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Spectroscopic detection and characterization of an irradiated substellar donor planet in an accreting white-dwarf binary system reveals a donor mass of 0.055 ± 0.008 solar masses, an average spectral type of L1 ± 1 and an average irradiation-induced temperature difference between the dayside and nightside of 57 kelvin. An accreting white-dwarf binary system This paper reports simultaneous optical and near-infrared time-resolved spectroscopy of an accreting white-dwarf binary system, termed J1433, using the X-Shooter instrument at the Very Large Telescope (operated by the European Southern Observatory). The spectra reveal the presence of an irradiated substellar donor with a mass of 0.055 ± 0.008 solar masses, an average spectral type of L1 and an average irradiation-induced temperature difference between the dayside and nightside of 57 kelvin. These observations provide an empirical benchmark for models of irradiated substellar atmospheres and interiors, a regime that includes hot Jupiters and short-period brown-dwarf binaries. Interacting compact binary systems provide a natural laboratory in which to study irradiated substellar objects. As the mass-losing secondary (donor) in these systems makes a transition from the stellar to the substellar regime, it is also irradiated by the primary (compact accretor) 1 , 2 . The internal and external energy fluxes are both expected to be comparable in these objects, providing access to an unexplored irradiation regime. The atmospheric properties of donors are largely unknown 3 , but could be modified by the irradiation. To constrain models of donor atmospheres, it is necessary to obtain accurate observational estimates of their physical properties (masses, radii, temperatures and albedos). Here we report the spectroscopic detection and characterization of an irradiated substellar donor in an accreting white-dwarf binary system. Our near-infrared observations allow us to determine a model-independent mass estimate for the donor of 0.055 ± 0.008 solar masses and an average spectral type of L1 ± 1, supporting both theoretical predictions and model-dependent observational constraints that suggest that the donor is a brown dwarf. Our time-resolved data also allow us to estimate the average irradiation-induced temperature difference between the dayside and nightside of the substellar donor (57 kelvin) and the maximum difference between the hottest and coolest parts of its surface (200 kelvin). The observations are well described by a simple geometric reprocessing model with a bolometric (Bond) albedo of less than 0.54 at the 2 σ confidence level, consistent with high reprocessing efficiency, but poor lateral heat redistribution in the atmosphere of the brown-dwarf donor 4 , 5 . These results add to our knowledge of binary evolution, in that the donor has survived the transition from the stellar to the substellar regime, and of substellar atmospheres, in that we have been able to test a regime in which the irradiation and the internal energy of a brown dwarf are comparable.

Stellar-mass black holes are found in X-ray-emitting binary systems, where their mass can be determined from the dynamics of their companion stars. Models of stellar evolution have difficulty producing black holes in close binaries with masses more than ten times that of the Sun (>10; ref. 4), which is consistent with the fact that the most massive stellar black holes known so far all have masses within one standard deviation of 10. Here we report a mass of (15.65 +/- 1.45) for the black hole in the recently discovered system M 33 X-7, which is located in the nearby galaxy Messier 33 (M 33) and is the only known black hole that is in an eclipsing binary. To produce such a massive black hole, the progenitor star must have retained much of its outer envelope until after helium fusion in the core was completed. On the other hand, in order for the black hole to be in its present 3.45-day orbit about its (70.0 +/- 6.9) companion, there must have been a 'common envelope' phase of evolution in which a significant amount of mass was lost from the system. We find that the common envelope phase could not have occurred in M 33 X-7 unless the amount of mass lost from the progenitor during its evolution was an order of magnitude less than what is usually assumed in evolutionary models of massive stars.

Herculean task achieved DI Herculis is well known to astrophysicists as a binary star system with an orbit that precesses (changes orientation) at a rate that seemingly cannot be accounted for by conventional physics and stellar models. Many theories have been offered to explain this anomaly, including a failure of general relativity, a 'circumbinary' planet and an unprecedentedly large tilt between the spin axes of the stars and the orbital axis. Now this long-standing mystery has been solved. Analysis of spectra obtained during a series of binary eclipses reveals that both stars in the binary are tipped over on their sides, rotating with their spin axes nearly perpendicular to the orbital axis. The slow precession arises from extra forces associated with the stars being on their 'sides'. For most binary stars, the theoretical and observed precession rates are in agreement, but the observed precession rate for the DI Herculis system is a factor of four slower than the theoretical rate, a disagreement that once was interpreted as evidence for a failure of general relativity. Here, both stars of DI Herculis are reported to rotate with their spin axes nearly perpendicular to the orbital axis, an observation that leads to the reconciliation of the theoretical and observed precession rates. The orbits of binary stars precess as a result of general relativistic effects, forces arising from the asphericity of the stars, and forces from any additional stars or planets in the system. For most binaries, the theoretical and observed precession rates are in agreement 1 . One system, however—DI Herculis—has resisted explanation for 30 years 2 , 3 , 4 . The observed precession rate is a factor of four slower than the theoretical rate, a disagreement that once was interpreted as evidence for a failure of general relativity 5 . Among the contemporary explanations are the existence of a circumbinary planet 6 and a large tilt of the stellar spin axes with respect to the orbit 7 , 8 . Here we report that both stars of DI Herculis rotate with their spin axes nearly perpendicular to the orbital axis (contrary to the usual assumption for close binary stars). The rotationally induced stellar oblateness causes precession in the direction opposite to that of relativistic precession, thereby reconciling the theoretical and observed rates.

Let G be a connected, simple, and undirected graph with a vertex set V(G) and an edge set E(G). Total k-labeling is a function fe from the edge set to the first ke natural number, and a function fv from the vertex set to the non negative even number up to 2kv, where k = max{ke, 2kv}. An edge irregular reflexive k labeling of the graph G is the total k-labeling, if for every two different edges x1x2 and x1′x2′ of G,wt(x1x2)≠wt(x1′x2′), where wt(x1x2)=fv(x1)+fe(x1x2)+fv(x2). The minimum k for graph G which has an edge irregular reflexive k-labelling is called the reflexive edge strength of the graph G, denoted by res(G). In this paper, we determined the exact value of the reflexive edge strength of family trees, namely generalized sub-divided star graph, broom graphs, and double star graph.

X-ray binaries are composed of a normal star in orbit around a neutron star or stellar-mass black hole. Radio and x-ray observations have led to the presumption that some x-ray binaries called microquasars behave as scaled-down active galactic nuclei. Microquasars have resolved radio emission that is thought to arise from a relativistic outflow akin to active galactic nuclei jets, in which particles can be accelerated to large energies. Very high energy [gamma]-rays produced by the interactions of these particles have been observed from several active galactic nuclei. Using the High Energy Stereoscopic System, we find evidence for gamma-ray emission of >100 gigaelectron volts from a candidate microquasar, LS 5039, showing that particles are also accelerated to very high energies in these systems.

Using fuzzy graph theoretical and computational methods, the multidisciplinary discipline of chemical graph theory examines the molecular formation of a chemical molecule as a fuzzy graph and looks into related mathematical questions. An effective tool in this field that links a numerical value to a graph formation is the topological index. The neighborhood inverse sum indeg index stands out as a contemporary index derived from neighborhood degree considerations. Neighborhood inverse sum indeg index is a crucial graph metric that is applied in real-world applications like corporate networking and signalling on traffic. So this index is generalized in fuzzy graph. In this paper, the neighborhood inverse sum indeg index is explored for some fuzzy graphs like a tree, double star, subgraph, star, complete fuzzy graph, complete bipartite graph, etc. . We evaluate the effect of neighborhood inverse sum indeg index value when the vertex or edge is deleted from a graph. Moreover, the relationship between two isomorphic fuzzy graphs are determined. We have determined the boundedness of this index for some fuzzy graphs like C S ( n , α 1 ) , K p 1 ∨ ( K q 1 ∪ K r 1 ) , etc. Also a couple of results are found. We all aware that one cause of global warming is the carbon emission. Finally we have found out the country which needs to reduce the carbon emissions by applying the concept of neighborhood inverse sum indeg index.

An n×n matrix A is called eventually exponentially positive (EEP) if etA=∑k=0∞tkAkk!>0 for all t≥t0, where t0≥0. A matrix whose entries belong to the set +,−,0 is called a sign pattern. An n×n sign pattern A is called potentially eventually exponentially positive (PEEP) if there exists some real matrix realization A of A that is EEP. Characterizing the PEEP sign patterns is a longstanding open problem. In this article, A is called minimally potentially eventually exponentially positive (MPEEP), if A is PEEP and no proper subpattern of A is PEEP. Some preliminary results about MPEEP sign patterns and PEEP sign patterns are established. All MPEEP sign patterns of orders n≤3 are identified. For the n×n tridiagonal sign patterns Tn, we show that there exists exactly one MPEEP tridiagonal sign pattern Tno. Consequently, we classify all PEEP tridiagonal sign patterns as the superpatterns of Tno. We also classify all PEEP star sign patterns Sn and double star sign patterns DS(n,m) by identifying all the MPEEP star sign patterns and the MPEEP double star sign patterns, respectively.

Identifying and classifying the potentially eventually positive sign patterns and the potentially eventually exponentially positive sign patterns of orders greater than 3 have been raised as two open problems since 2010. In this article, we investigate the potential eventual positivity of the class of double star-like sign patterns S(n,m,1) whose underlying graph G(S(n,m,1)) is obtained from the underlying graph G(S(n,m)) of the (n+m)-by-(n+m) double star sign patterns S(n,m) by adding an additional vertex adjacent to the two center vertices and removing the edge between the center vertices. We firstly establish some necessary conditions for a double star-like sign pattern to be potentially eventually positive, and then identify all the minimal potentially eventually positive double star-like sign patterns. Secondly, we classify all the potentially eventually positive sign patterns in the class of double star-like sign patterns S(n,m,1). Finally, as an application of our results about the potentially eventually positive double star-like sign patterns, we identify all the minimal potentially eventually exponentially positive sign patterns and characterize all the potentially eventually exponentially positive sign patterns in the class of double star-like sign patterns S(n,m,1).

A model is proposed to explain the observed influence of gravity waves of relativistic double stars on the vertical component of the Earth’s electric field in the atmospheric boundary layer. The considered mechanism is the perturbation of the Earth’s orbit by the gravity waves from the relativistic double star systems leading to a small displacement between the Earth and the free electric charge of the Earth’s atmosphere. The proposed model gives estimates of the amplitude of the E z components spectrally localized at the frequencies of the gravity waves from the relativistic double star systems that do not contradict the observations.