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Register a new userTrans-ethyl methyl ether in space - A new look at a complex molecule in selected hot core regions
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An extensive search for the complex molecule trans-ethyl methyl ether towards several hot core regions has been performed. Using the IRAM 30m telescope and the SEST 15m we looked at several frequencies where trans-ethyl methyl ether has strong transitions, as well as lines which are particularly sensitive to the physical conditions in which the molecule can be found. We included G34.26, NGC6334(I), Orion KL, and W51e2 which have previously been proven to have a rich chemistry of complex molecules. Our observations cannot confirm the tentative Orion KL detection made by Charnley et al. (2001) within their stated column density limits, but we confirm the existence of the trans-ethyl methyl ether towards W51e2 with a column density of 2x10^14 cm-2. The dimethyl ether/methanol ratio of 0.6 as well as the newly found ethyl methyl ether/ethanol ratio of 0.13 indicate relative high abundances of ethers toward W51e2. Furthermore, the observation of ethyl methyl ether also confirms the importance of ethanol as a grain mantle constituent. We present new upper limits of around 8x10^13 cm-2 for the column densities of the molecule toward Orion KL, G34.26, NGC6334(I) and estimate the column density towards SgrB2(N) to be of the same order. The W51e2 observations are discussed in more detail.
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We report on the tentative detection of $trans$ Ethyl Methyl Ether (tEME), $t-CH_3CH_2OCH_3$, through the identification of a large number of rotational lines from each one of the spin states of the molecule towards Orion KL. We also search for $gauche$-$trans$-n-propanol, $Gt-n-CH_3CH_2CH_2OH$, an isomer of tEME in the same source. We have identified lines of both species in the IRAM 30m line survey and in the ALMA Science Verification data. We have obtained ALMA maps to establish the spatial distribution of these species. Whereas tEME mainly arises from the compact ridge component of Orion, Gt-n-propanol appears at the emission peak of ethanol (south hot core). The derived column densities of these species at the location of their emission peaks are $leq(4.0pm0.8)times10^{15} cm^{-2}$ and $leq(1.0pm0.2)times10^{15} cm^{-2}$ for tEME and Gt-n-propanol, respectively. The rotational temperature is $sim100 K$ for both molecules. We also provide maps of $CH_3OCOH$, $CH_3CH_2OCOH$, $CH_3OCH_3$, $CH_3OH$, and $CH_3CH_2OH$ to compare the distribution of these organic saturated O-bearing species containing methyl and ethyl groups in this region. Abundance ratios of related species and upper limits to the abundances of non-detected ethers are provided. We derive an abundance ratio $N(CH_3OCH_3)/N(tEME)geq150$ in the compact ridge of Orion.
G31.41+0.31 is a well known chemically rich hot molecular core (HMC). Using Band 3 observations of Atacama Large Millimeter Array (ALMA), we have analyzed the chemical and physical properties of the source. We have identified methyl isocyanate (CH3NCO), a precursor of prebiotic molecules, towards the source. In addition to this, we have reported complex organic molecules (COMs) like methanol (CH3OH), methanethiol (CH3SH), and methyl formate (CH3OCHO). Additionally, we have used transitions from molecules like HCN, HCO+, SiO to trace the presence of infall and outflow signatures around the star-forming region. For the COMs, we have estimated the column densities and kinetic temperatures, assuming molecular excitation under local thermodynamic equilibrium (LTE) conditions. From the estimated kinetic temperatures of certain COMs, we found that multiple temperature components may be present in the HMC environment. Comparing the obtained molecular column densities between the existing observational results toward other HMCs, it seems that the COMs are favourably produced in the hot-core environment ($sim 100$ K or higher). Though the spectral emissions towards G31.41+0.31 are not fully resolved, we find that CH$_3$NCO and other COMs are possibly formed on the grain/ice phase and populate the gas environment similar to other hot cores like Sgr B2, Orion KL, and G10.47+0.03, etc.
We discuss the hot hand paradox within the framework of the backward Kolmogorov equation. We use this approach to understand the apparently paradoxical features of the statistics of fixed-length sequences of heads and tails upon repeated fair coin flips. In particular, we compute the average waiting time for the appearance of specific sequences. For sequences of length 2, the average time until the appearance of the sequence HH (heads-heads) equals 6, while the waiting time for the sequence HT (heads-tails) equals 4. These results require a few simple calculational steps by the Kolmogorov approach. We also give complete results for sequences of lengths 3, 4, and 5; the extension to longer sequences is straightforward (albeit more tedious). Finally, we compute the waiting times $T_{nrm H}$ for an arbitrary length sequences of all heads and $T_{nrm(HT)}$ for the sequence of alternating heads and tails. For large $n$, $T_{2nrm H}sim 3 T_{nrm(HT)}$.
We present a multiwavelength study of 28 Galactic massive star-forming H II regions. For 17 of these regions, we present new distance measurements based on Gaia DR2 parallaxes. By fitting a multicomponent dust, blackbody, and power-law continuum model to the 3.6 $mu$m through 10 mm spectral energy distributions, we find that ${sim}34$% of Lyman continuum photons emitted by massive stars are absorbed by dust before contributing to the ionization of H II regions, while ${sim}68$% of the stellar bolometric luminosity is absorbed and reprocessed by dust in the H II regions and surrounding photodissociation regions. The most luminous, infrared-bright regions that fully sample the upper stellar initial mass function (ionizing photon rates $N_C ge 10^{50}~{rm s}^{-1}$ and dust-processed $L_{rm TIR}ge 10^{6.8}$ L$_{odot}$) have on average higher percentages of absorbed Lyman continuum photons ($sim$51%) and reprocessed starlight ($sim$82%) compared to less luminous regions. Luminous H II regions show lower average PAH fractions than less luminous regions, implying that the strong radiation fields from early-type massive stars are efficient at destroying PAH molecules. On average, the monochromatic luminosities at 8, 24, and 70 $mu$m combined carry 94% of the dust-reprocessed $L_{rm TIR}$. $L_{70}$ captures ${sim}52$% of $L_{rm TIR}$, and is therefore the preferred choice to infer the bolometric luminosity of dusty star-forming regions. We calibrate SFRs based on $L_{24}$ and $L_{70}$ against the Lyman continuum photon rates of the massive stars in each region. Standard extragalactic calibrations of monochromatic SFRs based on population synthesis models are generally consistent with our values.
Making use of the modern techniques of non-holonomic geometry and constrained variational calculus, a revisitation of Ostrogradskys Hamiltonian formulation of the evolution equations determined by a Lagrangian of order >= 2 in the derivatives of the configuration variables is presented.
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