Deformation analysis with Total Least Squares

Deformation analysis is one of the main research fields in geodesy. Deformation analysis process comprises measurement and analysis phases. Measurements can be collected using several techniques. The output of the evaluation of the measurements is mainly point positions. In the deformation analysis phase, the coordinate changes in the point positions are investigated. Several models or approaches can be employed for the analysis. One approach is based on a Helmert or similarity coordinate transformation where the displacements and the respective covariance matrix are transformed into a unique datum. Traditionally a Least Squares (LS) technique is used for the transformation procedure. Another approach that could be introduced as an alternative methodology is the Total Least Squares (TLS) that is considerably a new approach in geodetic applications. In this study, in order to determine point displacements, 3-D coordinate transformations based on the Helmert transformation model were carried out individually by the Least Squares (LS) and the Total Least Squares (TLS), respectively. The data used in this study was collected by GPS technique in a landslide area located nearby Istanbul. The results obtained from these two approaches have been compared

CN in prestellar cores

Determining the structure of and the velocity field in prestellar cores is essential to understanding protostellar evolution.} {We have observed the dense prestellar cores L 1544 and L 183 in the $N = 1 \to 0$ rotational transition of CN and \thcn in order to test whether CN is depleted in the high--density nuclei of these cores.} {We have used the IRAM 30 m telescope to observe along the major and minor axes of these cores. We compare these observations with the 1 mm dust emission, which serves as a proxy for the hydrogen column density.}{We find that while CN\jone is optically thick, the distribution of \thcn\jone intensity follows the dust emission well, implying that the CN abundance does not vary greatly with density. We derive an abundance ratio of \rm [CN]/[\hh]=\dix{-9} in L 183 and 1-3\tdix{-9} in L 1544, which, in the case of L 183, is similar to previous estimates obtained by sampling lower--density regions of the core.}{We conclude that CN is not depleted towards the high--density peaks of these cores and thus behaves like the N-containing molecules \nnhp and \nhhh. CN is, to our knowledge, the first C--containing molecule to exhibit this characteristic.Comment: Accepted for publication in A&A Letter

HIFI spectroscopy of low-level water transitions in M82

We present observations of the rotational ortho-water ground transition, the two lowest para-water transitions, and the ground transition of ionised ortho-water in the archetypal starburst galaxy M82, performed with the HIFI instrument on the Herschel Space Observatory. These observations are the first detections of the para-H2O(111-000) (1113\,GHz) and ortho-H2O+(111-000) (1115\,GHz) lines in an extragalactic source. All three water lines show different spectral line profiles, underlining the need for high spectral resolution in interpreting line formation processes. Using the line shape of the para-H2O(111-000) and ortho-H2O+(111-000) absorption profile in conjunction with high spatial resolution CO observations, we show that the (ionised) water absorption arises from a ~2000 pc^2 region within the HIFI beam located about ~50 pc east of the dynamical centre of the galaxy. This region does not coincide with any of the known line emission peaks that have been identified in other molecular tracers, with the exception of HCO. Our data suggest that water and ionised water within this region have high (up to 75%) area-covering factors of the underlying continuum. This indicates that water is not associated with small, dense cores within the ISM of M82 but arises from a more widespread diffuse gas component.Comment: 5 pages, 4 figures. Accepted for publication in A&

CCH in prestellar cores

We study the abundance of CCH in prestellar cores both because of its role in the chemistry and because it is a potential probe of the magnetic field. We also consider the non-LTE behaviour of the N=1-0 and N=2-1 transitions of CCH and improve current estimates of the spectroscopic constants of CCH. We used the IRAM 30m radiotelescope to map the N=1-0 and N=2-1 transitions of CCH towards the prestellar cores L1498 and CB246. Towards CB246, we also mapped the 1.3 mm dust emission, the J=1-0 transition of N2H+ and the J=2-1 transition of C18O. We used a Monte Carlo radiative transfer program to analyse the CCH observations of L1498. We derived the distribution of CCH column densities and compared with the H2 column densities inferred from dust emission. We find that while non-LTE intensity ratios of different components of the N=1-0 and N=2-1 lines are present, they are of minor importance and do not impede CCH column density determinations based upon LTE analysis. Moreover, the comparison of our Monte-Carlo calculations with observations suggest that the non-LTE deviations can be qualitatively understood. For L1498, our observations in conjunction with the Monte Carlo code imply a CCH depletion hole of radius 9 x 10^{16} cm similar to that found for other C-containing species. We briefly discuss the significance of the observed CCH abundance distribution. Finally, we used our observations to provide improved estimates for the rest frequencies of all six components of the CCH(1-0) line and seven components of CCH(2-1). Based on these results, we compute improved spectroscopic constants for CCH. We also give a brief discussion of the prospects for measuring magnetic field strengths using CCH.Comment: 14 pages, 13 figures, to be published in Astronomy and Astrophysic

HIFI observations of warm gas in DR21: Shock versus radiative heating

The molecular gas in the DR21 massive star formation region is known to be affected by the strong UV field from the central star cluster and by a fast outflow creating a bright shock. The relative contribution of both heating mechanisms is the matter of a long debate. By better sampling the excitation ladder of various tracers we provide a quantitative distinction between the different heating mechanisms. HIFI observations of mid-J transitions of CO and HCO+ isotopes allow us to bridge the gap in excitation energies between observations from the ground, characterizing the cooler gas, and existing ISO LWS spectra, constraining the properties of the hot gas. Comparing the detailed line profiles allows to identify the physical structure of the different components. In spite of the known shock-excitation of H2 and the clearly visible strong outflow, we find that the emission of all lines up to > 2 THz can be explained by purely radiative heating of the material. However, the new Herschel/HIFI observations reveal two types of excitation conditions. We find hot and dense clumps close to the central cluster, probably dynamically affected by the outflow, and a more widespread distribution of cooler, but nevertheless dense, molecular clumps.Comment: Accepted for publication by A&

Herschel observations in the ultracompact HII region Mon R2: Water in dense Photon-dominated regions (PDRs)

Mon R2, at a distance of 830 pc, is the only ultracompact HII region (UC HII) where the photon-dominated region (PDR) between the ionized gas and the molecular cloud can be resolved with Herschel. HIFI observations of the abundant compounds 13CO, C18O, o-H2-18O, HCO+, CS, CH, and NH have been used to derive the physical and chemical conditions in the PDR, in particular the water abundance. The 13CO, C18O, o-H2-18O, HCO+ and CS observations are well described assuming that the emission is coming from a dense (n=5E6 cm-3, N(H2)>1E22 cm-2) layer of molecular gas around the UC HII. Based on our o-H2-18O observations, we estimate an o-H2O abundance of ~2E-8. This is the average ortho-water abundance in the PDR. Additional H2-18O and/or water lines are required to derive the water abundance profile. A lower density envelope (n~1E5 cm-3, N(H2)=2-5E22 cm-2) is responsible for the absorption in the NH 1_1-0_2 line. The emission of the CH ground state triplet is coming from both regions with a complex and self-absorbed profile in the main component. The radiative transfer modeling shows that the 13CO and HCO+ line profiles are consistent with an expansion of the molecular gas with a velocity law, v_e =0.5 x (r/Rout)^{-1} km/s, although the expansion velocity is poorly constrained by the observations presented here.Comment: 4 pages, 5 figure

HIFI spectroscopy of low-level water transitions in M82

We present observations of the rotational ortho-water ground transition, the two lowest para-water transitions, and the ground transition of ionised ortho-water in the archetypal starburst galaxy M82, performed with the HIFI instrument on the Herschel Space Observatory. These observations are the first detections of the para-H2O(111-000) (1113\,GHz) and ortho-H2O+(111-000) (1115\,GHz) lines in an extragalactic source. All three water lines show different spectral line profiles, underlining the need for high spectral resolution in interpreting line formation processes. Using the line shape of the para-H2O(111-000) and ortho-H2O+(111-000) absorption profile in conjunction with high spatial resolution CO observations, we show that the (ionised) water absorption arises from a ~2000 pc^2 region within the HIFI beam located about ~50 pc east of the dynamical centre of the galaxy. This region does not coincide with any of the known line emission peaks that have been identified in other molecular tracers, with the exception of HCO. Our data suggest that water and ionised water within this region have high (up to 75%) area-covering factors of the underlying continuum. This indicates that water is not associated with small, dense cores within the ISM of M82 but arises from a more widespread diffuse gas component.Comment: 5 pages, 4 figures. Accepted for publication in A&

The origin of the [C II] emission in the S140 PDRs - new insights from HIFI

Using Herschel's HIFI instrument we have observed [C II] along a cut through S140 and high-J transitions of CO and HCO+ at two positions on the cut, corresponding to the externally irradiated ionization front and the embedded massive star forming core IRS1. The HIFI data were combined with available ground-based observations and modeled using the KOSMA-tau model for photon dominated regions. Here we derive the physical conditions in S140 and in particular the origin of [C II] emission around IRS1. We identify three distinct regions of [C II] emission from the cut, one close to the embedded source IRS1, one associated with the ionization front and one further into the cloud. The line emission can be understood in terms of a clumpy model of photon-dominated regions. At the position of IRS1, we identify at least two distinct components contributing to the [C II] emission, one of them a small, hot component, which can possibly be identified with the irradiated outflow walls. This is consistent with the fact that the [C II] peak at IRS1 coincides with shocked H2 emission at the edges of the outflow cavity. We note that previously available observations of IRS1 can be well reproduced by a single-component KOSMA-tau model. Thus it is HIFI's unprecedented spatial and spectral resolution, as well as its sensitivity which has allowed us to uncover an additional hot gas component in the S140 region.Comment: accepted for publication in Astronomy and Astrophysics (HIFI special issue

Gas morphology and energetics at the surface of PDRs: new insights with Herschel observations of NGC 7023

We investigate the physics and chemistry of the gas and dust in dense photon-dominated regions (PDRs), along with their dependence on the illuminating UV field. Using Herschel-HIFI observations, we study the gas energetics in NGC 7023 in relation to the morphology of this nebula. NGC 7023 is the prototype of a PDR illuminated by a B2V star and is one of the key targets of Herschel. Our approach consists in determining the energetics of the region by combining the information carried by the mid-IR spectrum (extinction by classical grains, emission from very small dust particles) with that of the main gas coolant lines. In this letter, we discuss more specifically the intensity and line profile of the 158 micron (1901 GHz) [CII] line measured by HIFI and provide information on the emitting gas. We show that both the [CII] emission and the mid-IR emission from polycyclic aromatic hydrocarbons (PAHs) arise from the regions located in the transition zone between atomic and molecular gas. Using the Meudon PDR code and a simple transfer model, we find good agreement between the calculated and observed [CII] intensities. HIFI observations of NGC 7023 provide the opportunity to constrain the energetics at the surface of PDRs. Future work will include analysis of the main coolant line [OI] and use of a new PDR model that includes PAH-related species.Comment: Accepted for publication in Astronomy and Astrophysics Letters (Herschel HIFI special issue), 5 pages, 5 figure