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Database of Asteroid Models from Inversion Techniques – more about DAMIT

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Database – Description

Light curve inversion

We present asteroid models that were derived using the lightcurve inversion method (Kaasalainen et al. 2001; Kaasalainen & Torppa 2001), combined with other inversion techniques in some cases. For each asteroid, we list the ecliptic coordinates of its spin axis, its sidereal rotation period, the reference to the original publication, and other parameters and comments related to the model. Please note that results presented here may differ from those published in the original papers. The main reason for this is a limited dataset used in the original publication or/and a narrow range of periods scanned during the inversion.

File formats

Shape models (SHP), spins (SPIN)

The shape models are represented as polyhedrons with triangular surface facets. The format of shape files (SHP) is as follows: The first line gives the number of vertices and facets, then follow the vertex x, y, z coordinates (defining radius vectors rast), then for each facet the order numbers of facet vertices (anticlockwise seen from outside the body). The orientation of a model at epoch t is given by a transformation between vectors rast in the asteroid co-rotating coordinate frame and vectors recl in the ecliptic coordinate frame. The transformation is given by the equation

formula 1

where Ri(θ) is the rotation matrix corresponding to the rotation of a vector through the angle θ along the i-axis in the anticlockwise direction

formula 2

λ and β are ecliptic longitude and latitude of the spin axis respectively, P is the rotation period, φ0 is the initial rotation angle, and t0 is the initial epoch. In some cases, the nonzero linear change of the rotation rate υ caused by the YORP effect must be taken into account. The corresponding rotation matrix is then

formula 2

Values λ, β (degrees), P (hours), t0 (JD epoch), and φ0 (degrees) are given in spin (SPIN) files. If there is the third line in a spin file, it gives the scattering parameters described in the corresponding comment column.

Lightcurves (LC)

The models are based on lightcurve data that are stored in lightcurve files (LC). The first line gives the total number of lightcurves, then the individual lightcurves follow in blocks. Each lightcurve starts with the number of points and 0/1 code for a relative (0) or calibrated (1) lightcurve. Then there are lines with the light-time corrected JD epoch, the brightness in intensity units (reduced to unit distances from the Earth and the Sun when calibrated), the ecliptic asteroid-centric cartesian coordinates x, y, z of the Sun and of the Earth in AU. Follow the references for a detailed description of the lightcurve data (observers, telescopes, filters,...).

Lightcurve References (LCref)

The LCref files list references for lightcurves (served in LC files). The references are in the same order as the lightcurves: For example the third line/reference in the LCref corresponds to the third lightcurve in the LC file. The columns in the LCref files are: the serial number of the reference/lightcuve; the mean year, month and day of observation; the reference shortcut. The references are fully expanded in references.txt file.

Shape vizualization (PNG, 3D)

Each shape model is shown from three directions in the corresponding PNG file. There are two views from asteroid's equator and one from its pole. The three views correspond to the views from the positive x, y, z axes, respectively. The light-scattering model used for rendering has no physical meaning and was chosen just for visualization purposes. For each model, there is also an interactive 3D animation that works with Acrobat Reader 8 or higher.

Spin parameters according to the IAU recommendation (IAUspin)

The IAUspin file gives the parameters of the rotation state according to the recommendations of the IAU (Seidelmann et al. 2007, Celestial Mech. Dyn. Astr. 98, 155): α0, δ0, dW / dt (the first line), and t0, W0 (the second line). Here α0 and δ0 are equatorial coordinates of the pole (degrees), dW / dt is the rotation rate (deg/day), and t0 is the initial epoch for which the position of the prime meridian is W0 (degrees). The position of the prime meridian at the time t is W = W0 + dW / dt (t - t0). The prime meridian is defined by the positive x axis.

Occultations (occ)

Some models in the database were scaled to fit the occultation data. For these asteroids, the sky-plane projection of the model was computed for the time of occultation and plotted together with the occultation chords. The meaning of different types of lines and curves is explained in occ_explanation.pdf (PDF 9.8 KiB). For more details see Ďurech et al. (2011), Icarus, in press, preprint (PDF 468 KiB).

Wavefront .obj file (OBJ)

The shape model is also provided in the OBJ format, that is recognized by most 3D graphics applications. More about this format can be found at http://en.wikipedia.org/wiki/Wavefront_.obj_file.

Models visualisation (sky projection)

Besides the PNG and 3D files, we also provide an on-line service for models visualisation. The service allows you to generate a model's sky projection for an arbitrary time (Julian Date). The service is available for all models, which have a corresponding shape file (SHP) in the database. The link to the service is accessible from the detailed view of an asteroid, in the model row Services, and redirects you to a pre-filled form, where you can adjust the Julian Date. Note that the pre-filled Julian Date corresponds to today's noon. After clicking the Show projection button, a new tab (or window) with the projection will open. The projection takes usually several seconds, so, please, don't reload the page if the results are not displayed immediately.

The projection shows two pictures. First represents a given model illuminated by the Sun, second represents the model under artificial illumination to show its outline in the sky. Both pictures show the model as viewed from Earth at a given Julian Date; the north is up and west is right. The projection also takes into account the light-time effect: The model's orientation is computed for the retarded time tret = tΔ/c, where t is the observation time, Δ is the distance between the asteroid and Earth and c is the speed of light.

The database structure

The data are presented in the table form, ordered by the selected asteroid label (number, name, designation). Below the asteroid label row there are generally several rows containing corresponding models which represent solutions to the lightcurve inversion problem.

The meaning of the columns (database fields) is as follows:

Asteroid columns
Column Meaning
Number Asteroid's number label.
Name Asteroid's name label.
Designation Asteroid's designation label.
Files The corresponding files (LC).
Comment The field reserved for additional information.
Model columns – standard
Column Meaning
λ Ecliptic longitude of the spin axis direction (J2000.0, in degrees).
β Ecliptic latitude of the spin axis direction (J2000.0, in degrees).
P Sidereal rotation period (hours).
Files The corresponding files. See section File formats above.
Comment The field reserved for additional information. The comment 'wrong inertia tensor' means that the ratio of the moment of inertia along the principal axis to that along the actual rotation axis is >1.05.
Model columns – extended
Column Meaning
Reference List of the references related to the model.
Reference (obsolete) List of the obsolete references. Obsolete means that these references are not related to the most recent model, but were related to an older (today obsolete) model.
YORP The linear change in the rotation rate (dω / dt) caused by the Yarkovsky-O'Keefe-Radzievskii-Paddack effect (rad / day2).
JD0 The initial Julian date.
φ0 The initial rotation angle for JD0 (degrees).
LSM 1  Light-scattering model – LSL = Lambert + Lommel-Seeliger; H = Hapke.
p1 1  The lambertian part of LSL; the single-particle scattering albedo w for H.
p2 1  The amplitude a of the phase angle function for LSL; the assymetry parameter of the single-particle phase function g for H.
p3 1  The width d of the phase angle function for LSL; the opposition surge amplitude B0 for H.
p4 1  The slope k of the phase angle function for LSL; the opposition surge width h for H.
p5 1  The macroscopic roughness θ0 for H.
Cal. size Calibrated size – 'yes' when the shape model is scaled to the real size (in km), 'no' otherwise (model is scaled to unit volume).
D Equivalent diameter (in km) – the diameter of a sphere that has the same volume as the shape model.
σD Equivalent diameter error (in km) – the estimated error of the equivalent diameter.
Γ Thermal inertia (in J m−2 s−1/2 K−1).
Γmin Lower limit for Γ – estimation of the uncertainty interval.
Γmax Upper limit for Γ – estimation of the uncertainty interval.
pV Visual geometric albedo.
σpV Error of the visual geometric albedo.
γc Opening angle of craters (in deg) – for describing the surface roughness.
ρc Areal density of craters – for describing the sufrace roughness.
Version The version of the model. Usually in the format of date (YYYY-MM-DD).

Note 1: Default values are: Light-scattering model = 'LSL'; p1 = 0.1; p2, p3, p4, p5 not defined.

References

  • M. Kaasalainen et al. (2001): Optimization methods for asteroid lightcurve inversion. II. The complete inverse problem. Icarus 153, 37.
  • M. Kaasalainen and J. Torppa (2001): Optimization methods for asteroid lightcurve inversion. I. Shape determination. Icarus 153, 24.