# Posts Tagged correlation

## Recent Postings from correlation

### 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 [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.

### 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.

### 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 [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

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.

### Data compression for local correlation tracking of solar granulation

Context. Several upcoming and proposed space missions, such as Solar Orbiter, will be limited in telemetry and thus require data compression. Aims. We test the impact of data compression on local correlation tracking (LCT) of time-series of continuum intensity images. We evaluate the effect of several lossy compression methods (quantization, JPEG compression, and a reduced number of continuum images) on measurements of solar differential rotation with LCT. Methods. We apply the different compression methods to tracked and remapped continuum intensity maps obtained by the Helioseismic and Magnetic Imager (HMI) onboard the Solar Dynamics Observatory. We derive 2D vector velocities using the local correlation tracking code FLCT and determine the additional bias and noise introduced by compression to differential rotation. Results. We find that probing differential rotation with LCT is very robust to lossy data compression when using quantization. Our results are severely affected by systematic errors of the LCT method and the HMI instrument. The sensitivity of LCT to systematic errors is a concern for Solar Orbiter.

### Effects of pairing correlation on low-lying quasi-particle resonance in neutron drip-line nuclei

We discuss effects of pairing correlation on quasi-particle resonance. We analyze in detail how the width of low-lying quasi-particle resonance is governed by the pairing correlation in the neutron drip-line nuclei. We consider the 46Si + n system to discuss low-lying p wave quasi-particle resonance. Solving the Hartree-Fock-Bogoliubov equation in the coordinate space with scattering boundary condition, we calculate the phase shift, the elastic cross section, the resonance width and the resonance energy. We found that the pairing correlation has an effect to reduce the width of quasi-particle resonance which originates from a particle-like orbit in weakly bound nuclei.

### The Rest-Frame Golenetskii Correlation via a Hierarchical Bayesian Analysis

Gamma-ray bursts (GRBs) are characterised by a strong correlation between the instantaneous luminosity and the spectral peak energy within a burst. This correlation, which is known as the hardness-intensity correlation or the Golenetskii correlation, not only holds important clues to the physics of GRBs but is thought to have the potential to determine redshifts of bursts. In this paper, I use a hierarchical Bayesian model to study the universality of the rest-frame Golenetskii correlation and in particular I assess its use as a redshift estimator for GRBs. I find that, using a power-law prescription of the correlation, the power-law indices cluster near a common value, but have a broader variance than previously reported ($\sim 1-2$). Furthermore, I find evidence that there is spread in intrinsic rest-frame correlation normalizations for the GRBs in our sample ($\sim 10^{51}-10^{53}$ erg s$^{-1}$). This points towards variable physical settings of the emission (magnetic field strength, number of emitting electrons, photospheric radius, viewing angle, etc.). Subsequently, these results eliminate the Golenetskii correlation as a useful tool for redshift determination and hence a cosmological probe. Nevertheless, the Bayesian method introduced in this paper allows for a better determination of the rest frame properties of the correlation, which in turn allows for more stringent limitations for physical models of the emission to be set.

### Observational constraints on star cluster formation theory - I. The mass-radius relation

Stars form predominantly in groups usually denoted as clusters or associations. The observed stellar groups display a broad spectrum of masses, sizes and other properties, so it is often assumed that there is no underlying structure in this diversity. Here we show that the assumption of an unstructured multitude of cluster or association types might be misleading. Current data compilations of clusters show correlations between cluster mass, size, age, maximum stellar mass etc. In this first paper we take a closer look at the correlation of cluster mass and radius. We use literature data to explore relations in cluster and molecular core properties in the solar neighborhood. We show that for embedded clusters in the solar neighborhood there exists a clear correlation between cluster mass and half-mass radius of the form $M_c = C R_c^{\gamma}$ with gamma = 1.7 +/-0.2. This correlation holds for infra red K band data as well as X-ray sources and for clusters containing a hundred stars up to those consisting of a few tens of thousands of stars. The correlation is difficult to verify for clusters containing <30 stars due to low-number statistics. Dense clumps of gas are the progenitors of the embedded clusters. We find a similar slope for the mass-size relation of dense, massive clumps as for the embedded star clusters. This might point at a direct translation from gas to stellar mass: however, it is difficult to relate size measurements for clusters (stars) to those for gas profiles. Taking into account multiple paths for clump mass into cluster mass, we obtain an average star-formation efficiency of 18%{+9.3}{-5.7} for the embedded clusters in the solar neighborhood. The derived mass-radius relation gives constraints for the theory of clustered star formation. Analytical models and simulations of clustered star formation have to reproduce this relation in order to be realistic (abridged)

### Two-gluon rapidity correlations of strong colour field in $pp$, $pA$ and $AA$ collisions [Cross-Listing]

Using the CGC formalism, we calculate the two-gluon rapidity correlations of strong colour fields in $pp$, $pA$ and $AA$ collisions, respectively. If one trigger gluon is fixed at central rapidity, a ridge-like correlation pattern is obtained in symmetry $pp$ and $AA$ collisions, and a huge bump-like correlation pattern is presented in asymmetry $pA$ collisions. It is demonstrated that the ridge-like and the bump-like correlation patterns are caused by different-$x$ degree of freedom and their correlations. The transverse momentum and incident energy dependence of the ridge-like correlation pattern is systematically studied.

### Two-gluon rapidity correlations of strong colour field in $pp$, $pA$ and $AA$ collisions

Using the CGC formalism, we calculate the two-gluon rapidity correlations of strong colour fields in $pp$, $pA$ and $AA$ collisions, respectively. If one trigger gluon is fixed at central rapidity, a ridge-like correlation pattern is obtained in symmetry $pp$ and $AA$ collisions, and a huge bump-like correlation pattern is presented in asymmetry $pA$ collisions. It is demonstrated that the ridge-like and the bump-like correlation patterns are caused by different-$x$ degree of freedom and their correlations. The transverse momentum and incident energy dependence of the ridge-like correlation pattern is systematically studied.

### The number of tidal dwarf satellite galaxies in dependence of bulge index

We show that a significant correlation (up to 5sigma) emerges between the bulge index, defined to be larger for larger bulge/disk ratio, in spiral galaxies with similar luminosities in the Galaxy Zoo 2 of SDSS and the number of tidal-dwarf galaxies in the catalogue by Kaviraj et al. (2012). In the standard cold or warm dark-matter cosmological models the number of satellite galaxies correlates with the circular velocity of the dark matter host halo. In generalized-gravity models without cold or warm dark matter such a correlation does not exist, because host galaxies cannot capture in-falling dwarf galaxies due to the absence of dark-matter-induced dynamical friction. However, in such models a correlation is expected to exist between the bulge mass and the number of satellite galaxies, because bulges and tidal-dwarf satellite galaxies form in encounters between host galaxies. This is not predicted by dark matter models in which bulge mass and the number of satellites are a priori uncorrelated because higher bulge/disk ratios do not imply higher dark/luminous ratios. Hence, our correlation reproduces the prediction of scenarios without dark matter, whereas an explanation is not found readily from the a priori predictions of the standard scenario with dark matter. Further research is needed to explore whether some application of the standard theory may explain this correlation.

### The physical fundamental plane of black hole activity: revisited

The correlation between the jet power and accretion disk luminosity is investigated for active galactic nuclei (AGNs) and black hole X-ray binaries (BHXBs) from the literature. The power-law correlation index is steep ($\mu \sim$ 1.0--1.4) for radio loud quasars and the outliers' track of BHXBs, and it is flatter ($\mu \sim$ 0.3--0.6) for radio loud galaxies and the standard track of BHXBs. The steep-index groups are mostly at higher accretion rates (peaked at Eddington ratio $>$ 0.01) and the flatter-index groups are at relatively low accretion rates (peaked at Eddington ratio $<$ 0.01), implying that the former groups could be dominated by the inner disk accretion of black hole, while the jet in latter groups would be a hybrid production of the accretion and black hole spin. We could still have a fundamental plane of black hole activity for the BHXBs and AGNs with diverse (maybe two kinds of) correlation indices. It is noted that the fundamental plane of black hole activity should be referred to the correlation between the jet power and disk luminosity or equivalently to the correlation between jet power, Eddington ratio and black hole mass, rather than the jet power, disk luminosity and black hole mass.

### Correlation of hard X-ray and white light emission in solar flares

A statistical study of the correlation between hard X-ray and white light emission in solar flares is performed in order to search for a link between flare-accelerated electrons and white light formation. We analyze 43 flares spanning GOES classes M and X using observations from RHESSI (Reuven Ramaty High Energy Solar Spectroscopic Imager) and HMI (Helioseismic and Magnetic Imager). We calculate X-ray fluxes at 30 keV and white light fluxes at 6173 \r{A} summed over the hard X-ray flare ribbons with an integration time of 45 seconds around the peak hard-X ray time. We find a good correlation between hard X-ray fluxes and excess white light fluxes, with a highest correlation coefficient of 0.68 for photons with energy of 30 keV. Assuming the thick target model, a similar correlation is found between the deposited power by flare-accelerated electrons and the white light fluxes. The correlation coefficient is found to be largest for energy deposition by electrons above ~50 keV. At higher electron energies the correlation decreases gradually while a rapid decrease is seen if the energy provided by low-energy electrons is added. This suggests that flare-accelerated electrons of energy ~50 keV are the main source for white light production.

### Supermassive black holes and their host spheroids II. The red and blue sequence in the $M_{\rm BH} - M_{\rm *,sph}$ diagram

In our first paper, 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, $M_{BH}$, that had been imaged at $3.6~\mu m$ with Spitzer. Our sample is the largest to date and, for the first time, the decompositions were checked for consistency with the galaxy kinematics. We present correlations between $M_{ BH}$ and the host spheroid (and galaxy) luminosity, $L_{sph}$ (and $L_{gal}$), and also stellar mass, $M_{*,sph}$. While most previous studies have used galaxy samples that were overwhelmingly dominated by high-mass, early-type galaxies, our sample includes 17 spiral galaxies, half of which have $M_{BH} < 10^7~M_\odot$, and allows us to better investigate the poorly studied low-mass end of the $M_{BH} - M_{*,sph}$ correlation. The bulges of early-type galaxies follow $M_{BH} \propto M_{*,sph}^{1.04 \pm 0.10}$ and define a tight red sequence with intrinsic scatter $\epsilon = 0.43 \pm 0.06~dex$ and a median $M_{BH}/M_{*,sph}$ ratio of $0.68 \pm 0.04\%$, i.e.~a $\pm 2\sigma$ range of 0.1-5%. At the low-mass end, the bulges of late-type galaxies define a much steeper blue sequence, with $M_{BH} \propto M_{*,sph}^{2-3}$, indicating that gas-rich processes feed the black hole more efficiently than the host bulge as they coevolve. We additionally report that: i) our Sersic galaxy sample follows a less steep sequence than previously reported; ii) bulges with Sersic index $n<2$, argued by some to be pseudo-bulges, are not offset to lower $M_{BH}$ from the correlation defined by the current bulge sample with $n>2$; and iii) $L_{sph}$ and $L_{gal}$ correlate equally well with $M_{BH}$, in terms of intrinsic scatter, only for early-type galaxies - once reasonable numbers of spiral galaxies are included, the correlation with $L_{ sph}$ is better than that with $L_{gal}$.

### Effect of correlation on cumulants in heavy-ion collisions [Cross-Listing]

We study the effects of correlation on cumulants and their ratios of net-proton multiplicity distribution which have been measured for central (0-5\%) Au+Au collisions at Relativistic Heavy Ion Collider (RHIC). This effect has been studied assuming individual proton and anti-proton distributions as Poisson or Negative Binomial Distribution (NBD). In-spite of significantly correlated production due to baryon number, electric charge conservation and kinematical correlations of protons and anti-protons, the measured cumulants of net-proton distribution follow the independent production model. In the present work we demonstrate how the introduction of correlations will affect the cumulants and their ratios for the difference distributions. We have also demonstrated this study using the proton and anti-proton distributions obtained from HIJING event generator.

### Locating the gamma-ray emission site in Fermi/LAT blazars. II Multifrequency correlations

In an attempt to constrain and understand the emission mechanism of gamma rays, we perform a cross-correlation analysis of 15 blazars using light curves in millimetre, optical and gamma rays. We use discrete correlation function and consider only correlations significant at 99 per cent level. A strong correlation was found between 37 and 95 GHz with a near-zero time delay in most of the sources, and ~1 month or longer in the rest. A similar result was obtained between the optical and gamma-ray bands. Of the 15 sources, less than 50 per cent showed a strong correlation between the millimetre and gamma-ray or millimetre and optical bands. The primary reason for the lack of statistically significant correlation is the absence of a major outburst in the millimetre bands of most of the sources during the 2.5 yr time period investigated in our study. This may indicate that only the long-term variations or large flares are correlated between these bands. The variability of the sources at every waveband was also inspected using fractional rms variability. The fractional rms variability displays an increase with frequency reaching its maximum in the gamma rays.

### Update on the GRB universal scaling E$_{\rm{X,iso}}$-E$_{\rm{\gamma,iso}}$-E$_{\rm{pk}}$ with ten years of $Swift$ data

From a comprehensive statistical analysis of $Swift$ X-ray light-curves of gamma-ray bursts (GRBs) collected from December 2004 to the end of 2010, we found a three-parameter correlation between the isotropic energy emitted in the rest frame 1-10$^4$ keV energy band during the prompt emission (E$_{\rm{\gamma,iso}}$), the rest frame peak of the prompt emission energy spectrum (E$_{\rm{pk}}$), and the X-ray energy emitted in the rest frame 0.3-30 keV observed energy band (E$_{\rm{X,iso}}$), computed excluding the contribution of the flares. In this paper, we update this correlation with the data collected until June 2014, expanding the sample size with $\sim$35% more objects, where the number of short GRBs doubled. With this larger sample we confirm the existence of a universal correlation that connects the prompt and afterglow properties of long and short GRBs. We show that this correlation does not depend on the X-ray light-curve morphology and that further analysis is necessary to firmly exclude possible biases derived by redshift measurements. In addition we discuss about the behavior of the peculiar objects as ultra-long GRBs and we propose the existence of an intermediate group between long and short GRBs. Interestingly, two GRBs with uncertain classification fall into this category. Finally, we discuss the physics underlying this correlation, in the contest of the efficiency of conversion of the prompt $\gamma$-ray emission energy into the kinetic energy of the afterglow, the photosferic model, and the cannonball model.

### A jet model for Galactic black-hole X-ray sources: the cutoff energy-phase-lag correlation

Galactic black-hole X-ray binaries emit a compact, optically thick, mildy relativistic radio jet when they are in the hard and hard-intermediate states. In a series of papers, we have developed a jet model and have shown, through Monte Carlo simulations, that our model can explain many observational results. In this work, we investigate one more constraining relationship between the cutoff energy and the phase lag during the early stages of an X-ray outburst of the black-hole X-ray binary GX 339-4: the cutoff energy decreases while the phase lag increases during the brightening of the hard state. We demonstrate that our jet model naturally explains the above correlation, with a minor modification consisting of introducing an acceleration zone at the base of the jet. The observed correlation between the cutoff energy and the phase lag suggests that the lags are produced by the hard component. Here we show that this correlation arises naturally if Comptonization in the jet produces these two quantities.

### A possible correlation between planetary radius and orbital period for small planets

We suggest the existence of a correlation between the planetary radius and orbital period for planets with radii smaller than 4 R_Earth. Using the Kepler data, we find a correlation coefficient of 0.5120, and suggest that the correlation is not caused solely by survey incompleteness. While the correlation coefficient could change depending on the statistical analysis, the statistical significance of the correlation is robust. Further analysis shows that the correlation originates from two contributing factors. One seems to be a power-law dependence between the two quantities for intermediate periods (3-100 days), and the other is a dearth of planets with radii larger than 2 R_Earth in short periods. This correlation may provide important constraints for small-planet formation theories and for understanding the dynamical evolution of planetary systems.

### Intrinsic alignment contamination to CMB lensing-galaxy weak lensing correlations from tidal torquing

Correlations of galaxy ellipticities with large-scale structure, due to galactic tidal interactions, provide a potentially significant contaminant to measurements of cosmic shear. However, these intrinsic alignments are still poorly understood for galaxies at the redshifts typically used in cosmic shear analyses. For spiral galaxies, it is thought that tidal torquing is significant in determining alignments resulting in zero correlation between the intrinsic ellipticity and the gravitational potential in linear theory. Here, we calculate the leading-order correction to this result in the tidal-torque model from non-linear evolution, using second-order perturbation theory, and relate this to the contamination from intrinsic alignments to the recently-measured cross-correlation between galaxy ellipticities and the CMB lensing potential. We find that the angular cross-correlation from tidal torquing has a very similar scale dependence as in the linear alignment model (believed to be appropriate for elliptical galaxies), but the opposite sign and so increases the observable correlation between CMB lensing and spiral galaxies. The amplitude of the cross-correlation is predicted to depend strongly on the formation redshift, being smaller for galaxies that formed at higher redshift when the bispectrum of the gravitational potential was smaller. Finally, we make simple forecasts for constraints on intrinsic alignments from the correlation of forthcoming cosmic shear measurements with current CMB lensing measurements.

### ISW-Galaxy Cross Correlation:A probe of Dark Energy clustering and distribution of Dark Matter tracers

The Integrated Sachs Wolfe (ISW) cross correlation with the galaxy distribution in late time is a promising tool to constrain the dark energy properties. In this work we study the effect of dark energy clustering on the ISW-galaxy cross correlation. Indicating the fact that the bias parameter between the distribution of the galaxies and the underlying dark matter introduce a degeneracy and complications. We argue that as the time of the galaxy's host halo formation is different from the observation time, we have to consider the evolution of the halo bias parameter. We indicate that any deviation from $\Lambda$CDM model will change the evolution of the bias as well. Also we show that the halo bias strongly depends on the sub-sample of galaxies which is chosen for cross correlation. We show that joint kernel of ISW effect and the galaxy distribution have the dominant effect on the observed signal, accordingly we can enhance the signal of a specific dark energy model by choosing an appropriate tracer. More specifically we compare the clustered dark energy models with two samples of galaxies. First is a sub-sample of galaxies from Sloan Digital chosen with the r-band magnitude $18 < r < 21$ with a host dark matter halos of mass $M \sim10^{12}M_{\odot}$ and formation redshift of $z\sim 2.5$. Secondly with the sub-sample of Luminous Red galaxies with a host dark matter halos of mass $M \sim 10^{13}M_{\odot}$ and formation redshift of $z\sim 2.0$. Using the evolved bias we improve the $\chi^2$ for the $\Lambda$CDM which it reconcile the $\sim$1-2$\sigma$ tension of the ISW-galaxy signal and $\Lambda$CDM prediction. Finally we show how sub-samples change the bias parameter and will improve the constrains on dark energy clustering.

### Measuring dark energy with the $E_{\rm iso}-E_{\rm p}$ correlation of gamma-ray bursts using model-independent methods [Replacement]

In this paper, we use two model-independent methods to standardize long gamma-ray bursts (GRBs) using the $E_{\rm iso}-E_{\rm p}$ correlation, where $E_{\rm iso}$ is the isotropic-equivalent gamma-ray energy and $E_{\rm p}$ is the spectral peak energy. We update 42 long GRBs and try to make constraint on cosmological parameters. The full sample contains 151 long GRBs with redshifts from 0.0331 to 8.2. The first method is the simultaneous fitting method. The extrinsic scatter $\sigma_{\rm ext}$ is taken into account and assigned to the parameter $E_{\rm iso}$. The best-fitting values are $a=49.15\pm0.26$, $b=1.42\pm0.11$, $\sigma_{\rm ext}=0.34\pm0.03$ and $\Omega_m=0.79$ in the flat $\Lambda$CDM model. The constraint on $\Omega_m$ is $0.55<\Omega_m<1$ at the 1$\sigma$ confidence level. If reduced $\chi^2$ method is used, the best-fit results are $a=48.96\pm0.18$, $b=1.52\pm0.08$ and $\Omega_m=0.50\pm0.12$. The second method is using type Ia supernovae (SNe Ia) to calibrate the $E_{\rm iso}-E_{\rm p}$ correlation. We calibrate 90 high-redshift GRBs in the redshift range from 1.44 to 8.1. The cosmological constraints from these 90 GRBs are $\Omega_m=0.23^{+0.06}_{-0.04}$ for flat $\Lambda$CDM, and $\Omega_m=0.18\pm0.11$ and $\Omega_{\Lambda}=0.46\pm0.51$ for non-flat $\Lambda$CDM. For the combination of GRB and SNe Ia sample, we obtain $\Omega_m=0.271\pm0.019$ and $h=0.701\pm0.002$ for the flat $\Lambda$CDM, and for the non-flat $\Lambda$CDM, the results are $\Omega_m=0.225\pm0.044$, $\Omega_{\Lambda}=0.640\pm0.082$ and $h=0.698\pm0.004$. These results from calibrated GRBs are consistent with that of SNe Ia. Meanwhile, the combined data can improve cosmological constraints significantly, comparing to SNe Ia alone. Our results show that the $E_{\rm iso}-E_{\rm p}$ correlation is promising to probe the high-redshift universe.

### Measuring dark energy with the $E_{\rm iso}-E_{\rm p}$ correlation of GRBs using model-independent methods

In this paper, we use two model-independent methods to standardize long gamma-ray bursts (GRBs) using the $E_{\rm iso}-E_{\rm p}$ correlation, where $E_{\rm iso}$ is the isotropic-equivalent gamma-ray energy and $E_{\rm p}$ is the spectral peak energy. We update 42 long GRBs and try to make constraint on cosmological parameters. The full sample contains 151 long GRBs with redshifts from 0.0331 to 8.2. The first method is the simultaneous fitting method. The extrinsic scatter $\sigma_{\rm ext}$ is taken into account and assigned to the parameter $E_{\rm iso}$. The best-fitting values are $a=49.15\pm0.26$, $b=1.42\pm0.11$, $\sigma_{\rm ext}=0.34\pm0.03$ and $\Omega_m=0.79$ in the flat $\Lambda$CDM model. The constraint on $\Omega_m$ is $0.55<\Omega_m<1$ at the 1$\sigma$ confidence level. If reduced $\chi^2$ method is used, the best-fit results are $a=48.96\pm0.18$, $b=1.52\pm0.08$ and $\Omega_m=0.50\pm0.12$. The second method is using type Ia supernovae (SNe Ia) to calibrate the $E_{\rm iso}-E_{\rm p}$ correlation. We calibrate 90 high-redshift GRBs in the redshift range from 1.44 to 8.1. The cosmological constraints from these 90 GRBs are $\Omega_m=0.23^{+0.06}_{-0.04}$ for flat $\Lambda$CDM, and $\Omega_m=0.18\pm0.11$ and $\Omega_{\Lambda}=0.46\pm0.51$ for non-flat $\Lambda$CDM. For the combination of GRB and SNe Ia sample, we obtain $\Omega_m=0.271\pm0.019$ and $h=0.701\pm0.002$ for the flat $\Lambda$CDM, and for the non-flat $\Lambda$CDM, the results are $\Omega_m=0.225\pm0.044$, $\Omega_{\Lambda}=0.640\pm0.082$ and $h=0.698\pm0.004$. These results from calibrated GRBs are consistent with that of SNe Ia. Meanwhile, the combined data can improve cosmological constraints significantly, comparing to SNe Ia alone. Our results show that the $E_{\rm iso}-E_{\rm p}$ correlation is promising to probe the high-redshift universe.

### Polarized galactic synchrotron and dust emission and their correlation

We present an analysis of the level of polarized dust and synchrotron emission using the WMAP9 and Planck data. The primary goal of this study is to inform the assessment of foreground contamination in the cosmic microwave background (CMB) measurements below $\ell\sim200$ from 23 to 353 GHz. We compute angular power spectra as a function of sky cut based on the Planck 353 GHz polarization maps. Our primary findings are the following. (1) There is a spatial correlation between the dust emission as measured by Planck at 353 GHz and the synchrotron emission as measured by WMAP at 23 GHz with $\rho\approx0.4$ or greater for $\ell<20$ and $f_{\mathrm{sky}}\geq0.5$, dropping to $\rho\approx0.2$ for $30<\ell<200$. (2) A simple foreground model with dust, synchrotron, and their correlation fits well to all possible cross spectra formed with the WMAP and Planck 353 GHz data given the current uncertainties. (3) In the 50$\%$ cleanest region of the polarized dust map, the ratio of synchrotron to dust amplitudes at 90 GHz for 50 $\leq \ell \leq$110 is $0.3_{-0.2}^{+0.3}$. Smaller regions of sky can be cleaner although the uncertainties in our knowledge of synchrotron emission are larger. A high-sensitivity measurement of synchrotron below 90 GHz will be important for understanding all the components of foreground emission near 90 GHz.

### Polarized galactic synchrotron and dust emission and their correlation [Replacement]

We present an analysis of the level of polarized dust and synchrotron emission using the WMAP9 and Planck data. The primary goal of this study is to inform the assessment of foreground contamination in the cosmic microwave background (CMB) measurements below $\ell\sim200$ from 23 to 353 GHz. We compute angular power spectra as a function of sky cut based on the Planck 353 GHz polarization maps. Our primary findings are the following. (1) There is a spatial correlation between the dust emission as measured by Planck at 353 GHz and the synchrotron emission as measured by WMAP at 23 GHz with $\rho\approx0.4$ or greater for $\ell<20$ and $f_{\mathrm{sky}}\geq0.5$, dropping to $\rho\approx0.2$ for $30<\ell<200$. (2) A simple foreground model with dust, synchrotron, and their correlation fits well to all possible cross spectra formed with the WMAP and Planck 353 GHz data given the current uncertainties. (3) In the 50$\%$ cleanest region of the polarized dust map, the ratio of synchrotron to dust amplitudes at 90 GHz for 50 $\leq \ell \leq$110 is $0.3_{-0.2}^{+0.3}$. Smaller regions of sky can be cleaner although the uncertainties in our knowledge of synchrotron emission are larger. A high-sensitivity measurement of synchrotron below 90 GHz will be important for understanding all the components of foreground emission near 90 GHz.

### The extension of variability properties in gamma-ray bursts to blazars

Both gamma-ray bursts (GRBs) and blazars have relativistic jets pointing at a small angle from our line of sight. Several recent studies suggested that these two kinds of sources may share similar jet physics. In this work, we explore the variability properties for GRBs and blazars as a whole. We find that the correlation between minimum variability timescale (MTS) and Lorentz factor, $\Gamma$, as found only in GRBs by Sonbas et al. can be extended to blazars with a joint correlation of $\rm MTS\propto\Gamma^{-4.7\pm0.3}$. The same applies to the $\rm MTS\propto \it L_{\gamma}^{\rm -1.0\pm0.1}$ correlation as found in GRBs, which can be well extended into blazars as well. These results provide further evidence that the jets in these two kinds of sources are similar despite of the very different mass scale of their central engines. Further investigations of the physical origin of these correlations are needed, which can shed light on the nature of the jet physics.

### Constraining slope parameter of symmetry energy from nuclear structure

Four quantities deducible from nuclear structure experiments have been claimed to correlate to the slope parameter $L$ of the symmetry energy; the neutron skin thickness, the cross section of low-energy dipole (LED) mode, dipole polarizability $\alpha_D$, and $\alpha_D S_0$ (i.e. product of $\alpha_D$ and the symmetry energy $S_0$). By the calculations in the Hartree-Fock plus random-phase approximation with various effective interactions, we compare the correlations between $L$ and these four quantities. The correlation derived from different interactions and the correlation from a class of interactions that are identical in the symmetric matter as well as in $S_0$ are simultaneously examined. These two types of correlations may behave differently, as exemplified in the correlation of $\alpha_D$ to $L$. It is found that the neutron skin thickness and $\alpha_DS_0$ correlate well to $L$, and therefore are suitable for narrowing down the value of $L$ via experiments. The LED emergence and upgrowth makes the $\alpha_DS_0$-$L$ correlation strong, although these correlations are disarranged when neutron halo appears in the ground state.

### The Extreme Ultraviolet Deficit - Jet Connection in the Quasar 1442+101

In previous studies, it has been shown that the long term time average jet power, $\overline{Q}$, is correlated with the spectral index in the extreme ultraviolet (EUV), $\alpha_{EUV}$ (defined by $F_{\nu} \sim \nu^{-\alpha_{EUV}}$ computed between 700\AA\, and 1100\AA\,). Larger $\overline{Q}$ tends to decrease the EUV emission. This is a curious relationship because it connects a long term average over $\sim 10^{6}$ years with an instantaneous measurement of the EUV. The EUV appears to be emitted adjacent to the central supermassive black hole and the most straightforward explanation of the correlation is that the EUV emitting region interacts in real time with the jet launching mechanism. Alternatively stated, the $\overline{Q}$ - $\alpha_{EUV}$ correlation is a manifestation of a contemporaneous (real time) jet power, $Q(t)$, correlation with $\alpha_{EUV}$. In order to explore this possibility, this paper considers the time variability of the strong radio jet of the quasar 1442+101 that is not aberrated by strong Doppler enhancement. This high redshift (z = 3.55) quasar is uniquely suited for this endeavor as the EUV is redshifted into the optical observing window allowing for convenient monitoring. More importantly, it is bright enough to be seen through the Lyman forest and its radio flux is strong enough that it has been monitored frequently. Quasi-simultaneous monitoring (five epochs spanning $\sim 40$ years) show that increases in $Q(t)$ correspond to decreases in the EUV as expected.

### Interpreting the radio/X-ray correlation of black hole sources based on the accretion-jet model [Replacement]

Two types of correlations between the radio and X-ray luminosities ($L_R$ and $L_X$) have been found in black hole X-ray binaries. For some sources, they follow the original' type of correlation which is described by a single power-law. Later it was found that some other sources follow a different correlation consisting of three power-law branches, with each branch having different power-law indexes. In this work, we explain these two types of correlation under the coupled accretion--jet model. We attribute the difference between these two types of sources to the different value of viscosity parameter $\alpha$. One possible reason for different $\alpha$ is the different configuration of magnetic field in the accretion material coming from the companion stars. For the single power-law' sources, their $\alpha$ is high; so their accretion is always in the mode of advection-dominated accretion flow (ADAF) for the whole range of X-ray luminosity. For those hybrid power-law' sources, the value of $\alpha$ is small so their accretion mode changes from an ADAF to a luminous hot accretion flow, and eventually to two-phase accretion as the accretion rate increases. Because the dependence of radiative efficiency on the mass accretion rate is different for these three accretion modes, different power-law indexes in the $L_R--L_X$ correlation are expected. Constraints on the ratio of the mass loss rate into the jet and the mass accretion rate in the accretion flow are obtained, which can be tested in future by radiative magnetohydrodynamic numerical simulations of jet formation.

### Interpreting the radio/X-ray correlation of black hole sources based on the accretion-jet model

Two types of correlations between the radio and X-ray luminosities ($L_R$ and $L_X$) of black hole sources has been found. For the traditional type of sources, the correlation can be described by a single power-law. For the other type of sources, while the correlation can still be described by power-law forms, it consists three branches according to the X-ray luminosity, with different power-law indexes. In this paper, we try to explain these correlations in the framework of the coupled accretion-jet model. We attribute the difference between these two types of sources to the difference in the value of viscous parameter $\alpha$. For the "single power-law" sources, their $\alpha$ is high; so their accretion is always in the mode of ADAF (advection-dominated accretion flow) for the whole range of X-ray luminosity. For those "hybrid power-law" sources, the value of $\alpha$ is small so their accretion modes change from ADAF to LHAF (luminous hot accretion flow) to two-phase accretion as the accretion rate increases. Because the radiative efficiency of the hot accretion flow on the mass accretion rate is different for these three accretion modes, they will lead to different power-law indexes in the $L_R$ -- $L_X$ correlation. The reason of the different $\alpha$ may be because of the different configuration of magnetic field in the accretion material coming from the companion stars. Constraints on the ratio of the mass lost rate into the jet and the mass accretion rate in the accretion flow have been obtained, which can be tested in future by radiative magnetohydrodynamic (MHD) numerical simulations on jet formation.

### Transit-Depth Metallicity Correlation: A Bayesian Approach

A negative correlation was previously reported between the transit depth of Kepler's Q1-Q12 gas giant candidates and the stellar metallicity. In this present work, we revisit this correlation to better understand the role of the stellar metallicity in the formation of giant planets, in particular, to investigate the effect of the metallicity on the transit depth. We selected the 82 confirmed giant planets from the cumulative catalog. This is the first large and homogeneous sample of confirmed giant planets used to study this correlation. Such samples are suitable to perform robust statistical analysis. We present the first hierarchical Bayesian linear regression model to revise this correlation. The advantages of using a Bayesian framework are to incorporate measurement errors in the model and to quantify both the intrinsic scatter and the uncertainties on the parameters of the model. Our statistical analysis reveals no correlation between the transit depth of confirmed giant planets and the stellar metallicity.

### VHE $\gamma$-ray/X-ray correlation studies in Mrk 421 down to the quiescent state

The blazar Mrk 421 is one of the closest, brightest and fastest varying source in the extragalactic X-ray/TeV sky. In the last years, many multi-wavelength campaigns have been carried out to study the correlation between the very high energy (VHE) $\gamma$-ray and X-ray fluxes of this source and, although the activity in these two energy ranges seems to be correlated in many observations, no conclusive results have been achieved yet. In this work we present a robust study of the VHE $\gamma$-ray/X-ray correlation of Mrk 421 with data taken with different VHE experiments on different time scales and for different levels of activity of the source, with special focus on the low activity states. In particular, we discuss the robustness of the correlation at the lowest fluxes corresponding to the quiescent state of Mrk 421.

### The subarcsecond mid-infrared view of local active galactic nuclei: II. The mid-infrared--X-ray correlation

We present an updated mid-infrared (MIR) versus X-ray correlation for the local active galactic nuclei (AGN) population based on the high angular resolution 12 and 18um continuum fluxes from the AGN subarcsecond MIR atlas and 2-10 keV and 14-195 keV data collected from the literature. We isolate a sample of 152 objects with reliable AGN nature and multi-epoch X-ray data and minimal MIR contribution from star formation. Although the sample is not homogeneous or complete, we show that our results are unlikely to be affected by biases. The MIR--X-ray correlation is nearly linear and within a factor of two independent of the AGN type and the wavebands used. The observed scatter is <0.4 dex. A possible flattening of the correlation slope at the highest luminosities probed (~ 10^45 erg/s) is indicated but not significant. Unobscured objects have, on average, an MIR--X-ray ratio that is only <= 0.15 dex higher than that of obscured objects. Objects with intermediate X-ray column densities (22 < log N_H < 23) actually show the highest MIR--X-ray ratio on average. Radio-loud objects show a higher mean MIR--X-ray ratio at low luminosities, while the ratio is lower than average at high luminosities. This may be explained by synchrotron emission from the jet contributing to the MIR at low-luminosities and additional X-ray emission at high luminosities. True Seyfert 2 candidates and double AGN do not show any deviation from the general behaviour. Finally, we show that the MIR--X-ray correlation can be used to verify the AGN nature of uncertain objects. Specifically, we give equations that allow to determine the intrinsic 2-10 keV luminosities and column densities for objects with complex X-ray properties to within 0.34 dex. These techniques are applied to the uncertain objects of the remaining AGN MIR atlas, demonstrating the usefulness of the MIR--X-ray correlation as an empirical tool.

### Far-UV to mid-IR properties of nearby radio galaxies

We investigate whether the far-UV continuum of nearby radio galaxies reveals evidence for the presence of star forming or non-stellar components. If a UV excess due to an extra radiation component exists we compare this with other properties such as radio power, optical spectral type and the strength of the emission lines. We also discuss the possible correlation between the ultra-violet flux, IR properties and central black hole mass. We use two sampes of low luminosity radio galaxies with comparable redshifts ($z < 0.2$). Spectral Energy Distributions are constructed using a number of on-line databases: GALEX, SDSS, 2MASS, and WISE. The parameter $XUV$ is introduced, which measures the excess slope of the UV continuum between 4500 and 2000 \AA, with respect to the UV radiation produced by the underlying old galaxy component. We find that the UV excess is usually small or absent in low luminosity sources, but sets in abruptly at the transition radio power above which we find mostly FRII sources. $XUV$ behaves very similarly to the strength of the optical emission lines (in particular $H\alpha$). Below $P_{1.4 GHz} < 10^{24}$ WHz$^{-1}$ $XUV$ is close to zero. $XUV$ correlates strongly with the $H\alpha$ line strength, but only in sources with strong $H\alpha$ emission. There is a strong correlation between $XUV$ and the slope of the mid-IR, as measured by the WISE bands in the interval 3.4 to 22 $\mu$m, in the sense that sources with a strong UV excess also have stronger IR emission. There is an inverse correlation between $XUV$ and central black hole mass: strong UV excess objects have, on average, $M_{BH}$ about 2-3 times less massive than those without UV excess. Low luminosity radio galaxies tend to be more massive and contain more massive black holes.

### The application of the Mid-IR radio correlation to the $\hat{G}$ sample and the search for advanced extraterrestrial civilisations

Wright et al. 2014 have embarked on a search for advanced Karadashev Type III civilisations via the compilation of a sample of sources with extreme mid-IR emission and colours. In this scenario, the mid-IR emission is then primarily associated with waste heat energy by-products. I apply the Mid-IR radio correlation to this $\hat{G}$ sample (Griffith et al. 2015). I demonstrate that the mid-IR and radio luminosities are correlated for the sample with $q_{22}=1.35\pm0.42$. By comparison, the First Look Survey (FLS) has $q_{22}=0.87\pm0.27$. The fact that the G-HAT sample largely follows the Mid-IR radio correlation, strongly suggests the vast majority of these sources are associated with galaxies in which natural astrophysical processes are dominant. This simple application of the mid-IR radio correlation can substantially reduce the number of false positives in the $\hat{G}$ catalogue, since galaxies occupied by advanced Kardashev Type III civilisations would be expected to exhibit very high values of $q$. Indeed I identify 9 outliers in the sample with $q_{22} > 2$ of which at least 3 have properties that are relatively well explained via standard astrophysical interpretations e.g. dust emission associated with nascent star formation and/or nuclear activity from a heavily obscured AGN. I also note that the comparison of resolved Mid-IR and radio images of galaxies on sub-galactic (kpc) scales can also be useful in identifying and recognising artificial mid-IR emission from less advanced intermediate Type II/III civilisations. Nevertheless, from the bulk properties of the $\hat{G}$ sample, I conclude that Kardashev Type-III civilisations are either very rare or do not exist in the local Universe.

### The beaming effect and $\rm{\gamma}$-ray emission for Fermi blazars

We study the $\rm{\gamma}$-ray luminosity and beaming effect for Fermi blazars. Our results are as follows. (i) There are significant correlations between $\rm{\gamma}$-ray luminosity and radio core luminosity, and between $\rm{\gamma}$-ray luminosity and $\rm{R_{v}}$, which suggests that the $\rm{\gamma}$-ray emissions have strong beaming effect. (ii) Using the $\rm{L_{ext}/M_{abs}}$ as an indicator of environment effects, we find that there have no significant correlation between $\rm{\gamma}$-ray luminosity and $\rm{L_{ext}/M_{abs}}$ for all sources when remove the effect of redshift. FSRQs considered alone also do not show a significant correlation, while BL Lacs still show a significant correlation when remove the effect of redshift. These results suggest that the $\rm{\gamma}$-ray emission may be affected by environment on the kiloparsec-scale for BL Lacs.

### Dipole Modulation of Cosmic Microwave Background Temperature and Polarization

We analyze the Cosmic Microwave Background Radiation (CMBR) temperature and polarization data in order to extract the signal of correlation between l and l+1 multipoles in the multipole ranges, 2-64, 30-64 and 30-100. Such a correlation is predicted by the dipole modulation model proposed on the basis of the observed hemispherical anisotropy in temperature field. An anisotropic or inhomogeneous model of primordial power spectrum which leads to such correlations in temperature field also predicts similar correlations in CMBR polarization. Our results for the case of temperature using the latest PLANCK data agree with those obtained by earlier analysis. We also find a very strong signal of correlation in the polarization data. Surprisingly, however, the preferred direction in the case of polarization points in the direction close to the CMBR dipole which is very different from the corresponding direction in the case of temperature.

### Dipole Modulation of Cosmic Microwave Background Temperature and Polarization [Cross-Listing]

We analyze the Cosmic Microwave Background Radiation (CMBR) temperature and polarization data in order to extract the signal of correlation between l and l+1 multipoles in the multipole ranges, 2-64, 30-64 and 30-100. Such a correlation is predicted by the dipole modulation model proposed on the basis of the observed hemispherical anisotropy in temperature field. An anisotropic or inhomogeneous model of primordial power spectrum which leads to such correlations in temperature field also predicts similar correlations in CMBR polarization. Our results for the case of temperature using the latest PLANCK data agree with those obtained by earlier analysis. We also find a very strong signal of correlation in the polarization data. Surprisingly, however, the preferred direction in the case of polarization points in the direction close to the CMBR dipole which is very different from the corresponding direction in the case of temperature.

### The angular two-point correlation of NVSS galaxies revisited

We measure the angular two-point correlation and angular power spectrum from the NRAO VLA Sky Survey (NVSS) of radio galaxies. Contrary to previous claims in the literature, we show that it is consistent with primordial Gaussianity on all angular scales and it is consistent with the best-fit cosmological model from the Planck analysis, as well as the redshift distribution obtained from the Combined EIS-NVSS Survey Of Radio Sources (CENSORS). Our analysis is based on an optimal estimation of the two-point correlation function and makes use of a new mask, which takes into account direction dependent effects of the observations, side lobe effects of bright sources and galactic foreground. We also use a lower flux threshold and take the cosmic radio dipole into account. The latter turns out to be an essential step in the analysis. This improved cosmological analysis of the NVSS stresses the importance of a flux calibration that is robust and stable on large angular scales for future radio continuum surveys.

### Measuring primordial anisotropic correlators with CMB spectral distortions

We show that inflationary models with broken rotational invariance generate testable off-diagonal signatures in the correlation between the $\mu$-type distortion and temperature fluctuations of the Cosmic Microwave Background. More precisely, scenarios with a quadrupolar bispectrum asymmetry, usually generated by fluctuations of primordial vector fields, produce a non-vanishing $\mu$-$T$ correlation when $|\ell_1-\ell_2|=2$. Since spectral distortions are sensitive to primordial fluctuations up to very small scales, a cosmic variance limited spectral distortion experiment can detect such effects with high signal-to-noise.