Effect of Binary Source Companions on the Microlensing Optical Depth Determination toward the Galactic Bulge Field

Currently, gravitational microlensing survey experiments toward the Galactic bulge field utilize two different methods of minimizing blending effect for the accurate determination of the optical depth \tau. One is measuring \tau based on clump giant (CG) source stars and the other is using `Difference Image Analysis (DIA)' photometry to measure the unblended source flux variation. Despite the expectation that the two estimates should be the same assuming that blending is properly considered, the estimates based on CG stars systematically fall below the DIA results based on all events with source stars down to the detection limit. Prompted by the gap, we investigate the previously unconsidered effect of companion-associated events on $\tau$ determination. Although the image of a companion is blended with that of its primary star and thus not resolved, the event associated with the companion can be detected if the companion flux is highly magnified. Therefore, companions work effectively as source stars to microlensing and thus neglect of them in the source star count could result in wrong \tau estimation. By carrying out simulations based on the assumption that companions follow the same luminosity function of primary stars, we estimate that the contribution of the companion-associated events to the total event rate is ~5f_{bi}% for current surveys and can reach up to ~6f_{bi}% for future surveys monitoring fainter stars, where f_{bi} is the binary frequency. Therefore, we conclude that the companion-associated events comprise a non-negligible fraction of all events. However, their contribution to the optical depth is not large enough to explain the systematic difference between the optical depth estimates based on the two different methods.Comment: 4 pages, 1 figure, 1 table, ApJ, submitte

Design Knowledge for Virtual Learning Companions from a Value-centered Perspective

The increasing popularity of conversational agents such as ChatGPT has sparked interest in their potential use in educational contexts but undermines the role of companionship in learning with these tools. Our study targets the design of virtual learning companions (VLCs), focusing on bonding relationships for collaborative learning while facilitating students’ time management and motivation. We draw upon design science research (DSR) to derive prescriptive design knowledge for VLCs as the core of our contribution. Through three DSR cycles, we conducted interviews with working students and experts, held interdisciplinary workshops with the target group, designed and evaluated two conceptual prototypes, and fully coded a VLC instantiation, which we tested with students in class. Our approach has yielded 9 design principles, 28 meta-requirements, and 33 design features centered around the value-in-interaction. These encompass Human-likeness and Dialogue Management, Proactive and Reactive Behavior, and Relationship Building on the Relationship Layer (DP1,3,4), Adaptation (DP2) on the Matching Layer, as well as Provision of Supportive Content, Fostering Learning Competencies, Motivational Environment, and Ethical Responsibility (DP5-8) on the Service Layer

On the Nature and Location of the Microlenses

This paper uses the caustic crossing events in the microlens data sets to explore the nature and location of the lenses. We conclude that the large majority of lenses, whether they are luminous or dark, are likely to be binaries. Further, we demonstrate that blending is an important feature of all the data sets. An additional interpretation suggested by the data, that the caustic crossing events along the directions to the Magellanic Clouds are due to lenses located in the Clouds, implies that most of the LMC/SMC events to date are due to lenses in the Magellanic Clouds. All of these conclusions can be tested. If they are correct, a large fraction of lenses along the direction to the LMC may be ordinary stellar binary systems, just as are the majority of the lenses along the direction to the Bulge. Thus, a better understanding of the larger-than-anticipated value derived for the Bulge optical depth may allow us to better interpret the large value derived for the optical depth to the LMC. Indeed, binarity and blending in the data sets may illuminate connections among several other puzzles: the dearth of binary-source light curves, the dearth of non-caustic-crossing perturbed binary-lens events, and the dearth of obviously blended point-lens events.Comment: 15 pages, 2 figures. Submitted to the Astrophysical Journal Letters, 4 January 199

Mass distribution in our Galaxy

This article summarizes recent work on the luminosity and mass distribution of the Galactic bulge and disk, and on the mass of the Milky Way's dark halo. A new luminosity model consistent with the COBE NIR data and the apparent magnitude distributions of bulge clump giant stars has bulge/bar length of \simeq 3.5\kpc, axis ratios of 1:(0.3-0.4):0.3, and short disk scale-length (\simeq 2.1\kpc). Gas-dynamical flows in the potential of this model with constant M/L fit the terminal velocities in $10\deg\le |l| \le 50\deg$ very well. The luminous mass distribution with this M/L is consistent with the surface density of known matter near the Sun, but still underpredicts the microlensing optical depth towards the bulge. Together, these facts argue strongly for a massive, near-maximal disk in our $\sim L^\ast$, Sbc spiral Galaxy. While the outer rotation curve and global mass distribution are not as readily measured as in similar spiral galaxies, the dark halo mass estimated from satellite velocities is consistent with a flat rotation curve continuing on from the luminous mass distribution

An inner ring and the micro lensing toward the Bulge

All current Bulge-Disk models for the inner Galaxy fall short of reproducing self-consistently the observed micro-lensing optical depth by a factor of two ($> 2\sigma$). We show that the least mass-consuming way to increase the optical depth is to add density roughly half-way the observer and the highest micro-lensing-source density. We present evidence for the existence of such a density structure in the Galaxy: an inner ring, a standard feature of barred galaxies. Judging from data on similar rings in external galaxies, an inner ring can contribute more than 50% of a pure Bulge-Disk model to the micro-lensing optical depth. We may thus eliminate the need for a small viewing angle of the Bar. The influence of an inner ring on the event-duration distribution, for realistic viewing angles, would be to increase the fraction of long-duration events toward Baade's window. The longest events are expected toward the negative-longitude tangent point at $\ell\sim$ -22\degr . A properly sampled event-duration distribution toward this tangent point would provide essential information about viewing angle and elongation of the over-all density distribution in the inner Galaxy.Comment: 9 pages, 7(15) figs, LaTeX, AJ (accepted

The EROS2 search for microlensing events towards the spiral arms: the complete seven season results

The EROS-2 project has been designed to search for microlensing events towards any dense stellar field. The densest parts of the Galactic spiral arms have been monitored to maximize the microlensing signal expected from the stars of the Galactic disk and bulge. 12.9 million stars have been monitored during 7 seasons towards 4 directions in the Galactic plane, away from the Galactic center. A total of 27 microlensing event candidates have been found. Estimates of the optical depths from the 22 best events are provided. A first order interpretation shows that simple Galactic models with a standard disk and an elongated bulge are in agreement with our observations. We find that the average microlensing optical depth towards the complete EROS-cataloged stars of the spiral arms is $\bar{\tau} =0.51\pm .13\times 10^{-6}$, a number that is stable when the selection criteria are moderately varied. As the EROS catalog is almost complete up to $I_C=18.5$, the optical depth estimated for the sub-sample of bright target stars with $I_C<18.5$ ($\bar{\tau}=0.39\pm >.11\times 10^{-6}$) is easier to interpret. The set of microlensing events that we have observed is consistent with a simple Galactic model. A more precise interpretation would require either a better knowledge of the distance distribution of the target stars, or a simulation based on a Galactic model. For this purpose, we define and discuss the concept of optical depth for a given catalog or for a limiting magnitude.Comment: 22 pages submitted to Astronomy & Astrophysic

Risk estimators for choosing regularization parameters in ill-posed problems - Properties and limitations

This paper discusses the properties of certain risk estimators that recently regained popularity for choosing regularization parameters in ill-posed problems, in particular for sparsity regularization. They apply Stein’s unbiased risk estimator (SURE) to estimate the risk in either the space of the unknown variables or in the data space. We will call the latter PSURE in order to distinguish the two different risk functions. It seems intuitive that SURE is more appropriate for ill-posed problems, since the properties in the data space do not tell much about the quality of the reconstruction. We provide theoretical studies of both approaches for linear Tikhonov regularization in a finite dimensional setting and estimate the quality of the risk estimators, which also leads to asymptotic convergence results as the dimension of the problem tends to infinity. Unlike previous works which studied single realizations of image processing problems with a very low degree of ill-posedness, we are interested in the statistical behaviour of the risk estimators for increasing ill-posedness. Interestingly, our theoretical results indicate that the quality of the SURE risk can deteriorate asymptotically for ill-posed problems, which is confirmed by an extensive numerical study. The latter shows that in many cases the SURE estimator leads to extremely small regularization parameters, which obviously cannot stabilize the reconstruction. Similar but less severe issues with respect to robustness also appear for the PSURE estimator, which in comparison to the rather conservative discrepancy principle leads to the conclusion that regularization parameter choice based on unbiased risk estimation is not a reliable procedure for ill-posed problems. A similar numerical study for sparsity regularization demonstrates that the same issue appears in non-linear variational regularization approaches

The Black Hole Mass of NGC 4151: Comparison of Reverberation Mapping and Stellar Dynamical Measurements

We present a stellar dynamical estimate of the black hole (BH) mass in the Seyfert 1 galaxy, NGC 4151. We analyze ground-based spectroscopy as well as imaging data from the ground and space, and we construct 3-integral axisymmetric models in order to constrain the BH mass and mass-to-light ratio. The dynamical models depend on the assumed inclination of the kinematic symmetry axis of the stellar bulge. In the case where the bulge is assumed to be viewed edge-on, the kinematical data give only an upper limit to the mass of the BH of ~4e7 M_sun (1 sigma). If the bulge kinematic axis is assumed to have the same inclination as the symmetry axis of the large-scale galaxy disk (i.e., 23 degrees relative to the line of sight), a best-fit dynamical mass between 4-5e7 M_sun is obtained. However, because of the poor quality of the fit when the bulge is assumed to be inclined (as determined by the noisiness of the chi^2 surface and its minimum value), and because we lack spectroscopic data that clearly resolves the BH sphere of influence, we consider our measurements to be tentative estimates of the dynamical BH mass. With this preliminary result, NGC 4151 is now among the small sample of galaxies in which the BH mass has been constrained from two independent techniques, and the mass values we find for both bulge inclinations are in reasonable agreement with the recent estimate from reverberation mapping (4.57[+0.57/-0.47]e7 M_sun) published by Bentz et al.Comment: 20 pages, including 11 low-res figures. Accepted for publication in ApJ. High resolution version available upon reques

The MACHO project: Microlensing Optical Depth towards the Galactic Bulge from Difference Image Analysis

We present the microlensing optical depth towards the Galactic bulge based on the detection of 99 events found in our Difference Image Analysis (DIA) survey. This analysis encompasses three years of data, covering ~ 17 million stars in ~ 4 deg^2, to a source star baseline magnitude limit of V = 23. The DIA technique improves the quality of photometry in crowded fields, and allows us to detect more microlensing events with faint source stars. We find this method increases the number of detection events by 85% compared with the standard analysis technique. DIA light curves of the events are presented and the microlensing fit parameters are given. The total microlensing optical depth is estimated to be tau_(total)= 2.43^(+0.39/-0.38) x 10^(-6) averaged over 8 fields centered at l=2.68 and b=-3.35. For the bulge component we find tau_(bulge)=3.23^(+0.52/-0.50) x 10^(-6) assuming a 25% stellar contribution from disk sources. These optical depths are in good agreement with the past determinations of the MACHO Alcock et al. (1997) and OGLE Udalski et al. (1994) groups, and are higher than predicted by contemporary Galactic models. We show that our observed event timescale distribution is consistent with the distribution expected from normal mass stars, if we adopt the stellar mass function of Scalo (1986) as our lens mass function. However, we note that as there is still disagreement about the exact form of the stellar mass function, there is uncertainty in this conclusion. Based on our event timescale distribution we find no evidence for the existence of a large population of brown dwarfs in the direction of the Galactic bulge.Comment: Updated references and corrected optical depth values. tau_tot= [2.91(+0.47/-0.45) -> 2.43^(+0.39/-0.38)] x 10^(-6) tau_bul = [3.88(+0.63/-0.60) -> 3.23^(+0.52/-0.50)] x 10^(-6

Exploiting transient protein states for the design of small-molecule stabilizers of mutant p53

The destabilizing p53 cancer mutation Y220C creates an extended crevice on the surface of the protein that can be targeted by small-molecule stabilizers. Here, we identify different classes of small molecules that bind to this crevice and determine their binding modes by X-ray crystallography. These structures reveal two major conformational states of the pocket and a cryptic, transiently open hydrophobic subpocket that is modulated by Cys220. In one instance, specifically targeting this transient protein state by a pyrrole moiety resulted in a 40-fold increase in binding affinity. Molecular dynamics simulations showed that both open and closed states of this subsite were populated at comparable frequencies along the trajectories. Our data extend the framework for the design of high-affinity Y220C mutant binders for use in personalized anticancer therapy and, more generally, highlight the importance of implementing protein dynamics and hydration patterns in the drug-discovery process