arXiv subjects

Jessy Jose

Publications and source records attributed to Jessy Jose.

At least 37 records · Page 2Linked to original sources

arXiv2024

Search for Brown Dwarfs in IC 1396 with Subaru HSC: Interpreting the Impact of Environmental Factors on Sub-stellar Population

Young stellar clusters are predominantly the hub of star formation and hence, ideal to perform comprehensive studies over the least explored sub-stellar regime. Various unanswered questions like the mass distribution in brown dwarf regime and the effect of diverse cluster environment on brown dwarf formation efficiency still plague the scientific community. The nearby young cluster, IC 1396 with its feedback-driven environment, is ideal to conduct such study. In this paper we adopt a multi-wavelength approach, using deep Subaru HSC, Gaia DR3, Pan-STARRS, UKIDSS/2MASS photometry and machine learning techniques to identify the cluster members complete down to $\sim$ 0.03 M$_{\odot}$ in the central 22$^{\prime}$ area of IC 1396. We identify 458 cluster members including 62 brown dwarfs which are used to determine mass distribution in the region. We obtain a star-to-brown dwarf ratio of $\sim$ 6 for a stellar mass range 0.03 -- 1 M$_{\odot}$ in the studied cluster. The brown dwarf fraction is observed to increase across the cluster as radial distance from the central OB-stars increases. This study also compiles 15 young stellar clusters to check the variation of star-to-brown dwarf ratio relative to stellar density and UV flux ranging within 4-2500 stars pc$^{-2}$ and 0.7-7.3 G$_{0}$ respectively. The brown dwarf fraction is observed to increase with stellar density but the results about the influence of incident UV flux are inconclusive within this range. This is the deepest study of IC 1396 as of yet and it will pave the way to understand various aspects of brown dwarfs using spectroscopic observations in future.

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arXiv2024

An outburst and FU Ori-type disk of a former low luminosity protostar

Strong accretion outbursts onto protostars are associated with emission dominated by a viscously heated disk, which is characterized by high luminosities. We report the discovery and characterization of a strong mid-IR (3.4, 4.6 $μ$m) outburst in the embedded protostar SSTgbs J21470601+4739394 (hereafter SSTgbsJ214706). SSTgbsJ214706 has steadily brightened in the mid-infrared by $\sim2$ magnitudes over the past decade, as observed by NEOWISE. Follow-up investigations with the Gemini near-IR spectrograph reveal that SSTgbsJ214706 is a binary system with a spatially extended outflow. The outburst is occurring on the more embedded southeast (SE) component, which dominates the mid- and far-infrared emission from the source. The outbursting component exhibits a spectrum consistent with an FU Ori-type outburst, including the presence of enhanced absorption observed in the molecular bands of CO. The luminosity of the SE component is estimated to be $\sim 0.23\,$ L$_\odot$ before the outburst and $\sim 0.95\,$ L$_\odot$ during the outburst, which is 1 to 2 orders of magnitude fainter than bonafide FU Ori outbursts. We interpret this eruption as an FU Ori-type outburst, although the possibility of brightening following an extinction episode cannot be ruled out. We discuss the implications and potential explanations for such a low-luminosity eruption.

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arXiv2023

Protoplanetary disks around young stellar and substellar objects in the $σ$ Orionis cluster

Understanding the evolution and dissipation of protoplanetary disks are crucial in star and planet formation studies. We report the protoplanetary disk population in the nearby young $σ$ Orionis cluster (d$\sim$408 pc; age$\sim$1.8 Myr) and analyse the disk properties such as dependence on stellar mass and disk evolution. We utilise the comprehensive census of 170 spectroscopic members of the region refined using astrometry from Gaia DR3 for a wide mass range of $\sim$19-0.004 M$_\odot$. Using the near infrared (2MASS) and mid infrared (WISE) photometry we classify the sources based on the spectral index into class I, class II, flat spectrum and class III young stellar objects. The frequency of sources hosting a disk with stellar mass $<$2 M$_\odot$ in this region is 41$\pm$7% which is consistent with the disk fraction estimated in previous studies. We see that there is no significant dependence of disk fraction on stellar mass among T Tauri stars ($<$2 M$_\odot$), but we propose rapid disk depletion around higher mass stars ($>$2 M$_\odot$). Furthermore we find the lowest mass of a disk bearing object to be $\sim$ 20 M$_\mathrm{Jup}$ and the pronounced disk fraction among the brown dwarf population hints at the formation scenario that brown dwarfs form similar to low-mass stars.

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arXiv2023

H$α$ emission line sources from VLT-MUSE in a low-metallicity star forming region -- Dolidze 25

The process of accretion through circumstellar disks in young stellar objects is an integral part of star formation and the $Hα$ emission line is a prominent signature of accretion in low-mass stars. We present the detection and characterization of $Hα$ emission line sources in the central region of a distant, low-metallicity young stellar cluster - Dolidze 25 (at $\sim$ 4.5 kpc) - using medium-resolution optical spectra (4750-9350 Å ) obtained with the Multi-Unit Spectroscopic Explorer (MUSE) at the VLT. We have identified 14 potential accreting sources within a rectangular region of (2$'$ x 1$'$) towards the center of the cluster based on the detection of strong and broad emissions in $Hα$ as well as the presence of other emission lines such as [OI] and $Hβ$. Based on their positions in both photometric color-magnitude and color-color diagrams, we have also confirmed that these objects belong to the pre-main sequence phase of star formation. Our results were compared with the disk and diskless members of the cluster previously identified by Guarcello et al. (2021) using near-IR colors, and all sources they had identified as disks were confirmed to be accreting based on the spectroscopic characteristics.

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arXiv2023

The role of magnetic fields in the fragmentation of the Taurus B213 filament into Sun-type star-forming cores

Fragmentation is a key step in the process of transforming clouds (and their substructures such as filaments, clumps, and cores) into protostars. The thermal gas pressure and gravitational collapse are believed to be the primary agents governing this process, referred to as the thermal Jeans fragmentation. However, the contributions of other factors (such as magnetic fields and turbulence) to the fragmentation process remain less explored. In this work, we have tested possible fragmentation mechanisms by estimating the mean core mass and mean inter-core separation of the B213 filament. We have used the $\sim$14" resolution James Clerk Maxwell Telescope (JCMT) Submillimetre Common-User Bolometer Array 2 (SCUBA-2)/POL-2 850 $μ$m dust continuum map and combined it with a Planck 850 $μ$m map and Herschel data. We find that in addition to the thermal contribution, the presence of ordered magnetic fields could be important in the fragmentation of the B213 filament.

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arXiv2023

A novel survey for young substellar objects with the W-band filter VI: Spectroscopic census of sub-stellar members and the IMF of $σ$ Orionis cluster

Low-mass stars and sub-stellar objects are essential in tracing the initial mass function (IMF). We study the nearby young $σ$ Orionis cluster (d$\sim$408 pc; age$\sim$1.8 Myr) using deep NIR photometric data in J, W and H-bands from WIRCam on the Canada-France-Hawaii Telescope. We use the water absorption feature to photometrically select the brown dwarfs and confirm their nature spectroscopically with the IRTF-SpeX. Additionally we select candidate low-mass stars for spectroscopy and analyze their membership and that of literature sources using astrometry from Gaia DR3. We obtain the near-IR spectra for 28 very low-mass stars and brown dwarfs and estimate their spectral type between M3-M8.5 (mass ranging between 0.3-0.01 M$_{\odot}$). Apart from these, we also identify 5 new planetary mass candidates which require further spectroscopic confirmation of youth. We compile the comprehensive catalog of 170 spectroscopically confirmed members in the central region of the cluster, for a wide mass range of $\sim$19-0.004 M$_{\odot}$. We estimate the star/BD ratio to be $\sim$4, within the range reported for other nearby star forming regions. With the updated catalog of members we trace the IMF down to 4 M$_\mathrm{Jup}$ and we find that a two-segment power-law fits the sub-stellar IMF better than the log-normal distribution.

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arXiv2023

Photometric and Spectroscopic monitoring of YSOs in nearby star forming regions. I. Eruptive YSOs

Mid-infrared (mid-IR) variability in young stellar objects (YSOs) is driven by several physical mechanisms, which produce a variety of amplitudes and light curve shapes. One of these mechanisms, variable disk accretion is predicted by models of episodic accretion to drive secular variability, including in the mid-IR. Because the largest accretion bursts are rare, adding new objects to the YSO eruptive variable class aids our understanding of the episodic accretion phenomenon and its possible impact on stellar and planetary formation. A previous analysis of 6.5 yr of NeoWISE light curves (3-5 $μ$m) of ~7000 nearby YSOs found an increase in the fraction of variability and variability amplitude for objects at younger stages of evolution. To help interpret these light curves, we have obtained low- and high-resolution near-IR spectra of 78 objects from this sample of YSOs. In this work, we present the analysis of nine nearby YSOs (d$<$1 kpc) that show the characteristics of known classes of eruptive variable YSOs. We find one FUor-like source, one EX Lupi-type object, and six YSOs with mixed characteristics, or V1647 Ori-like objects. The varied characteristics observed in our sample are consistent with recent discoveries of eruptive YSOs. We discuss how a wide range in YSO outburst parameters (central mass, maximum accretion rate during outburst, evolutionary stage and/or instability leading to the outburst) may play a significant role in the observed spectro-photometric properties of YSO outbursts.

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arXiv2023

Membership analysis and 3D kinematics of the star-forming complex around Trumpler 37 using Gaia-DR3

Identifying and characterizing young populations of star-forming regions is crucial to unravel their properties. In this regard, Gaia-DR3 data and machine learning tools are very useful for studying large star-forming complexes. In this work, we analyze the $\rm \sim7.1degree^2$ area of one of our Galaxy's dominant feedback-driven star-forming complexes, i.e., the region around Trumpler 37. Using the Gaussian mixture and random forest classifier methods, we identify 1243 high-probable members in the complex, of which $\sim60\%$ are new members and are complete down to the mass limit of $\sim$0.1 $-$ 0.2~$\rm M_{\odot}$. The spatial distribution of the stars reveals multiple clusters towards the complex, where the central cluster around the massive star HD 206267 reveals two sub-clusters. Of the 1243 stars, 152 have radial velocity, with a mean value of $\rm -16.41\pm0.72~km/s$. We investigate stars' internal and relative movement within the central cluster. The kinematic analysis shows that the cluster's expansion is relatively slow compared to the whole complex. This slow expansion is possibly due to newly formed young stars within the cluster. We discuss these results in the context of hierarchical collapse and feedback-induced collapse mode of star formation in the complex.

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arXiv2023

Survey of Hα emission-line stars in the star-forming region IC 5070

Actively accreting young stellar objects show H$α$ emission line in their spectra. We present the results of survey for H$α$ emission-line stars in the star-forming region IC~5070 taken with 2-m Himalyan {\it Chandra} Telescope. Based on the H$α$ slitless spectroscopy data, we identified 131 emission-line stars in $\sim$ 0.29 square degrees area of the IC~5070 region. Using Gaia Early Data Release 3, we estimated the mean proper motion and parallax of the emission-line stars. We also estimated the mean distance and reddening toward the region using the emission-line stars, that are $\sim$ 833 pc and $\sim$2 mag, respectively. By examining the locations of these stars in the color-magnitude diagrams constructed using Gaia and PanSTARRS1 data, we found that a majority of the H$α$ emitters are young low-mass ($<$ 1.5 $M\odot$) stars. We also compared our catalog of emission-line stars with the available young stellar catalogs and found that most of them are Class~{II}/ flat spectrum sources with the spectral type ranging from K to M. Based on the proper motion/ parallax values and locations on the color-magnitude diagrams, about 20 emission-line stars are flagged as non-members. The relative proper motion of the emission-line stars with respect to the ionizing source suggest the possibility of the `rocket effect' scenario in the remnant cloud (BRC~31).

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arXiv2022

A Novel Survey for Young Substellar Objects with the W band Filter.V. IC 348 and Barnard 5 in the Perseus Cloud

We report the discovery of substellar objects in the young star cluster IC 348 and the neighboring Barnard 5 dark cloud, both at the eastern end of the Perseus star-forming complex. The substellar candidates are selected using narrowband imaging, i.e., on and off photometric technique with a filter centered around the water absorption feature at 1.45 microns, a technique proven to be efficient in detecting water-bearing substellar objects. Our spectroscopic observations confirm three brown dwarfs in IC 348. In addition, the source WBIS 03492858+3258064, reported in this work, is the first confirmed brown dwarf discovered toward Barnard 5. Together with the young stellar population selected via near- and mid-infrared colors using the Two Micron All Sky Survey and the Wide-field Infrared Survey Explorer, we diagnose the relation between stellar versus substellar objects with the associated molecular clouds. Analyzed by Gaia EDR3 parallaxes and kinematics of the cloud members across the Perseus region, we propose the star formation scenario of the complex under influence of the nearby OB association.

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arXiv2022

Diagnosing FUor-like Sources: The Parameter Space of Viscously Heated Disks in the Optical and Near-IR

FU Ori type objects (FUors) are decades-long outbursts of accretion onto young stars that are strong enough to viscously heat disks so that the disk outshines the central star. We construct models for FUor objects by calculating emission components from a steady-state viscous accretion disk, a passively-heated dusty disk, magnetospheric accretion columns, and the stellar photosphere. We explore the parameter space of the accretion rate and stellar mass to investigate implications on the optical and near-infrared spectral energy distribution and spectral lines. The models are validated by fitting to multi-wavelength photometry of three confirmed FUor objects, FU Ori, V883 Ori and HBC 722 and then comparing the predicted spectrum to observed optical and infrared spectra. The brightness ratio between the viscous disk and the stellar photosphere, $η$, provides an important guide for identifying viscous accretion disks, with $η=1$ ("transition line") and $η=5$ ("sufficient dominance line") marking turning points in diagnostics, evaluated here in the near-infrared. These turning points indicate the emergence and complete development of FUor-characteristic strong CO absorption, weak metallic absorption, the triangular spectral continuum shape in the $H$-band, and location in color-magnitude diagrams. Lower stellar mass $M_*$ and higher accretion rate $\dot{M}$ lead to larger $η$; for $M_*=0.3~{\rm M_\odot}$, $η=1$ corresponds to $\dot{M}=2\times10^{-7}~{\rm M_\odot}/$yr and $η=5$ to $\dot{M}=6\times10^{-7}~{\rm M_\odot}/$yr. The sufficient dominance line also coincides with the expected accretion rate where accreting material directly reaches the star. We discuss implications of the models on extinction diagnostics, FUor brightening timescales, viscous disks during initial protostellar growth, and eruptive young stellar objects (YSO) associated with FUors.

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arXiv2022

Tracers of Dense Gas in the Outer Galaxy

We have mapped HCN and HCO$^{+}$ (J = 1 $\to$ 0) line emission toward a sample of seven star-forming regions (with 12 + log[O/H] range from 8.34 to 8.69) in the outer Milky Way (Galactocentric distance > 9.5 kpc), using the 14-meter radio telescope of the Taeduk Radio Astronomy Observatory (TRAO). We compare these two molecular lines with other conventional tracers of dense gas, millimeter-wave continuum emission from dust and extinction thresholds ($A_{V} \geq 8$ mag), inferred from the $^{13}$CO line data. HCN and HCO$^{+}$ correlate better with the millimeter emission than with the extinction criterion. A significant amount of luminosity comes from regions below the extinction criterion and outside the millimeter clump for all the clouds. The average fraction of HCN luminosity from within the regions with $A_{V} \geq 8$ mag is $0.343\pm0.225$; for the regions of millimeter emission, it is $0.478\pm0.149$. Based on a comparison with column density maps from Herschel, HCN and HCO$^{+}$ trace dense gas in high column density regions better than does $^{13}$CO. HCO$^{+}$ is less concentrated than HCN for outer Galaxy targets, in contrast with the inner Galaxy sample, suggesting that metallicity may affect the interpretation of tracers of dense gas. The conversion factor between the dense gas mass ($M_{dense}$) and line luminosities of HCN and HCO$^{+}$, when integrated over the whole cloud, is comparable with factors used in extragalactic studies.

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arXiv2022

Revealing the dust grain polarization properties as a function of extinction and distance towards NGC 1893

Dust polarization observations at optical wavelengths help to understand the dust grain properties and trace the plane-of-the-sky component of the magnetic field. In this study, we make use of the $I$-band polarization data acquired from AIMPOL along with the distances ($d$) and extinction ($A_{V}$) data to study the variation of polarization fraction ($P$) as a function of $A_{V}$ and $d$ towards the star-forming region, NGC 1893. We employ a broken power-law fit and Bayesian analysis on extinction ($A_{V}$) versus polarization efficiency ($P$/$A_{V}$) and distance ($d$) versus rate of polarization ($P$/$d$). We find that $P$/$A_{V}$ shows a break at an extinction of $\sim$0.9 mag, whereas $P/d$ exhibits a break at a distance of $\sim$1.5 kpc. Based on these, we categorize the dust towards NGC 1893 into two populations: (i) foreground dust confined to $A_{V}$ $<$ $\sim$1 mag and distance up to $\sim$2 kpc and (ii) Perseus spiral arm dust towards NGC 1893 characterized with $A_{V}$ $>$ $\sim$1 mag and distance beyond $\sim$2 kpc. Foreground dust exhibits higher polarization efficiency but a lower polarization rate, whereas Perseus dust shows a lower polarization efficiency but a slightly higher polarization rate. Hence, we suggest that while polarization efficiency reveals the dust grain alignment, the rate of polarization infers about the distribution of dust grains towards NGC 1893. Further, we also shed a light on the spatial variation of intrinsic polarization and magnetic field orientation, and other parameters within the intra-cluster medium of NGC 1893.

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arXiv2021

Subaru Hyper Suprime-Cam Survey of Cygnus OB2 Complex -- I: Introduction, Photometry and Source Catalog

Low mass star formation inside massive clusters is crucial to understand the effect of cluster environment on processes like circumstellar disk evolution, planet and brown dwarf formation. The young massive association of Cygnus OB2, with a strong feedback from massive stars, is an ideal target to study the effect of extreme environmental conditions on its extensive low-mass population. We aim to perform deep multi-wavelength studies to understand the role of stellar feedback on the IMF, brown dwarf fraction and circumstellar disk properties in the region. We introduce here, the deepest and widest optical photometry of 1.5$^\circ$ diameter region centred at Cygnus OB2 in r$_{2}$, i$_{2}$, z and Y-filters using Subaru Hyper Suprime-Cam (HSC). This work presents the data reduction, source catalog generation, data quality checks and preliminary results about the pre-main sequence sources. We obtain 713,529 sources in total, with detection down to $\sim$ 28 mag, 27 mag, 25.5 mag and 24.5 mag in r$_{2}$, i$_{2}$, z and Y-band respectively, which is $\sim$ 3 - 5 mag deeper than the existing Pan-STARRS and GTC/OSIRIS photometry. We confirm the presence of a distinct pre-main sequence branch by statistical field subtraction of the central 18$^\prime$ region. We find the median age of the region as $\sim$ 5 $\pm$ 2 Myrs with an average disk fraction of $\sim$ 9$\%$. At this age, combined with A$_V$ $\sim$ 6 - 8 mag, we detect sources down to a mass range $\sim$ 0.01 - 0.17 M$_\odot$. The deep HSC catalog will serve as the groundwork for further studies on this prominent active young cluster.

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arXiv2021

A Novel Survey for Young Substellar Objects with the W-band filter III: Searching for very low mass brown dwarfs in Serpens South and Serpens Core

We present CFHT photometry and IRTF spectroscopy of low-mass candidate members of Serpens South and Serpens Core ($\sim$430 pc, $\sim$0.5 Myr), identified using a novel combination of photometric filters, known as the W-band method. We report SC182952+011618, SS182959-020335 and SS183032-021028 as young, low-mass Serpens candidate members, with spectral types in the range M7-M8, M5-L0 and M5-M6.5 respectively. Best-fit effective temperatures and luminosities imply masses of $<$ 0.12M$_{\odot}$ for all three candidate cluster members. We also present Hubble Space Telescope imaging data (F127M, F139M and F850LP) for six targets in Serpens South. We report the discovery of the binary system SS183044-020918AB. The binary components are separated by $\approx$45 AU, with spectral types of M7-M8 and M8-M9, and masses of 0.08-0.1 and 0.05-0.07M$_{\odot}$. We discuss the effects of high dust attenuation on the reliability of our analysis, as well as the presence of reddened background stars in our photometric sample.

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arXiv2021

The Sharpest Ultraviolet view of the star formation in an extreme environment of the nearest Jellyfish Galaxy IC 3418

We present the far ultraviolet (FUV) imaging of the nearest Jellyfish or Fireball galaxy IC3418/VCC 1217, in the Virgo cluster of galaxies, using Ultraviolet Imaging Telescope (UVIT) onboard the ASTROSAT satellite. The young star formation observed here in the 17 kpc long turbulent wake of IC3418, due to ram pressure stripping of cold gas surrounded by hot intra-cluster medium, is a unique laboratory that is unavailable in the Milkyway. We have tried to resolve star forming clumps, seen compact to GALEX UV images, using better resolution available with the UVIT and incorporated UV-optical images from Hubble Space Telescope archive. For the first time, we resolve the compact star forming clumps (fireballs) into sub-clumps and subsequently into a possibly dozen isolated stars. We speculate that many of them could be blue supergiant stars which are cousins of SDSS J122952.66+112227.8, the farthest star (~17 Mpc) we had found earlier surrounding one of these compact clumps. We found evidence of star formation rate (4 - 7.4 x 10^-4 M_sun per yr ) in these fireballs, estimated from UVIT flux densities, to be increasing with the distance from the parent galaxy. We propose a new dynamical model in which the stripped gas may be developing vortex street where the vortices grow to compact star forming clumps due to self-gravity. Gravity winning over turbulent force with time or length along the trail can explain the puzzling trend of higher star formation rate and bluer/younger stars observed in fireballs farther away from the parent galaxy.

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arXiv2021

Testing the role of environmental effects on the initial mass function of low-mass stars

In the star formation process, the vital impact of environmental factors such as feedback from massive stars and stellar density on the form of the initial mass function (IMF) at low-mass end is yet to be understood. Hence a systematic, highly sensitive observational analysis of a sample of regions under diverse environmental conditions is essential. We analyse the IMF of eight young clusters ($<$5 Myr), namely IC1848-West, IC1848-East, NGC 1893, NGC 2244, NGC 2362, NGC 6611, Stock 8 and Cygnus OB2, which are located at the Galactocentric distance ($R_g$) range $\sim$6-12 kpc along with nearby cluster IC348 using deep near-IR photometry and Gaia DR2. These clusters are embedded in massive stellar environments of radiation strength $log(L_{FUV}/L_{\odot})$ $\sim$2.6 to 6.8, $log(L_{EUV})$ $\sim$42.2 to 50.85 photons/s, with stellar density in the range of $\sim$170 - 1220 stars/pc$^2$. After structural analysis and field decontamination we obtain an unbiased, uniformly sensitive sample of pre-main-sequence members of the clusters down to brown-dwarf regime. The lognormal fit to the IMF of nine clusters gives the mean characteristic mass ($m_c$) and $σ$ of 0.32$\pm$0.02 $M_\odot$ and 0.47$\pm$0.02, respectively. We compare the IMF with that of low- and high-mass clusters across the Milky Way. We also check for any systematic variation with respect to the radiation field strength, stellar density as well with $R_g$. We conclude that there is no strong evidence for environmental effect in the underlying form of the IMF of these clusters.

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arXiv2021

Testing the star formation scaling relations in the clumps of the North American and Pelican cloud complexes

The processes which regulate the star-formation within molecular clouds are still not well understood. Various star-formation scaling relations have been proposed to explain this issue by formulating a relation between star-formation rate surface density ($\rm Σ_{SFR}$) and the underlying gas surface density ($\rm Σ_{gas}$). In this work, we test various star formation scaling relations, such as Kennicutt-Schmidt relation, volumetric star-formation relation, orbital time model, crossing time model, and multi free-fall time scale model towards the North American and Pelican Nebulae complexes and in cold clumps associated with them. Measuring stellar-mass from young stellar objects and gaseous mass from CO measurements, we estimated mean $\rm Σ_{SFR}$, star formation rate per free-fall time, and star formation efficiency (SFE) for clumps to be 1.5 $\rm M{_\odot}~yr^{-1}~kpc^{-2}$, 0.009, 2.0$\%$, respectively, while for the entire NAN complex the values are 0.6 $\rm M{_\odot}~yr^{-1}~kpc^{-2}$, 0.0003, and 1.6$\%$, respectively. For clumps, we notice that the observed properties are in line with the correlation obtained between $\rm Σ_{SFR}$ and $\rm Σ_{gas}$, and between $\rm Σ_{SFR}$ and $\rm Σ_{gas}$ per free-fall time and orbital time for Galactic clouds. At the same time, we do not observe any correlation with $\rm Σ_{gas}$ per crossing time and multi free-fall time. Even though we see correlations in former cases, however, all models agree with each other within a factor of 0.5 dex, and discriminating between these models is not possible due to the current uncertainties in the input observables. We also test the variation of $\rm Σ_{SFR}$ versus the dense gas, but due to low statistics, a weak correlation is seen in our analysis.

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