Representative galaxy age-metallicity relationships

The ongoing surveys of galaxies and those for the next generation of telescopes will demand the execution of high-CPU consuming machine codes for recovering detailed star formation histories (SFHs) and hence age-metallicity relationships (AMRs). We present here an expeditive method which provides quick-look AMRs on the basis of representative ages and metallicities obtained from colour-magnitude diagram (CMD) analyses. We have tested its perfomance by generating synthetic CMDs for a wide variety of galaxy SFHs. The representative AMRs turn out to be reliable down to a magnitude limit with a photometric completeness factor higher than $\sim$ 85 per cent, and trace the chemical evolution history for any stellar population (represented by a mean age and an intrinsic age spread) with a total mass within ~ 40 per cent of the more massive stellar population in the galaxy.Comment: 12 pages, 11 figures. Accepted for publication in Monthly Notices of the Royal Astronomical Societ

The age-metallicity relationship in the Fornax spheroidal dwarf galaxy

We produce a comprehensive field star age-metallicity relationship (AMR) from the earliest epoch until ~ 1 Gyr ago for three fields in the Fornax dSph galaxy by using VI photometric data obtained with FORS1 at the VLT. We find that the innermost one does not contains dominant very old stars (age > 12 Gyr), whereas the relatively outer field does not account for representative star field populations younger than ~ 3 Gyr. When focusing on the most prominent stellar populations, we find that the derived AMRs are engraved by the evidence of a outside-in star formation process. The studied fields show bimodal metallicity distributions peaked at [Fe/H] = (-0.95 +- 0.15) dex and (-1.15 or -1.25 +- 0.05) dex, respectively, but only during the first half of the entire galaxy lifetime. Furthermore, the more metal-rich population appears to be more numerous in the outer fields, while in the innermost Fornax field the contribution of both metallicity populations seems to be similar. We also find that the metallicity spread ~ 6 Gyr ago is remarkable large, while the intrinsic metallicity dispersion at ~ 1-2 Gyr results smaller than that for the relatively older generations of stars. We interpret these outcomes as a result of a possible merger of two galaxies that would have triggered a star formation bursting process that peaked between ~ 6 and 9 Gyr ago, depending on the position of the field in the galaxy.Comment: 7 pages, 5 figures, MNRAS, in pres

Rational points in the moduli space of genus two

We build a database of genus 2 curves defined over $\mathbb Q$ which contains all curves with minimal absolute height $h \leq 5$, all curves with moduli height $\mathfrak h \leq 20$, and all curves with extra automorphisms in standard form $y^2=f(x^2)$ defined over $\mathbb Q$ with height $h \leq 101$. For each isomorphism class in the database, an equation over its minimal field of definition is provided, the automorphism group of the curve, Clebsch and Igusa invariants. The distribution of rational points in the moduli space $\mathcal M_2$ for which the field of moduli is a field of definition is discussed and some open problems are presented

Dual Mode Control of an Inverted Pendulum: Design, Analysis and Experimental Evaluation

We present an inverted pendulum design using readily available V-slot rail components and 3D printing to construct custom parts. To enable the examination of different pendulum characteristics, we constructed three pendulum poles of different lengths. We implemented a brake mechanism to modify sliding friction resistance and built a paddle that can be attached to the ends of the pendulum poles. A testing rig was also developed to consistently apply disturbances by tapping the pendulum pole, characterizing balancing performance. We perform a comprehensive analysis of the behavior and control of the pendulum. This begins by considering its dynamics, including the nonlinear differential equation that describes the system, its linearization, and its representation in the s-domain. The primary focus of this work is the development of two distinct control modes for the pendulum: a velocity control mode, designed to balance the pendulum while the cart is in motion, and a position control mode, aimed at maintaining the pendulum cart at a specific location. For this, we derived two different state space models: one for implementing the velocity control mode and another for the position control mode. In the position control mode, integral action applied to the cart position ensures that the inverted pendulum remains balanced and maintains its desired position on the rail. For both models, linear observer-based state feedback controllers were implemented. The control laws are designed as linear quadratic regulators (LQR), and the systems are simulated in MATLAB. To actuate the physical pendulum system, a stepper motor was used, and its controller was assembled in a DIN rail panel to simplify the integration of all necessary components. We examined how the optimized performance, achieved with the medium-length pendulum pole, translates to poles of other lengths. Our findings reveal distinct behavioral differences between the control modes

Spatially resolved LMC star formation history: I. Outside in evolution of the outer LMC disk

We study the evolution of three fields in the outer LMC disk Rgc=3.5-6.2 Kpc. Their star formation history indicates a stellar populations gradient such that younger stellar populations are more centrally concentrated. We identify two main star forming epochs, separated by a period of lower activity between ~7 and ~4 Gyr ago. Their relative importance varies from a similar amount of stars formed in the two epochs in the innermost field, to only 40% of the stars formed in the more recent epoch in the outermost field. The young star forming epoch continues to the present time in the innermost field, but lasted only till ~0.8 and 1.3 Gyr ago at Rgc=5.5 degrees and 7.1 degrees, respectively. This gradient is correlated with the measured HI column density and implies an outside-in quenching of the star formation, possibly related to a variation of the size of the HI disk. This could either result from gas depletion due to star formation or ram-pressure stripping, or from to the compression of the gas disk as ram-pressure from the Milky Way halo acted on the LMC interstellar medium. The latter two situations may have occurred when the LMC first approached the Milky Way.Comment: 15 pages, 13 figures, 4 tables. MNRAS, in pres