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NASA NTRS1993

Polarimetric thermal emission from rough surfaces

Recent theoretical works have suggested the potential of passive polarimetry in the remote sensing of geophysical media. It was shown that the third Stokes parameter U of the thermal emission may become larger for azimuthally asymmetric fields of observation. In order to investigate the potential applicability of passive polarimetry to the remote sensing of ocean surface, measurements of the polarimetric thermal emission from a sinusoidal water surface and a numerical study of the polarimetric thermal emission from randomly rough ocean surfaces were performed. Measurements of sinusoidal water surface thermal emission were performed using a sinusoidal water surface which was created by placing a thin sheet of fiberglass with a sinusoidal profile in two dimensions extended infinitely in the third dimension onto a water surface. The theory of thermal emission from a 'two-layer' periodic surface is derived and the exact solution is performed using both the extended boundary condition method (EBC) and the method of moments (MOM). The theoretical predictions are found to be in good agreement with the experimental results once the effects of the radiometer antenna pattern are included and the contribution of background noise to the measurements is modeled. The experimental results show that the U parameter indicates the direction of periodicity of the water surface and can approach values of up to 30 K for the surface observed. Next, a numerical study of polarimetric thermal emission from randomly rough surfaces was performed. A Monte Carlo technique utilizing an exact method for calculating thermal emission was chosen for the study to avoid any of the limitations of the commonly used approximate methods in rough surface scattering. In this Monte Carlo technique, a set of finite rough surface profiles in two dimensions with desired statistics was generated and extended periodically. The polarimetric thermal emission from each surface of the set was then calculated using both the EBC and the MOM and the results were averaged. The surface statistics chosen were intended to model a wind perturbed ocean surface in the X to Ku band microwave region. The results indicate that the U parameter is sensitive to the azimuthal angle between the surface periodicity and the looking angle and to the rms height of the surface, and that the U parameter is fairly insensitive to variations in polar angle, permittivity, surface power law spectrum, and surface spectrum high frequency cutoff. These properties give further strength to the idea of using the U parameter to detect wind direction over the ocean.

Johnson, J. T.↗
NASA NTRS1996

Physical and Optical/Radiative Characteristics of Aerosol and Cloud Particles in Tropical Cirrus: Importance in Radiation Balance

Whether cirrus clouds heat or cool the Earth-atmosphere system depends on the relative importance of the cloud shortwave albedo effect and the cloud thermal greenhouse effect. Both are determined by the distribution of ice condensate with cloud particle size. The microphysics instrument package flown aboard the NASA DC-8 in TOGA/COARE included an ice crystal replicator, a 2D Greyscale Cloud Particle Probe and a Forward Scattering Spectrometer Aerosol Probe. In combination, the electro-optical instruments permitted particle size measurements between 0.5 micrometer and 2.6 millimeter diameter. Ice crystal replicas were used to validate signals from the electrooptical instruments. Both optical and scanning electron microscopy were utilized to analyze aerosol and ice particle replicas between 0.1 micrometer and several 100 micrometer diameter. In first approximation, the combined aerosol-cloud particle spectrum in several clouds followed a power law N alpha D(sup -2.5). Thus, large cloud particles carried most of the condensate mass, while small cloud and aerosol particles determined the surface area. The mechanism of formation of small particles is growth of (hygroscopic, possibly ocean-derived) aerosol particles along the Kohler curves. The concentration of small particles is higher and less variable in space and time, and their tropospheric residence time is longer, than those of large cloud particles because of lower sedimentation velocities. Small particles shift effective cloud particle radii to sizes much smaller than the mean diameter of the cloud particles. This causes an increase in shortwave reflectivity and IR emissivity, and a decrease in transmissivity. Occasionally, the cloud reflectivity increased with altitude (decreasing temperature) stronger than did cloud emissivity, yielding enhanced radiative cooling at higher altitudes. Thus, cirrus produced by deep convection in the tropics may be critical in controlling processes whereby energy from warm tropical oceans is injected to different levels in the atmosphere to subsequently influence not only tropical but mid-latitude climate.

Pueschel, R. F.↗
NASA NTRS1991

Pair-density transitions in accretion disk coronae

The thermal and e(+)e(-)-pair equilibrium structure of two-temperature disk coronae above a cool (about 10 exp 6 K) disk around a black hole of 10 solar masses are investigated. Soft photons are assumed to be amply supplied from the cool disk. Two-pair thermal equilibrium points are found for a given proton column density: the low state with very small pair density and the high state dominated by pairs. Both states are thermally unstable, while for perturbations in pair density the high state is unstable and the low state is stable. Two possible scenarios are discussed for the fate of a two-temperature corona. When the proton optical depth is relatively small (e.g., less than 1) and the temperature of input soft photons is low (e.g., less than 10 exp 6 K), the corona will undergo a limit cycle between the high state and the low state on a time scale of milliseconds. As a consequence of Compton scattering of the soft photons, the emergent spectrum in the high state is rather flat with a big Wien bump at about 100 keV, whereas it is composed of a power-law component in the low state. Some observational consequences are briefly discussed in connection with the high-low spectral transition in Cyg X-1.

Kusunose, Masaaki↗
NASA NTRS1976

Diurnal variation of thermal plasma in the plasmasphere

All of the OGO-5 light ion density measurements were used to determine the average global topology of the equatorial plasmasphere density distribution. The variation of the light ion equatorial density at L less than or equal to 3.2 with local time was deduced by determining the average density observed within one hour of a specific local time and within 0.1 of a given L coordinate. The average H(+) density showed a semidiurnal variation with peaks near noon and midnight. The He(+) observations also revealed multiple peaks throughout the day but with smaller amplitudes than those of H(+). At L above 3.2 plasma trough conditions increase the scatter of densities. The average variation of the H(+) density with L within the plasmasphere is found to be steepest near midnight and can be least-squares fitted equally well to either an exponential variation or to a power law.

Chen, A. J.↗
NASA NTRS1989

Reddening and extinction towards H II regions

The light emitted by the gas in H II regions is attenuated by dust. This extinction can be measured by comparing H alpha, H beta, and radio continuum fluxes, since the intrinsic ratios of the Balmer line and thermal radio continuum emissivities are nearly constant for reasonable conditions in H II regions. In the case of giant extragalactic H II regions, the extinction was found to be considerably greater than expected. The dust between the Earth and the emitting gas may have an optical thickness which varies. The dust may be close enough to the source that scattered light contributes to the flux, or the dust may be actually mixed with the emitting gas. It is difficult to decide which configuration is correct. A rediscussion of this question in light of recent observations, with the Fabry-Perot spectrophotometers, of the large Galactic H II region is presented. The color excesses are compared for stars embedded in these H II regions with those derived (assuming the standard law) from the nebular extinction and reddening.

Caplan, James↗
NASA NTRS1996

The Geminga Pulsar: Soft X-Ray Variability and an EUVE Observation

We observed the Geminga pulsar with the EUVE satellite, detecting pulsed emission in the Deep Survey imager. Joint spectral fits of the EUVE flux with ROSAT PSPC data are consistent with thermal plus power-law models in which the thermal component makes the dominant contribution to the soft X-ray flux seen by EUVE and ROSAT. The data are consistent with blackbody emission of T = (4-6) x 10(exp 5) K over most of the surface of the star at the measured parallax distance of 160 pc. Although model atmospheres are more realistic, and can fit the data with effective temperatures a factor of 2 lower, current data would not discriminate between these and blackbody models. We also find evidence for variability of Geminga's soft X-ray pulse shape. Narrow dips in the light curve that were present in 1991 had largely disappeared in 1993/1994, causing the pulsed fraction to decline from 32% to 18%. If the dips are attributed to cyclotron resonance scattering by an e(+/-) plasma on closed magnetic field lines, then the process that resupplies that plasma must be variable.

Halpern, Jules P.↗
NASA NTRS1989

Infrared Emission from Comets

A brief discussion of the infrared observations from 4 to 20 micrometers of seven comets is presented. The observed infrared emission from comets depends primarily on their heliocentric distance. A model based on grain populations composed of a mixture of silicate and amorphous carbon particles in the mass ratio of about 40 to 1, with a power-law size distribution similar to that inferred for comet Halley, is applied to the observations. The model provides a good match to the observed heliocentric variation of both the 10 micrometers feature and the overall thermal emission from comets West and Halley. Matches to the observations of comet IRAS-Araki-Alcock and the antitail of comet Kohoutek require slightly larger grains. While the model does not match the exact profile and position of the 3.4 micrometers feature discovered in comet Halley, it does produce a qualitative fit to the observed variation of the feature's strength as a function of heliocentric distance. The calculations predict that the continuum under the 3.4 micrometers feature is due primarily to thermal emission from the comet dust when the comet is close to the Sun and to scattered solar radiation at large heliocentric distances, as is observed. A brief discussion of the determination of cometary grain temperatures from the observed infrared emission is presented. It is found that the observed shape of the emission curve from about 4 to 8 micrometers provides the best spectral region for estimating the cometary grain temperature distribution.

Swamy, K. S. Krishna↗
NASA NTRS2001

The Geminga Pulsar: Soft X-Ray Variability and an EUVE Observation

We observed the Geminga pulsar with the EUVE satellite, detecting pulsed emission in the Deep Survey imager. Joint spectral fits of the EUVE flux with ROSAT PSPC data are consistent with thermal plus power-law models in which the thermal component makes the dominant contribution to the soft X-ray flux seen by EUVE and ROSAT. The data are consistent with blackbody emission of T = (4 - 6) x 10(exp 5) K over most of the surface of the star at the measured parallax distance of 160 pc. Although model atmospheres are more realistic, and can fit the data with effective temperatures a factor of 2 lower, current data would not discriminate between these and blackbody models. We also find evidence for variability of Geminga's soft X-ray pulse shape. Narrow dips in the light curve that were present in 1991 had largely disappeared in 1993/1994, causing the pulsed fraction to decline from 32% to 18%. If the dips are attributed to cyclotron resonance scattering by an e1 plasma on closed magnetic field lines, then the process that resupplies that plasma must be variable.

Halpern, Jules P.↗
NASA NTRS1982

High-resolution X-ray observations of M87 - Nucleus, jet and radio halo

X-ray observations of M87 made using the Einstein Observatory HRI show the presence of four components. A broad, diffuse component associated with hot gas in the galaxy follows an approximate inverse power law; the pressure of the gas could be sufficient to confine the inner and outer radio lobes. A diffuse, asymmetrical X-ray distribution to the east and southwest appears similar to the radio morphology and is consistent with an inverse Compton model. An X-ray source centered on the nucleus of the galaxy is extended by 2-3 arcsec and may be due to thermal bremsstrahlung; a possible compact source of less than 10 to the 41st ergs/sec is weak compared with other active galaxies, and its implications for the presence of a massive black hole are discussed. A structure correlated with the radio-optical jet is also seen; the X-ray flux is consistent with an extrapolation of the optical synchrotron spectrum. The four components suggest that all three canonical astrophysical X-ray emission mechanisms are present in M87: thermal bremsstrahlung, inverse Compton scattering, and synchrotron radiation.

Schreier, E. J.↗
NASA NTRS1989

On the detectability of infrared echo arcs around supernova 1987A

The ring-like interstellar visual echoes of radii 33 and 54 arcsec detected around SN 1987A should coincide with infrared echoes (thermal reradiation) from dust at T approximately equal to 15 to 30 K. Whether these infrared echoes are detectable at present is considered. They will be brightest at approximately 100 microns, the range of the Texas infrared photometer. Detectability depends on the ratio zeta congruent to tan(sub a)/tan(sub s)P(theta), where tan(sub a) and tan(sub s) are the visual absorption and scattering optical thicknesses of the echo layer, and P is the phase function function for small-angle scattering (theta approximately equal to 2 to 4 degrees). Zeta approximately greater than 1 is needed for a detectable signal (approximately 0.3 Jy), but zeta cannot be much less than 1; otherwise the visual echoes could not be as bright as they are. Typical dust mixtures of Mathis-Rumpl-Nordsieck type have zeta much less than 1. Zeta remains small even if a population of very small grains with power-law index as steep as approximately 5.5 is added. A population with even more small grains and/or fewer large grains could have a zeta similar to 1 and be detectable at present, but this seems unlikely. The echoes will move, but should remain accessible for many years and should be detected eventually.

Felten, James E.↗
NASA NTRS2023

CLASS Observation of Polarized Cloud Emission at Millimeter Wavelengths

The dynamic atmosphere imposes challenges to ground-based cosmic microwave background observation, especially for measurements on large angular scales. The hydrometeors in the atmosphere, mostly in the form of clouds, scatter the ambient thermal radiation and are known to be the main linearly polarized source in the atmosphere. This scattering-induced polarization is significantly enhanced for ice clouds due to the alignment of ice crystals under gravity, which are also the most common clouds seen at the millimeter-astronomy sites at high altitudes. This work presents a multifrequency study of cloud polarization observed by the Cosmology Large Angular Scale Surveyor experiment on Cerro Toco in the Atacama Desert of northern Chile, from 2016–2022, at the frequency bands centered around 40, 90, 150, and 220 GHz. Using a machine-learning-assisted cloud classifier, we made connections between the transient polarized emission found in all four frequencies with the clouds imaged by monitoring cameras at the observing site. The polarization angles of the cloud events are found to be mostly 90° from the local meridian, which is consistent with the presence of horizontally aligned ice crystals. The90 and 150 GHz polarization data are consistent with a power law with a spectral index of 3.90±0.06, while an excess/deficit of polarization amplitude is found at 40/220 GHz compared with a Rayleigh scattering spectrum. These results are consistent with Rayleigh-scattering-dominated cloud polarization, with possible effects from supercooled water absorption and/or Mie scattering from a population of large cloud particles that contribute to the220 GHz polarization.

Earth's clouds↗
NASA NTRS2020

Inverse Compton Cooling in the Coronae of Simulated Black Hole Accretion Flows

We present a formulation for a local cooling function to be employed in the diffuse, hot corona region of 3D GRMHD simulations of accreting black holes. This new cooling function calculates the cooling rate due to inverse Compton scattering by considering the relevant microphysics in each cell in the corona and approximating the radiation energy density and Compton temperature there by integrating over the thermal seed photon flux from the disk surface. The method either assumes ion and electron tem- peratures are equal (1T), or calculates them separately (2T) using an instantaneous equilibrium approach predicated on the actual relevant rate equations (Coulomb and Compton). The method is shown to be consistent with a more detailed ray-tracing calculation where the bulk of the cooling occurs, but is substantially less costly to per- form. As an example, we apply these methods to a harm3d simulation of a 10M⊙, non-spinning black hole, accreting at nominally 1% the Eddington value. Both 1T and 2T approaches lead to increased radiative efficiency and a larger fraction of total cooling in the corona as compared to the original target-temperature cooling function used by harm3d, especially in the 1T case. Time-averaged post-processing reveals that the continuum spectral observations predicted from these simulations are qualitatively similar to actual X-ray binary data, especially so for the 1T approach which yields a harder power-law component (Γ = 2.25) compared to the 2T version (Γ = 2.53).

Brooks E. Kinch↗
NASA NTRS2004

Non-Thermal Hard X-Ray Emission in Galaxy Clusters Observed with the BeppoSAX PDS

We study the X-ray emission in a sample of galaxy clusters using the BeppoSAX PDS instrument in the 20-80 keV energy band. We estimate the nonthermal hard X-ray (HXR) cluster emission by modeling the thermal contribution from the cluster gas and the nonthermal contamination from the unobscured active galactic nuclei (AGNs) in the clusters. We also evaluate the systematic uncertainties due to the background fluctuations. Assuming negligible contamination from the obscured AGNs, the resulting nonthermal component is detected at a 2 sigma level in approx. 50% of the nonsignificantly AGN-contaminated clusters: A2142, A2199, A2256, A3376, Coma, Ophiuchus, and Virgo. The data are consistent with a scenario whereby relaxed clusters have no hard X-ray component of nonthermal origin, whereas merger clusters do, with a 20-80 keV luminosity of approx. 10(exp 43)-10(exp 44) h(sup -2 sub 50) ergs/s. The co-added spectrum of the above clusters indicates a power-law spectrum for the HXR emission with a photon index of 2.8(sup +0.3 sub -0.4) in the 12-115 keV band, and we find indication that it has extended distribution. These indications argue against significant contamination from obscured AGNs, which have harder spectra and a centrally concentrated distribution. These results are supportive of the assumption of the merger shock acceleration of electrons in clusters, which has been proposed as a possible origin of the nonthermal hard X-ray emission models. Assuming that the cosmic microwave background photons experience inverse Compton scattering from the merger-accelerated relativistic electrons and thus produce the observed HXR, the measured hard X-ray slope corresponds to a differential momentum spectra of the relativistic electrons with a slope of mu = 3.8-5.0. In presence of cluster magnetic fields this relativistic electron population produces synchrotron emission with a spectral index of 1.4-2.1, consistent with radio halo observations of merger clusters. Thus both hard X-ray and radio observations of merger clusters are consistent with the inverse Compton model.

Nevalainen, J.↗
NASA NTRS2001

The Detection of Circumnuclear X-Ray Emission from the Seyfert Galaxy NGC 3516

We present the first high-resolution, X-ray image of the circumnuclear regions of the Seyfert 1 galaxy NGC 3516, using the Chandra X-ray Observatory (CXO). All three of the CXO observations reported were performed with one of the two grating assemblies in place, and here we restrict our analysis to undispersed photons (i.e. those detected in the zeroth-order). A previously-unknown X-ray source is detected approximately 6 arcsec (1.1h(sub 75)(exp -1) kpc) NNE of the nucleus (position angle approximately 29 degrees) which we designate CXOU 110648.1 + 723412. Its spectrum can be characterized as a power law with a photon index (Gamma) approximately 1.8 - 2.6, or as thermal emission with a temperature kT approximately 0.7 - 3 keV. Assuming a location within NGC 3516, isotropic emission implies a luminosity L approximately 2 - 8 x 10(exp 39)h(sub 75)(exp-2) erg s(exp -1) in the 0.4 - 2 keV band. If due to a single point source, the object is super-Eddington for a 1.4 solar mass neutron star. However, multiple sources or a small, extended source cannot be excluded using the current data. Large-scale extended S-ray emission is also detected out to approximately 10 arcsec (approximately 2h(sub 75)(exp -1) kpc) from the nucleus to the NE and SW, and is approximately aligned with the morphologies of the radio emission and extended narrow emission line region (ENLR). The mean luminosity of this emission is 1 - 5 x 10(exp 37)h(sub 75)(exp -2) erg s(exp -1) arcsec(exp -2), in the 0.4 - 2 keV band. Unfortunately the current data cannot usefully constrain its spectrum. These results are consistent with earlier suggestions of circumnuclear X-ray emissi in NGC 3516 based on ROSAT observations, and thus provide the first clear detection of extended X-ray emission in a Seyfert 1.0 galaxy. If the extended emission is due to scattering of the nuclear X-ray continuum, then the pressure in the X-ray emitting gas is at least two orders of magnitude too small to provide the confining medium for the ENLR clouds.

George, I. M.↗
NASA NTRS2002

A Chandra X-ray Study of Cygnus A: The Nucleus - 2

We report Chandra Advanced CCD Imaging Spectrometer and quasi-simultaneous Rossi X-Ray Timing Explorer (RXTE) observations of the nearby, powerful radio galaxy Cygnus A, with the present paper focusing on the properties of the active nucleus. In the Chandra observation, the hard (less than a few keV) X-ray emission is spatially unresolved with a size is approximately 1" (1.5 kpc, H(sub 0) = 50 km/s/Mpc) and coincides with the radio and near-infrared nuclei. In contrast, the soft (less than 2 keV) emission exhibits a bipolar nebulosity that aligns with the optical bipolar continuum and emission-line structures and approximately with the radio jet. In particular, the soft X-ray emission corresponds very well with the [O III] (lambda)5007 and H(alpha) + [N II] lambda(lambda)6548, 6583 nebulosity imaged with Hubble Space Telescope. At the location of the nucleus, there is only weak soft X-ray emission, an effect that may be intrinsic or result from a dust lane that crosses the nucleus perpendicular to the source axis. The spectra of the various X-ray components have been obtained by simultaneous fits to the six detectors. The compact nucleus is detected to 100 keV and is well described by a heavily absorbed power-law spectrum with Gamma(sub h) = 1.52(sup + 0.12, sub -0.12) (similar to other 0.12 narrow-line radio galaxies) and equivalent hydrogen column N(sub H)(nuc) = 2.0(sup +0.1, sub -0.1) x 10(exp 23)/sq cm. This 0.2 column is compatible with the dust obscuration to the near-infrared source for a normal gas-to-dust ratio. The soft (less than 2 keV) emission from the nucleus may be described by a power-law spectrum with the same index (i.e., Gamma(sub l) = Gamma(sub h), although direct fits suggest a slightly larger value for Gamma(sub l). Narrow emission lines from highly ionized neon and silicon, as well as a "neutral" Fe K(alpha) line, are detected in the nucleus and its vicinity (r approximately less than 2 kpc). The equivalent width (EW) of the Fe K(alpha) line (182(sup +40, sub -54) eV) is in good agreement with theoretical predictions for the EW versus N(sub H)(nuc) relationship in various geometries. An Fe K edge is also seen. The RXTE observations indicate a temperature of kT = 6.9(sup +0., sub -1.0) keV for the cluster gas (discussed in Paper III of this series) and cluster emission lines of Fe K(alpha) and Fe K(beta) and/or Ni K(alpha). We consider the possibility that the extended soft X-ray emission is electron-scattered nuclear radiation. Given that 1% of the unabsorbed 2 - 10 keV nuclear radiation would have to be scattered, the necessary gas column [N(sub H)(Scattering) approx. = 3.5 x 10(exp 22)/sq cm] would absorb the X-rays rather than scatter them if the gas is cold. Thus, the scattering plasma must be highly ionized. If this ionization is achieved through photoionization by the nucleus, the ionization parameter zeta greater than 1 ergs cm/s and the electron density n(sub e) approx. = 6 cc given the observed distance of the soft X-ray emission from the nucleus. The electron column density inferred from the X-ray observations is much too low to account for the extended optical scattered light, strongly suggesting that the polarized optical light is scattered by dust. The presence of highly ionized Ne lines in the soft X-ray spectrum requires 20 ergs cm/s approximately less than zeta approximately less than 300 ergs cm/s these lines may originate closer to the nucleus than the extended soft continuum or in a lower density gas. A collisionally ionized thermal model of the extended soft X-rays cannot be ruled out but is unattractive in view of the low metal abundance required (Z = 0.03 Z(mass)). The hard X-ray to far-infrared ratio for the nucleus of Cygnus A is similar to that seen in Seyfert 1 and unobscured radio galaxies. By means of the correlation between hard X-ray luminosity and nuclear optical absolute magnitude for these classes of object, we estimate M(sub B) = -22.4 for Cygnus A, near the .borderline between Seyfert galaxies and QSOs.

Young, Andrew J.↗
NASA NTRS1999

Dynamics of Single Chains of Suspended Ferrofluid Particles

We present an experimental study of the dynamics of isolated chains made of super-paramagnetic particles under the influence of a magnetic field. The motivation of this work is to understand if the chain fluctuations exist and, if it does, how does the fluctuation affect chain aggregation. We find that single chains strongly fluctuate and that the characteristic frequency of their fluctuations is inversely proportional to the magnetic field strength. The higher the field the lower the characteristic frequency of the chain fluctuations. In the high magnetic field limit, chains behave like rigid rods without any internal motions. In this work, we used ferrofluid particles suspended in water. These particles do not have any intrinsic magnetization. Once a magnetic field is applied, a dipole moment is induced in each particle, proportional to the magnetic field. A dipolar magnetic interaction then occurs between particles. If dipole-dipole magnetic energy is higher than the thermal energy, the result is a structure change inside the dipolar fluid. The ratio of these two energies is expressed by a coupling constant lambda as: lambda = (pi(a(exp 3))(chi(exp 2))(mu(sub 0))(H(sub 0))(exp 2))/18kT Where a is the particle radius, mu(sub 0) is the vacuum magnetic permeability, H(sub 0) the applied magnetic field, k the Boltzmann constant and T the absolute temperature. If lambda > 1, magnetic particles form chains along the field direction. The lateral coalescence of several chains may form bigger aggregates especially if the particle volume fraction is high. While many studies and applications deal with the rheological properties and the structural changes of these dipolar fluids, this work focuses on the understanding of the chain dynamics. In order to probe the chain dynamics, we used dynamic light scattering (DLS) in self-beating mode as our experimental technique. The experimental geometry is such that the scattering plane is perpendicular to the magnetic field. Therefore, only motions in this plane are probed. A very dilute sample of a ferrofluid emulsion with a particle volume fraction of 10(exp -5) is used in this experiment. We chose such a low volume fraction to avoid multiple light scattering as well as lateral chain-chain aggregation. DLS measures the dynamic structure factor S(q,t) of the sample (q is the scattering wave vector, t is the time). In the absence of the magnetic field, identical particles of ferrofluid droplets are randomly distributed and S(q,t) reduces to exp(-q(exp 2)2D(sub 0)t). D(sub 0)=(kT/(6(pi)(eta)(a)) is the diffusion coefficient of Brownian particles (where Xi = (6(pi)(eta)(a)) is the Stokes frictional coefficient of a spherical particle in a fluid of viscosity eta). If interactions or polydispersity can not be ignored, an effective diffusion coefficient is introduced. Formally, D(sub eff) is defined as: D(sub eff) = - q(exp -2) partial derivative of (ln(S(q,t)) with respect to time, as t goes to 0. D(sub eff) reduces to D(sub 0) if no interactions and only a few particles size are present. Therefore, we can use DLS to measure particle size. The particle radius was found to be a=0.23 mu m with 7% of polydispersity. In this case, if we vary the scattering angle theta (and so q) we do not have any change in the measured diffusion coefficient: it is q-independent. When a magnetic field is applied, particles aggregate into chains if lambda > 1. We first studied the kinetics of the chain formation when lambda = 406. At a fixed scattering angle, we measured diffusion coefficient D(sub eff) as a function of time. Experimentally, we find that D(sub eff) decreases monotonously with time. Physically, this means that chains are becoming longer and longer. Since we are only sensitive to motions in the scattering plane and since chains have their main axis perpendicular to this plane, the measured diffusion coefficient is the trans-verse diffusion coefficient. We can relate D(sub eff) to the mean number of particles per chain N(t) at a given time and to the diffusion coefficient of an isolated particle D(sub 0) as D(sub eff)=f(N(t))D(sub 0). Since f(N) is known from other recent work, N can be expressed as a function of the time. We found a square root dependency: N(t) proportional to the square root of t. As expected for very low volume fraction, this behavior is characteristic of a diffusion-limited aggregation as suggested by several authors and by our previous work. In this study, we focus on the dependence of the effective diffusion coefficient on the scattering angle and the magnetic field strength. After the magnetic field is applied (lambda = 406) for a long time, typically 6 hours, kinetics of chain formation becomes very slow. Chain size does not vary much over the next hour period. Thus, we can perform different interesting experiments. First, at a fixed magnetic field, we measure the effective diffusion coefficient as a function of the scattering angle (from 5 to 130 deg). Our results show that the measured diffusion coefficient increases linearly with the scattering angle: D(sub eff) proportional to q. If we do the same experiment for different lambda values, D(sub eff) depends on lambda as D(sub eff) proportional to lambda(exp -1/2). We also find for different lambda values that the same asymptotic D(sub eff) value is obtained when q approaches zero. The angle dependency of D(sub eff) suggests that an additional motion exists besides chain drifting. Chain size is constant during experiment, which was verified by measuring the same diffusion coefficient at the beginning and at the end of the angle switching. If chains are rigid, D(sub eff) is independent of q. Therefore, we found that D(sub eff) not only measures the motion of the entire chain but also its internal fluctuations. These internal motions are the fluctuations of the particles in the chain. To understand the q dependency of D(sub eff), let us look at the probing length used. In our study, the characteristic length scale probed is l=2pi/q which is in the range of 0.9<l/a<20. When l is much larger than the particle radius (l/a going to infinity) we are mainly sensitive to the center of mass diffusion of the chain. D(sub eff) is then the diffusion of the entire chain and depends only on N but not on q and lambda. The value D(sub eff) allows us to obtain the number of particles per chain N. In the opposite limit (i.e. l/a < 1), we are sensitive to motions on the size of individual particles. The main contributions to the measured diffusion coefficient come from internal motions of the chains (i.e. particles' fluctuations inside the chain). We investigated also the effect of the chain size on D(sub eff). For the same value of the magnetic interaction lambda and different chain sizes, we found that the slope of D(sub eff) versus q decreases when N increases as a power law D(sub eff) proportional to N(exp -0.7). This is an important behavior because this means that the longer the chain the slower its internal fluctuations besides the whole chain motion.

Cutillas, S.↗