Toward Understanding Astrophysical Phenomena

Fast radio bursts (FRBs), a novel type of radio pulse, whose physics is not yet understood at all. Only a handful of FRBs had been detected when we started this project. Taking account of the scant observations, we put physical constraints on FRBs. We excluded proposals of a galactic origin for their extraordinarily high dispersion measures (DM), in particular stellar coronas and HII regions. Therefore our work supports an extragalactic origin for FRBs. We show that the resolved scattering tail of FRB 110220 is unlikely to be due to propagation through the intergalactic plasma. Instead the scattering is probably caused by the interstellar medium in the FRB's host galaxy, and indicates that this burst sits in the central region of that galaxy. Pulse durations of order $\ms$ constrain source sizes of FRBs implying enormous brightness temperatures and thus coherent emission. Electric fields near FRBs at cosmological distances would be so strong that they could accelerate free electrons from rest to relativistic energies in a single wave period. When we worked on FRBs, it was unclear whether they were genuine astronomical signals as distinct from `perytons', clearly terrestrial radio bursts, sharing some common properties with FRBs. Recently, in April 2015, astronomers discovered that perytons were emitted by microwave ovens. Radio chirps similar to FRBs were emitted when their doors opened while they were still heating. Evidence for the astronomical nature of FRBs has strengthened since our paper was published. Some bursts have been found to show linear and circular polarizations and Faraday rotation of the linear polarization has also been detected. I hope to resume working on FRBs in the near future. But after we completed our FRB paper, I decided to pause this project because of the lack of observational constraints.

The pulsar triple system, J0733+1715, has its orbital parameters fitted to high accuracy owing to the precise timing of the central $\ms$ pulsar. The two orbits are highly hierarchical, namely $P_{\mathrm{orb,1}}\ll P_{\mathrm{orb,2}}$, where 1 and 2 label the inner and outer white dwarf (WD) companions respectively. Moreover, their orbital planes almost coincide, providing a unique opportunity to study secular interaction associated purely with eccentricity beyond the solar system. Secular interaction only involves effect averaged over many orbits. Thus each companion can be represented by an elliptical wire with its mass distributed inversely proportional to its local orbital speed. Generally there exists a mutual torque, which vanishes only when their apsidal lines are parallel or anti-parallel. To maintain either mode, the eccentricity ratio, $e_1/e_2$, must be of the proper value, so that both apsidal lines precess together. For J0733+1715, $e_1\ll e_2$ for the parallel mode, while $e_1\gg e_2$ for the anti-parallel one. We show that the former precesses $\sim 10$ times slower than the latter. Currently the system is dominated by the parallel mode. Although only a little anti-parallel mode survives, both eccentricities especially $e_1$ oscillate on $\sim 10^3\yr$ timescale. Detectable changes would occur within $\sim 1\yr$. We demonstrate that the anti-parallel mode gets damped $\sim 10^4$ times faster than its parallel brother by any dissipative process diminishing $e_1$. If it is the tidal damping in the inner WD, we proceed to estimate its tidal quantity parameter ($Q$) to be $\sim 10^6$, which was poorly constrained by observations. However, tidal damping may also happen during the preceding low-mass X-ray binary (LMXB) phase or hydrogen thermal nuclear flashes. But, in both cases, the inner companion fills its Roche lobe and probably suffers mass/angular momentum loss, which might cause $e_1$ to grow rather than decay.

Several pairs of solar system satellites occupy mean motion resonances (MMRs). We divide these into two groups according to their proximity to exact resonance. Proximity is measured by the existence of a separatrix in phase space. MMRs between Io-Europa, Europa-Ganymede and Enceladus-Dione are too distant from exact resonance for a separatrix to appear. A separatrix is present only in the phase spaces of the Mimas-Tethys and Titan-Hyperion MMRs and their resonant arguments are the only ones to exhibit substantial librations. When a separatrix is present, tidal damping of eccentricity or inclination excites overstable librations that can lead to passage through resonance on the damping timescale. However, after investigation, we conclude that the librations in the Mimas-Tethys and Titan-Hyperion MMRs are fossils and do not result from overstability.

Rubble piles are common in the solar system. Monolithic elements touch their neighbors in small localized areas. Voids occupy a significant fraction of the volume. In a fluid-free environment, heat cannot conduct through voids; only radiation can transfer energy across them. We model the effective thermal conductivity of a rubble pile and show that it is proportional the square root of the pressure, $P$, for $P\leq \epsy^3\mu$ where $\epsy$ is the material's yield strain and $\mu$ its shear modulus. Our model provides an excellent fit to the depth dependence of the thermal conductivity in the top $140\,\mathrm{cm}$ of the lunar regolith. It also offers an explanation for the low thermal inertias of rocky asteroids and icy satellites. Lastly, we discuss how rubble piles slow down the cooling of small bodies such as asteroids.

Electromagnetic (EM) follow-up observations of gravitational wave (GW) events will help shed light on the nature of the sources, and more can be learned if the EM follow-ups can start as soon as the GW event becomes observable. In this paper, we propose a computationally efficient time-domain algorithm capable of detecting gravitational waves (GWs) from coalescing binaries of compact objects with nearly zero time delay. In case when the signal is strong enough, our algorithm also has the flexibility to trigger EM observation {\it before} the merger. The key to the efficiency of our algorithm arises from the use of chains of so-called Infinite Impulse Response (IIR) filters, which filter time-series data recursively. Computational cost is further reduced by a template interpolation technique that requires filtering to be done only for a much coarser template bank than otherwise required to sufficiently recover optimal signal-to-noise ratio. Towards future detectors with sensitivity extending to lower frequencies, our algorithm's computational cost is shown to increase rather insignificantly compared to the conventional time-domain correlation method. Moreover, at latencies of less than hundreds to thousands of seconds, this method is expected to be computationally more efficient than the straightforward frequency-domain method.

Normal structures and automorphism groups of t-designs

Combinatorial configurations known as t-designs are studied. These are pairs ˂B, ∏˃, where each element of B is a k-subset of ∏, and each t-design occurs in exactly λ elements of B, for some fixed integers k and λ. A theory of internal structure of t-designs is developed, and it is shown that any t-design can be decomposed in a natural fashion into a sequence of “simple” subdesigns. The theory is quite similar to the analysis of a group with respect to its normal subgroups, quotient groups, and homomorphisms. The analogous concepts of normal subdesigns, quotient designs, and design homomorphisms are all defined and used.

This structure theory is then applied to the class of t-designs whose automorphism groups are transitive on sets of t points. It is shown that if G is a permutation group transitive on sets of t letters and ф is any set of letters, then images of ф under G form a t-design whose parameters may be calculated from the group G. Such groups are discussed, especially for the case t = 2, and the normal structure of such designs is considered. Theorem 2.2.12 gives necessary and sufficient conditions for a t-design to be simple, purely in terms of the automorphism group of the design. Some constructions are given.

Finally, 2-designs with k = 3 and λ = 2 are considered in detail. These designs are first considered in general, with examples illustrating some of the configurations which can arise. Then an attempt is made to classify all such designs with an automorphism group transitive on pairs of points. Many cases are eliminated of reduced to combinations of Steiner triple systems. In the remaining cases, the simple designs are determined to consist of one infinite class and one exceptional case.

New variational principles for systems of partial differential equations

The question of finding variational principles for coupled systems of first order partial differential equations is considered. Using a potential representation for solutions of the first order system a higher order system is obtained. Existence of a variational principle follows if the original system can be transformed to a self-adjoint higher order system. Existence of variational principles for all linear wave equations with constant coefficients having real dispersion relations is established. The method of adjoining some of the equations of the original system to a suitable Lagrangian function by the method of Lagrange multipliers is used to construct new variational principles for a class of linear systems. The equations used as side conditions must satisfy highly-restrictive integrability conditions. In the more difficult nonlinear case the system of two equations in two independent variables can be analyzed completely. For systems determined by two conservation laws the side condition must be a conservation law in addition to satisfying the integrability conditions.

Anatomical and developmental patterns of interleukin-2 gene expression in the mouse: analysis of IL-2 expressing cells and partial characterization of interactions involved in mediating IL-2 gene expression in vivo

Interleukin-2 (IL-2) is an important mediator in the vertebrate immune system. IL-2 is a potent growth factor that mature T lymphocytes use as a proliferation signal and the production of IL-2 is crucial for the clonal expansion of antigen-specific T cells in the primary immune response. IL-2 driven proliferation is dependent on the interaction of the lymphokine with its cognate multichain receptor. IL-2 expression is induced only upon stimulation and transcriptional activation of the IL-2 gene relies extensively on the coordinate interaction of numerous inducible and constitutive trans-acting factors. Over the past several years, thousands of papers have been published regarding molecular and cellular aspects of IL-2 gene expression and IL-2 function. The vast majority of these reports describe work that has been carried out in vitro. However, considerably less is known about control of IL-2 gene expression and IL-2 function in vivo.

To gain new insight into the regulation of IL-2 gene expression in vivo, anatomical and developmental patterns of IL-2 gene expression in the mouse were established by employing in situ hybridization and immunohistochemical staining methodologies to tissue sections generated from normal mice and mutant animals in which T -cell development was perturbed. Results from these studies revealed several interesting aspects of IL-2 gene expression, such as (1) induction of IL-2 gene expression and protein synthesis in the thymus, the primary site of T-cell development in the body, (2) cell-type specificity of IL-2 gene expression in vivo, (3) participation of IL-2 in the extrathymic expansion of mature T cells in particular tissues, independent of an acute immune response to foreign antigen, (4) involvement of IL-2 in maintaining immunologic balance in the mucosal immune system, and (5) potential function of IL-2 in early events associated with hematopoiesis.

Extensive analysis of IL-2 mRNA accumulation and protein production in the murine thymus at various stages of development established the existence of two classes of intrathymic IL-2 producing cells. One class of intrathymic IL-2 producers was found exclusively in the fetal thymus. Cells belonging to this subset were restricted to the outermost region of the thymus. IL-2 expression in the fetal thymus was highly transient; a dramatic peak ofiL-2 mRNA accumulation was identified at day 14.5 of gestation and maximal IL-2 protein production was observed 12 hours later, after which both IL-2 mRNA and protein levels rapidly decreased. Significantly, the presence of IL-2 expressing cells in the day 14-15 fetal thymus was not contingent on the generation of T-cell receptor (TcR) positive cells. The second class of IL-2 producing cells was also detectable in the fetal thymus (cells found in this class represented a minority subset of IL-2 producers in the fetal thymus) but persist in the thymus during later stages of development and after birth. Intrathymic IL-2 producers in postnatal animals were located in the subcapsular region and cortex, indicating that these cells reside in the same areas where immature T cells are consigned. The frequency of IL-2 expressing cells in the postnatal thymus was extremely low, indicating that induction of IL-2 expression and protein synthesis are indicative of a rare activation event. Unlike the fetal class of intrathymic IL-2 producers, the presence of IL-2 producing cells in the postnatal thymus was dependent on to the generation of TcR+ cells. Subsequent examination of intrathymic IL-2 production in mutant postnatal mice unable to produce either αβ or γδ T cells showed that postnatal IL-2 producers in the thymus belong to both αβ and γδ lineages. Additionally, further studies indicated that IL-2 synthesis by immature αβ -T cells depends on the expression of bonafide TcR αβ-heterodimers. Taken altogether, IL-2 production in the postnatal thymus relies on the generation of αβ or γδ-TcR^+ cells and induction of IL-2 protein synthesis can be linked to an activation event mediated via the TcR.

With regard to tissue specificity of IL-2 gene expression in vivo, analysis of whole body sections obtained from normal neonatal mouse pups by in situ hybridization demonstrated that IL-2 mRNA^+ cells were found in both lymphoid and nonlymphoid tissues with which T cells are associated, such as the thymus (as described above), dermis and gut. Tissues devoid of IL-2 mRNA^+ cells included brain, heart, lung, liver, stomach, spine, spinal cord, kidney, and bladder. Additional analysis of isolated tissues taken from older animals revealed that IL-2 expression was undetectable in bone marrow and in nonactivated spleen and lymph nodes. Thus, it appears that extrathymic IL-2 expressing cells in nonimmunologically challenged animals are relegated to particular epidermal and epithelial tissues in which characterized subsets of T cells reside and thatinduction of IL-2 gene expression associated with these tissues may be a result of T-cell activation therein.

Based on the neonatal in situ hybridization results, a detailed investigation into possible induction of IL-2 expression resulting in IL-2 protein synthesis in the skin and gut revealed that IL-2 expression is induced in the epidermis and intestine and IL-2 protein is available to drive cell proliferation of resident cells and/or participate in immune function in these tissues. Pertaining to IL-2 expression in the skin, maximal IL-2 mRNA accumulation and protein production were observed when resident Vγ_3^+ T-cell populations were expanding. At this age, both IL-2 mRNA^+ cells and IL-2 protein production were intimately associated with hair follicles. Likewise, at this age a significant number of CD3ε^+ cells were also found in association with follicles. The colocalization of IL-2 expression and CD3ε^+ cells suggests that IL-2 expression is induced when T cells are in contact with hair follicles. In contrast, neither IL-2 mRNA nor IL-2 protein were readily detected once T-cell density in the skin reached steady-state proportions. At this point, T cells were no longer found associated with hair follicles but were evenly distributed throughout the epidermis. In addition, IL-2 expression in the skin was contingent upon the presence of mature T cells therein and induction of IL-2 protein synthesis in the skin did not depend on the expression of a specific TcR on resident T cells. These newly disclosed properties of IL-2 expression in the skin indicate that IL-2 may play an additional role in controlling mature T-cell proliferation by participating in the extrathymic expansion of T cells, particularly those associated with the epidermis.

Finally, regarding IL-2 expression and protein synthesis in the gut, IL-2 producing cells were found associated with the lamina propria of neonatal animals and gut-associated IL-2 production persisted throughout life. In older animals, the frequency of IL-2 producing cells in the small intestine was not identical to that in the large intestine and this difference may reflect regional specialization of the mucosal immune system in response to enteric antigen. Similar to other instances of IL-2 gene expression in vivo, a failure to generate mature T cells also led to an abrogation of IL-2 protein production in the gut. The presence of IL-2 producing cells in the neonatal gut suggested that these cells may be generated during fetal development. Examination of the fetal gut to determine the distribution of IL-2 producing cells therein indicated that there was a tenfold increase in the number of gut-associated IL-2 producers at day 20 of gestation compared to that observed four days earlier and there was little difference between the frequency of IL-2 producing cells in prenatal versus neonatal gut. The origin of these fetally-derived IL-2 producing cells is unclear. Prior to the immigration of IL-2 inducible cells to the fetal gut and/or induction of IL-2 expression therein, IL-2 protein was observed in the fetal liver and fetal omentum, as well as the fetal thymus. Considering that induction of IL-2 protein synthesis may be an indication of future functional capability, detection of IL-2 producing cells in the fetal liver and fetal omentum raises the possibility that IL-2 producing cells in the fetal gut may be extrathymic in origin and IL-2 producing cells in these fetal tissues may not belong solely to the T lineage. Overall, these results provide increased understanding of the nature of IL-2 producing cells in the gut and how the absence of IL-2 production therein and in fetal hematopoietic tissues can result in the acute pathology observed in IL-2 deficient animals.

Studies of Zγ production and constraints on anomalous triple gauge couplings in pp collisions at √s = 7 TeV

In this thesis, we test the electroweak sector of the Standard Model of particle physics through the measurements of the cross section of the simultaneous production of the neutral weak boson Z and photon γ, and the limits on the anomalous Zγγ and ZZγ triple gauge couplings h3 and h4 with the Z decaying to leptons (electrons and muons). We analyze events collected in proton-proton collisions at center of mass energy of sqrt(s) = 7 TeV corresponding to an integrated luminosity of 5.0 inverse femtobarn. The analyzed events were recorded by the Compact Muon Solenoid detector at the Large Hadron Collider in 2011.

The production cross section has been measured for hard photons with transverse momentum greater than 15 GeV that are separated from the the final state leptons in the eta-phi plane by Delta R greater than 0.7, whose sum of the transverse energy of hadrons over the transverse energy of the photon in a cone around the photon with Delta R less than 0.3 is less than 0.5, and with the invariant mass of the dilepton system greater than 50 GeV. The measured cross section value is 5.33 +/- 0.08 (stat.) +/- 0.25 (syst.) +/- 0.12 (lumi.) picobarn. This is compatible with the Standard Model prediction that includes next-to-leading-order QCD contributions: 5.45 +/- 0.27 picobarn.

The measured 95 % confidence-level upper limits on the absolute values of the anomalous couplings h3 and h4 are 0.01 and 8.8E-5 for the Zγγ interactions, and, 8.6E-3 and 8.0E-5 for the ZZγ interactions. These values are also compatible with the Standard Model where they vanish in the tree-level approximation. They extend the sensitivity of the 2012 results from the ATLAS collaboration based on 1.02 inverse femtobarn of data by a factor of 2.4 to 3.1.