In BF Eri, we detect the absorption spectrum of a secondary star of spectral type K3 $\pm 1$ subclass, which leads to a distance estimate of $\sim 1$ kpc. However, BF Eri has a large proper motion ($\sim 100$ mas yr*-1*), and we have a preliminary parallax measurement that confirms the large proper motion and yields only an upper limit for the parallax. BF Eri’s space velocity is evidently large, and it appears to belong to the halo population. In CZ Aql, the emission lines have strong wings that move with large velocity amplitude, suggesting a magnetically-channeled accretion flow. The orbital period of V1006 Cyg places it squarely within the 2- to 3-hour ‘gap’ in the distribution of cataclysmic binary orbital periods.

novae, cataclysmic variables — stars: individual (LX And, CZ Aql, LU Cam, GZ Cnc, V632 Cyg, V1006 Cyg, BF Eri, BI Ori, FO Per) — stars: distances — binaries: close — binaries: spectroscopic

1 Introduction

Cataclysmic variables (CVs) are binary star systems in which the secondary, usually a late-type main sequence star, fills its Roche lobe and loses mass to the white dwarf primary (Warner, 1995). CVs are long-lived systems that are stable against mass transfer, so the mass transfer must be driven by gradual changes in the orbit, or in the secondary star, or both. It is commonly believed that the evolution of most CVs is driven by the slow loss of angular momentum from the orbit, most likely through magnetic braking of the co-rotating secondary star, at least at longer orbital periods $P_{\rm orb}$ where gravitational radiation is ineffective (Andronov & Pinsonneault 2004 give a recent discussion). The loss of angular momentum constricts the Roche critical lobe around the secondary and causes the system to transfer mass as it evolves toward shorter $P_{\rm orb}$. In this scenario, $P_{\rm orb}$ serves as a proxy measurement for the system’s evolutionary state. Correct and complete orbital period measurements are fundamental to any accurate theory of CV evolution. Given the usefulness of $P_{\rm orb}$, it is fortunate that it can usually be measured accurately and precisely.

This paper presents optical spectroscopy of the nine CVs listed in Table 1. We took these observations mostly for the purpose of finding orbital periods using radial velocities (none of these systems are known to eclipse). The long cumulative exposures also allowed us to look for any unusual features. The Catalog and Atlas of Cataclysmic Variables Archival Edition (Downes et al., 2001) 222Available at http://archive.stsci.edu/prepds/cvcat/index.html; this had been called the Living Edition until its author retired and ceased updates. lists seven of the stars as dwarf novae, one as either a dwarf nova or a DQ Her star, and one simply as a cataclysmic, possibly a dwarf nova similar to U Gem or SS Cygni (type UGSS). Except for CZ Aql, for which we confirm a 4.8-hour candidate period suggested by Cieslinski et al. (1998), all of these objects lacked published orbital periods when we began working on them. Subsequently Tappert & Bianchini (2003) found $P_{\rm orb}=0.0883$ d for GZ Cancri; we had communicated our advance findings to these authors so they could disambiguate their period determination.

2 Observations, Reductions, and Analysis

2.1 Observations

All our spectra were taken at the MDM Observatory on Kitt Peak, Arizona, using either the 1.3m McGraw-Hill telescope or the 2.4m Hiltner telescope. The earliest observations we report here are from 1995, and the latest were obtained 2007 January. Table 2 gives a journal of the observations.

At the 1.3m we used the Mark III spectrograph and a SITe $1024\times 1024$ CCD detector. The spectral resolution is 5.0 Å, covering a range of either 4480 to 6760 Å with 2.2 Å pixel*-1* for the 2001 December BF Eri data, or 4646 to 6970 Å with 2.3 Å pixel*-1* for the remaining data. The 2.4m spectra, except for those of FO Per, were obtained with the modular spectrograph and a SITe $2048^{2}$ CCD detector, with 2.0 Å pixel*-1*, over a range of 4210 to 7500 Å  and with a spectral resolution of 3.5 Å. The relatively small number of 2.4 m spectra of FO Per were taken with a LORAL $2048^{2}$-pixel detector, and cover from 4285 to 6870 Å at 1.25 Å pixel*-1*.

2.2 Reductions

For the most part we reduced the spectra using standard IRAF333IRAF is distributed by the National Optical Astronomy Observatories. procedures. The wavelength calibration was based on exposures of Hg, Ne, and Xe lamps. Prior to 2003 we took lamp exposures through the night and whenever the telescope was moved. For the 2.4m data from 2003 to the present, we used lamp exposures taken in twilight to find the shape of the pixel-to-wavelength relation, and set the zero point individually for each nighttime exposure using the OI $\lambda 5577$ night-sky feature. The apparent velocity of the telluric OH emission bands at the far red end of the spectrum, found with a cross-correlation routine, provided a check; although these are far from the feature used to set the zero point, their apparent velocity typically remain within 10 km s*-1* of zero. Because of the increased efficiency of this technique, we attempted to use it at the 1.3m telescope also, during the 2004 June/July observing run. For unknown reasons the results were unsatisfactory. To salvage the H$\alpha$ emission velocities from that run, we determined a correction by cross-correlating the night-sky emission features in the 6200-6625 Å range with a well-calibrated night-sky spectrum obtained with a similar instrument. The correction was calculated for each individual spectrum and then applied to each measured velocity, and it did reduce the scatter somewhat, evidently because the wavelength range used includes the H$\alpha$ emission line for which we measured velocities.

On all our runs, we observed flux standards during twilight when the sky was clear, and applied the resulting calibration to the data. The reproducibility of these observations suggests that our fluxes are typically accurate to $\pm 20$ per cent. We also took short exposures of bright O and B stars in twilight to map the telluric absorption features and divide them out approximately from our program object spectra. Before flux calibration, we divided our program star spectra by a mean hot-star continuum, in order to remove the bulk of the response variation. Table 1 lists $V$ magnitudes synthesized from our mean spectra, using the IRAF sbands task and the passband tabulated by Bessell (1990); clouds, losses at the slit, and calibration errors make these uncertain by a few tenths of a magnitude, but they do give a rough indication of the brightness of each system at the time of our observation.

2.3 Analysis

Except for a few spectra taken in outburst (which show weak emission or absorption on a strong continuum), all of the stars show the prominent emission lines. Figs. 1 and  2 show averaged spectra, and Table LABEL:tab:quie gives the equivalent width and FWHM of each line measured for each star from its averaged spectrum.

Two stars, BF Eri and BI Ori, showed the spectral features of a late-type star. To quantify the secondary contribution in these objects, we began by preparing averaged flux-calibrated spectra (in BF Eri’s case the secondary’s radial velocity curve was measurable, so we shifted the individual spectra to the secondary’s rest frame before averaging). Over time we have used the 2.4 m and modular spectrograph to collect spectra of K and M stars classified by Keenan & McNeil (1989) or Boeshaar (1976). The wavelength coverage and spectral resolution of these data are similar to the 1.3m data. We applied a range of scaling factors to the library spectra, subtracted them from the averaged spectra, and examined the results by eye to estimate a range of spectral types and scaling factors giving acceptable cancellation of the late-type features.

We use the spectral type and secondary flux to estimate the distance in the following manner. We begin by finding the surface brightness of the secondary star in $V$, on the assumption that the surface brightness is similar to that of main-sequence stars of the same spectral type; the Barnes-Evans relation for late-type stars is discussed by Beuermann (2006). Combining the known $P_{\rm orb}$ with the assumption that the secondary fills its Roche critical lobe yields the secondary’s radius $R_{2}$ as a function of its mass, $M_{2}$. In the relevant range of mass ratio, $R_{2}\propto M_{2}^{1/3}$, approximately, and the dependence on $M_{1}$ is weak enough to ignore. We generally do not know $M_{2}$, so we guess at a generous allowable range for this parameter using evolutionary simulations by Baraffe & Kolb (2000) as a guideline; the weakness of the dependence of $R_{2}$ on $M_{2}$ means that this (rather questionable) step does not dominate the error budget. Combining the surface brightness with $R_{2}$ yields the absolute magnitude $M_{V}$. Subtracting this from the apparent magnitude measured for the secondary star gives a distance modulus. The reddening maps of Schlegel et al. (1998) then can be used to estimate the extinction. Note carefully that we do not assume that the secondary is a ‘normal’ main-sequence star; we assume only that the secondary’s surface brightness is similar to field stars of the same spectral type. The normalization of the secondary’s contribution also depends on the assumption that the spectral features used to judge the subtraction are similar in strength to those of a normal star.

As noted earlier, the immediate aim of our observations was to find orbital periods from radial velocity time series data. The H$\alpha$ emission line is usually the strongest feature, and it generally gives good results in dwarf novae. All the emission-line velocities reported here are of H$\alpha$.

We measured radial velocities of H$\alpha$ emission using convolution methods described by Schneider & Young (1980) and Shafter (1983). In this technique one convolves an antisymmetric function with the line profile, and takes the zero of the convolution (where the two sides of the line contribute equally) as the line center. For the antisymmetric function with which the spectrum is convolved, we used either the derivative of a Gaussian with adjustable width, or positive and negative Gaussians of adjustable width offset from each other by an adjustable separation. Uncertainties in the convolution velocities are estimated by propagating forward the counting-statistics errors in the individual data channels; in practice, these are lower limits to the true uncertainties, since the line profile can vary in ways unrelated to the orbital modulation. The choice of convolution parameters is dictated by the shape and width of the line, and in practice the parameters are adjusted to give the best detection of the orbit. The physical interpretation of CV emission lines is complicated and controversial (see, e.g., Shafter 1983, Marsh 1988, Robinson 1992), but in almost all cases the emission-line periodicity accurately reflects $P_{\rm orb}$ (though Araujo-Betancor et al. 2005 describe a noteworthy exception to this rule). A sample of the radial velocities for each object are listed in Table 4, while the full tables can be found online.

One of our systems, BF Eri, has a K-type absorption component in its spectrum. We measured velocities of this using the cross-correlation radial velocity package described by Kurtz & Mink (1998), using the region from 5000 to 6500 Å, and excluding the region containing the He I $\lambda$5876 emission line and and the NaD absorption complex. For a cross-correlation template spectrum, we used the a velocity-compensated sum of many observations of IAU velocity standards taken with the same instrument, as described in Thorstensen et al. (2004).

We searched for periods in all the velocity time series using the “residualgram” method (Thorstensen et al., 1996); the resulting periodograms are given in Figs. 3 and 4. At the best candidate periods we fitted least-squares sinusoids of the form $v(t)=\gamma+K\sin[2\pi(t-T_{0})/P]$. Fig. 5 shows the velocities folded on the best-fitting periods, and Table 5 gives the parameters of these fits. Because of limitations of the sampling (e.g., the need to observe only at night from a single site), a single periodicity generally manifests as a number of alias frequencies. To assess the confidence with which we could assert that the strongest alias is the true period, we used a Monte Carlo test described by Thorstensen & Freed (1985).

The alias problem can be particularly irksome over longer timescales; in this case the uncertain number of cycles elapsed between observing runs causes fine-scale “ringing” in the periodogram. The individual periods have tiny error bars, because of the large time span covered, but the ambiguity in period means that a realistic error bar – one that covers the range of possibilities – is much larger. In those cases, the period uncertainties given in Table 5 are estimated by analyzing data from the individual observing runs separately. When only two observing runs are available, the allowable fine-scale frequencies are well-described by a fitting formula

[TABLE]

Here $t_{1}$ and $t_{2}$ are the epochs of blue-to-red velocity crossing observed on the two runs, and $n$ is the integer number of cycles that have passed between $t_{1}$ and $t_{2}$. The allowed range of $n$ is determined from the weighted average of the periods derived from separate fits to the two runs’ data. When more than two observing runs are available, the situation becomes more complex. In some happy cases there are enough overlapping constraints that only a single, very precise period remains tenable. We were able to find such precise periods for LX And, LU Cam, and BF Eri.

3 Notes on Individual Objects

We discuss the stars in alphabetical order by constellation.

3.1 LX Andromedae

LX And was first identified as a variable star (RR V-3) in the Lick RR Lyrae search (Kinman et al., 1982). It was classified incorrectly as an RV Tauri star, and its dwarf nova nature was unrecognized until the photometric study by Uemura et al. (2000). Morales-Rueda & Marsh (2002) obtained spectra of LX And as part of their study of dwarf novae in outburst and determined the equivalent widths and FWHMs of the Balmer and He II lines. Our mean spectrum appears typical for a dwarf nova at minimum light.

Because of the large hour-angle span, the radial velocity time series leaves no doubt about the daily cycle count, which is near 6.6 cycle d*-1*. The several observing runs constrain the fine-scale period in a more complicated way, but the Monte Carlo test indicates that a precise period of 0.1509743(5) d is preferred with about 98 per cent confidence. Two other candidate periods separated from this by 1 cycle per 53.2 d in frequency are much less likely.

3.2 CZ Aquilae

Very little has been published on CZ Aql, which is listed in the Archival Edition as a U-Gem dwarf nova. Cieslinski et al. (1998) included the star in their spectroscopic study of irregular variables, and noted a probable 4.8 hour period and emission lines typical of dwarf novae. Our velocities confirm the suggested 4.8-hour period, but we cannot determine a unique cycle count between our observing runs.

While the spectrum superficially resembles that of a dwarf nova, a closer look reveals interesting behavior. Fig. 6, constructed using methods described by Taylor et al. (1999), presents our spectra as a phase-averaged greyscale image. There is a striking broad component in the stronger Balmer and HeI lines that shows a large velocity excursion, with the red wing of H$\alpha$ reaching to $+3100$ km s*-1* at phase 0.3 (where phase 0 corresponds to the blue-to-red crossing of the line core). The broad components around H$\beta$ and $\lambda 6678$ move in phase with those of H$\alpha$ and range from 900 to 2600 and $-2500$ to $-900$ km s*-1* and 700 to 2100 and $-1000$ to $-600$ km s*-1*, respectively. The wings of $\lambda 5876$ also move in phase with the others, but the red edge is difficult to follow at its minimum because of interference from the NaD absorption lines, which are stationary and hence interstellar. The maximum of the red edge is 3200 km s*-1*, while the blue edge ranges from $-1500$ to $-600$ km s*-1*. The blueward wing of all these lines is noticeably weaker than the redward wing.

Other emission lines present include HeII $\lambda 4686$, HeI $\lambda 4713$ and $\lambda 4921$, and, very weakly, FeII $\lambda 5169$. We also detect unidentified emission lines at $\lambda 6344$, as is also seen in LS Peg (Taylor et al., 1999), and at $\lambda 5046$. The strength of the $\lambda 5780$ diffuse interstellar band (Jenniskens & Desert, 1994) and the NaD lines suggest that a good deal of interstellar material lies along the line of sight, and that the luminosity is relatively high.

High-velocity wings reminiscent of the ones seen here have been seen in V795 Her (Casares et al., 1996; Dickinson et al., 1997), LS Peg (Taylor et al., 1999), V533 Her (Thorstensen & Taylor, 2000), and RX J1643+34 (Patterson et al., 2002), all of which are SW Sex stars. We do not, however, detect another SW Sex characteristic, namely phase-dependent absorption in the HeI lines (Thorstensen et al., 1991). The orbital periods of most SW Sex stars are shorter than 4 hours, so CZ Aql’s 4.8-h period would be unusually long for an SW Sex star.

3.3 LU Camelopardalis

Jiang et al. (2000) obtained the first spectrum of this dwarf nova in a follow-up study of CV candidates from the ROSAT All Sky Survey. We found no other published spectroscopic studies. Our velocities constrain the period to a unique value, 0.1499685(7) d. The averaged spectrum shows a rather strong, blue continuum, which may indicate a state somewhat above true minimum.

3.4 GZ Cancri

Jiang et al. (2000) confirmed the cataclysmic nature of GZ Cnc by obtaining the first spectrum of the object. Kato et al. (2002) suggested that this star, originally labeled as a dwarf nova, could possibly be an intermediate polar (DQ Her star), based on similarities in its long-term photometric behavior to that of other intermediate polars. Tappert & Bianchini (2003) conducted a photometric and spectroscopic study of the system. Using advance results from the present study to help decide the daily cycle count, they found $P_{\rm orb}=0.08825(28)$ d, or 2.118(07) h, placing the system near the lower edge of the so-called gap in the CV period distribution – a dearth of systems in the period range from roughly 2 to 3 hr. Tappert & Bianchini (2003) also saw characteristics that could indicate an intermediate polar classification, but did not claim their evidence was definitive on this point.

Almost all our observations come from two observing runs a year apart. The full set of velocities strongly indicates an orbital frequency near 11.4 cycle d*-1*, with the Monte Carlo test giving a discriminatory power greater than 0.99 for the choice of daily cycle count. However, the number of cycles between the two observing runs is not determined. Precise periods that fit the combined data set are given by $P=[349.785(3)\ {\rm d}]/n$, where $n$ is the integer number of cycle counts; $n=3972\pm 8$ corresponds to roughly $1$ standard deviation. While our period agrees well with that of Tappert & Bianchini (2003), our data neither support nor disprove the claim that GZ Cnc may be an intermediate polar.

3.5 V632 Cygni

Liu et al. (1999) offer the only published spectrum of this dwarf nova. They measured the equivalent widths and integrated line fluxes of the Balmer, HeI, and HeII emission lines and suggested that the orbital period is likely short based on the very strong Balmer emission. Our spectrum appears similar to theirs, and our measured flux level is also nearly the same. The periodigram in Fig. 3 clearly favors an orbital frequency near 15.7 cycles d*-1*, with a discriminatory power of 95 per cent and a correctness likelihood near unity. This confirms the suggestion of Liu et al. (1999) that the period is rather short and suggests that it is an SU UMa-type dwarf nova.

3.6 V1006 Cygni

Bruch & Schimpke (1992) present the only published spectrum we know of, and characterized it as a “textbook example” of a dwarf nova spectrum. They noted a slightly blue continuum with strong Balmer and He I emission, as well as clear He II $\lambda 4686$ and Fe II emission. Our spectrum (Fig. 1) is similar to theirs both in appearance and normalization, and our line measurements (Table LABEL:tab:quie) are also comparable.

The periodogram (Fig. 4) indicates a frequency near 10.1 cycles d*-1*, and the Monte Carlo test confirms that the daily cycle count is securely determined. Most of our data are from 2004 June, but we returned in 2005 June/July to confirm the unusual period indicated in the earlier data. The periods found by analyzing the two runs separately are consistent within their uncertainties. As with GZ Cnc, there are multiple choices for the cycle count between the two observing runs; the best-fitting periods are given by $P=[369.006(4)\ {\rm d}]/n$, where $n=3726\pm 4$ corresponds to 1 standard deviation. Including a few velocities from other observing runs suggests that $n$ is slightly larger, perhaps 3728. In any case, the period amounts to 2.38 h, which places V1006 Cyg firmly in the period gap (Warner, 1995), where there is apparently a true scarcity of dwarf novae (Hellier & Naylor, 1998).

3.7 BF Eri

The first evidence that BF Eridani was a cataclysmic variable came when an Einstein X-ray source, 1ES0437-046, was matched to the variable (Elvis et al., 1992). Schachter et al. (1996) confirmed this match and presented an optical spectrum. Kato (1999) and the Variable Star Observers’ League in Japan (VSOLJ) found photometric variability characteristic of a dwarf nova.

The spectrum of BF Eri (Fig. 2) shows a significant contribution from a K star along with the usual dwarf-nova emission lines. Normally, this suggests that $P_{\rm orb}>6$ h. Nearly all our spectra yielded good cross-correlation radial velocity measurements as well as emission-line velocities. The absorption- and emission-line velocities independently give a period near 6.50 h (Table 5), in accordance with expectation based on the spectrum. There is no ambiguity in cycle count over the 5-year span of the observations, so the period is precise to a few parts per million. Fig. 6 shows a phase-resolved average of the BF Eri spectra, with the absorption spectrum shifting in antiphase to the emission lines.

If the emission-line velocities faithfully trace the primary’s center-of-mass motion, and the absorption-line velocities also trace the secondary’s motion, then the two velocity curves should be exactly one-half cycle out of phase. In BF Eri, we find a shift of $0.515\pm 0.007$ cycles between the two curves, consistent with 0.5 cycles, so we feel emboldened to explore the system dynamics.

Masses can only be derived when the orbital inclination is known, as in eclipsing systems. To see if BF Eri might eclipse, we derived differential magnitudes from images that were taken for astrometry (discussed below) and plotted them as a function of orbital phase. Some images were taken at the phase at which an eclipse would appear, but no evidence for an eclipse was found. Limits on the depth and duration of the eclipse are difficult to quantify because the data were taken in short bursts in the presence of strong intrinsic variability, so a weak eclipse cannot be ruled out, but the photometry does suggest that the inclination is not close to edge-on.

Because the system apparently does not eclipse, we cannot derive masses; rather, we find broad constraints on the inclination by assuming astrophysically reasonable masses for the components. Taken at face value, the velocity amplitudes $K$ imply a mass ratio $q=M_{2}/M_{1}=0.60\pm 0.03$. If we arbitrarily choose a white dwarf mass $M_{1}=0.9$ M*⊙* (so that $M_{2}=0.53$ M*⊙), the observed $K$ velocities imply $i=50$ degrees. To find a rough lower limit on the inclination, we consider a massive white dwarf ($M_{1}=1.2$ M⊙) and, ignoring the constraint on $q$ for the moment, take $M_{2}=0.4$ M⊙; this yields $i=40$ degrees. For a rough upper limit, we assume $M_{1}=0.6$ M⊙* and $M_{2}=0.4$ M*⊙*, which gives $i=67$ degrees.

The decomposition procedure described earlier yielded a spectral type of K3 $\pm 1$ subclass; the result of the subtraction is shown in Fig. 2. Using the $V$ passband tabulated by Bessell (1990) and the IRAF sbands task, we find a synthetic $V=16.9\pm 0.3$ for the K star’s contribution. Taking the range of plausible secondary star masses to be 0.4 to 0.8 M*⊙* yields $R_{2}=0.7\pm 0.1$ R*⊙* at this $P_{\rm orb}$. Combining this with the surface brightness expected at this spectral type yields $M_{V}=6.8\pm 0.4$ for the secondary. If there is no significant interstellar extinction, we have $m-M=10.1\pm 0.5$, or a distance of approximately $1100\pm 300$ pc. The dust maps of Schlegel et al. (1998) give a total $E(B-V)=0.062$ in this direction. Assuming that BF Eri is beyond the Galactic dust and taking $A_{V}/E(B-V)=3.3$ gives an extinction-corrected $(m-M)_{0}=9.9$, and a distance estimate of 950 ($+250,-200$) pc.

We can also estimate a distance using the relation found by Warner (1987) between $P_{\rm orb}$, $i$, and the absolute magnitude at maximum light $M_{V}({\rm max})$. Using our inclination constraints, the Warner relation predicts $M_{V}{\rm max}=3.9\pm 0.7$ at this orbital period. The General Catalog of Variable Stars (Kholopov et al., 1999) lists $m_{p}=13.2$ at maximum light; taking this to be similar to $V_{\rm max}$ yields $m-M=9.3$, or 9.1 corrected for extinction, which corresponds to 660 pc.

Given these distance estimates, it is surprising that BF Eri has a very substantial proper motion. The Lick proper motion survey (Hanson et al., 2004) gives $[\mu_{X},\mu_{Y}]=[+34,-97]$ mas yr*-1*. We have begun a series of parallax observations with the Hiltner 2.4m telescope using the protocols described by Thorstensen (2003); so far we have five epochs from 2005 November and 2007 January. The proper motion relative to the background stars is $[\mu_{X},\mu_{Y}]=[32,-111]$ mas yr*-1*, and the parallax is not detected, with a nominal value of $1\pm 2$ mas. The parallax determination is very preliminary, but given the data so far we estimate the lower limit on the distance based on the astrometry alone to be $\sim 200$ pc.

At the nominal 950 pc distance derived from the secondary star, a 100 mas yr*-1* proper motion corresponds to a transverse velocity $v_{T}=451$ km s*-1*. This is implausibly large, so we are left wondering how we might have overestimated the distance. One effect might be as follows. Our distance is based on the secondary’s apparent brightness, and we estimate the secondary’s contribution to the total light by searching for the best cancellation of its features. If the secondary’s absorption lines are weaker than those in the spectral-type standards, we would underestimate the secondary’s contribution. In our best decomposition, the secondary is about 2.2 magnitudes fainter than the total light in $V$. Assuming (unrealistically) that all the light is from the secondary would therefore decrease the distance modulus by 2.2 magnitudes, to a distance of 340 pc.

We do not yet have enough information to resolve the conundrum posed by BF Eri’s unmistakably large proper motion and its apparently large distance, but a reasonable compromise might be to put it at something like 400-500 pc, with an underluminous, low-metallicity secondary. The cross-correlation velocities of the secondary have a zero point determined to $\pm 5$ km s*-1*, more or less, and give a substantial systemic velocity of $-72\pm 3$ km s*-1*, or $-86$ km s*-1* in the local standard of rest. If the star is at 450 pc, its space velocity with respect to the local standard of rest is $\sim$250 km s*-1*, with Galactic components $[U,V,W]$ = $[-180,-180,-3]$ km s*-1*, that is, the velocity is mostly parallel to the Galactic plane and lags far behind the rotation of the Galactic disk. This would put BF Eri on a highly eccentric orbit; these are halo-population kinematics (even though the star remains close to the plane). These kinematics would be qualitatively consistent with the weak-line conjecture used earlier.

3.8 BI Ori

Szkody (1987) published the first quiescent spectrum of BI Orionis, which showed emission lines typical of dwarf novae. Morales-Rueda & Marsh (2002) show a spectrum in outburst and note the possible presence of weak HeII $\lambda 4686$ emission.

Only the 2006 January velocities are extensive enough for period finding; they give $P_{\rm orb}=4.6$ hr, with no significant ambiguity in the daily cycle count. The average spectrum shows the usual emission lines; M-dwarf absorption features are also visible, though the signal-to-noise of the individual spectra was not adequate for finding absorption-line velocities. Using the procedures described earlier, we estimate the secondary’s spectral type to be M2.5 $\pm$ 1.5, with the secondary alone having $V=20.0\pm 0.4$. Assuming that the secondary’s mass lies in the broad range from 0.2 to 0.6 M*⊙, its radius at this $P_{\rm orb}$ would be 0.35 to 0.6 R⊙*. Combining this with the surface brightness derived from the spectral types gives an absolute magnitude $M_{V}=10.2\pm 1.0$. The distance modulus, uncorrected for extinction, is therefore $m-M=+9.8\pm 1.1$, corresponding to $910(+600,-360)$ pc. Schlegel et al. (1998) estimate a total reddening $E(B-V)=0.11$ in this direction; assuming that BI Ori lies beyond all the dust, and taking $A_{V}/E(B-V)=3.3$ reduces the distance to $\sim 770$ pc. At maximum light, BI Ori has $m_{p}=13.2$ (Kholopov et al., 1999). Assuming the color is neutral, we find $M_{V}=3.4\pm 1.1$ at maximum. At BI Ori’s period, the Warner (1987) relation predicts $M_{V}>3.6$ (with the brightest value corresponding to $i=0$). This agrees broadly with our nominal value based on the secondary star’s distance, but is a little fainter, suggesting that BI Ori is not too far from face-on, or a little closer than our nominal distance, or both.

3.9 FO Per

FO Persei was apparently discovered by Morgenroth (1939), but its cataclysmic nature was not immediately recognized. Bruch (1989) obtained spectra and gave equivalent widths for the Balmer lines for two different nights of observations, between which the continuum changed from relatively flat to inclined toward the red.

The emission lines in FO Per are rather narrow (Fig. 1, Table LABEL:tab:quie). This is often taken to indicate a low orbital inclination. The velocity amplitude $K$ is small, so that $K/\sigma\approx 1.6$ for the best fits (Table 5). Because of this, the daily cycle count remains ambiguous; the orbital frequency is either 5.8 or 6.8 cycle d*-1*, corresponding to $P_{\rm orb}$ of 3.52 or 4.13 hr. CVs with periods in the 3-4 hour range tend to be novalike variables (Shafter, 1992), whereas FO Per is a dwarf nova; thus the 4.13 hr period is more likely a priori.

4 Summary

We have determined the orbital periods of eight CVs without significant daily cycle count ambiguity; for FO Per, the period is narrowed to two choices. For three of the systems we find high-precision periods by establishing secure cycle counts over long baselines.

While most of these objects are similar to others already known, three stand out as especially interesting. CZ Aql shows asymmetric, high-velocity wings around the Balmer and HeI $\lambda 5876$ and $\lambda 6678$ lines, possibly indicating a magnetic system. BF Eri’s proper motion of $\sim 100$ mas yr*-1* is surprising in view of the large distance indicated by its secondary spectrum and by the Warner relation; even if it is somewhat nearer than these indicators suggest, its kinematics are not typical of disk stars. Finally, the orbital period of V1006 Cyg places it squarely in the middle of the so-called period gap between 2 and 3 hours.

Acknowledgments. We are most grateful for support from the National Science Foundation through grants AST-9987334 and AST-0307413. Bill Fenton took most of the spectra of GZ Cnc, and J. Cameron Brueckner assisted with the BF Eri spectroscopy. Some of the astrometric images of BF Eri were obtained by Sébastien Lépine and Michael Shara of the American Museum of Natural History. We would like to thank the MDM Observatory staff for their skillful and conscientious support. Finally, we are grateful to the Tohono O’odham for leasing us their mountain for a while, so that we may study the glorious universe in which we all live.