A geometrical origin for the covariant entropy bound

Causal diamond-shaped subsets of space-time are naturally associated with operator algebras in quantum field theory, and they are also related to the Bousso covariant entropy bound. In this work we argue that the net of these causal sets to which are assigned the local operator algebras of quantum theories should be taken to be non orthomodular if there is some lowest scale for the description of space-time as a manifold. This geometry can be related to a reduction in the degrees of freedom of the holographic type under certain natural conditions for the local algebras. A non orthomodular net of causal sets that implements the cutoff in a covariant manner is constructed. It gives an explanation, in a simple example, of the non positive expansion condition for light-sheet selection in the covariant entropy bound. It also suggests a different covariant formulation of entropy bound.Comment: 20 pages, 8 figures, final versio

Derivation and comparison of formulae for the adjustment of total calcium

Background: Free ionized calcium (Ca2+) is the biologically active component of total calcium (TCa) and hence responsible for its biological action. TCa is routinely adjusted for albumin using several formulae (e.g. James, Orell, Payne and Berry) to more closely reflect Ca2+. Here, we derive a novel formula to estimate Ca2+ and compare its performance to established formulae. Methods: Cohort for prediction of Ca2+: 2806 serum samples (TCa) taken contemporaneously with blood gas samples (Ca2+) at Imperial College Healthcare NHS Trust were used to derive formulae to estimate Ca2+ using multivariable linear regression. Cohort for prediction of PTH: Performance of novel and existing formulae to predict PTH in 5510 patients was determined by Spearman correlation. Results: Ca2+ prediction Cohort: Adjusted calcium (r2 = 0.269) was less strongly associated with Ca2+, than TCa (r2 = 0.314). Prediction of Ca2+ from a newly derived formula incorporating TCa, potassium, albumin, and hematocrit had an improved r2 of 0.327, whereas inclusion of all available parameters increased the r2 further to 0.364. Of the established formulae, James performed best in predicting Ca2+ (r2 = 0.27). PTH prediction cohort: Berry resulted in higher whereas Orell in lower adjusted calcium levels. Prediction of PTH was strongest in the setting of hypercalcemia, with James having the highest Spearman correlation coefficient (+0.496) similar to including all parameters (+0.499). Conclusion: Adjustment of calcium for albumin using established formulae does not always outperform unadjusted TCa in the reflection of Ca2+. Further prospective studies are needed to optimise adjustment of TCa and to establish bounds for validity

Unsigned magnetic flux as a proxy for radial-velocity variations in Sun-like stars

We estimate disc-averaged RV variations of the Sun over the last magnetic cycle, from the single Fe I line observed by SDO/HMI, using a physical model for rotationally modulated magnetic activity that was previously validated against HARPS-N solar observations. We estimate the disc-averaged, unsigned magnetic flux and show that a simple linear fit to it reduces the RMS of RV variations by 62%, i.e. a factor of 2.6. We additionally apply the FF' method, which predicts RV variations based on a star's photometric variations. At cycle maximum, we find that additional physical processes must be at play beyond suppression of convective blueshift and velocity imablances resulting from brightness inhomogeneities, in agreement with recent studies of solar RV variations. By modelling RV variations over the magnetic cycle using a linear fit to the unsigned magnetic flux, we recover injected planets at an orbital period of about 300 days with RV semi-amplitudes down to 0.3 m/s. To reach semi-amplitudes of 0.1 m/s, we will need to identify and model additional physical phenomena that are not well traced by the unsigned magnetic flux or FF'. The unsigned magnetic flux is an excellent proxy for rotationally modulated, activity-induced RV variations, and could become a key tool in confirming and characterising Earth analogs orbiting Sun-like stars. The present study motivates ongoing and future efforts to develop observation and analysis techniques to measure the unsigned magnetic flux at high precision in slowly rotating, relatively inactive stars like the Sun.Comment: 25 pages, 11 figures, 3 tables, submitted to Ap

Geometric entropy, area, and strong subadditivity

The trace over the degrees of freedom located in a subset of the space transforms the vacuum state into a density matrix with non zero entropy. This geometric entropy is believed to be deeply related to the entropy of black holes. Indeed, previous calculations in the context of quantum field theory, where the result is actually ultraviolet divergent, have shown that the geometric entropy is proportional to the area for a very special type of subsets. In this work we show that the area law follows in general from simple considerations based on quantum mechanics and relativity. An essential ingredient of our approach is the strong subadditive property of the quantum mechanical entropy.Comment: Published versio

Stellar jitter from variable gravitational redshift: implications for RV confirmation of habitable exoplanets

A variation of gravitational redshift, arising from stellar radius fluctuations, will introduce astrophysical noise into radial velocity measurements by shifting the centroid of the observed spectral lines. Shifting the centroid does not necessarily introduce line asymmetries. This is fundamentally different from other types of stellar jitter so far identified, which do result from line asymmetries. Furthermore, only a very small change in stellar radius, ~0.01%, is necessary to generate a gravitational redshift variation large enough to mask or mimic an Earth-twin. We explore possible mechanisms for stellar radius fluctuations in low-mass stars. Convective inhibition due to varying magnetic field strengths and the Wilson depression of starspots are both found to induce substantial gravitational redshift variations. Finally, we investigate a possible method for monitoring/correcting this newly identified potential source of jitter and comment on its impact for future exoplanet searches.Comment: 6 pages, 1 figure, 1 tabl

The Rossiter-McLaughlin effect in Exoplanet Research

The Rossiter-McLaughlin effect occurs during a planet's transit. It provides the main means of measuring the sky-projected spin-orbit angle between a planet's orbital plane, and its host star's equatorial plane. Observing the Rossiter-McLaughlin effect is now a near routine procedure. It is an important element in the orbital characterisation of transiting exoplanets. Measurements of the spin-orbit angle have revealed a surprising diversity, far from the placid, Kantian and Laplacian ideals, whereby planets form, and remain, on orbital planes coincident with their star's equator. This chapter will review a short history of the Rossiter-McLaughlin effect, how it is modelled, and will summarise the current state of the field before describing other uses for a spectroscopic transit, and alternative methods of measuring the spin-orbit angle.Comment: Review to appear as a chapter in the "Handbook of Exoplanets", ed. H. Deeg & J.A. Belmont

Rotation of planet-harbouring stars

The rotation rate of a star has important implications for the detectability, characterisation and stability of any planets that may be orbiting it. This chapter gives a brief overview of stellar rotation before describing the methods used to measure the rotation periods of planet host stars, the factors affecting the evolution of a star's rotation rate, stellar age estimates based on rotation, and an overview of the observed trends in the rotation properties of stars with planets.Comment: 16 pages, 4 figures: Invited review to appear in 'Handbook of Exoplanets', Springer Reference Works, edited by Hans J. Deeg and Juan Antonio Belmont

Temporal evolution and correlations of optical activity indicators measured in Sun-as-a-star observations

A.C.C. acknowledges support from the Science and Technology Facilities Council (STFC) consolidated grant number ST/R000824/1.Context. Understanding stellar activity in solar-type stars is crucial for the physics of stellar atmospheres as well as for ongoing exoplanet programmes. Aims. We aim to test how well we understand stellar activity using our own star, the Sun, as a test case. Methods. We performed a detailed study of the main optical activity indicators (Ca II H & K, Balmer lines, Na I D1 D2, and He I D3) measured for the Sun using the data provided by the HARPS-N solar-telescope feed at the Telescopio Nazionale Galileo. We made use of periodogram analyses to study solar rotation, and we used the pool variance technique to study the temporal evolution of active regions. The correlations between the different activity indicators as well as the correlations between activity indexes and the derived parameters from the cross-correlation technique are analysed. We also study the temporal evolution of these correlations and their possible relationship with indicators of inhomogeneities in the solar photosphere like sunspot number or radio flux values. Results. The value of the solar rotation period is found in all the activity indicators, with the only exception being Hδ. The derived values vary from 26.29 days (Hγ line) to 31.23 days (He I). From an analysis of sliding periodograms we find that in most of the activity indicators the spectral power is split into several “bands” of periods around 26 and 30 days. They might be explained by the migration of active regions between the equator and a latitude of ∼30°, spot evolution, or a combination of both effects. A typical lifetime of active regions of approximately ten rotation periods is inferred from the pooled variance diagrams, which is in agreement with previous works. We find that Hα, Hβ, Hγ, Hϵ, and He I show a significant correlation with the S index. Significant correlations between the contrast, bisector span, and the heliocentric radial velocity with the activity indexes are also found. We show that the full width at half maximum, the bisector, and the disc-integrated magnetic field correlate with the radial velocity variations. The correlation of the S index and Hα changes with time, increasing with larger sun spot numbers and solar irradiance. A similar tendency with the S index and radial velocity correlation is also present in the data. Conclusions. Our results are consistent with a scenario in which higher activity favours the correlation between the S index and the Hα activity indicators and between the S index and radial velocity variations.PostprintPeer reviewe