mass stars — just slightly agitated by the special circumstances of their imprisonment (enforced rapid rotation, struggles with thermal equilibrium, the occasional nova outburst, etc.). 14. SUMMARY 1. We report photometric campaigns on the eclipsing dwarf novae XZ Eridani and OU Virginis. These showed common superhumps with ε=0.0270(15) and 0.0326(15), respectively, for the two stars. 2. We do the same for the novalike variable UU Aquarii. The 2000 observing campaign showed strong superhumps — a stable wave with ε=0.0702(24), lasting essentially throughout the 50-day campaign. 3. We discovered and tracked the superhump wave of the black-hole X-ray transient KV Ursae Majoris (= XTE J1118+480) through its 2000 outburst. The properties of the superhump were a little different — smaller, more long-lived, more stable in period, more sinusoidal in waveform — from those of the common superhumps of dwarf novae. Nevertheless, the resemblances are sufficient to warrant adopting the hypothesis of a common origin. We found ε=0.0047(7). 4. We discuss the important constraints set by the nondetection of superhumps in U G pecially) and IP Pegasi. Assuming that there is a critical ratio qcrit for superhump manufacture, we infer that qcrit does not exceed 0.38. 5. We report a season’s photometry on the novalike variable BB Doradus (= EC 05287-5857), yielding three noncommensurate frequencies. No help is available to guide us in interpreting 28 They are somewhat larger than ZAMS stars, but this is probably due to the extra heating CV secondaries suffer as they struggle with thermal equilibrium (Paczynski & Sienkiewicz 1983). There is still room for abundance anomalies (C/N, etc.), but their interpretations should not invoke too much H burning

Since superhump properties appear to be tightly correlated with q (independently measurable in ~12-15 cases) and Porb (measurable in all cases), we adopt the working hypothesis that q is the controlling parameter, and derive an estimate for qcrit. Superhumps are absent in all CVs with a certifiable q>0.36, and present in all CVs with a certifiable q<0.25. DW UMa and UU Aqr are of particular interest since they have a fairly high q (near 0.3) and yet show welldefined superhumps with ε not quite at the top of the range. We use this to estimate qcrit=0.35±0.02. This is also consistent with an estimate based on the 50% threshold at 3.1 hr. 9. We use all available data to establish an empirical ε(q) law, Eq. (8). This should be useful in estimating system parameters of any star showing superhumps. It also provides a mass- radius law for the secondary stars in short-period CVs, subject to the adopted value of <M1>. Plausible choices are <M1>=0.75 M, R2=1.15 RZAMS. The resultant mass-radius law shows an apparent discontinuity near 0.20 M, which agrees with the expectation from a disrupted magnetic braking model. 10. The mass-radius law, shown in Figures 10-12 and Eq. (14), demonstrates that CV secondaries follow a theoretical ZAMS pretty well, with just two clear departures: near 0.08 and 0.20 M. It’sfirst is well-understood as the result of the star’s inability to contract fast enough to keep up with its timescale of mass loss (first described by Paczynski 1981). The second is less understood, but probably arises from the same effect, where the timescale is set by the strength of magnetic braking. It should be noted, however, that these departures are mainly gradual. Essentially all CVs have secondaries slightly above the single-star ZAMS, and this bloating seems to steadily increase as they approach the transitions at 0.20 and 0.08 possible that this arises because the secondaries are always losing matter on timescales pretty close to their thermal timescales [see Figure 23 of Patterson (1984) and the accompanying discussion

short-period CVs. These stars range in apparent < M& > from 10-11 M /yr (WZ Sge stars) to 10-9 (ER UMa stars) to 10-8 (CP Pup, BK Lyn). It is not easy to understand how the secondaries can muster a common mass-radius law in the face of such variety. Long-term mass-transfer cycles, possibly associated with classical nova eruptions, could perhaps explain this… but at present it looms as a mystery. 13. There are still some loose ends needing clarification. The question of U TV Col nuperhumps is important and will affect our results. If the Smak & Waagen result is correct, then ε=0.130(14) at q=0.36(2). Adding this point to Figure 9 and refitting, we find a somewhat steeper ε(q) with a larger quadratic term. That implies a smaller q above the period gap, which would increase the discontinuity in radius we find near 0.2 M eeds clarification too, although cannot be easily compared with these other stars, since it lacks a q constraint and is magnetic. And a radial-velocity study of BB Dor would be very welcome, since we found an annoying ambiguity of interpretation there. Finally, ε(q) still needs help at the low-q end this will be critical in measuring q and M2 for the very oldest CVs, after they have passed minimum period. This paper reports results from 262 nights and ~1000 hours — and that’s just for the five stars with newly reported positive results. The negative results, and summary reports on stars not yet published, span another thousand nights. Keeping this collaboration humming along takes a lot of community mojo. Even outside the big author list, we benefited from the data of Gordon Garradd, Stan Walker, Bill Allen, Panos Niarchos, Bernard Heathcote, David Messier, Sarah Tuttle, Donn Starkey, and Fred Velthuis. The NSF provided some mojo too, in financial support through grants AST 00-98254 and 04-06813

J. Kemp QCRIT, ε(Q), & MASS-RADIUS 22 TABLE 1 OU VIR OBSERVING LOG (2003 MAY - JUNE) Telescope(s) Observer(s) Nights/Hours MDM 2.4 m, 1.3 m T. Krajci 12/46 CBA-Uzbekistan 28 cm R. Rea 08/43 CBA-Nelson 35 cm J. Foote 07/34 CBA-Utah 50 cm R. Fried 04/25 CBA-Flagstaff 40 cm B. Monard 03/18 CBA-Pretoria 30 cm T. Vanmunster 03/14 CBA-Belgium 35 cm of Athens P. 03/11 University D. Messier Niarchos 02/14 CBA-Connecticut 25 cm D. Skillman 1/7 CBA-East 66 cm Mia B. Heathcote 1/5 CBA-Mia 1/4

E. Armstrong QCRIT, ε(Q), & MASS-RADIUS 23 TABLE 2 XZ ERI OBSERVING LOG (2003 JANUARY - FEBRUARY) Telescope(s) Observer(s) Nights/Hours MDM 1.3 m B. Monard 9/23 CBA-Pretoria 30 cm G. Bolt 6/22 CBA-Perth 30 cm R. Rea 6/22 CBA-Nelson 35 cm P. Warhurst 5/16 University of Auckland 35 cm B. Allen 3/50 CBA-Blenheim 40 cm D. Starkey 2/50 CBA-Indiana 25 cm J. Foote 1/50 CBA-Utah 50 cm 1/40

R. Fried QCRIT, ε(Q), & MASS-RADIUS 24 TABLE 3 UU AQR OBSERVING LOG (2000) Telescope(s) Observer(s) Nights/Hours CBA-Flagstaff 40 cm J. McCormick, F. Velthuis 11/62 CBA-Farm Cove 25 cm L. Jensen 09/39 CBA-Denmark 25 cm J. Gunn 08/26 CBA-Illinois 20 cm R. Rea 07/24 CBA-Nelson 35 cm N. Butterworth 06/32 CBA-Townsville 20 cm M. Bos 06/26 CBA-Otahuhu 30 cm L. Cook 04/24 CBA-Concord 44 cm G. Garradd 02/10 CBA-Tamworth 45 cm S. Walker 2/9 CBA-Waiharara 25 cm T. Vanmunster 2/9 CBA-Belgium 25 cm J. Kemp 2/7 CTIO 0.9 m 1/2

D. Harvey QCRIT, ε(Q), & MASS-RADIUS 25 TABLE 4 KV UMA (= XTE J1118+480) OBSERVING LOG Telescope(s) Observer(s) Nights/Hours CBA-West 35 cm L. Cook 32/180 CBA-Concord 44 cm D. Skillman 18/630 CBA-East 66 cm R. Fried 16/510 CBA-Flagstaff 40 cm T. Vanmunster 14/101 CBA-Belgium 25 cm J. Kemp 10/460 MDM 1.3 m, 2.4 m G. Masi 10/150 CBA-Italy 28 cm 3/11 Interval00000000 Superhump Period Semi-Amplitude (JD)00000000 (d) (mag) 2451634-48 0.17094(20) 0.028 2451647-60 0.17074(14) 0.029 2451657-71 0.17027(27) 0.037 2451670-83 0.17047(22) 0.034 2451686-99 0.17065(22) 0.036 2451700-10 0.17062(26) 0.040 Date00000000000 QPO Period (JD)00000000000 (s) 2451658 11.5±0.2 2451665 09.9±0.1 2451677 08.8±0.2

B. Monard QCRIT, ε(Q), & MASS-RADIUS 26 TABLE 5 BB DOR (= EC 05287-5857) Telescope(s) Observer(s) Nights/Hours CBA-Pretoria 30 cm J. Kemp 13/65 CTIO 0.9 m R. Rea 10/53 CBA-Nelson 35 cm G. Bolt 04/10 CBA-Perth 30 cm 03/12

QCRIT, ε(Q), & MASS-RADIUS 27 TABLE 6 SUPERHUMP SUCCESS RATE Porb Superhumps/Searched (d) 0.05→0.06 22/24 0.06→0.07 40/41 0.07→0.08 37/38 0.08→0.10 20/23 0.10→0.13 09/13 0.13→0.15 08/25 0.15→0.17 2/8 0.17→0.20 00/11 0.20→0.30 00/13 0.30→0.40 0/4 0.40→0.50 0/4 0.50→0.60 0/2 NOTE — These refer to stars with detections and strong upper limits (roughly <0.04 mag). Weak upper limits (~0.1 mag) are not counted as searches

IY UMa 0.0260(10) <0.125(8)0 Steeghs et al. 2000c Z Cha 2003 Zhang et al. 0.0364(9)0 <0.145(15) Warner & O’Donoghue 1988, Wade & Horne 1988 HT Cas 0.0330(30) <0.15(1)00 Horne et al. 1986 Patterson et al. 1991 DV UMa 0.0343(10) <0.150(1)0 Feline et al. 2000b Feline et al. 2004b OU Vir 0.0326(15) <0.175(25) this paper Baptista et al. 2004a V2051 Oph 0.030(2)00 <0.19(3)00 Araujo-Betancor et al. 1998, Kiyota & Kato 1998, P03 DW UMa 0.0644(20) <0.28(4)00 Patterson et al. 2003, this paper Baptista et al. 2002b UU Aqr 0.0702(19) <0.30(7)00 but these are always internal errors, not including the (usually unknown) systematic error in the method used. 2. In P01 we included X-ray binaries in this discussion. They are somewhat relevant, and do as a class establish that low ε is always associated with low q (compare our Figure 9 to Figure 1 of P01). But the observational errors in these stars are generally too large to be a significant constraint, and there are some worries about cycle count too

Star M1 M2 R2 Porb q References (M ) (M ) (R ) (d) XZ Eri 0.77(2)00 0.084(2)0 0.131(2)0 0.06116 0.110(2)0 Wood et al. 2004b OY Car 0.685(11) 0.070(2)0 0.127(2)0 0.06312 0.10(1)00 Hoogerwerf et al. 1989 EX Hya 0.49(13)0 0.081(13) 0.138(6)0 0.06823 0.165(30) Beuermann et al. 2004 Feline et al. 2003 OU Vir 0.9(2)000 0.15(4)00 0.177(24) 0.07271 0.175(25) Horne et al. 2004a HT Cas 0.61(4)00 0.09(2)00 0.154(13) 0.07365 0.15(1)00 Steeghs et al. 1991 IY UMa 0.79(4)00 0.10(1)00 0.160(4)0 0.07391 0.125(8)0 Z Cha 2003 Wood et al. 0.56(1)00 0.083(3)0 0.149(4)0 0.07450 0.145(15) Wade & Horne 1988, Wood 1990 Feline et al. 1986 DV UMa 1.09(8)00 0.15(1)00 0.207(16) 0.08585 0.151(1)0 Araujo-Betancor et al. 2004b DW UMa 0.73(3)00 0.21(3)00 0.305(15) 0.13661 0.28(4)00 Martin et al. 2003, this paper IP Peg 0.94(10)0 0.42(8)00 0.43(3)00 0.15821 0.45(4)00 Smak 2002 Baptista et al. 1989, Hessman 1989 UU Aqr 0.67(14)0 0.20(7)00 0.34(4)00 0.16358 0.30(7)00 U Gem 1994 GY Cnc 0.82(14)0 0.33(7)00 0.41(3)00 0.17544 0.40(8)00 Thorstensen 2000 Horne et al. 1.07(8)00 0.39(2)00 0.45(1)00 0.17691 0.36(2)00 Smak 2001 DQ Her 0.60(7)00 0.40(5)00 0.48(3)00 0.19362 0.66(4)00 Baptista et al. 1993 EX Dra 0.75(15)0 0.55(8)00 0.58(4)00 0.20994 0.72(6)00 Thoroughgood et al. 2000 V347 Pup 0.63(4)00 0.52(6)00 0.60(2)00 0.23194 0.83(5)00 North et al. 2005 EM Cyg 1.12(8)00 0.99(12)0 0.87(7)00 0.29091 0.88(5)00 Thoroughgood et al. 2000 AC Cnc 0.76(3)00 0.77(5)00 0.83(3)00 0.30048 1.02(4)00 Thoroughgood et al. 2004 V363 Aur 0.90(6)00 1.06(11)0 0.97(4)00 0.32124 1.17(7)00 2004

QCRIT, ε(Q), & MASS-RADIUS 32