## DDA 2015 – The Relative Influence of Dynamical Nature and Nurture on the Formation of Disk Galaxies

This is one of a series of notes taken during the 2015 meeting of the AAS Division on Dynamical Astronomy, 3-7 May, at CalTech. An index to this series (all the papers presented at the meeting) is here.

Jonathan Bird (Vanderbilt) (invited)

[None]

#### Notes

• Are disk galaxies formed by nature or nurture?
• e.g. NGC 891
• Thick disk and thin disk (Gilmore & Reid 1983)
• Extragalactic thick disks are ubiquitous (Dalcanton & Bernstein 2002, Yoachim & Dalcanton 2006)
• Nature:
• Stellar kinematics dominated by those of gas from which stars formed
• Subsequent dynamics are second-order
• Planetary disk: core accretion; static
• $\alpha$ abundance is a tracer for stellar age
• plot: [$\alpha$/Fe] vs [Fe/H]
• Thick disk is old, $\alpha$-rich, kinematically hot
• Thin disk is young, (relatively to Fe) $\alpha$-poor, dynamically cold
• Smooth correlation between chemistry and kinematics
• APOGEE survey: velocity dispersion increases with stellar age
• power law
• $\rightarrow$ disk grows over time
• Nurture:
• Stellar kinematics dominated by dynamical interactions after birth
• Most stars born in dynamical cold gas (level playing field)
• Resonances play huge role; pebble accretion
• Scattering processes heat stellar velocity distributions
• Sellwood & Binney 2002: can redistribute stars without globally heating the disk
• Can outwardly migrating stars create the thick disk?
• No: vertical action is conserved. (Tolfree et al. 2014)

## DDA 2015 – Cross Sections for Planetary Systems Interacting with Passing Stars and Binaries

This is one of a series of notes taken during the 2015 meeting of the AAS Division on Dynamical Astronomy, 3-7 May, at CalTech. An index to this series (all the papers presented at the meeting) is here.

### Fred C. Adams (U. Michigan)

#### Abstract

Numerous spectroscopic and photometric studies have provided strong evidence of the presence of multiple stellar populations in globular clusters and raised many fundamental questions concerning the formation and dynamical evolution of these stellar systems. After a brief review of the main observational studies, I will present the results of theoretical investigations exploring a number of aspects of the internal dynamics of multiple-population clusters and their formation history. Most planetary systems are formed within stellar clusters, and these environments can shape their properties. This talk considers scattering encounters between solar systems and passing cluster members, and calculates the corresponding interaction cross sections. The target solar systems are generally assumed to have four giant planets, with a variety of starting states, including circular orbits with the semimajor axes of our planets, a more compact configuration, an ultracompact state with multiple mean motion resonances, and systems with massive planets. We then consider the effects of varying the cluster velocity dispersion, the relative importance of binaries versus single stars, different stellar host masses, and finite starting eccentricities of the planetary orbits. For each state of the initial system, we perform an ensemble of numerical scaRering experiments and determine the cross sections for eccentricity increase, inclination angle increase, planet ejection, and capture. This talk reports results from over 2 million individual scattering simulations. Using supporting analytic considerations, and fibng functions to the numerical results, we find a universal formula that gives the cross sections as a function of stellar host mass, cluster velocity dispersion, starting planetary orbital radius, and final eccentricity. The resulting cross sections can be used in a wide variety of applications. As one example, we revisit constraints on the birth aggregate of our Solar System due to dynamical scattering and find N < 10,000 (consistent with previous estimates).

#### Notes

• Most stars form in clusters
• particle fluxes
• dynamical interactions
• need to know cross sections and rates at which things fly by
• closest approach distribution = power law
• Simulationstodetermine cross sections
• many Monte Carlo simulations
• 2 million runs
• many parameters + chaotic behavior
• do planetary eccentricities get pumped up?
• yes
• Results:
• by and large, $\sigma \gg A$
• $\dfrac{\sigma}{a} = A v^{-\frac{7}{5}} \exp\left[b(1-e)\right]$
• $\sigma = \sigma_0 \exp\left[b(1-\sin \Delta i)\right]$
• $\Delta i \propto \Delta e$
• size of birth cluster constrained to $< 10^4$ stars
• G. Li & Adams 2015 (MNRAS 448:344)

## DDA 2015 – Dynamical Evolution of Multiple-Population Globular Clusters

This is one of a series of notes taken during the 2015 meeting of the AAS Division on Dynamical Astronomy, 3-7 May, at CalTech. An index to this series (all the papers presented at the meeting) is here.

### Session: Star Cluster and Galaxy Dynamics

Enrico Vesperini (Indiana University) (invited) [withdrawn]

#### Abstract

Numerous spectroscopic and photometric studies have provided strong evidence of the presence of multiple stellar populations in globular clusters and raised many fundamental questions concerning the formation and dynamical evolution of these stellar systems. After a brief review of the main observational studies, I will present the results of theoretical investigations exploring a number of aspects of the internal dynamics of multiple-population clusters and their formation history.

## DDA 2015 – Lense-Thirring Effect Measurement from LAGEOS Node: Limitation from Radiation Forces

This is one of a series of notes taken during the 2015 meeting of the AAS Division on Dynamical Astronomy, 3-7 May, at CalTech. An index to this series (all the papers presented at the meeting) is here.

### Session: Dynamics of Small Solar System Bodies III

Victor J. Slabinski (USNO)

#### Abstract

The Lense‑Thirring (L‑T) effect from General Relativity predicts a small secular increase to the node right ascension for close Earth satellites. For the LAGEOS 1 satellite, the predicted node increase is 31 mas/y. There is a current effort to observationally evaluate L‑T to 1 percent accuracy through an orbit analysis of the laser‑ranged LAGEOS 1, LAGEOS 2, and LARES satellites. Uncertainty in the computed gravitational perturbations to the satellite nodes, due to parameter uncertainties, is largely eliminated by taking a linear combination of the node positions which eliminates the uncertainty due to the major terms. One then looks for the L‑T effect on this composite node.

But there remains uncertainty in the computed perturbations due to two radiation (non‑gravitational) forces: the solar radiation (SR) force and thermal thrust (Yarkovsky effects). This paper treats LAGEOS 1 perturbations. For simplicity in discussion, we treat perturbations to its node rather than perturbations to the composite node.

Uncertainty in the perturbation rates arises from ignorance of parameter values for the LAGEOS 1 exterior aluminum surface, specifically, the solar absorbtance and thermal emiRance. The LAGEOS 1 Phase B design study proposed three different sets of aluminum surface parameters without recommending a particular set. The LAGEOS 1 as-built surface parameters were not measured prior to spacecraft launch.

The possible spread in LAGEOS 1 solar absorbtance values gives a spread of ±0.42 mas/y in the SR force contribution to its node rate. This results in a ±1.3 percent uncertainty to the L‑T determination. But because of its long‑period perturbation to the eccentricity vector, evaluating the SR force parameter as a solved‑for parameter in the orbit analysis should significantly reduce the uncertainty in the corresponding node motion. The possible spread in LAGEOS 1 surface values gives a spread of ±0.16 mas/y in the thermal thrust contribution to its node rate. This represents a ±0.53 percent uncertainty in the L‑T determination which leaves little room for other error sources. Ground-based satellite brightness measurements could improve knowledge of the surface absorbtance and reduce the uncertainty from thermal thrust.

#### Notes

• Lense-Thirring
• gravitomagnetic effect
• spinning Earth:
• $\rightarrow$ frame-dragging
• $\rightarrow$ precession of $\Omega$ and $\omega$
• LAGEOS 1 & 2: linear motion of $\Omega \approx 1.8$ m/yr
• Goal: 1% measurement of L-T effect
• Other perturbing forces
• requires knowledge of satellite surface material properties
• notably: aging
• Thermal thrust
• IR from Earth
• fused silica of corner-cube reflectors is an excellent absorber of IR
• Oops
• thermal phase lag: max recoil force not at local midnight but somewhat past
• $\rightarrow \sim 3 \mathrm{pm/s^2}$ acceleration component along orbit track
• $\rightarrow$ also a component perpendicular to orbital plane
• affects nodal precession rate
• Satellite surface properties
• Corner-cube reflectors: no problem. We know fused silica.
• Aluminum frame: uh oh…
• Not measured beforeLAGEOS 1 launch!
• thermal absorptance
• thermal emittance
• Node precession from solar radiation term: ~1/4 L-T effect
• But radiation force also changes eccentricity vector, from which you can get diffuse reflection coefficient
• but not specular
• One solution: brightness measurements from the ground
• Magnitude range: 11.5-14

## DDA 2015 – New Trans-Neptunian Objects in the Dark Energy Survey Supernova Fields

This is one of a series of notes taken during the 2015 meeting of the AAS Division on Dynamical Astronomy, 3-7 May, at CalTech. An index to this series (all the papers presented at the meeting) is here.

David W. Gerdes (U. Michigan)

#### Abstract

The Dark Energy Survey (DES) observes ten separate 3 sq. deg. fields approximately weekly for six months each year. Although intended primarily to detect Type Ia supernovae, this data set provides a rich time series that is well suited for the detection of objects in the outer solar system, which move slowly enough that they can remain in the same field of view for weeks, months, or even across multiple DES observing seasons. Because the supernova fields have ecliptic latitudes ranging from -15 to -45 degrees, DES is particularly sensitive to the dynamically hot population of Kuiper Belt objects, as well as detached/inner Oort cloud objects. Here I report the results of a search for new trans-Neptunian objects in the first two seasons of DES data, to limiting magnitudes of r~23.8 in the eight shallow fields and ~24.5 in the two deep fields. The 22 objects discovered to date include two new Neptune trojans, a number of objects in mean motion resonances with Neptune, two objects with orbital inclinations above 45 degrees, a Uranian resonator, and several distant scaRered disk objects including one with an orbital period of nearly 6000 years. This latter object is among the half-dozen longest-period trans-Neptunian objects known, and like the other such objects has an argument of perihelion near zero degrees. I will discuss the properties and orbital dynamics of objects discovered to date, and will also discuss prospects for extending the search to the full 5000 sq. deg. DES wide survey.

#### Notes

• Piggy back on DES to find and characterizeTNOs
• Will surpass all previous TNO surveys
• DECam:
• 570 Mpix imager
• CTIO 4-meter
• 3 deg fov
• first light Sep. 2012
• first two of five seasons complete
• 125 nights/yr, 5 optical bands
• 60 2k$\times$4k CCDs (two died)
• Biased towards high inclination objects
• Sensitive to hot population
• New objects identified via difference imaging
• Confusion an issue
• But KBOs move slowly
• Once you find a 3-visit orbit consistent with KB motion, it’s easy
• Should be able to discover a ~600 km object at 80 AU
• 23 new objects discovered in first two seasons (~10% of hot population)
• Case studies
• 2013RG98
• 3:4 Uranian MMR (temporary)
• Likely to become a Jupiter family comet, or maybe ejected
• 2014QO441, 2014QP441
• Neptune Trojans
• libration period ~9100 yr
• stable on Gyr timescales
• 2013RF98
• An extreme TNO
• $a = 325$ AU, $i = 30^\circ$, $e = 0.89$, $P = 5682$ yr
• Clustering of $\omega$

## DDA 2015 – Stochastic YORP On Real Asteroid Shapes

This is one of a series of notes taken during the 2015 meeting of the AAS Division on Dynamical Astronomy, 3-7 May, at CalTech. An index to this series (all the papers presented at the meeting) is here.

Jay W. McMahon (UC Boulder)

#### Abstract

Since its theoretical foundation and subsequent observational verification, the YORP effect has been understood to be a fundamental process that controls the evolution of small asteroids in the inner solar system. In particular, the coupling of the YORP and Yarkovsky effects are hypothesized to be largely responsible for the transport of asteroids from the main belt to the inner solar system populations. Furthermore, the YORP effect is thought to lead to rotational fission of small asteroids, which leads to the creation of multiple asteroid systems, contact binary asteroids, and asteroid pairs. However recent studies have called into question the ability of YORP to produce these results. In particular, the high sensitivity of the YORP coefficients to variations in the shape of an asteroid, combined with the possibility of a changing shape due to YORP accelerated spin rates can combine to create a stochastic YORP coefficient which can arrest or change the evolution of a small asteroid’s spin state. In this talk, initial results are presented from new simulations which comprehensively model the stochastic YORP process. Shape change is governed by the surface slopes on radar based asteroid shape models, where the highest slope regions change first. The investigation of the modification of YORP coefficients and subsequent spin state evolution as a result of this dynamically influenced shape change is presented and discussed.

#### Notes

• Background
• YORP controls small asteroid spin evolution
• YORP highly sensitive to location of features on surface (Statler 2009)
• “stochastic YORP” (Cotto-Figueroa 2013)
• “stochastic YORP” $\rightarrow$ evolution of asteroid families (Bottke et al. 2015)
• Motivation
• Do shapes change as spin increases?
• How does shape evolution map to YORP coefficients?
• Shape evolution
• Regolith will flow “downhill”
• Body will reshape to relax to some slope limit (Scheeres 2015)
• This study: use actual radar-derived asteroid shapes instead of idealized sphere/ellipsoid
• Use (101955)Bennu
• Apollo asteroid
• OSIRIS-REx sample return target
• Results
• 5-m boulder (as spin limitis approached):
• effect on obliquity very small
• larger effects on spin rate
• shape of boulder matters
• Much future work to do

## DDA 2015 – Contact Binary Asteroids

This is one of a series of notes taken during the 2015 meeting of the AAS Division on Dynamical Astronomy, 3-7 May, at CalTech. An index to this series (all the papers presented at the meeting) is here.

Samantha Rieger (UC Boulder)

#### Abstract

Recent observations have found that some contact binaries are oriented such that the secondary impacts with the primary at a high inclination. This research investigates the evolution of how such contact binaries came to exist. This process begins with an asteroid pair, where the secondary lies on the Laplace plane. The Laplace plane is a plane normal to the axis about which the pole of a satellite’s orbit precesses, causing a near constant inclination for such an orbit. For the study of the classical Laplace plane, the secondary asteroid is in circular orbit around an oblate primary with axial tilt. This system is also orbiting the Sun. Thus, there are two perturbations on the secondary’s orbit: J2 and third body Sun perturbations. The Laplace surface is defined as the group of orbits that lie on the Laplace plane at varying distances from the primary. If the secondary is very close to the primary, the inclination of the Laplace plane will be near the equator of the asteroid, while further from the primary the inclination will be similar to the asteroid-Sun plane. The secondary will lie on the Laplace plane because near the asteroid the Laplace plane is stable to large deviations in motion, causing the asteroid to come to rest in this orbit. Assuming the secondary is asymmetrical in shape and the body’s rotation is synchronous with its orbit, the secondary will experience the BYORP effect. BYORP can cause secular motion such as the semi-major axis of the secondary expanding or contracting. Assuming the secondary expands due to BYORP, the secondary will eventually reach the unstable region of the Laplace plane. The unstable region exists if the primary has an obliquity of 68.875 degrees or greater. The unstable region exists at 0.9 Laplace radius to 1.25 Laplace radius, where the Laplace radius is defined as the distance from the central body where the inclination of the Laplace plane orbit is half the obliquity. In the unstable region, the eccentricity of the orbit increases. Once the eccentricity becomes very large or approaching 1, the orbit of the secondary intersects with the primary and will eventually collide and becomes a contact binary.

#### Notes

• Motivation
• contact binaries exist with high obliquity, ~90 deg
• Does Laplace plane have a role?
• Resonances between binary orbit and solar perturbations?
• Laplace plane
• $\omega_2 \sin 2 \phi + \omega_s \sin 2(\phi – \epsilon) = 0$
• $\phi$ = incl. orbit relative to equator
• Near asteroid, orbit lies close to equator. Further, orbit lies near orbit plane.
• LP unstable in $e$ for obliquity above 68.875 deg and $a$ between 0.9 and 1.25 Laplace radii (Tremaine et al. 2009)
• Evolution of contact binary
• Fission occurs. Jacobson & Scheeres 2011
• Dissipation $\rightarrow$ stable circ. orbit in LP
• Model: simple model — secular expansion of $a$ from BYORP and tides
• Const. accel. perp. to radial vector
• Use first Fourier coefficient for BYORP accel.
• Results
• Verify instability region
• Unstable region: eccentric instability causes deviation from LP, collision
• New (eccentricity) instability mode
• cf Cuk & Nesvorny 2010
• reimpact
• regardless of obliquity
• $\rightarrow$ contact binary
• Evection resonance could also play a role

## DDA 2015 – Gravity and Tide Parameters Determined from Satellite and Spacecraft Orbits

This is one of a series of notes taken during the 2015 meeting of the AAS Division on Dynamical Astronomy, 3-7 May, at CalTech. An index to this series (all the papers presented at the meeting) is here.

### Session: Dynamics of Small Solar System Bodies II

Robert A. Jacobson (JPL)

#### Abstract

As part of our work on the development of the Jovian and Saturnian satellite ephemerides to support the Juno and Cassini missions, we determined a number of planetary system gravity parameters. This work did not take into account tidal forces. In fact, we saw no obvious observational evidence of tidal effects on the satellite or spacecraft orbits. However, Lainey et al. (2009 Nature 459, 957) and Lainey et. al (2012 Astrophys. J. 752, 14) have published investigations of tidal effects in the Jovian and Saturnian systems, respectively. Consequently, we have begun a re-examination of our ephemeris work that includes a model for tides raised on the planet by the satellites as well as tides raised on the satellites by the planet. In this paper we briefly review the observations used in our ephemeris production; they include astrometry from the late 1800s to 2014, mutual events, eclipses, occultatons, and data acquired by the Pioneer, Voyager, Ulysses, Cassini, Galileo, and New Horizons spacecraft. We summarize the gravity parameter values found from our original analyses. Next we discuss our tidal acceleration model and its impact on the gravity parameter determination. We conclude with preliminary results found when the reprocessing of the observations includes tidal forces acting on the satellites and spacecraft.

#### Notes

• Jupiter and Saturn gravity fields program at JPL
• started with Pioneer
• probably end with Juno (or proposed Europa) mission
• also Earth-based
• 1874-2014
• Saturnrigh stellar occultations
• pole orientation
• Saturn ring plane crossing times
• pole orientation
• spacecraft:
• imaging
• VLBI
• Saturn ring occultations
• But no tidal forces used in any analysis so far.
• But tidal effects are not zero
• Lainey et al. 2009, 2012
• Efroimsky & Lainey 2007 (JGR 112)
• $U_{jk} = k_2^k \left(\dfrac{\mu_j}{R_k}\right)^3 \left(\dfrac{R_k}{r}\right)^3 \left(\dfrac{R_k}{r^*_{jk}}\right)^3 P_2\left(\hat{r} \cdot \hat{r}^*_{jk}\right)$
• $r^*_{jk} = r_{jk} – \Delta t_j \left[\dot{r}_{jk} + \dot{W}_k\left(\hat{r}_{jk}\times\hat{h}_k\right)\right]$
• Tidal lag effects
• Put tides in fitting model
• $\rightarrow k_2$
• $\rightarrow$ gravity harmonic coefficients
• tidal lags: indeterminate from existing data
• tidal dissipation function $Q = \dfrac{2 \pi E}{\Delta E} = f(\Delta t)$
• $E$ = max energy stored in one tidal cycle
• $\Delta E$ = energy dissipated during that cycle
• $f(\Delta t) = \dfrac{1}{\omega^{\alpha} \Delta t}$
• comparison to Lainey for Jupiter:
• indeterminate
• comparison to Lainey for Saturn (common $Q$):
• $\Delta t$ and $\dfrac{k_2}{Q}$ successfully detected for Mimas, Enceladus, Tethys, Dione, and Rhea, $k_2 = 0.379 \pm 0.011$
• Lainey: $\dfrac{k_2}{Q} = 2.3\pm0.7 \times 10^{-4}$, $k_2 = 0.341$
• JPL:$\dfrac{k_2}{Q} = 1.0\pm0.2 \times 10^{-4}$, $k_2 = 0.381 \pm 0.011$

## DDA 2015 – The Evidence for Slow Migration of Neptune from the Inclination Distribution of Kuiper Belt Objects

This is one of a series of notes taken during the 2015 meeting of the AAS Division on Dynamical Astronomy, 3-7 May, at CalTech. An index to this series (all the papers presented at the meeting) is here.

David Nesvorny (SWRI)

#### Abstract

Much of the dynamical structure of the Kuiper Belt can be explained if Neptune migrated over several AU, and/or if Neptune was scattered to an eccentric orbit during planetary instability. An outstanding problem with the existing formation models is that the distribution of orbital inclinations predicted by them is narrower than the one inferred from observations. Here we perform numerical simulations of the Kuiper belt formation starting from an initial state with Neptune at $20\lt a^{N,0} \lt 30$ AU and a dynamically cold outer disk extending from beyond $a^{N,0}$ to 30 AU. Neptune’s orbit is migrated into the disk on an e-folding timescale $1 \le \tau \le 100$ Myr. A small fraction ($\sim10^{-3}$) of disk planetesimals become implanted into the Kuiper belt in the simulations. By analyzing the orbital distribution of the implanted bodies in different cases we find that the inclination constraint implies that $\tau \ge 10$ Myr and $a^{N,0} \le 26$ AU.The models with $\tau \lt 10$ Myr do not satisfy the inclination constraint, because there is not enough time for various dynamical processes to raise inclinations. The slow migration of Neptune is consistent with other Kuiper belt constraints, and with the recently developed models of planetary instability/migration. Neptune’s eccentricity and inclination are never large in these models ($e^N \lt 0.1$, $i^N \lt 2$ deg), as required to avoid excessive orbital excitation in the $\gt 40$ AU region, where the Cold Classicals presumably formed.

#### Notes

• Early SS evolution
• giant planets emerged from dispersing protopl disk on compact orbits (inside massive belt)
• planetesimal driven migration?
• dynamical instability?
• giant planets now spread from 5 to 30 AU
• Kuiper Belt is the best clue to evolution of Neptune’s orbit
• KB structure is complex (plot: $e$ vs $a$)
• between 3:2 and 2:1 MMRs: a mess, but hot and cold populations
• where did hot population come from (including high-$i$ 3:2 objects)?
• model: too many Plutinos compared to observations
• New model
• 4 outer planets
• ICs:
• Neptune starting points: 22, 24, 26, 28 AU
• Neptune migration e-folding timescales 1, 3, 10, 30, 100 Myr
• 1e6 particles, Rayleigh initial distribution
• swift_rmvs3 integrator
• 500 cores of Pleiades supercomputer
• 20 jobs total, most stopped 1 Gyr, interesting ones to 4 Gyr
• $\rightarrow$ result matches observed distribution
• 24 AU, 30 Myr
• but too manyPlutinos(?)
• observational bias?
• cf Petit et al. 2012
• CFEPS detection simulator
• agreement (of hot population) is actually pretty good
• Gomes capture mechanism:Gomes 2003
• 2:1 MMR secular structure is complex
• Conclusions:
• Neptune migrated into a massive cometary disk at $\lt 30$ AU
• Neptune’s migration hadto be slow
• need time to increase inclinations
• Model also explains other KB properties
• Initial disk had to be $\sim 20 M_\oplus$

## DDA 2015 – The Evolution of the Grand Tack’s Main Belt through the Solar System’s Age

This is one of a series of notes taken during the 2015 meeting of the AAS Division on Dynamical Astronomy, 3-7 May, at CalTech. An index to this series (all the papers presented at the meeting) is here.

Rogerio Deienno (National Institute for Space Research)

#### Abstract

The Asteroid Belt is marked by the mixture of physical properties among its members, as well as its peculiar distribution of orbital eccentricities and inclinations. Formation models of the Asteroid Belt show that its formation is strongly linked to the process of terrestrial planet formation. The Grand Tack model presents a possible solution to the conundrum of reconciling the small mass of Mars with the properties of the Asteroid Belt, providing also a scenario for understanding the mixture of physical properties of the Belt objects. Regarding the orbital distribution of these objects, the Grand Tack model achieved good agreement with the observed inclination distribution, but failed in relation to the eccentricities, which are systematically skewed towards too large values at the end of the dynamical phase described by the Grand Tack model. Here, we evaluate the evolution of the orbital characteristics of the Asteroid Belt from the end of the phase described by the Grand Tack model, throughout the subsequent evolution of the Solar System. Our results show the concrete possibility that the eccentricity distribution after the Grand Tack phase is consistent with the current distribution. Finally, favorable and unfavorable issues faced by the Grand Tack model will be discussed, together with the influence of the primordial eccentricities of Jupiter and Saturn. Acknowledgement: FAPESP.

#### Notes

• Asteroid belt:
• formation process halted before formation of a planet due to Jupiter
• so-called “Grand Tack” model
• Walsh et al. 2011
• Jup &  Sat migrate inwards, Saturn faster
• inward stops, outward begins
• but fails to explain a lot
• current MB structure different from Grand Tack predictions
• especially dist. in $e$, also $a$ ($i$ not bad)
• This work
• Num int 5 planets & 10,000 test particles, 4.5 Gyr
• ICs: Grand Tack
• Mercury integrator, 10-day time step — expensive
• E-belt (Bottke et al. 2012) results @ 0.4 Gyr (planetary instability)
• at 0.4 Gyr, reset planets to their current orbits
• $\rightarrow$ asteroid belt of today — almost
• much better match to observed $a$-$e$-$i$ distributions
• lost somewhat more asteroids than observed
• Influence of primordial eccentricities ofJup & Saturn
• destabilizes MMRs
• $\rightarrow$ constraints on primordial eccentricities

## DDA 2015 – The onset of dynamical instability and chaos in navigation satellite orbits

This is one of a series of notes taken during the 2015 meeting of the AAS Division on Dynamical Astronomy, 3-7 May, at CalTech. An index to this series (all the papers presented at the meeting) is here.

Aaron Jay Rosengren (IFAC-CNR)

#### Abstract

Orbital resonances are ubiquitous in the Solar System and are harbingers for the onset of dynamical instability and chaos. It has long been suspected that the Global Navigation Satellite Systems exist in a background of complex resonances and chaotic motion; yet, the precise dynamical character of these phenomena remains elusive. Here we will show that the same underlying physical mechanism, the overlapping of secular resonances, responsible for the eventual destabilization of Mercury and recently proposed to explain the orbital architecture of extrasolar planetary systems (Lithwick Y., Wu Y., 2014, PNAS; Batygin K., Morbidelli A., Holman M.J., 2015, ApJ) is at the heart of the orbital instabilities of seemingly more mundane celestial bodies—the Earth’s navigation satellites. We will demonstrate that the occurrence and nature of the secular resonances driving these dynamics depend chiefly on one aspect of the Moon’s perturbed motion, the regression of the line of nodes. This talk will present analytical models that accurately reflect the true nature of the resonant interactions, and will show how chaotic diffusion is mediated by the web-like structure of secular resonances. We will also present an atlas of FLI stability maps, showing the extent of the chaotic regions of the phase space, computed through a hierarchy of more realistic, and more complicated, models, and compare the chaotic zones in these charts with the analytical estimation of the width of the chaotic layers from the heuristic Chirikov resonance overlap criterion. The obtained results have remarkable practical applications for space debris mitigation and for satellite technology, and are both of essential dynamical and theoretical importance, with broad implications for planetary science.

#### Notes

• Motivation: space debris problem
• Active debris removal is becoming necessary
• New: exploit resonant orbits to obtain relatively stable graveyards or highly unstable disposal orbits
• Resonance overlap & chaos
• asteroid belt resonances: cf. DeMeo & Carry 2014 (Nature Rev)
• What is resonant structure of cislunar space?
• actually less well known than resonant structure of asteroid belt
• Cislunar resonant phenomena:
• tesseral resonances
• MMRs
• lunisolar semi-secular resonances (sun-synchronous, evection resonance)
• secular resonances (crit. inclination, Kxxxx resonance)
• Navsat orbits (European) are unstable!
• Chao 2000, Jenkin & Gick 2002, Chao & Gick 2004
• Also: interference from sats in disposal orbits
• Ref: Mercury’s orbit and secular chaos
• Harmonic analysis of Lunar perturbations
• Tesseral and lunisolar semi-secular resonances cannot be the cause of orbital instabilities observed in numerical surveys
• Role of secular resonances in producing chaos
• simplifications:
• 2nd order in ratio of semimajor axes
• short periodic terms of disturbing function can be averaged out
• resonance: $\dot{\psi} = (2-2p) \dot{\omega} + m \dot{\Omega} \pm s\dot{\Omega}_2 \approx 0$
• chaotic diffusion (~250 yr)
• Daquin et al. CMDA (in prep)
• Chirikov res overlap criterion
• chaotic web
• plot: $e$ vs $i$
• FLI stability maps
• heat map: $e$ vs $i$
• too many dimensions $\rightarrow$ far from understood

## DDA 2015 – Increasing Space Situational Awareness for NEOs

This is one of a series of notes taken during the 2015 meeting of the AAS Division on Dynamical Astronomy, 3-7 May, at CalTech. An index to this series (all the papers presented at the meeting) is here.

Daniel J.G.J. Hestroffer (IMCCE/Paris observatory)

#### Abstract

Over the past years, Europe has strengthened its commitment to foster space situational awareness. Apart from the current efforts in tracking space weather, artificial satellites and space debris, Near Earth Asteroid threat assessment is a key task. NEOshield has been part of this European effort. We will give an overview over national projects and European programs with French participation such as PoDET, ESTERS, FRIPON, NEOShield, Gaia-FUN-SSO and Stardust. Future plans regarding Near Earth Object threat assessment and mitigation are described. The role of the IMCCE in this framework is discussed using the example of the post mitigation impact risk analysis of Gravity Tractor and Kinetic Impactor based asteroid deflection demonstration mission designs.

#### Notes

• SSA:
• debris
• short-term & long-term stability
• evolution of debris clouds
• meteorites
• fish-eye cameras
• FRIPON network
• triangulation, orbit/trajectory reconstruction
• people don’t look up anymore
• NEOs
• NEOs
• ~1500 detections/yr from various surveys
• ~12,000 catalogued so far
• still missing many — very incomplete
• large NEOs: fairly complete census by now
• GAIA: much ofunobservability cone overlaps NEO territory
• ongoing ground-based surveys go fainter anyway
• Need ~250 day arcs to get CEU $\le 1$ arcsec
• http://neo.ssa.esa.edu
• ESA appears to be starting to get serious about detection and mitigation schemes

## DDA 2015 – The 2014 KCG meteor outburst: clues to a parent body

This is one of a series of notes taken during the 2015 meeting of the AAS Division on Dynamical Astronomy, 3-7 May, at CalTech. An index to this series (all the papers presented at the meeting) is here.

### Session: Dynamics of Small Solar System Bodies I

#### Abstract

The κ Cygnid (KCG) meteor shower exhibited unusually high activity in 2014, producing ten times the typical number of meteors. The shower was detected in both radar and optical systems and meteoroids associated with the outburst spanned at least five decades in mass. In total, the Canadian Meteor Orbit Radar, European Network, and NASA All Sky and Southern Ontario Meteor Network produced thousands of KCG meteor trajectories. Using these data, we have undertaken a new and improved characterization of the dynamics of this little-studied, variable meteor shower. The κ Cygnids have a diffuse radiant and a significant spread in orbital characteristics, with multiple resonances appearing to play a role in the shower dynamics. We conducted a new search for parent bodies and found that several known asteroids are orbitally similar to the KCGs. N-body simulations show that the two best parent body candidates readily transfer meteoroids to the Earth in recent centuries, but neither produces an exact match to the KCG radiant, velocity, and solar longitude. We nevertheless identify asteroid 2001 MG1 as a promising parent body candidate.

#### Notes

• $\kappa$Cygnid shower:
• Competes with the Perseids, so unfairly obscure.
• Observations go back to 1869.
• Orb elements unusually spread out.
• Relatively slow: $v_g \sim 24$ km/s
• Short trajectories
• Multiple flares
• 2014:
• Unusually active year
• European network
• Showermemberselection:
• Use established shower orbits to select members (Drummond 1981)
• Use observed (Sun-centered) radiantandvelocity to select members
• drift over time — fit curve
• peaks in stacked prob. distribution (in $a$) correspond to MMRs
• Parent body search
• Use D parameter to rank objects from JPL Small Body Database
• 2002 LV,2008ED69,2001MG1
• Not quite…
• via location of descending node — intersection with Earth’s orbit (Jenniskens & Vaubaillon 2008)
• Integrate and search for close encounters
• Hard to get a parent body to match all search criteria

## DDA 2015 – High precision comet trajectory estimates: the Mars flyby of C/2013 A1 (Siding Spring)

This is one of a series of notes taken during the 2015 meeting of the AAS Division on Dynamical Astronomy, 3-7 May, at CalTech. An index to this series (all the papers presented at the meeting) is here.

### Session: Dynamics of Small Solar System Bodies

Davide Farnocchia (JPL, CalTech)

#### Abstract

The Mars flyby of C/2013 A1 (Siding Spring) represented a unique opportunity for imaging a long-period comet and resolving its nucleus and rotation period. Because of the small encounter distance and the high relative velocity, the goal of successfully observing C/2013 A1 from the Mars orbiting spacecrafts posed strict requirements on the accuracy of the comet ephemeris estimate. These requirements were hard to meet, as comets are known for being highly unpredictable: astrometric observations can be significantly biased and nongravitational perturbations significantly affect the trajectory. Therefore, we remeasured a couple of hundred astrometric positions from images provided by ground-based observers and also observed the comet with the Mars Reconnaissance Orbiter’s HiRISE camera on 2014 October 7. In particular, the HiRISE observations were decisive in securing the trajectory and revealed that nongravitational perturbations were larger than anticipated. The comet was successfully observed and the analysis of the science data is still ongoing. By adding some post-encounter data and using the Rotating Jet Model for nongravitational accelerations we constrain the rotation pole of C/2013 A1.

#### Notes

• Observations
• 140,000 km close approach
• HiRISE FoV: 4×4 mrad $\rightarrow 280$ km
• post-conjunction updates: positions kind of all over the place
• center of light is not coincident with position
• PSF is diffuse, not starlike
• most astrometry was from amateurs
• non-grav perturbations
• previously unknown for this comet
• use observations fromMRO!
• provided good constraints on non-grav params
• post-flyby
• astrometric predictions sucked!
• rotating jet model
• spin pole
• thrust angle between jet and pole
• superposition of two jets
• avg over rotation
• $\rightarrow$ better trajectory
• $\rightarrow$ spin pole direction

## DDA 2015 – Dialing the Love Number of Hot Jupiter HAT-P-13b

This is one of a series of notes taken during the 2015 meeting of the AAS Division on Dynamical Astronomy, 3-7 May, at CalTech. An index to this series (all the papers presented at the meeting) is here.

Peter Buhler (CalTech) (Duncombe award winner)

#### Abstract

HAT-P-13b is Jupiter-mass transiting planet in a 0.04 AU orbit around its host star. It has an outer companion, HAT-P-13c, with a minimum mass of 14.7 $M_{Jup}$ in a highly eccentric 1.2 AU orbit. These two companions form an isolated dynamical system with their host star [1]. The nature of this system allows the two bodies to settle into a fixed eccentricity state where the eccentricity of HAT-P-13b is directly related to its oblateness as described by the Love number, $k_2$ [2]. In order to constrain the eccentricity, and therefore $k_2$, of HAT-P-13b, we use the Spitzer Space Telescope to measure the timing of its secondary eclipses at 3.6 and 4.5 μm. We then simultaneously fit our secondary eclipse data in conjunction with previously measured radial velocity and transit data. Finally, we apply the fact that, if the orbits of HAT-P-13b and HAT-P-13c are coplanar, then their apsides are aligned [3]. The apsidal orientation of HAT-P-13c is much better constrained because of its high eccentricity, which helps break the degeneracy between the eccentricity and apsidal orientation in interpreting the measured secondary eclipse time. Our analysis allows us to measure the eccentricity of HAT-P-13b’s orbit with a precision approximately ten times better than that of previously published values, in the coplanar case, and allows us to place the first meaningful constraints on the core mass of HAT-P-13b. [1] Becker & Batygin 2013, ApJ 778, 100 [2] Wu & Goldreich 2002, ApJ 564, 1024 [3] Batygin+ 2009, ApJ 704, L49

#### Notes

• Trying to understand interior mass distribution ofHAT-P-13b
• data from Spitzer Space Telescope, 2010
• measure secondary eclipse timing
• constrain $e$
• constrain tidal Love number $k_2$ and interior
• HAT-P-13: 5 Gyr G-type, 1.2 $M_\odot$, ~5650K
• 13b: ~0.9$M_J$
• 13d: driver of the dynamics
• Secondary eclipse:
• difference in timing from circular $\rightarrow e$
• signal ~1% of noise
• fit jitter model
• fit eclipse model (Mandel & Agol 2002)
• bin data after noise removal
• depth: ~0.05%
• 3.6 μm: ~24 min early eclipse time
• secondary eclipse constrains $e \cos \omega_b$
• RV measurements constrain $e \sin \omega_b$
• eccentricity result: $e \sim 0.01$ at $3 \sigma$ level
• tidal Love number:
• tidal friction extracts energy
• system quickly finds fixed point under tidal friction
• fixed point implies aligned apsides and identical precession rates
• system maintainsconfig over long timescales
• $k_{2,b} = f(e_b)$
• apsidal alignment helps constrain $e$ by constraining $e\cos\omega$ and $e\sin\omega$ since $\omega_b=\omega_c$ (if coplanar)
• apsidal alignment increases precision
• use to connect $e$ to $k_2$
• result:
• ~10$\times$ tighter constraint
• core mass of 13b has to be very small
• problems:
• noncoplanarity
• EoS not known