Abstracts of Interest

Selected by: Gary Hill


Abstract: 1810.08206
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Title: Constraining Black Hole Formation with 2M05215658+4359220

Abstract: We show that the recently discovered binary 2M05215658+4359220, comprised of a giant star (GS) orbiting a suspected black hole (BH) in a ~80 day orbit, may be instrumental in shedding light on uncertain BH-formation physics and can be a test case for studying wind accretion models. Using binary population synthesis and a realistic prescription of the star formation history and metallicity evolution of the Milky Way, we analyze the formation histories of detached BH-GS binaries like 2M05215658+4359220, and find that all such systems with orbital periods less than 5 years went through a common envelope. Furthermore, the `rapid' and `delayed' supernova engine models produce very different BH mass distributions in BH-GS binaries, and one current mass estimate for the BH in 2M05215658+4359220 is inconsistent with the rapid model. An improved measurement of the orbit of 2M05215658+4359220, which we argue is imminent with the next Gaia data release, therefore has widespread implications including for SN engine models and for the types of binaries detectable by LIGO and LISA. Finally, we show that the reported X-ray non-detection is a challenge for wind accretion theory, making 2M05215658+4359220 a prime target for further study with accretion models.

Comments: 7 pages, 5 figures, Submitted to ApJL, Comments welcome


Abstract: 1810.08211
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Title: Machine Learning Applied to the Reionization History of the Universe

Abstract: The Epoch of Reionization (EoR) features a rich interplay between the first luminous sources and the low-density gas of the intergalactic medium (IGM), where photons from these sources ionize the IGM. There are currently few observational constraints on key observables related to the EoR, such as the midpoint and duration of reionization. Although upcoming observations of the 21 cm power spectrum with next-generation radio interferometers such as the Hydrogen Epoch of Reionization Array (HERA) and the Square Kilometre Array (SKA) are expected to provide information about the midpoint of reionization readily, extracting the duration from the power spectrum alone is a more difficult proposition. As an alternative method for extracting information about reionization, we present an application of convolutional neural networks (CNNs) to images of reionization. These images are two-dimensional in the plane of the sky, and extracted at a series of redshift values to generate "image cubes" that are qualitatively similar to those HERA and the SKA will generate in the near future. Additionally, we include the impact that the bright foreground signal from the Milky Way galaxy imparts on such image cubes from interferometers, and degrade the simulated images accordingly. We show that we are able to recover the duration of reionization $\Delta z$ to within 10% using CNNs, assuming that the midpoint of reionization is already relatively well constrained. These results have exciting impacts for estimating $\tau$, the optical depth to the CMB, which can help constrain other cosmological parameters.

Comments: 10 pages, 5 figures, submitted to ApJ


Abstract: 1810.08454
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Title: Renormalization group computation of likelihood functions for cosmological data sets

Abstract: I show how a renormalization group (RG) method can be used to incrementally integrate the information in cosmological large-scale structure data sets (including CMB, galaxy redshift surveys, etc.). I show numerical tests for Gaussian fields, where the method allows arbitrarily close to exact computation of the likelihood function in order $\sim N$ time, even for problems with no symmetry, compared to $N^3$ for brute force linear algebra (where $N$ is the number of data points -- to be fair, methods already exist to solve the Gaussian problem in at worst $N \log N$ time, and this method will not necessarily be faster in practice). The method requires no sampling or other Monte Carlo (random) element. Non-linearity/non-Gaussianity can be accounted for to the extent that terms generated by integrating out small scale modes can be projected onto a sufficient basis, e.g., at least in the sufficiently perturbative regime. The formulas to evaluate are straightforward and require no understanding of quantum field theory, but this paper may also serve as a pedagogical introduction to Wilsonian RG for astronomers.

Comments: 13 pg, 4 fig


Abstract: 1810.08482
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Title: Fermi-LAT counterparts of IceCube neutrinos above 100 TeV

Abstract: The IceCube Collaboration has published four years of data and the observed neutrino flux is significantly in excess of the expected atmospheric background. Due to the steeply falling atmospheric background spectrum, events at the highest energies are most likely extraterrestrial. In our previous approach we have studied blazars as the possible origin of the High-Energy Starting Events (HESE) neutrino events at PeV energies. In this work we extend our study to include all HESE neutrinos (which does not include IC 170922A) at or above a reconstructed energy of 100 TeV, but below 1 PeV. We study the X-ray and $\gamma$-ray data of all ($\sim200$) 3LAC blazars that are positionally consistent with the neutrino events above 100 TeV to determine the maximum neutrino flux from these sources. This larger sample allows us to better constrain the scaling factor between the observed and maximum number of neutrino events. We find that when we consider a realistic neutrino spectrum and other factors, the number of neutrinos is in good agreement with the detected number of IceCube HESE events. We also show that there is no direct correlation between \Fermi-LAT $\gamma$-ray flux and the IceCube neutrino flux and that the expected number of neutrinos is consistent with the non-detection of individual bright blazars.

Comments: accepted for publication by A&A


Abstract: 1810.08499
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Title: Sensitivity of the KM3NeT/ARCA neutrino telescope to point-like neutrino sources

Authors: The KM3NeT Collaboration: S. Aiello, S. E. Akrame, F. Ameli, E. G. Anassontzis, M. Andre, G. Androulakis, M. Anghinolfi, G. Anton, M. Ardid, J. Aublin, T. Avgitas, C. Bagatelas, G. Barbarino, B. Baret, J. Barrios-Martí, A. Belias, E. Berbee, A. van den Berg, V. Bertin, S. Biagi, A. Biagioni, C. Biernoth, J. Boumaaza, S. Bourret, M. Bouta, M. Bouwhuis, C. Bozza, H.Brânzas, M. Bruchner, R. Bruijn, J. Brunner, E. Buis, R. Buompane, J. Busto, D. Calvo, A. Capone, S. Celli, M. Chabab, N. Chau, S.Cherubini, V. Chiarella, T. Chiarusi, M. Circella, R. Cocimano, J. A. B. Coelho, A. Coleiro, M. Colomer Molla, R. Coniglione, P. Coyle, A. Creusot, G. Cuttone, A. D'Onofrio, R. Dallier, C. De Sio, I. Di Palma, A. F. Díaz, D. Diego-Tortosa, C. Distefano, A. Domi, R. Donà, C. Donzaud,
D. Dornic, M. Dörr, M. Durocher, T. Eberl, D. van Eijk, I. El Bojaddaini, H. Eljarrari, D. Elsaesser, A. Enzenhöfer, P. Fermani, G. Ferrara, M. D. Filipovic, L. A. Fusco, T. Gal, A. Garcia, F. Garufi, L. Gialanella, E. Giorgio, A. Giuliante, S. R. Gozzini, R. Gracia, K. Graf, D. Grasso, T. Grégoire, G. Grella, S. Hallmann, H. Hamdaoui, H. van Haren, T. Heid, A. Heijboer, A. Hekalo, J. J. Hernández-Rey, J. Hofestädt, G. Illuminati, C. W. James, M. Jongen, M. de Jong, P. de Jong, M. Kadler, P. Kalaczynski, O. Kalekin, U. F. Katz, N. R. Khan Chowdhury, D. Kiessling, E. N. Koffeman, P. Kooijman, A. Kouchner, M. Kreter, V. Kulikovskiy, M. Kunhikannan-Kannichankandy, R. Lahmann, G. Larosa, R. Le Breton, F. Leone, E. Leonora, G. Levi, M. Lincetto, A. Lonardo, F. Longhitano, D. Lopez Coto, M. Lotze, L. Maderer, G. Maggi, J. Manczak, K. Mannheim, A. Margiotta, A. Marinelli, C. Markou, L. Martin, J. A. Martínez-Mora, A. Martini, F. Marzaioli, R. Mele, K. W. Melis, P. Migliozzi, E. Migneco, P. Mijakowski, L. S. Miranda, C. M. Mollo, M. Morganti, M. Moser, A. Moussa, R. Muller, M. Musumeci, L. Nauta, S. Navas, C. A. Nicolau, C. Nielsen, B. Ó Fearraigh, M. Organokov, A. Orlando, S. Ottonello, V. Panagopoulos, G. Papalashvili, R. Papaleo, G. E. Păvălaş, C. Pellegrino, M. Perrin-Terrin, P. Piattelli, K. Pikounis, O. Pisanti, C. Poirè, G. Polydefki, V. Popa, M. Post, T. Pradier, G. Pühlhofer, S. Pulvirenti, L. Quinn, F. Raffaelli, N. Randazzo, S. Razzaque, D. Real, L. Resvanis, J. Reubelt, G. Riccobene, M. Richer, L. Rigalleau, A. Rovelli, M. Saffer, I. Salvadori, D. F. E. Samtleben, A. Sánchez Losa, M. Sanguineti, A. Santangelo, D. Santonocito, P. Sapienza, J. Schumann, V. Sciacca, J. Seneca, I. Sgura, R. Shanidze, A. Sharma, F. Simeone, A. Sinopoulou, B. Spisso, M. Spurio, D. Stavropoulos, J. Steijger, S. M. Stellacci, B. Strandberg, D. Stransky, T. Stüven, M. Taiuti, F. Tatone, Y. Tayalati, E. Tenllado, T. Thakore, A. Trovato, E. Tzamariudaki, D. Tzanetatos, V. Van Elewyck, F. Versari, S. Viola, D. Vivolo, J. Wilms, E. de Wolf, D. Zaborov, J. D. Zornoza, J. Zúñiga
et al. (160 additional authors not shown)
Abstract: KM3NeT will be a network of deep-sea neutrino telescopes in the Mediterranean Sea. The KM3NeT/ARCA detector, to be installed at the Capo Passero site (Italy), is optimised for the detection of high-energy neutrinos of cosmic origin. Thanks to its geographical location on the Northern hemisphere, KM3NeT/ARCA can observe upgoing neutrinos from most of the Galactic Plane, including the Galactic Centre. Given its effective area and excellent pointing resolution, KM3NeT/ARCA will measure or significantly constrain the neutrino flux from potential astrophysical neutrino sources. At the same time, it will test flux predictions based on gamma-ray measurements and the assumption that the gamma-ray flux is of hadronic origin. Assuming this scenario, discovery potential and sensitivity to a selected list of Galactic sources and to generic point sources with an $E^{-2}$ spectrum are presented. These spectra are assumed to be time independent. The results indicate that an observation with $3\sigma$ significance is possible in about six years of operation for the most intense sources, such as Supernovae Remnants RX J1713.7-3946 and Vela Jr. If no signal will be found during this time, the fraction of the gamma-ray flux coming from hadronic processes can be constrained to be below 50% for these two objects.

Comments: 32 pages, 10 figures, submitted to Astroparticle Physics


Abstract: 1810.07427
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Title: The Tunguska Event Revisited

Abstract: The 1908 Tunguska Event is one of the best studied cases of a cosmic body impacting the Earth with global effects. However, still today, significant doubts are casted on the different proposed event reconstructions. In the present work, we would like to revisit the atmospheric fragmentation of the Tunguska Cosmic Body (TCB) by taking into account the possibility that a metre-sized fragment caused the formation of the Lake Cheko, located at about 9km NW the epicentre. Our work favours the hypothesis that the TCB was a rubble-pile asteroid composed by boulders with very different materials with different mechanical strengths, density, and porosity. The TCB was divided at least into two pieces by a close encounter with the Earth, short before the impact with our Planet: the main body (60m) produced the well-known airburst that devastated more than 2000km^2 of Siberian taig\`a, while the secondary one (6-10m) fell without fragmentation in the Kimchu river region and excavated a 50m depression, which presently hosts the Lake Cheko. This hypothesis requires that the secondary body was an extremely compact stone with high mechanical strength (300MPa). It is a high, but not unrealistic, value, as shown by a similar case that occurred in 2007 near the village of Carancas (Peru). An extreme compactness is not necessary, if one considers that the crater excavation could be enhanced by the explosion of permafrost-trapped methane released and ignited during the impact process. In this case, a smaller fragment (2m) with an average mechanical strength could reach the ground without fragmentation and is sufficient to excavate the Lake Cheko. We exclude the hypothesis of a single cosmic body ejecting a metre-sized fragment during or shortly before the airburst, because the resulting lateral velocity of such a large boulder was not enough to deviate to reach the alleged impact site.

Comments: 21 pages, 5 figures, 1 table


Abstract: 1810.07410
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Title: Testing isotropy in the Universe using photometric and spectroscopic data from the SDSS

Abstract: We analyze two volume limited galaxy samples from the SDSS photometric and spectroscopic data to test the isotropy in the local Universe. We use information entropy to quantify the global anisotropy in the galaxy distribution at different length scales and find that the galaxy distribution is highly anisotropic on small scales. The observed anisotropy diminishes with increasing length scales and nearly plateaus out beyond a length scale of 200 Mpc/h in both the datasets. We compare these anisotropies with those predicted by the mock catalogues from the N-body simulations of the Lambda CDM model and find an excellent agreement with the observations. We find a small residual anisotropy on large scales which decays in a way that is consistent with the linear perturbation theory. The slopes of the observed anisotropy converge to the slopes predicted by the linear theory beyond a length scale of ~ 200 Mpc/h indicating a transition to isotropy. We separately compare the anisotropies observed across the different parts of the sky and find no evidence for a preferred direction in the galaxy distribution.

Comments: 13 pages, 10 figures, 1 table, Submitted in MNRAS


Abstract: 1810.07176
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Title: Dark matter gets DAMPE

Abstract: The DArk Matter Particle Explorer (DAMPE) recently reported an excess of electrons/positrons above expected background fluxes even when a double power-law background spectrum is assumed. Several dark matter models that involve TeV-scale leptophilic WIMPs have been suggested in the literature to account for this excess. All of these models are associated with the presence of a nearby dark matter clump/over-density.
In this work we set out to explore how current constraints from observational data impact the suggested parameter space for a dark matter explanation of the DAMPE excess, as well as make projections of the capacity of LOFAR and the up-coming SKA to observe indirect radio emissions from the nearby dark matter over-density.
We show that LOFAR is incapable of probing the parameter space for DAMPE excess models, unless the dark matter clump is in the form of an ultra-compact mini halo. Fermi-LAT limits on dark matter annihilation are unable to probe these models in all cases. Limits derived from diffuse Coma cluster radio emission can probe a substantial portion of the parameter space and muon neutrino limits inferred from galactic centre gamma-ray fluxes heavily restrict muon coupling for the proposed WIMPs. The SKA is shown to able to fully probe the parameter space of all the studied models using indirect emissions from the local dark matter over-density.

Comments: 6 pages, 2 figures. Submitted to proceedings of South African Institute of Physics conference 2018


Abstract: 1810.07032
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Title: Fundamental Concepts

Abstract: This chapter briefly discusses the fundamental properties of black holes in general relativity, the discovery of astrophysical black holes and their main astronomical observations, how X-ray and $\gamma$-ray facilities can study these objects, and ends with a list of open problems and future developments in the field.

Comments: 14 pages, 4 figures. To appear in "Tutorial Guide to X-ray and Gamma-ray Astronomy: Data Reduction and Analysis" (Ed. C. Bambi, Springer Singapore, expected in 2019). arXiv admin note: text overlap with arXiv:1711.10256


Abstract: 1810.06678
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Title: Future ground arrays for ultrahigh-energy cosmic rays: recent updates and perspectives

Abstract: The origin and nature of ultrahigh-energy cosmic rays (UHECRs) are one of the most intriguing mysteries in particle astrophysics and astronomy. The two largest observatories, the Pierre Auger Observatory and the Telescope Array Experiment, are steadily observing UHECRs in both hemispheres in order to better understand their origin and associated acceleration mechanisms at the highest energies. We highlight their latest results including on-going upgrades, AugerPrime and TAx4, and then address the requirements for a next-generation observatory. We share recent updates and perspectives for a future ground array of fluorescence detectors, addressing the requirements for a large-area, low-cost detector suitable for measuring the properties of the highest energy cosmic rays with an unprecedented aperture.

Comments: Invited talk in ISVHECRI 2018, Nagoya, Japan


Abstract: 1810.06672
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Title: Probing $Λ$CDM cosmology with the Evolutionary Map of the Universe survey

Abstract: The Evolutionary Map of the Universe (EMU) is an all-sky survey in radio-continuum which uses the Australian SKA Pathfinder (ASKAP). Using galaxy angular power spectrum and the integrated Sachs-Wolfe effect, we study the potential of EMU to constrain models beyond $\Lambda$CDM (i.e., local primordial non-Gaussianity, dynamical dark energy, spatial curvature and deviations from general relativity), for different design sensitivities. We also include a multi-tracer analysis, distinguishing between star-forming galaxies and galaxies with an active galactic nucleus, to further improve EMU's potential. We find that EMU could measure the dark energy equation of state parameters around 35\% more precisely than existing constraints, and that the constraints on $f_{\rm NL}$ and modified gravity parameters will improve up to a factor $\sim2$ with respect to Planck and redshift space distortions measurements. With this work we demonstrate the promising potential of EMU to contribute to our understanding of the Universe.

Comments: 15 pages (29 with references and appendices), 6 figures and 10 tables


Abstract: 1810.06585
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Title: Probing the Jets of Blazars Using the Temporal Symmetry of Their Multi-Wavelength Outbursts

Abstract: We compare the rise and decay timescales of $\sim$200 long-term ($\sim$weeks-months) GeV and R-band outbursts and $\sim$25 short-term ($\sim$hr-day) GeV flares in a sample of 10 blazars using light curves from the Fermi-LAT and the Yale/SMARTS monitoring project. We find that most of the long-term outbursts are symmetric, indicating that the observed variability is dominated by the crossing timescale of a disturbance, e.g., a shock. A larger fraction of short-term flares are asymmetric with an approximately equal fraction of longer and shorter decay than rise timescale. We employ the MUlti-ZOne Radiation Feedback (MUZORF) model to interpret the above results. We find that the outbursts with slow rise times indicate a gradual acceleration of the particles to GeV energy. A change in the bulk Lorentz factor of the plasma or the width of the shocked region can lead to an increase of the cooling time causing a faster rise than decay time. Parameters such as the luminosity or the distance of the broad line region (BLR) affects the cooling time strongly if a single emission mechanism, e.g., external Compton scattering of BLR photons is considered but may not if other mechanisms, e.g., synchrotron self-compton and external Compton scattering of the torus photon are included. This work carries out a systematic study of the symmetry of flares, which can be used to estimate relevant geometric and physical parameters of blazar jets in the context of the MUZORF model.

Comments: 22 pages, 14 figures. Accepted for publication in MNRAS


Abstract: 1810.06483
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Title: Benchmarking Geant4 for Simulating Galactic Cosmic Ray Interactions Within Planetary Bodies

Abstract: Galactic cosmic rays undergo complex nuclear interactions with nuclei within planetary bodies that have little to no atmosphere. Radiation transport simulations are a key tool used in understanding the neutron and gamma-ray albedo coming from these interactions and tracing these signals back to geochemical composition of the target. We study the validity of the code Geant4 for simulating such interactions by comparing simulation results to data from the Apollo 17 Lunar Neutron Probe Experiment. Different assumptions regarding the physics are explored to demonstrate how these impact the Geant4 simulation results. In general, all of the Geant4 results over-predict the data, however, certain physics lists perform better than others. In addition, we show that results from the radiation transport code MCNP6 are similar to those obtained using Geant4.



Abstract: 1810.06403
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Title: Evidence for diffuse molecular gas and dust in the hearts of gamma-ray burst host galaxies

Abstract: Here we built up a sample of 22 GRBs at redshifts $z > 2$ observed with X-shooter to determine the abundances of hydrogen, metals, dust, and molecular species. This allows us to study the metallicity and dust depletion effects in the neutral ISM at high redshift and to answer the question whether (and why) there might be a lack of H$_2$ in GRB-DLAs. We fit absorption lines and measure the column densities of different metal species as well as atomic and molecular hydrogen. The derived relative abundances are used to fit dust depletion sequences and determine the dust-to-metals ratio and the host-galaxy intrinsic visual extinction. There is no lack of H$_2$-bearing GRB-DLAs. We detect absorption lines from H$_2$ in 6 out of 22 GRB afterglow spectra, with molecular fractions ranging between $f\simeq 5\cdot10^{-5}$ and $f\simeq 0.04$, and claim tentative detections in three other cases. The GRB-DLAs in the present sample have on average low metallicities ($\mathrm{[X/H]}\approx -1.3$), comparable to the rare population of QSO-ESDLAs (log N(HI) $> 21.5$). H$_2$-bearing GRB-DLAs are found to be associated with significant dust extinction, $A_V > 0.1$ mag, and have dust-to-metals ratios DTM$ > 0.4$. All of these systems exhibit column densities of log N(HI) $> 21.7$. The overall fraction of H$_2$ detections is $\ge 27$% (41% including tentative detections), which is three times larger than in the general population of QSO-DLAs. For $2<z<4$, and for log N(HI) $> 21.7$, the H$_2$ detection fraction is 60-80% in GRB-DLAs as well as in extremely strong QSO-DLAs. This is likely a consequence of the fact that both GRB- and QSO-DLAs with high N(HI) probe sight-lines with small impact parameters that indicate that the absorbing gas is associated with the inner regions of the absorbing galaxy, where the gas pressure is higher and the conversion of HI to H$_2$ takes place.

Comments: 45 pages, 39 figures


Abstract: 1810.06396
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Title: TeV-PeV Cosmic-Ray Anisotropy and Local Interstellar Turbulence

Abstract: We calculate the shape of the large-scale anisotropy of TeV-PeV cosmic-rays (CR) in different models of the interstellar turbulence. In general, the large-scale CR anisotropy (CRA) is not a dipole, and its shape can be used as a new probe of the turbulence. The 400 TeV and 2 PeV data sets of IceTop can be fitted with Goldreich-Sridhar turbulence and a broad resonance function, but other possibilities are not excluded. We then present our first numerical calculations of the CRA down to 3 TeV energies in 3D isotropic Kolmogorov turbulence. At these low energies, the large-scale CRA aligns well with the direction of local magnetic field lines around the observer. In this type of turbulence, the CR intensity is flat in a broad region perpendicular to field lines. Even though the CRA is quite gyrotropic, we show that the local configuration of the turbulence around the observer does result in the appearance of weak, "non-gyrotropic" small-scale anisotropies, which contain information on the local turbulence level.

Comments: 6 pages, 3 figures. Submitted to Journal of Physics: Conference Series. Talk presented at the 26th Extended European Cosmic Ray Symposium, Barnaul, July 2018


Abstract: 1810.06164
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Title: Cosmological Lorentzian Wormholes via Noether symmetry approach

Abstract: Noether symmetry has been invoked to explore the forms of a couple of coupling parameters and the potential appearing in a general scalar-tensor theory of gravity in the background of Robertson-Walker space-time. Exact solutions of Einstein's field equations in the familiar Brans-Dicke, Induced gravity and a General non-minimally coupled scalar-tensor theories of gravity have been found using the conserved current and the energy equation, after being expressed in a set of new variables. Noticeably, the form of the scale factors remains unaltered in all the three cases and represents cosmological Lorentzian wormholes, analogous to the Euclidean ones. While classical Euclidean wormholes requires an imaginary scalar field, the Lorentzian wormhole do not, and the solutions satisfy the weak energy condition.

Comments: 13 pages. arXiv admin note: text overlap with arXiv:1302.3748 by other authors


Abstract: 1810.05756
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Title: New constraints on sterile neutrino dark matter from the Galactic Center

Abstract: We calculate the most stringent constraints up to date on the parameter space for sterile neutrino warm dark matter models possessing a radiative decay channel into X-rays. These constraints arise from the X-ray flux observations from the Galactic center (central parsec), taken by the XMM and NuSTAR missions. We compare the results obtained from using different dark matter density profiles for the Milky Way, such as NFW, Burkert or Einasto, to that produced by the Ruffini-Arg\"uelles-Rueda (RAR) fermionic model, which has the distinct feature of depending on the particle mass. We show that due to the novel core-halo morphology present in the RAR profile, the allowed particle mass window is narrowed down to $m_s\sim 10-15$ keV, when analyzed within the $\nu$MSM sterile neutrino model. We further discuss on the possible effects in the sterile neutrino parameter-space bounds due to a self-interacting nature of the dark matter candidates.

Comments: 35 pages, 11 figures, 2 tables; prepared for sumbission to JCAP


Abstract: 1810.06445
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Title: Quintessential Starobinsky inflation and swampland criteria

Abstract: A simple model for the late-time cosmic acceleration problem is presented in the Starobinsky inflation with a negative bare cosmological constant as well as a non-minimal coupling to Higgs boson. After electroweak symmetry breaking, the Starobinsky inflaton is frozen until very recently becoming a thawing quintessence, and a comparable magnitude to the observed dark energy density can be achieved without fine-tuning. Our proposal essentially links the cosmological constant problem to the electroweak hierarchy problem, and it is also consistent with the recently proposed swampland criteria.

Comments: v1, 6 pages, two columns, two figures; v2, references added, minor improvement


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