arXiv subjects

T. Natusch

Publications and source records attributed to T. Natusch.

At least 19 recordsLinked to original sources

arXiv2022

Precision measurement of a brown dwarf mass in a binary system in the microlensing event OGLE-2019-BLG-0033/MOA-2019-BLG-035

Context. Brown dwarfs are poorly understood transition objects between stars and planets, with several competing mechanisms having been proposed for their formation. Mass measurements are generally difficult for isolated objects but also for brown dwarfs orbiting low-mass stars, which are often too faint for spectroscopic follow-up. Aims. Microlensing provides an alternative tool for the discovery and investigation of such faint systems. Here we present the analysis of the microlensing event OGLE-2019-BLG-0033/MOA-2019-BLG-035, which is due to a binary system composed of a brown dwarf orbiting a red dwarf. Methods. Thanks to extensive ground observations and the availability of space observations from Spitzer, it has been possible to obtain accurate estimates of all microlensing parameters, including parallax, source radius and orbital motion of the binary lens. Results. After accurate modeling, we find that the lens is composed of a red dwarf with mass $M_1 = 0.149 \pm 0.010M_\odot$ and a brown dwarf with mass $M_2 = 0.0463 \pm 0.0031M_\odot$, at a projected separation of $a_\perp = 0.585$ au. The system has a peculiar velocity that is typical of old metal-poor populations in the thick disk. Percent precision in the mass measurement of brown dwarfs has been achieved only in a few microlensing events up to now, but will likely become common with the Roman space telescope.

astro-ph.SR↗

arXiv2021

Single-lens mass measurement in the high-magnification microlensing event Gaia19bld located in the Galactic disc

We present the photometric analysis of Gaia19bld, a high-magnification ($A\approx60$) microlensing event located in the southern Galactic plane, which exhibited finite source and microlensing parallax effects. Due to a prompt detection by the Gaia satellite and the very high brightness of $I = 9.05~$mag at the peak, it was possible to collect a complete and unique set of multi-channel follow-up observations, which allowed us to determine all parameters vital for the characterisation of the lens and the source in the microlensing event. Gaia19bld was discovered by the Gaia satellite and was subsequently intensively followed up with a network of ground-based observatories and the Spitzer Space Telescope. We collected multiple high-resolution spectra with Very Large Telescope (VLT)/X-Shooter to characterise the source star. The event was also observed with VLT Interferometer (VLTI)/PIONIER during the peak. Here we focus on the photometric observations and model the light curve composed of data from Gaia, Spitzer, and multiple optical, ground-based observatories. We find the best-fitting solution with parallax and finite source effects. We derived the limit on the luminosity of the lens based on the blended light model and spectroscopic distance. We compute the mass of the lens to be $1.13 \pm 0.03~M_{\odot}$ and derive its distance to be $5.52^{+0.35}_{-0.64}~\mathrm{kpc}$. The lens is likely a main sequence star, however its true nature has yet to be verified by future high-resolution observations. Our results are consistent with interferometric measurements of the angular Einstein radius, emphasising that interferometry can be a new channel for determining the masses of objects that would otherwise remain undetectable, including stellar-mass black holes.

astro-ph.GA↗

arXiv2020

Gamma-ray emission in radio galaxies under the VLBI scope -- II. The relationship between gamma-ray emission and parsec-scale jets in radio galaxies

Following our study of the radio and high-energy properties of $γ$-ray-emitting radio galaxies, here we investigate the kinematic and spectral properties of the parsec-scale jets of radio galaxies that have not yet been detected by Fermi-LAT. We take advantage of the regular VLBI observations provided by the TANAMI monitoring program, and explore the kinematic properties of six $γ$-ray-faint radio galaxies. We include publicly available VLBI kinematics of $γ$-ray-quiet radio galaxies monitored by the MOJAVE program and perform a Fermi-LAT analysis, deriving upper limits. We combine these results with those from our previous paper to construct the largest sample of radio galaxies with combined VLBI and $γ$-ray measurements to date. We find superluminal motion up to $β_\mathrm{app}=3.6$ in the jet of PKS 2153$-$69. We find a clear trend of higher apparent speed as a function of distance from the jet core on scales of $\sim10^5\,R_s$, corresponding to the end of the collimation and acceleration zone in nearby radio galaxies. We find evidence of subluminal apparent motion in the jets of PKS 1258$-$321 and IC 4296, and no measurable motion for PKS 1549$-$79, PKS 1733$-$565 and PKS 2027$-$308. We compare the VLBI properties of $γ$-ray-detected and undetected radio galaxies, and find significantly different distributions of median core flux density, and, possibly, of median core brightness temperature. We find a significant correlation between median core flux density and $γ$-ray flux, but no correlation with typical Doppler boosting indicators such as median core brightness temperature and core dominance. Our study suggests that high-energy emission from radio galaxies is related to parsec-scale radio emission from the inner jet, but is not driven by Doppler boosting effects, in contrast to the situation in their blazar counterparts.

astro-ph.HE↗

arXiv2019

OGLE-2013-BLG-0911Lb: A Secondary on the Brown-Dwarf Planet Boundary around an M-dwarf

We present the analysis of the binary-lens microlensing event OGLE-2013-BLG-0911. The best-fit solutions indicate the binary mass ratio of q~0.03 which differs from that reported in Shvartzvald+2016. The event suffers from the well-known close/wide degeneracy, resulting in two groups of solutions for the projected separation normalized by the Einstein radius of s~0.15 or s~7. The finite source and the parallax observations allow us to measure the lens physical parameters. The lens system is an M-dwarf orbited by a massive Jupiter companion at very close (M_{host}=0.30^{+0.08}_{-0.06} M_{Sun}, M_{comp}=10.1^{+2.9}_{-2.2} M_{Jup}, a_{exp}=0.40^{+0.05}_{-0.04} au) or wide (M_{host}=0.28^{+0.10}_{-0.08} M_{Sun}, M_{comp}=9.9^{+3.8}_{-3.5}M_{Jup}, a_{exp}=18.0^{+3.2}_{-3.2} au) separation. Although the mass ratio is slightly above the planet-brown dwarf (BD) mass-ratio boundary of q=0.03 which is generally used, the median physical mass of the companion is slightly below the planet-BD mass boundary of 13M_{Jup}. It is likely that the formation mechanisms for BDs and planets are different and the objects near the boundaries could have been formed by either mechanism. It is important to probe the distribution of such companions with masses of ~13M_{Jup} in order to statistically constrain the formation theories for both BDs and massive planets. In particular, the microlensing method is able to probe the distribution around low-mass M-dwarfs and even BDs which is challenging for other exoplanet detection methods.

astro-ph.EP↗

arXiv2019

Spitzer + VLTI-GRAVITY Measure the Lens Mass of a Nearby Microlensing Event

We report the lens mass and distance measurements of the nearby microlensing event TCP J05074264+2447555. We measure the microlens parallax vector $π_{\rm E}$ using Spitzer and ground-based light curves with constraints on the direction of lens-source relative proper motion derived from Very Large Telescope Interferometer (VLTI) GRAVITY observations. Combining this $π_{\rm E}$ determination with the angular Einstein radius $θ_{\rm E}$ measured by VLTI GRAVITY observations, we find that the lens is a star with mass $M_{\rm L} = 0.495 \pm 0.063~M_{\odot}$ at a distance $D_{\rm L} = 429 \pm 21~{\rm pc}$. We find that the blended light basically all comes from the lens. The lens-source proper motion is $μ_{\rm rel,hel} = 26.55 \pm 0.36~{\rm mas\,yr^{-1}}$, so with currently available adaptive-optics (AO) instruments, the lens and source can be resolved in 2021. This is the first microlensing event whose lens mass is unambiguously measured by interferometry + satellite parallax observations, which opens a new window for mass measurements of isolated objects such as stellar-mass black holes.

astro-ph.IM↗

arXiv2019

Spitzer Microlensing Program as a Probe for Globular Cluster Planets. Analysis of OGLE-2015-BLG-0448

The microlensing event OGLE-2015-BLG-0448 was observed by Spitzer and lay within the tidal radius of the globular cluster NGC 6558. The event had moderate magnification and was intensively observed, hence it had the potential to probe the distribution of planets in globular clusters. We measure the proper motion of NGC 6558 ($μ_{\rm cl}$(N,E) = (+0.36+-0.10, +1.42+-0.10) mas/yr) as well as the source and show that the lens is not a cluster member. Even though this particular event does not probe the distribution of planets in globular clusters, other potential cluster lens events can be verified using our methodology. Additionally, we find that microlens parallax measured using OGLE photometry is consistent with the value found based on the light curve displacement between Earth and Spitzer.

astro-ph.SR↗

arXiv2019

Potential Kick Velocity distribution of black hole X-ray binaries and implications for natal kicks

We use Very Long Baseline Interferometry to measure the proper motions of three black hole X-ray binaries (BHXBs). Using these results together with data from the literature and Gaia-DR2 to collate the best available constraints on proper motion, parallax, distance and systemic radial velocity of 16 BHXBs, we determined their three dimensional Galactocentric orbits. We extended this analysis to estimate the probability distribution for the potential kick velocity (PKV) a BHXB system could have received on formation. Constraining the kicks imparted to BHXBs provides insight into the birth mechanism of black holes (BHs). Kicks also have a significant effect on BH-BH merger rates, merger sites, and binary evolution, and can be responsible for spin-orbit misalignment in BH binary systems. $75\%$ of our systems have potential kicks $>70\,\rm{km~s^{-1}}$. This suggests that strong kicks and hence spin-orbit misalignment might be common among BHXBs, in agreement with the observed quasi-periodic X-ray variability in their power density spectra. We used a Bayesian hierarchical methodology to analyse the PKV distribution of the BHXB population, and suggest that a unimodal Gaussian model with a mean of $107\pm16\,\rm{km~s^{-1}}$ is a statistically favourable fit. Such relatively high PKVs would also reduce the number of BHs likely to be retained in globular clusters. We found no significant correlation between the BH mass and PKV, suggesting a lack of correlation between BH mass and the BH birth mechanism. Our Python code allows the estimation of the PKV for any system with sufficient observational constraints.

astro-ph.HE↗

arXiv2019

Gamma-ray emission in radio galaxies under the VLBI scope -- I. Parsec-scale kinematics and high-energy properties of $γ$-ray detected TANAMI radio galaxies

In the framework of the TANAMI multi-wavelength and VLBI monitoring, we study the evolution of the parsec-scale radio emission in radio galaxies in the southern hemisphere and their relationship to the $γ$-ray properties. In this first paper, we focus on Fermi-LAT-detected sources. We perform a kinematic analysis for five $γ$-ray detected radio galaxies using multi-epoch 8.4 GHz VLBI images, deriving limits on intrinsic jet parameters. We analyzed Fermi-LAT data in order to study possible connections between the $γ$-ray properties and the pc-scale jets of Fermi-LAT-detected radio galaxies, both in terms of variability and average properties. We discuss the individual source results and draw preliminary conclusions on sample properties including published VLBI results from the MOJAVE survey, with a total of fifteen sources. We find that the first $γ$-ray detection of Pictor A might be associated with the passage of a new VLBI component through the radio core. For the peculiar AGN PKS 0521-36, we detect subluminal parsec-scale jet motions, and we confirm the presence of fast $γ$-ray variability in the source down to timescales of 6 hours. We robustly confirm the presence of significant superluminal motion, up to $β_{app}\sim$3, in the jet of the TeV radio galaxy PKS 0625-35. Finally, we place a lower limit on the age of the Compact Symmetric Object (CSO) PKS 1718-649. We draw some preliminary conclusions on the relationship between pc-scale jets and $γ$-ray emission in radio galaxies. We find that the VLBI core flux density correlates with the $γ$-ray flux, as seen in blazars. On the other hand, the $γ$-ray luminosity does not show any dependence on the core brightness temperature and core dominance, two indicators of Doppler boosting, suggesting that $γ$-ray emission in radio galaxies is not driven by orientation-dependent effects.

astro-ph.HE↗

arXiv2018

First Resolution of Microlensed Images

We employ VLTI GRAVITY to resolve, for the first time, the two images generated by a gravitational microlens. The measurements of the image separation θ_{-,+}=3.78 +/- 0.05 mas, and hence the Einstein radius θ_E =1.87 +/- 0.03 mas, are precise. This demonstrates the robustness of the method, provided that the source is bright enough for GRAVITY (K <~ 10.5) and the image separation is of order or larger than the fringe spacing. When θ_E is combined with a measurement of the "microlens parallax" π_E, the two will together yield the lens mass and lens-source relative parallax and proper motion. Because the source parallax and proper motion are well measured by Gaia, this means that the lens characteristics will be fully determined, whether or not it proves to be luminous. This method can be a powerful probe of dark, isolated objects, which are otherwise quite difficult to identify, much less characterize. Our measurement contradicts Einstein's (1936) prediction that "the luminous circle [i.e., microlensed image] cannot be distinguished" from a star.

astro-ph.SR↗

arXiv2018

OGLE-2016-BLG-1045: A Test of Cheap Space-Based Microlens Parallaxes

Microlensing is a powerful and unique technique to probe isolated objects in the Galaxy. To study the characteristics of these interesting objects based on the microlensing method, measurement of the microlens parallax is required to determine the properties of the lens. Of the various methods to measure microlens parallax, the most robust way is to make simultaneous ground- and space-based observations, i.e., by measuring the space-based microlens parallax. However, space-based campaigns usually require "expensive" resources. Gould & Yee (2012) proposed an idea called the "cheap space-based microlens parallax" that can measure the lens-parallax using only $2$ or $3$ space-based observations of high-magnification events. This cost-effective observation strategy to measure microlens parallaxes could be used by space-borne telescopes to build a complete sample for studying isolated objects. This would enable a direct measurement of the mass function including both extremely low-mass objects and high-mass stellar remnants. However, to adopt this idea requires a test to check how it would work in actual situations. Thus, we present the first practical test of the idea using the high-magnification microlensing event OGLE-2016-BLG-1045, for which a subset of Spitzer observations fortuitously duplicate the prescription of Gould & Yee (2012). From the test, we confirm that the measurement of the lens-parallax adopting this idea has sufficient accuracy to determine the physical properties of the isolated lens.

astro-ph.SR↗

arXiv2017

TANAMI: Tracking Active Galactic Nuclei with Austral Milliarcsecond Interferometry - II. Additional Sources

TANAMI is a multiwavelength program monitoring active galactic nuclei (AGN) south of -30deg declination including high-resolution Very Long Baseline Interferometry (VLBI) imaging, radio, optical/UV, X-ray and gamma-ray studies. We have previously published first-epoch 8.4GHz VLBI images of the parsec-scale structure of the initial sample. In this paper, we present images of 39 additional sources. The full sample comprises most of the radio- and gamma-ray brightest AGN in the southern quarter of the sky, overlapping with the region from which high-energy (>100TeV) neutrino events have been found. We characterize the parsec-scale radio properties of the jets and compare with the quasi-simultaneous Fermi/LAT gamma-ray data. Furthermore, we study the jet properties of sources which are in positional coincidence with high-energy neutrino events as compared to the full sample. We test the positional agreement of high-energy neutrino events with various AGN samples. Our observations yield the first images of many jets below -30deg declination at milliarcsecond resolution. We find that gamma-ray loud TANAMI sources tend to be more compact on parsec-scales and have higher core brightness temperatures than gamma-ray faint jets, indicating higher Doppler factors. No significant structural difference is found between sources in positional coincidence with high-energy neutrino events and other TANAMI jets. The 22 gamma-ray brightest AGN in the TANAMI sky show only a weak positional agreement with high-energy neutrinos demonstrating that the >100TeV IceCube signal is not simply dominated by a small number of the $γ$-ray brightest blazars. Instead, a larger number of sources have to contribute to the signal with each individual source having only a small Poisson probability for producing an event in multi-year integrations of current neutrino detectors.

astro-ph.HE↗

arXiv2016

OGLE-2012-BLG-0563Lb: a Saturn-mass Planet around an M Dwarf with the Mass Constrained by Subaru AO imaging

We report the discovery of a microlensing exoplanet OGLE-2012-BLG-0563Lb with the planet-star mass ratio ~1 x 10^{-3}. Intensive photometric observations of a high-magnification microlensing event allow us to detect a clear signal of the planet. Although no parallax signal is detected in the light curve, we instead succeed at detecting the flux from the host star in high-resolution JHK'-band images obtained by the Subaru/AO188 and IRCS instruments, allowing us to constrain the absolute physical parameters of the planetary system. With the help of a spectroscopic information about the source star obtained during the high-magnification state by Bensby et al., we find that the lens system is located at 1.3^{+0.6}_{-0.8} kpc from us, and consists of an M dwarf (0.34^{+0.12}_{-0.20} M_sun) orbited by a Saturn-mass planet (0.39^{+0.14}_{-0.23} M_Jup) at the projected separation of 0.74^{+0.26}_{-0.42} AU (close model) or 4.3^{+1.5}_{-2.5} AU (wide model). The probability of contamination in the host star's flux, which would reduce the masses by a factor of up to three, is estimated to be 17%. This possibility can be tested by future high-resolution imaging. We also estimate the (J-Ks) and (H-Ks) colors of the host star, which are marginally consistent with a low metallicity mid-to-early M dwarf, although further observations are required for the metallicity to be conclusive. This is the fifth sub-Jupiter-mass (0.2<m_p/M_Jup<1) microlensing planet around an M dwarf with the mass well constrained. The relatively rich harvest of sub-Jupiters around M dwarfs is contrasted with a possible paucity of ~1--2 Jupiter-mass planets around the same type of star, which can be explained by the planetary formation process in the core-accretion scheme.

astro-ph.EP↗

arXiv2015

Reanalyses of Anomalous Gravitational Microlensing Events in the OGLE-III Early Warning System Database with Combined Data

We reanalyze microlensing events in the published list of anomalous events that were observed from the OGLE lensing survey conducted during 2004-2008 period. In order to check the existence of possible degenerate solutions and extract extra information, we conduct analyses based on combined data from other survey and follow-up observation and consider higher-order effects. Among the analyzed events, we present analyses of 8 events for which either new solutions are identified or additional information is obtained. We find that the previous binary-source interpretations of 5 events are better interpreted by binary-lens models. These events include OGLE-2006-BLG-238, OGLE-2007-BLG-159, OGLE-2007-BLG-491, OGLE-2008-BLG-143, and OGLE-2008-BLG-210. With additional data covering caustic crossings, we detect finite-source effects for 6 events including OGLE-2006-BLG-215, OGLE-2006-BLG-238, OGLE-2006-BLG-450, OGLE-2008-BLG-143, OGLE-2008-BLG-210, and OGLE-2008-BLG-513. Among them, we are able to measure the Einstein radii of 3 events for which multi-band data are available. These events are OGLE-2006-BLG-238, OGLE-2008-BLG-210, and OGLE-2008-BLG-513. For OGLE-2008-BLG-143, we detect higher-order effect induced by the changes of the observer's position caused by the orbital motion of the Earth around the Sun. In addition, we present degenerate solutions resulting from the known close/wide or ecliptic degeneracy. Finally, we note that the masses of the binary companions of the lenses of OGLE-2006-BLG-450 and OGLE-2008-BLG-210 are in the brown-dwarf regime.

astro-ph.EP↗

arXiv2015

OGLE-2011-BLG-0265Lb: a Jovian Microlensing Planet Orbiting an M Dwarf

We report the discovery of a Jupiter-mass planet orbiting an M-dwarf star that gave rise to the microlensing event OGLE-2011-BLG-0265. Such a system is very rare among known planetary systems and thus the discovery is important for theoretical studies of planetary formation and evolution. High-cadence temporal coverage of the planetary signal combined with extended observations throughout the event allows us to accurately model the observed light curve. The final microlensing solution remains, however, degenerate yielding two possible configurations of the planet and the host star. In the case of the preferred solution, the mass of the planet is $M_{\rm p} = 0.9\pm 0.3\ M_{\rm J}$, and the planet is orbiting a star with a mass $M = 0.22\pm 0.06\ M_\odot$. The second possible configuration (2$σ$ away) consists of a planet with $M_{\rm p}=0.6\pm 0.3\ M_{\rm J}$ and host star with $M=0.14\pm 0.06\ M_\odot$. The system is located in the Galactic disk 3 -- 4 kpc towards the Galactic bulge. In both cases, with an orbit size of 1.5 -- 2.0 AU, the planet is a "cold Jupiter" -- located well beyond the "snow line" of the host star. Currently available data make the secure selection of the correct solution difficult, but there are prospects for lifting the degeneracy with additional follow-up observations in the future, when the lens and source star separate.

astro-ph.EP↗

arXiv2014

Can the masses of isolated planetary-mass gravitational lenses be measured by terrestrial parallax?

Recently Sumi et al. (2011) reported evidence for a large population of planetary-mass objects (PMOs) that are either unbound or orbit host stars in orbits > 10 AU. Their result was deduced from the statistical distribution of durations of gravitational microlensing events observed by the MOA collaboration during 2006 and 2007. Here we study the feasibility of measuring the mass of an individual PMO through microlensing by examining a particular event, MOA-2011-BLG-274. This event was unusual as the duration was short, the magnification high, the source-size effect large and the angular Einstein radius small. Also, it was intensively monitored from widely separated locations under clear skies at low air masses. Choi et al. (2012) concluded that the lens of the event may have been a PMO but they did not attempt a measurement of its mass. We report here a re-analysis of the event using re-reduced data. We confirm the results of Choi et al. and attempt a measurement of the mass and distance of the lens using the terrestrial parallax effect. Evidence for terrestrial parallax is found at a 3 sigma level of confidence. The best fit to the data yields the mass and distance of the lens as 0.80 +/- 0.30 M_J and 0.80 +/- 0.25 kpc respectively. We exclude a host star to the lens out to a separation ~ 40 AU. Drawing on our analysis of MOA-2011-BLG-274 we propose observational strategies for future microlensing surveys to yield sharper results on PMOs including those down to super-Earth mass.

astro-ph.EP↗

arXiv2014

A Terrestrial Planet in a ~1 AU Orbit Around One Member of a ~15 AU Binary

We detect a cold, terrestrial planet in a binary-star system using gravitational microlensing. The planet has low mass (2 Earth masses) and lies projected at $a_{\perp,ph}$ ~ 0.8 astronomical units (AU) from its host star, similar to the Earth-Sun distance. However, the planet temperature is much lower, T<60 Kelvin, because the host star is only 0.10--0.15 solar masses and therefore more than 400 times less luminous than the Sun. The host is itself orbiting a slightly more massive companion with projected separation $a_{\perp,ch}=$10--15 AU. Straightforward modification of current microlensing search strategies could increase their sensitivity to planets in binary systems. With more detections, such binary-star/planetary systems could place constraints on models of planet formation and evolution. This detection is consistent with such systems being very common.

astro-ph.EP↗

arXiv2014

MOA-2013-BLG-220Lb: Massive Planetary Companion to Galactic-Disk Host

We report the discovery of MOA-2013-BLG-220Lb, which has a super-Jupiter mass ratio $q=3.01\pm 0.02\times 10^{-3}$ relative to its host. The proper motion, $μ=12.5\pm 1\, {\rm mas}\,{\rm yr}^{-1}$, is one of the highest for microlensing planets yet discovered, implying that it will be possible to separately resolve the host within $\sim 7$ years. Two separate lines of evidence imply that the planet and host are in the Galactic disk. The planet could have been detected and characterized purely with follow-up data, which has important implications for microlensing surveys, both current and into the LSST era.

astro-ph.EP↗

arXiv2014

OGLE-2012-BLG-0455/MOA-2012-BLG-206: Microlensing event with ambiguity in planetary interpretations caused by incomplete coverage of planetary signal

Characterizing a microlensing planet is done from modeling an observed lensing light curve. In this process, it is often confronted that solutions of different lensing parameters result in similar light curves, causing difficulties in uniquely interpreting the lens system, and thus understanding the causes of different types of degeneracy is important. In this work, we show that incomplete coverage of a planetary perturbation can result in degenerate solutions even for events where the planetary signal is detected with a high level of statistical significance. We demonstrate the degeneracy for an actually observed event OGLE-2012-BLG-0455/MOA-2012-BLG-206. The peak of this high-magnification event $(A_{\rm max}\sim400)$ exhibits very strong deviation from a point-lens model with $Δχ^{2}\gtrsim4000$ for data sets with a total number of measurement 6963. From detailed modeling of the light curve, we find that the deviation can be explained by four distinct solutions, i.e., two very different sets of solutions, each with a two-fold degeneracy. While the two-fold (so-called "close/wide") degeneracy is well-understood, the degeneracy between the radically different solutions is not previously known. The model light curves of this degeneracy differ substantially in the parts that were not covered by observation, indicating that the degeneracy is caused by the incomplete coverage of the perturbation. It is expected that the frequency of the degeneracy introduced in this work will be greatly reduced with the improvement of the current lensing survey and follow-up experiments and the advent of new surveys.

astro-ph.EP↗