DUST PROPERTIES OF TWO NEW CAVITY STRUCTURES NEARBY ASYMPTOTIC GIANT BRANCH STARS: THE IRAS SURVEY

We studied the dust properties of two cavity structures (namely FIC21+54 and FIC16-56) nearby Asymptotic Giant Branch (AGB) stars using Infrared Astronomical Satellite (IRAS) maps. Dust color temperature, Planck function, dust mass, and visual extinction with their distribution within the region of interest were examined. The temperature of dust was found to lie in the range of 22.24 ± 0.81 K to 23.27 ± 0.21 K, and 25.12 ± 0.43 K to 26.17 ± 0.62 K, and the mass of dust was obtained within the range of 4.21 × 1026 kg to 3.6 × 1027 kg, and 2.1 × 1027 kg to 3.31 × 1028 kg, for FIC21+54 and FIC16-56, respectively. Some unusual behaviors on the distribution of dust temperature indicated the effect of nearby sources within the studied structures. Moreover, we observed the trend of dust particles along the major and minor diameters, and plots represented that the particles were oscillating with a sinusoidal pattern in both cavities. The negative slope between 25 μm and 60 μm in far-infrared spectral distribution was encountered for both structures, which portrayed less number density of particles in 60 μm band; interaction between AGB wind and the ambient interstellar medium could be the possible reason behind this. These findings support the prior results of cavity structures nearby AGB stars within the galactic plane -10° < b < +10°.


INTRODUCTION
Last evolutionary stage of the low and intermediate-mass (0.8M⊙ < M < 10M⊙) star devoid of nuclear fuel is known as the Asymptotic Giant Branch (AGB) star (Herwig, 2005). In its core region, as the star consumes the supply of hydrogen, the core compresses, which results in the increment in its temperature and causes the extension of the boundary layer; ultimately, it cools the star, resulting in their shift to a red giant, upper-right corner of the HR diagram (Iben Jr, 1967). At around 3×10 8 K, helium burning begins in the core, which prohibits further cooling and increases their luminosity; this phenomenon is common to stars with a mass of more than about 2M⊙ (Vassiliadis & Wood, 1993). The star goes to the right and upward portion of the HR diagram when helium fusion is completed in the center, which is known as the AGB phase.
AGBs are regarded as the major dust sources to the galaxies through their strong wind, which recreates the surroundings with dust particles (Gehrz, 1989). The red giants form carbon (C) or oxygen (O) rich solid dust in the stellar photosphere depending upon the number of dredgeup events and its evolutionary stages. In the spectral energy distribution (SED) of AGB stars, prominent dust characteristics can be analyzed, including 9.7 and 18 µm silicates features in O-rich AGBs, and 11.3 µm silicon carbonate dust features in C-rich stars (Gobrecht et al., 2016). By utilizing interferometric data, Danchi et al. (1994) observed that the dust forming area is situated within 10R*, where R* represents the star's radius from the stellar photosphere. The stellar pulsation produces the periodic shock, which pushes warm and dense gas layers to the large radii, making a favorable environment for the formation of solids. Due to radiation pressure on dust particles and the high opacity of dust, this event helps to accelerate the stellar wind (Bowen, 1988). These thick layers facilitate the production of molecules and various gas-phase components in both C & O-rich AGBs (Cernicharo et al., 2008;Justtanont et al., 2012). The non-equilibrium phenomena driven by the periodic flow of the shocks regulate the creation of O or C-bearing components in the wind of both carbon-and oxygen-rich AGBs (Gobrecht et al., 2016). The C/O ratio and partial dissociation of the CO molecule both impact the growth of molecules within the photosphere. In a carbon-rich star, the shock wave dissociated oxygen atoms that form O-bearing components such as H2O in the wind, but in oxygen-rich AGB, carbons are released due to shock, which forms C-bearing species (Willacy & Cherchneff, 1998;Groom, 2018). Several literatures (e.g.: Neufeld et al., 2011;Justtanont et al., 2012) provide a basic for the existence of warm water, HCN in the C-rich AGBs. These shreds of evidence support the shock-induced mechanism in the creation of molecules in the wind of AGBs. There is almost (90-98) % mass loss of AGB stars in the form of massive winds (Rees, 1984) in the interstellar medium (ISM).
Dust in ISM was first observed through interstellar extinction curves. It absorbs the Ultraviolet (UV) radiation and re-emits infrared radiation, suggesting that AGB is a major IR source; this UV radiation causes the molecular dissociation of dust, providing the site for a star formation (Gehrz, 1981;Gobrecht et al., 2016). The study of different types of AGB stars helps to understand the nature of the mass loss to ISM (Vassiliadis & Wood, 1993;Ventura et al., 2012). The O-rich AGB mainly produces silicates-type grains in the outflow, C-rich produces mainly carbonaceous grains in the outflow (Gautam & Aryal, 2020). Due to the different dust compositions of these two types of AGB stars, we obtain different infrared spectral features. Suh and Kwon (2009) prepared a detailed catalogue of AGB stars in the IRAS point source catalogue. From the study of farinfrared (FIR) loops, Kiss et al. (2004) and Könyves et al. (2007) stated that such structures were probably generated by high-pressure events, such as AGB wind, in the past. Several studies (e.g., Aryal & Weinberger, 2006, Aryal et al., 2010 presented the discovery of new nebula structures using the IRAS survey. In the past, various studies (e.g., Jha & Aryal, 2018;Gautam & Aryal, 2019a;Gautam & Aryal, 2019b;Sapkota & Aryal, 2019;Gautam & Aryal 2020;Tiwari et al., 2021) aimed to investigate dust properties of far-infrared cavities located around the AGB stars at different coordinates using IRAS maps.
The study of dust properties in the ISM serves essential reference for understanding dust status around the various sources, and ultimately, it helps to upgrade our idea of shaping mechanisms in the ISM. This paper presents results from the study of the physical parameters, namely temperature and mass of the dust, visual extinction, radiation intensity distribution, and far-infrared spectral distribution of two new far-infrared cavity structures. We compared our findings with the previously studied structures to validate the existing results for the new cavities within a galactic plane -10° < b < +10°.

Far-Infrared cavities
Using the Sky View Virtual Observatory (http://skyview.gsfc.nasa.gov/), we performed a methodical investigation at 60 and 100-micron IRAS survey to find a new cavity structure. We investigated far-infrared cavities around the 1168 carbon-rich AGB stars presented by Suh and Kwon (2009) in their catalogue. We selected the far-infrared cavity structures around the AGB stars based on the following similar selection criteria as performed by Gautam and Aryal (2019a): (i) At 100 µm IRAS maps, the central region of the structure should have the lowest flux, (ii) the major width of the structure should be greater than 0.3° (iii) it should maintain the position within the 3° area from C-rich AGB stars, and (iv) it should be situated within the Galactic coordinates -10° < b < 10°. For our study, we selected two new far-infrared cavity structures. Minimum flux zones were defined by selecting the region with depression in the far-infrared background emission by photometric analysis using SalsaJ software. The first structure, namely FIC21+55 (size 61.8 pc × 46.5 pc), was situated in the sky coordinates at R.A. (J2000): 21h 32m 44.47s, and Dec. (J2000): +55d 15m 16.8s around C-rich AGB star, AGB21+54, located at R.A.: 21h 28m 58.56s, and Dec.: +54d 33m 34.57s, about ~3580 pc distance away (calculated using parallax value given by Gaia DR2, https://www.cosmos.esa.int/web/gaia/dr2).

MATERIALS AND METHODS
At 60 and 100 µm, we retrieved the FITS (Flexible Image Transport System) images of both selected structures. We used the tool ALADIN v2.5 (https://aladin.u-strasbg.fr/) to analyze those images. We constructed contours to separate the minimal flux zones. Further, the appropriate flux at 60 and 100 microns at each pixel within the area of interest was measured. The SIMBAD database (https://simbad.u-strasbg.fr/simbad/) was used to investigate the possible contributing sources for the background flux. Background flux within the cavities was estimated using the SalsaJ software. Finally, we subtracted the background flux from 60-and 100-micron flux density measured for both structures. Methods of calculating the temperature of the dust, Planck function, the dust mass, structure size, and visual extinction of the cavity structures around the AGBs are briefly discussed below.

Dust color temperature
The mathematical formula expressed by Wood et al. (1994), later revised by Arce and Goodman (1999), Dupac et al. (2003), and Schnee et al. (2005), was used for the estimation of the dust temperature at each pixel. According to them, the formula to estimate the temperature of dust is given by, (1) Where (60  ) and (100  ) represent the flux densities at 60 and 100 microns, respectively, the value of is known as the spectral emissivity index, and it is determined by grain properties including composition, size, compactness, etc. Jha and Aryal, 2018). A pure blackbody has a value of =0, the amorphous layerlattice matter has ~ 1, and the metals and crystalline dielectrics have ~ 2 (Gautam & Aryal, 2020). We used = 2 for our calculation; Equation (1) provides the temperature of dust from 60-and 100-microns bands of IRAS.

Planck function
The Planck function or radiation intensity depends on the wavelength (frequency) and temperature. It can be estimated using the expression of Beichman et al. (1998). The calculated Planck function at each pixel was used for the evaluation of dust mass.
( 2) where h represents the Planck constant, c is the speed of light in a vacuum, and indicates the frequency at emission, and T is the calculated dust temperature at each pixel. Equation (2) implies that ( , ) at larger wavelengths gives a greater value than that of smaller wavelengths. For the fixed temperature, if the wavelength of the image increases, the ( , ) range becomes narrow.

Dust mass
To compute the dust mass, at first, we measured the flux at 100-micron IRAS maps and applied Hildebrand's formula (Hildebrand et al., 1977;Hildebrand, 1983), which depends on various properties of dust particles, dust temperature, and distance. The expression for the estimation of dust mass is given by, Where a, ρ, and ( ) are the size, density, and emissivity of the dust particles, respectively. ( ) = × 5.228 × 10 −9 × −1 , represents the flux density of the region of study. B(υ, T) is the Planck function calculated using Equation (2). By applying the constant values, a = 0.1 μm, ρ = 3000 kgm -3 , and ( ) = 0.0010 for 100 μm and 0.0046 for 60 μm, respectively as suggested by Young et al. (1993) (4) Equation (4) was used for the calculation of the dust mass within the selected cavity structures.

Visual extinction
Visual extinction can be obtained by using the technique of Wood et al. (1994). According to them, the expression for the calculation of visual extinction is given by, Where, 100 = Here, 100 is called optical depth at 100 μm wavelength. and are the flux density and Planck function respectively at the band of 100-micron.

Size of the structure
To measure the major and minor diameter of the structure, we adopted a similar method used by Gautam and Aryal (2019a). The expression for the calculation of the size of the structure is given by, Here ′ is the distance to the structure from us, and is the pixel size (in radian).

RESULTS AND DISCUSSION
This section discusses the physical properties of two new far-infrared cavity structures, namely FIC21+55 and FIC16-56 located within the galactic plane -10° < b < +10° and compares the results with the previous studies. Figures 1(a) and 2(a) show the JPEG image of the cavity structures FIC21+55 and FIC16-56, respectively, where the central position of the cavity is shown by '+' sign. Black colored area indicates the lower flux region, and the yellowcolored area depicts the maximum flux-region. The study region was separated by the contour, and the flux densities at 60 microns and 100 microns were computed using ALADIN v2.5 software. The background fluxes contributed by other nearby sources (stars, IRAS sources, etc.) were subtracted, for the accurate study of the distribution of flux of the cavity structure, using SalsaJ software (http://euhou.net/index.php/salsaj-softwaremainmenu-9). The contour plot of the flux density at 100micron IRAS map for both cavities was drawn using the software ORIGIN v8.5, which are represented in Figures  1(b) and 2(b). The colored region in the figure represents the flux density within the right ascension (R.A.) and declination (Dec.) associated with the structures. The fluxregion in FIC21+55 was found to be separated into the region with different pieces with minimum flux-region at the center and maximum flux-region across the boundary; however, distribution for FIC16-56 was separated into different layers with minimum flux-region covered by maximum flux regions. Similar nature of the flux distribution was also encountered and studied in the previous cavity structures (Gautam & Aryal, 2019a, b;Gautam & Aryal, 2020, Tiwari et al., 2021. Figures 1(c) and 2(c) show the linear fit between flux density at 100-micron F(100) and 60-micron F(60) of the cavity structures FIC21+55 and FIC16-56, respectively. The slope of the line was 0.20 and 0.30, and they were positively correlated with the correlation coefficient, R = 0.84 and 0.93, for FIC21+55 and FIC16-56, respectively. These obtained values of the slope of the best fit were used to set the error bars as suggested by Weinberger and Armsdorfer (2004), , and Gautam and Aryal (2019a) . Figures 1(d) and 2(d) show the contour map of the dust color temperature of each pixel of the cavities FIC21+55 and FIC16-56, respectively. We evaluated the dust color temperature of each pixel of the cavities using Equation (1) and found it in the range of 22.24 ± 0.81 K to 23.27 ± 0.21 K for FIC21+55, and 25.12 ± 0.43 K to 26.17 ± 0.62 K for FIC16-56, with an offset of about 1 K for both structures. This small value of offset signified that the dust in the cavities has a higher possibility to be in thermal equilibrium (Weinberger & Armsdorfer, 2004). In other words, the absorption coefficient of the far-infrared and the mean free path of the dust was of the same order. From the comparison of the contour plot of temperature distribution (Figures 1(d) and 2(d)) with the distribution of flux density (Figures 1(b) and 2(b)), we observed that the minimum temperature region did not exactly coincide with the minimum-flux region for both studied cavities. Such a shifting trend was also observed in previous sources (e.g., Sapkota & Aryal, 2019;Tiwari et al., 2021); this unusual behavior can be expected due to the effect of nearby sources (e.g., AGB wind) Tiwari et al., 2021). Figures 1(e) and 2(e) represent histograms of the number of pixels with a temperature between to +Δ( ) within the cavity structures FIC21+55 and FIC16-56, respectively. The dust color distribution of FIC21+55 showed a Gaussian nature with the value of Gaussian center 22.80 K, whereas a positively skewed Gaussian-like nature with a Gaussian center 25.43 K was observed for FIC16-56. Dust mass of the structure was calculated using Equation 4, where the distance to the structure (D) = ~3580 pc (for FIC21+55) and 2449 pc for (FIC16-56) was used. The total mass of the cavity structure FIC21+55 was obtained to be 2.19 × 10 31 kg with an average mass of 2.28 × 10 28 kg. On the other hand, a total mass of 1.59×10 30 kg with an average mass of 4.16×10 27 kg was estimated for the cavity FIC15-56. The contour map of dust mass of the cavity structures FIC21+55 and FIC16-56 are shown in Figures 1(f) and 2(f), respectively. The contour plots of dust color temperature (Figures 1(d) and 2(d)) and the dust mass of the cavity (Figures 1(f) and 2(f)) showed that the majority of the minimum temperature region corresponds to a denser mass region. This phenomenon indicates a homogeneous and isotropic distribution of the dust within the structures (Gautam & Aryal, 2020).  Histograms of the number of pixels with a temperature between to +Δ( ) within the cavities FIC21+55 and FIC16-56 is shown in Figures 1(g) and 2(g), respectively. The distribution of dust mass showed a Gaussian trend, indicating symmetric behavior of dust mass. Moreover, the unusual behavior of shifting of minimum temperature region and the maximum mass region in the cavity FIC16-56 was also supported by the Gaussian plots of dust temperature and mass (Figures 2(e) and 2(g)). The value of optical depth was used in Equation (5) to calculate visual extinction at each pixel within the studied cavities. Figures 1(h) and 2(h) show the linear fit between visual extinction and dust color temperature; these plots showed the possible linear relationship between Td and Aυ with a negative correlation (R) = -0.63 for FIC21+55, and R = -0.54 for FIC16-56. Since the value of Aυ was greater in a denser mass region, which implies a smaller value of temperature in the corresponding region. As the minimum temperature region was shifted from the maximum mass region (maybe due to possible external effects), it might have pushed to the lower value of the correlation coefficient between Td and Aυ. The product of Td and Aυ was less than one, i.e., Av × Td < 1, indicating that the lower visual extinction for the higher temperature and vice versa. These results were also in accordance with the previous findings (e.g., Gautam & Aryal, 2019a, Gautam & Aryal, 2019b; however, they have estimated a slightly larger value of correlation coefficients between the temperature of dust and visual extinction. show the plots of variation of Planck function along major and minor diameters passing through the flux minima at 100 microns of the cavity structures FIC21+55 and FIC16-56, respectively. These distributions followed the sinusoidal trend, indicating that the particles along both diameters of studied cavities were not in thermal equilibrium and oscillated to acquire dynamical equilibrium (Tiwari et al., 2021). This nature of oscillation was well-described in previous literature (Gautam & Aryal, 2019a).

Figures 3(c) and 4(c)
show the FIR spectral distribution of the cavity structures FIC21+55 and FIC16-56, respectively. In both structures, it has a positive slope in between the flux at the wavelengths 12 to 25 microns as well as 60 to 100 microns; however, a negative slope was noticed between the flux at wavelengths 60 to 100 microns, suggesting lower dust particles number density at 60micron band. Possibly, as a consequence of the interplay between the AGB wind and the ambient interstellar medium, the far-infrared cavity has a notable drop at 60micron flux density instead of a continuous rise. FIR spectral distribution with skeleton nebula (Aryal & Weinberger, 2006) and high latitude molecular cloud (Weiland et al., 1986) showed continuous rise with different slopes. This discrepancy in the nature of FIR indicated the possible role of AGB wind. As the cavity emitted less radiation at a 60-micron wavelength and thus signified the deficiency of dust and grains in the cavities. These materials were expected to be swept away by the AGB wind from the cavity. This phenomenon was also observed in the case of AGBs and pulsars (Weiland et al., 1986;Ferriere, 2001;Suh & Kwon, 2009;Gautam & Aryal, 2019a).
Furthermore, we calculated the major and minor diameters of the selected far-infrared cavity using Equation (7). The value of distance (D') = ~3580 pc for FIC21+55 and 2449 pc for FIC16-56 were used, and the pixel size (in radian) of the structure was measured using ALADIN v2.5. The distance of the major and minor axis of FIC21+55 was measured to be ~ 61.8 pc and ~ 46.5 pc, and of FIC16-56 was estimated to be ~ 25.55 pc and ~ 17.92 pc, respectively. Hence, the size of the FIC21+55 and FIC16-56 were estimated as 61.8 pc × 46.5 pc and 25.55 pc × 17.92 pc, respectively.

CONCLUSIONS
This paper elucidated the physical properties such as dust color temperature, dust mass, Planck function, and visual extinction of the far-infrared cavity structures, namely FIC21+55 and FIC16-56 at 60 µm and 100 µm IRAS maps located nearby AGB stars within -10˚ < b < 10˚ Galactic planes. We summarized the results as follows: • The values of dust color temperature were found in the range 22.24 ± 0.81 K to 23.27 ± 0.21 K for FIC21+55, and 25.12 ± 0.43 K to 26.17 ± 0.62 K for FIC16-56, with an offset of about 1 K. • The size of the structures, FIC21+55, and FIC16-56, were found to be 61.8 pc × 46.5 pc and 25.55 pc × 17.92 pc, respectively. • The majority of the minimum flux regions corresponded to the minimum mass regions in both cavities. This suggests that the distribution of dust was homogeneous and isotropic. However, the minimum flux-region was shifted from the minimum temperature region of the cavity. Moreover, although the dust color temperature and dust mass distributions in the cavities showed the Gaussian (like) nature, for temperature vs. number plot of FIC21+55, we see some bumps at the beginning. These unusual behavior indicated the possible effect of nearby sources (e.g., AGB wind). • The distribution of Planck function along both of the diameters in both structures was sinusoidal. This indicated that the particles along these diameters were oscillating. • We observed a negative correlation between Aυ and Td in both cavities; less value of correlation coefficient between Aυ and Td was obtained in comparison to previous studies; we expected the role of external sources behind this. • There was a significant decrease in the flux density between 25 µm to 60 µm wavelengths in FIR spectral distribution for both cavities. This significant dip at 60 µm instead of the continuous increase was possible due to the interaction of AGB wind with the interstellar medium.
Hence, dust grains obscure the light from distant stars, track physical parameters (such as Galactic magnetic fields and gas temperature) and have direct interaction with other interstellar medium components (e.g., the formation of molecules and stars) (Williams, 2005). It also has a direct impact on the star formation processes. Due to this reason, the study of dust around different environments in the ISM is a crucial task. Dust properties trend nearby different AGB stars can be revealed by a model from an extensive number of similar works. Further, the rate of mass loss from the AGB star also can be studied. Following these methods, comparative study of dust properties of other large numbers of new cavity structures nearby various sources such as AGSs, Pulsars, White Dwarfs have to be carried out in the future. It provides crucial information for a better understanding of a dust grain status in the ISM. We believe this research work will contribute as a block of references for future studies about the shaping process of the Interstellar Medium.