# Posts Tagged correlation

## Recent Postings from correlation

### 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.

### 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.

### 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

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 [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.

### 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

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 [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

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

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

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

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

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

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

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

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

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

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

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

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

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

### 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.

### 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.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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