arXiv subjects

Sun Hong Rhie

Publications and source records attributed to Sun Hong Rhie.

At least 19 recordsLinked to original sources

arXiv2011

Puzzles in Time Delay and Fermat Principle in Gravitational Lensing

The current standard time delay formula (CSTD) in gravitational lensing and its claimed relation to the lens equation through Fermat's principle (least time principle) have been puzzling to the author for some time. We find that the so-called geometric path difference term of the CSTD is an error, and it causes a double counting of the correct time delay. We examined the deflection angle and the time delay of a photon trajectory in the Schwarzschild metric that allows exact perturbative calculations in the gravitational parameter $GM$ in two coordinate systems -- the standard Schwarzschild coordinate system and the isotropic Schwarzschild coordinate system. We identify a coordinate dependent term in the time delay which becomes irrelevant for the arrival time difference of two images. It deems necessary to sort out unambiguously what is what we measure. We calculate the second order corrections for the deflection angle and time delay. The CSTD does generate correct lens equations including multiple scattering lens equations under the variations and may be best understood as a generating function. It is presently unclear what the significance is. We call to reanalyze the existing strong lensing data with time delays.

physics.gen-ph↗

arXiv2010

Elliptically Symmetric Lenses and Violation of Burke's Theorem

We show that the outside equation of a bounded elliptically symmetric lens (ESL) exhibits a pseudo-caustic that arises from a branch cut. A pseudo-caustic is a curve in the source plane across which the number of images changes by one. The inside lens equation of a bounded ESL is free of a pseudo-caustic. Thus the total parity of the images of a point source lensed by a bounded elliptically symmetric mass is not an invariant in violation of the Burke's theorem. A smooth mass density function does not guarantee the validity of the Burke's theorem. Pseudo-caustics of various lens equations are discussed. In the Appendix, Bourassa and Kantowski's deflection angle formula for an elliptically symmetric lens is reproduced using the Schwarz function of the ellipse for an easy access; the outside and inside lens equations of an arbitrary set of truncated circularly or elliptically symmetric lenses, represented as points, sticks, and disks, are presented as a reasonable approximation of the realistic galaxy or cluster lenses. One may consider smooth density functions that are not bounded but fall sufficiently fast asymptotically to preserve the total parity invariance. Any bounded function may be sufficiently closely approximated by an unbounded smooth function obtained by truncating its Fourier integral at a high frequency mode. Whether to use a bounded function or an unbounded smooth function for an ESL lens mass density, whereby whether to observe the total parity invariance or not, incurs philosophical questions. For example, is it sensible to insist that the elliptical symmetry of an elliptic lens galaxy be valid in the entire sky? How a pseudo-caustic close to or intersecting with a caustic must be withered away during a smoothing process and what it means will be investigated in a separate work.

astro-ph.EP↗

arXiv2009

Perturbation of Gravitational Lensing

A gravitational lens system can be perturbed by "rogue systems" in angular proximities but at different distances. A point mass perturbed by another point mass can be considered as a large separation approximation of the double scattering two point mass (DSTP) lens. The resulting effective lens depends on whether the perturber is closer to or farther from the observer than the main lens system. The caustic is smaller than that of the large separation binary lens when the perturber is the first scatterer; the caustic is similar in size with the large separation binary lens when the perturber is the last scatterer. Modelling of a gravitational lensing by a galaxy requires extra terms other than constant shear for the perturbers at different redshifts. Double scattering two distributed mass (DSTD) lens is considered. The perturbing galaxy behaves as a monopole -- or a point mass -- because the dipole moment of the elliptic mass distribution is zero.

astro-ph.GA↗

arXiv2006

A Thought of Wrapping Space Shuttle External Tank with Ceramic Fiber Fishnet Stockings

The new camera system of the shuttle Discovery on STS-114 that blasted off at 10:39am, Tuesday, July 26, 2005, after 906 days of grounding since the Columbia accident, has produced high resolution data of foam sheddings. The 0.9 lbs piece from the Protuberance Air Load (PAL) ramp on the LH2 tank is believed to be comparable in its potential adversities to the $\sim 1.67$ lbs BX-250 foam from the $-Y$ bipod ramp that demised shuttle Columbia in 2003. The two known incidences indicate that protuberant foams, possibly in conjunction with the liquid hydrogen temperature, offer lame targets of the aerodynamic forces. Seven other relatively large divots in the STS-114 external tank foam insulation have been reported, and foam shedding remains to be a challenge to be resolved before the next space shuttle launch. The relatively large divots from the newly streamlined foam around the -Y bipod area suggests a potential necessity for a new line of resolution. We suggest an option to wrap the insulated external fuel tank with a grid of high temperature resistant ceramic fibers ({\it ceramic fiber fishnet stockings}). Assuming fiducial acreage of $20000 ft^2 $, one inch square cell single fiber grid will weigh only $60g$ with fiber cost \$66. Even with 1500-fiber-equivalent strength, one inch square cell grid will add only $200 lbs$ and "miniscule" \$100,000.

physics.gen-ph↗

arXiv2005

How Far Away are Gravitational Lens Caustics? Wrong Question

It has been a persistent question at least for a decade where the gravitational lens caustics are in the radial direction: whether in front of the lensing mass, behind the lensing mass, or on the plane normal to the line of sight that passes through the lensing mass, the radiation source, or the observer. It is a wrong question. And, the truth angers certain referees who somehow possess the ability to write lengthy rubbish referee reports and delay certain papers indefinitely. General relativity is a metric theory, particularly of Riemannian geometry, which is characterized by the existence of an inner product -- or, the invariance of the proper time. According to Einstein field equations, a compact mass defines a spherical geometry around it and focuses photons from a distant source to an observer with the source and observer as the two focal points. When the mass is spherically symmetric, the two dimensional lens equation that relates the angular positions of a source and its images defines a point caustic at the angular position of the lensing mass. The third (radial) position of the point caustic is not defined. For an arbitrary mass, the caustic extends into a web of piecewise smooth curves punctuated by cusps and again its notion exists only within the context of the lens equation. We point out a few errors in a couple of papers, published in the Astrophysical Journal, which may be influential.

astro-ph↗

arXiv2003

n-point Gravitational Lenses with 5(n-1) Images

It has been conjectured (astro-ph/0103463) that a gravitational lens consisting of n point masses can not produce more than 5(n-1) images as is known to be the case for n = 2 and 3. The reasoning is based on the number of finite limit points 2(n-1) which we believe to set the maximum number of positive images and the fact that the number of negative images exceeds the number of positive images by (n-1). It has been known that an n-point lens system (n\ge 3) can produce (3n+1) images and so has been an explicit lens configuration with (3n+1) images. We start with the well-known n-point lens configuration that produces (3n+1) images and produce (2n-1) extra images by adding a small (n+1)-th mass so that the resulting (n+1)-point lens configuration has (2n) discrete limit points and produces 5n images of a source. It still remains to confirm in abstraction that the maximum number of positive image domains of a caustic domain is bounded by the number of the limit points.

astro-ph↗

arXiv2002

Addendum to Astro-ph/0207612: Reflection Symmetry of Cusps in Gravitational Lensing

A contour plot of positive iso-J curves is shown for a gravitational binary lens epsilon_2 = 0.1883 and ell = 0.687. The caustic curve is made of 4-cusped central caustic (so-called "stealth bomber") on the lens axis and two triangular caustics off the lens axis. The cusps of the trioids are all negative cusps. The positive image magnification contours outside the positive cusps on the lens axis are elongated along the symmetry axis. It is in contrast with figure 4 of astro-ph/0206162 (Gaudi and Petters) where the contours appear to contract along the symmetry axis. We apologize if our citation of their figure 4 without the caution played any role of causing confusion with readers.

astro-ph↗

arXiv2002

Reflection Symmetry of Cusps in Gravitational Lensing

Criticality in graviational microlensing is an everyday issue because that is what generates microlensing signals which may be of photon-challenged compact objects such as black holes or planetary systems ET calls home. The criticality of these quasi-analytic lenses is intrinsically quadratic, and the critical curve behaves as a mirror generating two mirror images along the image line (parallel +/- E_-) at the same distances from the critical curve in the opposite sides. At the (pre)cusps where the caustic curve "reflects" and develops cusps, however, "would-be" two pairs of quadratic images "superpose" to produce three mirror images because of the degenerate criticality. The critical curve behaves as a parabolic mirror, and the image inside the parabola is indeed a superposed image having the sum of the magnifications of the other two that are outside the parabola. All three images lie on a parabolic image curve shaped by a property (nabla J) of the (pre)cusp, and two distances of the system determine the position of the image curve and positions of the three images on the image curve. The triplet images satisfy sum J^{-1} = 0, and the function sum J^{-1} is discontinuous at a caustic crossing where a pair of quadratic images disappear into a critical point. The reflection symmetry of the image curve is a manifestation of the symmetry of the cusp which is also respected by a trio of parabolic curves that are tangnet at the (pre)cusp and define the image domains. The symmetry is guaranteed when J_{+-} vanishes or can be ignored, and the cusps on the lens axis of the binary lenses are strongly symmetric having J_{+-} = 0 because of the global reflection symmetry of the binary lenses. "E_{+/-}-algebra" is laid out for users' convenience.

astro-ph↗

arXiv2002

Line Caustic Revisted: Which distance is $δ$ in $J^{-1}\propto \sqrt{δ^{-1}}$?

The line caustic behavior has been discussed since Chang and Refsdal (1979) mentioned inverse-square-root-of-the-distance dependence of the amplification of the images near the critical curve in a study of a single point mass under the influence of a constant shear due to a larger mass. A quarter century later, Gaudi and Petters (2001) interprets that the distance is {\it a vertical distance to the caustic}. It is an erroneous misinterpretation. We rehash Rhie and Bennett (1999) where the caustic behavior of the binary lenses was derived to study the feasibility of limb darkening measurements in caustic crossing microlensing events. ~({\it 1}) $J = \pm \sqrt{4δω_{2-} J_-}$ where ~$δω\parallel\bar\partial J$, and $δω_{2-}$ and $J_-$ are $E_-$-components of $δω$ (the source position shift from the caustic curve) and $2\bar\partial J$ (the gradient of the Jacobian determinant) respectively; ~({\it 2}) The critical eigenvector $\pm E_-$ is normal to the caustic curve and easily determined from the analytic function $κ$-field; ~({\it 3}) Near a cusp ($J_- = 0$) is of a behavior of the third order, and the direction of $\bar\partial J$ with respect to the caustic curve changes rapidly because a cusp is an accumulation point; ~({\it 4}) On a planetary caustic, $|\partial J|\sim \sqrt{1/ε_{pl}}$ is large and power expansion does not necessarily converge over the size of the lensed star. In practice, direct numerical summation is inevitable. We also note that a lens equation with constant shear is intrinsically incomplete and requires supplementary physical assumptions and interpretations in order to be a viable model for a lensing system.

astro-ph↗

arXiv2002

How Cumbersome is a Tenth Order Polynomial?: The Case of Gravitational Triple Lens Equation

Three point mass gravitational lens equation is a two-dimensional vector equation that can be embedded in a tenth order analytic polynomial equation of one complex variable, and we can solve the one variable equation on the source trajectories using recipies for Fortran or $C$ (portable for $C$++ or $C_{jj}$) in Numerical Recipes, or using packages such as Mathemetica, Matlab, etc. This ready solvability renders fitting microlensing light curves including triple lenses a normal process, and such was done in a circumbinary planet fit for MACHO-97-BLG-41. Subsequently, there was a claim that converting the triple lens equation into the analytic equation was rather cumbersome, and the impressionable judgement has caused an effect of mysterious impedance around the perfectly tractable lens equation. There are judgements. Then, there is nature. We looked up for one of the quantities of highest precision measurements: electron $g$-factor correction $a_e \equiv g/2-1$. The current best experimental values of $a_e$ agree to eight significant digits with the theoretical value, and the theoretical calculation involves more than one thousand Feynman diagrams -- many orders of magnitude messier than the triple lens equation coefficients. We seem to have only choice to be compliant to nature and its appetite for elegant mess and precision numerics. In fact, the triple lens equation coefficients take up less than a page to write out and are presented here for users' convenience.

astro-ph↗

arXiv2002

Simulation of a Space-Based Microlensing Survey for Terrestrial Extra-Solar Planets

We show that a space-based gravitational microlensing survey for terrestrial extra-solar planets is feasible in the near future, and could provide a nearly complete picture of the properties of planetary systems in our Galaxy. We present simulations of such a survey using a 1-2m aperture space telescope with a ~2 square degree field-of-view which is used to continuously monitor ~10^8 Galactic bulge main sequence stars. The microlensing techniques allows the discovery of low mass planets with high signal-to-noise, and the space mission that we have studied are sensitive to planets with masses as low as that of Mars. By targeting main sequence source stars, which can only be resolved from space, the space-based microlensing survey is able to detect enough light from the lens stars to determine the spectral type of one third of the lens stars with detected planets, including virtually all of the F, G, and K stars which comprise one quarter of the event sample. This enables the determination of the planetary masses and separations in physical units, as well as the abundance of planets as a function of stellar type and distance from the Galactic center. We show that a space-based microlensing planet search program has its highest sensitivity to planets at orbital separations of 0.7-10 AU, but it will also have significant sensitivity at larger separations and will be able to detect free-floating planets in significant numbers. This complements the planned terrestrial planet transit missions which are sensitive to terrestrial planets at separations of =< 1 AU. Such a mission also detect ~50,000 giant planets via transits, and it is, therefore, the only proposed planet detection method that is sensitive to planets at all orbital radii.

astro-ph↗

arXiv2001

Can A Gravitational Quadruple Lens Produce 17 images?

Gravitational lensing can be by a faint star, a trillion stars of a galaxy, or a cluster of galaxies, and this poses a familiar struggle between particle method and mean field method. In a bottom-up approach, a puzzle has been laid on whether a quadruple lens can produce 17 images. The number of images is governed by the gravitational lens equation, and the equation for $n$-tuple lenses suggests that the maximum number of images of a point source potentially increases as $n^2+1$. Indeed, the classes of $n=1, 2, 3$ lenses produce up to $n^2+1 = 2, 5, 10$ images. We discuss the $n$-point lens system as a two-dimensional harmonic flow of an inviscid fluid, count the caustics topologically, recognize the significance of the limit points and discuss the notion of image domains. We conjecture that the total number of positive images is bounded by the number of finite limit points $2(n-1): n>1$ (1 limit point at $\infty$ if $n=1$). A corollary is that the total number of images of a point source produced by an $n$-tuple lens can not exceed $5(n-1):n>1$. We construct quadruple lenses with distinct finite limit points that can produce up to 15 images and argue why there can not be more than 15 images. We show that the maximum number of images is bounded from below by $3(n+1): n \ge 3$. We also comment on "thick Einstein rings" that can have one or more holes.

astro-ph↗

arXiv2001

GEST

Galactic Exoplanet Survey Telescope (GEST) was proposed for a discovery mission to search for microlensing terrestrial planets toward the Galactic bulge and also Kuiper Belt Objects (KBOs) that are believed to hold vital information of the early history of the solar system. Earth mass planets require massive survey, angular resolution, temporal resolution, and continuous monitoring capability in a statistically stable observing condition. A 2m scale wide FOV space telescope with a large focal plane such as the GSET meets the needs. During the non-bulge time, the GEST will be ideal for high resolution mapping of the large scale structures which will include weak lensing by dark matter, quasar lensing and host galaxies, strong lensing by clusters, and a large volume of galaxies, which with selective follow-up measurements of whose redshifts and IR images will shed light on the dark stuff (matter, energy, essesnce, extra dimenstions, topological defects, ...). The data base can be mined for foreground objects such as high proper motion white dwarfs. We discuss microlensing, planets, and the necessity for a space imager.

astro-ph↗

arXiv2000

The Galactic Exoplanet Survey Telescope: A Proposed Space-Based Microlensing Survey for Terrestrial Extra-Solar Planets

We present a conceptual design for a space based Galactic Exoplanet Survey Telescope (GEST) which will use the gravitational microlensing technique to detect extra solar planets with masses as low as that of Mars at all separations >~ 1 AU. The microlensing data would be collected by a diffraction limited, wide field imaging telescope of ~ 1.5m aperture equipped with a large array of red-optimized CCD detectors. Such a system would be able to monitor $\sim 2\times 10^8$ stars in $\sim 6$ square degrees of the Galactic bulge at intervals of 20-30 minutes, and it would observe $\sim 12000$ microlensing events in three bulge seasons. If planetary systems like our own are common, GEST should be able to detect $\sim 5000$ planets over a 2.5 year lifetime. If gas giants like Jupiter and Saturn are rare, then GEST would detect $\sim 1300$ planets in a 2.5 year mission if we assume that most planetary systems are dominated by planets of about Neptune's' mass. Such a mission would also discover $\sim 100$ planets of an Earth mass or smaller if such planets are common. This is a factor of $\sim 50$ better than the most ambitious ground based programs that have been proposed. GEST will also be sensitive to planets which have been separated from their parent stars.

astro-ph↗

arXiv2000

Superluminal Caustic is Just a Common Misconception: A Comment on astro-ph/0001199 by Zheng Zheng and Andrew Gould

When angular objects in lensing are considered as linear objects, interesting phenomena start happening. Tachyonic caustics are one example. We review that the intrinsic variables of the lens equation are angular variables. We argue that the "fast glance effect" of a caustic curve that is far away from lenses does not share the physical bearing of the well-known (apparent) superluminal motion. There is no dbout that it would be a useful exercise to study the null geodesics in the metric of, say, a rapidly rotating black hole binary. Lienard-Wiechert potentials ($A_μ$) satisfy Maxwell's equations in Minkowski space. Authors' claim that swapping eQ and GM makes the time component ($A_0$) of the Lienard-Wiechert potentials into "the gravitational analog" that governs the behavior of the null geodesics near a relativistic binary system seems to be unfounded.

astro-ph↗

arXiv1999

Line Caustic Microlensing and Limb Darkening

In a line caustic crossing microlensing event, the caustic line moving across the surface of the source star provides a direct method to measure the integrated luminosity profile of the star. Combined with the enormous brightening at the caustic crossings, microlensing offers a promising tool for studying stellar luminosity profiles. We derive the amplification behavior of the two extra images that become partial images conjoined across the critical curve at a line caustic crossing. We identify the multiplicative factors that depend on the caustic crossing point and the relative size of the star, and the shape function that depends on the stellar luminosity profile. We examine the analytic limb-darkening models -- linear, square root, and square -- using the analytic form of the shape function. We find that the microlensing lightcurves must be determined to an accuracy of better than 0.3-0.8% in order to be able to determine the linear limb-darkening parameter $c_1$ with precision of $δc_1 = 0.1$. This is similar to the accuracy level required in eclipsing binaries as reported by Popper (1984).

astro-ph↗

arXiv1999

Binary Microlensing Event MACHO-98-SMC-1

The recent binary microlensing event toward the Small Magellanic Cloud MACHO-98-SMC-1 was alerted by the MACHO collaboration and monitored by many microlensing experiments for its complete coverage of the second caustic crossing. The purpose of this global monitoring campaign was to determine the relative proper motion $|\vecμ|$ of the lensing object with respect to the source star that may be indicative of the location of the lensing object. (``Is it a Galactic halo object or not, that is the question.") The estimated value $|\vecμ| \approx 1.3 km/(s \kpc)$ indicates that the binarylensing object belongs to the stellar population of the SMC. We discuss the implication of this binary event for the halo dark matter.

astro-ph↗

arXiv1996

Infimum Microlensing Amplification of the Maximum Number of Images of $n$-point Lens Systems

The total amplification of a source inside a caustic curve of a binary lens is no less than 3. Here we show that the infimum amplification 3 is satisfied by a family of binary lenses where the source position is at the mid-point between the lens positions independently of the mass ratio which parameterizes the family. We present a new proof of an underlying constraint that the total amplification of the two positive images is bigger than that of the three negative images by one inside a caustic. We show that a similar constraint holds for an arbitrary class of $n$-point lens systems for the sources in the `maximal domains'. We introduce the notion that a source plane consists of {\it graded caustic domains} and the `maximal domain' is the area of the source plane where a source star results in the maximum $n^2+1$ images. We show that the infimum amplification of a three point lens is 7, and it is bigger than $n^2+1-n$ for $n\ge 4$. This paper has raised many interesting and very basic questions such as ``whether lensing is a physical process, a mathematical process, or both" since it was submitted for publication a year ago. The result is the addition of 8 page appendix, and that is the reason of this replacement. We hope that the future authors wouldn't have to pay so long for using the elegant Jacobian matrix in complex coordinate basis. (They are neither wrong nor funny!!)

astro-ph↗