On the classification of plane graphs representing structurally stable rational Newton flows

We study certain plane graphs, called Newton graphs, representing a special class of dynamical systems which are closely related to Newton's iteration method for finding zeros of (rational) functions defined on the complex plane. These Newton graphs are defined in terms of nonvanishing angles between edges at the same vertex. We derive necessary and sufficient conditions -of purely combinatorial nature- for an arbitrary plane graph in order to be topologically equivalent with a Newton graph. Finally, we analyse the structure of Newton graphs and prove the existence of a polynomial algorithm to recognize such graphs

Optical spectroscopy of (candidate) ultra-compact X-ray binaries: constraints on the composition of the donor stars

We present optical spectroscopy of several (candidate) ultra-compact X-ray binaries (UCXBs) obtained with the ESO VLT and Gemini-North telescopes. In only one of five observed UCXB candidates did we find evidence for H in its spectrum (4U 1556-60). For XB 1905+00 the optical counterpart is not detected. For the known UCXBs 4U 1626-67 and XB 1916-05 we find spectra consistent with a C/O and a He/N accretion disc respectively, the latter is the first optical spectrum of a He-rich donor in an UCXB. Interestingly, the C/O spectrum of 4U 1626-67 shows both similarities as well as marked differences from the optical C/O spectrum of 4U 0614+09. We obtained phase resolved spectroscopy of 4U 0614+09 and the 44 min transient XTE J0929-314. In neither object were we able to detect clear orbital periodicities, highlighting the difficulties of period determinations in UCXBs. We reanalysed the spectra of XTE J0929-314 that were taken close to the peak of its 2003 X-ray outburst and do not confirm the detection of Halpha emission as was claimed in the literature. The peak spectra do show strong C or N emission around 4640A, as has also been detected in other UCXBs. We discuss the implications of our findings for our understanding of the formation of UCXBs and the Galactic population of UCXBs. At the moment all studied systems are consistent with having white dwarf donors, the majority being C/O rich.Comment: Accepted for publication in MNRA

Detection of the radial velocity curve of the B5-A0 supergiant companion star of Cir X-1?

In this Paper we report on phase resolved I-band optical spectroscopic and photometric observations of CirX-1 obtained with the Very Large Telescope. The spectra are dominated by Paschen absorption lines at nearly all orbital phases except near phase zero (coinciding with the X-ray dip) when the absorption lines are filled-in by broad Paschen emission lines. The radial velocity curve of the absorption lines corresponds to an eccentric orbit (e=0.45) whose period and time of periastron passage are consistent with the period and phase predicted by the most recent X-ray dip ephemeris. We found that the I-band magnitude decreases from 17.6 to ~16.8 near phase 0.9-1.0, this brightening coincides in phase with the X-ray dip. Even though it is likely that the absorption line spectrum is associated with the companion star of CirX-1, we cannot exclude the possibility that the spectrum originates in the accretion disc. However, if the spectrum belongs to the companion star, it must be a supergiant of spectral type B5-A0. If we assume that the compact object does not move through the companion star at periastron, the companion star mass is constrained to ~<10 Msun for a 1.4 Msun neutron star, whereas the inclination has to be ~> 13.7 degrees. Alternatively, the measured absorption lines and their radial velocity curve can be associated with the accretion disc surrounding a 1.4 Msun neutron star and its motion around the centre of mass. An absorption line spectrum from an accretion disc is typically found when our line-of-sight passes through the accretion disc rim implying a high inclination. However, from radio observations it was found that the angle between the line-of-sight and the jet axis is smaller than 5 degrees implying that the jet ploughs through the accretion disc in this scenario.Comment: 8 pages, 4 figures, 3 tables, accepted by MNRA

The mass function of GX 339-4 from spectroscopic observations of its donor star

We obtained 16 VLT/X-shooter observations of GX 339-4 in quiescence in the period May - September 2016 and detected absorption lines from the donor star in its NIR spectrum. This allows us to measure the radial velocity curve and projected rotational velocity of the donor for the first time. We confirm the 1.76 day orbital period and we find that $K_2$ = $219 \pm 3$ km s$^{-1}$, $\gamma = 26 \pm 2$ km s$^{-1}$ and $v \sin i = 64 \pm 8$ km s$^{-1}$. From these values we compute a mass function $f(M) =1.91 \pm 0.08~M_{\odot}$, a factor $\sim 3$ lower than previously reported, and a mass ratio $q = 0.18 \pm 0.05$. We confirm the donor is a K-type star and estimate that it contributes $\sim 45-50\%$ of the light in the $J$- and H-band. We constrain the binary inclination to $37^\circ < i < 78^\circ$ and the black hole mass to $2.3~M_{\odot} < M_\mathrm{BH} < 9.5~M_{\odot}$. GX 339-4 may therefore be the first black hole to fall in the 'mass-gap' of $2-5~M_{\odot}$.Comment: 11 pages, 7 figures, accepted for publication in Ap

Two fast X-ray transients in archival Chandra data

We present the discovery of two new X-ray transients in archival Chandra data. The first transient, XRT 110103, occurred in January 2011 and shows a sharp rise of at least three orders of magnitude in count rate in less than 10 s, a flat peak for about 20 s and decays by two orders of magnitude in the next 60 s. We find no optical or infrared counterpart to this event in preexisting survey data or in an observation taken by the SIRIUS instrument at the Infrared Survey Facility 2.1 yr after the transient, providing limiting magnitudes of J>18.1, H>17.6 and Ks>16.3. This event shows similarities to the transient previously reported in Jonker et al. which was interpreted as the possible tidal disruption of a white dwarf by an intermediate mass black hole. We discuss the possibility that these transients originate from the same type of event. If we assume these events are related a rough estimate of the rates gives 1.4*10^5 per year over the whole sky with a peak 0.3-7 keV X-ray flux greater than 2*10^-10 erg cm^-2 s^-1 . The second transient, XRT 120830, occurred in August 2012 and shows a rise of at least three orders of magnitude in count rate and a subsequent decay of around one order of magnitude all within 10 s, followed by a slower quasi-exponential decay over the remaining 30 ks of the observation. We detect a likely infrared counterpart with magnitudes J=16.70+/-0.06, H=15.92+/-0.04 and Ks=15.37+/-0.06 which shows an average proper motion of 74+/-19 milliarcsec per year compared to archival 2MASS observations. The JHKs magnitudes, proper motion and X-ray flux of XRT 120830 are consistent with a bright flare from a nearby late M or early L dwarf.Comment: Accepted for publication in MNRAS, 6 pages, 5 figure

Proffessor Dr.H.G. Schulze: Der Drosse Anreger.

Met die aftrede van prof. dr. H. G.Schulze met pensioen word ons blikterug gevoer na een van die persoonlikhedewat die Potchefstroomse Universiteitvir C.H.O. in sy wordingsjare gehelpdra en bou het

Characterisation of a candidate dual AGN

We present Chandra and optical observations of a candidate dual AGN discovered serendipitously while searching for recoiling black holes via a cross-correlation between the serendipitous XMM source catalog (2XMMi) and SDSS-DR7 galaxies with a separation no larger than ten times the sum of their Petrosian radii. The system has a stellar mass ratio M$_{1}$/M$_{2}\approx 0.7$. One of the galaxies (Source 1) shows clear evidence for AGN activity in the form of hard X-ray emission and optical emission-line diagnostics typical of AGN ionisation. The nucleus of the other galaxy (Source 2) has a soft X-ray spectrum, bluer colours, and optical emission line ratios dominated by stellar photoionisation with a "composite" signature, which might indicate the presence of a weak AGN. When plotted on a diagram with X-ray luminosity vs [OIII] luminosity both nuclei fall within the locus defined by local Seyfert galaxies. From the optical spectrum we estimate the electron densities finding n$_{1} < 27$ e$^{-}$ cm$^{-3}$ and n$_{2} \approx 200$ e$^{-}$ cm$^{-3}$. From a 2D decomposition of the surface brightness distribution we infer that both galaxies host rotationally supported bulges (Sersic index $< 1$). While the active nature of Source 1 can be established with confidence, whether the nucleus of Source 2 is active remains a matter of debate. Evidence that a faint AGN might reside in its nucleus is, however, tantalising.Comment: 16 pages, 9 figures. Accepted for publication on MNRAS. Comments welcom