How Does Particle Size Influence Emissivity in Circumstellar Dust?

[robotopia]

In this 1984 paper on circumstellar dust, the author says, speaking of the emissivity/absorption of dust grains at visual and infrared wavelengths:

The dust shell model is consistent with the observed shape of the [IR] excess and the observed size of the $60 \, \mu \text{m}$ source, provided that $(\varepsilon_\text{vis}/\varepsilon_\text{IR})$ is near unity. Since $\varepsilon_\text{vis}$ for most material is near unity... it follows that $\varepsilon_\text{IR}$ also has to be near unity. This condition will normally be satisfied if the particle radius, $a$, is comparable to or larger than $\lambda_p / 2\pi$, where $\lambda_p$ is the wavelength of the peak emission.

My question is: where did the expression $\lambda_p / 2\pi$ come from, and what is the physical justification for it? I understand that small objects whose size is comparable to the wavelength of the incident light can't be resolved by that light, but what does that have to do with blackbody radiation and emissivity?

 

[Chronos]

Read the latest Planck mission results. They have some good information on this.

 

[robotopia]

Planck Mission results seem vast...

Thanks, Chronos, for the reply.

I made my way to http://www.sciops.esa.int/index.php?project=PLANCK&page=Planck_Published_Papers, tried to find something specifically relating to my question, and failed, feeling overwhelmed by the sheer amount of their publications. I can see that the Planck Mission is obviously very concerned with dust and its properties, and I'm sure the answer is buried in there somewhere, but in the meantime, is there a specific paper, or webpage that you could send me a link for?

 

[Chronos]

I too could find nothing specifically relevant to your question. I took the liberty of doing some additional research and came up with this: Astrophysics of Dust in Cold Clouds, http://arxiv.org/abs/astro-ph/0304488. Hope that helps

 

[robotopia]

Thanks again, Chronos. The article is helpful, but will require more careful reading to find the answer I'm looking for. I feel as though there's something basic that I'm missing, but I can't quite put my finger on it.
I'll post again if I have any luck.