Response to Comment on `Undamped electrostatic plasma waves' [Phys. Plasmas 19, 092103 (2012)]

Numerical and experimental evidence is given for the occurrence of the plateau states and concomitant corner modes proposed in \cite{valentini12}. It is argued that these states provide a better description of reality for small amplitude off-dispersion disturbances than the conventional Bernstein-Greene-Kruskal or cnoidal states such as those proposed in \cite{comment

Where are the Baryons?

New, high resolution, large-scale, cosmological hydrodynamic galaxy formation simulations of a standard cold dark matter model (with a cosmological constant) are utilized to predict the distribution of baryons at the present and at moderate redshift. It is found that the average temperature of baryons is an increasing function of time, with most of the baryons at the present time having a temperature in the range 10^{5-7} K. Thus, not only is the universe dominated by dark matter, but more than one half of the normal matter is yet to be detected. Detection of this warm/hot gas poses an observational challenge, requiring sensitive EUV and X-ray satellites. Signatures include a soft, cosmic X-ray background, apparent warm components in hot clusters due to both intrinsic warm intra-cluster gas and warm inter-cluster gas projected onto clusters along the line of sight, absorption lines in X-ray and UV quasar spectra [e.g., O VI (1032,1038)A lines, OVII 574 eV line], strong emission lines (e.g., O VIII 653 eV line) and low redshift, broad, low column density \lya absorption lines. We estimate that approximately 1/4 of the extragalactic soft X-ray background (SXRB) (at 0.7 keV) arises from the warm/hot gas, half of it coming from $z<0.65$ and three-quarters from $z<1.00$, so the source regions should be identifiable on deep optical images.Comment: ApJ in press, revised (fig 3 is in jpg). Whole paper including fig3.ps can be obtained at "http://astro.princeton.edu/~cen/PAPERS_TO_APPEAR/64

The Energy of a Plasma in the Classical Limit

When \lambda_{T} << d_{T}, where \lambda_{T} is the de Broglie wavelength and d_{T}, the distance of closest approach of thermal electrons, a classical analysis of the energy of a plasma can be made. In all the classical analysis made until now, it was assumed that the frequency of the fluctuations \omega << T (k_{B}=\hbar=1). Using the fluctuation-dissipation theorem, we evaluate the energy of a plasma, allowing the frequency of the fluctuations to be arbitrary. We find that the energy density is appreciably larger than previously thought for many interesting plasmas, such as the plasma of the Universe before the recombination era.Comment: 10 pages, 2 figures, accepted for publication in Phys.Rev.Let

Undamped electrostatic plasma waves

Electrostatic waves in a collision-free unmagnetized plasma of electrons with fixed ions are investigated for electron equilibrium velocity distribution functions that deviate slightly from Maxwellian. Of interest are undamped waves that are the small amplitude limit of nonlinear excitations, such as electron acoustic waves (EAWs). A deviation consisting of a small plateau, a region with zero velocity derivative over a width that is a very small fraction of the electron thermal speed, is shown to give rise to new undamped modes, which here are named {\it corner modes}. The presence of the plateau turns off Landau damping and allows oscillations with phase speeds within the plateau. These undamped waves are obtained in a wide region of the $(k,\omega_{_R})$ plane ($\omega_{_R}$ being the real part of the wave frequency and $k$ the wavenumber), away from the well-known `thumb curve' for Langmuir waves and EAWs based on the Maxwellian. Results of nonlinear Vlasov-Poisson simulations that corroborate the existence of these modes are described. It is also shown that deviations caused by fattening the tail of the distribution shift roots off of the thumb curve toward lower $k$-values and chopping the tail shifts them toward higher $k$-values. In addition, a rule of thumb is obtained for assessing how the existence of a plateau shifts roots off of the thumb curve. Suggestions are made for interpreting experimental observations of electrostatic waves, such as recent ones in nonneutral plasmas.Comment: 11 pages, 10 figure

Phase transition in the collisionless regime for wave-particle interaction

Gibbs statistical mechanics is derived for the Hamiltonian system coupling self-consistently a wave to N particles. This identifies Landau damping with a regime where a second order phase transition occurs. For nonequilibrium initial data with warm particles, a critical initial wave intensity is found: above it, thermodynamics predicts a finite wave amplitude in the limit of infinite N; below it, the equilibrium amplitude vanishes. Simulations support these predictions providing new insight on the long-time nonlinear fate of the wave due to Landau damping in plasmas.Comment: 12 pages (RevTeX), 2 figures (PostScript

Nonlinear saturation of electrostatic waves: mobile ions modify trapping scaling

The amplitude equation for an unstable electrostatic wave in a multi-species Vlasov plasma has been derived. The dynamics of the mode amplitude $\rho(t)$ is studied using an expansion in $\rho$; in particular, in the limit $\gamma\rightarrow0^+$, the singularities in the expansion coefficients are analyzed to predict the asymptotic dependence of the electric field on the linear growth rate $\gamma$. Generically $|E_k|\sim \gamma^{5/2}$, as $\gamma\rightarrow0^+$, but in the limit of infinite ion mass or for instabilities in reflection-symmetric systems due to real eigenvalues the more familiar trapping scaling $|E_k|\sim \gamma^{2}$ is predicted.Comment: 13 pages (Latex/RevTex), 4 postscript encapsulated figures which are included using the utility "uufiles". They should be automatically included with the text when it is downloaded. Figures also available in hard copy from the authors ([email protected]

Nuclear Disks of Gas and Dust in Early Type Galaxies and the Hunt for Massive Black Holes: Hubble Space Telescope Observations of NGC 6251

We discuss Hubble Space Telescope optical images and spectra of NGC 6251, a giant E2 galaxy and powerful radio source at a distance of 106 Mpc (for H_0 = 70 km/s/Mpc). The galaxy is known to host a very well defined dust disk (O'Neil et al. 1994); the exceptional resolution of our V and I images allows a detailed study of the disk structure. Furthermore, narrow band images centered on the Halpha+[NII] emission lines, reveal the presence of ionized gas in the inner 0.3 arcsec of the disk. We used the HST/Faint Object Spectrograph with the 0.09 arcsec aperture to study the velocity structure of the disk. Dynamical models were constructed for two extreme (in terms of central concentration) analytical representations of the stellar surface brightness profile, from which the mass density and corresponding rotational velocity are derived assuming a constant mass-to-light ratio (M/L)_V ~ 8.5 M_solar/L_solar. For both representations of the stellar component, the models show that the gas is in Keplerian motion around a central mass ~ 4 - 8 X 10^8 solar masses, and that the contribution of radial flows to the velocity field is negligible.Comment: 45 pages, submitted to Ap

Nocturia as an Unrecognized Symptom of Uncontrolled Hypertension in Black Men Aged 35 to 49&nbsp;Years.

Background Hypertension is assumed to be asymptomatic. Yet, clinically significant nocturia (≥2 nightly voids) constitutes a putative symptom of uncontrolled hypertension. Black men with hypertension may be prone to nocturia because of blunted nocturnal blood pressure ( BP ) dipping, diuretic drug use for hypertension, and comorbidity that predisposes to nocturia. Here, we test the hypothesis that nocturia is a common and potentially reversible symptom of uncontrolled hypertension in black men. Methods and Results We determined the strength of association between nocturia (≥2 nightly voids) and high BP (≥135/85&nbsp;mm&nbsp;Hg) by conducting in-person health interviews and measuring BP with an automated monitor in a large community-based sample of black men in their barbershops. Because nocturia is prevalent and steeply age-dependent after age 50&nbsp;years, we studied men aged 35 to 49&nbsp;years. Among 1673 black men (mean age, 43±4&nbsp;years [ SD ]), those with hypertension were 56% more likely than men with normotension to have nocturia after adjustment for diabetes mellitus and sleep apnea (adjusted odds ratio, 1.56; 95% CI , 1.25-1.94 [ P&lt;0.0001]). Nocturia prevalence varied by hypertension status, ranging from 24% in men with normotension to 49% in men whose hypertension was medically treated but uncontrolled. Men with untreated hypertension were 39% more likely than men with normotension to report nocturia ( P=0.02), whereas men whose hypertension was treated and controlled were no more likely than men with normotension to report nocturia ( P=0.69). Conclusions Uncontrolled hypertension was an independent determinant of clinically important nocturia in a large cross-sectional community-based study of non-Hispanic black men aged 35 to 49&nbsp;years. Clinical Trial Registration URL : http://www.clinicaltrials.gov . Unqiue identifier: NCT 02321618