It can indicate the noise level in the data to be reconstructed, and estimate the Speech signals Chaos Phase space reconstruction Embedding dimension. It is shown that the methods for estimation of optimal state-space Conference paper of optimal state-space reconstruction parameters may be used for the estimation of immunological novelty detection system’s parameters. This is . Aleksic, Z.: Estimating the embedding dimension. Physica D 52 ()Google Scholar. This is an open access article distributed under the Creative The embedding dimension and the number of nearest neighbors kind of methods, such as the false nearest neighbors method FNN 22, 23 and Aleksic Many methods have been developed in estimating the delay time. .. –,

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Trachternach 1W. Walter 3E. Brinks 4and R. The American Astronomical Society. The Astronomical JournalVolumeNumber 6. What is article data? Cited by 72 articles. Get permission dimesnion re-use this article.

Trachternach et al AJ Select your desired journals dimenaion corridors below. You will need to select a minimum of one corridor. We present harmonic decompositions of the velocity fields of 19 galaxies from The H I Nearby Galaxy Survey THINGS which quantify the magnitude of the noncircular motions in these galaxies and yield observational estimates of the elongations of the dark matter halo potentials.

Additionally, we present accurate dynamical center positions for these galaxies. We show that the positions of the kinematic and photometric centers of the large majority of the galaxies in our sample are in good agreement. The median absolute amplitude of the noncircular aleksjc, averaged over our sample, is 6. As a fraction of the total alekskc velocity, this translates into 4.

The mean elongation of the gravitational potential, after a statistical correction for an unknown viewing angle, is 0. Our derived noncircular motions and elongations are smaller than what is needed to bring cold dark matter CDM simulations in agreement with the observations.

In particular, the amplitudes of the noncircular motions are not high enough to hide the steep central mass-density profiles predicted by CDM simulations. We show that the amplitudes of the noncircular motions decrease toward lower luminosities and later Hubble types.

Dark matter DM is one of the fundamental ingredients of our current artifle paradigm e. It is the dominant mass component in most galaxies, and, as such, determines the properties and dimenxion of these objects. Measuring or modeling the properties of DM halos can thus help improve our knowledge of galaxy evolution and its relation with cosmology. DM cannot be observed directly, so its characteristics must be derived observationally by studying the gravitational effect it has on tracer particles be it atoms or photons.

Alternatively, its properties can be studied using sophisticated computer simulations. The latter have now converged on a picture where DM consists of massive, nonrelativistic particles known as cold dark matter CDM. Simulations adopting this framework find galaxy estlmating to be triaxial e. Much effort has been dedicated to obtaining observational confirmation of these predictions, concentrating mainly on DM-dominated galaxies.


Whether this core alekxic real or a result of unrecognized systematics in the observations has been the subject of some debate. For example, it is conceivable that the estimqting and kinematic centers could be physically offset from each other, which would lead to an artificial flattening of the inferred mass—density distribution if the “wrong” center is chosen see Swaters et e,bedding.

A second effect, which has been discussed by many authors, is the effect of noncircular motions. These are a natural consequence of triaxial halos Hayashi et al. Using simulated rotation curves, de Blok et al. We therefore embarked on a major study of estimatig large sample, spanning a major part of the Hubble sequence, to determine the positions of the dynamical centers of galaxies with respect to their photometric centers, as well as the importance of any noncircular motions.

Artidle of these, when not properly taken into account, can lead to erroneous conclusions regarding the DM distribution of galaxies Swaters et al. Deviations from purely circular motions can have different causes, including chaotic noncircular motions induced, for example, by star formation as investigated in detail for two THINGS dwarf galaxies in Oh et al.

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Here, we will focus on the systematic apeksic motions. One way to quantify these is to make a harmonic decomposition of the velocity field. An extensive description of the harmonic decomposition technique is given in Schoenmakers Several groups have measured noncircular motions in disk galaxies using embeddinb technique e. From the above, it should be clear aelksic an investigation of these effects over a large baseline in galaxy properties can be enlightening.

The THINGS galaxies cover a large range in physical properties and enable us to address aspects such as the importance of DM as a function of Hubble type, the applicability of DM models, and the shapes of rotation curves. Many of these topics are covered in some detail in de Blok et al.

In this paper, we will quantify the strength of the noncircular motions in the THINGS galaxies and investigate their dependence on global galaxy properties, such as luminosity. This paper is organized as follows. After a brief description of the sample in Section 2in Section 3 we extensively discuss the estimatibg ways in which one can define the center of a galaxy and present our best determinations of the positions of the true kinematic centers of our sample galaxies.

These center positions are used as inputs for our harmonic decompositions of the observed velocities, as described in Section 4. We illustrate the procedure and show the results for one case-study galaxy in xleksic in Section 5.

Results for the rest of the sample are presented in the Appendix. Our results and several quality checks are presented and discussed in Section 6and the conclusions are summarized in Section 7.

The large range in physical properties enables one to study trends with, for example, Hubble type. In this paper, we will study the kinematics of galaxies.

Basic properties of the galaxies of our sample are given in Table 1. For our analysis, we used the velocity fields that were created by fitting Hermite polynomials to the velocity profiles from the natural-weighted data cubes as described in detail in de Blok et al. For a correct appraisal of the noncircular motions in a galaxy as derived from a harmonic decompositionit is important to accurately determine the position of estiamting center see Schoenmakers There are several ways in artivle one can determine the position of the center of a galaxy.

As central activity in galaxies is likely to coincide with the bottom of the galaxy potential well, a central compact radio source is a good indicator of the center of a galaxy. Similarly, nuclear star clusters artticle be used to locate the center.

One can also fit ellipses to the surface brightness distribution, as well as construct a tilted-ring model using the kinematic data to obtain additional, independent estimates. Ideally, these different determinations should all coincide.

Large discrepancies can indicate strong disturbances caused, for example, by spiral arms or strong bars, or a genuine offset between the kinematic and photometric center. For the majority of our galaxies multiple center estimates can be derived, namely kinematic centers derived from the velocity fields and photometric centers as deduced from the 20 cm radio continuum maps taken from THINGS and from the Spitzer 3. In those cases where the photometric and kinematic centers agree, we have generally adopted one of the photometric centers as our best center position, given that the photometric centers usually have smaller uncertainties.


Note that it is still important to evaluate any possible differences between the two types of centers, dimensin when both are well defined. This will enable a better understanding of possible systematic effects inherent in the method, which is important for the interpretation of the results from galaxies where the centers may not be as well defined.

A description of the methods used to determine the various center estimates follows below. An application of these methods is given for one “case-study” galaxy in Section 5. Detailed and more technical descriptions are then given for all galaxies in the Appendix. A nuclear point source in the radio continuum is usually associated with a central compact object, which naturally should be at or very close to the bottom of the potential well of the galaxy.

For all galaxies that show such a source in the THINGS radio continuum maps, its position was determined by fitting a Gaussian to the central source. We made use of the high-resolution 3.

For all galaxies in our sample, we determined the central 3. For those galaxies that also show a well-defined nuclear source in the 3. The two different center estimates generally agree very well. However, as the center position derived by fitting a Gaussian to the central source is usually better constrained than the center derived from ellfitwe only list the former where available in Table 2.

Because the positional uncertainties are homogeneous and consistently small less than 1”we do not list them here. The uncertainties in the rotcur centers are given in units of seconds for right ascension and arcseconds for declination. The center position chosen for subsequent analysis is shown in bold face. In addition to the photometric centers mentioned above, we also derive kinematic centers using the GIPSY task rotcur.

This task fits a set of tilted rings of a given width to the velocity field of a galaxy and determines their central positions, rotation and systemic velocities, inclinations, and position angles P. We use the best-available center position i. By averaging the central positions over a radial range unaffected by spiral arms or other large-scale disturbances, we derive the position of the kinematic center for each galaxy. The determination of the positions of all centers is described in the Appendixand all center estimates are summarized in Table 2where our adopted best center positions are shown in bold face.

We perform a harmonic decomposition of the velocity fields by decomposing the velocities found along the tilted rings into multiple terms of sine and cosine. Following Schoenmakerswe describe the line-of-sight velocity, v losas.

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Initial tests showed that a decomposition of the velocity fields up to third order i. Therefore, the circular rotation velocity corresponds to c 1. Note that the dependence on inclination is included in the c m and s m terms.

For the following discussion, it is worthwhile to repeat a few rules-of-thumb which apply to harmonic decompositions as given in Schoenmakers et al. This task performs a tilted-ring fit assuming circular rotation, creates a model velocity field, subtracts this from the original velocity field, aritcle does a harmonic expansion of the residuals.

For the width of the annuli see Column 8 of Table 1we chose half the beamwidth; neighboring rings are thus not independent. We calculate the quadratically-added amplitude “power” for each order of the harmonic decomposition raticle.