The Lagrangian formalism applied to Keplerian orbits with corrections due to Special Relativity is explored. A Lagrangian is defined using kinetic energy that is consistent with the relativistic momentum of Special Relativity and Newtonian gravitational potential energy with relativistic mass. The corresponding equations of motion are solved in a Keplerian limit, resulting in an approximate relativistic orbit equation that has the same form as that derived from General Relativity in the same limit and clearly describes three characteristics of relativistic Keplerian orbits: precession of perihelion; reduced radius of circular orbit; and increased eccentricity. The prediction for the rate of precession of perihelion of Mercury is one-third that derived from General Relativity. All three characteristics are qualitatively correct, though suppressed when compared to more accurate general-relativistic calculations. A more accurate solution of Lagrange's equations results in an approximate relativistic orbit equation that predicts the rate of precession of perihelion to be one-half that predicted by General Relativity, but does not have the symmetry of the general-relativistic orbit equation in this limit. This treatment of the relativistic central-mass problem is approachable by undergraduate physics majors and nonspecialists whom have not had a course dedicated to relativity. The approximate relativistic orbit equations are useful for a qualitative understanding of general-relativistic corrections to Keplerian orbits.

Photospheric magnetic fields are studied using synoptic maps from 1976 to 2003 produced at the National Solar Observatory, Kitt Peak (NSO/KP). Synoptic maps were averaged over the time interval of nearly three solar cycles (Solar Cycles 21-23). The change in the latitudinal distribution was considered for the following groups of magnetic field values: B = 0-5 G, B = 5-15 G, B = 15-50 G, and B>50 G. Magnetic fields in each of the above groups have common latitudinal distribution features, while for different field groups these features are significantly different. Each of the groups is closely related to a certain manifestation of solar activity. Strong magnetic fields are connected with two types of solar activity: active regions (magnetic fields B>15 G)that are related to sunspot zones, and polar faculae (magnetic fields 50 G > B > 15 G) that occupy latitudes around 65$^\circ$-75$^\circ$. Fields from 5 to 15 G occupy the polar regions and are connected with polar coronal holes (the global solar dipole). Fields of B<5 G occupy a) the equatorial region and b) latitudes 40$^{\circ}$-60$^\circ$.

Globally disruptive events include asteroid/comet impacts, large igneous provinces and glaciations, all of which have been considered as contributors to mass extinctions. Understanding the overall relationship between the timings of the largest extinctions and their potential proximal causes remains one of science's great unsolved mysteries. Cycles of about 60 million years in both fossil diversity and environmental data suggest external drivers such as the passage of the Solar System through the galactic plane. While cyclic phenomena are recognised statistically, a lack of coherent mechanisms and a failure to link key events has hampered wider acceptance of multi-million year periodicity and its relevance to earth science and evolution. The generation of a robust predictive model of timings, with a clear plausible primary mechanism, would signal a paradigm shift. Here, we present a model of the timings of globally disruptive events and a possible explanation of their ultimate cause. The proposed model is a symmetrical pattern of 63 million-year sequences around a central value, interpreted as the occurrence of events along, and parallel to, the galactic midplane. The symmetry is consistent with multiple dark matter disks, aligned parallel to the midplane. One implication of the precise pattern of timings and the underlying physical model is the ability to predict future events, such as a major extinction in one to two million years.

We present a stacking analysis of the complete sample of Early Type Galaxies (ETGs) in the \textit{Chandra} COSMOS (C-COSMOS) survey, to explore the nature of the X-ray luminosity in the redshift and stellar luminosity ranges \(0<z<1.5\) and \({10}^{9}<L_K/L_{\astrosun}<{10}^{13}\). Using established scaling relations, we subtract the contribution of X-ray binary populations, to estimate the combined emission of hot ISM and AGN. To discriminate between the relative importance of these two components, we (1) compare our results with the relation observed in the local universe \(L_{X,gas}\propto L_K^{4.5}\) for hot gaseous halos emission in ETGs, and (2) evaluate the spectral signature of each stacked bin. We find two regimes where the non-stellar X-ray emission is hard, consisten t with AGN emission. First, there is evidence of hard, absorbed X-ray emission in stacked bins including relatively high z (\(\sim 1.2\)) ETGs with average high X-ray luminosity (\(L_{X-LMXB}\gtrsim 6\times{10}^{42}\mbox{ erg}/\mbox{s}\)). These luminosities are consistent with the presence ofhighly absorbed "hidden" AGNs in these ETGs, which are not visible in their optical-IR spectra and spectral energy distributions. Second, confirming the early indication from our C-COSMOS study of X-ray detected ETGs, we find significantly enhanced X-ray luminoaity in lower stellar mass ETGs (\(L_K\lesssim{10}^{11}L_{\astrosun}\)), relative to the local \(L_{X,gas}\propto L_K^{4.5}\) relation. The stacked spectra of these ETGs also suggest X-ray emission harder than expected from gaseous hot halos. This emission is consistent with inefficient accretion \({10}^{-5}-{10}^{-4}\dot{M}_{Edd}\) onto \(M_{BH}\sim {10}^{6}-{10}^{8}\,M_{\astrosun}\).

Recently, S.W. Kahler studied the solar energetic particle (SEP) event timescales associated with coronal mass ejections (CMEs) from spacecraft data analysis. They obtained different timescales of SEP events, such as TO, the onset time from CME launch to SEP onset, TR, the rise time from onset to half the peak intensity (0.5Ip), and TD, the duration of the SEP intensity above 0.5Ip. In this work, we solve SEPs transport equation considering ICME shocks as energetic particle sources. With our modeling assumptions, our simulations show similar results to Kahler's spacecraft data analysis that the weighted average of TD increases with both CME speed and width. Besides, our simulations show the results which were not achieved from the observation data analysis, i.e., TD is directly dependent on CME speed, but not dependent on CME width.

In this work we combine information from relic abundance, direct detection, cosmic microwave background, positron fraction, gamma rays, and colliders to explore the existing constraints on couplings between Dark Matter and Standard Model constituents when no underlying model or correlation is assumed. For definiteness, we include independent vector-like effective interactions for each Standard Model fermion. Our results show that low Dark Matter masses below 20 GeV are disfavoured at the $3 \sigma$ level with respect to higher masses, due to the tension between the relic abundance requirement and upper constraints on the Dark Matter couplings. Furthermore, large couplings are typically only allowed in combinations which avoid effective couplings to the nuclei used in direct detection experiments.

We compare the absolute gain photometric calibration of the Planck/HFI and Herschel/SPIRE instruments on diffuse emission. The absolute calibration of HFI and SPIRE each relies on planet flux measurements and comparison with theoretical far-infrared emission models of planetary atmospheres. We measure the photometric cross calibration between the instruments at two overlapping bands, 545 GHz / 500 $\mu$m and 857 GHz / 350 $\mu$m. The SPIRE maps used have been processed in the Herschel Interactive Processing Environment (Version 12) and the HFI data are from the 2015 Public Data Release 2. For our study we used 15 large fields observed with SPIRE, which cover a total of about 120 deg^2. We have selected these fields carefully to provide high signal-to-noise ratio, avoid residual systematics in the SPIRE maps, and span a wide range of surface brightness. The HFI maps are bandpass-corrected to match the emission observed by the SPIRE bandpasses. The SPIRE maps are convolved to match the HFI beam and put on a common pixel grid. We measure the cross-calibration relative gain between the instruments using two methods in each field, pixel-to-pixel correlation and angular power spectrum measurements. The SPIRE / HFI relative gains are 1.047 ($\pm$ 0.0069) and 1.003 ($\pm$ 0.0080) at 545 and 857 GHz, respectively, indicating very good agreement between the instruments. These relative gains deviate from unity by much less than the uncertainty of the absolute extended emission calibration, which is about 6.4% and 9.5% for HFI and SPIRE, respectively, but the deviations are comparable to the values 1.4% and 5.5% for HFI and SPIRE if the uncertainty from models of the common calibrator can be discounted. Of the 5.5% uncertainty for SPIRE, 4% arises from the uncertainty of the effective beam solid angle, which impacts the adopted SPIRE point source to extended source unit conversion factor (Abridged)

We study very-high rate spherically symmetric accretion flows onto a massive black hole (BH; 10^2 < M_BH < 10^6 Msun) embedded in a dense gas cloud with a low abundance of metals, performing one-dimensional hydrodynamical simulations which include multi-frequency radiation transfer and non-equilibrium primordial chemistry. We find that rapid gas supply from the Bondi radius at a hyper-Eddington rate can occur without being impeded by radiation feedback when (n/10^5 cm^-3) > (M_BH/10^4Msun)^{-1}(T/10^4 K)^{3/2}, where n and T are the density and temperature of ambient gas outside of the Bondi radius. The resulting accretion rate in this regime is steady, and larger than 3000 times the Eddington rate. At lower Bondi rates, the accretion is episodic due to radiative feedback and the average rate is limited below the Eddington rate. For the hyper-Eddington case, the steady solution consists of two parts: a radiation-dominated central core, where photon trapping due to electron scattering is important, and an accreting envelope which follows a Bondi profile with T~8000 K. When the emergent luminosity is limited below the Eddington luminosity because of photon trapping, radiation from the central region does not affect the gas dynamics at larger scales. We apply our result to the rapid formation of massive BHs in protogalaxies with a virial temperature of T_vir> 10^4 K. Once a seed BH forms at the center of the galaxy, it can grow up to a maximum ~10^5 (T_vir/10^4 K) Msun via gas accretion independent of the initial BH mass. Finally, we discuss possible observational signatures of rapidly accreting BHs with/without allowance for dust. We suggest that these systems could explain Lya emitters without X-rays and luminous infrared sources with hot dust emission, respectively.

The XMM-LSS, XMM-COSMOS, and XMM-CDFS surveys are complementary in terms of sky coverage and depth. Together, they form a clean sample with the least possible variance in instrument effective areas and PSF. Therefore this is one of the best samples available to determine the 2-10 keV luminosity function of AGN and its evolution. The samples and the relevant corrections for incompleteness are described. A total of 2887 AGN is used to build the LF in the luminosity interval 10^42-10^46 erg/s, and in the redshift interval 0.001-4. A new method to correct for absorption by considering the probability distribution for the column density conditioned on the hardness ratio is presented. The binned luminosity function and its evolution is determined with a variant of the Page-Carrera method, improved to include corrections for absorption and to account for the full probability distribution of photometric redshifts. Parametric models, namely a double power-law with LADE or LDDE evolution, are explored using Bayesian inference. We introduce the Watanabe-Akaike information criterion (WAIC) to compare the models and estimate their predictive power. Our data are best described by the LADE model, as hinted by the WAIC indicator. We also explore the 15-parameter extended LDDE model recently proposed by Ueda et al., and find that this extension is not supported by our data. The strength of our method is that it provides: un-absorbed non-parametric estimates; credible intervals for luminosity function parameters; model choice according to which one has more predictive power for future data.

The problem of obtaining canonical Hamiltonian structures from the equations of motion, without any knowledge of the action, is studied in the context of the spatially flat Friedmann-Robertson-Walker models. Modifications to Raychaudhuri equation are implemented independently as quadratic and cubic terms of energy density without introducing additional degrees of freedom. Depending on their sign, modifications make gravity repulsive above a curvature scale for matter satisfying strong energy condition, or more attractive than in the classical theory. Canonical structure of the modified theories is determined demanding that the total Hamiltonian be a linear combination of gravity and matter Hamiltonians. In the quadratic repulsive case, the modified canonical phase space of gravity is a polymerized phase space with canonical momentum as inverse trigonometric function of Hubble rate; the canonical Hamiltonian can be identified with the effective Hamiltonian in loop quantum cosmology. The repulsive cubic modification results in a `generalized polymerized' canonical phase space. Both of the repulsive modifications are found to yield singularity avoidance. In contrast, the quadratic and cubic attractive modifications result in a canonical phase space in which canonical momentum is non-trigonometric and singularities persist. Our results hint on connections between repulsive/attractive nature of modifications to gravity arising from gravitational sector and polymerized/non-polymerized gravitational phase space.