# Posts Tagged correlation

## Recent Postings from correlation

### Spatial Correlation Between Dust and H$\alpha$ Emission in Dwarf Irregular Galaxies

Using a sample of dwarf irregular galaxies selected from the ALFALFA blind HI-survey and observed using the VIMOS IFU, we investigate the relationship between H$\alpha$ emission and Balmer optical depth ($\tau_{\text{b}}$). We find a positive correlation between H$\alpha$ luminosity surface density and Balmer optical depth in 8 of 11 at $\geq$ 0.8$\sigma$ significance (6 of 11 at $\geq$ 1.0$\sigma$) galaxies. Our spaxels have physical scales ranging from 30 to 80 pc, demonstrating that the correlation between these two variables continues to hold down to spatial scales as low as 30 pc. Using the Spearman's rank correlation coefficient to test for correlation between $\Sigma_{\text{H}\alpha}$ and $\tau_{\text{b}}$ in all the galaxies combined, we find $\rho = 0.39$, indicating a positive correlation at 4$\sigma$ significance. Our low stellar-mass galaxy results are in agreement with observations of emission line regions in larger spiral galaxies, indicating that this relationship is independent of the size of the galaxy hosting the emission line region. The positive correlation between H$\alpha$ luminosity and Balmer optical depth within spaxels is consistent with the hypothesis that young star-forming regions are surrounded by dusty birth-clouds.

### Dependence of Small Planet Frequency on Stellar Metallicity Hidden by Their Prevalence

The dependence of gas giant planet occurrence rate on stellar metallicity has been firmly established. We extend this so-called planet-metallicity correlation to broader ranges of metallicities and planet masses/radii. In particular, we assume that the planet-metallicity correlation is a power law below some critical saturation threshold, and that the probability of hosting at least one planet is unity for stars with metallicity above the threshold. We then are able to explain the discrepancy between the tentative detection and null detection in previous studies regarding the planet-metallicity correlation for small planets. In particular, we find that the null detection of this correlation can be attributed to the combination of high planet occurrence rate and low detection efficiency. Therefore, a planet-metallicity correlation for small planets cannot be ruled out. We propose that stars with metallicities lower than the Solar value are better targets for testing the planet-metallicity correlation for small planets.

### Vortical fluid and $\Lambda$ spin correlations in high-energy heavy-ion collisions

Fermions become polarized in a vortical fluid due to spin-vorticity coupling. The spin polarization density is proportional to the local fluid vorticity at the next-to-leading order of a gradient expansion in a quantum kinetic theory. Spin correlations of two $\Lambda$-hyperons can therefore reveal the vortical structure of the dense matter in high-energy heavy-ion collisions. We employ a (3+1)D viscous hydrodynamic model with event-by-event fluctuating initial conditions from A MultiPhase Transport (AMPT) model to calculate the vorticity distributions and $\Lambda$ spin correlations. The azimuthal correlation of the transverse spin is shown to have a cosine form plus an offset due to a circular structure of the transverse vorticity around the beam direction and global spin polarization. The longitudinal spin correlation shows a structure of vortex-pairing in the transverse plane due to the convective flow of hot spots in the radial direction. The dependence on colliding energy, rapidity, centrality and sensitivity to the shear viscosity are also investigated.

### Vortical fluid and $\Lambda$ spin correlations in high-energy heavy-ion collisions [Cross-Listing]

Fermions become polarized in a vortical fluid due to spin-vorticity coupling. The spin polarization density is proportional to the local fluid vorticity at the next-to-leading order of a gradient expansion in a quantum kinetic theory. Spin correlations of two $\Lambda$-hyperons can therefore reveal the vortical structure of the dense matter in high-energy heavy-ion collisions. We employ a (3+1)D viscous hydrodynamic model with event-by-event fluctuating initial conditions from A MultiPhase Transport (AMPT) model to calculate the vorticity distributions and $\Lambda$ spin correlations. The azimuthal correlation of the transverse spin is shown to have a cosine form plus an offset due to a circular structure of the transverse vorticity around the beam direction and global spin polarization. The longitudinal spin correlation shows a structure of vortex-pairing in the transverse plane due to the convective flow of hot spots in the radial direction. The dependence on colliding energy, rapidity, centrality and sensitivity to the shear viscosity are also investigated.

### Vortical fluid and $\Lambda$ spin correlations in high-energy heavy-ion collisions [Cross-Listing]

Fermions become polarized in a vortical fluid due to spin-vorticity coupling. The spin polarization density is proportional to the local fluid vorticity at the next-to-leading order of a gradient expansion in a quantum kinetic theory. Spin correlations of two $\Lambda$-hyperons can therefore reveal the vortical structure of the dense matter in high-energy heavy-ion collisions. We employ a (3+1)D viscous hydrodynamic model with event-by-event fluctuating initial conditions from A MultiPhase Transport (AMPT) model to calculate the vorticity distributions and $\Lambda$ spin correlations. The azimuthal correlation of the transverse spin is shown to have a cosine form plus an offset due to a circular structure of the transverse vorticity around the beam direction and global spin polarization. The longitudinal spin correlation shows a structure of vortex-pairing in the transverse plane due to the convective flow of hot spots in the radial direction. The dependence on colliding energy, rapidity, centrality and sensitivity to the shear viscosity are also investigated.

### Evidence for a correlation between mass accretion rates onto young stars and the mass of their protoplanetary disks [Replacement]

A relation between the mass accretion rate onto the central young star and the mass of the surrounding protoplanetary disk has long been theoretically predicted and observationally sought. For the first time, we have accurately and homogeneously determined the photospheric parameters, mass accretion rate, and disk mass for an essentially complete sample of young stars with disks in the Lupus clouds. Our work combines the results of surveys conducted with VLT/X-Shooter and ALMA. With this dataset we are able to test a basic prediction of viscous accretion theory, the existence of a linear relation between the mass accretion rate onto the central star and the total disk mass. We find a correlation between the mass accretion rate and the disk dust mass, with a ratio that is roughly consistent with the expected viscous timescale when assuming an interstellar medium (ISM) gas-to-dust ratio. This confirms that mass accretion rates are related to the properties of the outer disk. We find no correlation between mass accretion rates and the disk mass measured by CO isotopologues emission lines, possibly owing to the small number of measured disk gas masses. This suggests that the mm-sized dust mass better traces the total disk mass and that masses derived from CO may be underestimated, at least in some cases.

### Evidence for a correlation between mass accretion rates onto young stars and the mass of their protoplanetary disks

A relation between the mass accretion rate onto the central young star and the mass of the surrounding protoplanetary disk has long been theoretically predicted and observationally sought. For the first time, we have accurately and homogeneously determined the photospheric parameters, the mass accretion rate, and the disk mass for an essentially complete sample of young stars with disks in the Lupus clouds. Our work combines the results of surveys conducted with VLT/X-Shooter and ALMA. With this dataset we are able to test a basic prediction of viscous accretion theory, the existence of a linear relation between the mass accretion rate onto the central star and the total disk mass. We find a correlation between the mass accretion rate and the disk dust mass, with a ratio that is roughly consistent with the expected viscous timescale when assuming an ISM gas-to-dust ratio. This confirms that mass accretion rates are related to the properties of the outer disk. We find no correlation between mass accretion rates and the disk mass measured by CO isotopologues emission lines, possibly due to the small number of measured disk gas masses. This suggests that the mm-sized dust mass better traces the total disk mass and that masses derived from CO may be underestimated, at least in some cases.

### A Correlation Between the Intrinsic Brightness and Average Decay Rate of Gamma-ray Burst X-ray Afterglow Light Curves

We present a correlation between the average temporal decay ({\alpha}X,avg,>200s) and early-time luminosity (LX,200s) of X-ray afterglows of gamma-ray bursts as observed by Swift-XRT. Both quantities are measured relative to a rest frame time of 200 s after the {\gamma}-ray trigger. The luminosity average decay correlation does not depend on specific temporal behavior and contains one scale independent quantity minimizing the role of selection effects. This is a complementary correlation to that discovered by Oates et al. (2012) in the optical light curves observed by Swift-UVOT. The correlation indicates that on average, more luminous X-ray afterglows decay faster than less luminous ones, indicating some relative mechanism for energy dissipation. The X-ray and optical correlations are entirely consistent once corrections are applied and contamination is removed. We explore the possible biases introduced by different light curve morphologies and observational selection effects, and how either geometrical effects or intrinsic properties of the central engine and jet could explain the observed correlation.

### On the Optical -- X-ray correlation from outburst to quiescence in Low Mass X-ray Binaries: the representative cases of V404 Cyg and Cen X-4

Low mass X-ray binaries (LMXBs) show evidence of a global correlation of debated origin between X-ray and optical luminosity. We study for the first time this correlation in two transient LMXBs, the black hole V404 Cyg and the neutron star Cen X-4, over 6 orders of magnitude in X-ray luminosity, from outburst to quiescence. After subtracting the contribution from the companion star, the Cen X-4 data can be described by a single power law correlation of the form $L_{opt}\propto\,L_{X}^{0.44}$, consistent with disk reprocessing. We find a similar correlation slope for V404 Cyg in quiescence (0.46) and a steeper one (0.56) in the outburst hard state of 1989. However, V404 Cyg is about $160-280$ times optically brighter, at a given $3-9$ keV X-ray luminosity, compared to Cen X-4. This ratio is a factor of 10 smaller in quiescence, where the normalization of the V404 Cyg correlation also changes. We show that once the bolometric X-ray emission is considered and the known main differences between V404 Cyg and Cen X-4 are taken into account (a larger compact object mass, accretion disk size, and the presence of a strong jet contribution in the hard state for the black hole system) the two systems lie on the same correlation. In V404 Cyg, the jet dominates spectrally at optical-infrared frequencies during the hard state, but makes a negligible contribution in quiescence, which may account for the change in its correlation slope and normalization. These results provide a benchmark to compare with data from the 2015 outburst of V404 Cyg and, potentially, other transient LMXBs as well.

### Disc-Jet Coupling in the Terzan 5 Neutron Star X-ray Binary EXO 1745$-$248

We present the results of VLA, ATCA, and Swift XRT observations of the 2015 outburst of the transient neutron star X-ray binary (NSXB), EXO 1745$-$248, located in the globular cluster Terzan 5. Combining (near-) simultaneous radio and X-ray measurements we measure a correlation between the radio and X-ray luminosities of $L_R\propto L_X^\beta$ with $\beta=1.68^{+0.10}_{-0.09}$, linking the accretion flow (probed by X-ray luminosity) and the compact jet (probed by radio luminosity). While such a relationship has been studied in multiple black hole X-ray binaries (BHXBs), this work marks only the third NSXB with such a measurement. Constraints on this relationship in NSXBs are strongly needed, as comparing this correlation between different classes of XB systems is key in understanding the properties that affect the jet production process in accreting objects. Our best fit disc-jet coupling index for EXO 1745$-$248 is consistent with the measured correlation in NSXB 4U 1728$-$34 ($\beta=1.5\pm 0.2$) but inconsistent with the correlation we fit using the most recent measurements from the literature of NSXB Aql X-1 ($\beta=0.76^{+0.14}_{-0.15}$). While a similar disc-jet coupling index appears to hold across multiple BHXBs in the hard accretion state, this does not appear to be the case with the three NSXBs measured so far. Additionally, the normalization of the EXO 1745$-$248 correlation is lower than the other two NSXBs, making it one of the most radio faint XBs ever detected in the hard state. We also report the detection of a type-I X-ray burst during this outburst, where the decay timescale is consistent with hydrogen burning.

### A fundamental plane for gamma-ray bursts with X-ray plateaus

A class of long Gamma-Ray Bursts (GRBs) presenting light curves with an extended plateau phase in their X-ray afterglows obeys a correlation between the rest frame end time of the plateau, $T_a$, and its corresponding X-ray luminosity, $L_{a}$, Dainotti et al. (2008). In this work we perform an analysis of a total sample of 176 {\it Swift} GRBs with known redshifts, exhibiting afterglow plateaus. By adding a third parameter, that is the peak luminosity in the prompt emission, $L_{peak}$, we discover the existence of a new three parameter correlation, a GRB fundamental plane'. The scatter of data about this plane becomes smaller when a class-specific GRB sample is defined. This sample of 122 GRBs is selected from the total sample by excluding GRBs with associated Supernovae (SNe), X-ray flashes and short GRBs with extended emission. Moreover, we further limit our analysis to GRBs with lightcurves having good data coverage and almost flat plateaus, 40 GRBs forming our gold sample'. The intrinsic scatter, $\sigma_{int}=0.27 \pm 0.04$, for the three-parameter correlation for this last subclass is more than twice smaller than the value for the $L_{a}-T_a$ one, making this the tightest three parameter correlation involving the afterglow plateau phase. Finally, we also show that a slightly less tight correlation is present between $L_{peak}$ and a proxy for the total energy emitted during the plateau phase, $L_a T_a$, confirming the existence of an energy scaling between prompt and afterglow phases.

### Statistical Properties of Quasi-Periodic Pulsations in White-Light Flares Observed With Kepler

We embark on a study of quasi-periodic pulsations (QPPs) in the decay phase of white-light stellar flares observed by Kepler. Out of the 1439 flares on 216 different stars detected in the short-cadence data using an automated search, 56 flares are found to have pronounced QPP-like signatures in the light curve, of which 11 have stable decaying oscillations. No correlation is found between the QPP period and the stellar temperature, radius, rotation period and surface gravity, suggesting that the QPPs are independent of global stellar parameters. Hence they are likely to be the result of processes occurring in the local environment. There is also no significant correlation between the QPP period and flare energy, however there is evidence that the period scales with the QPP decay time for the Gaussian damping scenario, but not to a significant degree for the exponentially damped case. This same scaling has been observed for MHD oscillations on the Sun, suggesting that they could be the cause of the QPPs in those flares. Scaling laws of the flare energy are also investigated, supporting previous reports of a strong correlation between the flare energy and stellar temperature/radius. A negative correlation between the flare energy and stellar surface gravity is also found.

### Neutron drops radii probed by the neutron skin thickness of nuclei [Cross-Listing]

Multi-neutron systems are crucial to understand the physics of neutron-rich nuclei and neutron stars. Neutron drops, neutrons confined in an external field, are investigated systematically in both non-relativistic and relativistic density functional theories and with ab initio calculations. We demonstrate a strong linear correlation, which is universal in the realm of mean-field models, between the root-mean-square (rms) radii of neutron drops and the neutron skin thickness of Pb-208 and Ca-48; i.e., the difference between the neutron and proton rms radii of a nucleus. Due to its high quality, this correlation can be used to deduce the radii of neutron drops from the measured neutron skin thickness in a model-independent way, and the radii obtained for neutron drops can provide a useful constraint for realistic three neutron forces. This correlation, together with high- precision measurements of the neutron skin thicknesses of Pb-208 and Ca-48, will have an enduring impact on the understanding of multi-neutron interactions, neutron-rich nuclei, neutron stars, etc.

### Neutron drops radii probed by the neutron skin thickness of nuclei

Multi-neutron systems are crucial to understand the physics of neutron-rich nuclei and neutron stars. Neutron drops, neutrons confined in an external field, are investigated systematically in both non-relativistic and relativistic density functional theories and with ab initio calculations. We demonstrate a strong linear correlation, which is universal in the realm of mean-field models, between the root-mean-square (rms) radii of neutron drops and the neutron skin thickness of Pb-208 and Ca-48; i.e., the difference between the neutron and proton rms radii of a nucleus. Due to its high quality, this correlation can be used to deduce the radii of neutron drops from the measured neutron skin thickness in a model-independent way, and the radii obtained for neutron drops can provide a useful constraint for realistic three neutron forces. This correlation, together with high- precision measurements of the neutron skin thicknesses of Pb-208 and Ca-48, will have an enduring impact on the understanding of multi-neutron interactions, neutron-rich nuclei, neutron stars, etc.

### Ultra faint dwarf galaxies: an arena for testing dark matter versus modified gravity

The scenario consistent with a wealth of observations for the missing mass problem is that of weakly interacting dark matter particles. However, arguments or proposals for a Newtonian or relativistic modified gravity scenario continue to be made. A distinguishing characteristic between the two scenarios is that dark matter particles can produce a gravitational effect, in principle, without the need of baryons while this is not the case for the modified gravity scenario where such an effect must be correlated with the amount of baryonic matter. We consider here ultra-faint dwarf (UFD) galaxies as a promising arena to test the two scenarios based on the above assertion. We compare the correlation of the luminosity with the velocity dispersion between samples of UFD and non-UFD galaxies, finding a trend of loss of correlation for the UFD galaxies. For example, we find for 28 non-UFD galaxies a strong correlation coefficient of -0.688 which drops to -0.077 for the 23 UFD galaxies. Incoming and future data will determine whether the observed stochasticity for UFD galaxies is physical or due to systematics in the data. Such a loss of correlation (if it is to persist) is possible and consistent with the dark matter scenario for UFD galaxies but would constitute a new challenge for the modified gravity scenario.

### Ultra faint dwarf galaxies: an arena for testing dark matter versus modified gravity [Cross-Listing]

The scenario consistent with a wealth of observations for the missing mass problem is that of weakly interacting dark matter particles. However, arguments or proposals for a Newtonian or relativistic modified gravity scenario continue to be made. A distinguishing characteristic between the two scenarios is that dark matter particles can produce a gravitational effect, in principle, without the need of baryons while this is not the case for the modified gravity scenario where such an effect must be correlated with the amount of baryonic matter. We consider here ultra-faint dwarf (UFD) galaxies as a promising arena to test the two scenarios based on the above assertion. We compare the correlation of the luminosity with the velocity dispersion between samples of UFD and non-UFD galaxies, finding a trend of loss of correlation for the UFD galaxies. For example, we find for 28 non-UFD galaxies a strong correlation coefficient of -0.688 which drops to -0.077 for the 23 UFD galaxies. Incoming and future data will determine whether the observed stochasticity for UFD galaxies is physical or due to systematics in the data. Such a loss of correlation (if it is to persist) is possible and consistent with the dark matter scenario for UFD galaxies but would constitute a new challenge for the modified gravity scenario.

### The influence of mergers and ram-pressure stripping on black hole-bulge correlations

We analyse the scatter in the correlation between super-massive black hole (SMBH) mass and bulge stellar mass of the host galaxy, and infer that it cannot be accounted for by mergers alone. The merger-only scenario, where small galaxies merge to establish a proportionality relation between the SMBH and bulge masses, leads to a scatter around the linear proportionality line that increases with the square root of the SMBH (or bulge) mass. By examining a sample of 96 galaxies we find that the intrinsic scatter increases more rapidly than expected from the merger-only scenario. The correlation between SMBH masses and their host galaxy properties is therefore more likely to be determined by a negative feedback mechanism that is driven by an active galactic nucleus. We find a hint that some galaxies with missing stellar mass reside close to the centre of clusters. We propose that ram-pressure stripping of gas off the young galaxy as it moves near the cluster centre, might explain the missing stellar mass at later times.

### Isoscalar pairing correlation in $^{100}{\rm Sn}+p+n$ system

We discuss the isoscalar $T=0, S=1$ pairing correlation in the low-lying states of $^{102}{\rm Sb}={}^{100}{\rm Sn}+p+n$ nucleus. To this end, we employ ${\rm core}+p+n$ three-body model with the model space constructed by self-consistent mean-field calculations. The model is developed with both non-relativistic and relativistic effective interactions, the latter of which are found to be more realistic for the present case due to the pseudo-spin symmetry. It turns out that the $(L,S,T)=(0,1,0)$ pairing scheme is strongly hindered in $^{102}$Sb with the relativistic model because of the near degeneracy of the $g_{7/2}$ and $d_{5/2}$ orbitals in the valence space. This pair-breaking effect is clearly seen in the charge-exchange Gamow-Teller-type transitions rather than in the binding energies of $T=0$ and $T=1$ states.

We investigate the $\Lambda\Lambda$ and $K^-p$ intensity correlations in high-energy heavy-ion collisions. First, we examine the dependence of the $\Lambda\Lambda$ correlation on the $\Lambda\Lambda$ interaction and the $\Lambda\Lambda$ pair purity probability $\lambda$. For small $\lambda$, the correlation function needs to be suppressed by the $\Lambda\Lambda$ interaction in order to explain the recently measured $\Lambda\Lambda$ correlation data. By comparison, when we adopt the $\lambda$ value evaluated from the experimentally measured $\Sigma^0/\Lambda$ ratio, the correlation function needs to be enhanced by the interaction. We demonstrate that these two cases correspond to the two analyses which gave opposite signs of the $\Lambda\Lambda$ scattering length. Next, we discuss the $K^-p$ correlation function. By using the local $\bar{K}N$ potential which reproduces the kaonic hydrogen data by SIDDHARTA, we obtain the $K^-p$ correlation function. We find that the $K^-p$ correlation can provide a complementary information with the $K^{-}p$ elastic scattering amplitude.

We investigate the $\Lambda\Lambda$ and $K^-p$ intensity correlations in high-energy heavy-ion collisions. First, we examine the dependence of the $\Lambda\Lambda$ correlation on the $\Lambda\Lambda$ interaction and the $\Lambda\Lambda$ pair purity probability $\lambda$. For small $\lambda$, the correlation function needs to be suppressed by the $\Lambda\Lambda$ interaction in order to explain the recently measured $\Lambda\Lambda$ correlation data. By comparison, when we adopt the $\lambda$ value evaluated from the experimentally measured $\Sigma^0/\Lambda$ ratio, the correlation function needs to be enhanced by the interaction. We demonstrate that these two cases correspond to the two analyses which gave opposite signs of the $\Lambda\Lambda$ scattering length. Next, we discuss the $K^-p$ correlation function. By using the local $\bar{K}N$ potential which reproduces the kaonic hydrogen data by SIDDHARTA, we obtain the $K^-p$ correlation function. We find that the $K^-p$ correlation can provide a complementary information with the $K^{-}p$ elastic scattering amplitude.

We investigate the $\Lambda\Lambda$ and $K^-p$ intensity correlations in high-energy heavy-ion collisions. First, we examine the dependence of the $\Lambda\Lambda$ correlation on the $\Lambda\Lambda$ interaction and the $\Lambda\Lambda$ pair purity probability $\lambda$. For small $\lambda$, the correlation function needs to be suppressed by the $\Lambda\Lambda$ interaction in order to explain the recently measured $\Lambda\Lambda$ correlation data. By comparison, when we adopt the $\lambda$ value evaluated from the experimentally measured $\Sigma^0/\Lambda$ ratio, the correlation function needs to be enhanced by the interaction. We demonstrate that these two cases correspond to the two analyses which gave opposite signs of the $\Lambda\Lambda$ scattering length. Next, we discuss the $K^-p$ correlation function. By using the local $\bar{K}N$ potential which reproduces the kaonic hydrogen data by SIDDHARTA, we obtain the $K^-p$ correlation function. We find that the $K^-p$ correlation can provide a complementary information with the $K^{-}p$ elastic scattering amplitude.

We investigate the $\Lambda\Lambda$ and $K^-p$ intensity correlations in high-energy heavy-ion collisions. First, we examine the dependence of the $\Lambda\Lambda$ correlation on the $\Lambda\Lambda$ interaction and the $\Lambda\Lambda$ pair purity probability $\lambda$. For small $\lambda$, the correlation function needs to be suppressed by the $\Lambda\Lambda$ interaction in order to explain the recently measured $\Lambda\Lambda$ correlation data. By comparison, when we adopt the $\lambda$ value evaluated from the experimentally measured $\Sigma^0/\Lambda$ ratio, the correlation function needs to be enhanced by the interaction. We demonstrate that these two cases correspond to the two analyses which gave opposite signs of the $\Lambda\Lambda$ scattering length. Next, we discuss the $K^-p$ correlation function. By using the local $\bar{K}N$ potential which reproduces the kaonic hydrogen data by SIDDHARTA, we obtain the $K^-p$ correlation function. We find that the $K^-p$ correlation can provide a complementary information with the $K^{-}p$ elastic scattering amplitude.

We investigate the $\Lambda\Lambda$ and $K^-p$ intensity correlations in high-energy heavy-ion collisions. First, we examine the dependence of the $\Lambda\Lambda$ correlation on the $\Lambda\Lambda$ interaction and the $\Lambda\Lambda$ pair purity probability $\lambda$. For small $\lambda$, the correlation function needs to be suppressed by the $\Lambda\Lambda$ interaction in order to explain the recently measured $\Lambda\Lambda$ correlation data. By comparison, when we adopt the $\lambda$ value evaluated from the experimentally measured $\Sigma^0/\Lambda$ ratio, the correlation function needs to be enhanced by the interaction. We demonstrate that these two cases correspond to the two analyses which gave opposite signs of the $\Lambda\Lambda$ scattering length. Next, we discuss the $K^-p$ correlation function. By using the local $\bar{K}N$ potential which reproduces the kaonic hydrogen data by SIDDHARTA, we obtain the $K^-p$ correlation function. We find that the $K^-p$ correlation can provide a complementary information with the $K^{-}p$ elastic scattering amplitude.

We investigate the $\Lambda\Lambda$ and $K^-p$ intensity correlations in high-energy heavy-ion collisions. First, we examine the dependence of the $\Lambda\Lambda$ correlation on the $\Lambda\Lambda$ interaction and the $\Lambda\Lambda$ pair purity probability $\lambda$. For small $\lambda$, the correlation function needs to be suppressed by the $\Lambda\Lambda$ interaction in order to explain the recently measured $\Lambda\Lambda$ correlation data. By comparison, when we adopt the $\lambda$ value evaluated from the experimentally measured $\Sigma^0/\Lambda$ ratio, the correlation function needs to be enhanced by the interaction. We demonstrate that these two cases correspond to the two analyses which gave opposite signs of the $\Lambda\Lambda$ scattering length. Next, we discuss the $K^-p$ correlation function. By using the local $\bar{K}N$ potential which reproduces the kaonic hydrogen data by SIDDHARTA, we obtain the $K^-p$ correlation function. We find that the $K^-p$ correlation can provide a complementary information with the $K^{-}p$ elastic scattering amplitude.

### Quantum canonical ensemble and correlation femtoscopy at fixed multiplicities [Cross-Listing]

Identical particle correlations at fixed multiplicity are considered by means of quantum canonical ensemble of finite systems. We calculate one-particle momentum spectra and two-particle Bose-Einstein correlation functions in the ideal gas by using recurrence relations for the partition function. Within such a model we investigate the validity of the thermal Wick theorem and its applicability for decomposition of the two-particle distribution function. A dependence of the Bose-Einstein correlation parameters on the average momentum of the particle pair is also investigated. Specifically, we present the analytical formulas that allow one to estimate the effect of suppressing the correlation functions in a finite canonical system. The results can be used for the femtoscopy analysis of the A+A and p+p collisions with selected (fixed) multiplicity.

### Quantum canonical ensemble and correlation femtoscopy at fixed multiplicities [Cross-Listing]

Identical particle correlations at fixed multiplicity are considered by means of quantum canonical ensemble of finite systems. We calculate one-particle momentum spectra and two-particle Bose-Einstein correlation functions in the ideal gas by using recurrence relations for the partition function. Within such a model we investigate the validity of the thermal Wick theorem and its applicability for decomposition of the two-particle distribution function. A dependence of the Bose-Einstein correlation parameters on the average momentum of the particle pair is also investigated. Specifically, we present the analytical formulas that allow one to estimate the effect of suppressing the correlation functions in a finite canonical system. The results can be used for the femtoscopy analysis of the A+A and p+p collisions with selected (fixed) multiplicity.

### Quantum canonical ensemble and correlation femtoscopy at fixed multiplicities

Identical particle correlations at fixed multiplicity are considered by means of quantum canonical ensemble of finite systems. We calculate one-particle momentum spectra and two-particle Bose-Einstein correlation functions in the ideal gas by using recurrence relations for the partition function. Within such a model we investigate the validity of the thermal Wick theorem and its applicability for decomposition of the two-particle distribution function. A dependence of the Bose-Einstein correlation parameters on the average momentum of the particle pair is also investigated. Specifically, we present the analytical formulas that allow one to estimate the effect of suppressing the correlation functions in a finite canonical system. The results can be used for the femtoscopy analysis of the A+A and p+p collisions with selected (fixed) multiplicity.

### Quantum canonical ensemble and correlation femtoscopy at fixed multiplicities [Cross-Listing]

Identical particle correlations at fixed multiplicity are considered by means of quantum canonical ensemble of finite systems. We calculate one-particle momentum spectra and two-particle Bose-Einstein correlation functions in the ideal gas by using recurrence relations for the partition function. Within such a model we investigate the validity of the thermal Wick theorem and its applicability for decomposition of the two-particle distribution function. A dependence of the Bose-Einstein correlation parameters on the average momentum of the particle pair is also investigated. Specifically, we present the analytical formulas that allow one to estimate the effect of suppressing the correlation functions in a finite canonical system. The results can be used for the femtoscopy analysis of the A+A and p+p collisions with selected (fixed) multiplicity.

### Supermassive black holes and their host spheroids III. The $M_{BH} - n_{sph}$ correlation

The S\'ersic $R^{1/n}$ model is the best approximation known to date for describing the light distribution of stellar spheroidal and disk components, with the S\'ersic index $n$ providing a direct measure of the central radial concentration of stars. The S\'ersic index of a galaxy's spheroidal component, $n_{sph}$, has been shown to tightly correlate with the mass of the central supermassive black hole, $M_{BH}$. The $M_{BH}-n_{sph}$ correlation is also expected from other two well known scaling relations involving the spheroid luminosity, $L_{sph}$: the $L_{sph}-n_{sph}$ and the $M_{BH}-L_{sph}$. Obtaining an accurate estimate of the spheroid S\'ersic index requires a careful modelling of a galaxy's light distribution and some studies have failed to recover a statistically significant $M_{BH}-n_{sph}$ correlation. With the aim of re-investigating the $M_{BH}-n_{sph}$ and other black hole mass scaling relations, we performed a detailed (i.e.~bulge, disks, bars, spiral arms, rings, halo, nucleus, etc.) decomposition of 66 galaxies, with directly measured black hole masses, that had been imaged at $3.6\rm~\mu m$ with Spitzer. In this paper, the third of this series, we present an analysis of the $L_{sph}-n_{sph}$ and $M_{BH}-n_{sph}$ diagrams. While early-type (elliptical+lenticular) and late-type (spiral) galaxies split into two separate relations in the $L_{sph}-n_{sph}$ and $M_{BH}-L_{sph}$ diagrams, they reunite into a single $M_{BH} \propto n_{sph}^{3.39 \pm 0.15}$ sequence with relatively small intrinsic scatter ($\epsilon \simeq 0.25 \rm~dex$). The black hole mass appears to be closely related to the spheroid central concentration of stars, which mirrors the inner gradient of the spheroid gravitational potential.

### Rapidity bin multiplicity correlations from a multi-phase transport model

The central-arbitrary bin and forward-backward bin multiplicity correlation patterns for Au+Au collisions at $\sqrt{s_{NN}}$= $7.7-62.4$ GeV are investigated within a multi-phase transport (AMPT) model. An interesting observation is that for $\sqrt{s_{NN}} <19.6$ GeV Au+Au collisions, these two correlation patterns both have an increase with the pseudorapidity gap, while for $\sqrt{s_{NN}} >19.6$ GeV Au+Au collisions, they decrease. We mainly discuss the influence of different evolution stages of collision system on the central-arbitrary bin correlations, such as the initial conditions, partonic scatterings, hadronization scheme and hadronic scatterings. Our results show that the central-arbitrary bin multiplicity correlations have different responses to partonic phase and hadronic phase, which can be suggested as a good probe to explore the dynamical evolution mechanism of the hot dense matter in high-energy heavy-ion collisions.

### Rapidity bin multiplicity correlations from a multi-phase transport model [Cross-Listing]

The central-arbitrary bin and forward-backward bin multiplicity correlation patterns for Au+Au collisions at $\sqrt{s_{NN}}$= $7.7-62.4$ GeV are investigated within a multi-phase transport (AMPT) model. An interesting observation is that for $\sqrt{s_{NN}} <19.6$ GeV Au+Au collisions, these two correlation patterns both have an increase with the pseudorapidity gap, while for $\sqrt{s_{NN}} >19.6$ GeV Au+Au collisions, they decrease. We mainly discuss the influence of different evolution stages of collision system on the central-arbitrary bin correlations, such as the initial conditions, partonic scatterings, hadronization scheme and hadronic scatterings. Our results show that the central-arbitrary bin multiplicity correlations have different responses to partonic phase and hadronic phase, which can be suggested as a good probe to explore the dynamical evolution mechanism of the hot dense matter in high-energy heavy-ion collisions.

### The Variable Line Width of Achernar

Spectroscopic observations of Achernar over the past decades, have shown the photospheric line width, as measured by the rotational parameter $v \sin i$, to vary in correlation with the emission activity. Here we present new observations, covering the most recent activity phase, and further archival data collected from the archives. The $v \sin i$ variation is confirmed. On the basis of the available data it cannot be decided with certainty whether the increased line width precedes the emission activity, i.e. is a signature of the ejection mechanism, or postdates is, which would make it a signature of re-accretion of some of the disk-material. However, the observed evidence leans towards the re-accretion hypothesis. Two further stars showing the effect of variable line width in correlation with emission activity, namely 66 Oph and $\pi$ Aqr, are presented as well.

### The SLUGGS Survey: globular clusters and the dark matter content of early-type galaxies

A strong correlation exists between the total mass of a globular cluster (GC) system and the virial halo mass of the host galaxy. However, the total halo mass in this correlation is a statistical measure conducted on spatial scales that are some ten times that of a typical GC system. Here we investigate the connection between GC systems and galaxy's dark matter on comparable spatial scales, using dynamical masses measured on a galaxy-by-galaxy basis. Our sample consists of 17 well-studied massive (stellar mass $\sim$10$^{11}$ M$_{\odot}$) early-type galaxies from the SLUGGS survey. We find the strongest correlation to be that of the blue (metal-poor) GC subpopulation and the dark matter content. This correlation implies that the dark matter mass of a galaxy can be estimated to within a factor of two from careful imaging of its GC system. The ratio of the GC system mass to that of the enclosed dark matter is nearly constant. We also find a strong correlation between the fraction of blue GCs and the fraction of enclosed dark matter, so that a typical galaxy with a blue GC fraction of 60 per cent has a dark matter fraction of 86 per cent over similar spatial scales. Both halo growth and removal (via tidal stripping) may play some role in shaping this trend. In the context of the two-phase model for galaxy formation, we find galaxies with the highest fractions of accreted stars to have higher dark matter fractions for a given fraction of blue GCs.

### Extreme blazars as counterparts of IceCube astrophysical neutrinos

We explore the correlation of $\gamma$-ray emitting blazars with IceCube neutrinos by using three very recently completed, and independently built, catalogues and the latest neutrino lists. We introduce a new observable, namely the number of neutrino events with at least one $\gamma$-ray counterpart, $N_{\nu}$. In all three catalogues we consistently observe a positive fluctuation of $N_{\nu}$ with respect to the mean random expectation at a significance level of $0.4 - 1.3$ per cent. This applies only to extreme blazars, namely strong, very high energy $\gamma$-ray sources of the high energy peaked type, and implies a model-independent fraction of the current IceCube signal $\sim 10 - 20$ per cent. An investigation of the hybrid photon -- neutrino spectral energy distributions of the most likely candidates reveals a set of $\approx 5$ such sources, which could be linked to the corresponding IceCube neutrinos. Other types of blazars, when testable, give null correlation results. Although we could not perform a similar correlation study for Galactic sources, we have also identified two (further) strong Galactic $\gamma$-ray sources as most probable counterparts of IceCube neutrinos through their hybrid spectral energy distributions. We have reasons to believe that our blazar results are not constrained by the $\gamma$-ray samples but by the neutrino statistics, which means that the detection of more astrophysical neutrinos could turn this first hint into a discovery.

### Extreme blazars as counterparts of IceCube astrophysical neutrinos [Cross-Listing]

We explore the correlation of $\gamma$-ray emitting blazars with IceCube neutrinos by using three very recently completed, and independently built, catalogues and the latest neutrino lists. We introduce a new observable, namely the number of neutrino events with at least one $\gamma$-ray counterpart, $N_{\nu}$. In all three catalogues we consistently observe a positive fluctuation of $N_{\nu}$ with respect to the mean random expectation at a significance level of $0.4 - 1.3$ per cent. This applies only to extreme blazars, namely strong, very high energy $\gamma$-ray sources of the high energy peaked type, and implies a model-independent fraction of the current IceCube signal $\sim 10 - 20$ per cent. An investigation of the hybrid photon -- neutrino spectral energy distributions of the most likely candidates reveals a set of $\approx 5$ such sources, which could be linked to the corresponding IceCube neutrinos. Other types of blazars, when testable, give null correlation results. Although we could not perform a similar correlation study for Galactic sources, we have also identified two (further) strong Galactic $\gamma$-ray sources as most probable counterparts of IceCube neutrinos through their hybrid spectral energy distributions. We have reasons to believe that our blazar results are not constrained by the $\gamma$-ray samples but by the neutrino statistics, which means that the detection of more astrophysical neutrinos could turn this first hint into a discovery.

### Extreme blazars as counterparts of IceCube astrophysical neutrinos [Cross-Listing]

We explore the correlation of $\gamma$-ray emitting blazars with IceCube neutrinos by using three very recently completed, and independently built, catalogues and the latest neutrino lists. We introduce a new observable, namely the number of neutrino events with at least one $\gamma$-ray counterpart, $N_{\nu}$. In all three catalogues we consistently observe a positive fluctuation of $N_{\nu}$ with respect to the mean random expectation at a significance level of $0.4 - 1.3$ per cent. This applies only to extreme blazars, namely strong, very high energy $\gamma$-ray sources of the high energy peaked type, and implies a model-independent fraction of the current IceCube signal $\sim 10 - 20$ per cent. An investigation of the hybrid photon -- neutrino spectral energy distributions of the most likely candidates reveals a set of $\approx 5$ such sources, which could be linked to the corresponding IceCube neutrinos. Other types of blazars, when testable, give null correlation results. Although we could not perform a similar correlation study for Galactic sources, we have also identified two (further) strong Galactic $\gamma$-ray sources as most probable counterparts of IceCube neutrinos through their hybrid spectral energy distributions. We have reasons to believe that our blazar results are not constrained by the $\gamma$-ray samples but by the neutrino statistics, which means that the detection of more astrophysical neutrinos could turn this first hint into a discovery.

### A pragmatic Bayesian perspective on correlation analysis: The exoplanetary gravity - stellar activity case

We apply the Bayesian framework to assess the presence of a correlation between two quantities. To do so, we estimate the probability distribution of the parameter of interest, $\rho$, characterizing the strength of the correlation. We provide an implementation of these ideas and concepts using python programming language and the pyMC module in a very short ($\sim$130 lines of code, heavily commented) and user-friendly program. We used this tool to assess the presence and properties of the correlation between planetary surface gravity and stellar activity level as measured by the log($R'_{\mathrm{HK}}$) indicator. The results of the Bayesian analysis are qualitatively similar to those obtained via p-value analysis, and support the presence of a correlation in the data. The results are more robust in their derivation and more informative, revealing interesting features such as asymmetric posterior distributions or markedly different credible intervals, and allowing for a deeper exploration. We encourage the reader interested in this kind of problem to apply our code to his/her own scientific problems. The full understanding of what the Bayesian framework is can only be gained through the insight that comes by handling priors, assessing the convergence of Monte Carlo runs, and a multitude of other practical problems. We hope to contribute so that Bayesian analysis becomes a tool in the toolkit of researchers, and they understand by experience its advantages and limitations.

### Transverse momentum-flow correlations in relativistic heavy-ion collisions [Replacement]

The correlation between the transverse momentum and the azimuthal asymmetry the flow is studied. A correlation coefficient is defined between the average transverse momentum of hadrons emitted in an event and the square of the elliptic or triangular flow coefficient. The hydrodynamic model predicts a positive correlation of the transverse momentum with the elliptic flow, and almost no correlation with the triangular flow in Pb-Pb collisions at LHC energies. In p-Pb collisions the new correlation observable is very sensitive to the mechanism of energy deposition in the first stage of the collision.

### Transverse momentum-flow correlations in relativistic heavy-ion collisions [Replacement]

The correlation between the transverse momentum and the azimuthal asymmetry the flow is studied. A correlation coefficient is defined between the average transverse momentum of hadrons emitted in an event and the square of the elliptic or triangular flow coefficient. The hydrodynamic model predicts a positive correlation of the transverse momentum with the elliptic flow, and almost no correlation with the triangular flow in Pb-Pb collisions at LHC energies. In p-Pb collisions the new correlation observable is very sensitive to the mechanism of energy deposition in the first stage of the collision.

### Transverse momentum-flow correlations in relativistic heavy-ion collisions [Replacement]

The correlation between the transverse momentum and the azimuthal asymmetry the flow is studied. A correlation coefficient is defined between the average transverse momentum of hadrons emitted in an event and the square of the elliptic or triangular flow coefficient. The hydrodynamic model predicts a positive correlation of the transverse momentum with the elliptic flow, and almost no correlation with the triangular flow in Pb-Pb collisions at LHC energies. In p-Pb collisions the new correlation observable is very sensitive to the mechanism of energy deposition in the first stage of the collision.

### Transverse momentum-flow correlations in relativistic heavy-ion collisions [Cross-Listing]

The correlation between the transverse momentum and the azimuthal asymmetry the flow is studied. A correlation coefficient is defined between the average transverse momentum of hadrons emitted in an event and the square of the elliptic or triangular flow coefficient. The hydrodynamic model predicts a positive correlation of the transverse momentum with the elliptic flow, and almost no correlation with the triangular flow in Pb-Pb collisions at LHC energies. In p-Pb collisions the new correlation observable is very sensitive to the mechanism of energy deposition in the first stage of the collision.

### Transverse momentum-flow correlations in relativistic heavy-ion collisions

The correlation between the transverse momentum and the azimuthal asymmetry the flow is studied. A correlation coefficient is defined between the average transverse momentum of hadrons emitted in an event and the square of the elliptic or triangular flow coefficient. The hydrodynamic model predicts a positive correlation of the transverse momentum with the elliptic flow, and almost no correlation with the triangular flow in Pb-Pb collisions at LHC energies. In p-Pb collisions the new correlation observable is very sensitive to the mechanism of energy deposition in the first stage of the collision.

### Transverse momentum-flow correlations in relativistic heavy-ion collisions [Cross-Listing]

The correlation between the transverse momentum and the azimuthal asymmetry the flow is studied. A correlation coefficient is defined between the average transverse momentum of hadrons emitted in an event and the square of the elliptic or triangular flow coefficient. The hydrodynamic model predicts a positive correlation of the transverse momentum with the elliptic flow, and almost no correlation with the triangular flow in Pb-Pb collisions at LHC energies. In p-Pb collisions the new correlation observable is very sensitive to the mechanism of energy deposition in the first stage of the collision.

### The spatially-resolved correlation between [NII] 205 {\mu}m line emission and the 24 {\mu}m continuum in nearby galaxies

A correlation between the 24 {\mu}m continuum and the [NII] 205 {\mu}m line emission may arise if both quantities trace the star formation activity on spatially-resolved scales within a galaxy, yet has so far only been observed in the nearby edge-on spiral galaxy NGC 891. We therefore assess whether the [NII] 205 - 24 {\mu}m emission correlation has some physical origin or is merely an artefact of line-of-sight projection effects in an edge-on disc. We search for the presence of a correlation in Herschel and Spitzer observations of two nearby face-on galaxies, M51 and M83, and the interacting Antennae galaxies NGC 4038 and 4039. We show that not only is this empirical relationship also observed in face-on galaxies, but also that the correlation appears to be governed by the star formation rate (SFR). Both the nuclear starburst in M83 and the merger-induced star formation in NGC 4038/9 exhibit less [NII] emission per unit SFR surface density than the normal star-forming discs. These regions of intense star formation exhibit stronger ionization parameters, as traced by the 70/160 {\mu}m far-infrared colour, that suggest the presence of higher ionization lines that may become more important for gas cooling, thereby reducing the observed [NII] 205 {\mu}m line emission in regions with higher star formation rates. Finally, we present a general relation between the [NII] 205 {\mu}m line flux density and SFR density for normal star-forming galaxies, yet note that future studies should extend this analysis by including observations with wider spatial coverage for a larger sample of galaxies.

### Measurement of spin correlation between top and antitop quarks produced in $p\bar{p}$ collisions at $\sqrt{s} = 1.96$ TeV [Replacement]

We present a measurement of the correlation between the spins of t and tbar quarks produced in proton-antiproton collisions at the Tevatron Collider at a center-of-mass energy of 1.96 TeV. We apply a matrix element technique to dilepton and single-lepton+jets final states in data accumulated with the D0 detector that correspond to an integrated luminosity of 9.7 fb$^{-1}$. The measured value of the correlation coefficient in the off-diagonal basis, $O_{off} = 0.89 \pm 0.22$ (stat + syst), is in agreement with the standard model prediction, and represents evidence for a top-antitop quark spin correlation difference from zero at a level of 4.2 standard deviations.

### Measurement of spin correlation between top and antitop quarks produced in $p\bar{p}$ collisions at $\sqrt{s} = 1.96$ TeV

We present a measurement of the correlation between the spins of t and tbar quarks produced in proton-antiproton collisions at the Tevatron Collider at a center-of-mass energy of 1.96 TeV. We apply a matrix element technique to dilepton and single-lepton+jets final states in data accumulated with the D0 detector that correspond to an integrated luminosity of 9.7 fb$^{-1}$. The measured value of the correlation coefficient in the off-diagonal basis, $O_{off} = 0.89 \pm 0.22$ (stat + syst), is in agreement with the standard model prediction, and represents evidence for a top-antitop quark spin correlation difference from zero at a level of 4.2 standard deviations.

### An Empirical Relation Between The Large-Scale Magnetic Field And The Dynamical Mass In Galaxies

The origin and evolution of cosmic magnetic fields as well as the influence of the magnetic fields on the evolution of galaxies are unknown. Though not without challenges, the dynamo theory can explain the large-scale coherent magnetic fields which govern galaxies, but observational evidence for the theory is so far very scarce. Putting together the available data of non-interacting, non-cluster galaxies with known large-scale magnetic fields, we find a tight correlation between the integrated polarized flux density and the rotation speed, v(rot), of galaxies. This leads to an almost linear correlation between the large-scale magnetic field B and v(rot), assuming that the number of cosmic ray electrons is proportional to the star formation rate. This correlation cannot be attributed to an active linear dynamo processes, as no correlation holds with shear or angular speed. It indicates instead a coupling between the large-scale magnetic field and the dynamical mass of the galaxies, B~M(dyn)^{0.2-0.3}. Hence, faster rotating and/or more massive galaxies have stronger large-scale magnetic fields. The observed B-v(rot) correlation shows that the anisotropic turbulent magnetic field dominates B in fast rotating galaxies as the turbulent magnetic field, coupled with gas, is enhanced and ordered due to the strong gas compression and/or shear in these systems. This study supports a stationary condition and no further evolution of the large-scale magnetic field as long as the dynamical mass of galaxies is constant.

### An Empirical Relation Between The Large-Scale Magnetic Field And The Dynamical Mass In Galaxies [Replacement]

The origin and evolution of cosmic magnetic fields as well as the influence of the magnetic fields on the evolution of galaxies are unknown. Though not without challenges, the dynamo theory can explain the large-scale coherent magnetic fields which govern galaxies, but observational evidence for the theory is so far very scarce. Putting together the available data of non-interacting, non-cluster galaxies with known large-scale magnetic fields, we find a tight correlation between the integrated polarized flux density, S(PI), and the rotation speed, v(rot), of galaxies. This leads to an almost linear correlation between the large-scale magnetic field B and v(rot), assuming that the number of cosmic ray electrons is proportional to the star formation rate, and a super-linear correlation assuming equipartition between magnetic fields and cosmic rays. This correlation cannot be attributed to an active linear alpha-Omega dynamo, as no correlation holds with global shear or angular speed. It indicates instead a coupling between the large-scale magnetic field and the dynamical mass of the galaxies, B ~ M^(0.25-0.4). Hence, faster rotating and/or more massive galaxies have stronger large-scale magnetic fields. The observed B-v(rot) correlation shows that the anisotropic turbulent magnetic field dominates B in fast rotating galaxies as the turbulent magnetic field, coupled with gas, is enhanced and ordered due to the strong gas compression and/or local shear in these systems. This study supports an stationary condition for the large-scale magnetic field as long as the dynamical mass of galaxies is constant.

### Energy calibration via correlation [Cross-Listing]

The main task of an energy calibration is to find a relation between pulse-height values and the corresponding energies. Doing this for each pulse-height channel individually requires an elaborated input spectrum with an excellent counting statistics and a sophisticated data analysis. This work presents an easy to handle energy calibration process which can operate reliably on calibration measurements with low counting statistics. The method uses a parameter based model for the energy calibration and concludes on the optimal parameters of the model by finding the best correlation between the measured pulse-height spectrum and multiple synthetic pulse-height spectra which are constructed with different sets of calibration parameters. A CdTe-based semiconductor detector and the line emissions of an 241 Am source were used to test the performance of the correlation method in terms of systematic calibration errors for different counting statistics. Up to energies of 60 keV systematic errors were measured to be less than 0.1 keV. Energy calibration via correlation can be applied to any kind of calibration spectra and shows a robust behavior at low counting statistics. It enables a fast and accurate calibration that can be used to monitor the spectroscopic properties of a detector system in near realtime.