BIBECHANA Vol. 21, No. 1, April 2024, 37–50 ISSN 2091-0762 (Print), 2382-5340 (Online) Journal homepage: http://nepjol.info/index.php/BIBECHANA Publisher:Dept. of Phys., Mahendra Morang A. M. Campus (Tribhuvan University)Biratnagar Comparative study of the dust color temperature and dust mass within the isolated dust in W51 giant molecular cloud in IRIS and AKARI data M. S. Paudel1,∗, H. K. Kushuwala1, S. Bhattarai2 1Department of Physics, Tri-Chandra Multiple Campus, Tribhuvan University, Nepal 2Central Department of Physics, Tribhuvan University, Nepal ∗Corresponding author. Email: mspaudel27@gmail.com,madhu.paudel@trc.tu.edu.np Abstract This work presents the comparative study of the properties of dust within the W51 Giant Molecular Cloud (GMC) located at (RA, DEC) (J2000): 290.91◦, +14.51◦. In the infrared data of Improved Reprocessing of the IRAS (IRIS) the dust structure seems single and iso- lated having size 0.45◦×0.45◦ but in AKARI infrared survey it breaks into two isolated regions having size 0.15◦ × 0.15◦ and 0.10◦ × 0.10◦, represented by AKARI-I and AKARI-II respec- tively. In IRIS map, 60 and 100 µm and in AKARI map, 90 and 140 µm image are used for extraction of the infrared flux. The dust color temperature (Td) and dust mass (Md) are calculated from the infrared flux and found to be 30.34 K in IRIS and 27.40 K and 23.55 K in AKARI-I and AKARI-II. A linear relationship between the infrared flux at two wavelengths is found except AKARI-I. The dust mass per pixel in the isolated (core) region is found to be increased compared to the total study region. To quantify the relation between flux, dust color temperature, and dust mass, the regression analysis is used and observed spectrum of relation. A huge SIMBAD background objected is found embedded in the dust cloud which might have been shaping the spatial variation of temperature and mass within the dust cloud. Keywords W51 Giant Molecular Cloud, Infrared flux, Dust Color Temperature, Dust Mass, IRIS, AKARI. Article information Manuscript received: September 26, 2023; Revised: December 17, 2023; Accepted: December 25, 2023 DOI https://doi.org/10.3126/bibechana.v21i1.58815 This work is licensed under the Creative Commons CC BY-NC License. https://creativecommons. org/licenses/by-nc/4.0/ 37 http://nepjol.info/index.php/BIBECHANA mspaudel27@gmail.com, madhu.paudel@trc.tu.edu.np https://doi.org/10.3126/bibechana.v21i1.58815 https://creativecommons.org/licenses/by-nc/4.0/ https://creativecommons.org/licenses/by-nc/4.0/ M. S. Paudel et al./ BIBECHANA 21 (2024) 37-50 38 1 Introduction A Giant Molecular Cloud (GMC) is a huge struc- ture in the interstellar medium that can nurture the various phases of star formation, often called the stellar nursery. It is believed that the massive stars are formed in GMC in the Milky Way Galaxy [1]. However, the formation of the star from the natal GMC is still an unclear topic. W51 is an example of the GMC in the Milky Way Galaxy located at the Sagittarius arm of the Galaxy [2]. It is found from the latest research that an active and massive star is forming in the W51 molecular cloud. In the Milky Way Galaxy, W51 is in the top 1% by size, top (5-10)% by mass [3], and top (50-15)% by star formation efficiency (SFE) [4]. It is found that the majority of the star has been formed within ∼ 3 Myr. Many HII and Cluster are embedded within the cloud. Moreover, W51 is hosting many objects which are revealed at different wavelengths, such as; various newly formed O stars are detected in the near-infrared wavelength, many third-generation of the massive proto-stars are detected in the mid- infrared wavelength, and numerous young stellar populations are detected in the microwave, millime- ter, and submillimeter wavelengths [5]. The infrared astronomy is crucial to explore the part of the Galaxy into those parts where the visible light is unable to reach. In the history of infrared astronomy, Infrared Astronomical Satellite (IRAS) was the first space satellite which was successful in mapping more than 96% of the Milky Way Galaxy in the infrared (IR) wavelength [6]. Infrared radia- tion is emitted by the hot dust molecules in Inter- Stellar Medium (ISM) due to the absorption of en- ergetic radiation, such as; X-ray, Ultra-Violet (UV), and visible ray emitted from nearby hot star and stellar remnants. The mass budget of the inter- stellar dust can be studied via infrared radiation. It is believed that the dominant dust formation mechanisms are the stellar wind created mass loss in AGB phase and Supernova Remnants (SNRs) phase of stellar evolution and in ISM, its abun- dance increases by coagulation, erosion, shattering, etc. [7, 8]. There have been many studies concerning the properties of dust using the infrared data from IRAS, Improved Reprocessing of IRAS Survey (IRIS) [9], AKARI [10], and Wide Infrared Sur- vey Explorer (WISE) [11]. Recently, the proper- ties of the North-East part of the Perseus molecular cloud is studied by Bhattarai et al., (2023) [12] us- ing IRIS and AKARI data, in which the dust color temperature (Td) in IRIS data (26.34 ± 0.11 K) is found higher than the AKARI data (17.63±0.02 K) but the dust mass (Md) is found higher in AKARI data. The spatial distribution of the infrared flux and temperature is almost similar in both IRIS and AKARI data but for dust mass and visual extinc- tion there is a huge difference between both data. Also, many background sources, such as; dense core, part of cloud, submillimeter Radio source, IR, dark and reflection nebula, etc., are found within the studied region which are considered as the ma- jor contributor of the dust mass. In most of the studies Td is found between 15 K and 45 K in IRAS/IRIS data, such as; 20 K to 24 K for the dust cloud nearby WD 0307+077 [13], 22.91 K to 34.58 K for the dust nearby PG 1225- 079 [14], 25.59 K to 36.82 K for the dust nearby WD 0011-399 [15], 22.67 K to 33.56 K for the dust nearby the Supernova Remnants (SNRs) in Galac- tic plane [16], 21.87 K to 24.09 K for the dust nearby WD 0352-049 [17], 23.77 K to 24.93 K nearby C- rich AGB star 19558+3333 [18], 20.75 to 35.90 K and 22.52 to 45.63 for the dust in two different neb- ula [19]. In AKARI data Td is also found in the same range, such as; 17.87 K to 43.47 K nearby PG 1225-079 [14], 16.31 K to 26.37 nearby WD 0011-399 [15] and 15.78 K to 28.86 nearby SNRs in Galactic planes [16] and 16.78 K to 17.71 nearby C-rich AGB star 19558+3333 [18]. However, the average value of Td is found less in AKARI data compared to IRAS/IRIS in all data. For WISE data, Td is found between 286.38 K nearby PG 1225-079 [14], 307.24 K to 353.72 K nearby WD 0011-399 [15], 122.55 K to 125.11 K nearby C-rich AGB star 19558+3333 [18]. A higher value of Td is observed in WISE data. In most of the work, the relationship between the temperature and mass of dust is trying to explain. In dust clouds around WD 0352-044 in IRIS data [17], dust cloud around SNRs in AKARI data [16], dust clouds around PG 1225-079 in WISE and AKARI data [14], dust cloud around WD 0011-399 in WISE data [15] the tem- perature and mass have an inverse relation, means higher dust mass is observed in the color map where the temperature is low and vice-versa. There are some other works in which no preferred relation- ship between Td and Md is found, for instance, dust cloud around SNRs in IRIS data [16], dust cloud around WD 0011-399 in IRIS and AKARI data [15], dust cloud around PG 1227-079 in IRIS data [14], etc. The inter-relationship between Td and Md is found independent of the infrared survey, such as; IRIS, AKARI, and WISE. More study is required for a clear conclusion. This work focused on the investigation of Td and Md from infrared flux within the W51 molecular cloud. Infrared flux is used to calculate Td and Md and their distribution is analyzed. The relationship of the infrared flux with Td and Md as well as the between Td and Md is presented. The impact of the background objects embedded within the dust cloud is tried to explain. M. S. Paudel et al./ BIBECHANA 21 (2024) 37-50 39 2 Sources of Data The major data used for this work is Flexible Im- age Transport System (FITS) images of infrared flux downloaded from SkyView Virtual Observatory (https://skyview.gsfc.nasa.gov/), for both IRIS [9] and AKARI [10]. Fig.1 shows the JPEG image at a longer wavelength, i.e., 100 µm in IRIS and 140 µm in AKARI. The distance of the W51 molec- ular cloud is taken from Genzel et al. (1981) [20]. The data from Set of Identification, Measurement Bibliography for Astronomical Data (SIMBAD) [https://simbad.u-strasbg.fr/simbad/sim-fid] [21] is used to study the background objects around the study region. 3 Method of Analysis 3.1 Infrared Flux and Dust Color Temper- ature The Planck’s law of blackbody spectrum gives the expression for the energy density emitted from a source in a wide range of the wavelength. The Planck’s law can be modified to apply for interstel- lar dust assuming (i) the beam emitted from each pixel in the infrared map is isothermal in nature and (ii) the beam is in thermal equilibrium along the line of sight. With these assumptions, the flux density Fλi at wavelength λi is given as; [22, 23] Fλi = [ 2hc λ3 i ( 1 e ( hc λikBTd ) − 1 )] Ndαλ −β i Ωi, (1) where Td is the dust color temperature, Nd is the column density of the dust grains, α is a constant related to the optical depth of the dust, β is the spectral emissivity index, and Ωi is the solid angle subtended at λi by the detector. Using equation (1), the ratio of the infrared flux at two wavelengths, Fλ1 /Fλ2 , can be modified un- der the assumptions that Ωλ1 ≈ Ωλ2 and for low dust color temperature, Td, we obtain, Td = −p ln [ R× q(3+β) ] (2) where, p = 96 for IRIS and 57 for AKARI data, q = 0.6 for IRIS and 0.64 for AKARI data, β is the spectral emissivity index. Also, the value of the wavelengths, λ1 and λ2, taken in this work are 60 µm and 100 µm for IRIS and 90 µm and 140 µm for AKARI data. 3.2 Dust Mass The mass of dust in the molecular cloud can be ob- tained from the dust color temperature size of dust grain. The Planck’s function at long wavelength can be used to estimate the dust mass more accu- rately. The expression of dust mass including all these quantities is given as [24,25]; Mdust = 0.4 [ SνD 2 B(ν, Td) ] , (3) where Sν is the absolute value of flux at long wave- length, D is the distance to the dust cloud, B(ν, Td) is the Planck’s function for the blackbody radiation. Once the mass of dust is estimated from equa- tion (3), the dust-to-gas ratio, Mgas ≈ 150Mdust [24], is used to find the total mass of cloud (gas) within the molecular cloud. 3.3 Inclination Angle The inclination angle of the dust cloud is the angle subtended by the line of sight to the normal to the plane of the dust cloud. It is calculated using the Holmberg (1946) [26] formula, which is given as: cos2 i = (b/a)2 − (q∗)2 1− (q∗)2 (4) where a and b are the major and minor axes of the cloud, and q∗ is the intrinsic flatness, which de- scribes the internal morphology. For a molecular cloud dominated by neutral particles, its value is taken as 0.23 [27]. The cloud is said to edge-on if i > 45o and face-on if i < 45o [28]. 3.4 Jeans Criteria The process of stellar evolution initiates in the molecular cloud if the cloud has enough mass to en- rich the gravitational compression against the gas pressure. The Jeans criteria describe the minimum mass and size required to trigger the evolution pro- cess, which is a function of the density and temper- ature of the cloud. The density of a cloud having radius R is given as: ρ = ( 3 4π )2/3 kBT mHGR2 (5) where kB , mH , T , and G are the Boltzmann constant, mass of neutral hydrogen, dust color tem- perature, and universal gravitational constant, re- spectively. The Jeans mass is given as: MJ = ( kBT mHG )3/2( 1 ρ )1/2 (6) To initiate the gravitational process the mass of the cloud must be greater than the Jeans mass of the cloud [29]. M. S. Paudel et al./ BIBECHANA 21 (2024) 37-50 40 3.5 Gaussian Distribution For any natural process, we always expect the Gaus- sian distribution if the size of the variables is large. For a continuous random variable x having mean µ and standard deviation σ, the Gaussian probability distribution function is given by: f(x) = 1 σ √ 2π exp ( − (x− µ)2 2σ2 ) (7) 4 Results and Discussion 4.1 Structure and Size In far infrared image the part of the W51 molecular cloud under study has prominent emission in both IRIS and AKARI map. In IRIS map it is single and isolated and elongated along North-South direction. But in AKARI map the core part is broken into two parts. In this paper these two parts are represented by AKARI-I and AKARI-II. The detail information about the center of the each structure, total size and size of isolated region is presented in Table 1. The pixels corresponds to maximum infrared flux in long wavelength infrared data, 100 µm in IRIS and 140 µm in AKARI data, is considered as a center of the structure under study. In all three struc- tures, the center of the structure is slightly beyond the geometrical center. The physical center is the point corresponding to the pixels having maximum flux. In this work, the size of the pixels used on the FITS image are 1.5 arcmin/pixels in IRIS map and 0.25 arcmin/pixels in AKARI map. Fig. 2 shows the FITS view in Aladin v2.5 [30] at longer wave- length (100 µm in IRIS and 140 µm in AKARI) in all three sub-structures. The major and minor axis of the isolated region of each structure can also be seen in Fig. 2. The different contours seen in the FITS image are the isoflux contour lines. Table 1: The table presents the geometrical center, center of structure with maximum flux, and size of both total square region and isolated region. Structure Geometrical Center (RA, DEC [ICRS]) Center of Structure (RA, DEC [ICRS]) Size of Structure Inclination Angle (i) Total Isolated IRIS-UP 290.910◦ +14.510◦ 290.935◦ +14.513◦ 0.45◦ × 0.45◦ 0.32◦ × 0.18◦ 59.19◦ AKARI-I 290.920◦ +14.520◦ 290.934◦ +14.506◦ 0.15◦ × 0.15◦ 0.14◦ × 0.07◦ 62.89◦ AKARI-II 290.798◦ +14.456◦ 290.797◦ +14.447◦ 0.10◦ × 0.10◦ 0.09◦ × 0.06◦ 50.01◦ Figure 1: The JPEG image of the dust cloud nearby the W51 Molecular Cloud is shown in figure. The figure are for IRIS 100 µm, AKARI 140 µm, AKARI-I 140 µm, and AKARI-II 140 µm, from left to right respectively. In AKARI 140 µm (second) figure dust cloud is seen broken clearly into two parts; AKARI-I and AKARI-II. M. S. Paudel et al./ BIBECHANA 21 (2024) 37-50 41 Figure 2: Aladin v2.5 view of the FITS image in IRIS (100 µm) and AKARI (140 µm) can be seen. In AKARI there are two structures; AKARI-I and AKARI-II. The geometrical center, maximum flux region (center of structure), major and minor axis are shown. The different contour line are isocontours with different values for three image. The region inside the outer isocontour is descried as an isolated region and is considered separately for analysis of the result in following section. Figure 3: The figure shows the linear relation between two infrared fluxes in IRIS (a) and AKARI (b and c) data for total region. Here, r2 is the coefficient of determination and m is slope of straight line. Table 2: Statistical information of infrared flux; maximum (Fmax), minimum (Fmin), average (Fav), range, standard deviation (σF ), and standard error (SE) at both wavelengths in dust structures in IRIS and AKARI data. Structure λ (µm) Infrared Flux (MJy sr−1) Fmax Fmin Fav ± S.E. Frange σF IRIS 60 17090.00 158.15 2346.46± 184.65 16932.37 3323.61 100 18277.80 427.97 3442.17± 212.98 17849.83 3833.71 AKARI-I 90 48455.82 2128.55 12161.23± 246.98 46327.28 8891.23 140 66261.41 2452.37 12230.88± 302.41 63809.04 10886.73 AKARI-II 90 26890.39 2959.25 8947.48± 175.98 23931.14 4223.62 140 23011.31 3643.55 10923.17± 204.30 19367.76 4903.08 4.2 Infrared Flux Density The FITS image is processed in Aladin v10.0 [30] software to extract the infrared flux density at two wavelengths, 60 µm and 100 µm in IRIS data and 90 µm and 140 µm in AKARI data. The W51 molecu- lar cloud and its both parts under study lie close to the galactic plane of the Milky Way Galaxy; there- fore, the infrared flux density is very high at all wavelengths under study. The information about the maximum, mini- mum, average, range, and standard deviation of the infrared flux in each wavelength for all structures can be seen in Table 2. Infrared flux is higher for AKARI data compared to IRIS data at both wave- M. S. Paudel et al./ BIBECHANA 21 (2024) 37-50 42 Table 3: The table presents the maximum (Tmax), minimum (Tmin), average (Tav), range, and standard deviation (SD) of Td in total and isolated regions within the W51 molecular cloud. Structure Region Tmax (K) Tmin (K) Tav ± S.E. (K) Trange (K) σT (K) IRIS Total 38.55± 4.10 25.29± 2.52 30.34± 0.16 13.26± 3.13 2.82 Isolated 37.63± 2.09 28.49± 2.48 33.45± 0.27 9.14± 2.28 2.35 AKARI-I Total 77.12± 24.86 17.01± 5.20 27.40± 0.21 60.11± 15.03 7.73 Isolated 59.56± 17.20 17.01± 4.08 25.17± 0.23 42.55± 10.64 5.40 AKARI-II Total 30.82± 3.64 18.85± 2.30 23.55± 0.08 11.87± 2.98 1.99 Isolated 27.81± 2.38 20.26± 1.40 23.06± 0.10 7.55± 1.89 1.59 Table 4: The table shows the parameters in the linear fit, where r2 is the coefficient of determination and T is the dust color temperature calculated using the slope. Structure Region Best fit equation r2 T(K) ∆T (K) IRIS Total FS = 0.85FL − 588.35 0.97 35.37 −5.03 Isolated FS = 0.98FL − 1946.38 0.94 37.30 −3.85 AKARI-I Total FS = 0.58FL + 5029.49 0.50 20.57 +6.83 Isolated FS = 0.47FL − 8504.23 0.37 19.09 +6.08 AKARI-II Total FS = 0.78FL + 415.54 0.82 23.00 −0.55 Isolated FS = 0.93FL − 2131.05 0.70 24.71 +1.65 lengths. The flux is greater at long wavelengths for IRIS and AKARI-I structure, whereas for AKARI- II, the maximum value of flux at short wavelength is higher, but the average value is again lower at short wavelengths. Furthermore, a linear relationship is found be- tween the flux at two wavelength both in IRIS and AKARI data. The infrared flux of total square re- gion as well as that of isolated region of all three structures is studied using the linear regression. For this study the infrared flux at long wavelength (FL) is taken along the X-axis and short wavelength (FS) is taken along the Y-axis, shown in Fig 3. The co- efficient of determination (r2) tells how closely the fitted data (red line) agree with the original data set (blue dots). It is found r2 is more for total square region compare to isolated region. In IRIS data it is very well fitted but in AKARI-I it is just acceptable for total data and bad fit for isolated data. For AKARI-II, it is good fit. The various information related to the regression study is pre- sented in Table 4 and the graph showing the linear relationship between two infrared fluxes is seen in Fig. 4. For AKARI-I, we found large number of background sources, such as; stars, clusters, YSO, different radio sources, HII region, infrared sources, etc., which can be seen in Fig. 10 (d e). Also, the Gaussian distribution of temperature is found more deviated from normal bell shape in Fig. 7(b). Moreover, the color map of infrared flux also shows the different nature of map for two wavelength in Fig. 5 (a b). These all studies tell us the poor re- lation between infrared flux at two wavelength for AKARI-I region. 4.3 Dust Color Temperature We use the method given by Wood et al. (1994) [22] and Schnee et al. (2005) [23] to estimate the dust color temperature (Td) of the interstellar dust cloud, dependent on infrared flux density at two wavelengths for which the spectral emissivity index (β) is taken as 2, assuming the interstellar dust hav- ing crystalline dielectric characteristic [31]. Table 3 presents various statistical information related to Td for both the total square region as well as the isolated region in all three structures. The error in the average temperature (Tav) is the standard error (σT / √ n), σT is the standard deviation, and n is the size of the data). But for maximum are minimum temperature are the half of the devia- tion from average value is taken. For range the average error in maximum and minimum value is used. The Td is found more for AKARI data com- pare to the IRIS. However, the minimum value is less in AKARI. The range is found more than 5 K in both IRIS and AKARI data representing the dust cloud is thermally dynamic. Moreover, Td and its range in AKARI-II is found more than AKARI- I, representing high thermal activities in AKARI- I. The Td is found more in IRIS data compare to AKARI data. This is according to Wien’s displace- ment law, which says the temperature is inversely proportional to wavelength. Furthermore, it is seen that the higher value of maximum Td is found in AKARI-I. In AKARI-I, the contour map (Fig. 5(c)) as well as the Gaussian plot of temperature (Fig.7) shows the high temperature (more than 50 K) is found only in small regions or pixels. Most of the region have temperature less than 40 K. In IRIS and AKARI-I the distribution of the temperature M. S. Paudel et al./ BIBECHANA 21 (2024) 37-50 43 Table 5: Dust and gas mass (kg and solar mass (M⊙) in dust structures and sub-structures. Structure Region Md Mean per Pixels (kg) Gas Mass (kg) (in kg) (in M⊙) (in kg) (in M⊙) IRIS Total 3.09× 1032 155.38 9.54× 1029 4.64× 1034 23307.50 Isolated 1.51× 1032 76.04 1.96× 1030 2.27× 1034 11406.70 AKARI-I Total 1.23× 1034 6172.64 9.47× 1030 1.84× 1036 925896.56 Isolated 9.96× 1033 5006.92 1.79× 1031 1.49× 1036 751038.71 AKARI-II Total 4.47× 1033 2248.04 7.76× 1030 6.71× 1035 337205.43 Isolated 2.73× 1033 1370.55 1.17× 1031 4.09× 1035 205582.88 is almost Gaussian. Also, the standard deviation is found maximum for the AKARI-I, suggesting the wide variation in the temperature distribution. The Gaussian distribution of the dust color temperature on total square region in all three structures is seen in Fig.7. Additionally, the slope of the best fit straight line could give the average temperature. The slope (m) of the straight line is the ratio (R) of the in- frared flux at two wavelengths, R = F (λlong) F (λshort) . This provides some insight to calculate the temperature using equation (2). Using this method, tempera- ture is calculated for both the total square region as well as in the isolated region. The results are presented in Table 4. The deviation in temperature (∆T ) between Table 3 and Table 4 is also presented. The deviation is due to the value of y-intercept (c). In the linear regression method we implement, Fs = R·FL+c, rather than Fs = R·FL. It is evident that the deviation is more for AKARI-I for which the data deviated much from Gaussian nature com- pare to other. For isolated region the deviation is less in IRIS and AKARI-I but for AKARI-II it is more. The background sources at the isolated re- gion is very much crowded for IRIS and AKAARI-I compare to AKARI-II, which can be seen in Fig. 10. 4.4 Dust Mass The mass of dust in each pixel of the dust struc- ture is calculated using the infrared flux at long wavelength, dust color temperature, Planck’s func- tion, and the distance to the dust cloud using the method of Hildebrand (1984) [24] and Young et al., (1993) [25]. Planck’s function is a function of tem- perature and wavelength. The distance to the W51 molecular cloud is taken as ∼17000 light years or ∼5410 pc [20]. The dust mass as well as the mass of gas within the total square region and isolated region of all three structures is presented in Table 5. The mass of dust within the isolated region is also calculated separately. Obviously, it is seen that the total dust mass in the isolated region is less than the total square region. One of the reasons is that the num- ber of pixels included within the isolated region is less compared to the total square region. Another effective reason is that the average dust mass per pixel is slightly more in the isolated region com- pared to the total square region. The mass of gas (Mg) is calculated using the fact that Mg ≈ 150Md [24]. Therefore, the mass of gas also follows the same trend as that of the dust mass within both the total square and isolated regions. 4.5 Contour Map The visualization of the infrared flux at two wave- lengths, dust color temperature, and dust mass is presented in Fig. 4, Fig. 5, and Fig. 6, respec- tively, for IRIS, AKARI-I, and AKARI-II. The con- tour maps of the infrared flux at 60 µm and 100 µm for the IRIS structure are almost identical, as de- scribed in the regression analysis with an r2 value of 0.97. Infrared flux is decreasing almost smoothly from the center to the outer region in IRIS data. In AKARI-I, the contour maps are less identical; a clear donut shape with local minima at the geomet- rical central part is observed in infrared flux at 90 µm, and an unbalanced dumbbell shape elongated along the diagonal is observed in infrared flux at 140 µm. The regression analysis between the fluxes at two wavelengths also shows a moderate value of r2, which is 0.50. For AKARI-II, the contour maps show quite a similar distribution, both elongated along the main diagonal of the square region with a slight rise towards the right-upper part. How- ever, the maximum value of the flux is seen at 140 µm, which is different from AKARI-I. The regres- sion analysis shows a quite good value of r2, which is 0.82. The qualitative distribution inferred from the contour map is in accordance with the quanti- tative analysis provided by the regression method. The IRIS data contour map of the dust color temperature (Td) also appears elongated along the main diagonal of the square region, but the over- all distribution is quite different compared to the flux at both wavelengths. The maximum value of the temperature is beyond the center with maxi- mum flux. Also, the temperature is not decreas- ing smoothly from the maximum value towards the outer regions; however, an isolated region is M. S. Paudel et al./ BIBECHANA 21 (2024) 37-50 44 observed elongated along the main diagonal. In AKARI-I, the color map of the dust color tempera- ture is very different from the infrared flux. An iso- lated low-temperature cavity can be seen within the region of interest, which is quite interesting. The maximum temperature is also deviated from the center, and the variation is also not smooth from its maximum value towards the outer region. Only very few pixels have a higher temperature (> 50K), which can also be seen in the Gaussian distribution in Fig. 7. In AKARI-II, the color map shows vari- ation of Td unevenly breaking into multiple sub- regions with multiple local minimum. The maxi- mum temperature lies at the lower-mid-edge of the square region. The contour map of the dust mass in IRIS structure seems like the color map of flux at both wavelength. It shows the two maxima re- gion at core. The pixels having maximum mass lies very close to the pixels having maximum flux. In outer region, the dust mass decreases smoothly showing the symmetric variation. A visual com- parison between contour map of dust color tem- perature and dust mass shows a very poor corre- lation. In AKARI-I structure, the contour map of dust mass shows double maxima, concentrated near the center and elongated along the off-diagonal of square region. The mass distribution is quite sim- ilar to the infrared flux at core region at 140 µm. The contour map of temperature and mass are seen nearly inverse within the core region. The back- ground sources, such as; HII region, infrared, mid- infrared, near infrared, etc., are crowed near the isolated cavity of temperature which might be con- tributing huge dust at core. In AKARI-II, the con- tour map of the dust color temperature is entirely different from the infrared flux at both wavelength. It is breaking unevenly into three sub-clumps. The background sources shown in Fig 10 (c) also shows crowd of background sources in the periphery of the region where the aggregation of the dust mass is more. This is an evident that the dust mass is pushed slightly far away from the background sources. The visual comparison shows the distri- bution of mass almost inverse of the temperature. The quantitative relationship between temperature and mass is presented in later section. Figure 4: The contour map for infrared fluxes (a and b), dust color temperature (c) and dust mass (d) for whole dust structure around W51 Molecular Cloud in IRIS map overlaid with the contour at different levels, in the interval of (X̄ ± k.σ), X̄ and σ are the mean and standard deviation of corresponding quantities, and k is the constant chosen in such a way that the contours are distributed evenly. The value of constant k is chosen [-0.5, 0, 0.5, 1, 1.5, 2.0, 2.5, 3, 3.5, 4] for flux at 60 µm, [-0.5, 0, 0.2, 1.0, 1.5, 2.0, 2.5, 3.0, 3.5] for flux at 100 µm, [-2.0, -1.5, -1.0, -0.5, 0, 0.5, 1, 1.5, 2.0, 2.5] for Td and [-0.75, -0.5, 0, 0.5, 1.0, 1.5, 2.0, 2.5] for Md for outer to inner contour. M. S. Paudel et al./ BIBECHANA 21 (2024) 37-50 45 Figure 5: The contour map for infrared fluxes (a and b), dust color temperature (c) and dust mass (d) for upper dust structure (AKARI-I) around W51 Molecular Cloud in AKARI-I map overlaid with the contour at different levels, in the interval of (X̄ ± k.σ), X̄ and σ are the mean and standard deviation of corresponding quantities, and k is the constant chosen in such a way that the contours are distributed evenly. The value of k is chosen [-0.75, -0.45, 0, 0.5, 1.0, 1.5, 2.0, 2.5, 3.0, 3.5] for flux at 90 µm, [-0.75, -0.5, -0.20, 0, 0.5, 1.0, 2.0, 3.0, 4.0] for flux at 140 µm, [-1.0, -0.5, 0, 1.0, 2.0, 3.0, 4.0, 5.0] for Td and [-0.25, 0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0] for Md form outer to inner contour. Figure 6: The contour map for infrared fluxes (a and b), dust color temperature (Td) (c) and dust mass (Md) (d) for lower dust structure (AKARI-II) around W51 Molecular Cloud in AKARI map overlaid with the contour at different levels, in the interval of (X̄±k.σ), X̄ and σ are the mean and standard deviation of corresponding quantities, and k is the constant chosen in such a way that the contours are distributed evenly. And the value of k are [1.0, -0.5, 0, 0.5, 1.0, 1.5, 2.0, 2.5, 3.0, 3.5] for flux at 90 µm, [-1.0, -0.5,-0.25, 0, 0.5, 1.0, 1.5, 2.0, 2.25] for flux at 140 µm, [-1.5, -1.0, 0.5, 0, 0.5, 1.0, 1.5, 2.0, 2.5, 3.0, 3.5] for Td and [-1.0, -0.5, 0, 0.9, 1.0, 1.5, 2.0, 2.5, 3.5] for Md form outer to inner contour. M. S. Paudel et al./ BIBECHANA 21 (2024) 37-50 46 Figure 7: Figure shows the Gaussian distribution for dust color temperature for all structures. In all figure the quantities dust color temperature is taken along X-axis and their Gaussian PDF are taken along Y-axis. 4.6 Flux-Temperature-Mass Relation The color map with contour is quite effective to understand the spatial distribution of the infrared flux, dust color temperature and dust mass. For a quantitative analysis the color map is not adequate to give the proper information. The linear regres- sion is used to quantify the relationship between them. The coefficient of determination (r2) is cal- culated for each pair of variables in all dust struc- ture. The selected plots for which the r2 > 0.50 are presented in Fig. 8. The temperature (Td) is found to be increased with flux at both wavelength in IRIS data but no clear relation for AKARI data. Also, the dust mass (Md) is found to be increase with increase in infrared flux at both wavelength, both IRIS and AKARI data. But for flux at short wavelength the r2 >0.50 for both region in AKARI. In overall, it can be said that the Td and Md both increases with increase in infrared flux in all regions. The graph between Td and Md is shown Fig. 9, in which all the plots have poor coefficient of determi- nation, r2 > 0.50. However, in IRIS and AKARI data a very clear difference can be seen. In IRIS data, the relation is direct where as in AKARI, in both graph, the relation is inverse. Moreover, the data in IRIS is more scattered compare to AKARI data. The value of r2 for each pair of variables is presented in Table 6. 4.7 SIMBAD Background Source Study of the background objects within the selected region is carried out with the help of catalog avail- able in SIMBAD. The Fig. 10 shows the back- ground sources overlaid in the isocontour lines that are same for infrared flux at longer wavelength, i.e., 100 µm for IRIS and 140 µm for AKARI–I and AKARI-II. In this work, the Young stellar ob- ject (YSO), YSO candidates, different varieties of the radio sources, dark nebula, interstellar bub- bles, HII region, star, dense core, part of cloud, etc., are numerous. For the better visualization the background objects are presented in three graph in IRIS data and two graph in AKARI-I data and single graph in AKARI-II. The number of back- ground sources within the region of IRIS structure is 1364, within AKARI-I structure is 401 and within AKARI-II structure 134. There are least but very important objects, like HII region, Infrared (IR), Mid IR, Far IR, dense core bubble, star forming regions, radio sources, etc., which are found to be concentrated within the core region of the cloud and it can be concluded that they are responsible for the huge infrared flux, temperature and mass as seen in color map of IRIS in Fig. 4. The background ob- jects around AKARI-I is more compare to AKARI- II, the effect of which can be seen in the average value, range and Gaussian curve of Td. The range of Td is more than 40 K for isolated region and more than 60 K for total square region which is very high compare to AKARI-II [Table 3], which represents more thermal instability in AKARI-II due to the presentence of background sources. Also, Gaussian distribution of Td is much deviated from Normal bell shape. The color map also shows the effect of background objects in both of the AKARI struc- tures. Cavity of cold and massive dust region is seen in the periphery of regions where background sources are crowded. Therefore, the entire dust properties, such as infrared flux, dust color tem- perature and dust mass can be explained on the basis of the background objects. 4.8 Density and Jeans Mass The isolated region in each dust structure as seen in Fig. 2 is studied separately for the Jeans criteria, whether the mass of the cloud under the isolated structure is sufficient or not to trigger the star for- mation process is checked. The average size, av- erage temperature, density, Jeans mass and total mass of cloud of isolated region within clouds in IRIS, AKARI-I and AKARI-II are presented in Ta- ble 7. From Table 1 it is clear that the size of the IRIS structure is largest and AKARI-II is smallest. M. S. Paudel et al./ BIBECHANA 21 (2024) 37-50 47 Conversely, the density of the AKARI-II is found maximum and IRIS is minimum. But, the Jeans mass (MJ) is maximum for IRIS structure due to its large size. The value of MJ is found less than the mass of the cloud in all structures. It is seen that there is no any possibility of further collapse of clouds either singly or part wise for the star for- mation process in the future. Table 6: The coefficient of determination (r2) for each pair of variables, FS and FL represents the flux at short and long wavelength. coefficient of determination (r2) FL vs Td FS vs Td FL vs Md FS vs Md Td vs Md IRIS 0.56 0.54 0.65 0.81 0.21 AKARI-I 0.24 0.05 0.07 0.79 0.23 AKARI-II 0.05 0.02 0.19 0.59 0.47 Figure 8: The best fit straight line between the infrared flux, dust color temperature and dust mass in IRIS data. The r2 represents the correlation coefficient. The plot with r2 < 0.50 are not included here. Figure 9: The best fit line between the Td and Md is seen in IRIS (a), AKARI-I (b) and AKARI-II (c) is shown. In all data a poor correlation is observed. M. S. Paudel et al./ BIBECHANA 21 (2024) 37-50 48 Figure 10: The figure shows the SIMBAD sources around W51 molecular cloud, for IRIS (a, b and c), AKARI-I (d and e) and AKARI-II (f). In all plot, RA is taken along X-axis, DEC is taken along Y-axis. The name of sources in the legend is according to the SIMBAD. For IRIS and AKARI-I there are more graph made for the better visualization of the numerous objects. Table 7: Average radius, dust color temperature, density, Jeans mass, and total mass of cloud in isolated regions of IRIS, AKARI-I, and AKARI-II. Structure Radius (m) Td (K) Density (kg/m3) Jeans Mass Cloud Mass (kg) M⊙ (kg) M⊙ IRIS 6.07× 1015 33.45 4.33× 10−17 4.05× 1031 20.36 2.27× 1034 11406.70 AKARI-I 2.55× 1015 25.17 1.85× 10−16 1.28× 1031 6.44 1.49× 1036 751038.71 AKARI-II 1.82× 1015 23.06 3.36× 10−16 8.39× 1030 4.22 4.09× 1035 205582.88 5 Conclusion A comparative study of the properties of dust is performed within the molecular cloud W51 located at (RA, DEC) (ICRS): 290.910◦,+14.510◦, having an angular size of 0.45◦× 0.45◦, using the IRIS and AKARI data. Following are the major conclusions: 1. Being situated in the galactic plane, the dust cloud is very bright in both AKARI and IRIS. Furthermore, it is divided into two iso- lated sub-structures having angular sizes of 0.15◦×0.15◦ and 0.10◦×0.10◦ in the AKARI map, represented as AKARI-I and AKARI-II, respectively. 2. The average dust color temperature is found to decrease in the isolated region compared to the total region in all sub-structures. The hot region is found to lie outside the isolated region. 3. The dust color temperature follows Wien’s displacement law, meaning the temperature is inversely proportional to wavelength. A lower temperature is found for AKARI data com- pared to IRIS data. 4. The range of temperature in all structures is found to be more than 10 K in total and 5 K in the isolated region, indicating that the struc- ture is far from thermal stability. In AKARI- I, the range is very high, representing huge thermal instability compared to AKARI-II. 5. The regression analysis shows a linear re- lationship between the infrared flux at two wavelengths in IRIS and AKARI-II, but the relation is very poor in AKARI-I for the iso- lated region. This might be the consequence of the large range in temperature. A mixed type (linear and quadratic) of relationship is M. S. Paudel et al./ BIBECHANA 21 (2024) 37-50 49 found between the infrared flux, dust color temperature, and dust mass. 6. The regression analysis shows that Td is poorly correlated with Md. In IRIS data, Md is directly proportional to Td, but for AKARI, Md is inverse to Td. 7. The dust mass is found to be more in both AKARI maps compared to IRIS map, even though the dust structure in IRIS is larger in size. Moreover, the mass per pixel is more for AKARI maps. The mass per pixel is more in the isolated region for both IRIS and AKARI maps. 8. The SIMBAD point sources within the study region show a large number of stars, young stellar objects (YSO), interstellar medium (ISM) sources, etc. YSOs, stars, radio sources, masers, HII regions, infrared sources, mid-infrared sources, etc., are mostly found within the core region of AKARI-I and AKARI-II structures. This is the manifesta- tion of the huge infrared flux within the core region. 9. The study of density and Jeans criteria shows that the dust structure is denser in AKARI data compared to IRIS data. Also, AKARI-II is found to be denser than AKARI-I. 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