Computation of the Relationships of X-ray to Radio Luminosities of a Sample of Starburst Galaxies

The goal of this research is to better understand the physical features of starburst galaxies. Radio and X-ray observations are good for exploring the stuff within the central regions of galaxies. A galaxy that is undergoing a strong star formation, usually in its central area, is known as a starburst galaxy. This paper provides the results of a statistical analysis of a sample of starburst galaxies. The data used in this research have been collected from NASA Extragalactic Database (NED), and HYPERLEDA. Those data have been used to examine possible luminosity correlations of X-ray to a radio of a sample of starburst galaxies. In this research, statistical software, known as statistic-win-program, has been used to investigate if there is a luminosity correlation between multiple-wavelength bands. The results of the statistical analysis conclude that there is a good correlation between X-ray luminosity and radio luminosity at 1.4GHz where the partial correlation coefficient is (R≈0.53) and slope (0.6±0.12). There is also a good correlation between X-ray luminosity and radio luminosity at 5GHz with a good partial correlation coefficient (R ≈ 0.65) and slope (0.77±0.11). There are good positive relationships between radio luminosity at (1.4GHz, 5GHz) with infrared and far-infrared luminosities (Log L 1.4GHz α log L FIR 0.89±0.04 α Log L IR 0.9±0.03 ) with a very strong correlation equal to R=0.9 (Log L 5GHz α Log L FIR 0.79±0.05 α Log L IR 0.81±0.05 ) with strong correlation R=0.8 both with very high probability level p≈10 -7 . One of the closest and most ubiquitous correlations known among the global features of local star formation and starburst galaxies is the link between far-infrared (FIR) and radio emission.


Introduction
Massive stars are the source of power for starbursts. Massive stars (Mstarbursts ≥ 10 Mʘ) produce ultraviolet resonance transitions by emitting photons with energy of tens of eV that are absorbed and re-emitted in their stellar winds. The stellar wind, on the other hand, is optically thin to most ultraviolet photons, which can travel tens of kilometers from the star before being absorbed and photoionizing the interstellar medium. The ionized gas is then cooled down using an emission line spectrum. In essence, this is a starburst galaxy's spectral dichotomy picture: a nebular emission line spectrum at optical wavelengths and an absorption-line spectrum at wavelengths shorter than the Balmer jump [1]. Starburst galaxies are objects in which star formation and associated processes dominate the total energy. They have a size range of 100 pc to 1000 pc, and Hα luminosity of 10 40 erg/s to 10 42 erg/s. As a result, the nebula requires an ionizing photon brightness of between 10 52 and 10 54 photons per second, which is supplied by a stellar cluster containing thousands of young massive stars. This concept encompasses a wide spectrum of galaxies, including blue compact dwarfs, HII galaxies, nuclear starbursts, and ultraluminous IRAS starbursts, among others. Typical bolometric luminosities range from 10 40 erg/s to 10 45 erg/s, with the lowest limit corresponding to super-star cluster luminosity and the greatest limit corresponding to infrared-luminous galaxies. The pace of star formation is significant (10-100 and up to 1000 Mʘ/yr in some ultraluminous infrared galaxies) that the present gas supply can only fuel the starburst for a fraction of the universe's history (few 10 8 yr) [2].
In earlier research, the ROSAT All Survey was cross-correlated with a sample of 14708 extragalactic IRAS sources taken from the point source database by statistical classification. The X-ray brilliant spirals are starbursts with steep spectra, which makes them simpler to identify by ROSAT. They discovered a positive link between X-ray luminosity, IR, and optical luminosities, with the steepest correlation for Seyfert galaxies [3]. In addition, [4] discovered that barred galaxies have lower overall FIR luminosity than unbarred galaxies in a volumelimited sample. Other researchers confirmed that IR bright barred galaxies have much larger FIR-optical and S25/S12 ratios than unbarred galaxies, with the effect being particularly noticeable in the IR hues. They further showed that the influence of bars on the SFR was linked to relative IR luminosity and that it could only be seen in galaxies with LFIR/LB ≥ 1/3 [5]. Moreover, [6] offered the results of a statistical study of AGNs chosen from an RBSC-NVSS sample as the strongest X-ray sources. They discovered that the slopes of the LX-LB relations were flat for Seyfert galaxies, including the presence of components unrelated to X-ray. [7] presented a statistical analysis of samples of bright X-ray galaxies with active galactic nuclei (Seyferts1, Seyferts2, and Quasars) from the ROSAT Bright Source Catalogue (RBSC) and the NRAO VLA Sky Survey (NVSS). Multi-wavelength observations in the radio (1.4GHz), blue optical (4400 A 0 ), and X-ray (0.1-2.4) keV bands were investigated. The results of their statistical analysis showed that there was a strong correlation between the quantities (LX-ray -D and L1.4 -D correlations), and the slopes of the relation (LB-D) were flatter than the slope of 0.5 expected for cosmologically nearby objects, whereas for Seyfert2 type galaxies, they found that there was a very strong correlation between relation (LX-ray -D and LB -D), indicating that in comparison to Seyfert1, Seyfert2 had active components unrelated to radio emission. They also discovered that the Seyfert 1 and 2 galaxies had a strong linear relationship between (LX-ray -D), which could be due to the presence of extremely high X-ray emission in broad emission lines in their nuclei. The IRAF ISOPHOTE ELLIPSE job with Griz-Filters was used to investigate the morphological and photometric properties of two lenticular galaxies (NGC 2577, NGC 4310). The Sloan Digital Sky Survey (SDSS) provided observations, which are now available in the Data Release (DR14). The SDSS pipeline was used to reduce the data in all of the photos (bias and flat field). Although the disk position angle, ellipticity, and inclination of the galaxies were investigated, the surface photometric investigations such as total magnitude, isophotal contour maps, surface brightness profiles, and a bulge/disk decomposition of the photos of the galaxies were done by [8]. Eventually, [9] used their data from Chandra XMM-Newton and other wavebands to analyze the X-ray emission for a sample of young radio AGNs. For VLBI radio-core, they discovered strong correlations between X-ray luminosity in (2-10( KeV and radio luminosities LR at 5GHz. In the current study, we use data from the following sources in this inquiry, the first source is NASA Extragalactic Database (NED), and the second is HYPERLEDA. Those data are used to examine possible luminosity correlations of X-ray to a radio of a sample of starburst galaxies. This article is organized as follows: The second section describes the mathematical procedure utilized in this project to produce the form used in mathematical analysis, as well as the derivation of the parameters used in this analysis. The third section presents the findings of the statistical analysis that have been carried out in this research. Finally, the work's conclusion will be summarized in section four.

The data utilized and estimated parameters in the sample.
A sample of starburst galaxies was selected from papers [ [18]. Based on the NASA/IPAC Extra-Galactic Database (NED), selected available data such as redshift(z), X-ray flux, infrared fluxes at near, medium, and far beams (S12, S25, S60, S100) in the unit (Jy), radio fluxes at 1.4GHz (λ=21cm) & 5GHz (λ=6cm), an optical flux of OII at (λ=372.6nm) and ultraviolet fluxes at near (λ=177nm) & far (λ=153.9nm). The total apparent corrected B-magnitude mB from the French website Lyon-Meudon Extragalactic Database (HYPERLEDA) was selected. The physical parameters (galaxies name, the morphology of starburst galaxies, z, mB, S12, S25, S60, S100, SX-ray, SOII, magnitudes of far ultraviolet (m-FUV (AB)) and near ultraviolet (m -NUV (AB)) and radio fluxes at ν=1.4GHz & ν=5GHz) of starburst galaxies are listed in Table (1). Schmidt and Green defined the relationship between observed flux density and luminosity as [6]: for an energy band, E1 to E2, where c(z)=k-correction term, A(z)=luminosity distance term, and S(E1, E2)=observed flux density between E1, E2 bands, and z=redshift. In astronomical ideas, redshift z is often used as a distance metric, and hence provides information about ages and temporal period [19]. The luminosity distance term A (z)and the k-correction term c (z) for power-law spectra with energy index and Friedman cosmology with q0 = 0.5 are given by [6]: To determine all the luminosities from X-ray to radio emission, "Eq. (4)" was employed.

X-ray Luminosity (LX-ray):
In the X-ray range, the energy index is αx = -1.02 for active galactic nuclei starburst galaxies [7], and the flux density SX-ray in (erg s -1 cm -2 ), as a result, the X-ray luminosity is acquired by the following equation: Where LX-ray = X-ray luminosity in a unit (erg/s).

Calculations, results and discussion.
We present the results of statistical analysis in this paper by using statistical software (statistic-win-program) application to see if there is a luminosity correlation between multiple bands. The statistical program is frequently used to analyze and evaluate numerous associations between variables, as well as to determine whether or not there is regression strength between the two variables' characteristics. The linear partial correlation coefficient (R) values are in the range of [+1, -1]. If the regression value is ±1, the two components are perfectly linked. Even so, when the measurement of regression correlation (R) is zero or close to zero, there is a weak regression correlation between the two components. The relationships between logarithms of luminosities of wavelength bands from radio to X-rays when using multiple regression analysis on our sample of 131 starburst galaxies were studied. The partial correlation coefficient (R), significance levels (P), and the slopes were calculated for each relationship.
The relationship between X-ray luminosity as a dependent variable and radio luminosity at (5GHz & 1.4 GHz) as independent variables. From the results of the statistical analysis, we find that there is a good correlation between X-ray luminosity and radio luminosity at 1.4GHz where the partial correlation coefficient is (R=0.53) and slope (0.6±0.12) for N=81, where N is the correct sample number under test (see Figures 1a, 1b). There is also a significant correlation between X-ray luminosity and radio luminosity at 5GHz with a good partial correlation coefficient (R≈ 0.65) and slope (0.77±0.11) for N=68. There are good positive relationships between radio luminosity at (1.4GHz, 5GHz) with infrared and farinfrared luminosities. (Log L1.4GHz α log LFIR 0.89±0.04 α Log LIR 0.9±0.03 ) with a very strong correlation equal to R≈0.9 and (Log L5GHz α Log LFIR 0.79±0.05 α Log LIR 0.81±0.05 ) with a strong correlation R≈0.8 both with very higher probability level p≈10 -7 , for N=108 (see Figures 2a,  2b, 2c and 2d).  (Log L1.4GHz) and (Log LFIR).
One of the closest and most correlations known among the global features of local star formation and starburst galaxies is the link between far-infrared (FIR) and radio emission. This tight global correlation was unexpected at the time of this significant discovery because the radio and FIR emissions were thought to be caused by distinctly different physical processes. Namely, the radio continuum emission is primarily caused by synchrotron emissions from relativistic cosmic-ray electrons gyrating around galactic magnetic fields, whereas the FIR emission is primarily caused by thermal emissions from dust grains submerged in an intense ultraviolet (UV) radiation field. The current qualitative physical explanation for such a global correlation is that FIR is caused by dust grain absorption of UV photons emitted by nearby young massive stars, whereas sources of relativistic cosmic-ray electrons are primarily associated with magneto hydro dynamic (MHD) shocks of massive stellar winds or supernova explosionsthe primary source of UV radiations that heat interstellar dust grains, and these results agree with [23].
Moreover, the link between radio luminosity at (5GHz) and optical luminosity (Log L5GHz α Log Lopt 0.43±0.10 ) is weaker than the link between radio luminosity at (1.4GHz) and optical luminosity (Log L1.4GHz α Log L opt 0.69±0.1 ) with correlation equal to R=0.39 & R=0.64 respectively both with very higher probability level p≈10 -7 , for N=117 (Figures 3a, 3b). Since radio emission from a starburst originates in H II regions and supernovae, it is mostly unaffected by extinction. Optical emission-line ratios can be used to determine the major energy source inside a galaxy since they represent local excitation conditions, with the caveat that optical wavelengths may not notice a substantially veiled starburst or AGN. The radiation of plasma accreting onto supermassive black holes dominates the optical emission of quasars, or active galactic nuclei (AGN), while plasma outflowing from black hole/accretion disk complexes dominates the radio emission. As a result, separate but complementary information about the cosmic development of AGNs and their relationship to structure formation in the universe may be acquired in both photon energy ranges. This correlation could be a result of the flux restrictions and the large range of redshifts. Furthermore, it could be a result of the stellar population and these agree with the results of [24]. There are weak relationships between far-ultraviolet as a dependent variable and (LOII, LXray, Lopt) as independent variables. The slopes of the relationships are not linear but rather flat (Log LFUV α Log LOII 0.34±0.12 α Log LX-ray 0.35±0.08 α Log Lopt 0.37±0.09 ) with a weak correlation equal to R≈0.348, R≈0.43, and R≈0.37 respectively, and probability level P≈9x10 -3 , P≈10 -4 & P≈10 -  There is a good positive relationship between LX-ray and LFIR with a good partial correlation equal to R≈0.57, slope (0.45±0.07), and high probability level p≈10 -7 , for N=84. An empirical correlation between the FIR and X-ray global luminosities from the young objects (e.g. HMXBs) has been reported in star-forming galaxies and the correlation is naturally interpreted in terms of star formation activities in galaxies, which in turn implies a correlation between Xray luminosity and star formation rate (SFR). David, Jones & Forman (1992) derived a linear relationship between the logarithms of X-ray (0.5-4.5) keV and FIR luminosities in the normal and starburst galaxies using the X-ray data of the EINSTEIN satellite and suggested a twocomponent model fit this correlation [25]. The existence of a strong link between global farinfrared (FIR) and radio continuum (1.4 and 4.8 GHz) fluxes/luminosities from star-forming galaxies has been known for two decades, which may be explained by tremendous star formation processes in these galaxies. As a result, a link between X-ray and FIR/radio global luminosities of galaxies may exist.

Figure 5:
The relationship between Log LX-ray and Log LFIR In addition, we find a strong significant correlation between LNUV & L1.4GHz and between LNUV & LFIR. The partial correlation between LNUV & L1.4GHz is equal to R≈0.631 and slope is (0.63±0.08), and for the relationship between LNUV & LFIR the slope is (0.68±0.08) and the partial correlation is equal to R≈0.64 with N=95 for both. This is why infrared measurements of starbursts are so important: infrared luminosities are significantly less susceptible to extinction. Two spectral "features" that are intrinsic to the same starburst are the infrared emission and the ultraviolet monochromatic continuum. The infrared is generated by photons from the continuing starburst in the photodissociation area immediately surrounding it. This infrared emission is unique to the photodissociation zone and occurs whether or not the starburst is obscured by dust. It is as much a part of the starburst as hot star radiation or emission lines from the HII region. The same obscuring dust in the surrounding cold molecular cloud affects both infrared and ultraviolet characteristics; however, the UV feature suffers significant extinction while the infrared feature suffers little extinction. (Log L1.4GHz) and (Log LNUV). We furthermore find that there is no strong correlation between the far-infrared and optical luminosities. The correlation is equal to R≈0.46 with slope (0.44±0.08) for N=120. A significant dispersion due to the uncorrelated temporal variability of star formation and accretion activity may overshadow a correlation between the optical and FIR luminosities.

Conclusion
Various correlations exist between the FIR, radio, and X-ray luminosities of starburst. From the results of the statistical analysis, we have found that there is a linear relationship between LX-ray and LFIR for star-forming regions, with a flat slope (0.45±0.07) and good partial correlation equal to R≈0.57. This correlation is naturally interpreted in terms of star formation activities in galaxies, which in turn implies a correlation between X-ray luminosity and star formation rate (SFR). There are good positive relationships between radio luminosity at (1.4GHz, 5GHz) with far-infrared luminosity, with steep slopes (Log L1.4GHz α log LFIR 0.89±0.04 ) & (Log L5GHz α Log LFIR 0.79±0.05 ). The current qualitative physical explanation for such a global correlation is that FIR emission is primarily caused by dust grain absorption of UV photons emitted by nearby young massive stars, whereas sources of relativistic cosmic-ray electrons are primarily associated with magnetohydrodynamic (MHD) shocks of massive stellar winds or supernova explosions.

ACKNOWLEDGMENT
We owe our gratitude to all of the organizers of the NASA/IPAC Extragalactic Database (NED) and the French website Lyon-Meudon Extragalactic Database (HYPERLEDA), from which we received our data, and to all of the people who taught us.