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Ionization compression impact on dense gas distribution and star formation, Probability density functions around H ii regions as seen by Herschel

Tremblin, P.; Schneider, N.; Minier, V.; Didelon, P.; Hill, T.; Anderson, L. D.; Motte, F.; Zavagno, A.; André, Ph.; Arzoumanian, D.; Audit, E.; Benedettini, M.; Bontemps, S.; Csengeri, T.; Di Francesco, J.; Giannini, T.; Hennemann, M.; Luong, Q. Nguyen;
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 28/01/2014 Português
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Ionization feedback should impact the probability distribution function (PDF) of the column density around the ionized gas. We aim to quantify this effect and discuss its potential link to the Core and Initial Mass Function (CMF/IMF). We used in a systematic way Herschel column density maps of several regions observed within the HOBYS key program: M16, the Rosette and Vela C molecular cloud, and the RCW 120 H ii region. We fitted the column density PDFs of all clouds with two lognormal distributions, since they present a double-peak or enlarged shape in the PDF. Our interpretation is that the lowest part of the column density distribution describes the turbulent molecular gas while the second peak corresponds to a compression zone induced by the expansion of the ionized gas into the turbulent molecular cloud. The condensations at the edge of the ionized gas have a steep compressed radial profile, sometimes recognizable in the flattening of the power-law tail. This could lead to an unambiguous criterion able to disentangle triggered from pre-existing star formation. In the context of the gravo-turbulent scenario for the origin of the CMF/IMF, the double peaked/enlarged shape of the PDF may impact the formation of objects at both the low-mass and the high-mass end of the CMF/IMF. In particular a broader PDF is required by the gravo-turbulent scenario to fit properly the IMF with a reasonable initial Mach number for the molecular cloud. Since other physical processes (e.g. the equation of state and the variations among the core properties) have already been suggested to broaden the PDF...

Viscous Instanton for Burgers' Turbulence

Balkovsky, E.; Falkovich, G.; Kolokolov, I.; Lebedev, V.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 31/03/1996 Português
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We consider the tails of probability density functions (PDF) for different characteristics of velocity that satisfies Burgers equation driven by a large-scale force. The saddle-point approximation is employed in the path integral so that the calculation of the PDF tails boils down to finding the special field-force configuration (instanton) that realizes the extremum of probability. We calculate high moments of the velocity gradient $\partial_xu$ and find out that they correspond to the PDF with $\ln[{\cal P}(\partial_xu)]\propto-(-\partial_xu/{\rm Re})^{3/2}$ where ${\rm Re}$ is the Reynolds number. That stretched exponential form is valid for negative $\partial_xu$ with the modulus much larger than its root-mean-square (rms) value. The respective tail of PDF for negative velocity differences $w$ is steeper than Gaussian, $\ln{\cal P}(w)\sim-(w/u_{\rm rms})^3$, as well as single-point velocity PDF $\ln{\cal P}(u)\sim-(|u|/u_{\rm rms})^3$. For high velocity derivatives $u^{(k)}=\partial_x^ku$, the general formula is found: $\ln{\cal P}(|u^{(k)}|)\propto -(|u^{(k)}|/{\rm Re}^k)^{3/(k+1)}$.; Comment: 15 pages, RevTeX 3.0

Intermittent scaling of the probability density function tail of the Kardar-Parisi-Zhang equation

Anderson, Johan; Johansson, Jonas
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
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This letter provides the first analytical estimation of the probability density function (PDF) tail of the interface width in the Kardar-Parisi-Zhang equation in the regime of strongly non-linear growth. We find that the PDF tail is proportional to $\exp{- c w_2^{3/2}}$. In addition, the effect of spatial dimensions on the PDF tail scaling is dicussed. The PDF tail is computed by the instanton method within the Martin-Rose-Siggia framework using a careful treatment of the non-linear term. This gives a novel approach to understand the rightmost PDF tail of the interface width distribution and the analysis suggests that there is no limit in the upper critical dimension.; Comment: 6 pages, 2 figures, submitted to EPL

Observational Diagnostics of Self-Gravitating MHD Turbulence in Giant Molecular Clouds

Burkhart, Blakesley; Collins, David C.; Lazarian, Alex
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 14/05/2015 Português
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We study the observable signatures of self-gravitating MHD turbulence by applying the probability density functions (PDFs) and the spatial density power spectrum to synthetic column density maps. We find that there exists three characterizable stages of the evolution of the collapsing cloud which we term "early," "intermediate," and "advanced." At early times, i.e. $t<0.15t_{ff}$, the column density has a power spectral slope similar to nongravitating supersonic turbulence and a lognormal distribution. At an intermediate stage, i.e. $0.15t_{ff}< t \leq 0.35t_{ff}$, there exists signatures of the prestellar cores in the shallower PDF and power spectrum power law slopes. The column density PDF power law tails at these times have line of sight averaged slopes ranging from -2.5 to -1.5 with shallower values belonging to simulations with lower magnetic field strength. The density power spectrum slope becomes shallow and can be characterized by $P(k)=A_1k^{\beta_2}e^{-k/k_c}$, where $A_1$ describes the amplitude, $k^{\beta_2}$ describes the classical power law behavior and the scale $k_c$ characterizes the turn over from turbulence dominated to self-gravity dominated. At advanced stages of collapse, i.e. $\approx t>0.35t_{ff}$, the power spectral slope is positive valued...

Incorporating Photometric Redshift Probability Density Information into Real-Space Clustering Measurements

Myers, Adam D; White, Martin; Ball, Nicholas M.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
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The use of photometric redshifts in cosmology is increasing. Often, however these photo-zs are treated like spectroscopic observations, in that the peak of the photometric redshift, rather than the full probability density function (PDF), is used. This overlooks useful information inherent in the full PDF. We introduce a new real-space estimator for one of the most used cosmological statistics, the 2-point correlation function, that weights by the PDF of individual photometric objects in a manner that is optimal when Poisson statistics dominate. As our estimator does not bin based on the PDF peak it substantially enhances the clustering signal by usefully incorporating information from all photometric objects that overlap the redshift bin of interest. As a real-world application, we measure QSO clustering in the Sloan Digital Sky Survey (SDSS). We find that our simplest binned estimator improves the clustering signal by a factor equivalent to increasing the survey size by a factor of 2-3. We also introduce a new implementation that fully weights between pairs of objects in constructing the cross-correlation and find that this pair-weighted estimator improves clustering signal in a manner equivalent to increasing the survey size by a factor of 4-5. Our technique uses spectroscopic data to anchor the distance scale and it will be particularly useful where spectroscopic data (e.g...

Evolution of Cosmological Density Distribution Function from the Local Collapse Model

Ohta, Yasuhiro; Kayo, Issha; Taruya, Atsushi
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 29/01/2003 Português
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We present a general framework to treat the evolution of one-point probability distribution function (PDF) for cosmic density $\delta$ and velocity-divergence fields $\theta$. In particular, we derive an evolution equation for the one-point PDFs and consider the stochastic nature associated with these quantities. Under the local approximation that the evolution of cosmic fluid fields can be characterized by the Lagrangian local dynamics with finite degrees of freedom, evolution equation for PDFs becomes a closed form and consistent formal solutions are constructed. Adopting this local approximation, we explicitly evaluate the one-point PDFs $P(\delta)$ and $P(\theta)$ from the spherical and the ellipsoidal collapse models as the representative Lagrangian local dynamics. In a Gaussian initial condition, while the local density PDF from the ellipsoidal model almost coincides with the that of the spherical model, differences between spherical and ellipsoidal collapse model are found in the velocity-divergence PDF. Importantly, the joint PDF of local density, $P(\delta,t;\delta',t')$, evaluated at the same Lagrangian position but at the different times $t$ and $t'$ from the ellipsoidal collapse model exhibits a large amount of scatter. The mean relation between $\delta$ and $\delta'$ does fail to match the one-to-one mapping obtained from spherical collapse model. Moreover...

An improved measurement of the flux distribution of the Ly-alpha forest in QSO absorption spectra: the effect of continuum fitting, metal contamination and noise properties

Kim, T. -S.; Bolton, J. S.; Viel, M.; Haehnelt, M. G.; Carswell, R. F.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 13/11/2007 Português
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We have performed an extensive Voigt profile analysis of the neutral hydrogen (HI) and metal absorption present in a sample of 18 high resolution, high signal-to-noise QSO spectra observed with VLT/UVES. We use this analysis to separate the metal contribution from the HI absorption and present an improved measurement of the flux probability distribution function (PDF) due to HI absorption alone at = 2.07, 2.52, and 2.94. The flux PDF is sensitive to the continuum fit in the normalised flux range 0.8 < F < 1.0 and to metal absorption at 0.2 < F < 0.8. Our new measurements of the flux PDF due to HI absorption alone are systematically lower at 0.2 < F < 0.8 by up to 30% compared to the widely used measurement of McDonald et al. (2000), based on a significantly smaller sample of Keck/HIRES data. This discrepancy is probably due to a combination of our improved removal of the metal absorption and cosmic variance, since variations in the flux PDF between different lines-of-sight are large. The HI effective optical depth at 1.7 < z < 4 is best fit with a single power law, (0.0023 +-0.0007) (1+z)^(3.65 +- 0.21), in good agreement with previous measurements from comparable data. As also found previously, the effect of noise on the flux distribution is not significant in high resolution...

The Probability Distribution Function of Light in the Universe: Results from Hydrodynamic Simulations

Ostriker, Jeremiah P.; Nagamine, Kentaro; Cen, Renyue; Fukugita, Masataka
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
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While second and higher order correlations of the light distribution have received extensive study, the lowest order probability distribution function (PDF) -- the probability that a unit volume of space will emit a given amount of light -- has received very little attention. We estimate this function with the aid of hydrodynamic simulations of the Lambda CDM model, finding it significantly different from the mass density PDF, and not simply related to it by linear bias or any of the other prescriptions commonly adopted. If the optical light PDF is, in reality, similar to what we find in the simulations, then some measures of Omega_M based on mass-to-light ratio and the cosmic virial theorem will have significantly underestimated Omega_M. Basically, the problem is one of selection bias, with galaxy forming regions being unrepresentative of the dark matter distribution in a way not described by linear bias. Knowledge of the optical PDF and the plausible assumption of a log-normal distribution for the matter PDF will allow one to correct for these selection biases. We find that this correction (which amounts to 20-30%) brings the values of Omega_M estimated by using the mass-to-light ratio and the cosmic virial theorem to the range 0.2-0.3...

Investigation of the errors in SDSS proper-motion measurements using samples of quasars

Dong, Ruobing; Gunn, James; Knapp, Gillian; Rockosi, Constance; Blanton, Michael
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 26/07/2011 Português
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We investigate in detail the probability distribution function (pdf) of the proper-motion measurement errors in the SDSS+USNO-B proper-motion catalog of \citet{mun04} using clean quasar samples. The pdf of the errors is well-represented by a Gaussian core with extended wings, plus a very small fraction ($<0.1%$) of "outliers". We find while formally the pdf could be well-fit by a five-parameter fitting function, for many purposes it is also adequately to represent the pdf with a one-parameter approximation to this function. We apply this pdf to the calculation of the confidence intervals on the true proper motion for a SDSS+USNO-B proper motion measurement, and discuss several scientific applications of the SDSS proper motion catalogue. Our results have various applications in studies of the galactic structure and stellar kinematics. Specifically, they are crucial for searching hyper-velocity stars in the Galaxy.; Comment: 26 pages (single column), 11 figures, accepted in AJ

Density Probability Distribution Functions in Supersonic Hydrodynamic and MHD Turbulence

Lemaster, M. Nicole; Stone, James M.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
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We study the probability distribution function (PDF) of the mass density in simulations of supersonic turbulence with properties appropriate for molecular clouds. For this study we use Athena, a new higher-order Godunov code. We find there are surprisingly similar relationships between the mean of the time-averaged PDF and the turbulent Mach number for driven hydrodynamic and strong-field MHD turbulence. There is, however, a large scatter about these relations, indicating a high level of temporal and spatial variability in the PDF. Thus, the PDF of the mass density is unlikely to be a good measure of magnetic field strength. We also find the PDF of decaying MHD turbulence deviates from the mean-Mach relation found in the driven case. This implies that the instantaneous Mach number alone is not enough to determine the statistical properties of turbulence that is out of equilibrium. The scatter about the mean-Mach relation for driven turbulence, along with the large departure of decaying turbulence PDFs from those of driven turbulence, may illuminate one factor contributing to the large observed cloud-to-cloud variation in the star formation rate per solar mass.; Comment: 4 pages, 2 figures, published in ApJL; corrected sign in eqn. (4)

The Gram-Charlier A Series based Extended Rule-of-Thumb for Bandwidth Selection in Univariate and Multivariate Kernel Density Estimations

C, Dharmani Bhaveshkumar
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 03/04/2015 Português
Relevância na Pesquisa
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The article derives a novel Gram-Charlier A (GCA) Series based Extended Rule-of-Thumb (ExROT) for bandwidth selection in Kernel Density Estimation (KDE). There are existing various bandwidth selection rules achieving minimization of the Asymptotic Mean Integrated Square Error (AMISE) between the estimated probability density function (PDF) and the actual PDF. The rules differ in a way to estimate the integration of the squared second order derivative of an unknown PDF $(f(\cdot))$, identified as the roughness $R(f''(\cdot))$. The simplest Rule-of-Thumb (ROT) estimates $R(f''(\cdot))$ with an assumption that the density being estimated is Gaussian. Intuitively, better estimation of $R(f''(\cdot))$ and consequently better bandwidth selection rules can be derived, if the unknown PDF is approximated through an infinite series expansion based on a more generalized density assumption. As a demonstration and verification to this concept, the ExROT derived in the article uses an extended assumption that the density being estimated is near Gaussian. This helps use of the GCA expansion as an approximation to the unknown near Gaussian PDF. The ExROT for univariate KDE is extended to that for multivariate KDE. The required multivariate AMISE criteria is re-derived using elementary calculus of several variables...

The momentum flux probability distribution function for ion-temperature-gradient turbulence

Anderson, Johan; Kim, Eun-jin
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 15/01/2009 Português
Relevância na Pesquisa
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There has been overwhelming evidence that coherent structures play a critical role in determining the overall transport in a variety of systems. We compute the probability distribution function (PDF) tails of momentum flux and heat flux in ion-temperature-gradient turbulence, by taking into account the interaction among modons, which are assumed to be coherent structures responsible for bursty and intermittent events, contributing to the PDF tails. The tail of PDF of momentum flux $R = < v_x v_y>$ is shown to be exponential with the form $\exp{\{-\xi R^{3/2}\}}$, which is broader than a Gaussian, similarly to what was found in the previous local studies. An analogous expression with the same functional dependence is found for the PDF tails of heat flux. Furthermore, we present a detailed numerical study of the dependence of the PDF tail on the temperature and density scale lengths and other physical parameters through the coefficient $\xi$.; Comment: 23 pages, 2 figures