Over time, the temperatures would have stopped, solar radiation having broken down water molecules into ...

Universe: The Solar System, Roger Freedman, ‎Robert Geller, ‎William J. Kaufmann, 2010 Macmillan

Can I paraphrase the bolded absolute clause to this:

the temperatures would have stopped, because solar radiation had broken down water molecules ...

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    Your link is not working. It just gives an error "我们检测到你可能是个爬虫程序,或者点开了别人给的做题链接,请从正规渠道练习,有疑问请与管理员联系!" – James K Aug 4 '16 at 18:11
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    @AlirezaN. I can't resist asking why a Persian (which I infer from your name, perhaps incorrectly) would prepare for the TOEFL by using a Chinese site. There are sites in Farsi! – P. E. Dant Aug 4 '16 at 19:13
  • @P.E.Dant Yes, I am Persian, I don't use these sites to prepare for the TOEFL, actually I have those in my hardware. To cite the sentence, I googled it and found just these Chinese websites which don't make any difference when my question is aimed at English language. However, I am sorry for making it uncomfortable for you. Thank you – Anfi Aug 4 '16 at 19:24
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    @AlirezaN. You have not made me nor anyone uncomfortable! I only wanted to be sure that you had access to useful resources in your own language, especially since some of the Chinese language sites are of very poor quality. !موفق باشید – P. E. Dant Aug 4 '16 at 19:51
  • But those TPOs are actually for simulating TOEFL exams whose materials are gathered by Chines through hacking ETS. Please, do not share them on the internet, especially here. – Cardinal Aug 4 '16 at 23:09

Yes, the participle clause "solar radiation having...." is giving the reason. This may be made explicit with a subordinating conjunction such as "because".

The participle clause sounds educated and mature. Perhaps more common in written rather than spoken English.

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    The quote is from Universe: The Solar System, Roger Freedman, ‎Robert Geller, ‎William J. Kaufmann, 2010 Macmillan. – P. E. Dant Aug 4 '16 at 19:16

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