A note on first-order spectra with binary relations

The spectrum of a first-order sentence is the set of the cardinalities of its finite models. In this paper, we consider the spectra of sentences over binary relations that use at least three variables. We show that for every such sentence $\Phi$, there is a sentence $\Phi'$ that uses the same number of variables, but only one symmetric binary relation, such that its spectrum is linearly proportional to the spectrum of $\Phi$. Moreover, the models of $\Phi'$ are all bipartite graphs. As a corollary, we obtain that to settle Asser's conjecture, i.e., whether the class of spectra is closed under complement, it is sufficient to consider only sentences using only three variables whose models are restricted to undirected bipartite graphs

EPIC 220204960: A Quadruple Star System Containing Two Strongly Interacting Eclipsing Binaries

We present a strongly interacting quadruple system associated with the K2 target EPIC 220204960. The K2 target itself is a Kp = 12.7 magnitude star at Teff ~ 6100 K which we designate as "B-N" (blue northerly image). The host of the quadruple system, however, is a Kp = 17 magnitude star with a composite M-star spectrum, which we designate as "R-S" (red southerly image). With a 3.2" separation and similar radial velocities and photometric distances, 'B-N' is likely physically associated with 'R-S', making this a quintuple system, but that is incidental to our main claim of a strongly interacting quadruple system in 'R-S'. The two binaries in 'R-S' have orbital periods of 13.27 d and 14.41 d, respectively, and each has an inclination angle of >89 degrees. From our analysis of radial velocity measurements, and of the photometric lightcurve, we conclude that all four stars are very similar with masses close to 0.4 Msun. Both of the binaries exhibit significant ETVs where those of the primary and secondary eclipses 'diverge' by 0.05 days over the course of the 80-day observations. Via a systematic set of numerical simulations of quadruple systems consisting of two interacting binaries, we conclude that the outer orbital period is very likely to be between 300 and 500 days. If sufficient time is devoted to RV studies of this faint target, the outer orbit should be measurable within a year.Comment: 20 pages, 18 figures, 7 tables; accepted for publication in MNRA

GU Boo: A New 0.6 Msun Detached Eclipsing Binary

We have found a new low-mass, double-lined, detached eclipsing binary, GU Boo, among a sample of new variables from the ROTSE-I database. The binary has an orbital period of 0.488728 +/- 0.000002 days, and estimated apparent magnitudes Vrotse = 13.7 and I = 11.8. Our analysis of the light and radial velocity curves of the system yields individual masses and radii of M1= 0.610 +/- 0.007 Msun, M2 = 0.599 +/- 0.006 Msun, R1= 0.623 +/- 0.016 Rsun, R2= 0.620 +/- 0.020 Rsun. The stars in GU Boo are therefore very similar to the components of the eclipsing binary YY Gem. For this study we have adopted a mean effective temperature for the binary of Teff = 3870 +/- 130 K. Based on its space velocities we suggest that GU Boo is a main sequence binary, possibly with an age of several Gyr. The metallicity of the binary is not well constrained at this point but we speculate that it should not be very different from solar. We have compared the physical parameters of GU Boo with current low-mass stellar models, where we accounted for uncertainties in age and metallicity by considering a wide range of values for those parameters. Our comparisons reveal that all the models underestimate the radii of the components of GU Boo by at least 10-15%. This result is in agreement with the recent studies of YY Gem and CU Cnc.Comment: 41 pages, 10 figures, 11 tables; accepted by Ap

Efficient computation of the gravitational wave spectrum emitted by eccentric massive black hole binaries in stellar environments

We present a fast and versatile method to calculate the characteristic spectrum $h_c$ of the gravitational wave background (GWB) emitted by a population of eccentric massive black hole binaries (MBHBs). We fit the spectrum of a reference MBHB with a simple analytic function and show that the spectrum of any other MBHB can be derived from this reference spectrum via simple scalings of mass, redshift and frequency. We then apply our calculation to a realistic population of MBHBs evolving via 3-body scattering of stars in galactic nuclei. We demonstrate that our analytic prescription satisfactorily describes the signal in the frequency band relevant to pulsar timing array (PTA) observations. Finally we model the high frequency steepening of the GWB to provide a complete description of the features characterizing the spectrum. For typical stellar distributions observed in massive galaxies, our calculation shows that 3-body scattering alone is unlikely to affect the GWB in the PTA band and a low frequency turnover in the spectrum is caused primarily by high eccentricities.Comment: 12 pages, 9 figures, published in MNRA

Ultra-low Amplitude Variables in the LMC -- Classical Cepheids, Pop. II Cepheids, RV Tau Stars and Binary Variables

A search for variable stars with ultra-low amplitudes (ULA), in the millimag range, has been made in the combined MACHO and OGLE data bases in the broad vicinity of the Cepheid instability strip in the HR diagram. A total of 25 singly periodic and 4 multiply periodic ULA objects has been uncovered. Our analysis does not allow us to distinguish between pulsational and ellipsoidal (binary) variability, nor between LMC and foreground objects. However, the objects are strongly clustered and appear to be associated with the pulsational instability strips of LMC Pop. I and II variables. When combined with the ULA variables of Buchler et al (2005) a total of 20 objects fall close to the classical Cepheid instability strip. However, they appear to fall on parallel period-magnitude relations that are shifted to slightly higher magnitude which would confer them a different evolutionary status. Low amplitude RV Tauri and Pop. II Cepheids have been uncovered that do not appear in the MACHO or OGLE catalogs. Interestingly, a set of binaries seem to lie on a PM relation that is essentially parallel to that of the RV Tauri/Pop. II Cepheids.Comment: 13 pages, 13 (color) figures. Astrophysical Journal (accepted for publlication

A New Low-Mass Eclipsing Binary from SDSS-II

We present observations of a new low-mass double-lined eclipsing binary system discovered using repeat observations of the celestial equator from the Sloan Digital Sky Survey II. Using near-infrared photometry and optical spectroscopy we have measured the properties of this short-period [P=0.407037(14) d] system and its two components. We find the following parameters for the two components: M_1=0.272+/-0.020 M_sun, R_1=0.268+/-0.010 R_sun, M_2=0.240+/-0.022 M_sun, R_2=0.248+/-0.0090 R_sun, T_1=3320+/-130 K, T_2=3300+/-130 K. The masses and radii of the two components of this system agree well with theoretical expectations based on models of low-mass stars, within the admittedly large errors. Future synoptic surveys like Pan-STARRS and LSST will produce a wealth of information about low-mass eclipsing systems and should make it possible, with an increased reliance on follow-up observations, to detect many systems with low-mass and sub-stellar companions. With the large numbers of objects for which these surveys will produce high-quality photometry, we suggest that it becomes possible to identify such systems even with sparse time sampling and a relatively small number of individual observations.Comment: 15 Pages, 9 Figures, 6 Tables. Replaced with version accepted to Ap