Investigation of the Characteristics of CO (1-0) Line Integrated Emission Intensity in Extragalactic Spirals

This paper aims to deal with the understanding of properties of molecular gas hydrogen in extragalactic spirals sample. It is critical to make observations of CO (J = 1-0) line emission for spiral galaxies, particularly those with an energetic nucleus. In a compiled sample of spiral galaxies, a carbon monoxide CO (1-0) emission line can be observed. This sample of galaxies' gas kinematics and star-forming should be analyzed statistically utilizing appropriate atomic gas HI, molecular gas H 2 , infrared (1μm-1000μm), visual (at λ blue-optical = 4400A 0 ), and radio spectrum (at ν radio =1.4 GHz and 5 GHz) databases. STATISTICA is a software that allows us to perform this statistical analysis. The presence of a high scale of star formation activity in these galaxies is dependent linearly on the correlations between galactic luminosities. Our findings show that thermal radio luminosity and L FIR are closely related to CO line emission luminosity. Further, L CO and MH 2 have a steep linear relationship, where the slope of the regression log L CO - LogMH 2 equals 1. The L CO -SFR and L FIR -SFR relationship slopes are nearly linear (slope ~1), with a strong partial correlation R CO-SFR of 0.73 between L CO -SFR and a significant correlation R FIR -SFR of 0.5 between L FIR -SFR, according to the statistical analysis. The correlation between the rate of star formation (SFR) and hydrogen gas in spirals is significant in several fields of astrophysics. Hence, it is asserted that the important point of the current study is that there is a significant link between SFR and the actual amount of cold hydrogen gas (M gas ) for the simple reason that in our spiral analysis, the mean atomic cold gas amount quantity is almost 6 times greater than the molecular gaseous amount.


1.
Introduction Extragalactic spirals have radio characteristics that can be observed in spectrum of radio region including spectral lines of hydrogen in addition, to ordinary molecules, like carbon monoxide spectroscopy, since the optical spiral arms are circumscribed by regions that generate stars [1]. The primary condensation and breakup of giant molecular clouds to thick accretion a disk including molecular clouds, that molecular interstellar medium plays an important part in star formation. So, the total mass of molecular gas in a galaxy is an important factor in determining star formation [2]. Even though, H 2 presents up at least 99 % of the molecular gas, it is difficult to detect directly in most of the molecular medium due to the absence of a stable dipole moment as well as its cold temperature, which is below the excited energy. As a consequence, observing the molecular gas is reliant on other molecules, especially CO, which is easily visible even in the thinnest molecular gas. To study interstellar molecular gas, the CO emission lines, especially the transition J = 1--0 at ν CO(1-0) = 115 GHz, can be compared to the 21 cm line. Carbon monoxide is the simplest molecule present in each molecular dust of the Milky Way, including any galaxy at any redshift, and it is utilized to calculate the masses of molecular gas systematically [2]. The molecular hydrogen is highly intertwined with atomic hydrogen, and the total amount of gas MH 2 +MHI is the most significant quantity for the evolution and formation of spiral galaxies including, in some way, star formation. Atomic gas (HI) and molecular gas are inextricably connected. Due to the continuous exchange between HI and H 2 , the gas must be fully studied, as well as its dynamics, transport characteristics, including interchanges alongside the intergalactic medium and interior regions, and concentration processes that lead to star formation and the effect of reactions on the gas [2]. Far-infrared luminosities of L FIR ≈ 10 13 L ʘ are observed in the majority of CO-detected sources. In local ultra-luminous infrared galaxies (ULIRGs), there exist a trend of higher values for the ratio of Far-infrared luminosity to CO radiance compared to the association between CO and FIR luminosities [3]. Interstellar gas must be studied at galactic measures to understand the composition and dynamics of galaxies, as well as how stars form. Apart from interstellar dust extinction, the bulk of the interstellar medium is inaccessible to optical astronomy due to the absence of emission at low temperatures, a lack of adequate visual absorption bands, and absorption line obscuring caused by massive dust extinction [4]. Several studies focused on galaxies were being conducted to investigate the properties of CO line emission in galactic centers and disks. Using single-dish extragalactic spectra synthetic emission, Lavezzi & Dickey (1997) investigated disk resolution testers, calculated distributions of gas density, and opacity to assess if CO line widths for use in the Tully-Fisher relationship are correct. Researchers used an HI of 21 cm line, confined gas density distributions, and opacity on extragalactic spirals spectra instead of an HI of 21 cm line to view if CO line widths were appropriate for use in the Tully-Fisher relation [5]. Boselli et al. (2002) analyzed the relationship between the H 2 to CO conversion factor and galactic parameters including UV, metallicity, and blue optical and near-infrared luminosities. The relationship between star formation activity and total mass of gas MH 2 + MHI has been discovered, with the understandable reason that for spirals, the mean MH 2 /MHI effect is nearly constant. [6]. In the following study [7], the researchers concentrated on knowledge of the large mass of H 2 traced by CO millimeter emission in regular molecular clouds. In the external galactic disk, an even greater mass of H 2 may be obscured as incredibly cold hydrogen. Since the first extragalactic CO surveys, there has been a clear correlation between CO flux energy (I CO ) and both radio continuum and Far-infrared luminosities. Making this association quantitative with SFR, except for non-starburst galaxies, poses many challenges, including the most critical case of spiral galaxies as exhibited in [8]. CO line intensity studies of molecular gas in galaxies bars, as demonstrated by Jogee et al. (2005), are critical for understanding their structure and dynamics, as well as their effect on the rate of star formation in the nuclear surroundings [9]. The author Al Najm (2020) discussed the physical properties of a sample of 65 CO(J=1-0) line spectra of extragalactic (normal and active galaxies), which are characterized by the effectiveness of stellar evolution. These galaxies have a large molecular mass as well as a large star formation activity per unit "mass", according to the findings [10]. This paper is structured as ensues: in Parts 2 and 3, we explain the sample and also the physical parameters derived from spectral information and used in the study. Part 4 delves into the results of the analyses. A summary is given in the final part.

The Computed Parameterization
Carbon monoxide CO is the most common compound in the interstellar medium. A rotating molecule of carbon monoxide, for example, emits dipole radiation at the frequency of its rotation, as follow [14]: where and a is the circumrotation speed of the molecule and its length (C separator and O atoms). The lowest frequency of the rotational transition from J = 1 to the ground level J = 0 for the CO line intensity is approximately ν J=1-0 = 115 GHz or λ J=1-0 =2.6 mm [04]. The following variables were computed separately: -0 To calculate the total H 2 mass ( MH 2 ), we began to calculate the CO radiance by combining the CO(1-0) line intensity across the speed profile. The luminance of the CO line is generally displayed in units of K.km/s.pc 2 as a result of the reference integrated velocity illumination temperature (T b ∆v) and the source area Ω s D A 2 , where Ωs is the solid angle that the source takes. The intensity of the observed integral line I CO = ∫ T mb dv, which decreases with redshift, measures the brightness weak temperature of the beam. If so, it is referred to as the main temperature beam T mb , which is roughly equal to the cloud temperature T b brightness [15,06]: T b ∆v Ω s = 23.5 I CO Ω sb (1+z)………………………………………….. (2) where Ω sb is the source's solid angle when coiled with the telescope beam. Therefore, the CO(1-0) line intensity luminosity is given by The luminosity distance D in the unit (Mpc) to the moving source by the redshift (z) can be viewed from the following [15,06]: D = D A (1 + z) 2 ………………………………………..……………..(4) where D A is the angular size distance. According to the NASA /IPAC Extragalactic Database site (NED), we adopt a Hubble constant of H0 = 100 h km s-1/ Mpc with uncertainty in the Hubble constant scale h=0.678 ±5 and cosmological parameters Ω matter =0.308 and Ω vacuum =0.692. In cosmology, the luminosity distance and the angular size have been calculated using the website (http://www.astro.ucla.edu/~wright/CosmoCalc.html). By substituting equations (2 & 4) in the expression equation (3), then, the CO line luminosity (L CO ) for a source takes the form: is measured in unit K. k ………. (5) where I CO is the line intensity by unit K km s −1 and beams solid angle of radio telescope Ω sb Hence, equation (5) can be rewritten as follows: …………………………………………..... (6) or the equation (6)  m Btc is the total value of the corrected blue color-magnitude for galactic and endogenous absorption. 9-The central radio continuum luminosity at frequency ν=5 GHz or wavelength can be written as [76]: L ʘ ) =17.078+2 Log + Log ……………………….……. (19) 10-The dust mass in galaxies (M dust ) is calculated from the temperature of the dust, T dust , which is inferred from the flux densities at the emission of 60 μm and 100 μm from the black body. Considering that the dust radiation attends the emissivity law F v α λ -1 , the M dust almost designated as [17,28]: (M ʘ )=4.5

Statistical Calculation Results and Discussion
We utilized a statistical software program (statistic-win-program) to see if there is a correlation between several variables in this article. The statistical program is commonly used to process and evaluate various relationships between variables, as well as to assess if there is regression strength between the characteristics of the two variables. The values of the linear partial correlation coefficient (R) are in the range [+1, -1]. The two components are completely associated if the regression value is ±1. Even so, there is a weak regression correlation between the two components when the measurement of regression correlation (R) is zero or close to zero [10,[31][32][33][34]. Due to Malmquist bias, both correlation coefficients and confidence levels have been adjusted for artificial reliance on parameters from galaxies distances in this work. Molecular hydrogen and neutral hydrogen are the most common cold interstellar medium ISM types. Carbon monoxide observations have allowed identifying the molecular gaseous hydrogen emission in detail to other observations at different frequencies ranging from ultraviolet-optical-infrared to radio bands. According to statistical regression techniques for the analysis of (140) extragalactic spirals, the average value of CO(1-0) luminosity with a standard error is equivalent to ˂Log L CO >= 8.10±0.073 (L CO =12.6x10 7 K. k ) with a minimum and maximum value ranging between L CO min. ~ 2.73 x10 5 K. k to L CO max. ~ 1.25x 10 10 K. k , while a mean value of IR-infrared (1-1000)μm to Far-infrared around 100μm luminosity can be evaluated ˂ L FIR (L ʘ ) > ≈ 8.5x10 9 ± 0.067 with L FIRmin. = 10 7 to L FIRmax. ≈ 3x10 12 L ʘ for the warm dust of temperature about ˂T dust >=42±0.925 K 0 . Since the dependence of the temperature dust on the CO (1-0) line-infrared emissions as shown as Figure (1a) existence a positive relationship between (Log L FIR , Log L CO , and T dust ) with a flat slope ≤ of 0.5 for relation Log L FIR -T dust and Log L CO -T dust . We adopted the following equation for linear fit regression Y=ax+b, where (a) is just the slope of linear regression, and (b) is the y-axis intercept, the most appropriate suitable fitting expression of linear regression is found using an acceptable standard error, which is described as: ……….
and we have seen that there is a partial correlation coefficient equal to (R FIR-Tdust =0.42, R CO-Tdust ≈ 0.3) in this relationship. Figure 1a exhibits the relationship between CO line -FIR infrared luminosity and dust temperature for the extragalactic spiral in this study. The correlation between L CO and T dust is slightly weaker than that between L FIR and T dust . Besides, results pointed also to a good positive relationship between L CO -L IR and L CO -L FIR (Log L CO α Log L IR 0.62±0.056 α Log L FIR 0.65±0.053 ) with a strong correlation is equal to R~ 0.7 and a very higher probability level of chance correlation P ≤10 -7 (see Figures 1b &1c). The physical meaning of these correlations can be clarified by the amount of interstellar medium gas in a molecular form (CO) that significantly increases with IR-FIR luminosities, according to our results. These galaxies show extremely high infrared detection lines from the line intensity of carbon monoxide CO as shown in a ratio L FIR /L CO =1.84 computed from our results, and also the warm dust element cohabits with the molecular layer formed of warm clouds (˂Tdust> ≈ 40K 0 ) at the actual scale, indicates that the warm dust element emits in the near-infrared range, with a peak of about 100 μm, since the dependence of the temperature dust on the infrared emission. The ultraviolet (UV) and optical emission absorbed from OB stars are the sources of the FIR -infrared emission's spectral energy. The broad range of observed radiation indicates that the distance measured will not influence the association between FIR and CO luminosities, showing an excess of far-infrared emission. It appears to us that the outcomes of our work here are in agreement with those of previous literature articles such as [20, 10, and 16] on the strong link between L CO -L IR and L CO -L FIR  and 2c) that there is a positive correlation between L CO and L 1.4 (R ≈ 0.5), however, there seems to be a statistically significant correlation coefficient between L CO and L 6cm , L B equals to R~ 0.7, in addition to a very significant level of confidence P ≤10 -7 , and we noticed differences in slopes between (Log L CO α Log L 1.4 0.58±0.05 ), (Log L CO α Log L 6cm 0.61±0.09 ), as well (Log L CO α Log L B 0.39±0.05 ). We found a tight linear relation between CO(J=1-0) line emission and radio continuum with either L CO -L 6cm or L CO -L 1.4GHz and the CO(1-0) line emission of spiral galaxies is also related to the blue optical emission (L B ). It can be understood in these types of galaxies, as well as an abundance of gases that pervade the entire galaxy. An ionized gas H α at line λ= 6 cm can emit a heavy radio and thermal emission. This implies that these extragalactic spirals with bright CO line densities or the radio thermal continuum have more atomic and molecular gas, regardless of form. It's interesting to note that the range of optical blue brightness difference in our sample is rather limited, or maybe suggesting that the correlation between CO (1-0) line emission and radio continuum seems to be more essential.  We estimated the mean values of atomic cold hydrogen gas (MHI), molecular cold gas content (MH 2 ), and dust mass (M dust ) for our galaxies. Consequently, to our sample of the extragalactic spirals the mean values with a standard error of LogMHI=9.43±0.059, Log MH 2 =8.68±0.074, and Log M dust =6.46±0.069 respectively. It is essential to see that for all morphological types of spiral galaxies, the hydrogen HI content is always greater than that of the content hydrogen H 2 , the cold atomic gas content increases approximately by a factor of 6 to the molecular mass value of the gas in spiral galaxies (˂ MHI / MH2 > ≈ 6). As we have previously indicated that the molecular gas mass is associated with the carbon monoxide gas CO line, furthermore, the CO(J=1-0) spectroscopic database was used to measure the molecular hydrogen amounts of spiral galaxies, accordingly, the neutral gas HI surface area in most morphology spiral galaxies is larger than the CO line amplitude. The CO radiation is focused in the interior some kiloparsecs whereas, a natural gas distribution indicates more depression in the galaxy's center. Besides that, for HI cold gas observations, the superposition of independent clouds in the emission region is more expensive than toward molecular gas CO observations. Our results calculated here are largely in agreement with those of the literature [76]. The average value of the ratios of M H2 /M dust was evaluated in this survey, for our types galaxies having ∆ Log (M H2 /M dust ) designated as ˂ LogM H2 > -˂ LogM dust > equals the mean value 2.21±0.047, this means that the molecular gas mass M H2 is about ~ 160 times larger from dust mass M dust of those galaxies. The method for calculating dust mass utilizing Far-infrared flux at 60 μm and 100 μm, and the molecular gas mass to dust mass ratio seems to be overestimated. This indicates that the dust components contain most of the cold dust and a fraction of warm dust. Two dust components, warm and cold dust, have been proposed as explanations for the difference in the gas-to-dust masses ratio. Cold (T dust =10-20 K 0 ) dust associated with quiescent molecular clouds and warm (T dust =30-60 K 0 ) dust associated with a star-forming activity. Our interpretation of this finding is identical to what was mentioned in the investigation article [28]. As shown in Figures (3a, 3b & 3c), the relation between atomic and molecular gas-to-dust content and CO line luminosity has also been discussed, and we discovered differences in the slopes between them. In Figure.3a we have noticed that there is a very tight linear relationship between L CO and MH 2 , the slope of Log L CO -LogMH 2 equal to unity (slope ≈ 0), with a very strong correlation coefficient corresponding to 1 (R CO-MH2 =1) and a very high probability of relationship P ≤10 -7 . In contrast, it is evident from Figure (3b) that there is a weak correlation between L CO and MHI, the slope of the relationship between CO line emission and atomic cold gas is not linear but rather flat (slope ~ 0.3) and a weak correlation R CO-MHI ~ 0.35, as for the relation L CO -M dust there is a good correlation between them (R CO-Mdust ~ 0.64), then the linear regression slope towards one as given as in Figure (3c). The very strong linear association potential between L CO with MH 2 distinct in these types of galaxies indicates that the molecular gas is more abundant due to its wide diffusion, due to the molecular gas's effectiveness in the MH 2 regions. Intergalactic gas emits a lot of 12 CO (J=1-0) lines, which is dominated by the molecular gas H 2 . As a result, gas content-to dust mass to CO line luminosity relationships in these spiral galaxies are varied and complex, dependent on a range of internal and external variables including the atmosphere, brightness, dynamics, structure, and star formation activity. Observing emission from CO line rotational transitions is the most popular form of pursuing intergalactic molecular clouds, which are almost completely made up of molecular hydrogen. All interstellar clouds are mostly made up of molecular hydrogen instead of atomic hydrogen. The transition from atomic hydrogen to molecular hydrogen appears at a medium interstellar surface region, suggesting that whole massive clouds are molecular gas. Molecular gas clouds provide the materials for starforming and are an important part of galaxies' evolution. Interstellar dust, on the other hand, is responsible for the massive CO emission to infrared luminosity seen in an extragalactic spiral, and all dense, dusty particles may be considered molecular.  It is seen from our work, the average value of star formation rate ˂SFR> = 8.98 ± 3.73 with lower and upper quartile values is located between 0.41 M ʘ yr -1 and 4.58 M ʘ yr -1 , regardless of the morphological type, in the most reliable SFR measurements. It has been estimated that there is a strong relationship between the star formation indicator rate SFR and both the far-infrared and CO luminosities. We noticed that slopes of the relationships L CO -SFR and L FIR -SFR are approximately linear ~ 1 with a strong partial correlation coefficient R CO-SFR ≈ 0.73 between L CO -SFR, whereas a clear correlation R FIR-SFR ≈ 0.5 between L FIR -SFR and probability of occurrence correlation is very high (P ≤ 10 -7 ) as illustrated in Figure 4a (left panel). Star formation rate seems to be the product of a complex interstellar medium mechanism that leads to the separation and collapse of stellar scale clusters. The majority of the steps indicate energy density at which the interstellar gas must be molecular gas including the extragalactic spirals. There should be strong significant relationships between the amount of molecular gas CO and star formation activity higher than the amount of Far-infrared radiation and spiral galaxies' SFR on all scales. For note, a portion of the Far-infrared radiation in some spiral galaxies can occur in the distributed atomic layer, making star formation regions irrelevant.
In Figure 4b (right panel/ solid blue line), we analyze the accumulated correlations of a range of variables such as the total mass of cold gas (MHI+MH2), and ratio L FIR /L B with star formation indicator. It is explicit that the main finding of the current study is that there is a significant relationship between SFR and the total amount of cold gas M gas . The slope for M gas ~ SFR should be close to the unit (Slope Mgas-SFR ~1) with a clear explanation that the mean value of the Log MHI / MH 2 ratio is approximately constant ~ 0.75 ±0.065 for extragalactic CO survey spirals. Consequently, the atomic gas-phase amount in our study of spirals is approximately 6 times greater than the molecular gaseous amount. The result of this statistical analysis is, in general, consistent with the results of [37, 77], however, it contrasts with Young and Knezek's [33] conclusion that the quantities of molecules and phases of an atomic gas are equal. All molecular and atomic forms of cold interstellar hydrogen gas in extragalactic spirals depend greatly on the type of morphology. We also revealed that the ratio (L FIR /L B > 1/3) for our spiral galaxies sample, which means the existence of spiral bar galaxies, undergoes bar-induced starbursts with illuminated blue optical and Far-infrared is approximate ~10 10 L⊙. The reason is thought to be the presence of a bar that activates the process of star formation in type spiral bar galaxies, this intimates that fuel availability is a factor that determines only galaxies that experience stellar explosions from bars, furthermore, our analysis confirms a good consensus with the literature [34]. Figure 4b (right panel/ dashed red line) exhibits the regression relationship between the ratio L FIR /L B and the star formation rate increasing with a tendency toward linearity (Slope ~ 1), and our results of multiple regression analysis indicate there exists a significant correlation (R ≈ 0.6) between these quantities. These extreme infrared luminosity galaxies are directly fuelled by massive starbursts, mainly dust-covered, at rates of star formation in the tens or yet hundreds M⊙ /yr, which can be concluded directly from L FIR if the global relationship, SFR FIR ≈ 1.7x10 -10 L FIR . The well-related far-infrared to blue optical-luminosity ratio L FIR /L B star formation indices are used to compare star formation behavior in galaxies. On a timescale of billions of years, the L B blue optical luminosity is a tracker of past star formation, while FIR and radio communication at a luminosity of 6 cm are trackers of modern star formation on a timescale of millions of years.

. Conclusion 5
As shown by the L FIR /L CO ratio computed from our results, these galaxies have exceptionally high lines of infrared detection at a factor twice as strong as the CO (J=1-0) line. We conclude that the contents of molecular hydrogen have a linear relationship with LCO. Based on our statistical analysis, we also found that the true meaning of the gas is revealed by the CO line emission spectra. CO observations are important for galaxies, particularly those with effective starbursts since it appears that molecular gas plays a role in the formation of stars. By calculating the rate of infrared luminosity (L FIR ) to determine its effect on spiral galaxies, we realized that it emits distinctively from dust within molecular (CO) clouds in these galaxies, resulting in a high infrared luminosity. Our conclusions designate that thermal radio luminosity and L FIR are well associated with the CO line luminosity. The results indicate that the dust components contain a plurality of cold dust and a plurality of warm dust. We've seen that L CO and MH 2 have a very strong linear relation, with the slope of Log L CO -LogMH 2 equivalent to 1, and a very steep correlation coefficient (R CO-MH2 =1). Due to the molecular gas's effectiveness in the MH 2 regions, the very high linear interaction potential between L CO and MH 2 distinct in these types of galaxies suggests that the molecular gas is more abundant owing to its broad diffusion. Eventually, the work concluded the relationship slopes of L CO -SFR and L FIR -SFR are nearly linear 1, with a high partial correlation R CO-SFR ~ 0.73 between L CO -SFR and a significant correlation R FIR-SFR ~ 0.5 between L FIR -SFR. There  should be very significant relationships between the amount of molecular gas CO and star formation indicator higher than the amount of far-infrared emission and spiral galaxies' SFR on all scales. For instance, a portion of the FIR radiation in some spiral galaxies can occur in the distributed atomic layer, making it insignificant to star formation regimes. We also remarked that the ratio (L FIR / L B > 0.3) of our extragalactic spirals sample, indicating the presence of spiral galaxies bar showing bar induced by stellar explosions with optical -blue and far-infrared illumination is approximate ~ 10 10 L⊙.