arXiv subjects

K. Lehtinen

Publications and source records attributed to K. Lehtinen.

At least 19 recordsLinked to original sources

arXiv2023

Light and colour of cirrus, translucent and opaque dust in the high-latitude area of LDN 1642

We have performed a 5-colour surface photometric study of the high-galactic-latitude area of dark nebula LDN 1642. Scattered light properties are presented of diffuse, translucent and opaque dust over the range of 3500 -- 5500 A. Far infrared absolute photometry at 200 um improves the precision of and provides a zero point to the extinction. The intensity of the scattered light depends on dust column density in a characteristic way: for optically thin dust the intensity first increases linearly, then turns to a saturation value; at still larger extinctions the intensity turns down to a slow decrease. The $A_V$ value of the saturated intensity maximum shifts in a systematic way, from $A_V\approx$ 1.5 mag at 3500 A, to $\sim 3$ mag at 5500 A. The intensity curves offer a straight-forward explanation for the behaviour of the scattered-light colours. At the intensity peak the colour agrees with the integrated starlight colour, while it is bluer at the low- and redder at the high-column-density side of the peak, respectively. These colour changes are a direct consequence of the wavelength dependence of the extinction. We have compared the colours of the LDN 1642 area with other relevant observational studies: high-latitude diffuse/translucent clouds, wide-field cirrus dust; and externally illuminated AGB-star envelopes. For extragalactic low-surface-brightness sources cirrus is an unwanted foreground contaminant. Our results for cirrus colours can help to distinguish cases where a diffuse plume or stream, apparently associated with a galaxy or a group or cluster, is more likely a local cirrus structure. Keywords: ISM: dust, extinction -- ISM: clouds, individual LDN 1642 -- Galaxy: solar neighbourhood -- Astronomical instruments, methods and techniques: methods -- Physical data and processes: scattering

astro-ph.GA↗

arXiv2018

Optical and UV surface brightness of translucent dark nebulae: Dust albedo, radiation field and fluorescence emission by H2

Photometry of the nebulae LDN1780, LDN1642 and LBN406 is used to derive scattering properties of dust and to investigate the presence of UV fluorescence emission by molecular hydrogen and the extended red emission (ERE). We used multi-wavelength optical photometry and imaging at ground-based telescopes and archival imaging and spectroscopic UV data from the spaceborn GALEX and SPEAR/FIMS instruments. We used Monte Carlo RT and both observational data and synthetic models for the ISRF in the solar neighbourhood. The line-of-sight extinctions through the clouds have been determined using near infrared excesses of background stars and the 200/250um far infrared emission by dust measured using the ISO and Herschel space observatories. The optical surface brightness of the target clouds can be explained in terms of scattered light. The dust albedo ranges from 0.58 at 3500A to 0.72 at 7500A. The SED of LDN1780 is explained in terms of optical depth and background scattered light effects instead of ERE. The FUV surface brightness of LDN 1780 cannot be explained by scattered light only. In LDN1780 H2 fluorescent emission in the wavelength range 1400A-1700A has been detected and analysed. Our albedo values agree with the predictions of the dust model of Weingartner and Draine and with the THEMIS CMM model for evolved core-mantle grains. The H2 fluorescent emission in LDN1780 shows a pronounced dichotomy with a preference for its southern side where enhanced illumination impinges from the Sco OB2 association and the O star zeta Oph. A good correlation is found between the H2 fluorescence and a previously mapped 21-cm excess emission. The H2 fluorescence emission in LDN1780 has been modelled using a PDR code; the resulting values for H2 column density and the total gas density are consistent with the estimates derived from CO observations and optical extinction along the line of sight.

astro-ph.GA↗

arXiv2018

Digitization and astrometric calibration of Carte du Ciel photographic plates with Gaia~DR1

We want to study whether the astrometric and photometric accuracies obtained for the Carte du Ciel plates digitized with a commercial digital camera are high enough for scientific exploitation of the plates. We use a digital camera Canon EOS~5Ds, with a 100mm macrolens for digitizing. We analyze six single-exposure plates and four triple-exposure plates from the Helsinki zone of Carte du Ciel (+39 degr < delta < 47 degr). Each plate is digitized using four images, with a significant central area being covered twice for quality control purposes. The astrometric calibration of the digitized images is done with the data from the Gaia TGAS (Tycho-Gaia Astrometric Solution) of the first Gaia data release (Gaia DR1), Tycho-2, HSOY (Hot Stuff for One Year), UCAC5 (USNO CCD Astrograph Catalog), and PMA catalogs. The best astrometric accuracy is obtained with the UCAC5 reference stars. The astrometric accuracy for single-exposure plates is sigma(R.A.)=0.16" and sigma(Dec.)=0.15" expressed as a Gaussian deviation of the astrometric residuals. For triple-exposure plates the astrometric accuracy is sigma(R.A.)=0.12" and sigma(Dec.)=0.13". The 1-sigma uncertainty of photometric calibration is about 0.28 mag and 0.24 mag for single- and triple-exposure plates, respectively. We detect the photographic adjacency (Kostinsky) effect in the triple-exposure plates. We show that accuracies at least of the level of scanning machines can be achieved with a digital camera, without any corrections for possible distortions caused by our instrumental setup. This method can be used to rapidly and inexpensively digitize and calibrate old photographic plates enabling their scientific exploitation.

astro-ph.IM↗

arXiv2017

Extragalactic Background Light: a measurement at 400 nm using dark cloud shadow I. Low surface brightness spectrophotometry in the area of Lynds 1642

We present the method and observations for the measurement of the Extragalactic Background Light (EBL) utilizing the shadowing effect of a dark cloud. We measure the surface brightness difference between the opaque cloud core and its unobscured surroundings. In the difference the large atmospheric and Zodiacal light components are eliminated and the only remaining foreground component is the scattered starlight from the cloud itself. Although much smaller, its separation is the key problem in the method. For its separation we use spectroscopy. While the scattered starlight has the characteristic Fraunhofer lines and 400 nm discontinuity the EBL spectrum is smooth and without these features. Medium resolution spectrophotometry at $λ$ = 380 - 580 nm was performed with ${VLT}$/FORS at ESO of the surface brightness in and around the high-galactic-latitude dark cloud Lynds 1642. Besides the spectrum for the core with $A_V \ge 15$ mag, further spectra were obtained for intermediate-opacity cloud positions. They are used as proxy for the spectrum of the impinging starlight spectrum and facilitate the separation of the scattered starlight (cf. Paper II, Mattila et al. 2017b). Our spectra reach a precision of $\sim 0.5$ $10^{-9}$ erg cm$^{-2}$s$^{-1}$sr$^{-1}$Å$^{-1}$ as required to measure an EBL intensity in range of $\sim$1 to a few times $10^{-9}$ erg cm$^{-2}$s$^{-1}$sr$^{-1}$Å$^{-1}$. Because all surface brightness components are measured using the same equipment the method does not require unusually high absolute calibration accuracy, a condition which has been a problem for some previous EBL projects

astro-ph.CO↗

arXiv2017

Extragalactic background Light: a measurement at 400 nm using dark cloud shadow II. Spectroscopic separation of dark cloud's light, and results

In a project aimed at measuring the optical Extragalactic Background Light (EBL) we are using the shadow of a dark cloud.We have performed, with the ESO VLT/FORS, spectrophotometry of the surface brightness towards the high-galactic-latitude dark cloud Lynds 1642. A spectrum representing the difference between the opaque core of the cloud and several unobscured positions around the cloud was presented in Paper I (Mattila et al. 2017a). The topic of the present paper is the separation of the scattered starlight from the dark cloud itself which is the only remaining foreground component in this difference. While the scattered starlight spectrum has the characteristic Fraunhofer lines and the discontinuity at 400 nm, typical of integrated light of galaxies, the EBL spectrum is a smooth one without these features. As template for the scattered starlight we make use of the spectra at two semi-transparent positions. The resulting EBL intensity at 400 nm is $I_{\rm EBL} = 2.9\pm1.1$ $10^{-9}$ erg cm$^{-2}$s$^{-1}$sr$^{-1}$Å$^{-1}$, or $11.6\pm4.4$ nW m$^{-2}$sr$^{-1}$, which represents a 2.6$σ$ detection; the scaling uncertainty is +20%/-16%. At 520 nm we have set a 2$σ$ upper limit of $I_{\rm EBL} \le$4.5 $10^{-9}$ erg cm$^{-2}$s$^{-1}$sr$^{-1}$Å$^{-1}$ or $\le$23.4 nW m$^{-2}$sr$^{-1}$ +20%/-16%. Our EBL value at 400 nm is $\ge 2$ times as high as the integrated light of galaxies. No known diffuse light sources, such as light from Milky Way halo, intra-cluster or intra-group stars appear capable of explaining the observed EBL excess over the integrated light of galaxies.

astro-ph.GA↗

arXiv2012

Spectroscopy of diffuse light in dust clouds. Scattered light and the solar neighbourhood radiation field

The optical surface brightness of dark nebulae is mainly due to scattering of integrated starlight by classical dust grains. It contains information on the impinging interstellar radiation field, cloud structure, and grain scattering properties. We have obtained spectra of the scattered light from 3500 to 9000 Angstrom in two globules, the Thumbprint Nebula and DC303.8-14.2. We use observations of the scattered light to study the impinging integrated starlight spectrum as well as the scattered H-alpha and other line emissions from all over the sky. We search also for the presence of other than scattered light in the two globules. We obtained long-slit spectra encompassing the whole globule plus adjacent sky in a one-slit setting, thus enabling efficient elimination of airglow and other foreground sky components. We calculated synthetic integrated starlight spectra for the solar neighbourhood using HIPPARCOS-based stellar distributions and the spectral library of Pickles. Spectra are presented separately for the bright rims and dark cores of the globules. The continuum spectral energy distributions and absorption line spectra can be well modelled with the synthetic integrated starlight spectra. Emission lines of H-alpha + NII, H-beta, and SII are detected and are interpreted in terms of scattered light plus an in situ warm ionized medium component behind the globules. We detected an excess of emission over the wavelength range 5200-8000 Angstrom in DC303.8-14.2 but the nature of this emission remains open.

astro-ph.GA↗

arXiv2012

Observations of 6 - 200 μm emission of the Ophiuchus cloud LDN 1688

We examine two positions, ON1 and ON2, within the Ophiuchus cloud LDN 1688 using observations made with the ISOPHOT instrument aboard the ISO satellite. The data include mid-IR spectra (~6-12μm) and several photometric bands up to 200μm. The data probe the emission from molecular PAH-type species, transiently-heated Very Small Grains (VSGs), and large classical dust grains. We compare the observations to earlier studies, especially those carried out towards an isolated translucent cloud in Chamaeleon (Paper I). The spectra towards the two LDN 1688 positions are very similar to each other, in spite of position ON1 having a larger column density and probably being subjected to a stronger radiation field. The ratios of the mid-IR features are similar to those found in other diffuse and translucent clouds. Compared to paper I, the 7.7/11.3μm band ratios are lower, ~2.0, at both LDN 1688 positions. A continuum is detected in the ~10μm region. This is stronger towards the position ON1 but still lower than on any of the sightlines in Paper I. The far-infrared opacities are higher than for diffuse medium. The value of the position ON2, τ200/N(H) = 3.9 x 10^{-25} cm^2/H, is twice the value found for ON1. The radiation field of LDN 1688 is dominated by the two embedded B type double stars, ρ Oph AB and HD 147889, with an additional contribution from the Upper Sco OB association. The strong heating is reflected in the high colour temperature, ~24 K, of the large grain emission. Radiative transfer modelling confirms a high level of the radiation field and points to an increased abundance of PAH grains. However, when the hardening of the radiation field caused by the local B-stars is taken into account, the observations can be fitted with almost no change to the standard dust models. However, all the examined models underestimate the level of the mid-IR continuum.

astro-ph.GA↗

arXiv2010

Scattered H-alpha emission from a large translucent cloud G294-24

We study an undocumented large translucent cloud, detected by means of its enhanced radiation on the SHASSA (Southern H-Alpha Sky Survey Atlas) survey. We consider whether its excess surface brightness can be explained by light scattered off the dust grains in the cloud, or whether emission from in situ ionized gas is required. In addition, we aim to determine the temperature of dust, the mass of the cloud, and its possible star formation activity. We compare the observed H-alpha surface brightness of the cloud with predictions of a radiative transfer model. We use the WHAM (Wisconsin H-Alpha Mapper) survey as a source for the Galactic H-alpha interstellar radiation field illuminating the cloud. Visual extinction through the cloud is derived using 2MASS J, H, and K band photometry. We use far-IR ISOSS (ISO Serendipitous Survey), IRAS, and DIRBE data to study the thermal emission of dust. The LAB (The Leiden/Argentine/Bonn Galactic HI Survey) is used to study 21cm HI emission associated with the cloud. Radiative transfer calculations of the Galactic diffuse H-alpha radiation indicate that the surface brightness of the cloud can be explained solely by radiation scattered off dust particles in the cloud. The maximum visual extinction through the cloud is about 1.2mag. The cloud is found to be associated with 21cm HI emission at a velocity of about -9 km/s. The total mass of the cloud is about 550-1000 solar masses. There is no sign of star formation in this cloud. The distance of the cloud is estimated from the Hipparcos data to be about 100 pc.

astro-ph.GA↗

arXiv2008

Detection of 6 K gas in Ophiuchus D

Cold cores in interstellar molecular clouds represent the very first phase in star formation. The physical conditions of these objects are studied in order to understand how molecular clouds evolve and how stellar masses are determined. The purpose of this study is to probe conditions in the dense, starless clump Ophichus D (Oph D). The ground-state (1(10)-1(11)) rotational transition of ortho-H2D+ was observed with APEX towards the density peak of Oph D. The width of the H2D+ line indicates that the kinetic temperature in the core is about 6 K. So far, this is the most direct evidence of such cold gas in molecular clouds. The observed H2D+ spectrum can be reproduced with a hydrostatic model with the temperature increasing from about 6 K in the centre to almost 10 K at the surface. The model is unstable against any increase in the external pressure, and the core is likely to form a low-mass star. The results suggest that an equilibrium configuration is a feasible intermediate stage of star formation even if the larger scale structure of the cloud is thought to be determined by turbulent fragmentation. In comparison with the isothermal case, the inward decrease in the temperature makes smaller, i.e. less massive, cores susceptible to externally triggered collapse.

astro-ph↗

arXiv2007

ISO far infrared observations of the high latitude cloud L1642. II. Correlated variations of far-infrared emissivity and temperature of "classical large" dust particles

Our aim is to compare the infrared properties of big, ``classical'' dust grains with visual extinction in the cloud L1642. In particular, we study the differences of grain emissivity between diffuse and dense regions in the cloud. The far-infrared properties of dust are based on large-scale 100um and 200um maps. Extinction through the cloud has been derived by using the star count method at B- and I-bands, and color excess method at J, H and Ks bands. Radiative transfer calculations have been used to study the effects of increasing absorption cross-section on the far-infrared emission and dust temperature. Dust emissivity, measured by the ratio of far-infrared optical depth to visual extinction, tau(far-IR)/A(V), increases with decreasing dust temperature in L1642. There is about two-fold increase of emissivity over the dust temperature range of 19K-14K. Radiative transfer calculations show that in order to explain the observed decrease of dust temperature towards the centre of L1642 an increase of absorption cross-section of dust at far-IR is necessary.This temperature decrease cannot be explained solely by the attenuation of interstellar radiation field. Increased absorption cross-section manifests itself also as an increased emissivity. We find that, due to temperature effects, the apparent value of optical depth tau(far-IR), derived from 100um and 200um intensities, is always lower than the true optical depth.

astro-ph↗

arXiv2006

A comparison of density structures of a star forming and a non-star-forming globule. DCld303.8-14.2 and Thumbprint Nebula

We present a study of radial density structure of the star forming globule, DCld303.8-14.2 (DC303), and a non-star forming globule, Thumbprint Nebula (TPN), using near-infrared data taken with the ISAAC instrument on the Very Large Telescope. We derive the extinction through the globules using the color excess technique and examine the radial density distribution using Bonnor-Ebert and power-law models. The two globules have significantly different density structures. The extinction profile of DC303 is best fitted with a single power-law with an exponent p = 2.29 \pm 0.08. An unstable Bonnor-Ebert model with a dimensionless parameter ξ_max = 23 \pm 3 provides equally good fit to data. The extinction profile of TPN flattens at small radii, making the profile significantly different from the profile of DC303. We are unable to fit the Bonnor-Ebert model for TPN in a robust manner, but derive the lower limit ξ_max > 8 for the dimensionless outer edge. The density profile derived for TPN is typical compared to recently observed pre-protostellar globules, with high ξ_max value which could be interpreted as the presence of significant additional support or very slow contraction.

astro-ph↗

arXiv2006

Scattered H-alpha light from Galactic dust clouds

Bright emission nebulae, or HII regions, around hot stars are readily seen in H-alpha light. However, the all-pervasive faint H-alpha emission has only recently been detected and mapped over the whole sky. Mostly the H-alpha emission observed along a line of sight is produced by ionised gas in situ. There are, however, cases where all or most of the H-alpha radiation is due to scattering by electrons or dust particles which are illuminated by an H-alpha emitting source off the line of sight. Here we demonstrate that diffuse, translucent and dark dust clouds at high galactic latitudes are in many cases observed to have an excess of diffuse H-alpha surface brightness, i.e. they are brighter than the surrounding sky. We show that the majority of this excess surface brightness can be understood as light scattered off the interstellar dust grains. The source of incident photons is the general Galactic H-alpha background radiation impinging on the dust clouds from all over the sky.

astro-ph↗

arXiv2006

Detection of H2D+ in a massive prestellar core in Orion B

Aims. The purpose of this study is to examine the prediction that the deuterated H3+ ion, H2D+, can be found exclusively in the coldest regions of molecular cloud cores. This is also a feasibility study for the detection of the ground-state line of ortho-H2D+ at 372 GHz with APEX. Methods. The 1(10)-1(11) transition of H2D+ at 372 GHz was searched towards selected positions in the massive star forming cloud OriB9, in the dark cloud L183, and in the low- to intermediate mass star-forming cloud R CrA. Results. The line was detected in cold, prestellar cores in the regions of OriB9 and L183, but only upper limits were obtained towards other locations which either have elevated temperatures or contain a newly born star. The H2D+ detection towards OriB9 is the first one in a massive star-forming region. The fractional ortho-H2D+ abundances (relative to H2) are estimated to be about 1.0E-10 in two cold cores in OriB9, and 3.0E-10 in the cold core of L183. Conclusions. The H2D+ detection in OriB9 shows that also massive star forming regions contain very cold prestellar cores which probably have reached matured chemical composition characterized, e.g., by a high degree of deuterium fractionation. Besides as a tracer of the interior parts of prestellar cores, H2D+ may therefore be used to put contraints on the timescales related to massive star formation.

astro-ph↗

arXiv2006

C18O (3-2) observations of the Cometary Globule CG 12: a cold core and a C18O hot spot

The feasibility of observing the C18O (3-2) spectral line in cold clouds with the APEX telescope has been tested. As the line at 329.330 GHz lies in the wing of a strong atmospheric H2O absorption it can be observed only at high altitude observatories. Using the three lowest rotational levels instead of only two helps to narrow down the physical properties of dark clouds and globules. The centres of two C18O maxima in the high latitude low mass star forming region CG 12 were mapped in C18O (3-2) and the data were analyzed together with spectral line data from the SEST. The T_MB(3-2)/T_MB(2-1) ratio in the northern C18O maximum, CG 12 N, is 0.8, and in the southern maximum, CG 12 S, ~2. CG 12 N is modelled as a 120'' diameter (0.4pc) cold core with a mass of 27 Msun. A small size maximum with a narrow, 0.8 kms-1, C18O (3-2) spectral line with a peak temperature of T_MB ~11 K was detected in CG 12 S. This maximum is modelled as a 60'' to 80'' diameter (~0.2pc) hot (80 K < Tex < 200 K) ~1.6 Msun clump. The source lies on the axis of a highly collimated bipolar molecular outflow near its driving source. This is the first detection of such a compact, warm object in a low mass star forming region.

astro-ph↗

arXiv2006

Properties of dust in the high-latitude translucent cloud L1780 I: Spatially distinct dust populations and increased dust emissivity from ISO observations

We have analyzed the properties of dust in the high galactic latitude translucent cloud Lynds 1780 using ISOPHOT maps at 100 and 200 micrometers and raster scans at 60, 80, 100, 120, 150 and 200 micrometers. In far-infrared (FIR) emission, the cloud has a single core that coincides with the maxima of visual extinction and 200um optical depth. At the resolution of 3.0 arcmin, the maximum visual extinction is 4.0 mag. At the cloud core, the minimum temperature and the maximum 200um optical depth are 14.9+/-0.4 K and 2.0+/-0.2x10^{-3}, respectively, at the resolution of 1.5 arcmin. The cloud mass is estimated to be 18M_{SUN}. The FIR observations, combined with IRAS observations, suggest the presence of different, spatially distinct dust grain populations in the cloud: the FIR core region is the realm of the "classical" large grains, whereas the very small grains and the PAHs have separate maxima on the Eastern side of the cold core, towards the "tail" of this cometary-shaped cloud. The color ratios indicate an overabundance of PAHs and VSGs in L1780. Our FIR observations combined with the optical extinction data indicate an increase of the emissivity of the big grain dust component in the cold core, suggesting grain coagulation or some other change in the properties of the large grains. Based on our observations, we also address the question, to what extent the 80um emission and even the 100um and the 120um emission contain a contribution from the small-grain component.

astro-ph↗

arXiv2005

The ratio of N(C18O) and Av in Chamaeleon I and III-B using 2MASS and SEST

We investigate the relationship between the C18O column density and the visual extinction in Chamaeleon I and in a part of the Chamaeleon III molecular cloud. The C18O column densities, N(C18O), are calculated from J=1-0 rotational line data observed with the SEST telescope. The visual extinctions, Av, are derived using JHK photometry from the 2MASS survey and the NICER color excess technique. In contrast with the previous results of Hayakawa et al. (2001), we find that the average N(C18O) / Av ratios are similar in Cha I and Cha III, and lie close to values derived for other clouds, i.e. N(C18O) ~ 2 x 10^14 cm^-2 (Av - 2). We find, however, clear deviations from this average relationship towards individual clumps. Larger than average N(C18O) / Av ratios can be found in clumps associated with the active star forming region in the northern part of Ch a I. On the other hand, some regions in the relatively quiescent southern part of Cha I show smaller than average N(C18O) / Av ratios and also very shallow proportionality between N(C18O) and Av. The shallow proportionality suggests that C18O is heavily depleted in these regions. As the degree of depletion is proportional to the gas density, these regions probably contain very dense, cold cores, which do not stand out in CO mappings. A comparison with the dust temperature map derived from the ISO data shows that the most prominent of the potentially depleted cores indeed coincides with a dust temperature minimum. It seems therefore feasible to use N(C18O) and Av data together for identifying old, dense cores in large scale mappings.

astro-ph↗

arXiv2004

ISO observations of 3 - 200 micron emission by three dust populations in an isolated local translucent cloud

We present ISOPHOT spectrophotometry of three positions within the isolated high latitude cirrus cloud G 300.2 - 16.8, spanning from the near- to far-infrared. The positions exhibit contrasting emission spectrum contributions from the UIBs, very small grains and large classical grains, and both semi-empirical and numerical models are presented. At all three positions, the UIB spectrum shapes are found to be similar, and the large grain emission may be fitted by an equilibrium temperature of ~17.5 K. The energy requirements of both the observed emission spectrum and optical scattered light are shown to be satisfied by the incident local ISRF. The FIR emissivity of dust in G 300.2 - 16.8 is found to be lower than in globules or dense clouds, and is even lower than model predictions for dust in the diffuse ISM. The results suggest physical differences in the ISM mixtures between positions within the cloud, possibly arising from grain coagulation processes.

astro-ph↗

arXiv2003

Morphology and kinematics of Lynds 1642

The high latitude translucent molecular cloud L1642 has been mapped in the J=1-0 and J=2-1 transitions of 12CO, 13CO and C18O using the SEST radio telescope. We have analysed the morphology and velocity structure of the cloud using the Positive Matrix Factorization (PMF) method. The results show that L1642 is composed of a main structure at radial velocity 0.2 km/s while the higher velocity components at ~0.5 and 1.0 km/s form an incomplete ring around it, suggesting an expanding shell structure. Fainter emission extends to the north with a still higher velocity of up to 1.6 km/s. Such a velocity structure suggests an elongated morphology in the line of sight direction. The physical properties of the cloud have been investigated assuming LTE conditions, but non-LTE radiative transfer models are also constructed for the 13CO observations. We confirm that L1642 follows an r^-1 density distribution in its outer parts while the distribution is considerably flatter in the core. The cloud is close to virial equilibrium. In an Appendix the PMF results are compared with the view obtained through the analysis of channel maps and by the use of Principal Component Analysis (PCA). Both PMF and PCA present the observations as a linear combination of basic spectral shapes that are extracted from the data. Comparison of the methods shows that the PMF method in particular is able to produce a presentation of the complex velocity that is both compact and easily interpreted.

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