Search for: All records

Abstract A recent study by Hon et al. reported that a close-in planet around the red clump star, 8 UMi, should have been engulfed during the expansion phase of its parent star’s evolution. They explained the survival of this exoplanet through a binary-merger channel for 8 UMi. The key to testing this formation scenario is to derive the true age of this star: is it an old “imposter” resulting from a binary merger, or a genuinely young red clump giant? To accomplish this, we derive kinematic and chemical properties for 8 UMi using astrometric data from Gaia DR3 and the element-abundance pattern measured from a high-resolution (R∼ 75,000) spectrum taken by SOPHIE. Our analysis shows that 8 UMi is a normal thin-disk star with orbital rotation speed ofV_ϕ= 244.96 km s⁻¹, and possesses a solar metallicity ([Fe/H] = −0.05 ± 0.07) andα-element-abundance ratio ([α/Fe] = +0.01 ± 0.03). By adopting well-established relationships between age and space velocities/elemental abundances, we estimate a kinematic age of ${3.50}_{-2.00}^{+3.00}$Gyr, and a chemical age of ${3.25}_{-1.50}^{+2.50}$Gyr from [C/N] and 3.47 ± 1.96 Gyr from [Y/Mg] for 8 UMi, respectively. These estimates are consistent with the isochrone-fitting age ( ${1.90}_{-0.30}^{+1.15}$Gyr) of 8 UMi, but are all much younger than the timescale required in a binary-merger scenario. This result challenges the binary-merger model; the existence of such a closely orbiting exoplanet around a giant star remains a mystery yet to be resolved. 

This paper develops competitive bidding strategies for an online linear optimization problem with inventory management constraints in both cost minimization and profit maximization settings. In the minimization problem, a decision maker should satisfy its time-varying demand by either purchasing units of an asset from the market or producing them from a local inventory with limited capacity. In the maximization problem, a decision maker has a time-varying supply of an asset that may be sold to the market or stored in the inventory to be sold later. In both settings, the market price is unknown in each timeslot and the decision maker can submit a finite number of bids to buy/sell the asset. Once all bids have been submitted, the market price clears and the amount bought/sold is determined based on the clearing price and submitted bids. From this setup, the decision maker must minimize/maximize their cost/profit in the market, while also devising a bidding strategy in the face of an unknown clearing price. We propose DEMBID and SUPBID, two competitive bidding strategies for these online linear optimization problems with inventory management constraints for the minimization and maximization setting respectively. We then analyze the competitive ratios of the proposed algorithms and show that the performance of our algorithms approaches the best possible competitive ratio as the maximum number of bids increases. As a case study, we use energy data traces from Akamai data centers, renewable outputs from NREL, and energy prices from NYISO to show the effectiveness of our bidding strategies in the context of energy storage management for a large energy customer participating in a real-time electricity market.