Parabolic Orbit

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Lixin Dai - One of the best experts on this subject based on the ideXlab platform.

  • the impact of bound stellar Orbits and general relativity on the temporal behavior of tidal disruption flares
    The Astrophysical Journal, 2013
    Co-Authors: Lixin Dai, Andres Escala, Paolo De Coppi
    Abstract:

    We have carried out general relativistic particle simulations of stars tidally disrupted by massive black holes. When a star is disrupted in a bound Orbit with moderate eccentricity instead of a Parabolic Orbit, the temporal behavior of the resulting stellar debris changes qualitatively. The debris is initially all bound, returning to pericenter in a short time about the original stellar Orbital timescale. The resulting fallback rate can thus be much higher than the Eddington rate. Furthermore, if the star is disrupted close to the hole, in a regime where general relativity is important, the stellar and debris Orbits display general relativistic precession. Apsidal precession can make the debris stream cross itself after several Orbits, likely leading to fast debris energy dissipation. If the star is disrupted in an inclined Orbit around a spinning hole, nodal precession reduces the probability of self-intersection, and circularization may take many dynamical timescales, delaying the onset of flare activity. An examination of the particle dynamics suggests that quasi-periodic flares with short durations, produced when the center of the tidal stream passes pericenter, may occur in the early-time light curve. The late-time light curve may still show power-law behavior which is generic to disk accretion processes.more » The detection triggers for future surveys should be extended to capture such 'non-standard' short-term flaring activity before the event enters the asymptotic decay phase, as this activity is likely to be more sensitive to physical parameters such as the black hole spin.« less

  • the impact of bound stellar Orbits and general relativity on the temporal behavior of tidal disruption flares
    arXiv: High Energy Astrophysical Phenomena, 2013
    Co-Authors: Lixin Dai, Andres Escala, Paolo De Coppi
    Abstract:

    We have carried out general relativistic particle simulations of stars tidally disrupted by massive black holes. When a star is disrupted in a bound Orbit with moderate eccentricity instead of a Parabolic Orbit, the temporal behavior of the resulting stellar debris changes qualitatively. The debris is initially all bound, returning to pericenter in a short time ~ the original stellar Orbital timescale. The resulting fallback rate can thus be much higher than the Eddington rate. Furthermore if the star is disrupted close to the hole, in a regime where general relativity is important, the stellar and debris Orbits display general relativistic precession. Apsidal precession can make the debris stream cross itself after several Orbits, likely leading to fast debris energy dissipation. If the star is disrupted in an inclined Orbit around a spinning hole, nodal precession reduces the probability of self-intersection, and circularization may take many dynamical timescales, delaying the onset of flare activity. An examination of the particle dynamics suggests that quasi-periodic flares with short durations, produced when the center of the tidal stream passes pericenter, may occur in the early-time light curve. The late-time light curve may still show power-law behavior which is generic to disk accretion processes. The detection triggers for future surveys should be extended to capture such "non-standard" short-term flaring activity before the event enters the asymptotic decay phase, as this activity is likely to be more sensitive to physical parameters such as the black hole spin.

Paolo De Coppi - One of the best experts on this subject based on the ideXlab platform.

  • the impact of bound stellar Orbits and general relativity on the temporal behavior of tidal disruption flares
    The Astrophysical Journal, 2013
    Co-Authors: Lixin Dai, Andres Escala, Paolo De Coppi
    Abstract:

    We have carried out general relativistic particle simulations of stars tidally disrupted by massive black holes. When a star is disrupted in a bound Orbit with moderate eccentricity instead of a Parabolic Orbit, the temporal behavior of the resulting stellar debris changes qualitatively. The debris is initially all bound, returning to pericenter in a short time about the original stellar Orbital timescale. The resulting fallback rate can thus be much higher than the Eddington rate. Furthermore, if the star is disrupted close to the hole, in a regime where general relativity is important, the stellar and debris Orbits display general relativistic precession. Apsidal precession can make the debris stream cross itself after several Orbits, likely leading to fast debris energy dissipation. If the star is disrupted in an inclined Orbit around a spinning hole, nodal precession reduces the probability of self-intersection, and circularization may take many dynamical timescales, delaying the onset of flare activity. An examination of the particle dynamics suggests that quasi-periodic flares with short durations, produced when the center of the tidal stream passes pericenter, may occur in the early-time light curve. The late-time light curve may still show power-law behavior which is generic to disk accretion processes.more » The detection triggers for future surveys should be extended to capture such 'non-standard' short-term flaring activity before the event enters the asymptotic decay phase, as this activity is likely to be more sensitive to physical parameters such as the black hole spin.« less

  • the impact of bound stellar Orbits and general relativity on the temporal behavior of tidal disruption flares
    arXiv: High Energy Astrophysical Phenomena, 2013
    Co-Authors: Lixin Dai, Andres Escala, Paolo De Coppi
    Abstract:

    We have carried out general relativistic particle simulations of stars tidally disrupted by massive black holes. When a star is disrupted in a bound Orbit with moderate eccentricity instead of a Parabolic Orbit, the temporal behavior of the resulting stellar debris changes qualitatively. The debris is initially all bound, returning to pericenter in a short time ~ the original stellar Orbital timescale. The resulting fallback rate can thus be much higher than the Eddington rate. Furthermore if the star is disrupted close to the hole, in a regime where general relativity is important, the stellar and debris Orbits display general relativistic precession. Apsidal precession can make the debris stream cross itself after several Orbits, likely leading to fast debris energy dissipation. If the star is disrupted in an inclined Orbit around a spinning hole, nodal precession reduces the probability of self-intersection, and circularization may take many dynamical timescales, delaying the onset of flare activity. An examination of the particle dynamics suggests that quasi-periodic flares with short durations, produced when the center of the tidal stream passes pericenter, may occur in the early-time light curve. The late-time light curve may still show power-law behavior which is generic to disk accretion processes. The detection triggers for future surveys should be extended to capture such "non-standard" short-term flaring activity before the event enters the asymptotic decay phase, as this activity is likely to be more sensitive to physical parameters such as the black hole spin.

Jiri Stavek - One of the best experts on this subject based on the ideXlab platform.

  • galileo s parabola observed from pappus directrix apollonius pedal curve line galileo s empty focus newton s evolute leibniz s subtangent and subnormal ptolemy s circle hodograph and durer simon parabola 16 03 2019
    Applied Physics research, 2019
    Co-Authors: Jiri Stavek
    Abstract:

    Galileo’s Parabola describing the projectile motion passed through hands of all scholars of the classical mechanics. Therefore, it seems to be impossible to bring to this topic anything new. In our approach we will observe the Galileo’s Parabola from Pappus’ Directrix, Apollonius’ Pedal Curve (Line), Galileo’s Empty Focus, Newton’s Evolute, Leibniz’s Subtangent and Subnormal, Ptolemy’s Circle (Hodograph), and Durer-Simon Parabola. For the description of events on this Galileo’s Parabola (this conic section parabola was discovered by Menaechmus) we will employ the interplay of the directrix of parabola discovered by Pappus of Alexandria, the pedal curve with the pedal point in the focus discovered by Apollonius of Perga (The Great Geometer), and the Galileo’s empty focus that plays an important function, too. We will study properties of this MAG Parabola with the aim to extract some hidden parameters behind that visible Parabolic Orbit in the Aristotelian World. For the visible Galileo’s Parabola in the Aristotelian World, there might be hidden curves in the Plato’s Realm behind the mechanism of that Parabola. The analysis of these curves could reveal to us hidden properties describing properties of that projectile motion. The Parabolic path of the projectile motion can be described by six expressions of projectile speeds. In the Durer-Simon’s Parabola we have determined tangential and normal accelerations with resulting acceleration g = 9.81 msec-2 directing towards to Galileo’s empty focus for the projectile moving to the vertex of that Parabola. When the projectile moves away from the vertex the resulting acceleration g = 9.81 msec-2 directs to the center of the Earth (the second focus of Galileo’s Parabola in the “infinity”). We have extracted some additional properties of Galileo’s Parabola. E.g., the Newtonian school correctly used the expression for “kinetic energy E = ½ mv2 for Parabolic Orbits and paths, while the Leibnizian school correctly used the expression for “vis viva” E = mv2 for hyperbolic Orbits and paths. If we will insert the “vis viva” expression into the Soldner’s formula (1801) (e.g., Fengyi Huang in 2017), then we will get the right experimental value for the deflection of light on hyperbolic Orbits. In the Plato’s Realm some other curves might be hidden and have been waiting for our future research. Have we found the Arriadne’s Thread leading out of the Labyrinth or are we still lost in the Labyrinth?

  • newton s parabola observed from pappus directrix apollonius pedal curve line newton s evolute leibniz s subtangent and subnormal castillon s cardioid and ptolemy s circle hodograph 09 02 2019
    Applied Physics research, 2019
    Co-Authors: Jiri Stavek
    Abstract:

    Johannes Kepler and Isaac Newton inspired generations of researchers to study properties of elliptic, hyperbolic, and Parabolic paths of planets and other astronomical objects Orbiting around the Sun. The books of these two Old Masters “Astronomia Nova” and “Principia…” were originally written in the geometrical language. However, the following generations of researchers translated the geometrical language of these Old Masters into the infinitesimal calculus independently discovered by Newton and Leibniz. In our attempt we will try to return back to the original geometrical language and to present several figures with possible hidden properties of Parabolic Orbits. For the description of events on Parabolic Orbits we will employ the interplay of the directrix of parabola discovered by Pappus of Alexandria, the pedal curve with the pedal point in the focus discovered by Apollonius of Perga (The Great Geometer), and the focus occupied by our Sun discovered in several stages by Aristarchus, Copernicus, Kepler and Isaac Newton (The Great Mathematician). We will study properties of this PAN Parabola with the aim to extract some hidden parameters behind that visible Parabolic Orbit in the Aristotelian World. In the Plato’s Realm some curves carrying hidden information might be waiting for our research. One such curve - the evolute of parabola - discovered Newton behind his famous gravitational law. We have used the Castillon’s cardioid as the curve describing the tangent velocity of objects on the Parabolic Orbit. In the PAN Parabola we have newly used six parameters introduced by Gottfried Wilhelm Leibniz - abscissa, ordinate, length of tangent, subtangent, length of normal, and subnormal. We have obtained formulae both for the tangent and normal velocities for objects on the Parabolic Orbit. We have also obtained the moment of tangent momentum and the moment of normal momentum. Both moments are constant on the whole Parabolic Orbit and that is why we should not observe the precession of Parabolic Orbit. We have discovered the Ptolemy’s Circle with the diameter a (distance between the vertex of parabola and its focus) where we see both the tangent and normal velocities of Orbiting objects. In this case the Ptolemy’s Circle plays a role of the hodograph rotating on the Parabolic Orbit without sliding. In the Plato’s Realm some other curves might be hidden and have been waiting for our future research. Have we found the Arriadne’s Thread leading out of the Labyrinth or are we still lost in the Labyrinth?

Andres Escala - One of the best experts on this subject based on the ideXlab platform.

  • the impact of bound stellar Orbits and general relativity on the temporal behavior of tidal disruption flares
    The Astrophysical Journal, 2013
    Co-Authors: Lixin Dai, Andres Escala, Paolo De Coppi
    Abstract:

    We have carried out general relativistic particle simulations of stars tidally disrupted by massive black holes. When a star is disrupted in a bound Orbit with moderate eccentricity instead of a Parabolic Orbit, the temporal behavior of the resulting stellar debris changes qualitatively. The debris is initially all bound, returning to pericenter in a short time about the original stellar Orbital timescale. The resulting fallback rate can thus be much higher than the Eddington rate. Furthermore, if the star is disrupted close to the hole, in a regime where general relativity is important, the stellar and debris Orbits display general relativistic precession. Apsidal precession can make the debris stream cross itself after several Orbits, likely leading to fast debris energy dissipation. If the star is disrupted in an inclined Orbit around a spinning hole, nodal precession reduces the probability of self-intersection, and circularization may take many dynamical timescales, delaying the onset of flare activity. An examination of the particle dynamics suggests that quasi-periodic flares with short durations, produced when the center of the tidal stream passes pericenter, may occur in the early-time light curve. The late-time light curve may still show power-law behavior which is generic to disk accretion processes.more » The detection triggers for future surveys should be extended to capture such 'non-standard' short-term flaring activity before the event enters the asymptotic decay phase, as this activity is likely to be more sensitive to physical parameters such as the black hole spin.« less

  • the impact of bound stellar Orbits and general relativity on the temporal behavior of tidal disruption flares
    arXiv: High Energy Astrophysical Phenomena, 2013
    Co-Authors: Lixin Dai, Andres Escala, Paolo De Coppi
    Abstract:

    We have carried out general relativistic particle simulations of stars tidally disrupted by massive black holes. When a star is disrupted in a bound Orbit with moderate eccentricity instead of a Parabolic Orbit, the temporal behavior of the resulting stellar debris changes qualitatively. The debris is initially all bound, returning to pericenter in a short time ~ the original stellar Orbital timescale. The resulting fallback rate can thus be much higher than the Eddington rate. Furthermore if the star is disrupted close to the hole, in a regime where general relativity is important, the stellar and debris Orbits display general relativistic precession. Apsidal precession can make the debris stream cross itself after several Orbits, likely leading to fast debris energy dissipation. If the star is disrupted in an inclined Orbit around a spinning hole, nodal precession reduces the probability of self-intersection, and circularization may take many dynamical timescales, delaying the onset of flare activity. An examination of the particle dynamics suggests that quasi-periodic flares with short durations, produced when the center of the tidal stream passes pericenter, may occur in the early-time light curve. The late-time light curve may still show power-law behavior which is generic to disk accretion processes. The detection triggers for future surveys should be extended to capture such "non-standard" short-term flaring activity before the event enters the asymptotic decay phase, as this activity is likely to be more sensitive to physical parameters such as the black hole spin.

Yang Bin - One of the best experts on this subject based on the ideXlab platform.

  • Narrow-band photometry of Long Period Comets with TRAPPIST telescopes in 2019-2020
    'Copernicus GmbH', 2020
    Co-Authors: Moulane Youssef, Jehin Emmanuel, José Pozuelos Francisco, Manfroid Jean, Benkhaldoun Zouhair, Yang Bin
    Abstract:

    audience: professionalLong Period Comets (LPCs) have Orbital periods longer than 200 years, perturbed from their resting place in the Oort cloud. Such gravitational influences may send these icy bodies on a path towards the center of the Solar system in highly elliptical Orbits. In this work, we present the activity and composition evolution of several LPCs observed with both TRAPPIST telescopes (TS and TN) during the period of 2019-2020. These comets include: C/2017 T2 (PANSTARRS), C/2018 Y1 (Iwamoto), C/2018 W2 (Africano), and disintegrated comet C/2019 Y4 (ATLAS). We monitored the OH, NH, CN, C2 and C3 production rates evolution and their chemical mixing ratios with respect to their distances to the Sun as well as the dust production rate proxy (A(0)fp) during the journey of these comets into the inner Solar system.C/2017 T2 (PANSTARRS) is a very bright comet which was discovered on October 2, 2017 when it was 9.20 au from the Sun. We started observing this comet with TS at the beginning of August 2019 when it was at 3.70 au. The comet made the closest approach to the Earth on December 28, 2019 at a distance of 1.52 au and it passed the perihelion on May 4, 2020 at 1.61 au. The water production rate of the comet reached a maximum of (4,27±0,12)1028 molecules/s and its dust production rate (A(0)fp(RC)) also reached the peak of 5110±25 cm on January 26, 2020, when the comet was at 2.08 au from the Sun (-100 days pre-perihelion). At the time of writing, we still monitoring the activity of the comet with TN at heliocentric distance of 1.70 au. Our observations show that C/2017 T2 is a normal LPC.C/2018 Y1 (Iwamoto) is a nearly Parabolic comet with a retrograde Orbit discovered on December 18, 2018 by Japanese amateur astronomer Masayuki Iwamoto. We monitored the activity and composition of Iwamoto with both TN and TS telescopes from January to March 2019. The comet reached its maximum activity on January 29, 2019 when it was at 1.29 au from the Sun (-8 days pre-perihelion) with Q(H2O)=(1,68±0,05)1028 molecules/s and A(0)fp(RC)= 92±5 cm. These measurements show that it was a dust-poor comet compared to the typical LPCs.C/2018 W2 (Africano) was discovered on November 27, 2018 at Mount Lemmon Survey with a visual magnitude of 20. The comet reached its perihelion on September 6, 2019 when it was at 1.45 au from the Sun. We monitored the comet from July 2019 (rh=1.71 au) to January 2020 (rh=2.18 au) with both TN and TS telescopes. The comet reached its maximum activity on September 21, 15 days post-perihelion (rh=1.47 au) with Q(H2O)=(0,40±0,03)1028 molecules/s.C/2019 Y4 (ATLAS) is a comet with a nearly Parabolic Orbit discovered on December 18, 2019 by the ATLAS survey. We started to follow its activity and composition with broad- and narrow-band filters with the TN telescope on February 22, 2019 when it was at 1.32 au from the Sun until May 3, 2020 when the comet was at a heliocentric distance of 0.90 au inbound. The comet activity reached a maximum on March 22 (rh=1.65 au) 70 days before perihelion. At that time, the water-production rate reached (1,53±0,04)1028 molecules/s and the A(0)fp reached (1096±14) cm in the red filter. After that, the comet began to fade and disintegrated into several fragments

  • Narrow-band photometry of Long Period Comets with TRAPPIST telescopes in 2019-2020
    2020
    Co-Authors: Moulane Youssef, Jehin Emmanuel, José Pozuelos Francisco, Manfroid Jean, Benkhaldoun Zouhair, Yang Bin
    Abstract:

    Long Period Comets (LPCs) have Orbital periods longer than 200 years, perturbed from their resting place in the Oort cloud. Such gravitational influences may send these icy bodies on a path towards the center of the Solar system in highly elliptical Orbits. In this work, we present the activity and composition evolution of several LPCs observed with both TRAPPIST telescopes (TS and TN) during the period of 2019-2020. These comets include: C/2017 T2 (PANSTARRS), C/2018 Y1 (Iwamoto), C/2018 W2 (Africano), and disintegrated comet C/2019 Y4 (ATLAS). We monitored the OH, NH, CN, C2 and C3 production rates evolution and their chemical mixing ratios with respect to their distances to the Sun as well as the dust production rate proxy (A(0)fp) during the journey of these comets into the inner Solar system.C/2017 T2 (PANSTARRS) is a very bright comet which was discovered on October 2, 2017 when it was 9.20 au from the Sun. We started observing this comet with TS at the beginning of August 2019 when it was at 3.70 au. The comet made the closest approach to the Earth on December 28, 2019 at a distance of 1.52 au and it passed the perihelion on May 4, 2020 at 1.61 au. The water production rate of the comet reached a maximum of (4,27±0,12)1028 molecules/s and its dust production rate (A(0)fp(RC)) also reached the peak of 5110±25 cm on January 26, 2020, when the comet was at 2.08 au from the Sun (-100 days pre-perihelion). At the time of writing, we still monitoring the activity of the comet with TN at heliocentric distance of 1.70 au. Our observations show that C/2017 T2 is a normal LPC.C/2018 Y1 (Iwamoto) is a nearly Parabolic comet with a retrograde Orbit discovered on December 18, 2018 by Japanese amateur astronomer Masayuki Iwamoto. We monitored the activity and composition of Iwamoto with both TN and TS telescopes from January to March 2019. The comet reached its maximum activity on January 29, 2019 when it was at 1.29 au from the Sun (-8 days pre-perihelion) with Q(H2O)=(1,68±0,05)1028 molecules/s and A(0)fp(RC)= 92±5 cm. These measurements show that it was a dust-poor comet compared to the typical LPCs.C/2018 W2 (Africano) was discovered on November 27, 2018 at Mount Lemmon Survey with a visual magnitude of 20. The comet reached its perihelion on September 6, 2019 when it was at 1.45 au from the Sun. We monitored the comet from July 2019 (rh=1.71 au) to January 2020 (rh=2.18 au) with both TN and TS telescopes. The comet reached its maximum activity on September 21, 15 days post-perihelion (rh=1.47 au) with Q(H2O)=(0,40±0,03)1028 molecules/s.C/2019 Y4 (ATLAS) is a comet with a nearly Parabolic Orbit discovered on December 18, 2019 by the ATLAS survey. We started to follow its activity and composition with broad- and narrow-band filters with the TN telescope on February 22, 2019 when it was at 1.32 au from the Sun until May 3, 2020 when the comet was at a heliocentric distance of 0.90 au inbound. The comet activity reached a maximum on March 22 (rh=1.65 au) 70 days before perihelion. At that time, the water-production rate reached (1,53±0,04)1028 molecules/s and the A(0)fp reached (1096±14) cm in the red filter. After that, the comet began to fade and disintegrated into several fragments