Spectral slope

Many asteroid spectra tend to be "redder" than the spectra of the corresponding meteorites. Reddened spectra have lower reflectivity, weaker absorptions, and spectral slopes that are flatter in the red end. This phenomenon has been attributed to "space weathering," a catchall term referring to any process that modifies the optical properties of surfaces of airless bodies exposed to the space environment. 

Helms, J. R., Stubbins, A., Ritchie, J. D., Minor, E. C, Kieber, D. J., and Mopper, K. (2008). Absorption spectral slopes and slope ratios as indicators of molecular weight, source, and photobleaching of chhromophoric dissolved organic matter, Limnol. Oceanogr. 53, 955-969. 

Since dust particles emit inefficiently at wavelengths much shorter than their size, it is necessary to observe at millimeter to centimeter wavelengths to probe particles that have experienced strong particle growth. The tracer of such large particles is the spectral slope ft of the emissivity of dust, defined as kv v at wavelengths > 500 pm. The disk spectral energy distribution (SED, see Chapter 3) is related to the opacity, rv = kvT (R) as ... 

The major tool that allows us to relate classes of meteorites to classes of asteroids is spectral reflectance (Burbine et al., 2002). Unfortunately, iron meteorites, with their paucity of silicate phases, have relatively featureless spectra with red spectral slopes and moderate albedos (e.g.. Clouds et al., 1990) (Figure 10). There appears to be no simple correlation between nickel abundance and spectra redness and, thus, distinguishing different chemical groups (e.g., low-nickel IIAB from... 

Figure 10 Normalized reflectance versus wavelength ( jLm) for M-type 16 Psyche versus iron and enstatite chondrite meteorites (lines) (Gaffey, 1976 Bell et al., 1988 Bus, 1999). All spectra are normalized to unity at 0.55 xm. Spectra for all three are relatively featureless with red spectral slopes and moderate albedos. While some M-class asteroids may be metallic core material, existing spectral and density data are inconsistent with this explanation for all M asteroids.

For the 9,000 m deep KTB scientific hole, heat production measurements were made with an average sampling interval of 3 m. The power spectrum of the vertical (one-dimensional) heat production profile appears to follow a power law oc K with /3 = 1.73 (Figure 6). Using this value for the one dimensional spectral slope, we obtain the exponent of the three-dimensional power spectrum using the equation /33 = /3i -f 2. (e.g., Maus and Dimri, 1994). We then find that the power spectrum of the surface heat flow Pq(K) oc This is a very smooth function,... 

FIGURE 21 Correlation of density with the spectral slope for roller compacted ribbons. 

We may consider another scenario which predicts a flattening of the L/M ratio at high energy due to reacceleration of the secondary cosmic rays. This would not appreciably affect the observable spectral slope of the primary species ([14]). Hence, for this case, and if we assume Ao = 0, we would expect no upturn in the energy spectra of the primary cosmic rays in spite of the flattening of the L/M ratio. 

Figure 6. Spectral slope of CDOM from two lakes (Hargreaves, unpublished). S (nm ) is an exponential parameter from the relationship agjo, =ae The value of S can be computed as the absolute value of the slope when Ln(acd<, j) is plotted against wavelength over the UV and blue range. Such plots tend to be linear over UV wavelengths when DOC is high (upper curve) but can sometimes be separated into a steeper UV-B slope (280-320 nm) and shallower UV-A slope (320-380 nm) when substantial photobleaching has occurred (lower curve). These lake samples are from the upper mixed layer, June 2001 (particles removed with GF/F filter, Shimadzu UV-1601 spectrophotometer, 10 cm quartz cuvette, low DOC deionized water spectrum subtracted small glitch at 345-350 nm in lower curve is caused by spectrophotometer imperfection).

B.R. Hargreaves, C.L. Osburn, D.P. Morris, R.E. Moeller (2001). Spectral slope response to solar and biotic processes Comparison of model with estimates from CDOM absorption and UV attenuation measurements. Aquatic Sciences Meeting of ASLO, Albuquerque, New Mexico, USA, February (abstract). 

When the dispersion rates are close to uniform and concentrated to a narrow band around A°° the Corrsin result 7 = 1+ 2b/ °° is recovered. Otherwise the minimum in (6.46) is achieved at A > A°°, i.e. the intermittency correction leads to a somewhat less steep spectral slope. This has been verified by Nam et al. (1999) using numerical simulations of chemical decay in a smooth two-dimensional flow. Note that (6.46) can also be obtained directly from the exact relationship between the spectral slope and the second order scaling exponent 7=1+ C2 ... 

Fig. 2. Distribution of events versus the apparent pair opening angle for two spectral slopes for the source with flux F(> 1 GeV)=5 10-5 cm-2 c-> T=1 year.

The most important control element in the glottal source is of course the rate at which the cycles occur. In Equation 11.30, this is determined by the positions oiN and N2, in Equation 11.32 by Tq, Te and 7b and in Equation 11.31 this is determined by the impulse function u n. In the last case, the glottal volume velocity function can be thought of as a low pass filtering of an impulse stream. From these expressions and empirical measurements, it is known that this low pass filter creates a roll off of about -12dB per octave. It is this, combined with the radiation effect, that gives all speech spectra their characteristic spectral slope. 

From the absorption coefQcients, spectral slope (5) can be calculated using a nonlinear fit of an exponential function to the absorption spectrum over the range of desired wavelengths using an equation such as ... 

Because the fluorescence spectrum of CDOM is broad, and its absorption spectrum monotonic, it is easy to establish relationships between FCDOM and flg over a large range of wavelengths. Nevertheless, for the purpose of using this technique to validate remote sensing retrievals of CDOM, it is convenient to report values at wavelengths covered by satellite sensors, and to provide data on the absorption spectra used to calibrate the FCDOM to flg including spectral slope S and how it was calculated. This facilitates comparison between published data. 

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