Flares in Open Clusters with K2. I. M45 (Pleiades), M44 (Praesepe) and M67

The presence and strength of a stellar magnetic field and activity is rooted in a star's fundamental parameters such as mass and age. Can flares serve as an accurate stellar "clock"? To explore if we can quantify an activity-age relation in the form of a flaring-age relation, we measured trends in the flaring rates and energies for stars with different masses and ages. We investigated the time-domain photometry provided by Kepler's follow-up mission K2 and searched for flares in three solar metallicity open clusters with well-known ages, M45 (0.125 Gyr), M44 (0.63 Gyr), and M67 (4.3 Gyr). We updated and employed the automated flare finding and analysis pipeline Appaloosa, originally designed for Kepler. We introduced a synthetic flare injection and recovery subroutine to ascribe detection and energy recovery rates for flares in a broad energy range for each light curve. We collected a sample of 1 761 stars, mostly late-K to mid-M dwarfs and found 751 flare candidates with energies ranging from $4\cdot10^{32}$ erg to $6\cdot10^{34}$ erg, of which 596 belong to M45, 155 to M44, and none to M67. We find that flaring activity depends both on $T_\mathrm{eff}$, and age. But all flare frequency distributions have similar slopes with $\alpha \approx2.0-2.4$, supporting a universal flare generation process. We discuss implications for the physical conditions under which flares occur, and how the sample's metallicity and multiplicity affect our results.Comment: 17 pages, 11 figures, appendix. Accepted to A&

Direct current superconducting quantum interferometers with asymmetric shunt resistors

We have investigated asymmetrically shunted Nb/Al-AlO$_x$/Nb direct current (dc) superconducting quantum interference devices (SQUIDs). While keeping the total resistance $R$ identical to a comparable symmetric SQUID with $R^{-1} = R_1^{-1} + R_2^{-1}$, we shunted only one of the two Josephson junctions with $R = R_{1,2}/2$. Simulations predict that the optimum energy resolution $\epsilon$ and thus also the noise performance of such an asymmetric SQUID can be 3--4 times better than that of its symmetric counterpart. Experiments at a temperature of 4.2\,K yielded $\epsilon \approx 32\,\hbar$ for an asymmetric SQUID with an inductance of $22\,\rm{pH}$. For a comparable symmetric device $\epsilon = 110\,\hbar$ was achieved, confirming our simulation results.Comment: 5 pages, 4 figure

Spectroscopy of a fractional Josephson vortex molecule

In long Josephson junctions with multiple discontinuities of the Josephson phase, fractional vortex molecules are spontaneously formed. At each discontinuity point a fractional Josephson vortex carrying a magnetic flux $|\Phi|<\Phi_0$, $\Phi_0\approx 2.07\times 10^{-15}$ Wb being the magnetic flux quantum, is pinned. Each vortex has an oscillatory eigenmode with a frequency that depends on $\Phi/\Phi_0$ and lies inside the plasma gap. We experimentally investigate the dependence of the eigenfrequencies of a two-vortex molecule on the distance between the vortices, on their topological charge $\wp=2\pi\Phi/\Phi_0$ and on the bias current $\gamma$ applied to the Josephson junction. We find that with decreasing distance between vortices, a splitting of the eigenfrequencies occurs, that corresponds to the emergence of collective oscillatory modes of both vortices. We use a resonant microwave spectroscopy technique and find good agreement between experimental results and theoretical predictions.Comment: submitted to Phys. Rev.

Aluminum Hard Mask Technique for the Fabrication of High-Quality Submicron Nb/Al-AlOx/Nb Josephson Junctions

We have developed a combined photolithography and electron-beam lithography fabrication process for sub-\mum to \mum-size Nb/Al-AlOx/Nb Josephson junctions. In order to define the junction size and protect its top electrode during anodic oxidation, we developed and used the new concept of an aluminum hard mask. Josephson junctions of sizes down to 0.5 \mum2 have been fabricated and thoroughly characterized. We found that they have a very high quality, which is witnessed by the IV curves with quality parameters Vm > 50 mV and Vgap = 2.8 mV at 4.2 K, as well as IcRN products of 1.75-1.93 mV obtained at lower temperatures. In order to test the usability of our fabrication process for superconducting quantum bits, we have also designed, fabricated and experimentally investigated phase qubits made of these junctions. We found a relaxation time of T1 = 26 ns and a dephasing time of T2 = 21 ns

The model and the planning method of volume and variety assessment of innovative products in an industrial enterprise

In the long term, the innovative development strategy efficiency is considered as the most crucial condition for assurance of economic system competitiveness in market conditions. It determines the problem relevance of such justification strategies with regard to specific systems features and conditions of their operation. The problem solution for industrial enterprises can be based on mathematical models of supporting the decision-making on the elements of the innovative manufacturing program. An optimization model and the planning method of innovative products volume and variety are suggested. The feature of the suggested model lies in the nonlinear nature of the objective function. It allows taking into consideration the law of diminishing marginal utility. The suggested method of optimization takes into account the system features and enables the effective implementation of manufacturing capabilities in modern conditions of production organization and sales in terms of market saturation

Flares in Open Clusters with K2. II. Pleiades, Hyades, Praesepe, Ruprecht 147, and M67

Flares, energetic eruptions on the surfaces of stars, are an unmistakable manifestation of magnetically driven emission. Their occurrence rates and energy distributions trace stellar characteristics such as mass and age. But before flares can be used to constrain stellar properties, the flaring-age-mass relation requires proper calibration. This work sets out to quantify flaring activity of independently age-dated main sequence stars for a broad range of spectral types using optical light curves obtained by the Kepler satellite. Drawing from the complete K2 archive, we searched 3435 $\sim 80$ day long light curves of 2111 open cluster members for flares using the open-source software packages K2SC to remove instrumental and astrophysical variability from K2 light curves, and AltaiPony to search and characterize the flare candidates. We confirmed a total of 3844 flares on high probability open cluster members with ages from zero age main sequence (Pleiades) to 3.6 Gyr (M67). We extended the mass range probed in the first study of this series to span from Sun-like stars to mid-M dwarfs. We added the Hyades (690 Myr) to the sample as a comparison cluster to Praesepe (750 Myr), the 2.6 Gyr old Ruprecht 147, and several hundred light curves from the late K2 Campaigns in the remaining clusters. The flare energy distribution was similar in the entire parameter space, following a power law relation with exponent $\alpha\approx 1.84-2.39$. The flaring rates declined with age, and declined faster for higher mass stars. We found evidence that a rapid decline in flaring activity occurred in M1-M2 dwarfs around Hyades/Praesepe age, when these stars spun down to rotation periods of about 10 days, while higher mass stars had already transitioned to lower flaring rates, and lower mass stars still resided in the saturated activity regime. (abridged)Comment: 27 pages, 13 figures. Accepted to A&