The Planet Nine hypothesis encompasses a body of about 5-8 Earth's masses whose orbital plane would be inclined to the ecliptic by one or two tens of degrees and whose perihelion distance would be as large as about 240-385 astronomical units. Recently, a couple of his epigones have appeared: Planet X and Planet Y. The former is a sort of minor version of Planet Nine in that all its physical and orbital parameters would be smaller. Instead, the latter would have a mass ranging from that of Mercury to the Earth's one and semimajor axis within 100-200 astronomical units. By using realistic upper bounds for the orbital precessions of Saturn, one can get insights on their position which, for Planet Nine, appears approximately confined around its aphelion. Planet Y can be just a Mercury-sized object at no less than about 125 astronomical units, while Planet X appears to be ruled out. Dedicated data reductions by modeling such perturber(s) are required to check the present conclusions, to be intended as hints of what might be detectable should planetary ephemerides include them. A probe on the same route of Voyager 1 would be perturbed by Planet Nine by about 20-40 km after some decades.
The hypothesized Planet Nine is thought to reside in the distant outer solar system, potentially explaining various anomalies in the orbits of extreme trans-Neptunian objects (ETNOs). In this work, we present a targeted observational search for Planet Nine in a field of approximately 98 square-degrees. This field is close to the highest probability region of finding Planet Nine, according to simulations, but poorly constrained by previous searches. Our observations and search methodology, based on the detection of parallax position shifts between consecutive nights, work well in these conditions. We provide 85% confidence exclusion limits for objects with Sloan r-band magnitudes brighter than between 21.0 and 21.4, with an average sensitivity limit of 21.3. No credible Planet Nine candidates were identified within this field and magnitude limits. A caveat to our approach is that it would miss a candidate if its position were affected by scattered light from bright stars in at least one of the nights. However, we estimate that the probability for this is very low, around 0.4%. We discuss several possible reasons for our Planet Nine non-detection. Our study complements prior searches
Evidence suggests the existence of a large planet in the outer Solar System, Planet Nine, with a predicted mass of 6.6 +2.6 / -1.7 Earth masses (Brown et al., 2024). Based on mass radius composition models, planet formation theory, and confirmed exoplanets with low mass and radius uncertainty and equilibrium temperature less than 600 K, we determine the most likely composition for Planet Nine is a mini-Neptune with a radius in the range 2.0 to 2.6 Earth radii and a H-He envelope fraction in the range of 0.6 percent to 3.5 percent by mass. Using albedo estimates for a mini-Neptune extrapolated from V-band data for the Solar Systems giant planets gives albedo values for Planet Nine in the range of 0.47 to 0.33. Using the most likely orbit and aphelion estimates from the Planet Nine Reference Population 3.0, we estimate Planet Nines absolute magnitude in the range of -6.1 to -5.2 and apparent magnitude in the range of +21.9 to +22.7. Finally, we estimate that, if the hypothetical Planet Nine exists and is detected by upcoming surveys, it will have a resolvable disk using some higher resolution world class telescopes.
The Ultra-Violet Imaging Telescope (UVIT) is one of the five payloads onboard the first Indian multiwavelength astronomical observatory, AstroSat, launched by the Indian Space Research Organisation on 28 September 2015. UVIT, designed for simultaneous imaging in the far-ultraviolet (FUV; 1300-1800 Å) and near-ultraviolet (NUV; 2000-3000 Å) channels, has completed nine years in orbit in 2024 despite the failure of the NUV channel in 2018. As the FUV optics is subject to possible reduction in sensitivity due to microscopic amounts of contaminants, we used the FUV data acquired by UVIT over the past nine years on the open cluster NGC 188 and the white dwarf HZ 4 to study sensitivity variations in the UVIT FUV channel. Our findings indicate no significant reduction in the sensitivity of the FUV channel over the last nine years, with no significant episodic variations due to unknown causes.
We prove a nine-distance theorem for Kronecker sequences on flat three-tori. That is, we show that among the first $N$ orbit points, at most nine distinct positive nearest-neighbour distances occur. This proves the conjecture of Haynes and Marklof. An example of Dettmann shows that nine is optimal. More generally, we prove that on a flat $d$-dimensional torus the number of such distances is at most $2^d+1$. The main tool is a new growth theorem for the denominators $q_1<q_2<\cdots$ of best simultaneous approximations in a $d$-dimensional inner-product space, which is of independent interest. We prove that, whenever $q_{n+2^d}$ is defined, either $q_{n+2^d}\ge2q_{n+1}$, or the indices $1,\ldots,2^d$ can be partitioned into disjoint pairs $\{j,k\}$, $j<k$, such that $q_{n+k}=q_n+q_{n+j}$. In particular, $$ q_{n+2^d}\ge \min\{2q_{n+1},q_n+q_{n+2^{d-1}}\}\ge q_n+q_{n+1}. $$
We prove that the lonely runner conjecture holds for nine runners. Our proof is based on a couple of improvements of the method we used to prove the conjecture for eight runners.
Hot Jupiters were many of the first exoplanets discovered in the 1990s, but in the decades since their discovery, the mysteries surrounding their origins remain. Here, we present nine new hot Jupiters (TOI-1855 b, TOI-2107 b, TOI-2368 b, TOI-3321 b, TOI-3894 b, TOI-3919 b, TOI-4153 b, TOI-5232 b, and TOI-5301 b) discovered by NASA's TESS mission and confirmed using ground-based imaging and spectroscopy. These discoveries are the first in a series of papers named the Migration and Evolution of giant ExoPlanets (MEEP) survey and are part of an ongoing effort to build a complete sample of hot Jupiters orbiting FGK stars, with a limiting Gaia $G$-band magnitude of 12.5. This effort aims to use homogeneous detection and analysis techniques to generate a set of precisely measured stellar and planetary properties that is ripe for statistical analysis. The nine planets presented in this work occupy a range of masses (0.55 Jupiter masses (M$_{\rm{J}}$) $<$ M$_{\rm{P}}$ $<$ 3.88 M$_{\rm{J}}$) and sizes (0.967 Jupiter radii (R$_{\rm{J}}$) $<$ R$_{\rm{P}}$ $<$ 1.438 R$_{\rm{J}}$) and orbit stars that range in temperature from 5360 K $<$ Teff $<$ 6860 K with Gaia $G$-band magn
Recent estimates of the characteristics of Planet Nine have suggested that it could be closer than originally assumed. Such a Planet Nine would also be brighter than originally assumed, suggesting the possibility that it has already been observed in wide-field moderate-depth surveys. We search for Planet Nine in the Zwicky Transient Facility public archive and find no candidates. Using known asteroids to calculate the magnitude limit of the survey, we find that we should have detected Planet Nine throughout most of the northern portion of its predicted orbit -- including within the galactic plane -- to a 95% detection efficiency of approximately $V=20.5$. To aid in understanding detection limits for this and future analyses, we present a full-sky synthetic Planet Nine population drawn from a statistical sampling of predicted Planet Nine orbits. We use this reference population to estimate that this survey rules out 56% of predicted Planet Nine phase space, and we demonstrate how future analyses can use the same synthetic population to continue to constrain the amount of parameter space effectively searched for Planet Nine.
We present a search for Planet Nine using the second data release of the Pan-STARRS1survey. We rule out the existence of a Planet Nine with the characteristics of that predicted in Brown & Batygin (2021) to a 50% completion depth of $V=21.5$. This survey, along with previous analyses of the Zwicky Transient Facility (ZTF) and Dark EnergySurvey (DES) data, rules out 78% of the Brown \& Batygin parameter space. Much of the remaining parameter space is at $V>21$ in regions near and in the area where the northern galactic plane crosses the ecliptic.
In this work we report the independent discovery and analysis of nine new compact triply eclipsing triple star systems found with the TESS mission: TICs 47151245, 81525800, 99013269, 229785001, 276162169, 280883908, 294803663, 332521671, and 356324779. Each of these nine systems exhibits distinct third-body eclipses where the third (`tertiary') star occults the inner eclipsing binary (EB), or vice versa. We utilize a photodynamical analysis of the TESS photometry, archival photometric data, TESS eclipse timing variations of the EBs, available archival spectral energy distribution curves (SED), and, in some cases, newly acquired radial velocity observations, to solve for the parameters of all three stars, as well as most of the orbital elements. From these analyses we find that the outer orbits of all nine systems are viewed nearly edge on (i.e., within $\lesssim 4^\circ$), and 6 of the systems are coplanar to within $5^\circ$; the others have mutual inclination angles of $20^\circ$, $41^\circ$, and possibly $179^\circ$ (i.e., a retrograde outer orbit). The outer orbital periods range from 47.8 days to 604 days, with eccentricities spanning 0.004 to 0.61. The masses of all 18 EB sta
Automated web accessibility testing tools have been found complementary. The implication: To catch as many issues as possible, use multiple tools. Doing this efficiently entails integration costs. Is there a small set of tools that, together, make additional tools redundant? I approach this problem by comparing nine comprehensive accessibility testing tools that are amenable to integration: alfa, axe-core, Continuum, Equal Access, HTML CodeSniffer, Nu Html Checker, QualWeb, Tenon, and WAVE. I tested 121 web pages of interest to CVS Health with these tools. Each tool only fractionally duplicated any other tool. Each discovered numerous issue instances missed by all the others. Thus, testing with all nine tools was substantially more informative than testing with any subset.
Thanks to the recent advances in metamaterials, reconfigurable intelligent surface (RIS) has emerged as a promising technology for future 6G wireless communications. Benefiting from its high array gain, low cost, and low power consumption, RISs are expected to greatly enlarge signal coverage, improve system capacity, and increase energy efficiency. In this article, we systematically overview the emerging RIS technology with the focus on its key basics, nine fundamental issues, and one critical problem. Specifically, we first explain the RIS basics, including its working principles, hardware structures, and potential benefits for communications. Based on these basics, nine fundamental issues of RISs, such as ``What's the differences between RISs and massive MIMO?'' and ``Is RIS really intelligent?'', are explicitly addressed to elaborate its technical features, distinguish it from existing technologies, and clarify some misunderstandings in the literature. Then, one critical problem of RISs is revealed that, due to the ``multiplicative fading'' effect, existing passive RISs can hardly achieve visible performance gains in many communication scenarios with strong direct links. To addr
A distant, as yet unseen ninth planet has been invoked to explain various observations of the outer solar system. While such a 'Planet Nine', if it exists, is most likely to be discovered via reflected light in the optical, it may emit much more strongly at 3$-$5$μ$m than simple blackbody predictions would suggest, depending on its atmospheric properties (Fortney et al. 2016). As a result, Planet Nine may be detectable at 3.4$μ$m with WISE, but single exposures are too shallow except at relatively small distances ($d_9 \lesssim 430$ AU). We develop a method to search for Planet Nine far beyond the W1 single-exposure sensitivity, to distances as large as 800 AU, using inertial coadds of W1 exposures binned into $\sim$1 day intervals. We apply our methodology to $\sim$2000 square degrees of sky identified by Holman & Payne (2016) as a potentially likely Planet Nine location, based on the Fienga et al. (2016) Cassini ranging analysis. We do not detect a plausible Planet Nine candidate, but are able to derive a detailed completeness curve, ruling out its presence within the parameter space searched at $W1 < 16.66$ (90% completeness). Our method uses all publicly available W1 ima
It has been proposed that mean motion resonances (MMRs) between Planet Nine and distant objects of the scattered disk might inform the semimajor axis and instantaneous position of Planet Nine. Within the context of this hypothesis, the specific distribution of occupied MMRs largely determines the available constraints. Here we characterize the behavior of scattered Kuiper Belt objects arising in the presence of an eccentric Planet Nine ($e_9 \in 0.1$, $0.7$), focusing on relative sizes of populations occupying particular commensurabilities. Highlighting the challenge of predicting the exact MMR of a given object, we find that the majority of resonant test particles have period ratios with Planet Nine other than those of the form $P_9/P=N/1$, $N/2$ $(N \in \mathbb{Z}^+)$. Taking into account the updated prior distribution of MMRs outlined in this work, we find that the close spacing of high-order resonances, as well as chaotic transport, preclude resonance-based Planet Nine constraints from current observational data.
Studies of the clustering of the most distant Kuiper belt objects in the outer solar system have hinted at the possible existence of a planet beyond Neptune referred to as Planet Nine (P9). Recent efforts have constrained the parameter space of the orbital elements of P9, allowing for the creation of a synthetic catalog of hypothetical P9s. By examining the potential recovery of such a catalog within numerous sky surveys, it is possible to further constrain the parameter space for P9, providing direction for a more targeted search. We examine the ability of the full six years of the Dark Energy Survey (DES) to recover a synthetic Planet Nine population presented in Brown and Batygin (2021a) [arXiv:2108.09868]. We find that out of 100,000 simulated objects, 11,709 cross the wide DES survey footprint of which 10,187 (87.0%) are recovered. This rules out an additional 5% of the parameter space after accounting for Planets Nine that would have been detected by both the Zwicky Transient Facility and DES.
Explicit formulae are given for the nine possible induced matrix norms corresponding to the 1-, 2-, and $\infty$-norms for Euclidean space. The complexity of computing these norms is investigated.
We evaluate the dynamical stability of a selection of outer solar system objects in the presence of the proposed new Solar System member Planet Nine. We use a Monte Carlo suite of numerical N-body integrations to construct a variety of orbital elements of the new planet and evaluate the dynamical stability of eight Trans-Neptunian objects (TNOs) in the presence of Planet Nine. These simulations show that some combinations of orbital elements ($a,e$) result in Planet Nine acting as a stabilizing influence on the TNOs, which can otherwise be destabilized by interactions with Neptune. These simulations also suggest that some TNOs transition between several different mean-motion resonances during their lifetimes while still retaining approximate apsidal anti-alignment with Planet Nine. This behavior suggests that remaining in one particular orbit is not a requirement for orbital stability. As one product of our simulations, we present an {\it a posteriori} probability distribution for the semi-major axis and eccentricity of the proposed Planet Nine based on TNO stability. This result thus provides additional evidence that supports the existence of this proposed planet. We also predict
The recent 'Planet Nine' hypothesis has led to many observational and archival searches for this giant planet proposed to orbit the Sun at hundreds of astronomical units. While trans-Neptunian object searches are typically conducted in the optical, models suggest Planet Nine could be self-luminous and potentially bright enough at ~3-5 microns to be detected by the Wide-field Infrared Survey Explorer (WISE). We have previously demonstrated a Planet Nine search methodology based on time-resolved WISE coadds, allowing us to detect moving objects much fainter than would be possible using single-frame extractions. In the present work, we extend our 3.4 micron (W1) search to cover more than three quarters of the sky and incorporate four years of WISE observations spanning a seven year time period. This represents the deepest and widest-area WISE search for Planet Nine to date. We characterize the spatial variation of our survey's sensitivity and rule out the presence of Planet Nine in the parameter space searched at W1 < 16.7 in high Galactic latitude regions (90% completeness).
Unexpected clustering in the orbital elements of minor bodies beyond the Kuiper belt has led to speculations that our solar system actually hosts nine planets, the eight established plus a hypothetical "Planet Nine". Several recent studies have shown that a planet with a mass of about 10 Earth masses on a distant eccentric orbit with perihelion far beyond the Kuiper belt could create and maintain this clustering. The evolutionary path resulting in an orbit such as the one suggested for Planet Nine is nevertheless not easily explained. Here we investigate whether a planet scattered away from the giant-planet region could be lifted to an orbit similar to the one suggested for Planet Nine through dynamical friction with a cold, distant planetesimal belt. Recent simulations of planetesimal formation via the streaming instability suggest that planetesimals can readily form beyond 100au. We explore this circularisation by dynamical friction with a set of numerical simulations. We find that a planet that is scattered from the region close to Neptune onto an eccentric orbit has a 20-30% chance of obtaining an orbit similar to that of Planet Nine after 4.6Gyr. Our simulations also result in
Cosmology experiments at mm-wavelengths can detect Planet Nine if it is the size of Neptune, has an effective temperature of 40 K, and is 700 AU from the Sun. It would appear as a ~30 mJy source at 1 mm with an annual parallax of ~5 arcmin. The challenge is to distinguish it from the approximately 4000 foreground asteroids brighter than 30 mJy. Fortunately, these asteroids are known to the Minor Planet Center and can be identified because they move across a resolution element in a matter of hours, orders of magnitude faster than Planet Nine. If Planet Nine is smaller, colder, and/or more distant than expected, then it could be as faint as 1 mJy at 1 mm. There are roughly $10^6$ asteroids this bright and many are unknown, making current cosmology experiments confusion limited for moving sources. Nonetheless, it may still be possible to find the proverbial needle in the haystack using a matched filter. This would require mm telescopes with high angular resolution and high sensitivity in order to alleviate confusion and to enable the identification of moving sources with relatively short time baselines. Regardless of its mm flux density, searching for Planet Nine would require frequen