Microlensing masses via photon bunching

In microlensing of a Galactic star by a brown dwarf or other compact object, the amplified image really consists of two unresolved images with slightly different light-travel times. The difference (of order a microsecond) is GM/c^3 times a dimensionless factor depending on the total magnification. Since magnification is well-measured in microlensing events, a single time-delay measurement would provide the mass of the lens, without degeneracies. The challenge is to find an observable that varies on sub-microsecond time scales. This paper notes that the narrow-band intensity of the unresolved image pair will show photon bunching (the Hanbury Brown and Twiss effect), and argues that the lensed intensity will have an auto-correlation peak at the lensing time delay. The ultrafast photon-counting technology needed for this type of measurement exists, but the photon numbers required to give sufficient signal-to-noise appear infeasible at present. Preliminary estimates suggest time-delayed photon bunching may be measurable for lensed early-type main-sequence stars at 10 kpc, with the help of 30 m-class telescopes.Comment: To appear in MNRA

Feasibility of observing Hanbury Brown and Twiss phase

The interferometers of Hanbury Brown and collaborators in the 1950s and 60s, and their modern descendants now being developed (intensity interferometers) measure the spatial power spectrum of the source from intensity correlations at two points. The quantum optical theory of the Hanbury Brown and Twiss (HBT) effect shows that more is possible, in particular the phase information can be recovered by correlating intensities at three points (bispectrum). In this paper we argue that such 3 point measurements are possible for bright stars such as Sirius and Betelgeuse using off the shelf single photon counters with collecting areas of the order of 100m2. It seems possible to map individual features on the stellar surface. Simple diameter measurements would be possible with amateur class telescopes.Comment: To appear in MNRA

Geometrical vs wave optics under gravitational waves

We present some new derivations of the effect of a plane gravitational wave on a light ray. A simple interpretation of the results is that a gravitational wave causes a phase modulation of electromagnetic waves. We arrive at this picture from two contrasting directions, namely null geodesics and Maxwell's equations, or, geometric and wave optics. Under geometric optics, we express the geodesic equations in Hamiltonian form and solve perturbatively for the effect of gravitational waves. We find that the well-known time-delay formula for light generalizes trivially to massive particles. We also recover, by way of a Hamilton-Jacobi equation, the phase modulation obtained under wave optics. Turning then to wave optics - rather than solving Maxwell's equations directly for the fields, as in most previous approaches - we derive a perturbed wave equation (perturbed by the gravitational wave) for the electromagnetic four-potential. From this wave equation it follows that the four-potential and the electric and magnetic fields all experience the same phase modulation. Applying such a phase modulation to a superposition of plane waves corresponding to a Gaussian wave packet leads to time delays.Comment: Accepted for publication in Physical Review D, matches published versio

Interpreting the Kustaanheimo-Stiefel transform in gravitational dynamics

The Kustaanheimo-Stiefel (KS) transform turns a gravitational two-body problem into a harmonic oscillator, by going to four dimensions. In addition to the mathematical-physics interest, the KS transform has proved very useful in N-body simulations, where it helps to handle close encounters. Yet the formalism remains somewhat arcane, with the role of the extra dimension being especially mysterious. This paper shows how the basic transformation can be interpreted as a rotation in three dimensions. For example, if we slew a telescope from zenith to a chosen star in one rotation, we can think of the rotation axis and angle as the KS transform of the star. The non-uniqueness of the rotation axis encodes the extra dimension. This geometrical interpretation becomes evident on writing KS transforms in quaternion form, which also helps to derive concise expressions for regularized equations of motio

Interpreting the Kustaanheimo-Stiefel transform in gravitational dynamics

The Kustaanheimo-Stiefel (KS) transform turns a gravitational two-body problem into a harmonic oscillator, by going to four dimensions. In addition to the mathematical-physics interest, the KS transform has proved very useful in N-body simulations, where it helps to handle close encounters. Yet the formalism remains somewhat arcane, with the role of the extra dimension being especially mysterious. This paper shows how the basic transformation can be interpreted as a rotation in three dimensions. For example, if we slew a telescope from zenith to a chosen star in one rotation, we can think of the rotation axis and angle as the KS transform of the star. The non-uniqueness of the rotation axis encodes the extra dimension. This geometrical interpretation becomes evident on writing KS transforms in quaternion form, which also helps to derive concise expressions for regularized equations of motio

Intensity interferometry with more than two detectors?

The original intensity interferometers were instruments built in the 1950s and 60s by Hanbury Brown and collaborators, achieving milli-arcsec resolutions in visible light without optical-quality mirrors. They exploited a then-novel physical effect, now known as HBT correlation after the experiments of Hanbury Brown and Twiss, and nowadays considered fundamental in quantum optics. Now a new generation of inten- sity interferometers is being designed, raising the possibility of measuring intensity correlations with three or more detectors. Quantum optics predicts some interesting features in higher-order HBT. One is that HBT correlation increases combinatorially with the number of detectors. Signal to noise considerations suggest, that many-detector HBT correlations would be mea- surable for bright masers, but very difficult for thermal sources. But the more modest three-detector HBT correlation seems measurable for bright stars, and would provide image information (namely the bispectrum) not present in standard HBT.Comment: 7 pages, 2 figures, Accepted for publication in MNRA

Clocks around Sgr A*

The S stars near the Galactic centre and any pulsars that may be on similar orbits, can be modelled in a unified way as clocks orbiting a black hole, and hence are potential probes of relativistic effects, including black hole spin. The high eccentricities of many S stars mean that relativistic effects peak strongly around pericentre; for example, orbit precession is not a smooth effect but almost a kick at pericentre. We argue that concentration around pericentre will be an advantage when analysing redshift or pulse-arrival data to measure relativistic effects, because cumulative precession will be drowned out by Newtonian perturbations from other mass in the Galactic-centre region. Wavelet decomposition may be a way to disentangle relativistic effects from Newton perturbations. Assuming a plausible model for Newtonian perturbations on S2, relativity appears to be strongest in a two-year interval around pericentre, in wavelet modes of timescale approximately 6 months.Comment: Accepted for publication in MNRA

Cluster Reconstruction from Combined Strong and Weak Lensing

The lensing information provided by multiple images, arclets, and statistical distortions can all be formulated as linear constraints on the arrival-time surface, and hence on the mass distribution. This reduces cluster lens reconstruction from combined strong and weak lensing to a standard type of inversion problem. Moreover, the mass sheet degeneracy is broken if there are sources at different redshifts.Comment: 8 pages incl 6 figures. Invited talk at "Gravitational Lensing: Recent Progress and Future Goals", Boston University, MA, July 1999, eds. T.G. Brainerd and C.S. Kochane

Pixelated Lenses and H_0 from Time-delay QSOs

Observed time delays between images of a lensed QSO lead to the determination of the Hubble constant by Refsdal's method, provided the mass distribution in the lensing galaxy is reasonably well known. Since the two or four QSO images usually observed are woefully inadequate by themselves to provide a unique reconstruction of the galaxy mass, most previous reconstructions have been limited to simple parameterized models, which may lead to large systematic errors in the derived H_0 by failing to consider enough possibilities for the mass distribution of the lens. We use non-parametric modeling of galaxy lenses to better explore physically plausible but not overly constrained galaxy mass maps, all of which reproduce the lensing observables exactly, and derive the corresponding distribution of H_0's. Blind tests - where one of us simulated galaxy lenses, lensing observables, and a value for H_0, and the other applied our modeling technique to estimate H_0 indicate that our procedure is reliable. For four simulated lensed QSOs the distribution of inferred H_0 have an uncertainty of \simeq 10% at 90% confidence. Application to published observations of the two best constrained time-delay lenses, PG1115+080 and B1608+656, yields H_0=61 +/- 11 km/s/Mpc at 68% confidence and 61 +/- 18 km/s/Mpc at 90% confidence.Comment: 27 pages, including 17 figs, LaTeX; accepted to A