Studying the Flux Density of Bright Active Galaxies at Different Spectral Bands

Statistical studies are reported in this article for an active galactic nuclei sample of different type of active galaxies Seyferts 1, Seyferts 2, and Quasars. These sources have been selected from a Catalogue for bright X-ray galaxies. The name of this index is ROSAT Bright Source Catalogue (RBSC) and the NRAO VLA Sky Survey (NVSS). In this research, multi-wavelength observational bands Radio at 1.4 GHz, Optical at 4400 A0, and X-ray at energy 0.1-2.4 KeV have been adopted in this study. The behavior of flux density ratios has been studied ,  with respect to the absolute magnitude . Furthermore, the Seyfert1 and Seyfert 2 objects are combined in one group and the QSOs are collectest in another group. Also, it has been found that the ratios , are increasing towards fainter optical absolute magnitude especially in Quasars.


Introduction:
All what is known about the galaxies comes from the light that we observe. This light is considered to be a very important component to understand and solve the puzzle of the universe. This component (light) contains a huge amount of information about the source emitted from it (e.g. mass, distance, age, and type …etc.). Among the information that can be extracted from the light is the galaxy's luminosity. This luminosity will lead us to know how much is the amount of flux density that radiate from the source, because the luminosity is directly proportional to flux.
As clarified before, there are many parameters that can be extracted from the light emitted from the galaxies. These parameters are correlated to each other in different ways. For instance, some researchers conclude there are correlation between absolute magnitude and redshift (M B -z) where both absolute magnitudes and apparent magnitudes increase with respect to the redshift in the Friedman universes model in which both the cosmological constant and the pressure are vanishing (1).
Department of Astronomy and Space, Collage of Science, University of Baghdad, Baghdad, Iraq. Corresponding author: yasir_ezz81@yahoo.com A recent example for the articles that study the correlation between magnitude and redshift, concludes that there is series relation extension, as they clarify in their research (2). Other astronomical scientists try to find the correlation between the black hole mass (M BH ) and the dispersion velocity of the stars (σ * ) for active galactic nuclei of the host galaxies (3,4). In this research, new correlations have been tried to be suggested like, the relationship between flux density ratio and luminosity distance, the relationship between flux density ratio and redshift and the relationship between flux density ratio and absolute magnitude.
In this article, the sections have been arranged as follow: Section Two: state the mathematical process that has been involved in this project to derive the form used in mathematical analysis as well as the derivation of the parameters that have been employed in this analysis. Section Three: Presentation of calculated results, as well as statistical analysis of samples approved in this work. In addition, in this section, the relationship between the ratio of flux density and absolute volume value will be addressed as well as the discussion of these correlations. Finally, in section Four, the conclusions of this work will be summarized.

The Bright Sources Sample and Parameters Estimation:
In this research, a statistical investigation has been presented of three different types of galaxies samples (Seyfert galaxies type 1 and 2 in addition to Quasars). These objects have been chosen from active galaxies catalogue for X-ray bright sources (5). The arrangement of these sources was as follows: we had 315 sample of Seyfert objects type (Sy1), and 32 sample of Seyfert objects type (Sy2), number 347 of (Sy1 + Sy2) together, in addition to 97 sample of Qausars (QSO).
The global emission characteristics comparison of different active galaxies type at different bands from X-ray to Radio, can give us a vision about the formation and evolution of this kind of active sources. For instance, the comparison between radio continuum and IRAS far-IR data led to the discovery of the eminent connection between the star formation and non-thermal radio emitting (6). Another example for such important comparison is the comparison between X-ray and radio continuum data, which will guide us to an important relationship between X-ray and Radio emission data (7). Furthermore, the global emission characteristics comparison in extensive range of different bands can show the relative importance of those parameters and the responsible processes for practical connections between the universal parameters of active galaxies.
Spectral flux density is donated by f λ or f ν where these parameters represent the quantity that defines the spectral power "energy" incident per unit surface "region" and per unit time. The monochromatic soft X-ray flux density ( ray X f  (2keV)) at (2.0 keV) band in units 1  , and X-ray energy index ( .The spectral index α is described by power law (f ν α ν -α ). In this work, the observed optical flux in the blue optical region f B has been used as well as the relative effective flux density equation to the ABmagnitude has been used at different wavelengths. The system monochromatic AB magnitude is defined by (9,10): We have Jansky(1Jy) = 10 -23 erg. cm −2 . s −1 . Hz −1 , yielding −2.5 log{363×10 −23 } = 48.6 So eq. 2 becomes: Depending on eq. 3 and from the equations mentioned in (11,12), we calculate the monochromatic flux density f B in units of . −2 . −1 . −1 within the optical bands (B-band)at 4400Å, where (λwavelength in unit angstroms Å: Here 3.631x10 -20 is zero point flux for all frequency ν (a flat spectrum source) in the AB system.
The relation between optical absolute magnitude ( B M ) and luminosity distance ) z ( d L has been derived accurately from the equation that mention in (13): According to eq. 5 , we have calculated ( B M ) via:  (13). We can define the luminosity distance d L (z) as a relation between the bolometric flux density which denoted by f ν at the corresponding frequency ν (i.e. combined comprehensive all the frequencies) and the luminosity bolometric (L) (14,15): It's found that the luminosity distance d L is relevant to the tangential comoving distance d M via (15,16): Where d M is given by (15): The Hubble distance d H defined as (15,17): Where (c) is the speed of light and (H o ) represent the Hubble constant, and this constant can be defined as the ratio between stagnation speed (v) and the distance (d) in the extending universe.
Assuming that dimensionless density parameters    , M = 1, 0 for Einstein-de-Sitter cosmology, then the deceleration parameter is just half value Ω M (q 0 =0.5) We assume energy index for the optical band 0.5 = B   for the Seyfert galaxies types 1, 2 and also Quasars type (6,13). The value of Hubble constant Ho can be variable of 70 ± 5 according to the cosmological models. Therefore, we adopted this value to be 70 Km s -1 Mpc -1 according to very recent publications (18)(19)(20)(21). Consequently, we have used the current value of Hubble constant (H 0 = 70 km s −1 Mpc −1 ) through this article to compute the blue absolute magnitudes.
The following information has been obtained from (5): First, the densities flux data of the X-ray at 0.1 -2.4 KeV and radio at 1.4 GHz. Second, the apparent blue magnitudes. Third, the redshifts. Fourth, the spectral classification morphology of the Seyfert galaxies (Sy1 and Sy2) and Quasars. In the next section, we used parametres that derived in previous section and (statistic-win-program) for calculate the correlations between the parameters that used in this work as well as discuss the results statistically for the extragalactic soft X-ray at (2 KeV) to radio emission at 1.4 GHz flux densities for Bright Seyfert galaxies (Sy1 and Sy2) and Quasars samples. According to eqs. 6,8, 9 and 10, we have computed a blue absolute magnitude ( B M ), and luminosity distance (d L ).

Results and Discussion:
Here we used a program named (statisticwin-program) deals statistically with the data to find either there is correlation between the parameters or not. The parameters statistically analyzed in this article to find if there is a correlation between them are as follow: (fluxes densities ratioblue absolute magnitude) and (fluxes densities ratiodistance). Moreover, different regressions are used in this article to get the plot between these factors and determine the levels of the significance (P) (the chance of probable relationship, P<0.01) as well as the degree of the partial correlation coefficient (R), which should be between (1 ≤ R ≤ -1). The goal of the linear reduction approach is to appropriately fit a line through the points. Accurately, the software that used in the research will determine a line, where this line will be reduced due to the points that is deviational squared. In general, a linear regression equation will be determined via eq. 11 (6): Y 1 = a 1 + β 1 X 1 , Y 2 =a 2 + β 1 X 2 and Y n = a n + βnX n …………… 11 Where: (Y 1 , Y 2 , …, Yn) : defined as the dependent variables. (X 1 , X 2 , …, X n ): defined as the independent variables(or predictors).
(a 1 , a 2 ,…..,a n ): represent the intercept with Y-axis. In this paper, the investigation of the observational flux density for radio, optical (blue), and soft X-ray bands of (Sy1, Sy2, and QSO) led us to some formulas as will exhibit later, according to the statistical program that we used in this research. Statistical data analysis are shown in Table 1   redshift (1+z) for (Seyfert1 and Seyfert2) sample galaxies, which is due to the effect of the distance factor and also that these galaxies are classified as earlier types compared with the (QSO) galaxies.     The results of statistical analysis shows many main points as following: Where believed that Quasars are objects with strong X-ray-radio radiation more than Seyfert galaxies and it could be detectable at very large distances. In comparison with previous results obtained by other authors (12,8,22), it has been found that these results are agreed with results of )12( for selected Schmidt BQX QSOs sample, while with results of (8, 22) they are differents. These differences between our sample RBSC-NVSS of active galaxies (Sy1, Sy2 and QSO) and IRAS (Infrared Astronomical Satellite) Seyfert1 galaxies and Warm IRAS AGNs galaxies do not dominate the distribution between ratio B f f ray X and B M , and also has high flux Infrared sources, while the sample of active galaxies that involved in this work has brightest X-ray sources.
3-The statistical investigation of the result shows that the QSO objects are the most luminous sources that has host active galactic nuclei in their center, in which we compare with other galaxies (i.e. normal spiral galaxies) in the same redshift, it will be very difficult to be detectable in many case, as well as, it will looks like very faint sources with respect to QSO.

Conclusions:
From the results illustrated in the previous section including the statistical investigation of the flux density at different band (radio, blue-optical, and soft X-ray) for the tested galaxy samples that have been selected in this work the following, the following points can be concluded: 1.
There are very strong linear correlation relationships between B f f ray X and B M for QSO sample galaxies with a very high level of significance 7 10 < P  more than for Sy1 + Sy2 type, and show different slopes in the relation between

2.
We believe that the energy indices α used for the radio, blue and X-ray spectra are of a similar value,and approximation proportional to frequency ν 0.5 (    f ) for QSO sample, based on a power law (L ν =Cν -α ) in the observed spectra radio to X-ray regions, while for Seyfert galaxies Sy1 + Sy2 the spectral indices are various values, and the ratio of flux densities monochromatic radio/blue,soft monochromatic X-ray (2 KeV)/ blue are independent of redshift (1+z) for QSO galaxies.