Magnetic field topology of the RS CVn star II Pegasi

The dynamo processes in cool active stars generate complex magnetic fields responsible for prominent surface stellar activity and variability at different time scales. For a small number of cool stars magnetic field topologies were reconstructed from the time series of spectropolarimetric observations using the Zeeman Doppler imaging (ZDI) method. In this study we follow a long-term evolution of the magnetic field topology of the RS CVn binary star II Peg. We collected high-resolution circular polarisation observations of II Peg using the SOFIN spectropolarimeter at the Nordic Optical Telescope. These data cover 12 epochs spread over 7 years. A multi-line diagnostic technique in combination with a new ZDI code is applied to interpret these observations. Magnetic inversions using these data reveals evolving magnetic fields with typical local strengths of 0.5-1.0 kG and complex topologies. Despite using a self-consistent magnetic and temperature mapping technique, we do not find a clear correlation between magnetic and temperature features in the ZDI maps. Neither do we confirm the presence of persistent azimuthal field rings found in other RS CVn stars. Reconstruction of the magnetic field topology of II Peg reveals significant evolution of both the surface magnetic field structure and the extended magnetospheric field geometry. From 2004 to 2010 the total field energy drastically declined and the field became less axisymmetric. This also coincided with the transition from predominantly poloidal to mainly toroidal field topology. A qualitative comparison of the ZDI maps of II Peg with the prediction of dynamo theory suggests that the magnetic field in this star is produced mainly by the turbulent alpha^2 dynamo rather than the solar alphaOmega dynamo. Our results do not show a clear active longitude system, nor is there an evidence of the presence of an azimuthal dynamo wave.Comment: 20 pages, 10 figures; accepted for publication in Astronomy & Astrophysic

Spot activity of the RS CVn star {\sigma} Geminorum

We model the photometry of RS CVn star $\sigma$ Geminorum to obtain new information on the changes of the surface starspot distribution, i.e., activity cycles, differential rotation and active longitudes. We use the previously published Continuous Periods Search-method (CPS) to analyse V-band differential photometry obtained between the years 1987 and 2010 with the T3 0.4 m Automated Telescope at the Fairborn Observatory. The CPS-method divides data into short subsets and then models the light curves with Fourier-models of variable orders and provides estimates of the mean magnitude, amplitude, period and light curve minima. These light curve parameters are then analysed for signs of activity cycles, differential rotation and active longitudes. We confirm the presence of two previously found stable active longitudes, synchronised with the orbital period $P_{\rm{orb}}=19.60$d and find eight events where the active longitudes are disrupted. The epochs of the primary light curve minima rotate with a shorter period $P_{\rm{min,1}}=19.47$d than the orbital motion. If the variations in the photometric rotation period were to be caused by differential rotation, this would give a differential rotation coefficient of $\alpha \ge 0.103$. The presence of two slightly different periods of active regions may indicate a superposition of two dynamo modes, one stationary in the orbital frame and the other one propagating in the azimuthal direction. Our estimate of the differential rotation is much higher than previous results. However, simulations show that this can be caused by insufficient sampling in our data.Comment: 10 pages, 6 figures. Submitted to A&

Surface distribution of small-scale magnetic field on the active cool star LQ Hydrae

It is well known that small-scale magnetism dominates the surface magnetic field topologies of active late-type stars. However, little information is available on the spatial distribution of this key magnetic field component. Here, we take advantage of the recently developed magnetic field diagnostic procedure relying on the magnetic intensification of iron atomic lines in the optical. We extend this methodology from measuring a single average field strength value to simultaneous Doppler imaging reconstruction of the two-dimensional maps of temperature and magnetic field strength. We applied this novel surface mapping approach to two spectroscopic data sets of the young active Sun-like star LQ Hya. For both epochs, we found a fairly uniform field strength distribution, apart from a latitudinal trend of the field strength increasing from 1.5-2.0 kG at low latitudes to 3.0-3.5 kG, close to the rotational poles. This distribution of the small-scale field does not display a clear correlation with the locations of temperature spots or the global magnetic field structure reconstructed for the same epochs.Comment: 7 pages, 6 figures; accepted for publication in A&

Risk, Uncertainty and Optimism in Venture Capital Relationships

We develop a dynamic, structural model to quantitatively assess the effects of risk, uncertainty and asymmetric beliefs about project quality on the characteristics of venture capital relationships. We estimate the model parameters with data about the distributions of total investments, payoffs, risks and returns of venture capital projects. Entrepreneurial optimism mitigates the agency costs of risk-sharing between venture capitalists (VCs) and entrepreneurs (ENs) by over 20 % and significantly enhances the VC’s expected payoffs. The EN optimism premium implied by the data explains the huge discrepancy between the discount rates used by VCs ( ∼ 40%), which adjust for optimistic payoff projections by ENs, and the average expected return of VC projects ( ∼ 15%). Consistent with observed contractual structures, the equilibrium dynamic contracts feature both equity-like and debt-like components for the VC and progressive vesting of the EN’s stake. The duration, project value and the VC’s expected payoff all increase with the project’s transient risk but decrease with its intrinsic risk

Stellar activity as noise in exoplanet detection I. Methods and application to solar-like stars and activity cycles

The detection of exoplanets using any method is prone to confusion due to the intrinsic variability of the host star. We investigate the effect of cool starspots on the detectability of the exoplanets around solar-like stars using the radial velocity method. For investigating this activity-caused "jitter" we calculate synthetic spectra using radiative transfer, known stellar atomic and molecular lines, different surface spot configurations, and an added planetary signal. Here, the methods are described in detail, tested and compared to previously published studies. The methods are also applied to investigate the activity jitter in old and young solar-like stars, and over a solar-like activity cycles. We find that the mean full jitter amplitude obtained from the spot surfaces mimicking the solar activity varies during the cycle approximately between 1 m/s and 9 m/s. With a realistic observing frequency a Neptune mass planet on a one year orbit can be reliably recovered. On the other hand, the recovery of an Earth mass planet on a similar orbit is not feasible with high significance. The methods developed in this study have a great potential for doing statistical studies of planet detectability, and also for investigating the effect of stellar activity on recovered planetary parameters.Comment: Accepted to MNRA

First measurement of the magnetic field on FK Com and its relation to the contemporaneous starspot locations

In this study we present simultaneous low-resolution longitudinal magnetic field measurements and high-resolution spectroscopic observations of the cool single giant FK Com. The variation of the magnetic field over the rotational period of 2.4 days is compared with the starspot location obtained using Doppler imaging techniques, V-band photometry and V-I colours. The chromospheric activity is studied simultaneously with the photospheric activity using high resolution observations of the Halpha, Hbeta and Hgamma line profiles. Both the maximum (272 +/- 24 G) and minimum (60 +/- 17 G) in the mean longitudinal magnetic field, , are detected close to the phases where cool spots appear on the stellar surface. A possible explanation for such a behaviour is that the active regions at the two longitudes separated by 0.2 in phase have opposite polarities.Comment: 10 Pages, 11 figures (quality of Figures 7,8 and 10 reduced), accepted for publication in MNRA

Expert Discovery Protections: Comparing District Courts with the PTAB

Expert witness testimony can be critical in patent litigation in all forums. In Patent Trial and Appeal Board (“PTAB”) proceedings, particularly inter partes review (“IPR”) and post-grant review (“PGR”), expert testimony through declarations and depositions plays a central role in both challenging and defending patents. In district courts, live expert testimony is key to proving infringement and invalidity. Accordingly, the legal protections governing the disclosure of expert testimony in discovery in both forums are carefully proscribed, but with notable distinctions