GHz Class Research Articles

The candidates of long-periodic variable sources in 6.7 GHz methanol masers associated with four high-mass star-forming regions

Abstract Results of the long-term monitoring observations by the Hitachi 32 m radio telescope of the 6.7 GHz Class II methanol masers associated with four high-mass star-forming regions are presented. We detected periodic flux variability in G06.795−0.257, G10.472+0.027, G12.209−0.102, and G13.657−0.599 with the periods of 968, 1624, 1272, and 1266 d, respectively, although the detected period is tentative due to the short monitoring term relative to the estimated period. The facts that the flux variation patterns show the symmetric sine curves and that the luminosities of the central protostar and periods of maser flux variation are consistent with the expected period–luminosity (PL) relation suggest that the mechanisms of maser flux variability of G10.472+0.027 and G12.209−0.102 can be explained by protostellar pulsation instability. From the PL relation, the central stars of these two sources are expected to be very high-mass protostars with a mass of $\sim 40\, M_{\odot }$ and to have a mass accretion rate of $\sim 2 \times 10^{-2}\, M_{\odot }\:$yr−1. On the other hand, G06.795−0.257 and G13.657−0.599 have intermittent variation patterns and have luminosities that are an order of magnitude smaller than those expected from the PL relation, suggesting that the variation mechanisms of these sources originated from a binary system. Since almost all the maser features vary with the same period regardless of the geometry, periodic accretion models may be appropriate mechanisms for flux variability in G06.795−0.257 and G13.657−0.599.

Star formation in G11.497-1.485: Two-epoch VLA study of a 6.7 GHz methanol maser flare

Context. Maser flares are particularly significant in the study of massive star formation as they not only signal but also provide unique insights into transient phenomena such as accretion bursts. Aims. With this project, we aim to investigate the context of the ongoing 6.7 GHz methanol maser flare in the little-known massive star-forming region G11.497-1.485. Methods We carried out two epochs of the Karl G. Jansky Very Large Array (VLA) observation for 6.7 GHz and 12 GHz class II methanol, 22 GHz water masers, and continuum in the C, Ku, and K bands. Results. The VLA overview revealed the presence of five distinct radio-continuum sources (CM1-4 and N) in G11.497-1.485. The central source, CM1, is found to show signs of accretion disc fragmentation, highlighted by the centimetre-continuum-traced fragments, and is found to drive a high-energy jet, the ends of which are marked by non-thermal knots CM2 and CM3. CM1 showed a gradual flaring of methanol masers and a fading of a 22 GHz water maser, which might be signalling an accretion burst. The two remaining sources of the region, CM4 and N, make up one of the most compact jet and disc–jet systems found to date. Conclusions. The obtained data reveal, for the first time, the structure of the G11.497-1.485 region. The change in fluxes of the maser and the continuum emission confirm a transient event and reveal its impact on multiple sources in the region.

The Discovery of the Zeeman Effect in 38 GHz Class II Methanol Masers

Magnetic fields likely play an important role in star formation, but the number of directly measured magnetic field strengths remains scarce. We observed the 38.3 and 38.5 GHz Class II methanol (CH3OH) maser lines toward the high-mass star-forming region NGC 6334 F for the Zeeman effect. The observed spectral profiles have two prominent velocity features that can be further decomposed through Gaussian component fitting. In several of these fitted Gaussian components we find significant Zeeman detections, with zB los in the range from 8 to 46 Hz. If the Zeeman splitting factor z for the 38 GHz transitions is of the order of ∼1 Hz mG−1, similar to that for several other CH3OH maser lines, then magnetic fields in the regions traced by these masers would be in the range of 8–46 mG. Such magnetic field values in high-mass star-forming regions agree with those detected in the better-known 6.7 GHz Class II CH3OH maser line. Since Class II CH3OH masers are radiatively pumped close to the protostar and likely occur in the accretion disk or the interface between the disk and outflow regions, such fields likely have significant impact on the dynamics of these disks.

An Approach to Increase Power-Added Efficiency in a 5 GHz Class E Power Amplifier in 0.18 µm CMOS Technology

A new approach to increasing the power-added efficiency (PAE) of a class E power amplifier (PA) is proposed in this paper. The PA operates at a 5 GHz frequency and a reactance compensation technique is utilized to maximize the bandwidth at the operating frequency. The driver stage creates either a half-wave rectified sine wave or a half-wave rectified sawtooth wave. By applying each one of the waves, the performance of the PA is examined and PAE = 70% and PAE = 50% is achieved. Plus, the output power of the PA is about 26 dBm when the DC voltage supply is 1.8 V. Advanced design system and TSMC 0.18 µm CMOS process are utilized to carry on the simulation.

ALMA observations of the Extended Green Object G19.01–0.03 – ii. A massive protostar with typical chemical abundances surrounded by four low-mass pre-stellar core candidates

ABSTRACT We present a study of the physical and chemical properties of the Extended Green Object (EGO) G19.01−0.03 using sub-arcsecond angular resolution Atacama Large Millimetre/submillimetre Array (ALMA) 1.05 mm and Karl G. Jansky Very Large Array (VLA) 1.21 cm data. G19.01−0.03 MM1, the millimetre source associated with the central massive young stellar object (MYSO), appeared isolated and potentially chemically young in previous Submillimetre Array observations. In our ∼0.4 arcsec-resolution ALMA data, MM1 has four low-mass millimetre companions within 0.12 pc, all lacking maser or outflow emission, indicating they may be pre-stellar cores. With a rich ALMA spectrum full of complex organic molecules, MM1 does not appear chemically young, but has molecular abundances typical of high-mass hot cores in the literature. At the 1.05 mm continuum peak of MM1, N(CH3OH) = (2.22 ± 0.01) × 1018 cm−2 and $T_{\mathrm{ex}} = 162.7\substack{+0.3 \\ -0.5}$ K based on pixel-by-pixel Bayesian analysis of LTE synthetic methanol spectra across MM1. Intriguingly, the peak CH3OH Tex = 165.5 ± 0.6 K is offset from MM1’s millimetre continuum peak by 0.22 arcsec ∼ 880 au, and a region of elevated CH3OH Tex coincides with free–free VLA 5.01 cm continuum, adding to the tentative evidence for a possible unresolved high-mass binary in MM1. In our VLA 1.21 cm data, we report the first NH3(3,3) maser detections towards G19.01−0.03, along with candidate 25 GHz CH3OH 5(2, 3) − 5(1, 4) maser emission; both are spatially and kinematically coincident with 44 GHz Class I CH3OH masers in the MM1 outflow. We also report the ALMA detection of candidate 278.3 GHz Class I CH3OH maser emission towards this outflow, strengthening the connection of these three maser types to MYSO outflows.

Inverse MultiView. II. Microarcsecond Trigonometric Parallaxes for Southern Hemisphere 6.7 GHz Methanol Masers G232.62+00.99 and G323.74–00.26

We present the first results from the Southern Hemisphere Parallax Interferometric Radio Astrometry Legacy Survey: 10 μas accurate parallaxes and proper motions for two Southern Hemisphere 6.7 GHz methanol masers obtained using the inverse MultiView calibration method. Using an array of radio telescopes in Australia and New Zealand, we measured trigonometric parallaxes and proper motions for the masers associated with the star formation region G232.62+00.99 of π = 0.610 ± 0.011 mas, μ x = −2.266 ± 0.021 mas yr−1, and μ y = 2.249 ± 0.049 mas yr−1, which implies its distance to be d = 1.637 ± 0.029 kpc. These measurements represent an improvement in accuracy by more than a factor of 3 over the previous measurements obtained through Very Long Baseline Array observations of the 12 GHz methanol masers associated with this region. We also measure the trigonometric parallax and proper motion for G323.74–00.26 as π = 0.364 ± 0.009 mas, μ x = −3.239 ± 0.025 mas yr−1, and μ y = − 3.976 ± 0.039 mas yr−1, which implies a distance of d = 2.747 ± 0.068 kpc. These are the most accurate measurements of trigonometric parallax obtained for 6.7 GHz class II methanol masers to date. We confirm that G232.62+00.99 is in the Local Arm and find that G323.74–00.26 is in the Scutum–Centaurus arm. We also investigate the structure and internal dynamics of both masers.

ATLASGAL: 3 mm class I methanol masers in high-mass star formation regions

Context. Class I methanol masers are known to be associated with shocked outflow regions around massive protostars, indicating a possible link between the maser properties and those of their host clumps. Aims. The main goals of this study are (1) to search for new class I methanol masers, (2) to statistically study the relationship between class I masers and shock tracers, (3) to compare the properties between class I masers and their host clumps, also as a function of their evolutionary stage, and (4) to constrain the physical conditions that excite multiple class I masers simultaneously. Methods. We analysed the 3 mm wavelength spectral line survey of 408 clumps identified by the APEX Telescope Large Area Survey of the Galaxy (ATLASGAL), which were observed with the IRAM 30-meter telescope, focusing on the class I methanol masers with frequencies near 84, 95, and 104.3 GHz. Results. We detect narrow maser-like features towards 54, 100, and 4 sources in the maser lines near 84, 95, and 104.3 GHz, respectively. Among them, 50 masers at 84 GHz, 29 masers at 95 GHz, and 4 rare masers at 104.3 GHz are new discoveries. The new detections increase the number of known 104.3 GHz masers from five to nine. The 95 GHz class I methanol maser is generally stronger than the 84 GHz maser counterpart. We find nine sources showing class I methanol masers, but no SiO emission, indicating that class I methanol masers might be the only signpost of protostellar outflow activity in extremely embedded objects at the earliest evolutionary stage. Class I methanol masers that are associated with sources that show SiO line wings are more numerous and stronger than those without such wings. The total integrated intensity of class I methanol masers is well correlated with the integrated intensity and velocity coverage of the SiO (2−1) emission. The properties of class I methanol masers are positively correlated with the bolometric luminosity, clump mass, and peak H2 column density of their associated clumps, but are uncorrelated with the luminosity-to-mass ratio, dust temperature, and mean H2 volume density. Conclusions. We suggest that the properties of class I masers are related to shocks traced by SiO. Based on our observations, we conclude that class I methanol masers at 84 and 95 GHz can trace a similar evolutionary stage to the H2O maser, and appear prior to 6.7 and 12.2 GHz methanol and OH masers. Despite their small number, the 104.3 GHz class I masers appear to trace a shorter and more evolved stage compared to the other class I masers.

Ammonia mapping observations of the Galactic infrared bubble N49: Three NH3 clumps along the molecular filament

Abstract We have carried out the NH3(J, K) = (1, 1), (2, 2), and (3, 3) mapping observations toward the Galactic infrared bubble N49 (G28.83−0.25) using the Nobeyama 45 m telescope. Three NH3 clumps (A, B, and C) were discovered along the molecular filament with the radial velocities of ∼96, 87, and 89 km s−1, respectively. The kinetic temperature derived from the NH3(2, 2)/NH3(1, 1) shows Tkin = 27.0 ± 0.6 K enhanced at Clump B in the eastern edge of the bubble, where position coincides with massive young stellar objects (MYSOs) associated with the 6.7 GHz class II methanol maser source. This result shows the dense clump is locally heated by stellar feedback from the embedded MYSOs. The NH3 Clump B also exists at the 88 km s−1 and 95 km s−1 molecular filament intersection. We therefore suggest that the NH3 dense gas formation in Clump B can be explained by a filament–filament interaction scenario. On the other hand, NH3 Clumps A and C at the northern and southern sides of the molecular filament might be the sites of spontaneous star formation because these clumps are located ∼ 5–10 pc away from the edge of the bubble.

Power Added Efficiency Enhancement in a 2.4 GHz Class E Power Amplifier in 0.13µm CMOS Technology

Power-Added-Efficiency (PAE) is one of the most significant factors by which the performance of a Power Amplifier (PA) can be scrutinized. A new approach to increase PAE is proposed in this paper. Plus, the trade-off between increasing VDD for more output power and more PAE is examined. In addition, new and precise calculations for both output voltage and output power are achieved. Furthermore, the concept of using an equivalent circuit of a transformer is described to justify the new way to increase PAE. The designed Power Amplifier (PA) operates at 2.4GHz. The simulation is performed by Advanced Design System (ADS) and MATLAB. Plus, the TSMC 0.13 µm CMOS process is utilized to fulfil the procedure. The class E PA is designed to gain two different objectives, including more output power and more PAE. With VDD= 1.18 V the output power is 19.52 dBm and PAE is 68.5 %. Ultimately, with VDD=4.4 V the output power is 31.24 dBm and PAE is 62.7 %.

Multi-wavelength maser observations of the Extended Green Object G19.01—0.03

AbstractWe report the detections of NH3(3,3) and 25 GHz and 278.3 GHz class I CH3OH maser emission associated with the outflow of the Extended Green Object G19.01–0.03 in sub-arcsecond resolution Atacama Large Millimeter/submillimeter Array (ALMA) and Karl G. Jansky Very Large Array (VLA) observations. For masers associated with the outer outflow lobes (> 12.5 ″ from the central massive young stellar object; MYSO), the spatial distribution of the NH3(3,3) masers is statistically indistinguishable from that of previously known 44 GHz Class I CH3OH masers, strengthening the connection of NH3(3,3) masers to outflow shocks. In sub-arcsecond resolution VLA observations, we resolve the 6.7 GHz Class II CH3OH maser emission towards the MYSO into a partial, inclined ring, with a velocity gradient consistent with the rotationally supported circumstellar disc traced by thermal gas emission.

Ultra-precise monitoring of a class I methanol maser

AbstractWe report the results of a 7-year monitoring program using the Australia Telescope Compact Array (ATCA) for the 9.9 GHz class I methanol maser in G331.13-0.24 where a periodic class II methanol maser is present. The great deal of the project was to control systematics at an unprecedented level. Although no periodic flux variation was found, the maser shows a very stable decline of 166±7 μJy/day. The radial velocity of the maser is stable down to 1 m/s level. We also report a marginal periodic signal in radial velocity (comparable to the level of systematics) of about 20±7 cm/s with the period of 475±22 days, close to that of the 6.7-GHz maser in the source. No hyperfine split was detected which suggests preferential excitation of a single hyperfine transition.

Complex Organic Molecules Detected in 12 High-mass Star-forming Regions with Atacama Large Millimeter/submillimeter Array

Recent astrochemical models and experiments have explained that complex organic molecules (COMs; molecules composed of six or more atoms) are produced on the dust grain mantles in cold and dense gas in prestellar cores. However, the detailed chemical processes and the roles of physical conditions on chemistry are still far from understood. To address these questions, we investigated 12 high-mass star-forming regions using Atacama Large Millimeter/submillimeter Array (ALMA) Band 6 observations. They are associated with 44/95 GHz class I and 6.7 GHz class II CH3OH masers, indicative of undergoing active accretion. We found 28 hot cores with COM emission among 68 continuum peaks at 1.3 mm and specified 10 hot cores associated with 6.7 GHz class II CH3OH masers. Up to 19 COMs are identified including oxygen- and nitrogen-bearing molecules and their isotopologues in cores. The derived abundances show a good agreement with those from other low- and high-mass star-forming regions, implying that the COM chemistry is predominantly set by the ice chemistry in the prestellar core stage. One clear trend is that the COM detection rate steeply grows with the gas column density, which can be attributed to the efficient formation of COMs in dense cores. In addition, cores associated with a 6.7 GHz class II CH3OH maser tend to be enriched with COMs. Finally, our results suggest that the enhanced abundances of several molecules in our hot cores could be originated by the active accretion as well as different physical conditions of cores.

Photonic-Assisted Arbitrary Waveform Generation for Uplink Applications in Beyond 5G Taking Advantage of Low Frequency Technology

We present a photonic-assisted arbitrary waveform generation for uplink applications in beyond 5G taking advantage of low frequency technology and it has a potential to upgrade signal frequency from MHz to more than tens GHz retaining the high ENOB of conventional low frequency electrical technology competitive to the state of the arts of tens GHz class AWG. In machine-to-machine communications over uplink traffic as one of application scenario examples, massive multi-data should be accommodated and be conveyed to beyond GHz region in the era of beyond 5G. The proposed photonic assistance for temporal waveform compression has a potential to upgrade signal frequency from MHz to more than tens GHz retaining the high ENOB of the low frequency technology and surpass the state of the arts of tens GHz class AWG. We successfully demonstrate the principle of the proposed approach in experiment and the potential of achievable ENOB over 12 bit at 50 GHz in simulation.

Mid-infrared and Maser Flux Variability Correlation in Massive Young Stellar Object G036.70+00.09

We present the discovery of the simultaneous flux variation of a massive young stellar object (MYSO) G036.70+00.09 (G036.70) both in the maser emission and mid-infrared (MIR; λ = 3–5 μm) bands. Using the ALLWISE and NEOWISE archival databases that cover a long time span of approximately 10 yr with a cadence of 6 months, we confirm that G036.70 indicates a stochastic year-long MIR variability with no signs of a WISE band color change of W1 (3.4 μm) −W2 (4.6 μm). Cross-matching the MIR data set with the high-cadence 6.7 GHz class II methanol maser flux using the Hitachi 32 m radio telescope that discovered its periodicity in the methanol maser of 53.0–53.2 days, we also determine the flux correlations between the two bands at two different timescales, year-long and day-long, both of which have never been reported in MYSOs, except when they are in the accretion burst phase. The results of our study support the scenario that a class II methanol maser is pumped up by infrared emission from accreting disks of MYSOs. We also discuss the possible origins of MIR and maser variability. To explain the two observed phenomena, a stochastic year-long MIR variability with no signs of significant color change and maser-MIR variability correlation or a change in mass accretion rate and line-of-sight extinction because of the nonaxisymmetric dust density distribution in a rotating accretion disk are possible origins. Observations through spectroscopic monitoring of accretion-related emission lines are essential for determining the origin of the observed variability in G036.70.

Water Masers as an Early Tracer of Star Formation

We present a study of the correlation between 22 GHz water maser emission and far-infrared/submillimeter (IR/sub-mm) sources. The generalized linear model (GLM) is used to predict H2O maser detection in a particular source with defined physical parameters. We checked the GLM predictions by observing a sample of selected sources with the Effelsberg 100 m telescope. In total, 359 sources were observed. H2O masers were detected in 124 sources, with 56 new detections. We found 22 sources with a significant flux variability. Using the GLM analysis, we estimate that 2392 ± 339 star formation regions (SFRs) in the Galaxy may harbor H2O masers detectable by single-dish observations at the noise level of ∼0.05 Jy. Analyzing the luminosity-to-mass ratio (L/M) of the ATLASGAL and Hi-GAL clumps associated with different maser species, we find that 22 GHz water masers have significantly lower values of L/M in comparison to 6.7 GHz class II methanol and 1665 MHz OH masers. This implies that 22 GHz water masers may appear prior to 6.7 GHz methanol and OH masers in the evolutionary sequence of SFRs. From the analysis of physical offsets between host clumps and maser interferometric positions, we found no significant difference between the H2O and class II methanol maser offsets against the host clump position. We conclude that the tight association between water masers and IR/sub-mm sources may provide insight into the pumping conditions of these masers and the evolutionary stages of their onset.

Coherence-based inequality for the discrimination of three-qubit GHZ and W class

Quantum coherence and entanglement originate from the superposition principle. We derive a rigorous relation between the \({l_1}\)-norm of coherence and concurrence, in that we show that the former is always greater than the latter. This result highlights the hierarchical relationship between coherence and concurrence, and proves coherence to be a fundamental and ubiquitous resource. We derive an analogous form of monogamy inequality, which is based on the partial coherence of the reduced two-qubit and reduced single qubit of the particular class of three-qubit state. Moreover, we provide coherence-based inequality for the classification of GHZ class and W class of three-qubit states. Finally, we provide theoretical discussion for the possible implementation of the scheme in an experiment.

Class I Methanol Masers Related to Shocks Induced by Bar Rotation in the Nearby Starburst Galaxy Maffei 2

Abstract We report the detection of class I methanol maser at the 36.2 GHz transition toward the nearby starburst galaxy Maffei 2 with the Karl G. Jansky Very Large Array. Observations of the 36.2 GHz transition at two epochs separated by ∼4 yr show consistencies in both the spatial distribution and flux density of the methanol emission in this transition. Similar to the detections in other nearby starbursts the class I methanol masers sites are offset by a few hundred pc from the center of the galaxy and appear to be associated with the bar edges of Maffei 2. Narrow spectral features with line widths of a few km s−1 are detected, supporting the hypothesis that they are masing. Compared to other nearby galaxies with the detections in the 36.2 GHz methanol maser transition, the maser detected in Maffei 2 has about an order of magnitude higher isotropic luminosity, and thus represents the first confirmed detection of class I methanol megamasers. The spatial distribution of the 36.2 GHz maser spot clusters may trace the rotational gas flow of the galactic bar, providing direct evidence that the class I methanol maser is related to shocks induced by galactic bar rotation. A tentative detection in the 6.7 GHz class II methanol maser (at a 5σ level) is also reported. This is comparable in luminosity to some of the 6.7 GHz maser sources detected in Galactic star-forming regions. The 6.7 GHz methanol emission appears to be associated with star formation activity in a smaller volume, rather than related to the larger-scale galactic activities.

A 12.2 GHz Methanol Maser Survey toward the 6.7 GHz Counterparts Associated with/without UC H ii Regions

Abstract We report a new survey of the 12.2 GHz Class II methanol masers toward a sample of 367 sources with the 6.7 GHz methanol masers conducted with the Shanghai 65 m Tianma Radio Telescope. This sample has been previously made with observations of the radio continuum emission of UC H ii regions by the VLA. A total of 176 sources were detected with the 12.2 GHz methanol maser, with a detection rate of 48%, including 8 new detections. A lower detection rate (<10%) was determined toward the sources in the Galactic longitude ranges of 60°–180°, revealing that the physical environments from those sources in the Local arm or the tails of Galactic arms do not easily excite the 12.2 GHz masers. In addition, two detections of highly excited-state OH masers at the 13.4 GHz transition were made, one of which is a new detection. Compared to previous surveys, one-third of the detected 12.2 GHz masers show considerable flux variations, implying the possible changes of their physical environments associated with variable radiation fields from their host high-mass young stellar objects. A positive log–log correlation is found between the luminosities of the 6.7 and 12.2 GHz masers in our observed sample, suggesting that both the transition masers have similar excitation conditions. The statistical analysis for the relationships between the methanol maser luminosity and UC H ii region spatial size indicates that the maser luminosities of both the 6.7 and 12.2 GHz transitions have a decreasing trend with the spatial sizes of the associated UC H ii regions, indicating that the Class II methanol masers might fade away with the H ii region evolution.

ALMA observations of the Extended Green Object G19.01−0.03 – I. A Keplerian disc in a massive protostellar system

ABSTRACT Using the Atacama Large Millimetre/submillimeter Array (ALMA) and the Karl G. Jansky Very Large Array (VLA), we observed the Extended Green Object (EGO) G19.01−0.03 with sub-arcsec resolution from 1.05 mm to 5.01 cm wavelengths. Our ∼0.4 arcsec ∼ 1600 au angular resolution ALMA observations reveal a velocity gradient across the millimetre core MM1, oriented perpendicular to the previously known bipolar molecular outflow, which is consistently traced by 20 lines of 8 molecular species with a range of excitation temperatures, including complex organic molecules (COMs). Kinematic modelling shows the data are well described by models that include a disc in Keplerian rotation and infall, with an enclosed mass of 40–70 M⊙ (within a 2000 au outer radius) for a disc inclination angle of i = 40○, of which 5.4–7.2 M⊙ is attributed to the disc. Our new VLA observations show that the 6.7 GHz Class II methanol masers associated with MM1 form a partial ellipse, consistent with an inclined ring, with a velocity gradient consistent with that of the thermal gas. The disc-to-star mass ratio suggests the disc is likely to be unstable and may be fragmenting into as-yet-undetected low-mass stellar companions. Modelling the centimetre–millimetre spectral energy distribution of MM1 shows the ALMA 1.05 mm continuum emission is dominated by dust, whilst a free–free component, interpreted as a hypercompact H ii region, is required to explain the VLA ∼5 cm emission. The high enclosed mass derived for a source with a moderate bolometric luminosity (∼104 L⊙) suggests that the MM1 disc may feed an unresolved high-mass binary system.

Classification witness operator for the classification of different subclasses of three-qubit GHZ class

It is well known that three-qubit system has two kind of inequivalent genuine entangled classes under stochastic local operation and classical communication (SLOCC). These classes are called as GHZ class and W class. GHZ class proved to be a very useful class for different quantum information processing task such as quantum teleportation, controlled quantum teleportation etc. In this work, we distribute pure three-qubit states from GHZ class into different subclasses denoted by $S_{1}$, $S_{2}$, $S_{3}$, $S_{4}$ and show that the three-qubit states either belong to $S_{2}$ or $S_{3}$ or $S_{4}$ may be more efficient than the three-qubit state belong to $S_{1}$. Thus, it is necessary to discriminate the states belong to $S_{i}, i=2,3,4$ and the state belong to $S_{1}$. To achieve this task, we have constructed different witness operators that can classify the subclasses $S_{i}, i=2,3,4$ from $S_{1}$. We have shown that the constructed witness operator can be decomposed into Pauli matrices and hence can be realized experimentally.