An Observational Upper Limit on the Interstellar Number Density of Asteroids and Comets
Toni Engelhardt, Robert Jedicke, Peter Veres, Alan Fitzsimmons, Larry Denneau, Ed Beshore, Bonnie Meinke
aa r X i v : . [ a s t r o - ph . E P ] F e b An Observational Upper Limit onthe Interstellar Number Density of Asteroids and Comets
Toni Engelhardt , , Robert Jedicke , Peter Vereˇs , , , Alan Fitzsimmons , ,Larry Denneau , Ed Beshore , Bonnie Meinke , Received ; accepted Institute for Astronomy, University of Hawaii, Honolulu, HI, USA Technical University of Munich, Munich, Germany Comenius University in Bratislava, Bratislava, Slovakia Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive,Pasadena, CA 91109, USA Queens University, Belfast, UK The University of Arizona, Lunar and Planetary Laboratory,Tucson, AZ, USA Space Telescope Science Institute, Baltimore, MD 2 –
Abstract
We derived 90% confidence limits (CL) on the interstellar number density ( ρ CLIS )of interstellar objects (ISO; comets and asteroids) as a function of the slope of theirsize-frequency distribution and limiting absolute magnitude. To account for gravitationalfocusing, we first generated a quasi-realistic ISO population to ∼
750 au from the Sun andpropagated it forward in time to generate a steady state population of ISOs with heliocentricdistance <
50 au. We then simulated the detection of the synthetic ISOs using pointingdata for each image and average detection efficiencies for each of three contemporary solarsystem surveys — Pan-STARRS1, the Mt. Lemmon Survey, and the Catalina Sky Survey.These simulations allowed us to determine the surveys’ combined ISO detection efficiencyunder several different but realistic modes of identifying ISOs in the survey data. Some ofthe synthetic detected ISOs had eccentricities as small as 1 .
01 — in the range of the largesteccentricities of several known comets. Our best CL of ρ CLIS = 1 . × − au − implies thatthe expectation that extra-solar systems form like our solar system, eject planetesimals inthe same way, and then distribute them throughout the galaxy, is too simplistic, or that theSFD or behavior of ISOs as they pass through our solar system is far from expectations.
1. Introduction
Simulations of the formation and evolution of our solar system suggest that theearly orbital migration of the gas and ice giant planets ejected up to 99% of the originalplanetesimals into interstellar space ( e.g.
Charnoz and Morbidelli 2003; Bottke et al. e.g.
Mann 2010). The spatial number densityof interstellar objects (ISO) and their composition and size-frequency distribution would 3 –provide valuable information about the commonality of solar system formation processessuch as the prevalence of giant Jupiter-like planets capable of ejecting planetesimals. Inthis work we calculate a limit on the ISO spatial number density using data from threecontemporary wide-field solar system surveys.We will use the term ‘interstellar object’ (ISO) to mean asteroids and comets that arenot gravitationally bound to a star. They almost always encounter our solar system onhyperbolic trajectories with heliocentric eccentricities significantly greater than 1. Underexceptional circumstances, they may be captured through a gravitational encounter withJupiter. Torbett (1986) calculated that the ISO capture rate must be about 1 per 60 millionyears if the interstellar ISO number density of objects with diameters ≥ pc − (10 − au − ), which corresponds to each stellar system ejecting about 10 ‘comets’. Forperspective, that interstellar ISO spatial density corresponds to about 2 ISOs in a spherewith the diameter of Saturn’s orbit without accounting for the Sun’s gravitational focusing.Given that the average dynamical lifetime of short period comets is about 0.45 million years(Levison and Duncan 1994), the steady state number of captured ISOs in the solar systemshould be about 0.01, or, roughly a 1% chance of there being a captured ISO at any time.The corollary to this statement is that most ISOs that are present in the solar system areunbound. In this work we will always provide the ISO number density in interstellar space, far fromthe gravitational focusing of a stellar-mass body. Torbett (1986) neglected the gravitationaldeflection of ISOs by the Sun, and we will show that the ISO number density near Jupiteris only marginally higher than the interstellar value. The steady state number of objects in a population ( N ) is related to the flux ( F ) ofobjects entering or leaving the population and their mean lifetime ( L ) as members of thepopulation by the N = F L equation. 4 –Comet 96P/Machholz is currently the best candidate for being an interstellar interloper(Schleicher 2008) because 1) it is the only known short-periodic comet with both highorbital inclination and high eccentricity and 2) it has an unusual composition, beingdepleted in both carbon and cyanogen, which suggests a different origin from other knowncomets. Backward propagation of 96P/Machholz’s orbit can not establish it as an ISO dueto close approaches with giant planets that cause chaotic jumps in semi-major axis which,combined with a Kozai resonance with Jupiter, may lead to a Sun impact within the next1 . × years (Gonczi et al. et al. N ( < H ) ≡ N ( H ) ∝ αH or N ( > D ) ≡ N ( D ) ∝ D − a where α = 0 . a = 2 . e.g. Dohnanyi 1969; Durda 1993), and H and D representthe objects’ absolute magnitudes and diameters respectively. We note that the Jupiterfamily comet (JFC) SFD has a ∼ . α ∼ . e.g. Snodgrass et al. et al.
D > ρ IS ) can be estimated by 1) assumingthat our solar system is typical, 2) using numerical simulations to calculate the number ofobjects that were ejected from our solar system, 3) multiplying that number by the number 5 –of star systems in the galaxy, 4) assuming that the galactic orbits of the ejected objects arerandomized through galactic tides and stellar encounters, and 5) dividing by the volume ofthe galaxy. Roughly this technique yields ρ IS ∼ − au − (McGlynn and Chapman 1989;Jewitt 2003) while Sen and Rama (1993)’s more detailed estimate predicts about a sixthof that value with ρ IS ∼ . × − au − . These values are considerably larger than the5 × − to 5 × − au − range predicted by Moro-Mart´ın et al. (2009) who suggest thatthe earlier values are too high due to neglecting important factors such as stellar mass andthe presence of giant planets in the star system.Some experimental measurements of the ISO number density have relied on indirecttechniques. Jura (2011) calculated the number density of ISOs using the hydrogen contentin helium-dominated atmospheres of hydrogen-depleted white dwarfs. Their analysisassumes that the present hydrogen is delivered by ISOs rather than an in situ debris diskand they claim that their results exclude ‘optimistic’ ISO number densities but can notexclude the Moro-Mart´ın et al. (2009) estimate. Another study suggests that Sgr A* flarescould be induced by asteroids or comets with radii larger than 10 km (Zubovas et al. e.g. Jedicke et al. Moro-Mart´ın et al. (2009) provided their estimates for the number of objects with radius > diameter standard by including afactor of 5 ∼ . , roughly correcting for the size-frequency distribution in the 1 km diameterrange according to the SFD expected for a self-similar collisional cascade (Dohnanyi 1969).We note that Moro-Mart´ın et al. (2009) implemented several different SFD slopes dependingon the object’s type and size and also assumed an albedo of 6% compared to the 4% usedhere. 6 –objects (NEO) but have been very successful at detecting comets and all classes of asteroidsfrom the main belt to the trans-Neptunian region. The current generation of surveys havefainter limiting magnitudes and are capable of surveying a significant fraction of the sky ona nightly basis, and the next generation will provide even deeper images over wider areas( e.g. LSST, Ivezic et al. (2008); SST, Monet et al. (2013)). The larger search volume of thenew surveys will provide a slightly better chance of detecting ISOs compared to existingsurveys ( e.g.
Cook et al.
292 objects with e > . e ≥ .
01, and the highesteccentricity object is C/1980 E1 (Bowell) with e = 1 . e.g. Buffoni et al. et al. (2007) made the astounding claim of detecting and obtaining aspectrum of a centimeter-scale intergalactic meteor using a multi-slit spectrometer on the6 m Special Astrophysical Observatory of the Russian Academy of Sciences. They furtherclaim that observations with a wide field camera identified a dozen meteors consistentwith the expected radiant for intergalactic objects coming from the direction of motion ofthe Milky Way through the Local Group of galaxies. Their suggestion that about 5% ofthe meteors they detected were intergalactic in origin is inconsistent with the lack of anysupporting evidence from other optical and meteor radar observatories ( e.g.
Musci et al. as of 2016 October 14 7 –Francis (2005) utilized the long-periodic comet population’s detectability with theLINEAR survey (Stokes et al. ρ CLIS ∼ . × − au − . In this work, we improve and extend the techniqueusing a synthetic ISO population and modeling the combined ISO detection efficiency forthree long-term contemporary surveys, the Catalina Sky Survey and Mt. Lemmon Survey(Christensen et al. et al.
2. Survey data2.1. Pan-STARRS1
The Pan-STARRS1 telescope (MPC Code F51; Kaiser et al. et al. . f /4 Ritchey-Chretien optical assembly and 1.4 gigapixel camera(Tonry and Onaka 2009) provide a ∼ field-of-view at ∼ . ′′ /pixel. The cameraconsists of an array of 60 CCDs that each consist of an 8 × ×
600 pixel ‘cells’that can be read in parallel. The system now devotes 90% of its time to surveying for NEOsbut in early 2014 it completed a 3-year survey of the sky north of ∼ − ◦ declination in5 Sloan-like filters (Fukugita et al. g P1 , r P1 , i P1 , z P1 and y P1 )cover the visible to NIR spectrum (Tonry et al. et al. et al. w P1 ∼ g P1 + r P1 + i P1 ) was specifically designed to maximizethe NEO detection efficiency.The 3-year Pan-STARRS1 survey had 5 distinct components, but most of the datawere suitable for detecting asteroids and comets. The main 3 π -steradian survey mode(Schlafly et al. ∼
56% of the survey time in the 5 primary filters. In this 8 –mode, the same field was visited 2 × or 4 × within a night in 30 to 40 sec exposures witha total time separation of about an hour. The time between two visits to the same field,a transient time interval (TTI), was typically 15 min. The medium deep survey (MD),with 25% of the survey time focused on 10 fields of cosmological and extragalactic interest(Tonry et al. × /night with filter-dependent exposure times of 120 to 240 sec in the3 π filters. The solar system survey (SS) used 5-6% of the survey time but was increasedto 12% of the survey time after 2012 (Denneau et al. w P1 filter with45 sec exposures and mostly visited fields near opposition, or the ‘sweetspots’ near theecliptic at solar elongations of 60 ◦ to 90 ◦ . In the SS survey each field was visited 4 × with ∼
20 min TTI near opposition and ∼ > , ∼ , ,
000 asteroid positions, and observed ∼ ,
000 distinct asteroids ( e.g.
Wainscoat et al. et al.
The Catalina Sky Survey consists of the 0 . . ∼ witheach image, allowing it to observe most of the night sky during a single lunation. The deeperbut narrower field MLS survey with its ∼ field of view concentrates its observationsnear opposition or along the ecliptic. The images from both telescopes are un-filtered tomaximize throughput and discovery statistics. In 2014, CSS and MLS accounted for justover 41 percent of all new NEO discoveries ( http://neo.jpl.nasa.gov/stats/ ). Thisstudy used all fields acquired by these surveys until the end of 2012, beginning in Feb 2005for MLS and in Jan 2005 for CSS.
3. Synthetic ISO population
Our goal is to set an observational upper limit on the steady-state, interstellar, spatialnumber density of ISOs using the fact that Pan-STARRS1, MLS, and CSS did not detect asingle ISO in about 19 cumulative survey-years. To do so requires determining the combinedISO detection efficiency of the three surveys. We accomplished this measurement usinga synthetic ISO population that was run through a survey simulation using actual fieldsobserved by Pan-STARRS1, MLS, and CSS, and each survey’s average detection efficiencyas a function of apparent magnitude for the appropriate filters.
Our ISO model expands upon the technique developed by Grav et al. (2011) thatincludes the propagation and gravitational focusing through our solar system of an originallyhomogeneous and random population of synthetic ISOs in a large heliocentric sphere withradius r . We generated random positions for the synthetic ISOs within the sphere at t
10 –(we will use t to indicate a specific time and T to represent a time duration) and assignedthem random direction vectors with random, Gaussian-distributed speeds. We refer to thispopulation as the synthetic ‘generated’ population. The relative speed of ISOs with respectto the Sun is expected to be of the same order as that of nearby stars with a mean speed of¯ v = 25 km sec − and σ = 5 km sec − ( e.g. Grav et al. v min = 10 km sec − and v max = 40 km sec − .The spatial and velocity distributions of the synthetic ISOs within the sphere withradius r at time t (both parameters to-be-determined below) are probably a finerepresentation of their steady-state distributions in interstellar space but are not at allrepresentative of their steady-state spatial and velocity distribution in the inner solar systemdue to gravitational focussing by the Sun. We generated a steady-state ISO population,‘the model’, within a ‘core’ sphere of radius r model = 50 au ≪ r centered on the Sun, bypropagating the trajectories of the synthetic generated interstellar ISO population forwardin time. The 50 au value was chosen because an ISO would have to be several hundredkilometers in diameter to be detected by any of the three surveys and an ISO of this sizewithin that distance is extremely improbable. To ensure that our steady-state model withinthe solar system is representative of the expected distribution, the slowest synthetic objectsat t within r model must be able to exit the core, and the generated volume must be largerthan the distance that can be traveled by the fastest objects in the model. We propagatedthe interstellar model for a ‘preparation time’ T prep ≥ r model v min (3.1)and ensured that r ≥ v max T prep (3.2)where the latter formula intentionally ignores the ISOs’ acceleration due to the Sun and 11 –assumes that they are on a direct path to the heliocenter. We used T prep ∼
70 yr and r ∼
750 au that both include margins of about 50%.The ISO model must represent the steady-state distribution of ISOs in the inner solarsystem during the combined survey time range of the three surveys, T survey = t f − t i , where t i = 53371 MJD and t f = 57387 MJD corresponding to the time period from 2005 January1 through 2015 January 1 that brackets the actual surveys’ duration. Thus, t = t i − T prep which we set to 27399 MJD (1933 Nov 23).We generated about 1.7 billion synthetic ISOs within r at t and preselected thosethat would be in the model (core) volume during the survey time as calculated usingthe hyperbolic Kepler equation. We also eliminated the relatively small number ofnon-hyperbolic synthetic objects with e < t that are artifacts of the synthetic ISOgeneration technique. Finally, we propagated the ∼ t i , with the OpenOrb n-body integrator (Granvik et al. ∼ .
66 au − .An ISO’s eccentricity is related to its perihelion distance and speed (fig. 1 and fig. 2a & b). The larger its perihelion or the faster it moves relative to the Sun, the less itstrajectory is modified by gravitational acceleration, and the higher its eccentricity. Thus,very distant ISOs will follow nearly straight lines and have eccentricities approachinginfinity. Conversely, the closer an ISO approaches the Sun and the slower it moves, thelower the eccentricity. The perihelion distance of generated objects peaks at about 500 aubecause of the truncation at r ∼
750 au i.e. it is unlikely to randomly generate objectswith perihelia just inside the maximum distance (fig. 2a). The model object population has 12 –Fig. 1.— Trajectories of 8 synthetic ISOs within the 50 au radius model centered on the Sunwith 100 day sampling. The two objects with the smallest eccentricities, with the smallestheliocentric distance and the most curvature in their trajectories, have e ∼ e ∼ e > e ∼
25 and only about 0.1% have e <
2. However,ISOs with e & . e ≤ . % o f g e n e r a t e d o b j e c t s a) % o f g e n e r a t e d o b j e c t s b) % o f o b j e c t s ( s ee c a p t i o n ) c) −50000 0 50000 100000perihelion passing time [MJD]0.00.51.01.52.02.53.03.54.04.5 % o f g e n e r a t e d o b j e c t s d) Fig. 2.— Panels a, b, and d) The generated (gray) and model (black) ISO orbital parameterdistributions as a percentage of the generated distribution as a function of a) periheliondistance, b) eccentricity, and d) time of perihelion. In panel c) the ISO model (black)inclination distribution is provided as a percentage of the model itself.The potentially observable model ISOs have essentially the same inclination distributionas the generated population because the selection criteria are independent of the inclination. 14 –Even if we had selected the observable model ISOs with a full n-body propagation into thesolar system the inclination distributions would have been nearly indistinguishable becauseonly extremely rare encounters with planets would affect the objects’ inclinations (fig. 2c).The distribution is a simple sin i function due to the phase space of available normals tothe orbital planes as a function of inclination. The time of perihelion ( t p ) for the generatedpopulation is pseudo-normally distributed around t = 27399 MJD by design as describedabove (fig. 2d). Similarly, t p for the model population is distributed pseudo-normally aroundthe time period during which the survey data used in this work was acquired. The modelwas designed such that within the survey duration the distribution of the times of perihelionpassages is essentially flat, as would be expected for objects making one passage throughthe solar system.The spatial number density of the model synthetic ISOs decreases asymptotically withheliocentric distance (fig. 3) and is essentially equal to the interstellar value at 50 au i.e. atTNO-like distances. The density increases near the Sun due to gravitational focusing and isabout 3 × higher than the interstellar value within about 1 au of the Sun i.e. within Earth’sorbit. Note that the ISO spatial density at Jupiter’s distance from the Sun, about 5 .
4. The Moving Object Processing System (MOPS)and ISO discovery efficiency
The Pan-STARRS1 MOPS can link multiple observations of the same object togetherwithin a night into ‘tracklets’, combine tracklets from different nights into ‘tracks’,calculate orbital elements, perform attribution of new tracklets to known objects, identify‘precoveries’ of historical tracklets associated with newly calculated orbits, and allow formanual vetting of all the data (Denneau et al. I S O s p a t i a l nu m b e r d e n s i t y [ a u − ] J S U N
Fig. 3.— Average ISO incremental number density in shells of 1 au thickness versus he-liocentric distance during the survey period. Note the asymptotic approach to the model’sinterstellar number density of about 0 .
66 au − indicated by the horizontal dashed grey line.Vertical gray lines represent the semi-major axes of Jupiter (J), Saturn (S), Uranus (U) andNeptune (N).detection of our synthetic ISOs in Pan-STARRS1, CSS, and MLS fields. In particular,we used MOPS to determine which of the million synthetic ISOs appeared in each ofthe 181,388 Pan-STARRS1 fields, 244,854 CSS fields and 208,464 MLS fields, as well asdetermining their heliocentric and geocentric distance at the time of each observation andtheir ‘interesting object score’ (described later in this section). We use these values tocalculate the probability that the object will be identified as an ISO candidate once weassign the ISO a diameter (or absolute magnitude). Tracklets for the model ISOs that havenon-zero detection efficiency comprise the set of ‘detectable’ objects. 16 –Each system’s time-averaged tracklet detection efficiency was fit to the empiricalfunction ǫ F ( m F ) = ǫ F h e mF − LFwF i − if m F ≤ L F m is the objects’ apparent magnitude, ǫ is the maximum detection efficiency forbright objects, L is the apparent magnitude at which the efficiency drops to 50% of itsmaximum and the limiting apparent magnitude at which we set the detection efficiency tozero, w is a measure of the range of apparent magnitudes over which the efficiency dropoccurs, and the F sub-scripts indicate that each parameter is filter dependent (see table 1).We impose ǫ F = 0 for m F > L F because without this requirement eq. 4.1 allows for smallefficiencies at faint apparent magnitudes where the size-frequency distribution would predicta large number of objects and this scenario can allow unrealistically faint objects to bedetected in the simulation.Survey (obs. code) Filter ǫ F L F w F g 0.69 20.1 0.22i 0.66 20.5 0.24PS1 (F51) r 0.67 20.5 0.23w 0.68 21.3 0.27y 0.53 18.7 0.21z 0.55 19.8 0.20CSS (703) none 0.70 19.4 0.39MLS (G96) none 0.85 21.1 0.42Table 1: Filter and survey dependent efficiency parameters (see eq. 4.1)There are numerous caveats that could be discussed in regard to using or calculatingthe surveys’ tracklet detection efficiency. In particular, the range of apparent rates of motion 17 –over which the quoted efficiency (eq. 4.1) is valid is mostly restricted to values typical ofmain belt asteroids simply because those are the most numerous objects from which theefficiency is measured. The fact that the surveys regularly identify objects moving at bothmuch faster (NEO) and slower (Centaur) rates suggests that it is not inappropriate for usto apply the efficiency function over a wider range of rates of motion. But our laissez-faireapplication clearly has its limits at both fast and small rates of motion and there is alsoa secondary-dependence on the seeing. For instance, Pan-STARRS1 and MOPS detecttransient objects through subtraction of consecutive images . If an object moves lessthan about a seeing disc between images they will be ‘self-subtracted’ with a concomitantreduction in detection efficiency. However, any ISO is likely to remain visible for monthsor years, it is unlikely that no revisits to the object will be in good observing conditions,and nights of better seeing naturally correspond to fainter limiting magnitudes and bettersensitivity. Thus, we consider our efficiency parameterization sufficient for setting a limiton the population for the ‘typical’ ISOs that might actually be detectable with one of thethree surveys.The discovery of an ISO requires not only that the tracklet be identified in a set ofimages but also that it be recognized as an interesting candidate worthy of followup andconfirmation as an ISO. The typical technique for identifying a tracklet as an unknownNEO candidate by the three NEO surveys is to use the MPC ‘digest’ score ( p ), apseudo-probability that a tracklet is ‘interesting’. It depends upon an object’s apparentangular speed ω , apparent magnitude, and apparent position relative to opposition.The visible ISOs typically have high digest scores by virtue of their isotropic inclinationdistribution and high speeds as they pass through our solar system. But if they do not The CSS and MLS surveys do not employ image differencing and are not affected bythis limitation. 18 –have high digest score, perhaps because they happen to appear with main belt like rates ofmotion in or near the ecliptic, it is unlikely that they would be detected as interstellar. Inpractice, tracklets submitted to the MPC with p & . % o f t r a c k l e t s Fig. 4.— The Minor Planet Center’s ‘digest’ score for detectable synthetic ‘cometary’ ISOtracklets in our simulation. The dashed line at digest=90 represents the limiting value abovewhich a tracklet becomes ‘interesting’ enough to trigger followup observations.We were surprised to find that roughly 2/3 of detectable ‘cometary’ ISO tracklets havedigest scores of <
90 (fig. 4) making them ‘uninteresting’ and unlikely to be targeted forfollowup by the many professional and amateur astronomers around the world who regularlyprovide this service (Jedicke et al. < >
90. This fact suggests that future sky surveys like LSST( e.g.
Ivezic et al. j th ISO in the synthetic model by thethree surveys is then ǫ j = 1 − Y F (cid:2) − ǫ jF H ( p j − . (cid:3) (4.2)where ǫ jF is the system’s tracklet detection efficiency for that ISO in filter F (eq. 4.1), p j is the digest score for that tracklet, and we have introduced the Heaviside function with H ( x ) = 0 for x < H ( x ) = 1 for x ≥ N ∗ = X j ǫ j (4.3)where we use the asterisk to denote the synthetic population and simulation. We cangeneralize the expression to the total number of synthetic detected ISOs with maximumabsolute magnitude < H max when they have a size-frequency distribution ∝ αH : N ∗ ( α, H max ) = X j ǫ j ( α, H max ) . (4.4) 20 – The ISO orbit distribution described above ( § H = 0, far larger thanany object that we could expect to detect with the surveys in the limited survey duration,to determine which fields the ISOs would appear in if they were bright enough, and theirapparent magnitude V , geocentric distance ∆, heliocentric distance r , and rate of motion ω at the time of each observation. MOPS calculates the asteroidal apparent magnitudeaccording to Bowell et al. (1988): V = H + 5 log( r ∆) − . (cid:2) (1 − G ) Φ + G Φ (cid:3) (4.5)where the slope is fixed at the standard value of G = 0 .
15, and Φ and Φ are phasefunctions that depend on an object’s phase angle. These parameters are then used todetermine a synthetic ISO’s digest score and apparent magnitude ( V ) when assigned anyother absolute magnitude ( H ): V = V + H .It is likely that most ISOs will contain some volatile material and display cometaryactivity which would cause them to be brighter than predicted using the standard asteroidalformula (eq. 4.5). The diameter of an inert (asteroidal) ISO with a cometary geometricalbedo of p V = 0 .
04 is given by D km = 665 × − H/ p − / V ≡ × − H/ (4.6)Under the assumption of either slow rotation and/or negligible thermal inertia, ignoringheat conduction into the interior, and a heliocentric distance of 1 au, simple sublimationtheory (Cowan and A’Hearn 1979) predicts that the sunlit hemisphere of a water-icedominated cometary nucleus will emit 4 . × H O molecules sec − m − . The totalsublimation rate will scale with the ISO’s surface area and we can also take into account 21 –that only a fraction f ( f = 0 →
1) of the ISO’s sunlit surface may be active. Thus, thesublimation rate of an ISO at r = 1 au under these assumptions is given by Q (H O)molecules sec − = 1 . × f " D km = 4 . × f − . H (4.7)The water sublimation rate for new Oort-cloud comets is ∝ r − . (Meisel and Morris1982) and, assuming this relationship holds within 10 au of the Sun, Jorda et al. (2008)found a strong correlation between Q (H O) and heliocentric cometary magnitude, V C ( r ),of log [ Q (H O)] = 30 . − . V C ( r ) for r ≤ . ∼ V C ( r ) which may be due to measurement uncertainties and variations in phaseangle scattering for the cometary dust comae that can dominate the apparent magnitude.Inverting the relationship for V C ( r ) and substituting the expression for Q (H O) yields V C ( r ) = 1 . H − . f + 6 . r − . . (4.8)To provide the most stringent confidence limit on the ISO spatial number density we assumethe ISO’s entire sunlit hemisphere is active ( f = 1). Given that V C ( r ) = V − ∆, theapparent magnitude of a fresh long-period active comet (an ISO) is V = 1 . H + 6 . r + 5 log ∆ − . r ∼ et al. because at this distance H Ois inert, but eq. 4.9 relies on the activity being water-driven. Second, the rate at which thesublimation rate increases at large r is not well characterized and may vary dramaticallybetween comets, and we have little substantive knowledge of how CO/CO sublimationdrives the dust coma and apparent brightness at large heliocentric distances. Finally, theactual apparent magnitude derived by Jorda et al. (2008) may not correspond to the flux 22 –identified by automated detection software that usually detects objects based on the fluxwithin a relatively small aperture with a radius on the order of the system’s point spreadfunction (perhaps 1 ′′ to 2 ′′ ). However long-period comets at r ≥ et al.
5. ISO interstellar spatial number density limit
Jewitt (2003) pointed out that ISO number density limits depend on the slope of theISO size-frequency distribution and the minimum detectable size (maximum detectableabsolute magnitude). Thus, we let the synthetic ISO number density as a function ofheliocentric distance (fig. 3), slope of the size-frequency distribution ( α ), and maximumabsolute magnitude ( H max ), be expressed as ρ ∗ ( r ; α, H max ) = f ∗ ( r ) ρ ∗ IS ( α, H max ) (5.1)where ρ ∗ IS is the interstellar number density that we wish to calculate. Since N ∗ ( r ) = ρ ∗ ( r ) V ∗ ( r ) (note that we do not show the dependence of each term on α and H for clarityand remember that we use the asterisk to denote synthetic values) the number of detectedsynthetic ISOs in the simulation is then N ∗ = f ∗ ( r ) ρ ∗ IS V ∗ . (5.2)Assuming that we can treat the observation statistics as a Poisson distribution, andsince the actual number of discovered ISOs is zero, the 90% confidence limit (CL) on the 23 –expected number of ISOs from the model is N CL = 2 . i.e. the expectation value must be ≤ . ≥
90% probability of detecting at least one ISO. Thus,the confidence limit on the interstellar ISO number density ( ρ CLIS ) from the actual surveys isgiven by N CL = f ( r ) ρ CLIS V. (5.3)Under the assumption that we have developed a reasonable ISO orbit distributionmodel and survey simulation, V ≈ V ∗ and ρ IS ≈ C ρ ∗ IS , where C is a normalization constantbetween the actual and synthetic ISO population, we can use eq. 5.2 and eq. 5.3 to solve for ρ CLIS ( α, H max ) = N CL N ∗ ( α, H max ) ρ ∗ IS ( α, H max ) . (5.4)The denominator is given by eq. 4.4 and ρ ∗ IS ( α, H max ) is extracted directly from oursynthetic population.The ISO size-frequency distribution (SFD) is not known but we assume that it can berepresented by a function ∝ αH like most known small body populations. If the ISOsare generated in a manner similar to the ejection of objects from our solar system duringits early formation, then ISOs are ejected from extra-solar systems during their high-massperiod when the conditions probably were consistent with the planetesimals being in aself-similar collisional cascade ( e.g. Dohnanyi 1969; O’Brien and Greenberg 2003). Underthese conditions the theoretical value of the SFD slope parameter is α = 0 .
5. Deviationsfrom the conditions required for the self-similar collision cascade typically induce ‘waves’in the SFD ( e.g.
Durda et al. α and H max combinations with 0 . ≤ α ≤ . ≤ H max ≤
20 in steps of 0.05 in the slope and1 mag in H . 24 –For each ( α, H max ) combination we assign the synthetic ISOs random H valuesdistributed according to that SFD and H max , compute their new apparent magnitude V ,then determine the objects’ tracklet detection efficiency and digest scores so that we cancalculate the total number of objects that would have been detected with H < H max if theSFD has slope α . Since each synthetic ISO was randomly assigned a different H value werepeated the procedure 10 × for each slope parameter and averaged the results. Changingthe absolute magnitude for each object has the effect of changing its apparent magnitudewhich directly affects the efficiency for detecting the object and alters its digest score. The10 × repetition was determined empirically to reduce the statistical noise in ρ CLIS ( α, H max ).
6. Results & Discussion
The synthetic detected ISOs have very different orbit element distributions from thegenerated population due to observational selection effects (fig. 5).The perihelion distribution (fig. 5a) is very different between inactive and active ISOswith the asteroidal ISOs typically being detected at about the distance of Mars while thecometary ISOs are typically detected between the distance of Jupiter and Saturn with anas-designed cutoff at 10 au, the distance at which we assume the onset of cometary activity.This behavior is explicable because with H max = 19 and α = 0 . % o f t r a c k l e t s a) % o f t r a c k l e t s b) % o f t r a c k l e t s c) Fig. 5.— Orbit element distributions for synthetic detected ISOs for a Pan-STARRS1 simu-lation at the nominal values of α = 0 . H max = 19 as described in the text and indicatedin fig. 6. The black lines represent the distributions for ‘active’ comets (eq. 4.9) and the graylines represent the case of inactive asteroids. We require that the ‘digest’ score be >
90 inboth cases. 26 –eccentricities are more skewed towards e & ∼
270 the detected synthetic ISOshave ∼ × smaller modes of ∼ . ∼ . e ∼ .
01, smaller than comet C/1980 E1 (Bowell) that has an eccentricity of ∼ . e ≥ .
01, suggesting that, based only on their orbitaleccentricity, it is possible, but not at all likely as described above, that these objects couldbe ISOs because our work shows that ISOs that have small perihelion distances will alsohave small eccentricities and may appear to be slightly perturbed Oort cloud comets.Finally, the inclination distribution of the synthetic detected objects (fig. 5c) retainsthe general shape of the sin i distribution of the underlying generated population for boththe asteroidal and cometary ISOs. The distributions are slightly skewed to retrograde orbitsby the requirement that the digest score be >
90 to flag the object as interesting enough totrigger a followup campaign and the retrograde orbits are ‘easier’ to flag as unusual.Our 90% confidence limit on the interstellar ISO number density improves, i.e. isnumerically smaller, as H max and α decrease (fig. 6a). This is because the distance at whichan ISO is detectable increases as the maximum detectable ISO diameter decreases ( H max increases) but not fast enough to compensate for the slope of the SFD and the apparentbrightness decreasing like ∆ . The CL improves with a shallower SFD slope because alarger fraction of the ISOs are large and bright enough to be detected. Furthermore, the CLimproves dramatically if we assume that the ISOs display cometary activity as they will bemuch brighter, and therefore more easily detected, at heliocentric distances up to 10 au, thedistance at which comets become active in our model (fig. 6b). The CLs with and without according to the JPL Small-Body Database Search Engine as of 2016 December 13 27 –cometary activity represent the full range of CLs in our analysis from about 10 − au − to10 − au − over the ( α, H max ) range.Fig. 6.— 90% confidence limit on the ISO number density versus SFD slope parameter α and limiting absolute magnitude H max ( left ) without cometary activity and ( right ) withcometary activity. The asterisk at a slope parameter of α = 0 . H = 19 correspond to the canonical slope for self-similar cascade (Dohnanyi1969) and a 1 km diameter ( H = 19 .
1) comet with an albedo of p V = 0 .
04 (eq. 4.6).To compare our CLs with theoretical predictions for the interstellar ISO number densitywe use the CLs corresponding to canonical values of H max = 19 . α = 0 .
5. Objects of this absolute magnitude aredetectable near opposition at heliocentric distances of about 2 . . . w P1 filter), MLS and CSS surveys respectively (using the limitingmagnitudes provided in table 1). The 90% CL for asteroidal photometric behavior at thecanonical values is 2 . × − au − . Given that solar gravitational focussing yields ISOspatial number densities about 2 × the interstellar value in the range 1 au . r . . α, H max ) valuesimproves by 2 orders of magnitude to 2 . × − au − if we assume that the ISOs’ Sun-facing 28 – -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 I S O s p a t i a l nu m b e r d e n s i t y [ a u − ] Moro-Martin et al.JewittMcGlynn & Chapman FrancisSen & Rana [ p c − ] Fig. 7.— Our ISO interstellar number density 90% confidence limit for three combinedsurveys and other theoretical values as a function of time. The uppermost solid line representsthe confidence limit assuming that the ISOs do not show any cometary activity (2 . × − au − ) while the dashed line represents the limit assuming that 100% of the ISO’s sun-facing surface is active (2 . × − au − ). The dotted line illustrates the limit assumingthat all ISO candidates would be identified even though their NEO digest score may notexceed the NEO threshold i.e. the ISO candidates could be identified by their non-stellarpoint-spread function rather than their unusual rates of motion (1 . × − au − ).surfaces are 100% active and show cometary activity that make them significantly brighterthan asteroids of the same size in the same geometrical configuration. In this case, there 29 –must be . .
05 active ISOs within 3 au of the Sun at any time or one of the 3 surveys wouldhave identified an ISO.The three asteroid surveys working in tandem over a cumulative 19 years can not setan interesting limit on the interstellar ISO spatial number density if the ISOs behave morelike asteroids than comets (fig. 7). In this case, the limit is an order of magnitude higherthan even the most optimistic predictions. However, we consider it unlikely that the ISOswill act more like asteroids than comets given that only a small percentage of objects withlong period orbits in our solar system are inactive (since 2006 there have been 107 LPCdiscoveries of which only 2 have no measurable activity ). Pan-STARRS1 is currently theleading discoverer system of these nearly inactive ‘Manx’ objects (Meech et al. . × − au − is considerably lower than thepredictions of Jewitt (2003) and McGlynn and Chapman (1989) but still higher than theupper limit determined by Francis (2005). Thus, this CL and Francis (2005) suggest thatthe asteroid surveys are beginning to probe an ISO spatial number density range that couldhave implications for planetary formation. Taken at face value, and in comparison to thepredicted values, the two CLs imply that other solar systems are not similar to our own interms of the ejection of proto-planetary material, that the ISOs have an unexpected SFD,or perhaps that the ISOs are not distributed homogeneously throughout the galaxy.The agreement between our CL with cometary activity and that of Francis (2005)is surprising given that he also assumed that the LINEAR survey would identify cometsby their unusual rates of motion (or they would not be reported as NEO candidates for Meech, K. J., University of Hawai’i, personal communication 30 –followup) and would detect them at ‘cometary’ distances due to their increased brightness.It is surprising because our analysis uses the results from 3 surveys, 2 of which have muchdeeper limiting magnitudes than LINEAR, over 19 years compared to the LINEAR data of3 years. We attribute the difference in the CLs to our use of a more sophisticated ISO modeland our direct access to the pointing history and detection efficiency estimates for our threesurveys. Also, Francis (2005) suggested that the “results are quite sensitive to the adoptedbright-end slope of the absolute magnitude distribution”. While our analysis explored theentire range of SFD slopes, we quote the CL for α = 0 . H max = 19 .
1, whereasFrancis (2005) used his own long-period comet SFD for the ISOs and suggests that most ofthe detected ISOs will have H ∼ . ρ CLIS = 1 . × − au − when α = 0 . H max = 19 . i.e. their NEO digest scores). This ISOidentification scenario is reasonable because 1) ISOs are likely to display cometary behavioras described above and 2) the Pan-STARRS1 manual vetting of each detection ensures thateach tracklet has been reviewed by an observer trained at discerning even weak cometarybehavior (Hsieh et al. The assumption that the ISOs will display cometary activityand be detected by the survey system results in a 90% CL that is more than 2 ordersof magnitude lower than the limit assuming no activity. Furthermore, a 1 km diameter( H max = 19 .
1) comet has an effective cometary absolute magnitude corresponding to a muchlarger object that should render them detectable at heliocentric distances where cometaryactivity turns on due to volatile sublimation, about 10 au. The ρ CLIS = 1 . × − au − value Manual Pan-STARRS1 vetting of known comets indicates that the realized comet de-tection efficiency was .
70% (Hsieh et al. i.e. within a heliocentric sphere with a radius comparable to Saturn’s distancefrom the Sun. This CL is on the threshold of being able to reject (fig. 7) the ISO spatialdensity prediction of Sen and Rama (1993).Our interstellar ISO limit is almost an order of magnitude smaller than the ρ IS = 10 − au − value used by Torbett (1986) to predict that the ISO capture rate byJupiter is about once per 60 Myr. Assuming that the capture rate scales with the ISOspatial density, our CL suggests that the ISO capture rate into heliocentric orbit is lessthan about once per ∼
400 Myr, making it less likely that the unusual comet 96P/Machholzis an interstellar interloper.Moro-Mart´ın et al. (2009)’s theoretical interstellar ISO number density predictionincluded several enhancements beyond the earlier estimates with the most importantbeing 1) a stellar-mass-dependent stellar number density, 2) stellar-mass-dependentprotoplanetary disk mass, 3) the fraction of stars that harbor the giant planets necessaryto scatter planetesimals into interstellar space, and 4) the ISO size-frequency distribution.Their detailed analysis dramatically reduces the expected interstellar ISO number densityto the range from about 10 − au − to 10 − au − , many orders of magnitude smaller thanour best experimental limit. If the actual ISO spatial number density lies somewhere inthat range it will be essentially impossible for the three surveys used in this analysis to everdetect ISOs barring a statistical fluke. Thus, the detection of the first non-microscopic ISOswill require new survey systems like the LSST ( e.g. Ivezic et al. -years of surveying(the product of its effective aperture area and the survey time), ∼ × more than the threecombined surveys in this analysis, Cook et al. (2011) suggest that LSST will not detect anyISOs beyond 5 au and the expected number within that distance is small. 32 –
7. Conclusions
The prospects for identifying a large chunk of material ejected by an extra-solar systempassing through our own solar system appear to be bleak. The fact that the existingmulti-year asteroid surveys, Pan-STARRS1, Catalina Sky Survey, and the Mt. LemmonSurvey, have not yet identified an ISO indicates either that other solar systems do not formlike ours, ejecting the vast majority of resident material in the process, or that the ISOsize distribution does not approximate that expected for a self-similar collisional cascade as(roughly) observed for populations of small bodies in our solar system. Our most stringent90% upper confidence limit on the interstellar number density of interstellar objects largerthan 1 km diameter is 1 . × − au − which assumes that the ISOs will display a behaviortypical of first time active comets entering the solar system with outgassing and associatedincreased apparent brightness beginning at about 10 au from the Sun. In this case theobject may be detected as cometary through its morphological appearance in the imageeven though its digest score may not be interesting.ISOs can have very small eccentricities approaching e = 1 for parabolic orbits, especiallyfor objects with small perihelion that are more efficiently detected by astronomical surveys.Roughly 0.003% of the model ISOs in our simulation had 1 . ≤ e ≤ .
06, a range in whichfive comets are also known. While it is more likely that the e > e > ∼
35% probability that it was notidentified as an ISO due to lack of followup. Future sky surveys like the LSST will havehigher ISO detection efficiency due to their regular self-followup surveying and automatedtracklet linking and orbit determination. 33 –
Acknowledgements
We thank Henry Hsieh for helping us understand Pan-STARRS1 comet detectionefficiency and Urs Hugentobler for reviewing and providing many suggestions to guide thework. Peter Brown was helpful in understanding interstellar meteor data. Dan Tamayowas very helpful in providing information and updates to their REBOUND software(Rein and Liu 2012) to handle hyperbolic orbits. Robert Weryk kindly provided assistancein determining the number of Pan-STARRS1 objects that never have followup observations.An anonymous reviewer provided helpful suggestions to improve the manuscript. We thankthe PS1 Builders and PS1 operations staff for construction and operation of the PS1 system.Peter Vereˇs’s Pan-STARRS MOPS Postdoctoral Fellowship at the Universityof Hawai‘i’s Institute for Astronomy was sponsored by NASA NEOO grant No.NNX12AR65G. Some of this research was conducted while he was employed at the JetPropulsion Laboratory, California Institute of Technology, under a contract with theNational Aeronautics and Space Administration. All rights reserved. Alan Fitzsimmonsacknowledges support from STFC grant ST/L000709/1. The CSS is currently supportedby NASA Near Earth Object Observations program grant NNX15AF79G, ”The CatalinaSky Survey for Near Earth Objects”. The Pan-STARRS1 Surveys (PS1) have been madepossible through contributions of the Institute for Astronomy, the University of Hawaii,the Pan-STARRS Project Office, the Max-Planck Society and its participating institutes,the Max Planck Institute for Astronomy, Heidelberg and the Max Planck Institute forExtraterrestrial Physics, Garching, The Johns Hopkins University, Durham University, theUniversity of Edinburgh, Queen’s University Belfast, the Harvard-Smithsonian Center forAstrophysics, the Las Cumbres Observatory Global Telescope Network Incorporated, theNational Central University of Taiwan, the Space Telescope Science Institute, the NationalAeronautics and Space Administration under Grant No. NNX08AR22G issued through the 34 –Planetary Science Division of the NASA Science Mission Directorate, the National ScienceFoundation under Grant No. AST-1238877, the University of Maryland, and Eotvos LorandUniversity (ELTE) and the Los Alamos National Laboratory. 35 –
REFERENCES
Afanasiev, V. L., V. V. Kalenichenko, and I. D. Karachentsev 2007. Detection of anintergalactic meteor particle with the 6-m telescope.
Astrophysical Bulletin ,301–310.Bottke, W. F., D. D. Durda, D. Nesvorn´y, R. Jedicke, A. Morbidelli, D. Vokrouhlick´y, andH. F. Levison 2005. Linking the collisional history of the main asteroid belt to itsdynamical excitation and depletion. Icarus , 63–94.Bowell, E., B. Hapke, D. Domingue, K. Lumme, J. Peltoniemi, and A. Harris 1988.Application of Photometric Models to Asteroids.
Asteroids II , 399–433.Buffoni, L., M. Scardia, and A. Manara 1982. The orbital evolution of comet Bowell/1980b/.
Moon and Planets , 311–315.Charnoz, S., and A. Morbidelli 2003. Coupling dynamical and collisional evolution of smallbodies:: an application to the early ejection of planetesimals from the jupiter–saturnregion. Icarus 166 (1), 141–156.Christensen, E., S. Larson, A. Boattini, A. Gibbs, A. Grauer, R. Hill, J. Johnson,R. Kowalski, and R. McNaught 2012. The Catalina Sky Survey: Current and FutureWork. In
AAS/Division for Planetary Sciences Meeting Abstracts , Volume 44 of
AAS/Division for Planetary Sciences Meeting Abstracts , pp. 210.13.Cook, N., D. Ragozzine, and D. Stephens 2011. Realistic Detectability of Close InterstellarComets. In
EPSC-DPS Joint Meeting 2011 , pp. 593.Cowan, J. J., and M. F. A’Hearn 1979. Vaporization of comet nuclei - Light curves and lifetimes.
Moon and Planets , 155–171. 36 –de la Fuente Marcos, C., R. de la Fuente Marcos, and S. J. Aarseth 2015. Flippingminor bodies: what comet 96P/Machholz 1 can tell us about the orbital evolutionof extreme trans-Neptunian objects and the production of near-Earth objects onretrograde orbits. MNRAS , 1867–1873.Dehnen, W., and J. J. Binney 1998. Local stellar kinematics from hipparcos data.
MonthlyNotices of the Royal Astronomical Society 298 (2), 387–394.Denneau, L., R. Jedicke, T. Grav, M. Granvik, J. Kubica, A. Milani, P. Vereˇs, R. Wainscoat,D. Chang, F. Pierfederici, N. Kaiser, K. C. Chambers, J. N. Heasley, E. A. Magnier,P. A. Price, J. Myers, J. Kleyna, H. Hsieh, D. Farnocchia, C. Waters, W. H.Sweeney, D. Green, B. Bolin, W. S. Burgett, J. S. Morgan, J. L. Tonry, K. W.Hodapp, S. Chastel, S. Chesley, A. Fitzsimmons, M. Holman, T. Spahr, D. Tholen,G. V. Williams, S. Abe, J. D. Armstrong, T. H. Bressi, R. Holmes, T. Lister,R. S. McMillan, M. Micheli, E. V. Ryan, W. H. Ryan, and J. V. Scotti 2013. ThePan-STARRS Moving Object Processing System.
PASP , 357–395.Dohnanyi, J. S. 1969. Collisional Model of Asteroids and Their Debris.
J. Geophys. Res. ,2531.Durda, D. D. 1993. The collisional evolution of the asteroid belt and its contribution to thezodiacal cloud . Ph. D. thesis, Florida University.Durda, D. D., R. Greenberg, and R. Jedicke 1998. Collisional Models and Scaling Laws:A New Interpretation of the Shape of the Main-Belt Asteroid Size Distribution.
Icarus , 431–440.Fern´andez, Y. R., M. S. Kelley, P. L. Lamy, I. Toth, O. Groussin, C. M. Lisse, M. F.A’Hearn, J. M. Bauer, H. Campins, A. Fitzsimmons, J. Licandro, S. C. Lowry, K. J.Meech, J. Pittichov´a, W. T. Reach, C. Snodgrass, and H. A. Weaver 2013. Thermal 37 –properties, sizes, and size distribution of Jupiter-family cometary nuclei.
Icarus ,1138–1170.Francis, P. J. 2005. The demographics of long-period comets.
The AstrophysicalJournal 635 (2), 1348.Fukugita, M., T. Ichikawa, J. E. Gunn, M. Doi, K. Shimasaku, and D. P. Schneider 1996.The Sloan Digital Sky Survey Photometric System. AJ , 1748.Gonczi, R., H. Rickman, and C. Froeschle 1992. The connection between Comet P/Machholzand the Quadrantid meteor. MNRAS , 627–634.Granvik, M., J. Virtanen, D. Oszkiewicz, and K. Muinonen 2009. OpenOrb: Open-sourceasteroid-orbit-computation software including Ranging.
Meteoritics and PlanetaryScience 44 (12), 1853–1862.Grav, T., R. Jedicke, L. Denneau, S. Chesley, M. J. Holman, and T. B. Spahr 2011. ThePan-STARRS Synthetic Solar System Model: A Tool for Testing and EfficiencyDetermination of the Moving Object Processing System.
PASP , 423–447.Hsieh, H. H., L. Denneau, R. J. Wainscoat, N. Sch¨orghofer, B. Bolin, A. Fitzsimmons,R. Jedicke, J. Kleyna, M. Micheli, P. Vereˇs, N. Kaiser, K. C. Chambers, W. S.Burgett, H. Flewelling, K. W. Hodapp, E. A. Magnier, J. S. Morgan, P. A. Price,J. L. Tonry, and C. Waters 2015. The main-belt comets: The Pan-STARRS1perspective.
Icarus , 289–312.Ivezic, Z., T. Axelrod, W. N. Brandt, D. L. Burke, C. F. Claver, A. Connolly, K. H. Cook,P. Gee, D. K. Gilmore, S. H. Jacoby, R. L. Jones, S. M. Kahn, J. P. Kantor, V. V.Krabbendam, R. H. Lupton, D. G. Monet, P. A. Pinto, A. Saha, T. L. Schalk, D. P.Schneider, M. A. Strauss, C. W. Stubbs, D. Sweeney, A. Szalay, J. J. Thaler, J. A. 38 –Tyson, and LSST Collaboration 2008. Large Synoptic Survey Telescope: FromScience Drivers To Reference Design.
Serbian Astronomical Journal , 1–13.Jedicke, R., M. Granvik, M. Micheli, E. Ryan, E. Spahr, and D. K. Yeomans 2015.
Surveys,Astrometric Follow-Up, and Population Statistics , pp. 795–814. University of ArizonaPress.Jewitt, D. 2003. Project Pan-STARRS and the Outer Solar System.
Earth, Moon, andPlanets 92 (1-4), 465–476.Jorda, L., J. Crovisier, and D. W. E. Green 2008. The Correlation Between VisualMagnitudes and Water Production Rates.
LPI Contributions , 8046.Jura, M. 2011. An upper bound to the space density of interstellar comets.
The AstronomicalJournal 141 (5), 155.Kaiser, N., H. Aussel, B. E. Burke, H. Boesgaard, K. Chambers, M. R. Chun, J. N. Heasley,K.-W. Hodapp, B. Hunt, R. Jedicke, D. Jewitt, R. Kudritzki, G. A. Luppino,M. Maberry, E. Magnier, D. G. Monet, P. M. Onaka, A. J. Pickles, P. H. H. Rhoads,T. Simon, A. Szalay, I. Szapudi, D. J. Tholen, J. L. Tonry, M. Waterson, andJ. Wick 2002. Pan-STARRS: A Large Synoptic Survey Telescope Array. In J. A.Tyson and S. Wolff (Eds.),
Society of Photo-Optical Instrumentation Engineers(SPIE) Conference Series , Volume 4836 of
Society of Photo-Optical InstrumentationEngineers (SPIE) Conference Series , pp. 154–164.Kaiser, N., W. Burgett, K. Chambers, L. Denneau, J. Heasley, R. Jedicke, E. Magnier,J. Morgan, P. Onaka, and J. Tonry 2010. The pan-starrs wide-field optical/nirimaging survey. In
SPIE Astronomical Telescopes and Instrumentation: ObservationalFrontiers of Astronomy for the New Decade , pp. 77330E–77330E. InternationalSociety for Optics and Photonics. 39 –Kresak, L. 1992. Are there any comets coming from interstellar space?
Astronomy andastrophysics 259 (2), 682–691.Levison, H. F., and M. J. Duncan 1994. The long-term dynamical behavior of short-periodcomets.
Icarus , 18–36.Magnier, E. A., E. Schlafly, D. Finkbeiner, M. Juric, J. L. Tonry, W. S. Burgett, K. C.Chambers, H. A. Flewelling, N. Kaiser, R.-P. Kudritzki, J. S. Morgan, P. A. Price,W. E. Sweeney, and C. W. Stubbs 2013. The Pan-STARRS 1 Photometric ReferenceLadder, Release 12.01.
ApJS , 20.Mann, I. 2010. Interstellar Dust in the Solar System.
ARA&A , 173–203.McGlynn, T. A., and R. D. Chapman 1989. On the nondetection of extrasolar comets. TheAstrophysical Journal , L105–L108.Meech, K. J., J. Pittichov´a, A. Bar-Nun, G. Notesco, D. Laufer, O. R. Hainaut, S. C.Lowry, D. K. Yeomans, and M. Pitts 2009. Activity of comets at large heliocentricdistances pre-perihelion.
Icarus , 719–739.Meech, K. J., B. Yang, J. Kleyna, M. Ansdell, H.-F. Chiang, O. Hainaut, J.-B. Vincent,H. Boehnhardt, A. Fitzsimmons, T. Rector, T. Riesen, J. V. Keane, B. Reipurth,H. H. Hsieh, P. Michaud, G. Milani, E. Bryssinck, R. Ligustri, R. Trabatti, G.-P.Tozzi, S. Mottola, E. Kuehrt, B. Bhatt, D. Sahu, C. Lisse, L. Denneau, R. Jedicke,E. Magnier, and R. Wainscoat 2013. Outgassing Behavior of C/2012 S1 (ISON) from2011 September to 2013 June.
ApJ , L20.Meech, K. J., B. Yang, J. Kleyna, O. R. Hainaut, S. Berdyugina, J. V. Keane, M. Micheli,A. Morbidelli, and R. J. Wainscoat 2016. Inner solar system material discovered inthe Oort cloud.
Science Advances , e1600038. 40 –Meisel, D. M., and C. S. Morris 1982. Comet head photometry - Past, present, andfuture. In L. L. Wilkening (Ed.), IAU Colloq. 61: Comet Discoveries, Statistics, andObservational Selection , pp. 413–432.Monet, D. G., T. Axelrod, T. Blake, C. F. Claver, R. Lupton, E. Pearce, R. Shah, andD. Woods 2013. Rapid Cadence Collections with the Space Surveillance Telescope.In
American Astronomical Society Meeting Abstracts , Volume 221 of
AmericanAstronomical Society Meeting Abstracts .Moro-Mart´ın, A., E. L. Turner, and A. Loeb 2009. Will the Large Synoptic SurveyTelescope detect extra-solar planetesimals entering the solar system?
TheAstrophysical Journal 704 (1), 733.Musci, R., R. Weryk, P. Brown, M. D. Campbell-Brown, and P. a. Wiegert 2012. An opticalsurvey for millimeter-sized interstellar meteoroids.
The Astrophysical Journal 745 (2),161.O’Brien, D. P., and R. Greenberg 2003. Steady-state size distributions for collisionalpopulations:. analytical solution with size-dependent strength.
Icarus , 334–345.Rein, H., and S.-F. Liu 2012. REBOUND: an open-source multi-purpose N-body code forcollisional dynamics.
A&A , A128.Schlafly, E. F., D. P. Finkbeiner, M. Juri´c, E. A. Magnier, W. S. Burgett, K. C. Chambers,T. Grav, K. W. Hodapp, N. Kaiser, R.-P. Kudritzki, N. F. Martin, J. S. Morgan,P. A. Price, H.-W. Rix, C. W. Stubbs, J. L. Tonry, and R. J. Wainscoat 2012.Photometric Calibration of the First 1.5 Years of the Pan-STARRS1 Survey.
ApJ , 158.Schleicher, D. G. 2008. The extremely anomalous molecular abundances of Comet 41 –96P/Machholz 1 from narrowband photometry.
The Astronomical Journal 136 (5),2204.Sen, A., and N. Rama 1993. On the missing interstellar comets.
Astronomy andAstrophysics , 298.Snodgrass, C., A. Fitzsimmons, S. C. Lowry, and P. Weissman 2011. The size distributionof Jupiter Family comet nuclei.
MNRAS , 458–469.Standish, E. 1998. JPL Planetary and Lunar Ephemerides, DE405/LE405.
JPL IOM312.F-98-048 .Stokes, G. H., J. B. Evans, H. E. M. Viggh, F. C. Shelly, and E. C. Pearce 2000. LincolnNear-Earth Asteroid Program (LINEAR).
Icarus , 21–28.Tonry, J., and P. Onaka 2009. The Pan-STARRS Gigapixel Camera. In
Advanced MauiOptical and Space Surveillance Technologies Conference .Tonry, J. L., C. W. Stubbs, M. Kilic, H. A. Flewelling, N. R. Deacon, R. Chornock,E. Berger, W. S. Burgett, K. C. Chambers, N. Kaiser, R.-P. Kudritzki, K. W.Hodapp, E. A. Magnier, J. S. Morgan, P. A. Price, and R. J. Wainscoat 2012.First Results from Pan-STARRS1: Faint, High Proper Motion White Dwarfs in theMedium-Deep Fields.
ApJ , 42.Tonry, J. L., C. W. Stubbs, K. R. Lykke, P. Doherty, I. S. Shivvers, W. S. Burgett, K. C.Chambers, K. W. Hodapp, N. Kaiser, R.-P. Kudritzki, E. A. Magnier, J. S. Morgan,P. A. Price, and R. J. Wainscoat 2012. The Pan-STARRS1 Photometric System.
ApJ , 99.Torbett, M. V. 1986. Capture of 20 km/s approach velocity interstellar comets bythree-body interactions in the planetary system.
Astronomical Journal , 171–175. 42 –Vereˇs, P., R. Jedicke, A. Fitzsimmons, L. Denneau, M. Granvik, B. Bolin, S. Chastel,R. J. Wainscoat, W. S. Burgett, K. C. Chambers, H. Flewelling, N. Kaiser, E. A.Magnier, J. S. Morgan, P. A. Price, J. L. Tonry, and C. Waters 2015. Absolutemagnitudes and slope parameters for 250,000 asteroids observed by Pan-STARRSPS1 - Preliminary results. Icarus , 34–47.Wainscoat, R. J., P. Veres, B. Bolin, L. Denneau, R. Jedicke, M. Micheli, and S. Chastel2013. The Pan-STARRS search for Near Earth Objects: recent progress and futureplans. In
AAS/Division for Planetary Sciences Meeting Abstracts , Volume 45 of
AAS/Division for Planetary Sciences Meeting Abstracts , pp. 401.02.Weissman, P. R. 1983. The mass of the Oort cloud.
A&A , 90–94.Weryk, R. J., and P. Brown 2004. A search for interstellar meteoroids using the CanadianMeteor Orbit Radar (CMOR).