273 research outputs found

### 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

### 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

### 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

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