# Posts Tagged correlation

## Recent Postings from correlation

### 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.

### 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

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.

### Measuring primordial anisotropic correlators with CMB spectral distortions [Cross-Listing]

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.

### Measuring primordial anisotropic correlators with CMB spectral distortions [Cross-Listing]

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.

### The progenitors of core-collapse supernovae suggest thermonuclear origin for the explosions

Core-collapse supernovae (CCSNe) are the explosions of massive stars following the collapse of the stars' iron cores. Poznanski (2013) has recently suggested an observational correlation between the ejecta velocities and the inferred masses of the red supergiant progenitors of type II-P explosions, which implies that the kinetic energy of the ejecta ($E_{\textrm{kin}}$) increases with the mass of the progenitor. I point out that the same conclusion can be reached from the model-free observed correlation between the ejected $^{56}$Ni masses ($M_{\textrm{Ni}}$) and the luminosities of the progenitors for type II supernovae, which was reported by Fraser et al. (2011). This correlation is in an agreement with the predictions of the collapse-induced thermonuclear explosions (CITE) for CCSNe and in a possible contradiction with the predictions of the neutrino mechanism. I show that a correlation between $M_{\textrm{Ni}}$ and $E_{\textrm{kin}}$ holds for all types of CCSNe (including type Ibc). This correlation suggests a common mechanism for all CCSNe, which is predicted for CITE, but is not produced by current simulations of the neutrino mechanism. Furthermore, the typical values of $E_{\textrm{kin}}$ and $M_{\textrm{Ni}}$ for type Ibc explosions are larger by an order of a magnitude than the typical values for II-P explosions, a fact which disfavors progenitors with the same initial mass range for these explosions. Instead, the progenitors of type Ibc explosions could be massive Wolf-Rayet stars, which are predicted to yield strong explosions with low ejecta masses (as observed) according to CITE. In this case, there is no deficit of high mass progenitors for CCSNe, which was suggested under the assumption of a similar mass range for the progenitors of types II-P and Ibc supernovae.

### Luminosity--time and luminosity--luminosity correlations for GRB prompt and afterglow plateau emissions

We present an analysis of 123 Gamma-ray bursts (GRBs) with known redshifts possessing an afterglow plateau phase. We reveal that $L_a-T^{*}_a$ correlation between the X-ray luminosity $L_a$ at the end of the plateau phase and the plateau duration, $T^*_a$, in the GRB rest frame has a power law slope different, within more than 2 $\sigma$, from the slope of the prompt $L_{f}-T^{*}_{f}$ correlation between the isotropic pulse peak luminosity, $L_{f}$, and the pulse duration, $T^{*}_{f}$, from the time since the GRB ejection. Analogously, we show differences between the prompt and plateau phases in the energy-duration distributions with the afterglow emitted energy being on average $10\%$ of the prompt emission. Moreover, the distribution of prompt pulse versus afterglow spectral indexes do not show any correlation. In the further analysis we demonstrate that the $L_{peak}-L_a$ distribution, where $L_{peak}$ is the peak luminosity from the start of the burst, is characterized with a considerably higher Spearman correlation coefficient, $\rho=0.79$, than the one involving the averaged prompt luminosity, $L_{prompt}-L_a$, for the same GRB sample, yielding $\rho=0.60$. Since some of this correlation could result from the redshift dependences of the luminosities, namely from their cosmological evolution we use the Efron-Petrosian method to reveal the intrinsic nature of this correlation. We find that a substantial part of the correlation is intrinsic. We apply a partial correlation coefficient to the new de-evolved luminosities showing that the intrinsic correlation exists.

### The Star Formation and AGN luminosity relation: Predictions from a semi-analytical model

In a Universe where AGN feedback regulates star formation in massive galaxies, a strong correlation between these two quantities is expected. If the gas causing star formation is also responsible for feeding the central black hole, then a positive correlation is expected. If powerful AGNs are responsible for the star formation quenching, then a negative correlation is expected. Observations so far have mainly found a mild correlation or no correlation at all (i.e. a flat relation between star formation rate (SFR) and AGN luminosity), raising questions about the whole paradigm of "AGN feedback". In this paper, we report the predictions of the GALFORM semi-analytical model, which has a very strong coupling between AGN activity and quenching of star formation. The predicted SFR-AGN luminosity correlation appears negative in the low AGN luminosity regime, where AGN feedback acts, but becomes strongly positive in the regime of the brightest AGN. Our predictions reproduce reasonably well recent observations by Rosario et al., yet there is some discrepancy in the normalisation of the correlation at low luminosities and high redshifts. Though this regime could be strongly influenced by observational biases, we argue that the disagreement could be ascribed to the fact that GALFORM neglects AGN variability effects. Interestingly, the galaxies that dominate the regime where the observations imply a weak correlation are massive early-type galaxies that are subject to AGN feedback. Nevertheless, these galaxies retain high enough molecular hydrogen contents to maintain relatively high star formation rates and strong infrared emission.

### The Star Formation and AGN luminosity relation: Predictions from a semi-analytical model [Replacement]

In a Universe where AGN feedback regulates star formation in massive galaxies, a strong correlation between these two quantities is expected. If the gas causing star formation is also responsible for feeding the central black hole, then a positive correlation is expected. If powerful AGNs are responsible for the star formation quenching, then a negative correlation is expected. Observations so far have mainly found a mild correlation or no correlation at all (i.e. a flat relation between star formation rate (SFR) and AGN luminosity), raising questions about the whole paradigm of "AGN feedback". In this paper, we report the predictions of the GALFORM semi-analytical model, which has a very strong coupling between AGN activity and quenching of star formation. The predicted SFR-AGN luminosity correlation appears negative in the low AGN luminosity regime, where AGN feedback acts, but becomes strongly positive in the regime of the brightest AGN. Our predictions reproduce reasonably well recent observations by Rosario et al., yet there is some discrepancy in the normalisation of the correlation at low luminosities and high redshifts. Though this regime could be strongly influenced by observational biases, we argue that the disagreement could be ascribed to the fact that GALFORM neglects AGN variability effects. Interestingly, the galaxies that dominate the regime where the observations imply a weak correlation are massive early-type galaxies that are subject to AGN feedback. Nevertheless, these galaxies retain high enough molecular hydrogen contents to maintain relatively high star formation rates and strong infrared emission.

### A Tight $L_{\rm p, iso}-E'_{\rm p}-\Gamma_0$ Correlation of Gamma-Ray Bursts

We select a sample of 34 gamma-ray bursts (GRBs) whose $\Gamma_0$ values are derived with the onset peak observed in the afterglow lightcurves (except for GRB 060218 whose $\Gamma_0$ is estimated with its radio data), and investigate the correlations among $\Gamma_0$, the isotropic peak luminosity ($L_{\rm p, iso}$), and the peak energy of the $\nu f_\nu$ spectrum in the cosmological rest frame ($E^{'}_{\rm p}$). An analysis of pair correlations among these observables well confirms the results reported by previous papers. In addition, a tight correlation among $L_{\rm p, iso}$, $E^{'}_{p}$, and $\Gamma_0$ is found from a multiple regression analysis, which takes the form of $L_{\rm p,iso} \propto {E'_{\rm p}}^{1.34\pm 0.14} \Gamma_0^{1.32\pm 0.19}$ or $E'_{\rm p} \propto L_{\rm p,iso}^{0.55\pm 0.06}\Gamma_0^{-0.50\pm 0.17}$. Nine other GRBs whose $\Gamma_0$ are derived via the pair production opacity constraint also follow such a correlation. We argue that this tighter $L_{\rm p, iso} - E^{'}_{p} - \Gamma_0$ correlation may be more physical than the $L_{\rm p,iso} - E'_{\rm p}$ correlation, since the relationship between the observed $L_{\rm p,iso}$ and $E'_{\rm p}$ not only depends on radiation physics, but also depends on the bulk motion of the jet. We explore possible origins of this correlation and discuss its physical implications for understanding GRB jet composition and radiation mechanism.

### Hadronization effects on the baryon-strangeness correlation in quark combination models

The baryon-strangeness correlation in the hadronization of the quark matter is studied within the quark combination mechanism. We calculate the correlation coefficient $C_{BS} = -3\big(\langle B S \rangle -\langle B\rangle \langle S\rangle\big)/\big( \langle S^2 \rangle-\langle S \rangle^2 \big)$ of initial hadrons produced from the deconfined free quark system with $C^{(q)}_{BS}=1$. The competition of the production of baryons against that of mesons is the key dynamics that is most relevant to the change of baryon-strangeness correlation during system hadronization. Results of quark combination under the Poisson statistics agree with the statistical model predictions for a hadron resonance gas at vanishing chemical potential but differ from those at relatively large chemical potentials. Results beyond Poisson statistics are also obtained and are compared with calculations of Lattice QCD in the phase boundary, giving the best agreement at temperature $T =163$ MeV. We predict the dependence of the $C_{BS}$ of hadron system on the baryon chemical potential and strangeness. These predictions are expected to be tested by the future Lattice QCD calculations at non-zero chemical potentials and/or by the Beam Energy Scan experiment of STAR Collaboration at RHIC.

### Recent measurements of the gravitational constant as a function of time

A recent publication (J.D. Anderson et. al., EPL 110, 1002) presented a strong correlation between the measured values of the gravitational constant $G$ and the 5.9-year oscillation of the length of day. Here, we provide a compilation of all published measurements of $G$ taken over the last 35 years. A least squares regression to a sine with a period of 5.9 years still yields a better fit than a straight line. However, our additions and corrections to the G data reported by Anderson {\it et al.} significantly weaken the correlation.

### Recent measurements of the gravitational constant as a function of time [Replacement]

A recent publication (J.D. Anderson et. al., EPL 110, 1002) presented a strong correlation between the measured values of the gravitational constant $G$ and the 5.9-year oscillation of the length of day. Here, we provide a compilation of all published measurements of $G$ taken over the last 35 years. A least squares regression to a sine with a period of 5.9 years still yields a better fit than a straight line. However, our additions and corrections to the G data reported by Anderson {\it et al.} significantly weaken the correlation.

### CO luminosity - line width correlation of sub-millimeter galaxies and a possible cosmological application

Context. A possible correlation between CO luminosity (L_CO ) and its line width (FWHM) has been suggested and denied in the literature. Such claims were often based on a small, or heterogeneous sample of galaxies, and thus inconclusive. Aims. We aim to prove or dis-prove the L_CO -FWHM correlation. Methods. We compile a large sample of submm galaxies at z>2 from the literature, and investigate the L_CO-FWHM relation. Results. After carefully evaluating the selection effects and uncertainties such as inclination and magnification via gravitational lensing, we show that there exist a weak but significant correlation between L_CO and FWHM. We also discuss a feasibility to measure the cosmological distance using the correlation.

### The observed radio/gamma-ray emission correlation for blazars with the Fermi-LAT and the RATAN-600 data

We study the correlation between gamma-ray and radio band radiation for 123 blazars, using the Fermi-LAT first source catalog (1FGL) and the RATAN-600 data obtained at the same period of time (within a few months). We found an apparent positive correlation for BL Lac and flat-spectrum radio quasar (FSRQ) sources from our sample through testing the value of the Pearson product-moment correlation coefficient. The BL Lac objects show higher values of the correlation coefficient than FSRQs at all frequencies, except 21.7 GHz, and at all bands, except $10-100$ GeV, typically at high confidence level (> 99%). At higher gamma-ray energies the correlation weakens and even becomes negative for BL Lacs and FSRQs. For BL Lac blazars, the correlation of the fluxes appeared to be more sensitive to the considered gamma-ray energy band, than to the frequency, while for FSRQ sources the correlation changed notably both with the considered radio frequency and gamma-ray energy band. We used a data randomization method to quantify the significance of the computed correlation coefficients. We find that the statistical significance of the correlations we obtained between the flux densities at all frequencies and the photon flux in all gamma-ray bands below 3 GeV is high for BL Lacs (chance probability $\sim 10^{-3} - 10^{-7}$). The correlation coefficient is high and significant for the $0.1-0.3$ GeV band and low and insignificant for the $10-100$ GeV band for both types of blazars for all considered frequencies.

### On the Physical Origin of Galactic Conformity

Correlations between the star formation rates (SFRs) of nearby galaxies (so-called galactic conformity) have been observed for projected separations up to 4 Mpc, an effect not predicted by current semi-analytic models. We investigate correlations between the mass accretion rates (dMvir/dt) of nearby halos as a potential physical origin for this effect. We find that pairs of host halos "know about" each others' assembly histories even when their present-day separation is greater than thirty times the virial radius of either halo. These distances are far too large for direct interaction between the halos to explain the correlation in their dMvir/dt. Instead, halo pairs at these distances reside in the same large-scale tidal environment, which regulates dMvir/dt for both halos. Larger halos are less affected by external forces, which naturally gives rise to a mass dependence of the halo conformity signal. SDSS measurements of galactic conformity exhibit a qualitatively similar dependence on stellar mass, including how the signal varies with distance. Based on the expectation that halo accretion and galaxy SFR are correlated, we predict the scale-, mass- and redshift-dependence of large-scale galactic conformity, finding that the signal should drop to undetectable levels by z > 1. These predictions are testable with current surveys to z ~ 1; confirmation would establish a strong correlation between dark matter halo accretion rate and central galaxy SFR.

### Time-reversal symmetry violation in several Lepton-Flavor-Violating processes

We compute a T-odd triple vector correlation for the $\mu\rightarrow e\gamma$ decay and the $\mu\rightarrow e$ conversion process. We find simple results in terms of the CP violating phases of the effective Hamiltonians. Then we focus on the minimal Left-Right symmetric extension of the Standard Model, which can lead to an appreciable correlation. We show that under rather general assumptions, this correlation can be used to discriminate between Parity or Charge-conjugation as the discrete Left-Right symmetry.

### Time-reversal symmetry violation in several Lepton-Flavor-Violating processes [Replacement]

We compute a T-odd triple vector correlation for the $\mu\rightarrow e\gamma$ decay and the $\mu\rightarrow e$ conversion process. We find simple results in terms of the CP violating phases of the effective Hamiltonians. Then we focus on the minimal Left-Right symmetric extension of the Standard Model, which can lead to an appreciable correlation. We show that under rather general assumptions, this correlation can be used to discriminate between Parity or Charge-conjugation as the discrete Left-Right symmetry.

### Time-reversal symmetry violation in several Lepton-Flavor-Violating processes [Replacement]

We compute a T-odd triple vector correlation for the $\mu\rightarrow e\gamma$ decay and the $\mu\rightarrow e$ conversion process. We find simple results in terms of the CP violating phases of the effective Hamiltonians. Then we focus on the minimal Left-Right symmetric extension of the Standard Model, which can lead to an appreciable correlation. We show that under rather general assumptions, this correlation can be used to discriminate between Parity or Charge-conjugation as the discrete Left-Right symmetry.

### The imprint of massive black-hole mergers on the correlation between nuclear clusters and their host galaxies

A literature compilation of nuclear cluster (NSC) masses is used to study the correlation between global and NSC properties. A comparison of observational data to the predictions of semi-analytical galaxy formation models places constraints on the co-evolution of NSCs, massive black holes (MBHs) and host galaxies. Both data and theoretical predictions show an increased scatter in the NSC scaling correlations at high galaxy masses, and we show that this is due to the progressively more efficient ejection of stars from NSCs caused by MBH binaries in more massive stellar spheroids. Our results provide a natural explanation of why in nucleated galaxies hosting a MBH, the ratio (M_NSC+M_MBH)/M_bulge (with M_bulge the host spheroid's mass) shows significantly less scatter than M_NSC/M_bulge, and suggest that the formation of MBHs and NSCs are not mutually exclusive, as also supported by observations of co-existing systems. Both MBHs and NSCs represent generic products of galaxy formation, with NSCs being destroyed or modified by the merger evolution of their companion MBHs.

### The imprint of massive black-hole mergers on the correlation between nuclear clusters and their host galaxies [Replacement]

A literature compilation of nuclear star cluster (NSC) masses is used to study the correlation between global and nuclear properties. A comparison of observational data to the predictions of semi-analytical galaxy formation models places constraints on the co-evolution of NSCs, massive black holes (MBHs) and host galaxies. Both data and theoretical predictions show an increased scatter in the NSC scaling correlations at high galaxy masses, and we show that this is due to the progressively more efficient ejection of stars from NSCs caused by MBH binaries in more massive stellar spheroids. Our results provide a natural explanation of why in nucleated galaxies hosting a MBH, the ratio (M_NSC+M_MBH)/M_bulge (with M_bulge the host spheroid's mass) shows significantly less scatter than M_NSC/M_bulge, and suggest that the formation of MBHs and NSCs are not mutually exclusive, as also supported by observations of co-existing systems. Both MBHs and NSCs represent generic products of galaxy formation, with NSCs being destroyed or modified by the merger evolution of their companion MBHs.

### The imprint of massive black-hole mergers on the correlation between nuclear clusters and their host galaxies [Replacement]

A literature compilation of nuclear star cluster (NSC) masses is used to study the correlation between global and nuclear properties. A comparison of observational data to the predictions of semi-analytical galaxy formation models places constraints on the co-evolution of NSCs, massive black holes (MBHs) and host galaxies. Both data and theoretical predictions show an increased scatter in the NSC scaling correlations at high galaxy masses, and we show that this is due to the progressively more efficient ejection of stars from NSCs caused by MBH binaries in more massive stellar spheroids. Our results provide a natural explanation of why in nucleated galaxies hosting a MBH, the ratio (M_NSC+M_MBH)/M_bulge (with M_bulge the host spheroid's mass) shows significantly less scatter than M_NSC/M_bulge, and suggest that the formation of MBHs and NSCs are not mutually exclusive, as also supported by observations of co-existing systems. Both MBHs and NSCs represent generic products of galaxy formation, with NSCs being destroyed or modified by the merger evolution of their companion MBHs.

### The imprint of massive black-hole mergers on the correlation between nuclear clusters and their host galaxies [Cross-Listing]

A literature compilation of nuclear cluster (NSC) masses is used to study the correlation between global and NSC properties. A comparison of observational data to the predictions of semi-analytical galaxy formation models places constraints on the co-evolution of NSCs, massive black holes (MBHs) and host galaxies. Both data and theoretical predictions show an increased scatter in the NSC scaling correlations at high galaxy masses, and we show that this is due to the progressively more efficient ejection of stars from NSCs caused by MBH binaries in more massive stellar spheroids. Our results provide a natural explanation of why in nucleated galaxies hosting a MBH, the ratio (M_NSC+M_MBH)/M_bulge (with M_bulge the host spheroid's mass) shows significantly less scatter than M_NSC/M_bulge, and suggest that the formation of MBHs and NSCs are not mutually exclusive, as also supported by observations of co-existing systems. Both MBHs and NSCs represent generic products of galaxy formation, with NSCs being destroyed or modified by the merger evolution of their companion MBHs.

### Time variation of Kepler transits induced by stellar rotating spots - a way to distinguish between prograde and retrograde motion. II. Application to KOIs

Mazeh, Holczer, and Shporer (2015) have presented an approach that can, in principle, use the derived transit timing variation (TTV) of some transiting planets observed by the Kepler mission to distinguish between prograde and retrograde motion of their orbits with respect to the rotation of their parent stars. The approach utilizes TTVs induced by spot-crossing events that occur when the transiting planet moves across a spot on the stellar surface, by looking for a correlation between the derived TTVs and the stellar brightness derivatives at the corresponding transits, even in data that can not resolve the spot-crossing events themselves. We present here the application of this approach to the Kepler KOIs, identifying nine systems where the photometric spot modulation is large enough and the transit timing accurate enough to allow detection of a TTV-brightness-slope correlation. Excluding KOI-1546, which has been found recently to be a stellar binary, we are left with eight hot-Jupiter systems with high sensitivity to the correlation detection. Five of those eight systems show highly significant prograde motion, including two confirmed planets (KOI-203.01 = Kepler-17b and KOI-217.01 = Kepler-71b) and three planetary candidates (KOI-883.01, KOI-895.01, and KOI-1074.01), while no system displays retrograde motion, consistent with the suggestion that planets orbiting cool stars have prograde motion. All five systems have derived impact parameter $\lesssim$0.5, and all systems with an impact parameter in that range show significant correlation, except KOI-3.01 (= Kepler-3b = HAT-P-11b) where the lack of a correlation is explained by its large stellar obliquity. Although our sample is small, these findings hint that stellar spots, or at least the larger ones, have a tendency to be located at a low latitude on the stellar disc, similar to the Sun.

### Time variation of Kepler transits induced by stellar spots - a way to distinguish between prograde and retrograde motion. II. Application to KOIs [Replacement]

Mazeh, Holczer, and Shporer (2015) have presented an approach that can, in principle, use the derived transit timing variation (TTV) of some transiting planets observed by the $Kepler$ mission to distinguish between prograde and retrograde motion of their orbits with respect to their parent stars' rotation. The approach utilizes TTVs induced by spot-crossing events that occur when the planet moves across a spot on the stellar surface, looking for a correlation between the derived TTVs and the stellar brightness derivatives at the corresponding transits. This can work even in data that cannot temporally resolve the spot-crossing events themselves. Here we apply this approach to the $Kepler$ KOIs, identifying nine systems where the photometric spot modulation is large enough and the transit timing accurate enough to allow detection of a TTV-brightness-derivatives correlation. Of those systems five show highly significant prograde motion (Kepler-17b, Kepler-71b, KOI-883.01, KOI-895.01, and KOI-1074.01), while no system displays retrograde motion, consistent with the suggestion that planets orbiting cool stars have prograde motion. All five systems have impact parameter $0.2\lesssim b\lesssim0.5$, and all systems within that impact parameter range show significant correlation, except HAT-P-11b where the lack of a correlation follows its large stellar obliquity. Our search suffers from an observational bias against detection of high impact parameter cases, and the detected sample is extremely small. Nevertheless, our findings may suggest that stellar spots, or at least the larger ones, tend to be located at a low stellar latitude, but not along the stellar equator, similar to the Sun.

### Image patch analysis of sunspots and active regions. I. Intrinsic dimension and correlation analysis

Complexity of an active region is related to its flare-productivity. Mount Wilson or McIntosh sunspot classifications measure such complexity but in a categorical way, and may therefore not use all the information present in the observations. Moreover, such categorical schemes hinder a systematic study of an active region's evolution for example. We propose fine-scale quantitative descriptors for an active region's complexity and relate them to the Mount Wilson classification. We analyze the local correlation structure within continuum and magnetogram data, as well as the cross-correlation between continuum and magnetogram data. We compute the intrinsic dimension, partial correlation, and canonical correlation analysis (CCA) of image patches of continuum and magnetogram active region images taken from the SOHO-MDI instrument. We use masks of sunspots derived from continuum as well as larger masks of magnetic active regions derived from the magnetogram to analyze separately the core part of an active region from its surrounding part. We find the relationship between complexity of an active region as measured by Mount Wilson and the intrinsic dimension of its image patches. Partial correlation patterns exhibit approximately a third-order Markov structure. CCA reveals different patterns of correlation between continuum and magnetogram within the sunspots and in the region surrounding the sunspots. These results also pave the way for patch-based dictionary learning with a view towards automatic clustering of active regions.

### A statistical correlation of sunquakes based on their seismic, white light, and X-ray emission

Several mechanisms have been proposed to explain the transient seis- mic emission, i.e., sunquakes, from some solar flares. Some theories associate high-energy electrons and/or white-light emission with sunquakes. High-energy charged particles and their subsequent heating of the photosphere and/or chro- mosphere could induce acoustic waves in the solar interior. We carried out a correlative study of solar flares with emission in hard-X rays (HXRs), enhanced continuum emission at 6173{\AA}, and transient seismic emission. We selected those flares observed by RHESSI (Reuven Ramaty High Energy Solar Spectroscopic Imager) with a considerable flux above 50 keV between January 1, 2010 and June 26, 2014. We then used data from the Helioseismic and Magnetic Imager onboard the Solar Dynamic Observatory (SDO/HMI) to search for excess visible continuum emission and new sunquakes not previously reported. We found a total of 18 sunquakes out of 75 investigated. All of the sunquakes were associated with a enhancement of the visible continuum during the flare time. Finally, we calculated a coefficient of correlation for a set of dichotomic variables related to these observations. We found a strong correlation between two of the standard helioseismic detection techniques, and between sunquakes and visible continuum enhancements. We discuss the phenomenological connectivity between these physical quantities and the observational difficulties of detecting seismic signals and excess continuum radiation.

### Searching for signatures of planet formation in stars with circumstellar debris discs

(Abridged) Tentative correlations between the presence of dusty debris discs and low-mass planets have been presented. In parallel, detailed chemical abundance studies have reported different trends between samples of planet and non-planet hosts. We determine in a homogeneous way the metallicity, and abundances of a sample of 251 stars including stars with known debris discs, with debris discs and planets, and only with planets. Stars with debris discs and planets have the same [Fe/H] behaviour as stars hosting planets, and they also show a similar <[X/Fe]>-Tc trend. Different behaviour in the <[X/Fe]>-Tc trend is found between the samples of stars without planets and the samples of planet hosts. In particular, when considering only refractory elements, negative slopes are shown in cool giant planet hosts, whilst positive ones are shown in stars hosting low-mass planets. Stars hosting exclusively close-in giant planets show higher metallicities and positive <[X/Fe]>-Tc slope. A search for correlations between the <[X/Fe]>-Tc slopes and the stellar properties reveals a moderate but significant correlation with the stellar radius and as well as a weak correlation with the stellar age. The fact that stars with debris discs and stars with low-mass planets do not show neither metal enhancement nor a different <[X/Fe]>-Tc trend might indicate a correlation between the presence of debris discs and the presence of low-mass planets. We extend results from previous works which reported differences in the <[X/Fe]>-Tc trends between planet hosts and non hosts. However, these differences tend to be present only when the star hosts a cool distant planet and not in stars hosting exclusively low-mass planets.

### T violation in radiative $β$ decay and electric dipole moments

In radiative $\beta$ decay, $T$ violation can be studied through a spin-independent $T$-odd correlation. We consider contributions to this correlation by beyond the standard model (BSM) sources of $T$-violation, arising above the electroweak scale. At the same time such sources, parametrized by dimension-6 operators, can induce electric dipole moments (EDMs). As a consequence, the manifestations of the $T$-odd BSM physics in radiative $\beta$ decay and EDMs are not independent. Here we exploit this connection to show that current EDM bounds already strongly constrain the spin-independent $T$-odd correlation in radiative $\beta$ decay.

### Reanalyzing the visible colors of Centaurs and KBOs: what is there and what we might be missing

Visible colors (BVRI) are a reasonable proxy for real spectra of Centaurs and Kuiper Belt Objects, which are rather linear in this range. Colors provide limited information but remain the best tool to study the bulk surface properties. We explore recurrent effects in the study of visible colors: i) how a correlation could be missed or weakened as a result of the data error bars, ii) the "risk" of missing an existing trend because of low sampling, and the possibility of making quantified predictions on the sample size needed to detect a trend at a given significance level, iii) the use of partial correlations to distinguish the mutual effect of two or more parameters, and iv) the sensitivity of the "reddening line" tool to the central wavelength of the filters used. We have compiled the visible colors of about 370 objects available in the literature and carried out an analysis per dynamical family. Our results show how a) data error bars impose a limit on the detectable correlations regardless of sample size and that therefore, once that limit is achieved, it is important to diminish the error bars, but it is pointless to enlarge the sampling with the same or larger errors; b) almost all dynamical families still require larger samplings to ensure the detection of correlations stronger than 0.5; c) the correlation strength between (V-R) vs. (R-I) is systematically lower than the one between (B-V) vs. (V-R) and is not related with error-bar differences between these colors; d) it is statistically equivalent to use any of the different flavors of orbital excitation or collisional velocity parameters regarding the color-inclination correlation of classical KBOs whereas the inclination and Tisserand parameter relative to Neptune cannot be separated from one another; and e) classical KBOs are the only dynamical family that shows neither (B-V) vs. (V-R) nor (V-R) vs. (R-I) correlations.

### Discovery of the correlation between peak episodic jet power and X-ray peak luminosity of the soft state in black hole transients

Episodic jets are usually observed in the intermediate state of black hole transients during their X-ray outbursts. Here we report the discovery of a strong positive correlation between the peak radio power of the episodic jet $P_{\rm jet}$ and the corresponding peak X-ray luminosity $L_{\rm x}$ of the soft state (in Eddington units) in a complete sample of the outbursts of black hole transients observed during the RXTE era of which data are available, which follows the relation $\log P_{\rm jet}=(2.17\pm{0.32})+(1.63\pm0.24)\times \log {L_{\rm x}}$. The transient ultra-luminous X-ray source in M31 and HLX-1 in EXO 243-49 fall on the relation if they contain stellar mass black hole and either stellar mass black hole or intermediate mass black hole, respectively. Besides, a significant correlation between the peak power of the episodic jet and the rate-of-increase of the X-ray luminosity $\rm dL_{x}/dt$ during the rising phase of those outbursts is also found, following $\log P_{\rm jet}=(1.97\pm{0.42})+(0.69\pm0.15)\times \log {\rm d}L_{\rm x}/{\rm d}t$. In GX 339$-$4 and H 1743$-$322 in which data for two outbursts are available, measurements of the peak radio power of the episodic jet and the X-ray peak luminosity (and its rate-of-change) shows similar positive correlations between outbursts, which demonstrate the dominant role of accretion over black hole spin in generating episodic jet power. On the other hand, no significant difference is seen among the systems with different measured black hole spin in current sample. This implies that the power of the episodic jet is strongly affected by non-stationary accretion characterised primarily by the rate-of-change of the mass accretion rate.

### Discovery of the correlation between peak episodic jet power and X-ray peak luminosity of the soft state in black hole transients [Replacement]

Episodic jets are usually observed in the intermediate state of black hole transients during their X-ray outbursts. Here we report the discovery of a strong positive correlation between the peak radio power of the episodic jet $P_{\rm jet}$ and the corresponding peak X-ray luminosity $L_{\rm x}$ of the soft state (in Eddington units) in a complete sample of the outbursts of black hole transients observed during the RXTE era of which data are available, which follows the relation $\log P_{\rm jet}=(2.2\pm{0.3})+(1.6\pm0.2)\times \log {L_{\rm x}}$. The transient ultra-luminous X-ray source in M31 and HLX-1 in EXO 243-49 fall on the relation if they contain stellar mass black hole and either stellar mass black hole or intermediate mass black hole, respectively. Besides, a significant correlation between the peak power of the episodic jet and the rate-of-increase of the X-ray luminosity $\rm dL_{x}/dt$ during the rising phase of those outbursts is also found, following $\log P_{\rm jet}=(2.0\pm{0.4})+(0.7\pm0.2)\times \log {\rm d}L_{\rm x}/{\rm d}t$. In GX 339$-$4 and H 1743$-$322 in which data for two outbursts are available, measurements of the peak radio power of the episodic jet and the X-ray peak luminosity (and its rate-of-change) shows similar positive correlations between outbursts, which demonstrate the dominant role of accretion over black hole spin in generating episodic jet power. On the other hand, no significant difference is seen among the systems with different measured black hole spin in current sample. This implies that the power of the episodic jet is strongly affected by non-stationary accretion instead of black hole spin characterized primarily by the rate-of-change of the mass accretion rate.

### Analysing the effects of apodizing windows on local correlation tracking using Nirvana simulations of convection

We employ different shapes of apodizing windows in the local correlation tracking (LCT) routine to retrieve horizontal velocities using numerical simulations of convection. LCT was applied on a time sequence of temperature maps generated by the Nirvana code with four different apodizing windows, namely--Gaussian, Lorentzian, trapezoidal and triangular, with varying widths. In terms of correlations (between the LCT-retrieved and simulated flow field), the triangular and the trapezoidal perform the best and worst, respectively. On segregating the intrinsic velocities in the simulations on the basis of their magnitudes, we find that for all windows, a significantly higher correlation is obtained for the intermediate and high-velocity bins and only modest or weak values in the low-velocity bins. The differences between the LCT-retrieved and simulated flow fields were determined spatially which show large residuals at or close to the boundary of granules. The extent to which the horizontal flow vectors retrieved by LCT compare with the simulated values, depends entirely on the width of the central peak of the apodizing window for a given $\sigma$. Even though LCT suffers from a lack of spatial content as seen in simulations, its simplicity and speed could serve as a viable first-order tool to probe horizontal flows--one that is ideal for large data sets.

### Extending the Correlation of $L_R - L_X$ to Gamma Ray Bursts

The well-known correlation between the radio luminosity ($L_R$) and the X-ray luminosity ($L_X$) $L_R / L_X \simeq 10^{-5}$ holds for a variety of objects like active galactic nuclei, galactic black holes, solar flares and cool stars. Here we extend the relation to gamma-ray bursts (GRBs), and find the GRBs also lay on the same $L_R-L_X$ relation, with a slightly different slope as $L_R \propto L_X^{1.1}$. This relation implies the explosions in different scales may have a common underlying origin.

### Radio--Far infrared correlation in "blue cloud" galaxies with 0<z<1.2

We study the radio--far infrared (FIR) correlation in "blue cloud" galaxies chosen from the PRism MUltiobject Survey (PRIMUS) up to redshift ($z$) of 1.2 in the XMM-LSS field. We use rest-frame emission at 1.4 GHz in the radio and both monochromatic (at 70$\mu$m) and bolometric (between $8-1000~\mu$m) emission in the FIR. To probe the nature of the correlation up to $z\sim1.2$, where direct detection of blue star-forming galaxies is impossible with current technology, we employ the technique of image stacking at 0.325 and 1.4 GHz in the radio and in six infrared bands, viz. 24, 70, 160, 250, 350 and $500~\mu$m. For comparison, we also study the correlation for more luminous galaxies that are directly detected. The stacking analysis allows us to probe the radio--FIR correlation for galaxies that are up to 2 orders of magnitude fainter than the ones detected directly. The $k-$correction in the infrared wavebands is obtained by fitting the observed spectral energy distribution (SED) with a composite mid-IR power law and a single temperature greybody model. We find that the radio luminosity at 1.4 GHz ($L_{\rm 1.4GHz}$) is strongly correlated with monochromatic FIR luminosity at 70 $\mu$m ($L_{\rm 70\mu m}$) having slope $1.09\pm0.05$ and with bolometric luminosity ($L_{\rm TIR}$) having slope $1.11\pm0.04$. The quantity $q_{\rm TIR} (=\log_{10}[L_{\rm TIR}/(3.75\times 10^{12} L_{\rm 1.4 GHz})])$ is observed to decrease with redshift as $q_{\rm TIR} \propto (1+z)^{-0.16\pm0.03}$ probably caused due to the non-linear slope of the radio--FIR correlation. Within the uncertainties of our measurement and the limitations of our flux-limited and color-selected sample, we do not find any evolution of the radio--FIR correlation with redshift.

### Breaking FIR-Radio Correlation: The Case of Interacting Galaxies

Far-infrared (FIR)--radio correlation is a well-established empirical connection between continuum radio and dust emission of star-forming galaxies, used as a tool in determining star-formation rates. Here we point out that in the case of interacting star-forming galaxies this tool might break. Galactic interactions and mergers have been known to give rise to tidal shocks and disrupt morphologies especially in the smaller of the interacting components. Moreover, these shocks can also heat the gas and dust and accelerate particles leading to tidal cosmic-ray population in addition to standard galactic cosmic rays. Both heating and additional non-thermal radiation will obviously affect the FIR-radio correlation of these systems. To test this hypothesis we have analyzed a sample of 43 infrared bright star-forming interacting galaxies at different merger stages. We have found that their FIR-radio correlation parameter and radio emission spectral index vary over different merger stages and behave as it would be expected from our tidal-shock scenario. Important implications of breaking the FIR-radio correlation are discussed.

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