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

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

Spectroscopic and dynamical properties of comet C/2018 F4, likely a true average former member of the Oort cloud

The population of comets hosted by the Oort cloud is heterogeneous. Most studies in this area focused on highly active objects, those with small perihelion distances or examples of objects with peculiar physical properties and/or unusual chemical compositions. This may have produced a biased sample of Oort cloud comets in which the most common objects may be rare, particularly those with perihelia well beyond the orbit of the Earth. Within this context, the known Oort cloud comets may not be representative of the full sample. Here, we study the spectral properties in the visible region and the cometary activity of Comet C/2018 F4 (PANSTARRS). We also explore its orbital evolution with the aim of understanding its origin within the context of known minor bodies moving along nearly parabolic or hyperbolic paths. We present observations obtained with the 10.4 m Gran Telescopio Canarias (GTC), derive the spectral class and visible slope of C/2018 F4 and characterise its level of cometary activity. Direct N-body simulations are carried out to explore its orbital evolution. The absolute magnitude of C/2018 F4 is Hr=13.62+/-0.04. Assuming a pV=0.04 its diameter is D<10.4 km. The object presents a conspicuous coma, with a level of activity comparable to those of other comets observed at similar heliocentric distances. Comet C/2018 F4 has a visible spectrum consistent with that of an X-type asteroid, and has a spectral slope S'=4.0+/-1.0 %/1000\AA and no evidence of hydration. The spectrum matches those of well-studied primitive asteroids and comets. The analysis of its dynamical evolution prior to discovery suggests that C/2018 F4 is not of extrasolar origin. Although the present-day heliocentric orbit of C/2018 F4 is slightly hyperbolic, its observational properties and past orbital evolution are consistent with those of a dynamically old comet with an origin in the Oort cloud.Comment: 6 pages, 5 figures. In pres