Scaling the universe: Gravitational lenses and the Hubble constant

Gravitational lenses, besides being interesting in their own right, have been demonstrated to be suitable as “gravitational standard rulers” for the measurement of the rate of expansion of the Universe (Ho), as well as to constrain the values of the cosmological parameters such as Ωo and Λo that control the evolution of the volume of the Universe with cosmic time.

Gravitational lensing of active galactic nuclei.

Most of the known cases of strong gravitational lensing involve multiple imaging of an active galactic nucleus. The properties of lensed active galactic nuclei make them promising systems for astrophysical applications of gravitational lensing; in particular, they show structure on scales of milliseconds of arc to tens of seconds of arc, they are variable, and they are polarized. More than 20 cases of strong gravitational lenses are now known, and about half of them are radio sources. High-resolution radio imaging is making possible the development of well-constrained lens models. Variability studies at radio and optical wavelengths are beginning to yield results of astrophysical interest, such as an independent measure of the distance scale and limits on source sizes.

The efficiency of propulsion by a rotating flagellum

[At very low Reynolds number, the regime in which fluid dynamics is governed by Stokes equations, a helix that translates along its axis under an external force but without an external torque will necessarily rotate. By the linearity of the Stokes equations, the same helix that is caused to rotate due to an external torque will necessarily translate. This is the physics that underlies the mechanism of flagellar propulsion employed by many microorganisms. Here, I examine the linear relationships between forces and torques and translational and angular velocities of helical objects to understand the nature of flagellar propulsion.]

Field theory in superfluid 3He: What are the lessons for particle physics, gravity, and high-temperature superconductivity?

There are several classes of homogeneous Fermi systems that are characterized by the topology of the energy spectrum of fermionic quasiparticles: (i) gapless systems with a Fermi surface, (ii) systems with a gap in their spectrum, (iii) gapless systems with topologically stable point nodes (Fermi points), and (iv) gapless systems with topologically unstable lines of nodes (Fermi lines). Superfluid 3He-A and electroweak vacuum belong to the universality class 3. The fermionic quasiparticles (particles) in this class are chiral: they are left-handed or right-handed. The collective bosonic modes of systems of class 3 are the effective gauge and gravitational fields. The great advantage of superfluid 3He-A is that we can perform experiments by using this condensed matter and thereby simulate many phenomena in high energy physics, including axial anomaly, baryoproduction, and magnetogenesis. 3He-A textures induce a nontrivial effective metrics of the space, where the free quasiparticles move along geodesics. With 3He-A one can simulate event horizons, Hawking radiation, rotating vacuum, etc. High-temperature superconductors are believed to belong to class 4. They have gapless fermionic quasiparticles with a “relativistic” spectrum close to gap nodes, which allows application of ideas developed for superfluid 3He-A.

Mapping the universe in three dimensions

The determination of the three-dimensional layout of galaxies is critical to our understanding of the evolution of galaxies and the structures in which they lie, to our determination of the fundamental parameters of cosmology, and to our understanding of both the past and future histories of the universe at large. The mapping of the large scale structure in the universe via the determination of galaxy red shifts (Doppler shifts) is a rapidly growing industry thanks to technological developments in detectors and spectrometers at radio and optical wavelengths. First-order application of the red shift-distance relation (Hubble’s law) allows the analysis of the large-scale distribution of galaxies on scales of hundreds of megaparsecs. Locally, the large-scale structure is very complex but the overall topology is not yet clear. Comparison of the observed red shifts with ones expected on the basis of other distance estimates allows mapping of the gravitational field and the underlying total density distribution. The next decade holds great promise for our understanding of the character of large-scale structure and its origin.

Cosmic microwave background theory

A long-standing goal of theorists has been to constrain cosmological parameters that define the structure formation theory from cosmic microwave background (CMB) anisotropy experiments and large-scale structure (LSS) observations. The status and future promise of this enterprise is described. Current band-powers in ℓ-space are consistent with a ΔT flat in frequency and broadly follow inflation-based expectations. That the levels are ∼(10−5)2 provides strong support for the gravitational instability theory, while the Far Infrared Absolute Spectrophotometer (FIRAS) constraints on energy injection rule out cosmic explosions as a dominant source of LSS. Band-powers at ℓ ≳ 100 suggest that the universe could not have re-ionized too early. To get the LSS of Cosmic Background Explorer (COBE)-normalized fluctuations right provides encouraging support that the initial fluctuation spectrum was not far off the scale invariant form that inflation models prefer: e.g., for tilted Λ cold dark matter sequences of fixed 13-Gyr age (with the Hubble constant H0 marginalized), ns = 1.17 ± 0.3 for Differential Microwave Radiometer (DMR) only; 1.15 ± 0.08 for DMR plus the SK95 experiment; 1.00 ± 0.04 for DMR plus all smaller angle experiments; 1.00 ± 0.05 when LSS constraints are included as well. The CMB alone currently gives weak constraints on Λ and moderate constraints on Ωtot, but theoretical forecasts of future long duration balloon and satellite experiments are shown which predict percent-level accuracy among a large fraction of the 10+ parameters characterizing the cosmic structure formation theory, at least if it is an inflation variant.

Autonomic Straightening after Gravitropic Curvature of Cress Roots1

Few studies have documented the response of gravitropically curved organs to a withdrawal of a constant gravitational stimulus. The effects of stimulus withdrawal on gravitropic curvature were studied by following individual roots of cress (Lepidium sativum L.) through reorientation and clinostat rotation. Roots turned to the horizontal curved down 62° and 88° after 1 and 5 h, respectively. Subsequent rotation on a clinostat for 6 h resulted in root straightening through a loss of gravitropic curvature in older regions and through new growth becoming aligned closer to the prestimulus vertical. However, these roots did not return completely to the prestimulus vertical, indicating the retention of some gravitropic response. Clinostat rotation shifted the mean root angle −36° closer to the prestimulus vertical, regardless of the duration of prior horizontal stimulation. Control roots (no horizontal stimulation) were slanted at various angles after clinostat rotation. These findings indicate that gravitropic curvature is not necessarily permanent, and that the root retains some commitment to its equilibrium orientation prior to gravitropic stimulation.

Very-long-baseline radio interferometry surveys of the compact structure in active galactic nuclei.

Very-long-baseline radio interferometry (VLBI) imaging surveys have been undertaken since the late 1970s. The sample sizes were initially limited to a few tens of objects but the snapshot technique has now allowed samples containing almost 200 sources to be studied. The overwhelming majority of powerful compact sources are asymmetric corejects of one form or another, most of which exhibit apparent superluminal motion. However 5-10% of powerful flat-spectrum sources are 100-parsec (pc)-scale compact symmetric objects; these appear to form a continuum with the 1-kpc-scale double-lobed compact steep-spectrum sources, which make up 15-20% of lower frequency samples. It is likely that these sub-galactic-size symmetric sources are the precursors to the large-scale classical double sources. There is a surprising peak around 90 degrees in the histogram of misalignments between the dominant source axes on parsec and kiloparsec scales; this seems to be associated with sources exhibiting a high degree of relativistic beaming. VLBI snapshot surveys have great cosmological potential via measurements of both proper motion and angular size vs. redshift as well as searches for gravitational "millilensing."

Probing active galactic nuclei with H2O megamasers.

We describe the characteristics of the rapidly rotating molecular disk in the nucleus of the mildly active galaxy NGC4258. The morphology and kinematics of the disk are delineated by the point-like watervapor emission sources at 1.35-cm wavelength. High angular resolution [200 microas where as is arcsec, corresponding to 0.006 parsec (pc) at 6.4 million pc] and high spectral resolution (0.2 km.s-1 or nu/Deltanu = 1.4 x 10(6)) with the Very-Long-Baseline Array allow precise definition of the disk. The disk is very thin, but slightly warped, and is viewed nearly edge-on. The masers show that the disk is in nearly perfect Keplerian rotation within the observable range of radii of 0.13-0.26 pc. The approximately random deviations from the Keplerian rotation curve among the high-velocity masers are approximately 3.5 km.s-1 (rms). These deviations may be due to the masers lying off the midline by about +/-4 degrees or variations in the inclination of the disk by +/-4 degrees. Lack of systematic deviations indicates that the disk has a mass of <4 x 10(6) solar mass (M[symbol: see text]). The gravitational binding mass is 3.5 x 10(7) M[symbol: see text], which must lie within the inner radius of the disk and requires that the mass density be >4 x 10(9) M[symbol: see text].pc-3. If the central mass were in the form of a star cluster with a density distribution such as a Plummer model, then the central mass density would be 4 x 10(12) M[symbol: see text].pc-3. The lifetime of such a cluster would be short with respect to the age of the galaxy [Maoz, E. (1995) Astrophys. J. Lett. 447, L91-L94]. Therefore, the central mass may be a black hole. The disk as traced by the systemic velocity features is unresolved in the vertical direction, indicating that its scale height is <0.0003 pc (hence the ratio of thickness to radius, H/R, is <0.0025). For a disk in hydrostatic equilibrium the quadrature sum of the sound speed and Alfven velocity is <2.5 km.s-1, so that the temperature of the disk must be <1000 K and the toroidal magnetic field component must be <250 mG. If the molecular mass density in the disk is 10(10) cm-3, then the disk mass is approximately 10(4) M[symbol: see text], and the disk is marginally stable as defined by the Toomre stability parameter Q (Q = 6 at the inner edge and 1 at the outer edge). The inward drift velocity is predicted to be <0.007 km.s-1, for a viscosity parameter of 0.1, and the accretion rate is <7 x 10(-5) M[symbol: see text].yr-1. At this value the accretion would be sufficient to power the nuclear x-ray source of 4 x 10(40) ergs-1 (1 erg = 0.1 microJ). The volume of individual maser components may be as large as 10(46) cm3, based on the velocity gradients, which is sufficient to supply the observed luminosity. The pump power undoubtedly comes from the nucleus, perhaps in the form of x-rays. The warp may allow the pump radiation to penetrate the disk obliquely [Neufeld, D. A. & Maloney, P. R. (1995) Astrophys. J. Lett. 447, L17-L19]. A total of 15 H2O megamasers have been identified out of >250 galaxies searched. Galaxy NGC4258 may be the only case where conditions are optimal to reveal a well-defined nuclear disk. Future measurement of proper motions and accelerations for NGC4258 will yield an accurate distance and a more precise definition of the dynamics of the disk