We present an attempt to reconstruct the complete evolutionary path followed by cataclysmic variables (CVs), based on the observed mass-radius relationship of their donor stars. Along the way, we update the semi-empirical CV donor sequence presented previously by one of us, present a comprehensive review of the connection between CV evolution and the secondary stars in these systems, and reexamine most of the commonly used magnetic braking (MB) recipes, finding that even conceptually similar ones can differ greatly in both magnitude and functional form. The great advantage of using donor radii to infer mass-transfer and angular-momentum-loss (AML) rates is that they sample the longest accessible timescales and are most likely to represent the true secular (evolutionary average) rates. We show explicitly that if CVs exhibit long-term mass-transfer-rate fluctuations, as is often assumed, the expected variability timescales are so long that other tracers of the mass-transfer rate-including white dwarf (WD) temperatures-become unreliable. We carefully explore how much of the radius difference between CV donors and models of isolated main-sequence stars may be due to mechanisms other than mass loss. The tidal and rotational deformation of Roche-lobe-filling stars produces 4.5% radius inflation below the period gap and 7.9% above. A comparison of stellar models to mass-radius data for non-interacting stars suggests a real offset of 1.5% for fully convective stars (i.e., donors below the gap) and 4.9% for partially radiative ones (donors above the gap). We also show that donor bloating due to irradiation is probably smaller than, and at most comparable to, these effects. After calibrating our models to account for these issues, we fit self-consistent evolution sequences to our compilation of donor masses and radii. In the standard model of CV evolution, AMLs below the period gap are assumed to be driven solely by gravitational radiation (GR), while AMLs above the gap are usually described by an MB law first suggested by Rappaport et al. We adopt simple scaled versions of these AML recipes and find that these are able to match the data quite well. The optimal scaling factors turn out to be f GR = 2.47 ± 0.22 below the gap and f MB = 0.66 ± 0.05 above (the errors here are purely statistical, and the standard model corresponds to f GR = f MB = 1). This revised model describes the mass-radius data significantly better than the standard model. Some of the most important implications and applications of our results are as follows. (1) The revised evolution sequence yields correct locations for the minimum period and the upper edge of the period gap; the standard sequence does not. (2) The observed spectral types of CV donors are compatible with both standard and revised models. (3) A direct comparison of predicted and observed WD temperatures suggests an even higher value for f GR , but this comparison is sensitive to the assumed mean WD mass and the possible existence of mass-transfer-rate fluctuations. (4) The pred...

We review the properties of the DQ Herculis stars: cataclysmic variables containing an accreting, magnetic, rapidly rotating white dwarf. These stars are characterized by strong X-ray emission, high-excitation spectra, and very stable optical and X-ray pulsations in their light curves. There is considerable resemblance to their more famous cousins, the AM Herculis stars, but the latter class is additionally characterized by spin-orbit synchronism and the presence of strong circular polarization. We list eighteen stars passing muster as certain or very likely DQ Her stars. The rotational periods range from 33 s to 2.0 hr. Additional periods can result when the rotating searchlight illuminates other structures in the binary. A single hypothesis explains most of the observed properties: magnetically channeled accretion within a truncated disk. Some accretion flow still seems to proceed directly to the magnetosphere, however. The white dwarfs' magnetic moments are in the range 10 32 -10 34 G cm 3 , slightly weaker than in AM Her stars but with some probable overlap. The more important reason why DQ Hers have broken synchronism is probably their greater accretion rate and orbital separation. The observed L x /L v values are surprisingly low for a radially accreting white dwarf, suggesting that most of the accretion energy is not radiated in a strong shock above the magnetic pole. The fluxes can be more satisfactorily explained if most of the radial infall energy manages to bypass the shock and deposit itself directly in the white dwarf photosphere, where it should emerge as EUV radiation. This also provides an adequate source of ionizing photons to power the high-excitation optical and UV emission lines. This is probably the DQ Her analog to the famous "soft X-ray excess" in AM Her stars. However, unlike the AM Her case, this radiation has not been directly observed, so the analogy must not (yet) be embraced too firmly. There is some conventional wisdom today which segregates the short-period from the long-period DQ Her stars. But the observational grounds for this distinction are slim, except in one respect: X-ray emission from short-period systems appears to be weaker and softer. This must be due to the shallower depth of the potential well, and/or the greater difficulty the fast rotators have in enforcing radial accretion flow.

We study the evolution of hydrogen-rich cataclysmic variables (CVs) near minimum orbital period at ∼78 minutes. As has been known for many years, these are among the most intrinsically common CVs, but they hide fairly well because of their faintness and low incidence of eruptions. We discuss their number and observational signatures, paying special attention to those that may have passed minimum orbital period-the "period bouncers." The status of binaries near minimum period is best determined by the mass ratio, and this is best constrained by measuring the accretion disk precession frequency, because that frequency is readily accessible to observation and proportional to the secondary star's mass. This method reveals four stars that are good candidates to have survived period bounce; two appear to have secondaries as puny as 0.02. But each star M , can have bounced only recently if at all. There is still no strong evidence of any long era of evolution in a state of increasing period. This conflicts sharply with discussions of observational data that have identified dozens of known CVs with this state. The total space density of cataclysmic variables is ∼10 Ϫ5 pc Ϫ3 , with short-period systems constituting ∼75% of the total. Both estimates are far less than predicted by simple theories of evolution. It is probably necessary to have some means of destroying CVs before they reach the predicted very high space densities. This can be done by invoking an angular momentum loss mechanism that does not quickly subside as the mass ratio becomes very low.

We report photometry of the 1995 superoutburst of the dwarf nova AL Comae Berenices. The overall eruption light curve was striking, suggestive of two superoutbursts in rapid succession. During the first week of eruption, the light curve sported a period of 81.63 ±0.07 min. This signal declined quickly in amplitude, and was replaced by a stronger signal at 82.55 ±0.03 min. The latter bears all the earmarks of a "common superhump," a feature usually seen in SU UMa-type dwarf novae in superoutburst. This superhump endured at least 40 d, with no secular period change. We reexamined the quiescent light curves to search for a stable photometric signal which might signify the true binary period. We found a stable double-humped wave with a fundamental period of 81.6025 ±0.0001 min-the shortest period yet seen among dwarf novae, and probably very nearly the shortest period attainable by any binary star with a hydrogen-rich secondary. In orbital period and quiescent light curve, as well as in the eruption light curve, the star is a virtual twin of WZ Sge. There are also large-amplitude waves with a period in the range 83-90 min; these "quiescent superhumps" are rarely found in cataclysmic variables, and require an origin somewhat different from that of the common superhumps characteristic of SU UMa stars in eruption. We speculate that they arise from instability at the 2:1 orbital resonance in the accretion disk, and that the secondary has been whittled down to <0.04 M 0 .

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Protons with energies up to ~ 10 15 eV are the main component 1 of cosmic rays, but evidence for the specific locations where they could have been accelerated to these energies has been lacking 2 . Electrons are known to be accelerated to cosmic-ray energies in supernova remnants 3,4 , and the shock waves associated with such remnants, when they hit the surrounding interstellar medium, could also provide the energy to accelerate protons. The signature of such a process would be the decay of pions (π 0 ), which are generated when the protons collide with atoms and molecules in an interstellar cloud: pion decay results in γ-rays with a particular spectral-energy distribution 5,6 . Here we report the observation of cascade showers of optical photons resulting fromγ-rays at energies of ~ 10 12 eV hitting Earth's upper atmosphere, in the direction of the supernova remnant RX J1713.7-3946. The spectrum is a good match to that predicted by pion decay, and cannot be explained by other mechanisms.

We redetermine the relationship between absolute magnitude and orbital period for dwarf novae, based on 46 stars with good distance estimates. This improves upon Warner's previous relation, building upon today's improved estimates of distance and binary inclination, and greater wavelength coverage. Together with other distance and dynamical constraints, this calibration is then applied to a set of ∼300 known or likely dwarf novae of short orbital period, to study the dependence of quiescent M v , time-averaged M v , mass ratio q and whitedwarf temperature T WD , on P orb . These distributions show that stars become much fainter as they approach the minimum P orb , and appear to show evolutionary tracks as the secondary is whittled down by mass-loss. Stars on the lower branch have the expected properties of 'period bouncers' -with a feeble secondary, faint accretion light, cool white dwarf and long recurrence time between eruptions. Period bounce seems to occur at a mass of 0.058 ± 0.008 M o . Stars on the lower branch may also have higher velocities and heights above the Galactic plane, consistent with a greater age. Some are very nearby, despite strong selection effects discriminating against the discovery of these faint binaries accreting at very low rates. Period bouncers appear to be very common, and probably would dominate a complete census of cataclysmic variables.

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