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**Asteroid Polarimetry: What do we measure ?**

Partial linear polarization and polarization – phase curves. Presence of a “Negative polarization branch” Curve described by a few parameters (%) 1 Ceres

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**Is a fundamental relation in asteroid science, where:**

D is the equivalent diameter in km. is a wavelength-dependent constant (the indicated value is for V colour) pv is the geometric albedo in V. It is defined as the ratio between the object brightness at zero phase angle and that of an ideal, flat and perfectly Lambertian disk, having the same projected surface of the object. The albedo is an important physical parameter, being related to surface composition, texture and more in general to the history of the object. H is the absolute magnitude in V, that is the apparent brightness that would be measured at unit distance from the Sun and the observer, and at zero phase angle.

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**The slope –Albedo “law”**

log pV = C1 log (h) + C2 log pV = C3 log (Pmin) + C4 Polarimetry is in principle an excellent technique to derive asteroid albedoes. Used in the past in asteroid taxonomy to distinguish between E, M, P classes (the big X complex). Some advantages over thermal radiometry, whose results are model-dependent, require observations in different IR bands, and generally suffer from poor knowledge of H (and lightcurve effects, when measurements in different thermal IR bands are not simultaneous). Radiometric albedoes for small asteroids observed in one single IR band have uncertainties of the order of 60%. Zellner et al. 1977

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**Some Problems of Polarimetry**

Polarimetry is not intrinsically efficient, since several observations of the same object at different phase angles are required. In the case of NEOs this problem is less severe, since the phase angle changes more quickly with respect to main belt asteroids. Moreover, NEOs can be observed at large phase angles, and the (positive) linear polarization of the objects at large phase angles is expected to be fairly different for low- and high-albedo objects. This is interesting for the ESA SSA project. Polarimetry is intrinsically demanding in terms of telescope size, since polarimeters split the incoming light into beams of radiation linearly polarized along different directions. Thus, a large collecting area is required.

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After the first pioneering era in the 70s, not very much was done in the next 20 years. Since mid-90s, there has been a phase of Renaissance of asteroid polarimetry due to the availability of new instruments and actively involved teams, mainly in Europe and Argentina

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**IRAS albedo distributions**

D > 50 km D < 50 km Problem: Is this true?

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Evidence for a slight systematic difference between IRAS and polarimetric albedoes (the latter being generally lower). Analysis limited to intermediate-albedo objects, due to instrumental limitations at CASLEO. Need of deriving polarimetric albedoes of small, low-albedo objects

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**Peculiar properties (inversion angles) of F-type Asteroids**

Some F-types exhibit evidence of a cometary nature (Phaeton, Wilson-Harrington). 2008 TC3 was an F-type!! (Belskaya et al., 2005)

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**An exciting discovery: the “Barbarians”**

(dashed and dotted lines show, for a comparison, typical polarization-phase curves for B-type ((24) Themis) and L-type ((12) Victoria) asteroids, respectively) Masiero and Cellino (2009)

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**The search for “Barbarians”: First results**

Gil-Hutton et al. (2008) Known objects: 234 (Ld - class), 172, 236, 387, 980 (L – class) 679 (K - class) Possible association with some dynamical families

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**Another result: VLT polarimetric observations of members of the Karin and Koronis families**

Cellino et al., Icarus 209, (2010) No statistically relevant difference has been found for the polarimetric phase curves of objects belonging to the Koronis family (> 1 Gyrs old) and to the “children” objects belonging to the Karin family (5.8 Myrs old). This suggests that the space-weathering mechanism acts very quickly in affecting the albedo of S-type asteroid surfaces

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**Wavelength dependence of linear polarization**

Opposite behaviour among moderate-albedo and low-albedo asteroids. Similar effects observed also for comets. UBVRI Itokawa observations at CASLEO Belskaya et al., Icarus 199, (2009)

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**Asteroid polarimetry as a support to space missions: the examples of Steins and Lutetia**

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**NEA Polarimetry C-type**

S-type Presence of a wide branch of positive polarization with a maximum near 90° NEO polarimetry is inherently efficient, since the rate of variation of the phase angle is fast for these objects, and a polarimetric slope can be obtained in a short time. Interesting for the purposes of ESA SSA E-type Even a single measurement of polarization at phase > 40 deg can be sufficient to obtain an overall albedo estimation! Very small (faint) NEAs are observable with the VLT (as shown by the case of Apophis).

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**EXAMPLE: POLARIMETRIC OBSERVATIONS OF (25143) ITOKAWA AT LARGE PHASE ANGLES in 2004 at CASLEO**

Linear fits of UBVRI data obtained in five consecutive nights, covering a large interval of phase angles

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From the obtained polarimetric slope, the geometric albedo of Itokawa turns out to be: pv = 0.24 ± 0.03 The size obtained from the polarimetric albedo pv = and H, derived from an extensive set of observations by different authors, gives a size which agrees within 7% with the Hayabusa results. But... How is it possible? Itokawa seems to be very depleted in regolith particles. How can it behave like much larger, and regolith-rich main belt asteroids?

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**General problem and Recommendation by IAU Comm.15:**

log pV = C1 log (h) + C2 Different authors are using different sets of C1 and C2 coefficients: C1 = -1.0 C2 = (Bowell & Zellner 1974) C1 = C2 = (Lupishko & Mohamed, 1996) C1 = C2 = (Cellino et al., 1999) Among them, only the latter was derived using thermal IR data reduced using the (H,G) system, which takes into account the opposition brightness surge at zero phase. It is urgent to converge to a new and unique choice of C1 and C2

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**Example: the determination of the albedo of the Potentially Hazardous Asteroid (99942) Apophis**

Observations performed at the UT2 ESO VLT (8-m Kueyen) telescope. (Delbò et al., 2007) Results: pv = 0.33 ± 0.08 The error is mostly a consequence of the calibration uncertainty Assuming G=0.25 (Q-type), H = 19.7, and the size of Apophis turns out to be D = 270 30 m

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The slope-albedo relation must be recalibrated using only high-quality V-band polarimetry of asteroids having accurately derived albedoes. The best target list at present is the one by Shevchenko and Tedesco (2006), including objects whose albedoes were derived from both occultation and in situ (four objects) size measurements, coupled with accurate estimates of absolute magnitudes (obtained using H,G, so let us keep our fingers crossed! ). 19

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**Current results of an on-going observing campaign at CASLEO**

Observed S&T objects C1 = ± 0.07 C2 = ± 0.08 The nominal errors on the two coefficients suggest that more work and additional observations are needed.

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**Testing different forms of the slope – albedo relation**

Comparison with S&T albedos Testing different forms of the slope – albedo relation C1 = ± 0.07 C2 = ± 0.08

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Looking also for new relations not purely based on the polarimetric slope only, but on more global fits of the whole phase – polarization curve.

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**A tentative “road map” for the future:**

Primary goal: New accurate polarization measurements of the Shevchenko-Tedesco targets, to improve albedo determination. Theoretical work certainly needed. Peculiar objects (Barbarians, F-class,...) Need of continuous collaborations between European researchers (Torino, Kharkiv, Helsinki, Paris, Nice, Armagh...).

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