Early evolution of disrupted asteroid P/2016 G1 (PANSTARRS)

We present deep imaging observations of activated asteroid P/2016 G1 (PANSTARRS) using the 10.4m Gran Telescopio Canarias (GTC) from late April to early June 2016. The images are best interpreted as the result of a relatively short-duration event with onset about $\mathop{350}_{-30}^{+10}$ days before perihelion (i.e., around 10th February, 2016), starting sharply and decreasing with a $\mathop{24}_{-7}^{+10}$ days (Half-width at half-maximum, HWHM). The results of the modeling imply the emission of $\sim$1.7$\times$10$^7$ kg of dust, if composed of particles of 1 micrometer to 1 cm in radius, distributed following a power-law of index --3, and having a geometric albedo of 0.15. A detailed fitting of a conspicuous westward feature in the head of the comet-like object indicates that a significant fraction of the dust was ejected along a privileged direction right at the beginning of the event, which suggests that the parent body has possibly suffered an impact followed by a partial or total disruption. From the limiting magnitude reachable with the instrumental setup, and assuming a geometric albedo of 0.15 for the parent body, an upper limit for the size of possible fragment debris of $\sim$50 m in radius is derived.Comment: Accepted by ApJ Letter

The dust environment of Main-Belt Comet P/2012 T1 (PANSTARRS)

Main-Belt Comet P/2012 T1 (PANSTARRS) has been imaged using the 10.4m Gran Telescopio Canarias (GTC) and the 4.2m William Herschel Telescope (WHT) at six epochs in the period from November 2012 to February 2013, with the aim of monitoring its dust environment. The dust tails brightness and morphology are best interpreted in terms of a model of sustained dust emission spanning 4 to 6 months. The total dust mass ejected is estimated at $\sim$6--25$\times10^6$ kg. We assume a time-independent power-law size distribution function, with particles in the micrometer to centimeter size range. Based on the quality of the fits to the isophote fields, an anisotropic emission pattern is favored against an isotropic one, in which the particle ejection is concentrated toward high latitudes ($\pm45^\circ$ to $\pm90^\circ$) in a high obliquity object ($I$=80$^\circ$). This seasonally-driven ejection behavior, along with the modeled particle ejection velocities, are in remarkable agreement to those we found for P/2010 R2 (La Sagra) \citep{Moreno11a}.Comment: Accepted for publication in The Astrophysical Journal Letter

The Measurement of Growth under Embodied Technical Change

New U.S. evidence from NIPA contradicts some of the well-known Kaldor stylized facts, and call for a reformulation of the modem theory of economic growth. Among these new facts, two must be stressed : A permanent decline in the relative price of durable goods, and a permanent increase in the real equipment to real GDP ratio. To be consistent with these new facts, growth models must include at least two sectors and address the problem of defining aggregate output. In this paper, the economic theory of index numbers is used to define the growth rate of real output in a growth model with embodied technical change. The main findings are : (i) NIPA's methodology measures growth in accordance with the economic theory on index numbers, and (ii) when the growth rate is measured as in NIPA, the contribution of embodied technical change to per capital GDP growth in the U.S. is 69%, which reinforce the claim that embodied technical change is important for growth.Embodied technical change, Growth facts, Growth accounting, Index number theory

The measurement of growth under embodied technical change.

Crecimiento económico; Números índices; Estados Unidos;

Astronomical Observations of Volatiles on Asteroids

We have long known that water and hydroxyl are important components in meteorites and asteroids. However, in the time since the publication of Asteroids III, evolution of astronomical instrumentation, laboratory capabilities, and theoretical models have led to great advances in our understanding of H2O/OH on small bodies, and spacecraft observations of the Moon and Vesta have important implications for our interpretations of the asteroidal population. We begin this chapter with the importance of water/OH in asteroids, after which we will discuss their spectral features throughout the visible and near-infrared. We continue with an overview of the findings in meteorites and asteroids, closing with a discussion of future opportunities, the results from which we can anticipate finding in Asteroids V. Because this topic is of broad importance to asteroids, we also point to relevant in-depth discussions elsewhere in this volume.Comment: Chapter to appear in the (University of Arizona Press) Space Science Series Book: Asteroids I

Dust environment of active asteroids P/2019 A4 (PANSTARRS) and P/2021 A5 (PANSTARRS)

We report on the characterisation of the dust activity and dynamical evolution of two faint active asteroids, P/2019 A4, and P/2021 A5, observed with the 10.4m GTC using both imaging and spectroscopy. Asteroid P/2019 A4 activity is found to be linked to an impulsive event occurring some $\pm$10 days around perihelion, probably due to a collision or a rotational disruption. Its orbit is stable over 100 Myr timescales. Dust tail models reveal a short-term burst producing (2.0$\pm$0.7)$\times$10$^6$ kg of dust for maximum particle radius rmax=1 cm. The spectrum of P/2019 A4 is featureless, and slightly redder than the Sun. P/2021 A5 was active $\sim$50 days after perihelion, lasting $\sim$5 to $\sim$60 days, and ejecting (8$\pm$2)$\times$10$^6$ kg of dust for rmax=1 cm. The orbital simulations show that a few percent of dynamical clones of P/2021 A5 are unstable on 20-50 Myr timescales. Thus, P/2021 A5 might be an implanted object from the JFC region or beyond. These facts point to water ice sublimation as the activation mechanism. This object also displays a featureless spectrum, but slightly bluer than the Sun. Nuclei sizes are estimated in the few hundred meters range for both asteroids. Particle ejection speeds ($\sim$0.2 m/s) are consistent with escape speeds from those small-sized objects.Comment: Accepted by MNRAS (June 24th, 2021

Compositional study of asteroids in the Erigone collisional family using visible spectroscopy at the 10.4 m GTC

Two primitive near Earth asteroids, (101955) Bennu and (162173) Ryugu, will be visited by a spacecraft with the aim of returning samples back to Earth. Since these objects are believed to originate in the inner main belt primitive collisional families (Erigone, Polana, Clarissa, and Sulamitis) or in the background of asteroids outside these families, the characterization of these primitive populations will enhance the scientific return of the missions. The main goal of this work is to shed light on the composition of the Erigone collisional family by means of visible spectroscopy. Asteroid (163) Erigone has been classified as a primitive object, and we expect the members of this family to be consistent with the spectral type of the parent body. We have obtained visible spectra (0.5 to 0.9 microns) for 101 members of the Erigone family, using the OSIRIS instrument at the 10.4 m Gran Telescopio Canarias. We found that 87 percent of the objects have typically primitive visible spectra consistent with that of (163) Erigone. In addition, we found that a significant fraction of these objects (approximately 50 percent) present evidence of aqueous alteration