The luminosity correlation analysis for Fermi blazars

In this paper, multiwavelength chromatic luminosity at radio (\(\log L _{\mathrm{R}}\)), optical (\(\log L_{\mathrm{O}}\)), X-ray (\(\log L _{\mathrm{X}}\)), and \(\gamma \)-rays (\(\log L_{\gamma }\)) for a sample of 442 Fermi blazars with known redshifts are collected from Fan et al. (2016), to study the correlations between the \(\gamma \)-rays and the low-energy bands using a multiple linear regression analysis. In this way, we can see which band is more important for the \(\gamma \)-ray emissions. Mutual correlation analysis is also used to discuss the correlations between the \(\gamma \)-ray and the low energy bands for the whole sample and subclasses. We come to following conclusions:

1. 1.
   The multiple linear correlation indicates that the \(\gamma \)-rays are correlated with the radio, optical and the X-ray emissions for the whole sample and the subclasses of flat spectrum radio quasars (FSRQs) and BL Lac objects (BL Lacs), the correlation between the \(\gamma \)-rays and the radio emissions is the strongest one.
    
2. 2.
   For BL Lacs, the optical emissions are more important than the X-rays for the \(\gamma \)-rays, while the X-ray emissions are more important than optical ones in FSRQs.
    
3. 3.
   The \(\gamma \)-ray emissions in HBL are from an synchrotron self-Compton, while those in FSRQs may be from external Compton and synchrotron self-Compton as well.
    

     

Fermi gamma-ray and multi-wave band emission from TeV active galactic nuclei

Using γ-ray data detected by Fermi Large Area Telescope (LAT) and multi-wave band data for 40 TeV active galactic nuclei (AGNs), we have studied the correlations between flux densities (F _R, F _IR, F _O, F _X and F _γ ) in the radio, infrared, optical, X-ray and γ-ray wave bands. Our results are the following: (1) For TeV HSP BL Lacertae objects (THBLs), there are strong correlations between F _γ and F _R and between F _γ and F _IR in all states (average/high/low); (2) The TeV radio galaxies (TRGs) deviate from the area occupied by THBLs; (3) The TeV flat-spectrum radio quasars (TFSRQs) have much stronger γ-ray emission than THBLs; (4) For THBLs, there are weak correlations between F _γ and F _X in all states as well as between F _γ and F _O in both average and high states, and a strong correlation between F _γ and F _O in the low state; (5) For THBLs, there are strong correlations between F _O and F _R in both low and average states as well as between F _O and F _IR in all states and between F _IR and F _R in all states, but no strong correlations among other bands are found. From these results, we suggest that for THBLs, the synchrotron self-Compton radiation (SSC) is the main mechanism of high energy γ-ray emission and the inverse Compton scattering of circum-nuclear dust is likely to be a important complementary mechanism. Compared with THBLs, TRGs and TFSRQs may have a different origin of high energy γ-ray.     

The connections between bulk Lorentz factor,black hole mass and accretion in Fermi FSRQs

We have analyzed a large sample of FSRQs detected by Fermi LAT. Our main intents are to investigate the relations between bulk Lorentz factor and black hole mass, between bulk Lorentz factor and Eddington ratio. Using archive and calculation, we obtained the distributions of bulk Lorentz factor, black hole mass and Eddington ratio. After excluding redshift effect, there is still significant correlation between bulk Lorentz factor and black hole mass, but not correlation between bulk Lorentz factor and Eddington ratio, which suggest that faster jets have a close relation with more massive black holes, and the Blandford–Znajek (BZ) mechanism may dominate over the Blandford–Payne (BP) mechanism for Fermi FSRQs.     

Period–luminosity relations for type II Cepheids and their application

JHK _s magnitudes corrected to mean intensity are estimated for Large Magellanic Cloud (LMC) type II Cepheids in the OGLE-III survey the third phase of the Optical Gravitational Lensing Experiment (OGLE). Period–luminosity (PL) relations are derived in JHK _s as well as in a reddening-free VI parameter. Within the uncertainties, the BL Her stars  ( P < 4 d)  and the W Vir stars (   P = 4  to 20 d) are colinear in these PL relations. The slopes of the infrared relations agree with those found previously for type II Cepheids in globular clusters within the uncertainties. Using the pulsation parallaxes of V553 Cen and SW Tau, the data lead to an LMC modulus uncorrected for any metallicity effects of  18.46 ± 0.10  mag. The type II Cepheids in the second-parameter globular cluster, NGC 6441, show a PL( VI ) relation of the same slope as that in the LMC, and this leads to a cluster distance modulus of  15.46 ± 0.11  mag, confirming the hypothesis that the RR Lyrae variables in this cluster are overluminous for their metallicity. It is suggested that the Galactic variable κ Pavonis is a member of the peculiar W Vir class found by the OGLE-III group in the LMC. Low-resolution spectra of OGLE-III type II Cepheids with   P > 20  d (RV Tau stars) show that a high proportion have TiO bands; only one has been found showing C₂. The LMC RV Tau stars, as a group, are not colinear with the shorter period type II Cepheids in the infrared PL relations in marked contrast to such stars in globular clusters. Other differences between LMC, globular cluster and Galactic field type II Cepheids are noted in period distribution and infrared colours.     

Inclination- and dust-corrected galaxy parameters: bulge-to-disc ratios and size–luminosity relations

While galactic bulges may contain no significant dust of their own, the dust within galaxy discs can strongly attenuate the light from their embedded bulges. Furthermore, such dust inhibits the ability of observationally determined inclination corrections to recover intrinsic (i.e. dust-free) galaxy parameters. Using the sophisticated 3D radiative transfer model of Popescu et al. and Tuffs et al., together with the recent determination of the average face-on opacity by Driver et al. in nearby disc galaxies, we provide simple equations to correct (observed) disc central surface brightness and scalelengths for the effects of both inclination and dust in the B , V , I , J and K passbands. We then collate and homogenize various literature data sets and determine the typical intrinsic scalelengths, central surface brightness and magnitudes of galaxy discs as a function of morphological type. All galaxies have been carefully modelled in their respective papers with a Sérsic   R ^{1/ n}   bulge plus an exponential disc. Using the bulge magnitude corrections from Driver et al., we additionally derive the average, dust-corrected, bulge-to-disc flux ratio as a function of galaxy type. With values typically less than 1/3, this places somewhat uncomfortable constraints on some current semi-analytic simulations. Typical bulge sizes, profile shapes, surface brightness and deprojected densities are provided. Finally, given the two-component nature of disc galaxies, we present luminosity–size and (surface brightness)–size diagrams for discs and bulges. We also show that the distribution of elliptical galaxies in the luminosity–size diagram is not linear but strongly curved.     

Statistical relations between stellar spectral and luminosity classes and stellar effective temperature and surface gravity

We have determined new statistical relations to estimate the fundamental atmospheric parameters of effective temperature and surface gravity, using MK spectral classification, and vice versa. The relations were constructed based on the published calibration tables(for main sequence stars) and observational data from stellar spectral atlases(for giants and supergiants). These new relations were applied to field giants with known atmospheric parameters, and the results of the comparison of our estimations with available spectral classification have been quite satisfactory.     

Period–luminosity relations for red supergiant variables – I.The calibration

We present CCD photometry of red supergiant long-period variables (LPVs) in the Per OB1 association, the Large Magellanic Cloud (LMC) and M33. The photometry was obtained in the Kron–Cousins R and I bandpasses and in a narrow bandpass ( λ ₀=8250 Å, FWHM=300 Å) chosen to avoid TiO bands in the spectral energy distribution of the LPVs. Because the strength of the TiO bands varies greatly with temperature, which varies with the phase of an LPV, avoiding TiO reduces the amplitude of the photometric variations seen in LPVs. The result is a lower dispersion and a well defined period–luminosity (PL) relation.
For the LMC sample we find an rms dispersion of 0.27 mag in the narrow-band PL relation and slightly larger dispersions for the LPVs in Per OB1 and M33. This dispersion is comparable to that of the Cepheid PL relation at similar wavelengths. Adopting a distance modulus of 18.5±0.1 mag for the LMC, we obtain distance moduli of 11.68±0.15 mag for Per OB1 and 24.85±0.13 mag for M33. These distances agree well with those based on main sequence fitting for Per OB1 and the Cepheid distance for M33. Since LPVs are ∼ 5 times more common than Cepheids and have a well defined PL relation, LPVs provide a promising method for estimating Galactic and extra galactic distances.     

The infrared luminosity of the torus and the visibility of scattered broad line emission in Seyfert 2 galaxies

A number of studies have shown that the visibility of scattered broad emission lines in Seyfert 2 galaxies is strongly dependent on the IRAS     flux ratio, where those Seyfert 2 galaxies with 'warm' IRAS colours show polarized broad line emission. It is now clear that this effect is owing to the increasing dominance of the galactic rather than the active galactic nucleus (AGN) emission at 60 μm in less-luminous 'cool' Seyfert 2 galaxies. However, we present evidence that the 25-μm emission is a good measure of the AGN luminosity for most Seyfert 2 galaxies. Using this result, we show that the visibility of scattered broad line emission has a dependence on the AGN luminosity. The observations can be interpreted self-consistently if the scaleheight of the scattering zone varies with central source luminosity whilst the scaleheight of the obscuring torus is approximately constant.     

Period–luminosity relations for red supergiant variables – II. The distance to M101

We report the discovery of 42 red supergiant variables (RSVs) in the late-type spiral galaxy M101. Periods for the luminosity variation of these RSVs were determined from 20 epochs of ground-based CCD photometry in the Kron–Cousins R band obtained with the KPNO 2.1-m and WIYN 3.5-m telescopes over a span of three years. The periods found were in the range 200–1300 days. Using the relationship between the RSV periods and their luminosity in the Kron–Cousins I band, we estimate a reddening-corrected distance modulus to M101 of 29.40±0.16 mag (based on a distance modulus of 18.5±0.1 mag for the Large Magellanic Cloud). This distance is consistent with the Hubble Space Telescope Key Project Cepheid distances of 29.34±0.17 mag for the outer field of M101 and 29.21±0.17 mag for the inner field.     

Colour–magnitude relations and spectral line strengths in the Coma cluster

We use the C₂4668, Fe4383, H γ _A and H δ _A spectral absorption line indices, together with U - and V -band photometry of 101 galaxies in the Coma cluster, to investigate how mean age and metal abundance correlate with galaxy luminosity. In particular, we use the line index measurements to address the origin of the colour–magnitude relation (CMR). We find that the CMR in Coma is driven primarily by a luminosity–metallicity correlation. We additionally show evidence for a relation between age and luminosity, in the direction predicted by the semi-analytic hierarchical clustering models of Kauffmann & Charlot, but this is only present in the C₂4668 index models, and could be an effect of the lack of non-solar abundance ratios in the Worthey models used.
By comparing deviations from the CMR with deviations in absorption index from analogous 'index–magnitude' relations, we find that colour deviations bluewards of the mean relation are strongly correlated with the hydrogen Balmer line series absorption. We show that the properties of these blue galaxies are consistent with the presence of a young stellar population in the galaxies, rather than with a reduced metallicity.     

Solar activity and planetary luminosity

The Chree superposition analysis of the luminosities of the planets Jupiter, Saturn, Uranus and Neptune indicates a correlation between solar activity and planetary luminosity. The variations of the solar constant in the visible range are considered to be too small to explain the observed changes in brightness. The interaction of solar extreme ultraviolet or solar wind particles with the atmospheres of these planets is probably responsible for the increased albedo during periods of high solar activity.     

Sun's inertial motion and luminosity

Fast Fourier analysis of the detrended record of solar irradiance obtained by the Nimbus-7 cavity pyrheliometer shows a rich spectrum of significant frequencies between about 30 and 850 nHz (periods between 13 and 400 days). Wolff and Hickey (1987a, b), elaborating on a model developed by Wolff (1974a, b, 1976, 1983, 1984), suggest that many of these peaks arise due to interference of rigidly rotating global solar oscillations (r- and g-modes). Their model fit is quite good in the region above about 135 nHz, but less satisfactory below this threshold. We note that the FFT spectrum of d² L/d² t, the second derivative of angular momentum of the solar inertial motion, contains peaks matching the large peaks in the irradiance spectrum below 400 nHz with periods near 0.08, 0.24, 0.65, and about 1 yr. We discuss the origins of the peaks in the d² L/d²t spectra and review some previous studies bearing on the question of a possible relationship of solar motion and solar activity. The future persistence of the observed spectral peaks of irradiance with periods near 0.24 and 0.65 yr will provide a key test for this hypothesis.     

The radio luminosity function and the luminosity diameter function of extragalactic radio sources

On the basis of a radio index-surface brightness diagram recently published, the luminosity function and the luminosity diameter function are obtained. The uncertainties due to the incompleteness of the sample are of the same order as the statistical uncertainties. The luminosity function differs considerably from a simple power law and supports the distinction of two populations. The density of the weak population (P<10³⁵ W Hz⁻¹ ster⁻¹ at 1400 MHz) follows nearly a power law in P and increases towards small diameters at least down to I kpc. The density of the strong population (the high luminosity and small diameter part of which is occupied by the quasars) has a maximum between 10²⁵ and 10²⁸ W Hz⁻¹ ster⁻¹ and around 100 kpc. A strong evolution effect is clearly present and is in a good agreement with the models obtained from the log N-log S counts.     

A Statistical Study of XBLs, RBLs and FSRQs at 1.5 GHz

BL Lac objects are similar to the fiat spectrum radio quasars in many aspects except regarding the emission lines.In order to study their relationship,we selected 56 BL Lacertae objects(33 X-ray-selected,23 radio-selected)and 45 flat spectrum radio quasars,analyzed their radio luminosities and core-dominance parameters.We found that the radio luminosities of the radio selected BL Lac objects located in between the X-ray selected BL Lac objects and the fiat spectrum radio quasars.However,this intermediate position does not bold for the core-dominance parameter:the RBLs have the largest core-dominance parameters.This sug- gests that the core-dominance parameter can not be taken as a sequencing criterion.We also investigated the correlation between the luminosity and the core-dominance parameter for the three subclasses.We concluded that,here,the sequence XBL-RBL—FSRQ still exists.     

Further empirical evidence for the non-linearity of the period–luminosity relations as seen in the Large Magellanic Cloud Cepheids

Recent studies, using OGLE data for LMC Cepheids in the optical, strongly suggest that the period–luminosity (PL) relation for the Large Magellanic Cloud (LMC) Cepheids shows a break or non-linearity at a period of 10 d. In this paper we apply statistical tests, the chi-squared test and the F -test, to the Cepheid data from the MACHO project to test for a non-linearity of the V - and R -band PL relations at 10 d, and extend these tests to the near-infrared ( JHK -band) PL relations with 2MASS data. We correct the extinction for these data by applying an extinction map towards the LMC. The statistical test we use, the F -test, is able to take account of small numbers of data points and the nature of that data on either side of the period cut at 10 d. With our data, the results we obtained imply that the VRJH -band PL relations are non-linear around a period of 10 d, while the K -band PL relation is (marginally) consistent with a single-line regression. The choice of a period of 10 d, around which this non-linearity occurs, is consistent with the results obtained when this 'break' period is estimated from the data. We show that robust parametric (including least-squares, least absolute deviation, robust regression) and non-parametric regression methods, which restrict the influence of outliers, produce similar results. Long-period Cepheids are supplemented from the literature to increase our sample size. The photometry of these long-period Cepheids is compared with our data and no trend with period is found. Our main results remain unchanged when we supplement our data set with these long-period Cepheids. By examining our data at maximum light, we also suggest arguments as to why errors in reddening are unlikely to be responsible for our results. The non-linearity of the mean V -band PL relation as seen in both of the OGLE and the MACHO data, using different extinction maps, suggests that this non-linearity is real.     

Solar interior structure and luminosity variations

The assumptions of standard solar evolution theory are mentioned briefly, and the principle conclusions drawn from them are described. The result is a rationalization of the present luminosity and radius of the Sun. Because there is some uncertainty about the interior composition of the Sun, a range of models is apparently acceptable.To decide which model is the most accurate, other more sensitive comparisons with observations must be made. Recent measurements of frequencies of dynamical oscillations are particularly valuable in this respect. The most accurate observations are of the five-minute oscillations, which suggest that the solar composition is not atypical of other stars of the same age as the Sun.The theory predicts that the solar luminosity has risen steadily from about 70% of its current value during the last 4.7 x 10⁹yr. Superposed on this there might have been variations on shorter timescales. Variations lasting about 10⁷yr and occurring at intervals of 10⁸yr have been suggested as being the cause of terrestrial ice ages. Moreover, there may be other variations, associated with instabilities arising from the coupling between the convection zone and the radiative interior, that occur on a timescale of 10⁵yr and which also have climatic consequences. These issues are quite uncertain.We do know that the Sun varies magnetically with a period of about 22 yr, and that this oscillation is modulated irregularly on a timescale of centuries. This appears to be a phenomenon associated with the convection zone and its immediate neighbourhood, though control from a more deeply-seated mechanism is not out of the question. There is a small luminosity variation associated with this cycle, and the way by which this might come about is discussed in terms of certain theories of the solar dynamo.Finally, there must be small surface flux variations associated with the dynamical oscillations mentioned above. Though the total luminosity variations are extremely small, the flux in any specific direction, and in particular that of the earth, may be measurable.Proceedings of the 14th ESLAB Symposium on Physics of Solar Variations, 16–19 September 1980, Scheveningen, The Netherlands.