Planetary systems around close binary stars: the case of the very dusty, Sun-like, spectroscopic binary BD+20 307

Field star BD+20 307 is the dustiest known main sequence star, based on the fraction of its bolometric luminosity, 4%, that is emitted at infrared wavelengths. The particles that carry this large IR luminosity are unusually warm, comparable to the temperature of the zodiacal dust in the solar system, and their existence is likely to be a consequence of a fairly recent collision of large objects such as planets or planetary embryos. Thus, the age of BD+20 307 is potentially of interest in constraining the era of terrestrial planet formation. The present project was initiated with an attempt to derive this age using the Chandra X-ray Observatory to measure the X-ray flux of BD+20 307 in conjunction with extensive photometric and spectroscopic monitoring observations from Fairborn Observatory. However, the recent realization that BD+20 307 is a short period, double-line, spectroscopic binary whose components have very different lithium abundances, vitiates standard methods of age determination. We find the system to be metal-poor; this, combined with its measured lithium abundances, indicates that BD+20 307 may be several to many Gyr old. BD+20 307 affords astronomy a rare peek into a mature planetary system in orbit around a close binary star (because such systems are not amenable to study by the precision radial velocity technique).Comment: accepted for ApJ, December 10, 200

The Orbital Light Curve of Aquila X-1

We obtained R- and I-band CCD photometry of the soft X-ray transient/neutron- star binary Aql X-1 in 1998 June while it was at quiescence. We find that its light curve is dominated by ellipsoidal variations, although the ellipsoidal variations are severely distorted and have unequal maxima. After we correct for the contaminating flux from a field star located only 0.46" away, the peak-to-peak amplitude of the modulation is ~0.25 mag in the R band, which requires the orbital inclination to be greater than 36 degrees. The orbital period we measure is consistent with the 18.95 h period measured by Chevalier & Ilovaisky (1998). During its outbursts the light curve of Aql X-1 becomes single humped. The outburst light curve observed by Garcia et al. (1999) agrees in phase with our quiescent light curve. We show that the single humped variation is caused by a ``reflection effect,'' that is, by heating of the side of the secondary star facing towards the neutron star.Comment: 18 manuscript pages, 7 figures; accepted by A

Spanning Trees on Lattices and Integration Identities

For a lattice $\Lambda$ with $n$ vertices and dimension $d$ equal or higher than two, the number of spanning trees $N_{ST}(\Lambda)$ grows asymptotically as $\exp(n z_\Lambda)$ in the thermodynamic limit. We present exact integral expressions for the asymptotic growth constant $z_\Lambda$ for spanning trees on several lattices. By taking different unit cells in the calculation, many integration identities can be obtained. We also give $z_{\Lambda (p)}$ on the homeomorphic expansion of $k$-regular lattices with $p$ vertices inserted on each edge.Comment: 15 pages, 3 figures, 1 tabl

Kepler-413b: a slightly misaligned, Neptune-size transiting circumbinary planet

We report the discovery of a transiting, Rp = 4.347+/-0.099REarth, circumbinary planet (CBP) orbiting the Kepler K+M Eclipsing Binary (EB) system KIC 12351927 (Kepler-413) every ~66 days on an eccentric orbit with ap = 0.355+/-0.002AU, ep = 0.118+/-0.002. The two stars, with MA = 0.820+/-0.015MSun, RA = 0.776+/-0.009RSun and MB = 0.542+/-0.008MSun, RB = 0.484+/-0.024RSun respectively revolve around each other every 10.11615+/-0.00001 days on a nearly circular (eEB = 0.037+/-0.002) orbit. The orbital plane of the EB is slightly inclined to the line of sight (iEB = 87.33+/-0.06 degrees) while that of the planet is inclined by ~2.5 degrees to the binary plane at the reference epoch. Orbital precession with a period of ~11 years causes the inclination of the latter to the sky plane to continuously change. As a result, the planet often fails to transit the primary star at inferior conjunction, causing stretches of hundreds of days with no transits (corresponding to multiple planetary orbital periods). We predict that the next transit will not occur until 2020. The orbital configuration of the system places the planet slightly closer to its host stars than the inner edge of the extended habitable zone. Additionally, the orbital configuration of the system is such that the CBP may experience Cassini-States dynamics under the influence of the EB, in which the planet's obliquity precesses with a rate comparable to its orbital precession. Depending on the angular precession frequency of the CBP, it could potentially undergo obliquity fluctuations of dozens of degrees (and complex seasonal cycles) on precession timescales.Comment: 48 pages, 13 figure

What is the probability of connecting two points ?

The two-terminal reliability, known as the pair connectedness or connectivity function in percolation theory, may actually be expressed as a product of transfer matrices in which the probability of operation of each link and site is exactly taken into account. When link and site probabilities are $p$ and $\rho$, it obeys an asymptotic power-law behavior, for which the scaling factor is the transfer matrix's eigenvalue of largest modulus. The location of the complex zeros of the two-terminal reliability polynomial exhibits structural transitions as $0 \leq \rho \leq 1$.Comment: a few critical polynomials are at the end of the .tex source fil

The Transiting Exocomets in the HD 172555 System

The Earth is thought to have formed dry, in a part of the Solar Nebula deficient in organic material, and to have acquired its organics and water through bombardment by minor bodies. Observations of this process in well-dated systems can provide insight into the probable origin and composition of the bombarding parent bodies. Transiting cometary activity has previously been reported in Ca II for the late-A member of the 241 Myr old Pictoris Moving Group member, HD 172555(Kiefer et al. 2014). We present HST STIS and COS spectra of HD 172555 demonstrating that the star has chromospheric emission and variable in falling gas features in transitions of silicon and carbon ions at times when no Fe II absorption is seen in the UV data, and no Ca II absorption is seen in contemporary optical spectra. The lack of CO absorption and stable gas absorption at the system velocity is consistent with the absence of a cold Kuiper belt analog (Riviere-Marichalar et al. 2012) in this system. The presence of infall in some species at one epoch and others at different epochs suggests that, like Pictoris, there may be more than one family of exocomets. If perturbed into star-grazing orbits by the same mechanism as for Pic, these data suggest that the wide planet frequency among A-early F stars in the PMG is at least 37.5, well above the frequency estimated for young moving groups independent of host star spectral type

Hubble Space Telescope Observations of UV Oscillations in WZ Sagittae During the Decline from Outburst

We present a time series analysis of Hubble Space Telescope observations of WZ Sge obtained in 2001 September, October, November and December as WZ Sge declined from its 2001 July superoutburst. Previous analysis of these data showed the temperature of the white dwarf decreased from ~29,000 K to ~18,000 K. In this study we binned the spectra over wavelength to yield ultraviolet light curves at each epoch that were then analyzed for the presence of the well-known 27.87 s and 28.96 s oscillations. We detect the 29 s periodicity at all four epochs, but the 28 s periodicity is absent. The origin of these oscillations has been debated since their discovery in the 1970s and competing hypotheses are based on either white dwarf non-radial g-mode pulsations or magnetically-channelled accretion onto a rotating white dwarf. By analogy with the ZZ Ceti stars, we argue that the non-radial g-mode pulsation model demands a strong dependence of pulse period on the white dwarf's temperature. However, these observations show the 29 s oscillation is independent of the white dwarf's temperature. Thus we reject the white dwarf non-radial g-mode pulsation hypothesis as the sole origin of the oscillations. It remains unclear if magnetically-funnelled accretion onto a rapidly rotating white dwarf (or belt on the white dwarf) is responsible for producing the oscillations. We also report the detection of a QPO with period ~18 s in the September light curve. The amplitudes of the 29 s oscillation and the QPO vary erratically on short timescales and are not correlated with the mean system brightness nor with each other.Comment: 20 pages, 3 figures, 1 table; accepted for publication in Ap

Some Exact Results on the Potts Model Partition Function in a Magnetic Field

We consider the Potts model in a magnetic field on an arbitrary graph $G$. Using a formula of F. Y. Wu for the partition function $Z$ of this model as a sum over spanning subgraphs of $G$, we prove some properties of $Z$ concerning factorization, monotonicity, and zeros. A generalization of the Tutte polynomial is presented that corresponds to this partition function. In this context we formulate and discuss two weighted graph-coloring problems. We also give a general structural result for $Z$ for cyclic strip graphs.Comment: 5 pages, late