# Posts Tagged correlation

## Recent Postings from correlation

### Physical properties of molecular clouds for the entire Milky Way disk

This study presents a catalog of 8107 molecular clouds that covers the entire Galactic plane and includes 98% of the $^{12}$CO emission observed within $b\pm5^\circ$. The catalog was produced using a hierarchical cluster identification method applied to the result of a Gaussian decomposition of the Dame et al. data. The total H$_2$ mass in the catalog is $1.2\times10^9$ M$_\odot$ in agreement with previous estimates. We find that 30% of the sight lines intersect only a single cloud, with another 25% intersecting only two clouds. The most probable cloud size is $R\sim30$ pc. We find that $M\propto R^{2.2\pm0.2}$, with no correlation between the cloud surface density, $\Sigma$, and $R$. In contrast with the general idea, we find a rather large range of values of $\Sigma$, from 2 to 300 M$_\odot$ pc$^{-2}$, and a systematic decrease with increasing Galactic radius, $R_{\rm gal}$. The cloud velocity dispersion as well as the normalization $\sigma_0=\sigma_v/R^{1/2}$ both decrease systematically with $R_{\rm gal}$. When studied over the whole Galactic disk, there is a large dispersion in the linewidth-size relation, and a significantly better correlation between $\sigma_v$ and $\Sigma R$. The normalization of this correlation is constant to better than a factor of two for $R_{\rm gal}<20$ kpc. This relation is used to disentangle the ambiguity between near and far kinematic distances. We report a strong variation of the turbulent energy injection rate. In the outer Galaxy it may be maintained by accretion through the disk and/or onto the clouds, but neither source can drive the 100 times higher cloud averaged injection rate in the inner Galaxy.

### Cosmology with gamma-ray bursts: I. The Hubble diagram through the calibrated $E_{\rm p,i}$ - $E_{\rm iso}$ correlation

Gamma-ray bursts are the most energetic explosions in the Universe. They are detectable up to very high redshifts, therefore can be used to study the expansion rate of the Universe and to investigate the observational properties of dark energy, provided that empirical correlations between spectral and intensity properties are appropriately calibrated. We used the type Ia supernova luminosity distances to calibrate the correlation between the peak photon energy, $E_{p, i}$, and the isotropic equivalent radiated energy, $E_{iso}$ in GRBs. With this correlation, we tested the reliability of applying GRBs to measure cosmological parameters and to obtain indications on the basic properties and evolution of dark energy. Using 162 GRBs with measured redshifts and spectra, we applied a local regression technique to calibrate the $E_{p, i}$-$E_{iso}$ correlation against the type Ia SN data to build a calibrated GRB Hubble diagram. We tested the possible redshift dependence of the correlation and its effect on the Hubble diagram. Finally, we used the GRB Hubble diagram to investigate the dark energy EOS. For this, we focused on the so-called Chevalier-Polarski-Linder (CPL) parametrization of the dark energy EOS and implemented the Markov chain Monte Carlo (MCMC) method to efficiently sample the space of cosmological parameters. Our analysis shows once more that the $E_{p, i}$-$E_{iso}$ correlation has no significant redshift dependence. Therefore the high-redshift GRBs can be used as a cosmological tool to determine the basic cosmological parameters and to test different models of dark energy in the redshift region ($z\geqslant 3$), which is unexplored by the SNIa and baryonic acoustic oscillations data. Our updated calibrated Hubble diagram of GRBs provides some marginal indication (at $1\sigma$ level) of an evolving dark energy EOS.

### Cosmology with the CMB temperature-polarization correlation

We demonstrate that the CMB temperature-polarization cross-correlation provides accurate and robust constraints on cosmological parameters. We compare them with the results from temperature or polarization and investigate the impact of foregrounds, cosmic variance and instrumental noise. This analysis makes use of the Planck high-l HiLLiPOP likelihood based on angular power spectra that takes into account systematics from the instrument and foreground residuals directly modeled using Planck measurements. The temperature-polarization correlation (TE) spectrum is less contaminated by astrophysical emissions than the temperature power-spectrum (TT) allowing to derive constraints that are less sensitive to foreground uncertainties. For LCDM parameters, TE gives very competitive results compared to TT. For LCDM model extensions, it is limited by the instrumental noise level in the polarization maps.

### SNR radio spectral index distribution and its correlation with polarization: a case study of Lupus Loop

We use radio-continuum all-sky surveys at 1420 and 408 MHz with the aim to investigate properties of the Galactic radio source Lupus Loop. The survey data at 1435 MHz, with the linear polarization of the southern sky, is also used. We calculate properties of this supernova remnant: the brightness temperature, surface brightness and radio spectral index. For determining borders and calculation of its properties, we use the method we have developed. The non-thermal nature of its radiation is confirmed. The distribution of spectral index over its area is also given. A significant correlation between the radio spectral index distribution and the corresponding polarized intensity distribution inside the loop borders is found, indicating that the polarization maps could provide us information about the distribution of interstellar medium, and thus could represent one additional way to search for new Galactic loops.

### BAT AGN Spectroscopic Survey-III. An observed link between AGN Eddington ratio and narrow emission line ratios

We investigate the observed relationship between black hole mass ($M_{\rm BH}$), bolometric luminosity ($L_{\rm bol}$), and Eddington ratio (${\lambda}_{\rm Edd}$) with optical emission line ratios ([NII] {\lambda}6583/H{\alpha}, [SII] {\lambda}{\lambda}6716,6731/H{\alpha}, [OI] {\lambda}6300/H{\alpha}, [OIII] {\lambda}5007/H{\beta}, [NeIII] {\lambda}3869/H{\beta}, and HeII {\lambda}4686/H{\beta}) of hard X-ray-selected AGN from the BAT AGN Spectroscopic Survey (BASS). We show that the [NII] {\lambda}6583/H{\alpha} ratio exhibits a significant correlation with ${\lambda}_{\rm Edd}$ ($R_{\rm Pear}$ = -0.44, $p$-value=$3\times10^{-13}$, {\sigma} = 0.28 dex), and the correlation is not solely driven by $M_{\rm BH}$ or $L_{\rm bol}$. The observed correlation between [NII] {\lambda}6583/H{\alpha} ratio and $M_{\rm BH}$ is stronger than the correlation with $L_{\rm bol}$, but both are weaker than the ${\lambda}_{\rm Edd}$ correlation. This implies that the large-scale narrow lines of AGN host galaxies carry information about the accretion state of the AGN central engine. We propose that the [NII] {\lambda}6583/H{\alpha} is a useful indicator of Eddington ratio with 0.6 dex of rms scatter, and that it can be used to measure ${\lambda}_{\rm Edd}$ and thus $M_{\rm BH}$ from the measured $L_{\rm bol}$, even for high redshift obscured AGN. We briefly discuss possible physical mechanisms behind this correlation, such as the mass-metallicity relation, X-ray heating, and radiatively driven outflows.

### Multiplicity fluctuation and correlation of identified baryons in quark combination model [Cross-Listing]

The dynamical fluctuation and correlation of multiplicity distributions of identified baryons and antibaryons produced by the hadronization of the bulk quark system are systematically studied in quark combination model. Starting from the most basic dynamics of quark combination which are necessary for multiplicity study, we analyze moments (variance, skewness and kurtosis) of inclusive multiplicity distribution of identified baryons, two-baryon multiplicity correlations, and baryon-antibaryon multiplicity correlations after the hadronization of quark system with given quark number and antiquark number. We obtain a series of interesting findings, e.g., binomial behavior of multiplicity moments, coincide flavor dependent two-baryon correlation and universal baryon-antibaryon correlation, which can be regarded as general features of quark combination. We further take into account correlations and fluctuations of quark numbers before hadronization to study their influence on multiple production of baryons and antibaryons. We find that quark number fluctuation and flavor conservation lead to a series of important results such as the negative $p\bar{\Omega}^{+}$ multiplicity correlation and universal two-baryon correlations. We also study the influence of resonance decay in order to compare our results with future experimental data in ultra-relativistic heavy ion collisions at LHC.

### The physical properties of \textit{Fermi} TeV BL Lac objects jets

We investigate the physical properties of \textit{Fermi} TeV BL Lac objects jets by modeling the quasi-simultaneous spectral energy distribution of 29 \textit{Fermi} TeV BL Lacs in the frame of a one-zone leptonic synchrotron self-Compton model. Our main results are the following: (i) There is a negative correlation between $B$ and $\delta$ in our sample, which suggests that $B$ and $\delta$ are dependent on each other mainly in Thomson regime. (ii) There are negative correlations between $\nu_{\text{sy}}$ and $r$, the $\nu_{\text{IC}}$ and $r$, which is a signature of the energy-dependence statistical acceleration or the stochastic acceleration. There is a significant correlation between $r$ and $s$, which suggests that the curvature of the electron energy distribution is attributed to the energy-dependence statistical acceleration mechanism. (iii) By assuming one proton per relativistic electron, we estimate the jet power and radiative power. A size relation $P_{\text{e}} \sim P_{\text{p}} > P_{\text{r}} \gtrsim P_{\text{B}}$ is found in our sample. The $P_{\text{e}}>P_{\text{B}}$ suggests that the jets are particle dominated, and the $P_{\text{e}}\sim P_{\text{p}}$ means that the mean energy of relativistic electrons approaches $m_{\text{p}}/m_{\text{e}}$. There are not significant correlations between $P_{\text{jet}}$ and black hole mass in high or low state with a sub-sample of 18 sources, which suggests that the jet power weakly depends on the black hole mass. (iv) There is a correlation between the changes in the flux density at 1 TeV and the changes in the $\gamma_{\text{peak}}$, which suggests the change/evolution of electron energy distribution may be mainly responsible for the flux variation.

### Curvature of the spectral energy distribution, the dominant process for inverse Compton component and other jet properties in Fermi 2LAC blazars

We fit the spectral energy distributions (SEDs) of members of a large sample of Fermi 2LAC blazars to synchrotron and inverse Compton (IC) models. Our main results are as follows. (i) As suggested by previous works, the correlation between peak frequency and curvature can be explained by statistical or stochastic particle acceleration mechanisms. For BL Lacs, we find a linear correlation between synchrotron peak frequency and its curvature. The slope of the correlation is consistent with the stochastic acceleration mechanisms and confirm previous studies. For FSRQs, we also find a linear correlation, but its slope cannot be explained by previous theoretical models. (ii) We find a significant correlation between IC luminosity and synchrotron luminosity. The slope of the correlation of FSRQs is consistent with the EC process. And the slope of the correlation of BL Lac is consistent with the SSC process. (iii) We find several significant correlations between IC curvature and several basic parameters of blazars (black hole mass, broad line luminosity, the Lorentz factor of jet). We also find significant correlations between bolometric luminosity and these basic parameters of blazars which suggest that the origin of jet is a mixture of the mechanisms proposed by Blandford $\&$ Znajek and by Blandford $\&$ Payne.

### The Role of Angular Momentum Transport in Establishing the Accretion Rate--Protostellar Mass Correlation

We model the mass accretion rate $\dot{M}$ to stellar mass $M_*$ correlation that has been inferred from observations of intermediate to upper mass T Tauri stars---that is $\dot{M} \propto M_*^{1.3 \pm 0.3}$. We explain this correlation within the framework of quiescent disk evolution, in which accretion is driven largely by gravitational torques acting in the bulk of the mass and volume of the disk. Stresses within the disk arise from the action of gravitationally driven torques parameterized in our 1D model in terms of Toomre's $Q$ criterion. We do not model the hot inner sub-AU scale region of the disk that is likely stable according to this criterion, and appeal to other mechanisms to remove or redistribute angular momentum and allow accretion onto the star. Our model has the advantage of agreeing with large-scale angle-averaged values from more complex nonaxisymmetric calculations. The model disk transitions from an early phase (dominated by initial conditions inherited from the burst mode of accretion) into a later self-similar mode characterized by a steeper temporal decline in $\dot{M}$. The models effectively reproduce the spread in mass accretion rates that have been observed for protostellar objects of $0.2\,\mbox{M}_\odot \le M_* \le 3.0\,\mbox{M}_\odot$, such as those found in the $\rho$ Ophiuchus and Taurus star forming regions. We then compare realistically sampled populations of young stellar objects produced by our model to their observational counterparts. We find these populations to be statistically coincident, which we argue is evidence for the role of gravitational torques in the late time evolution of quiescent protostellar disks.

### A new correlation with lower kilohertz quasi-periodic oscillation frequency in the ensemble of low-mass X-ray binaries

We study the dependence of kHz quasi-periodic oscillation (QPO) frequency on accretion-related parameters in the ensemble of neutron star low-mass X-ray binaries. Based on the mass accretion rate, $\dot{M}$, and the magnetic field strength, $B$, on the surface of the neutron star, we find a correlation between the lower kHz QPO frequency and $\dot{M}/B^{2}$. The correlation holds in the current ensemble of Z and atoll sources and therefore can explain the lack of correlation between the kHz QPO frequency and X-ray luminosity in the same ensemble. The average run of lower kHz QPO frequencies throughout the correlation can be described by a power-law fit to source data. The simple power-law, however, cannot describe the frequency distribution in an individual source. The model function fit to frequency data, on the other hand, can account for the observed distribution of lower kHz QPO frequencies in the case of individual sources as well as the ensemble of sources. The model function depends on the basic length scales such as the magnetospheric radius and the radial width of the boundary region, both of which are expected to vary with $\dot{M}$ to determine the QPO frequencies. In addition to modifying the length scales and hence the QPO frequencies, the variation in $\dot{M}$, being sufficiently large, may also lead to distinct accretion regimes, which would be characterized by Z and atoll phases.

### The evolution of far-infrared CO emission from protostars

We investigate the evolution of far-IR CO emission from protostars observed with Herschel/PACS for 50 sources from the combined sample of HOPS and DIGIT Herschel key programs. From the uniformly sampled spectral energy distributions, we computed $L_{\rm{bol}}$, $T_{\rm{bol}}$ and $L_{\rm {bol}}/L_{\rm {smm}}$ for these sources to search for correlations between far-IR CO emission and protostellar properties. We find a strong and tight correlation between far-IR CO luminosity ($L^{\rm fir}_{\rm CO}$) and the bolometric luminosity ($L_{\rm{bol}}$) of the protostars with $L^{\rm fir}_{\rm CO}$ $\propto$ $L_{\rm{bol}}^{0.7}$. We, however, do not find a strong correlation between $L^{\rm fir}_{\rm CO}$ and protostellar evolutionary indicators, $T_{\rm{bol}}$ and $L_{\rm {bol}}/L_{\rm {smm}}$. FIR CO emission from protostars traces the currently shocked gas by jets/outflows, and $L^{\rm fir}_{\rm CO}$ is proportional to the instantaneous mass loss rate, $\dot{M}_{\rm{out}}$. The correlation between $L^{\rm fir}_{\rm CO}$ and $L_{\rm{bol}}$ is indicative of instantaneous $\dot{M}_{\rm{out}}$ tracking instantaneous $\dot{M}_{\rm{acc}}$. The lack of correlation between $L^{\rm fir}_{\rm CO}$ and evolutionary indicators $T_{\rm{bol}}$ and $L_{\rm {bol}}/L_{\rm {smm}}$ suggests that $\dot{M}_{\rm{out}}$ and, therefore, $\dot{M}_{\rm{acc}}$ do not show any clear evolutionary trend. These results are consistent with mass accretion/ejection in protostars being episodic. Taken together with the previous finding that the time-averaged mass ejection/accretion rate declines during the protostellar phase (e.g., Bontemps et al. 1996), our results suggest that the instantaneous accretion/ejection rate of protostars is highly time variable and episodic, but the amplitude and/or frequency of this variability decreases with time such that the time averaged accretion/ejection rate declines with system age.

### Search for gamma-ray emission from star-forming galaxies with Fermi LAT

Recent studies have found a positive correlation between the star-formation rate of galaxies and their gamma-ray luminosity. Galaxies with a high star-formation rate are expected to produce a large amount of high-energy cosmic rays, which emit gamma-rays when interacting with the interstellar medium and radiation fields. We search for gamma-ray emission from a sample of galaxies within and beyond the Local Group with data from the LAT instrument onboard the Fermi satellite. We exclude recently detected galaxies (NGC 253, M82, NGC 4945, NGC 1068, NGC 2146, Arp 220) and use seven years of cumulative Pass 8 data from the LAT in the 100 MeV to 100 GeV range. No new detections are seen in the data and upper limits for the gamma- ray fluxes are calculated. The correlation between gamma-ray luminosity and infrared luminosity for galaxies obtained using our new upper limits is in agreement with a previously published correlation, but the new upper limits imply that some galaxies are not as efficient gamma-ray emitters as previously thought.

### Hydrodynamic Predictions for Mixed Harmonic Correlations in 200 GeV Au+Au Collisions [Replacement]

Recent measurements at the LHC involve the correlation of different azimuthal flow harmonics $v_n$. These new observables add constraints to theoretical models and probe aspects of the system that are independent of the traditional single-harmonic measurements such as 2- and multi-particle cumulants $v_n\{m\}$. Many of these new observables have not yet been measured at RHIC, leaving an opportunity to make predictions as a test of models across energies. We make predictions using NeXSPheRIO, a hydrodynamical model which has accurately reproduced a large set of single-harmonic correlations in a large range of transverse momenta and centralities at RHIC. Our predictions thus provide an important baseline for comparison to correlations of flow harmonics, which contain non-trivial information about the initial state as well as QGP transport properties. We also point out significant biases that can appear when using wide centrality bins and non-trivial event weighting, necessitating care in performing experimental analyses and in comparing theoretical calculations to these measurements.

### The rotation - Lithium depletion correlation in the beta Pictoris association and the LDB age determination

There is evidence in the 125-Myr Pleiades cluster, and more recently in the 5-Myr NGC 2264 cluster, that rotation plays a key role in the Lithium (Li) depletion processes among low-mass stars. Fast rotators appear to be less Li-depleted than equal-mass slow rotators. We intend to explore the existence of a Li depletion - rotation connection among the beta Pictoris members at an age of about 24 Myr, and to use such correlation either to confirm or to improve the age estimate based on the Lithium Depletion Boundary (LDB) modeling. We have photometrically monitored all the known members of the beta Pictoris association with at least one Lithium equivalent width (Li EW) measurement from the literature. We measured the rotation periods of 30 members for the first time and retrieved from the literature the rotation periods for other 36 members, building a catalogue of 66 members with measured rotation period and Li EW. We find that in the 0.3 < M < 0.8 Msun range, there is a strong correlation between rotation and Li EW. For higher mass stars, no significant correlation is found. For very low mass stars in the Li depletion onset, at about 0.1 Msun, data are too few to infer a significant correlation. The observed Li EWs are compared with those predicted by the Dartmouth stellar evolutionary models that incorporate the effects of magnetic fields. After decorrelating the Li EW from the rotation period, we find that the hot side of the LDB is fitted well by Li EW values corresponding to an age of 25$\pm$3 Myr in good agreement with independent estimates from the literature.

### The rotation - Lithium depletion correlation in the beta Pictoris association and LDB age determination [Replacement]

There is evidence in the 125-Myr Pleiades cluster, and more recently in the 5-Myr NGC 2264 cluster, that rotation plays a key role in the Lithium (Li) depletion processes among low-mass stars. Fast rotators appear to be less Li-depleted than equal-mass slow rotators. We intend to explore the existence of a Li depletion - rotation connection among the beta Pictoris members at an age of about 24 Myr, and to use such correlation either to confirm or to improve the age estimate based on the Lithium Depletion Boundary (LDB) modeling. We have photometrically monitored all the known members of the beta Pictoris association with at least one Lithium equivalent width (Li EW) measurement from the literature. We measured the rotation periods of 30 members for the first time and retrieved from the literature the rotation periods for other 36 members, building a catalogue of 66 members with measured rotation period and Li EW. We find that in the 0.3 < M < 0.8 Msun range, there is a strong correlation between rotation and Li EW. For higher mass stars, no significant correlation is found. For very low mass stars in the Li depletion onset, at about 0.1 Msun, data are too few to infer a significant correlation. The observed Li EWs are compared with those predicted by the Dartmouth stellar evolutionary models that incorporate the effects of magnetic fields. After decorrelating the Li EW from the rotation period, we find that the hot side of the LDB is fitted well by Li EW values corresponding to an age of 25$\pm$3 Myr in good agreement with independent estimates from the literature.

### The Relationship Between Star-formation Activity and Galaxy Structural Properties in CANDELS and a Semi-analytic Model [Replacement]

We study the correlation of galaxy structural properties with their location relative to the SFR-M* correlation, also known as the star formation "main sequence" (SFMS), in the CANDELS and GAMA surveys and in a semi-analytic model (SAM) of galaxy formation. We first study the distribution of median Sersic index, effective radius, star formation rate (SFR) density and stellar mass density in the SFR-M* plane. We then define a redshift dependent main sequence and examine the medians of these quantities as a function of distance from this main sequence, both above (higher SFRs) and below (lower SFRs). Finally, we examine the distributions of distance from the main sequence in bins of these quantities. We find strong correlations between all of these galaxy structural properties and the distance from the SFMS, such that as we move from galaxies above the SFMS to those below it, we see a nearly monotonic trend towards higher median Sersic index, smaller radius, lower SFR density, and higher stellar density. In the semi-analytic model, bulge growth is driven by mergers and disk instabilities, and is accompanied by the growth of a supermassive black hole which can regulate or quench star formation via Active Galactic Nucleus (AGN) feedback. We find that our model qualitatively reproduces the trends described above, supporting a picture in which black holes and bulges co-evolve, and AGN feedback plays a critical role in moving galaxies off of the SFMS.

### What determines the observational differences of blazars?

We examine the scenario that the Doppler factor determines the observational differences of blazars in this paper. Significantly negative correlations are found between the observational synchrotron peak frequency and the Doppler factor. After correcting the Doppler boosting, the intrinsic peak frequency further has a tightly linear relation with the Doppler factor. It is more interesting that this relation is consistent with the scenario that the black hole mass governs both the bulk Lorentz factor and the synchrotron peak frequency. In addition, the distinction of the kinetic jet powers between BL Lacs and FSRQs disappears after the boosting factor $\delta^2$ is considered. The negative correlation between the peak frequency and the observational isotropic luminosity, known as the blazar sequence, also disappears after the Doppler boosting is corrected. We also find that the correlation between the Compton dominance and the Doppler factor exists for all types of blazars. Therefore, this correlation is unsuitable to examine the external Compton emission dominance.

### Similarity of Jet Radiation between Flat Spectrum Radio Quasars and GeV Narrow-Line Seyfert 1 Galaxies: A Universal $\delta$-$L_{\rm c}$ Correlation

By modeling the broadband spectral energy distributions (SEDs) of a typical flat spectrum radio quasar (FSRQ, 3C 279) and two GeV narrow-line Seyfert 1 galaxies (NLS1s, PMN J0948+0022 and 1H 0323+342) in different flux stages with the one-zone leptonic models, we find a universal correlation between their Doppler factors ($\delta$) and peak luminosities ($L_{\rm c}$) of external Compton scattering bumps. Compiling a combined sample of FSRQs and GeV NLS1s, it is found that both FSRQs and GeV NLS1s in different stages and in different sources well follow the same $\delta$-$L_{\rm c}$ correlation. This indicates that the variations of observed luminosities may be essentially due to the Doppler boosting effect. And the universal $\delta$-$L_{\rm c}$ relation between FSRQs and GeV NLS1s in different stages may be further evidence that the particle acceleration and radiation mechanisms for the two kinds of sources are similar. In addition, by replacing $L_{\rm c}$ with the observed luminosity in the Fermi/LAT band ($L_{\rm LAT}$), this correlation holds, and it may serve as an empirical indicator of $\delta$. We estimate the $\delta$ values with $L_{\rm LAT}$ for 484 FSRQs in the Fermi/LAT Catalog and they range from 3 to 41, with a median of 16, which are statistically consistent with the values derived by other methods.

### A statistical investigation of the mass discrepancy-acceleration relation

We use the mass discrepancy-acceleration relation (the correlation between the ratio of dark-to-visible mass and acceleration in galaxies; MDAR) to test the galaxy-halo connection. We analyse the MDAR using a set of 14 statistics which quantify its four most important features: its shape, its scatter, the presence of a "characteristic acceleration scale," and the correlation of its residuals with other galaxy properties. We construct an empirical framework for the galaxy-halo connection in $\Lambda$CDM to generate predictions for these statistics, starting with conventional correlations (halo abundance matching; AM) and introducing more where required. Comparing to the SPARC data (Lelli, McGaugh & Schombert 2016), we find: 1) The approximate shape of the MDAR is readily reproduced by AM, and there is no evidence that the acceleration at which dark matter becomes negligible has less spread in the data than in AM mocks; 2) Even under conservative assumptions, AM significantly overpredicts the scatter in the relation and its normalisation at low acceleration, and furthermore positions dark matter too close to galaxies' centres on average; 3) The MDAR affords $2 \sigma$ evidence for a correlation of surface brightness with halo mass or concentration. Our analysis lays the groundwork for a bottom-up determination of the galaxy-halo connection from relations such as the MDAR, provides concrete statistical tests for specific galaxy formation models, and brings into sharper focus the relative evidence accorded by galaxy kinematics to $\Lambda$CDM and modified gravity alternatives.

### A luminous hot accretion flow in the low-luminosity active galactic nucleus NGC 7213 [Replacement]

The active galactic nucleus (AGN) NGC 7213 shows a complex correlation between the monochromatic radio luminosity $L_R$ and the 2--10 keV X-ray luminosity $L_X$, i.e. the correlation is unusually weak with $p\sim 0$ (in the form $L_R\propto L_X^p$) when $L_X$ is below a critical luminosity, and steep with $p>1$ when $L_X$ is above that luminosity. Such a hybrid correlation in individual AGNs is unexpected as it deviates from the Fundamental Plane of AGN activity. Interestingly, a similar correlation pattern is observed in the black hole X-ray binary H1743--322, where it has been modelled by switching between different modes of accretion. We propose that the flat $L_R$--$L_X$ correlation of NGC 7213 is due to the presence of a luminous hot accretion flow, an accretion model whose radiative efficiency is sensitive to the accretion rate. Given the low luminosity of the source, $L_X\sim 10^{-4}$ of the Eddington luminosity, the viscosity parameter is determined to be small, $\alpha\approx 0.01$. We also modelled the broad-band spectrum from radio to $\gamma$-rays, the time lag between the radio and X-ray light curves, and the implied size and the Lorentz factor of the radio jet. We predict that NGC 7213 will enter into a two-phase accretion regime when $L_X > 1.5 \times 10^{42}\, {\rm erg\,s^{-1}}$. When this happens, we predict a softening of the X-ray spectrum with the increasing flux and a steep radio/X-ray correlation.

### The far-infrared - radio correlation in dwarf galaxies

The far-infrared - radio correlation connects star formation and magnetic fields in galaxies, and has been confirmed over a large range of far-infrared luminosities. Recent investigations indicate that it may even hold in the regime of local dwarf galaxies, and we explore here the expected behavior in the regime of star formation surface densities below 0.1 M_sun kpc^{-2} yr^{-1}. We derive two conditions that can be particularly relevant for inducing a change in the expected correlation: a critical star formation surface density to maintain the correlation between star formation rate and the magnetic field, and a critical star formation surface density below which cosmic ray diffusion losses dominate over their injection via supernova explosions. For rotation periods shorter than 1.5x10^7 (H/kpc)^2 yrs, with H the scale height of the disk, the first correlation will break down before diffusion losses are relevant, as higher star formation rates are required to maintain the correlation between star formation rate and magnetic field strength. For high star formation surface densities Sigma_SFR, we derive a characteristic scaling of the non-thermal radio to the far-infrared / infrared emission with Sigma_SFR^{1/3}, corresponding to a scaling of the non-thermal radio luminosity L_s with the infrared luminosity L_{th} as L_{th}^{4/3}. The latter is expected to change when the above processes are no longer steadily maintained. In the regime of long rotation periods, we expect a transition towards a steeper scaling with Sigma_SFR^{2/3}, implying L_s~L_th^{5/3}, while the regime of fast rotation is expected to show a considerably enhanced scatter. These scaling relations explain the increasing thermal fraction of the radio emission observed within local dwarfs, and can be tested with future observations by the SKA and its precursor radio telescopes.

### The Evolution of Active Galactic Nuclei in Clusters of Galaxies from the Dark Energy Survey

The correlation between active galactic nuclei (AGN) and environment provides important clues to AGN fueling and the relationship of black hole growth to galaxy evolution. In this paper, we analyze the fraction of galaxies in clusters hosting AGN as a function of redshift and cluster richness for X-ray detected AGN associated with clusters of galaxies in Dark Energy Survey (DES) Science Verification data. The present sample includes 33 AGN with L_X > 10^43 ergs s^-1 in non-central, host galaxies with luminosity greater than 0.5 L* from a total sample of 432 clusters in the redshift range of 0.1<z<0.95. Analysis of the present sample reveals that the AGN fraction in red-sequence cluster members has a strong positive correlation with redshift such that the AGN fraction increases by a factor of ~ 8 from low to high redshift, and the fraction of cluster galaxies hosting AGN at high redshifts is greater than the low-redshift fraction at 3.6 sigma. In particular, the AGN fraction increases steeply at the highest redshifts in our sample at z>0.7. This result is in good agreement with previous work and parallels the increase in star formation in cluster galaxies over the same redshift range. However, the AGN fraction in clusters is observed to have no significant correlation with cluster mass. Future analyses with DES Year 1 and 2 data will be able to clarify whether AGN activity is correlated to cluster mass and will tightly constrain the relationship between cluster AGN populations and redshift.

### Pulse-wise GRB correlation: implication as a cosmological tool

Gamma-ray bursts (GRBs) are cosmological explosions which carry valuable information from the distant past of the expanding universe. One of the greatest discoveries in modern cosmology is the finding of the accelerated expansion of the universe using Type Ia supernovae (SN Ia) as standard candles. However, due to the interstellar extinction SN Ia can be seen only up to a redshift $z\sim 1.5$. GRBs are considered as the potential alternative to push this limit to as high as $z\sim 10$, a redshift regime corresponding to an epoch when the universe just started to form the first structures. There exist several correlations between the energy and an observable of a GRB which can be used to derive luminosity distance. In recent works, we have studied spectral evolution within the individual pulses and obtained such correlations within the pulses. Here we summarize our results of the pulse-wise GRB correlation study. It is worth mentioning that all GRB correlations are still empirical, and we cannot use them in cosmology unless we understand the basic physics of GRBs. To this end, we need to investigate the prompt emission spectrum which is so far generally described by the empirical Band function. We shall discuss our current understanding of the radiation process particularly the finding of two blackbodies and a powerlaw (the 2BBPL model) as the generic spectral model and its implication. This is a work in progress and we expect to obtain the most fundamental GRB correlation based on our improved spectral model.

### Do Circumnuclear Dense Gas Disks Drive Mass Accretion onto Supermassive Black Holes?

We present a positive correlation between the mass of dense molecular gas ($M_{\rm dense}$) of $\sim 100$ pc scale circumnuclear disks (CNDs) and the black hole mass accretion rate ($\dot{M}_{\rm BH}$) in total 10 Seyfert galaxies, based on data compiled from the literature and an archive (median aperture $\theta_{\rm med}$ = 220 pc). A typical $M_{\rm dense}$ of CNDs is 10$^{7-8}$ $M_\odot$, estimated from the luminosity of the dense gas tracer, the HCN($1-0$) emission line. Because dense molecular gas is the site of star formation, this correlation is virtually equivalent to the one between nuclear star formation rate and $\dot{M}_{\rm BH}$ revealed previously. Moreover, the $M_{\rm dense}-\dot{M}_{\rm BH}$ correlation was tighter for CND-scale gas than for the gas on kpc or larger scales. This indicates that CNDs likely play an important role in fueling black holes, whereas $>$kpc scale gas does not. To demonstrate a possible approach for studying the CND-scale accretion process with the Atacama Large Millimeter/submillimeter Array (ALMA), we used a mass accretion model where angular momentum loss due to supernova explosions is vital. Based on the model prediction, we suggest that only the partial fraction of the mass accreted from the CND ($\dot{M}_{\rm acc}$) is consumed as $\dot{M}_{\rm BH}$. However, $\dot{M}_{\rm acc}$ agrees well with the total nuclear mass flow rate (i.e., $\dot{M}_{\rm BH}$ + outflow rate). Although these results are still tentative with large uncertainties, they support the view that star formation in CNDs can drive mass accretion onto supermassive black holes in Seyfert galaxies.

### JIMWLK evolution of the odderon [Cross-Listing]

We study the effects of a parity-odd "odderon" correlation in JIMWLK renormalization group evolution at high energy. Firstly we show that in the eikonal picture where the scattering is described by Wilson lines, one obtains a strict mathematical upper limit for the magnitude of the odderon amplitude compared to the parity even pomeron one. This limit increases with N_c, approaching infinity in the infinite N_c limit. We use a systematic extension of the Gaussian approximation including both 2- and 3-point correlations which enables us to close the system of equations even at finite N_c. In the large-N_c limit we recover an evolution equation derived earlier. By solving this equation numerically we confirm that the odderon amplitude decreases faster in the nonlinear case than in the linear BFKL limit. We also point out that, in the 3-point truncation at finite N_c, the presence of an odderon component introduces azimuthal angular correlations ~ cos(n phi) at all n.

### JIMWLK evolution of the odderon

We study the effects of a parity-odd "odderon" correlation in JIMWLK renormalization group evolution at high energy. Firstly we show that in the eikonal picture where the scattering is described by Wilson lines, one obtains a strict mathematical upper limit for the magnitude of the odderon amplitude compared to the parity even pomeron one. This limit increases with N_c, approaching infinity in the infinite N_c limit. We use a systematic extension of the Gaussian approximation including both 2- and 3-point correlations which enables us to close the system of equations even at finite N_c. In the large-N_c limit we recover an evolution equation derived earlier. By solving this equation numerically we confirm that the odderon amplitude decreases faster in the nonlinear case than in the linear BFKL limit. We also point out that, in the 3-point truncation at finite N_c, the presence of an odderon component introduces azimuthal angular correlations ~ cos(n phi) at all n.

### Investigation of cosmic ray penetration with wavelet cross-correlation analysis

Aims. We use Fermi and Planck data to calculate the cross correlation between gamma ray signal and gas distribution in different scales in giant molecular clouds (GMC). Then we investigate the cosmic rays (CRs) penetration in GMCs with these informations. Methods.We use the wavelet technique to decompose both the gamma ray and dust opacity maps in different scales, then we calculate the wavelet cross correlation functions in these scales. We also define wavelet response as an analog to the impulsive response in Fourier transform and calculate that in different scales down to Fermi angular resolution. Results. The gamma ray maps above 2 GeV show strong correlation with the dust opacity maps, the correlation coefficient is larger than 0.9 above a scale of 0.4 degree.The derived wavelet response is uniform in different scales. Conclusions. We argue that the CR above 10 GeV can penetrate the giant molecular cloud freely and the CRs distributions in the same energy range are uniform down to parsec scale.

### Solving the $R_{AA}\otimes v_2$ puzzle [Replacement]

For the past ten years $R_{AA}(p_T)$, the nuclear modification factor that encodes the suppression of high $p_T$ particles due to energy loss within the medium was fairly well described by many theoretical models. However, the same models systematically under-predicted the high $p_T$ elliptic flow, $v_2$, which is experimentally measured as the correlation between soft and hard hadrons. All previous calculations neglected the effect of event-by-event fluctuations of an expanding viscous hydrodynamical background as well as the soft-hard flow harmonic correlations in the experimentally measured $v_2$. In this talk I show how event-by-event viscous hydrodynamics (computed using the v-USPhydro code) coupled to an energy loss model (BBMG) is able to simultaneously describe soft physics observables as well as the high-$p_T$ $R_{AA}$ and $v_2$. Suggestions for future more differential calculations at the LHC run2 are made to explore soft-hard flow correlations.

### Solving the $R_{AA}\otimes v_2$ puzzle [Cross-Listing]

For the past ten years $R_{AA}(p_T)$, the nuclear modification factor that encodes the suppression of high $p_T$ particles due to energy loss within the medium was fairly well described by many theoretical models. However, the same models systematically under-predicted the high $p_T$ elliptic flow, $v_2$, which is experimentally measured as the correlation between soft and hard hadrons. All previous calculations neglected the effect of event-by-event fluctuations of an expanding viscous hydrodynamical background as well as the soft-hard flow harmonic correlations in the experimentally measured $v_2$. In this talk I show how event-by-event viscous hydrodynamics (computed using the v-USPhydro code) coupled to an energy loss model (BBMG) is able to simultaneously describe soft physics observables as well as the high-$p_T$ $R_{AA}$ and $v_2$. Suggestions for future more differential calculations at the LHC run2 are made to explore soft-hard flow correlations.

### Solving the $R_{AA}\otimes v_2$ puzzle [Replacement]

For the past ten years $R_{AA}(p_T)$, the nuclear modification factor that encodes the suppression of high $p_T$ particles due to energy loss within the medium was fairly well described by many theoretical models. However, the same models systematically under-predicted the high $p_T$ elliptic flow, $v_2$, which is experimentally measured as the correlation between soft and hard hadrons. All previous calculations neglected the effect of event-by-event fluctuations of an expanding viscous hydrodynamical background as well as the soft-hard flow harmonic correlations in the experimentally measured $v_2$. In this talk I show how event-by-event viscous hydrodynamics (computed using the v-USPhydro code) coupled to an energy loss model (BBMG) is able to simultaneously describe soft physics observables as well as the high-$p_T$ $R_{AA}$ and $v_2$. Suggestions for future more differential calculations at the LHC run2 are made to explore soft-hard flow correlations.

### Solving the $R_{AA}\otimes v_2$ puzzle [Cross-Listing]

For the past ten years $R_{AA}(p_T)$, the nuclear modification factor that encodes the suppression of high $p_T$ particles due to energy loss within the medium was fairly well described by many theoretical models. However, the same models systematically under-predicted the high $p_T$ elliptic flow, $v_2$, which is experimentally measured as the correlation between soft and hard hadrons. All previous calculations neglected the effect of event-by-event fluctuations of an expanding viscous hydrodynamical background as well as the soft-hard flow harmonic correlations in the experimentally measured $v_2$. In this talk I show how event-by-event viscous hydrodynamics (computed using the v-USPhydro code) coupled to an energy loss model (BBMG) is able to simultaneously describe soft physics observables as well as the high-$p_T$ $R_{AA}$ and $v_2$. Suggestions for future more differential calculations at the LHC run2 are made to explore soft-hard flow correlations.

### Solving the $R_{AA}\otimes v_2$ puzzle [Replacement]

For the past ten years $R_{AA}(p_T)$, the nuclear modification factor that encodes the suppression of high $p_T$ particles due to energy loss within the medium was fairly well described by many theoretical models. However, the same models systematically under-predicted the high $p_T$ elliptic flow, $v_2$, which is experimentally measured as the correlation between soft and hard hadrons. All previous calculations neglected the effect of event-by-event fluctuations of an expanding viscous hydrodynamical background as well as the soft-hard flow harmonic correlations in the experimentally measured $v_2$. In this talk I show how event-by-event viscous hydrodynamics (computed using the v-USPhydro code) coupled to an energy loss model (BBMG) is able to simultaneously describe soft physics observables as well as the high-$p_T$ $R_{AA}$ and $v_2$. Suggestions for future more differential calculations at the LHC run2 are made to explore soft-hard flow correlations.

### Solving the $R_{AA}\otimes v_2$ puzzle

For the past ten years $R_{AA}(p_T)$, the nuclear modification factor that encodes the suppression of high $p_T$ particles due to energy loss within the medium was fairly well described by many theoretical models. However, the same models systematically under-predicted the high $p_T$ elliptic flow, $v_2$, which is experimentally measured as the correlation between soft and hard hadrons. All previous calculations neglected the effect of event-by-event fluctuations of an expanding viscous hydrodynamical background as well as the soft-hard flow harmonic correlations in the experimentally measured $v_2$. In this talk I show how event-by-event viscous hydrodynamics (computed using the v-USPhydro code) coupled to an energy loss model (BBMG) is able to simultaneously describe soft physics observables as well as the high-$p_T$ $R_{AA}$ and $v_2$. Suggestions for future more differential calculations at the LHC run2 are made to explore soft-hard flow correlations.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

### A fundamental plane for long gamma-ray bursts with X-ray plateaus [Replacement]

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

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

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

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

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

### Radii of neutron drops probed via the neutron skin thickness of nuclei [Replacement]

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

### Radii of neutron drops probed via the neutron skin thickness of nuclei [Replacement]

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