Simulation of optical observables for space missions to small bodies

The navigation of deep space spacecraft requires accurate measurement of the probe’s state and attitude with respect to a body whose ephemerides may not be known with good accuracy. The heliocentric state of the spacecraft is estimated through radiometric techniques (ranging, Doppler, and Delta-DOR), while optical observables can be introduced to improve the uncertainty in the relative position and attitude with respect to the target body. In this study, we analyze how simulated optical observables affect the estimation of parameters in an orbit determination problem, considering the case of the ESA’s Hera mission towards the binary asteroid system composed of Didymos and Dimorphos. To this extent, a shape model and a photometric function are used to create synthetic onboard camera images. Then, using a stereophotoclinometry technique on some of the simulated images, we create a database of maplets that describe the 3D geometry of the surface around a set of landmarks. The matching of maplets with the simulated images provides the optical observables, expressed as pixel coordinates in the camera frame, which are fed to an orbit determination filter to estimate a certain number of solve-for parameters. The noise introduced in the output optical observables by the image processing can be quantified using as a metric the quality of the residuals, which is used to fine-tune the maplet-matching parameters. In particular, the best results are obtained when using small maplets, with high correlation coefficients and occupation factors.

A spectroscopic and photometric study of MSP companions in Galactic Globular Clusters

This Thesis is devoted to the study of the optical companions of Millisecond Pulsars in Galactic Globular Clusters (GCs) as a part of a large project started at the Department of Astronomy of the Bologna University, in collaboration with other institutions (Astronomical Observatory of Cagliari and Bologna, University of Virginia), specifically dedicated to the study of the environmental effects on passive stellar evolution in galactic GCs. Globular Clusters are very efficient “Kilns” for generating exotic object, such as Millisecond Pulsars (MSP), low mass X-ray binaries(LMXB) or Blue Straggler Stars (BSS). In particular MSPs are formed in binary systems containing a Neutron Star which is spun up through mass accretion from the evolving companion (e.g. Bhattacharia & van den Heuvel 1991). The final stage of this recycling process is either the core of a peeled star (generally an Helium white dwarf) or a very light almos exhausted star, orbiting a very fast rotating Neutron Star (a MSP). Despite the large difference in total mass between the disk of the Galaxy and the Galactic GC system (up a factor 103), the percentage of fast rotating pulsar in binary systems found in the latter is very higher. MSPs in GCs show spin periods in the range 1.3 ÷ 30ms, slowdown rates ˙P 1019 s/s and a lower magnetic field, respect to ”normal” radio pulsars, B 108 gauss . The high probability of disruption of a binary systems after a supernova explosion, explain why we expect only a low percentage of recycled millisecond pulsars respect to the whole pulsar population. In fact only the 10% of the known 1800 radio pulsars are radio MSPs. Is not surprising, that MSP are overabundant in GCs respect to Galactic field, since in the Galactic Disk, MSPs can only form through the evolution of primordial binaries, and only if the binary survives to the supernova explosion which lead to the neutron star formation. On the other hand, the extremely high stellar density in the core of GCs, relative to most of the rest of the Galaxy, favors the formation of several different binary systems, suitable for the recycling of NSs (Davies at al. 1998). In this thesis we will present the properties two millisecond pulsars companions discovered in two globular clusters, the Helium white dwarf orbiting the MSP PSR 1911-5958A in NGC 6752 and the second case of a tidally deformed star orbiting an eclipsing millisecond pulsar, PSR J1701-3006B in NGC6266

Cosmic-Lab: Optical companions to binary Millisecond Pulsars

Millisecond Pulsars (MSPs) are fast rotating, highly magnetized neutron stars. According to the "canonical recycling scenario", MSPs form in binary systems containing a neutron star which is spun up through mass accretion from the evolving companion. Therefore, the final stage consists of a binary made of a MSP and the core of the deeply peeled companion. In the last years, however an increasing number of systems deviating from these expectations has been discovered, thus strongly indicating that our understanding of MSPs is far to be complete. The identification of the optical companions to binary MSPs is crucial to constrain the formation and evolution of these objects. In dense environments such as Globular Clusters (GCs), it also allows us to get insights on the cluster internal dynamics. By using deep photometric data, acquired both from space and ground-based telescopes, we identified 5 new companions to MSPs. Three of them being located in GCs and two in the Galactic Field. The three new identifications in GCs increased by 50% the number of such objects known before this Thesis. They all are non-degenerate stars, at odds with the expectations of the "canonical recycling scenario". These results therefore suggest either that transitory phases should also be taken into account, or that dynamical processes, as exchange interactions, play a crucial role in the evolution of MSPs. We also performed a spectroscopic follow-up of the companion to PSRJ1740-5340A in the GC NGC 6397, confirming that it is a deeply peeled star descending from a ~0.8Msun progenitor. This nicely confirms the theoretical expectations about the formation and evolution of MSPs.

Assessing the fit of unidimensional IRT models for binary data under model misspecification

Model misspecification affects the classical test statistics used to assess the fit of the Item Response Theory (IRT) models. Robust tests have been derived under model misspecification, as the Generalized Lagrange Multiplier and Hausman tests, but their use has not been largely explored in the IRT framework. In the first part of the thesis, we introduce the Generalized Lagrange Multiplier test to detect differential item response functioning in IRT models for binary data under model misspecification. By means of a simulation study and a real data analysis, we compare its performance with the classical Lagrange Multiplier test, computed using the Hessian and the cross-product matrix, and the Generalized Jackknife Score test. The power of these tests is computed empirically and asymptotically. The misspecifications considered are local dependence among items and non-normal distribution of the latent variable. The results highlight that, under mild model misspecification, all tests have good performance while, under strong model misspecification, the performance of the tests deteriorates. None of the tests considered show an overall superior performance than the others. In the second part of the thesis, we extend the Generalized Hausman test to detect non-normality of the latent variable distribution. To build the test, we consider a seminonparametric-IRT model, that assumes a more flexible latent variable distribution. By means of a simulation study and two real applications, we compare the performance of the Generalized Hausman test with the M2 limited information goodness-of-fit test and the Likelihood-Ratio test. Additionally, the information criteria are computed. The Generalized Hausman test has a better performance than the Likelihood-Ratio test in terms of Type I error rates and the M2 test in terms of power. The performance of the Generalized Hausman test and the information criteria deteriorates when the sample size is small and with a few items.