scholarly journals Imprints of relativistic effects on the asymmetry of the halo cross-correlation function: from linear to non-linear scales

2018 ◽  
Vol 483 (2) ◽  
pp. 2671-2696 ◽  
Author(s):  
Michel-Andrès Breton ◽  
Yann Rasera ◽  
Atsushi Taruya ◽  
Osmin Lacombe ◽  
Shohei Saga
Keyword(s):  
Correlation Function ◽  
Cross Correlation ◽  
Relativistic Effects ◽  
Cross Correlation Function ◽  
Non Linear ◽  
The Asymmetry

scholarly journals Measuring precise radial velocities and cross-correlation function line-profile variations using a Skew Normal density

2019 ◽  
Vol 622 ◽  
pp. A131 ◽  
Author(s):  
U. Simola ◽  
X. Dumusque ◽  
J. Cisewski-Kehe
Keyword(s):  
Correlation Function ◽  
Cross Correlation ◽  
Cross Correlation Function ◽  
Normal Density ◽  
Inverse Slope ◽  
Stellar Activity ◽  
New Model ◽  
The Mean ◽  
The Asymmetry ◽  
Skew Normal

Context. Stellar activity is one of the primary limitations to the detection of low-mass exoplanets using the radial-velocity (RV) technique. Stellar activity can be probed by measuring time-dependent variations in the shape of the cross-correlation function (CCF). It is therefore critical to measure with high-precision these shape variations to decorrelate the signal of an exoplanet from spurious RV signals caused by stellar activity. Aims. We propose to estimate the variations in shape of the CCF by fitting a Skew Normal (SN) density which, unlike the commonly employed Normal density, includes a Skewness parameter to capture the asymmetry of the CCF induced by stellar activity and the convective blueshift. Methods. We compared the performances of the proposed method to the commonly employed Normal density using both simulations and real observations with different levels of activity and signal-to-noise ratios. Results. When considering real observations, the correlation between the RV and the asymmetry of the CCF and between the RV and the width of the CCF are stronger when using the parameters estimated with the SN density rather than those obtained with the commonly employed Normal density. In particular, the strongest correlations have been obtained when using the mean of the SN as an estimate for the RV. This suggests that the CCF parameters estimated using a SN density are more sensitive to stellar activity, which can be helpful when estimating stellar rotational periods and when characterizing stellar activity signals. Using the proposed SN approach, the uncertainties estimated on the RV defined as the median of the SN are on average 10% smaller than the uncertainties calculated on the mean of the Normal. The uncertainties estimated on the asymmetry parameter of the SN are on average 15% smaller than the uncertainties measured on the Bisector Inverse Slope Span (BIS SPAN), which is the commonly used parameter to evaluate the asymmetry of the CCF. We also propose a new model to account for stellar activity when fitting a planetary signal to RV data. Based on simple simulations, we were able to demonstrate that this new model improves the planetary detection limits by 12% compared to the model commonly used to account for stellar activity. Conclusions. The SN density is a better model than the Normal density for characterizing the CCF since the correlations used to probe stellar activity are stronger and the uncertainties of the RV estimate and the asymmetry of the CCF are both smaller.

scholarly journals Modelling the asymmetry of the halo cross-correlation function with relativistic effects at quasi-linear scales

2020 ◽  
Vol 498 (1) ◽  
pp. 981-1001
Author(s):  
Shohei Saga ◽  
Atsushi Taruya ◽  
Michel-Andrès Breton ◽  
Yann Rasera
Keyword(s):  
Correlation Function ◽  
Doppler Effect ◽  
Cross Correlation ◽  
Relativistic Effects ◽  
Cross Correlation Function ◽  
Gravitational Redshift ◽  
Wide Angle ◽  
Redshift Surveys ◽  
Angle Effect ◽  
The Doppler Effect

ABSTRACT The observed galaxy distribution via galaxy redshift surveys appears distorted due to redshift-space distortions (RSD). While one dominant contribution to RSD comes from the Doppler effect induced by the peculiar velocity of galaxies, the relativistic effects, including the gravitational redshift effect, are recently recognized to give small but important contributions. Such contributions lead to an asymmetric galaxy clustering along the line of sight, and produce non-vanishing odd multipoles when cross-correlating between different biased objects. However, non-zero odd multipoles are also generated by the Doppler effect beyond the distant-observer approximation, known as the wide-angle effect, and at quasi-linear scales, the interplay between wide-angle and relativistic effects becomes significant. In this paper, based on the formalism developed by Taruya et al., we present a quasi-linear model of the cross-correlation function taking a proper account of both the wide-angle and gravitational redshift effects, as one of the major relativistic effects. Our quasi-linear predictions of the dipole agree well with simulations even at the scales below $20\, h^{-1}\,$Mpc, where non-perturbative contributions from the halo potential play an important role, flipping the sign of the dipole amplitude. When increasing the bias difference and redshift, the scale where the sign flip happens is shifted to a larger scale. We derive a simple approximate formula to quantitatively account for the behaviours of the sign flip.

scholarly journals Non-linear behavior of root and stem diameter changes in monopodial orchid

2021 ◽  
Vol 10 (6) ◽  
pp. 3452-3459
Author(s):  
Mohd Khairi Nordin ◽  
Mohammad Farid Saaid ◽  
Nooritawati Md Tahir ◽  
Ahmad Ihsan Mohd Yassin ◽  
Megat Syahirul Amin Megat Ali
Keyword(s):  
Correlation Function ◽  
Relative Humidity ◽  
Cross Correlation ◽  
Root Diameter ◽  
Stem Diameter ◽  
Cross Correlation Function ◽  
Linear Behavior ◽  
Non Linear ◽  
Scatter Plots ◽  
Monopodial Orchid

Precision agriculture aims to maximize yield with optimum resources. Vast majority of natural systems are acknowledged as complex and non-linear. However, prior to formulation of precise models, linearity tests are performed to validate plant behavior. This study has presented proof that the water uptake system in monopodial orchid is indeed non-linear. The change in physical growth of root and stem due to temperature and relative humidity factors are observed. The work focused on Ascocenda Fuchs Harvest Moon x (V. Chaophraya x Boots) orchid hybrid. Three complementary methods are presented: linearity tests through 1) regression fitting; 2) scatter plots; and 3) cross-correlation function tests. Root diameter, stem diameter, temperature, and relative humidity are logged at 15 minutes interval for a duration of 71 days. The polynomial equations derived for root diameter and stem diameter changes attained strong regression coefficients. The non-linear behavior is further confirmed by the scatter plots where no linear associations are present between the independent and dependent variables. Subsequently, the cross-correlation function tests conducted on temperature-root diameter, temperature-stem diameter, relative humidity-root diameter, and relative humidity-stem diameter combinations also revealed weak correlation. Despite using different techniques, the behavior of physical changes has been consistently proven to be non-linear.

Measurement of the Spatial Cross-Correlation Function of Damped Lyα Systems and Lyman Break Galaxies

2005 ◽  
Vol 636 (1) ◽  
pp. L9-L12 ◽  
Author(s):  
Jeff Cooke ◽  
Arthur M. Wolfe ◽  
Eric Gawiser ◽  
Jason X. Prochaska
Keyword(s):  
Correlation Function ◽  
Cross Correlation ◽  
Cross Correlation Function ◽  
Lyman Break Galaxies
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