arXiv subjects

Sarah E. Anderson

Publications and source records attributed to Sarah E. Anderson.

At least 19 recordsLinked to original sources

arXiv2026

Early Exploration of the Scientific Discovery Space for the Habitable Worlds Observatory

The Habitable Worlds Observatory (HWO) is a future NASA flagship mission concept identified by the Astro2020 Decadal Survey as the highest priority for large space missions. HWO should conduct "transformative astrophysics" and search for biosignatures in the atmospheres of approximately 25 potentially Earth-like planets. To further the early-stage development of HWO, NASA formed the Science, Technology, Architecture Review Team (START). In turn, START invited the scientific community to join working groups to explore the potential discovery space. In this paper, we present 70 science cases that resulted from this process. The cases address four scientific pillars: growth of galaxies (15 cases), evolution of the elements (13 cases), solar systems in context (32 cases), and living worlds (10 cases). Combined, they would address 27 of the 30 science questions and discovery areas identified by Astro2020. The 140 observing programs needed for the 70 investigations encompass a rich variety of spectroscopic (for 87% of science cases) and photometric (for 30%) observations extending from the UV to the NIR. Additionally, high-contrast and polarimetric capabilities would be needed for 34% and 27% of science cases, respectively. Access to UV wavelengths is critical: 83% of science cases need data at wavelengths <400 nm, and 26% extend to <100 nm. In the NIR, 26% of science cases need observations at wavelengths >=2000 nm. Pursuing the full portfolio of science would also necessitate precise astrometry for planet mass measurement, rapid response capabilities, a large instantaneous field of regard, non-sidereal tracking, saturation mitigation strategies, and high dynamic range.

astro-ph.IM↗

arXiv2026

Diamond-free, claw-free cubic graphs are (1, 1, 2, 3)-packing colorable

A $(1, 1, 2, k)$-packing coloring of a graph $G$ is a partition of $V(G)$ into two independent sets, a 2-packing, and a $k$-packing. Recently, the question was posed in [A short proof that every claw-free cubic graph is (1, 1, 2, 2)-packing colorable, arXiv:2512.24001v1] as to whether every claw-free cubic graph is $(1, 1, 2, 3)$-packing colorable. We provide an answer in the affirmative in the case that $G$ is a diamond-free, claw-free cubic graph.

math.CO↗

arXiv2026

Characterizing all nonbipartite well-edge-dominated graphs

Given a graph $G$, a set $F$ of edges is an edge dominating set of $G$ if every edge in $G$ is either in $F$ or adjacent to an edge in $F$. A graph $G$ is said to be well-edge-dominated if every minimal edge dominating set has the same cardinality. This definition is the edge version of domination in that a set $D\subseteq V(G)$ is a dominating set if every vertex in $G$ is in $D$ or adjacent to a vertex in $D$ and the domination number $γ(G)$ is the minimum cardinality among all dominating sets. In this paper, we complete the characterization of all nonbipartite, well-edge-dominated graphs. In addition, we produce an infinite class of graphs that satisfy the well-known Vizing's conjecture in domination theory that states $γ(G\Box H) \ge γ(G)γ(H)$ where $G\Box H$ is the Cartesian product of $G$ and $H$.

math.CO↗

arXiv2026

Shaken, not stirred: inefficient mixing of CM- and CI-like materials

A recent study suggests that CM chondrite-like planetesimals formed in the vicinity of Saturn, in a pressure bump outside the gap carved by proto-Jupiter. While a fraction of these objects was implanted into the asteroid belt as a consequence of Saturn's growth, it remains unclear whether the scattered remainder could reach the ice-giant region and mix with more distant carbonaceous reservoirs. We test whether outward scattering during Saturn's growth and migration can implant CM-like bodies onto long-lived orbits in the Uranus-Neptune region, where they could contaminate the CI reservoir. We performed N-body integrations of 100 km planetesimals launched from the outer edge of Jupiter's gap, including gas drag and the gravitational perturbations of growing Jupiter and Saturn, with optional inclusion of a nearby ice-giant embryo. We explored a range of gas surface-density profiles and growth timescales. While Saturn's growth efficiently scatters CM-like planetesimals, fewer than about 2 percent are implanted beyond 15 au, even under gas-rich conditions, because gas drag damps their eccentricities and drives them back toward their perihelia rather than allowing them to circularize at larger distances. Adding an ice-giant core modestly increases the outward reach (up to about 4 percent in the most gas-rich case), but Type-I migration further lowers perihelia, making long-term retention at large distances difficult. For a CM mass budget M_CM,tot about 1 M_Earth, this implies at most M_CM < 0.02-0.04 M_Earth reaches 15-25 au, corresponding to a diluted mass fraction < (1-2) x 10^-3 in the outer ring, hence negligible contamination of the CI reservoir. Combined with the distinct radial distributions of CM- and CI-like asteroids in the belt, these results imply limited mixing of carbonaceous reservoirs and isolation of the CI reservoir.

astro-ph.EP↗

arXiv2026

Characterizing all $K_4$-free well-edge-dominated graphs of girth 3

Given a graph $G$, a set $F$ of edges is an edge dominating set if all edges in $G$ are either in $F$ or adjacent to an edge in $F$. $G$ is said to be well-edge-dominated if every minimal edge dominating set is also minimum. In 2022, it was proven that there are precisely three nonbipartite, well-edge-dominated graphs with girth at least four. Then in 2025, a characterization of all well-edge-dominated graphs containing exactly one triangle was found. In this paper, we characterize all well-edge-dominated graphs that contain a triangle and yet are $K_4$-free.

math.CO↗

arXiv2025

Habitable from the start: How initial planetary formation conditions may create habitable worlds

The breadth of topics that encompass the search for life has expanded and evolved significantly since the emergence of the field of astrobiology. Initial astrobiology centered investigations focused on detecting biosignatures in the Martian soil with the Viking lander. The field now encompasses identification of biosignatures throughout the galaxy and habitable worlds, planets with sufficient liquid water and prebiotic chemistry to support life. This evolution mirrors the improvement in our understanding of environments that may harbor life. The bulk planetary chemistry governs the habitability of a planet, which is in turn set by the early solar system environment and planet formation processes. Therefore, investigations of solar and exoplanetary systems as a whole would provide insights into the factors that make a planet habitable. Bulk planetary chemistry govern planetary atmospheres, core sizes, magnetic fields, heat engines, volatile inventories, and silicate mantle compositions. We therefore advocate for investigations of formation conditions that establish planetary chemistry, and by extension, habitability.

astro-ph.IM↗

arXiv2025

Different arrival times of CM and CI-like bodies from the outer Solar System to the asteroid belt

Understanding the provenance of CI and CM chondrites, the most primitive materials in our meteorite collections, is critical for shedding light on the Solar System's early evolution and contextualizing findings from recent sample return missions. Here we show that the parent bodies of CM chondrites originate from the Saturn formation region, whereas those of CI chondrites originate essentially from the primordial trans-Uranian disk. Using Nbody simulations to investigate the effect of giant planet growth and inward Type-I migration, along with the current observed distribution of CM, CI, and comet-like P types bodies in the asteroid belt, we demonstrate that CI- and CM-like bodies must have been implanted at different times in the belt. In contrast, CI and comet-like bodies were implanted at the same time. These different implantation periods are imposed by the fact that the gas disk profile entirely governs the radial distribution of bodies implanted by aerodynamic drag in the asteroid belt. A preferred location coincides with the inner edge of a gap opened by Jupiter. Saturn's growth likely drove the migration of CM-like bodies. In contrast, CI and comet-like bodies were transported at a later stage during the outward migration of Uranus and Neptune, driven by remaining planetesimals. Since CM chondrites are chondrule-rich, it follows that chondrule formation occurred mostly inward of the ice giants formation zone (under 10 au). A byproduct of our simulations is that only CM-like, not CI-like, bodies contributed to the water budget of the telluric planets.

astro-ph.EP↗

arXiv2024

Triton and Pluto: same origin but separated at birth

Assessing the origin of Pluto and Triton has profound implications for the bigger picture of Solar System formation and evolution. In such a context, this chapter reviews our current knowledge of the formation conditions of Pluto and Triton's constitutive building blocks in the protosolar nebula, which can be derived from their known or estimated volatile contents. Assuming that the ultravolatiles carbon monoxide and dinitrogen detected in Pluto and Triton are primordial, the presence of these molecules suggest that the two bodies accreted material originating from the vicinity of the carbon monoxide and dinitrogen icelines. Dinitrogen--rich and water--poor comets such as comet C/2016 R2 (PanSTARRS) obviously present a compositional link with Pluto and Triton, indicating that their building blocks formed in nearby regions of the protosolar nebula, despite of the variation of the water abundance among those bodies. Also, the assumption of Triton's growth in Neptune's circumplanetary disk requires that its building blocks formed at earlier epochs in the protosolar nebula, to remain consistent with its estimated composition.

astro-ph.EP↗

arXiv2023

Relative hulls and quantum codes

Given two $q$-ary codes $C_1$ and $C_2$, the relative hull of $C_1$ with respect to $C_2$ is the intersection $C_1\cap C_2^\perp$. We prove that when $q>2$, the relative hull dimension can be repeatedly reduced by one, down to a certain bound, by replacing either of the two codes with an equivalent one. The reduction of the relative hull dimension applies to hulls taken with respect to the $e$-Galois inner product, which has as special cases both the Euclidean and Hermitian inner products. We give conditions under which the relative hull dimension can be increased by one via equivalent codes when $q>2$. We study some consequences of the relative hull properties on entanglement-assisted quantum error-correcting codes and prove the existence of new entanglement-assisted quantum error-correcting maximum distance separable codes, meaning those whose parameters satisfy the quantum Singleton bound.

cs.IT↗

arXiv2023

Surface Volatile Composition as Evidence for Hydrothermal Processes Lasting Longer in Triton's Interior than Pluto's

Ocean worlds, or icy bodies in the outer solar system that have or once had subsurface liquid water oceans, are among the most compelling topics of astrobiology. Typically, confirming the existence of a subsurface ocean requires close spacecraft observations. However, combining our understanding of the chemistry that takes place in a subsurface ocean with our knowledge of the building blocks that formed potential ocean worlds provides an opportunity to identify tracers of endogenic activity in the surface volatiles of Pluto and Triton. We show here that the current composition of the volatiles on the surfaces and in the atmospheres of Pluto and Triton are deficient in carbon, which can only be explained by the loss of CH4 through a combination of aqueous chemistry and atmospheric processes. Furthermore, we find that the relative nitrogen and water abundances are within the range observed in building block analogs, comets, and chondrites. A lower limit for N/Ar in Pluto's atmosphere also suggests source building blocks that have a cometary or chondritic composition, all pointing to an origin for their nitrogen as NH3 or organics. Triton's lower abundance of CH4 compared to Pluto, and the detection of CO2 at Triton but not at Pluto points to aqueous chemistry in a subsurface ocean that was more efficient at Triton than Pluto. These results have applications to other large Kuiper Belt objects as well as the assessment of formation locations and times for the four giant planets given future probe measurements of noble gas abundances and isotope ratios.

astro-ph.EP↗

arXiv2023

Orientable total domination in graphs

Given a directed graph $D$, a set $S \subseteq V(D)$ is a total dominating set of $D$ if each vertex in $D$ has an in-neighbor in $S$. The total domination number of $D$, denoted $γ_t(D)$, is the minimum cardinality among all total dominating sets of $D$. Given an undirected graph $G$, we study the maximum and minimum total domination numbers among all orientations of $G$. That is, we study the upper (or lower) orientable domination number of $G$, $\rm{DOM}_t(G)$ (or $\rm{dom}_t(G)$), which is the largest (or smallest) total domination number over all orientations of $G$. We characterize those graphs with $\rm{DOM}_t(G) =\rm{dom}_t(G)$ when the girth is at least $7$ as well as those graphs with $\rm{dom}_t(G) = |V(G)|-1$. We also consider how these parameters are effected by removing a vertex from $G$, give exact values of $\rm{DOM}_t(K_{m,n})$ and $\rm{dom}_t(K_{m,n})$ and bound these parameters when $G$ is a grid graph.

math.CO↗

arXiv2022

Graphs which satisfy a Vizing-like bound for power domination of Cartesian products

Power domination is a two-step observation process that is used to monitor power networks and can be viewed as a combination of domination and zero forcing. Given a graph $G$, a subset $S\subseteq V(G)$ that can observe all vertices of $G$ using this process is known as a power dominating set of $G$, and the power domination number of $G$, $γ_P(G)$, is the minimum number of vertices in a power dominating set. We introduce a new partition on the vertices of a graph to provide a lower bound for the power domination number. We also consider the power domination number of the Cartesian product of two graphs, $G \Box H$, and show certain graphs satisfy a Vizing-like bound with regards to the power domination number. In particular, we prove that for any two trees $T_1$ and $T_2$, $γ_P(T_1)γ_P(T_2) \leq γ_P(T_1 \Box T_2)$.

math.CO↗

arXiv2022

Power domination in cubic graphs and Cartesian products

The power domination problem focuses on finding the optimal placement of phase measurement units (PMUs) to monitor an electrical power network. In the context of graphs, the power domination number of a graph $G$, denoted $γ_P(G)$, is the minimum number of vertices needed to observe every vertex in the graph according to a specific set of observation rules. In \cite{ZKC_cubic}, Zhao et al. proved that if $G$ is a connected claw-free cubic graph of order $n$, then $γ_P(G) \leq n/4$. In this paper, we show that if $G$ is a claw-free diamond-free cubic graph of order $n$, then $γ_P(G) \le n/6$, and this bound is sharp. We also provide new bounds on $γ_P(G \Box H)$ where $G\Box H$ is the Cartesian product of graphs $G$ and $H$. In the specific case that $G$ and $H$ are trees whose power domination number and domination number are equal, we show the Vizing-like inequality holds and $γ_P(G \Box H) \ge γ_P(G)γ_P(H)$.

math.CO↗

arXiv2022

The N$_2$ Production Rate in Comet C/2016 R2 (PanSTARRS)

Observations of comet C/2016 R2 (PanSTARRS) have revealed exceptionally bright emission bands of N$_2^+$, the strongest ever observed in a comet spectrum. Alternatively, it appears to be poor in CN compared to other comets, and remarkably depleted in H$_2$O. Here we quantify the N$_2$ production rate from N$_2^+$ emission lines using the Haser model. We derived effective parent and daughter scalelengths for N2 producing N2+. This is the first direct measurement of such parameters. Using a revised fluorescence efficiency for N2+, the resulting production rate of molecular nitrogen is inferred to be Q(N$_2$) ~ 1 $\times 10^{28}$ molecules.s-1 on average for 11, 12, and 13 Feb. 2018, the highest for any known comet. Based on a CO production rate of Q(CO) ~ 1.1 $\times 10^{29}$ molecules.s-1, we find Q(N$-2$)/Q(CO)~0.09, which is consistent with the N$_2^+$/CO$^+$ ratio derived from the observed intensities of N$_2^+$ and CO$^+$ emission lines. We also measure significant variations in this production rate between our three observing nights, with Q(N$_2$) varying by plus or minus 20% according to the average value

astro-ph.EP↗

arXiv2021

On well-edge-dominated graphs

A graph is said to be well-edge-dominated if all its minimal edge dominating sets are minimum. It is known that every well-edge-dominated graph $G$ is also equimatchable, meaning that every maximal matching in $G$ is maximum. In this paper, we show that if $G$ is a connected, triangle-free, nonbipartite, well-edge-dominated graph, then $G$ is one of three graphs. We also characterize the well-edge-dominated split graphs and Cartesian products. In particular, we show that a connected Cartesian product $G\Box H$ is well-edge-dominated, where $G$ and $H$ have order at least $2$, if and only if $G\Box H = K_2 \Box K_2$.

math.CO↗

arXiv2021

Product Throttling

Throttling addresses the question of minimizing the sum or the product of the resources used to accomplish a task and the time needed to complete that task for various graph searching processes. Graph parameters of interest include various types of zero forcing, power domination, and Cops and Robbers. We provide a survey of product throttling for these parameters.

math.CO↗

arXiv2021

Photoionization of Rydberg Atoms in Optical Lattices

We develop a formalism for photoionization (PI) and potential energy curves (PECs) of Rydberg atoms in ponderomotive optical lattices and apply it to examples covering several regimes of the optical-lattice depth. The effect of lattice-induced PI on Rydberg-atom lifetime ranges from noticeable to highly dominant when compared with natural decay. The PI behavior is governed by the generally rapid decrease of the PI cross sections as a function of angular-momentum ($\ell$), and by lattice-induced $\ell$-mixing across the optical-lattice PECs. In GHz-deep lattices, $\ell$-mixing leads to a rich PEC structure, and the significant low-$\ell$ PI cross sections are distributed over many lattice-mixed Rydberg states. In lattices less than several tens-of-MHz deep, atoms on low-$\ell$ PECs are essentially $\ell$-mixing-free and maintain large PI cross sections, while atoms on high-$\ell$ PECs trend towards being PI-free. Characterization of PI in GHz-deep Rydberg-atom lattices may be beneficial for optical control and quantum-state manipulation of Rydberg atoms, while data on PI in shallower lattices are potentially useful in high-precision spectroscopy and quantum-computing applications of lattice-confined Rydberg atoms.

physics.atom-ph↗

arXiv2020

Product throttling for power domination

The product power throttling number of a graph is defined to study product throttling for power domination. The domination number of a graph is an upper bound for its product power throttling number. It is established that the two parameters are equal for certain families including paths, cycles, complete graphs, unit interval graphs, and grid graphs (on the plane, cylinder, and torus). Families of graphs for which the product power throttling number is less than the domination number are also exhibited. Graphs with extremely high or low product power throttling number are characterized and bounds on the product power throttling number are established.

math.CO↗