Size Distributions of Asteroid Families in the SDSS MOC 4

Alex Parker - University of Victoria

collaborating authors:Zeljko Ivezic - Mario Juric - Robert Lupton

Adam Kowalski - Michael Sekora

Asteroid Families

• Discovered in 1918 by K. Hirayama

• Clusters of asteroids in orbital element space

• Formed by the disruption or cratering of a large parent body

Size distributions of Asteroid Families

• Encode information about parent body, impact parameters, and post-formation collisional processing of fragments

• Usually fit as a single or double power-law of the form

dN/dR ∝ R -q or log(dH/dR) ∝ const + αH , where q = 5α + 1

• Ivezic et al 2001 fit the size distribution of the main belt with the following function, which changes slope from q1 to q2 smoothly at R ~ Rc

dN/dR = N0 where a = (q1 + q2)/2 and b = (q1-q2)/2

• (First) break in size distribution marks transition from gravitationally-dominated regime to strength-dominated regime

____10 aR ___ 10 bR + 10 -bR

sin(

i)

ecce

ntri

city

inner mid outer inner mid outer

semi-major axis (AU) semi-major axis (AU)

Method

• Visually identify largest clumps in e vs sin(i), iteratively fit and remove

• Define families as orthogonal ellipsoids in color-orbital space

• Only consider groups with N > 100. Interested in robust size distributions and statistics of dominant populations

Color-Orbital Selection

• Using a combination of orbital and color distributions, dynamically intermixed or “buried” families can be reliably isolated.

• Dorbit and Dcolor metrics assigned relative to a given family centroid

• Histograms of the differential increase in family membership vs Dorbit and Dcolor are used to identify cutoff values

VestaBaptistina

Identified Families

• 37 families with N > 100 identified, and contain ~50% of all objects in the sample.

• Several families identifiable only with the aid of SDSS colors, “dynamically buried”

• Baptistina from Flora, Mitidika from Juno, Lydia from Padua, McCuskey from Nysa-Polana

• Agree well with previous family lists (e.g., Zappala et al 1995, Nesvorny et al 2005, Mothe-Diniz et al 2005)

sin(i)

eccentricity

All

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Color separation of dynamically mixed families

Effects of Color Selection

Roughly 10% of dynamically identified family members are rejected based upon SDSS color

constraints.

Rejection rate slowly climbs for smaller radii.

Before color selection

After color selection

Yarkovsky effect and other size-dependent

systematics• Initial velocity field tends to spread

small objects further in orbital element space than large objects

• Radiation/spin coupled effects (eg., Yarkovsky/YORP effects) lead to enhanced symmetric spreading in semi-major axis

• Tested goodness of family extraction by varying cutoff threshold - family size distribution slopes limited by systematics to 0.05 - 0.1

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Fig. 9. The di!erential absolute magnitude distributions corresponding to panels in Figure 6 are shown as

symbols with (Poisson) error bars. The solid line shows arbitrarily renormalized best-fit distribution from

I01. The two dashed lines show the best-fit “broken” power law: a separate power-law fit for the bright and

faint end. In some cases, the two lines are indistinguishable. The best-fit parameters are listed in Table 3.

The two arrows show the best-fit break magnitude (left) and the adopted completeness limit (right).

41

Magnitude Distributions for composite, family, and background populations by semi-major axis

region

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Fig. 12. Analogous to Figure 9, except that the absolute magnitude distributions for selected asteroid

families are shown. The first three panels (from top left to bottom right) show examples of families that

follow a single power-law magnitude distribution, and the remaining six panels show magnitude distribu-

tions for families that require a double power-law fit. The best-fit parameters are listed in Tables 4 and 5,

respectively.

44

Magnitude Distributions for

nine robust families

Size distributions of identified families

• Broken power law size distributions twice as likely for red families (76%) than for blue families (36%)

• Size distributions systematically steeper for red families

• Ivezic et al 2001 fit still valid when considering the whole belt, but not for individual sub-populations

Population Ratios• Population fraction roughly constant

for red objects with H > 12

• However, population fraction declines for blue objects above this threshold

• If background population is composite of many families with small parent bodies, expect initial population ratios to decline similar to blue objects

• Collisional processing should equilibrate size distributions over time

Blue objects

Red objects

• Therefore, timescale to equilibrate red family and background size distribution shorter than for blue objects.

Age and Space Weathering

• Family ages taken from dynamical modeling (eg., Nesvorny 2004)

• Red families get redder with time

• Blue families get bluer with time

• Old families dominated by broken power-law size distributions, (red circles) while young families dominated by single-slope power-laws (blue squares).

Summary

• SDSS colors allow improved asteroid family definitions

• 37 families with N > 100 identified, 4 of which only with the aid of SDSS colors

• Red families twice as likely to have broken power-law size distributions, also appear to have collisionally equilibrated with red background

• Old families have broken power-law size distributions, young families have single power-law size distributions