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In X-ray astronomy, the source is considered to be in the hard or soft spectral state. So what is the meaning of the hard spectral state? What are the soft state and hard state in spectroscopy?

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Not only in X-ray astronomy (chemistry also and pretty much everything related to X-rays). If you have an X-ray spectrum, the region with photon energy > 5-10 Kev is called "hard" X-rays, less than that it is called "soft" X-rays. Wiki has a nice explanation for that (Energy Ranges): https://en.wikipedia.org/wiki/X-ray However, I find the book better: https://web.archive.org/web/20121111141255/http://ast.coe.berkeley.edu/sxreuv/

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  • $\begingroup$ When we express the spectral state in terms of a graph of photon count vs energy, then what is the difference in a soft state and a hard state? Is there any way to know that the source is in soft state or hard state just looking at it from the graph ? $\endgroup$ Feb 11 at 5:39
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Active galaxies are known to change state as seen by a change in slope of their X-ray and gamma-ray spectra. We say that a spectrum has become harder (or changed to its hard state) when the slope changes so that there are relatively more high energy photons, and it becomes softer when the ratio of low energy photons to high energy photons increases. The physics of why they change state is not yet understood.

If the high energy spectrum is in a thermally dominated state, ie a Planck-like spectrum, then it is certainly soft. If it is in a steep powerlaw dominated state with low $\alpha < 1, I_\nu = f^{-\alpha}$, then it is still usually considered soft. But if $\alpha$ is higher, then it is hard. But, it is also a relative term, so a system cycling between any two different values of $\alpha$ will be going between its hard state and its low state.

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  • $\begingroup$ When we express the spectral state in terms of a graph of photon count vs energy, then what is the difference in a soft state and a hard state? Is there any way to know that the source is in soft state or hard state just looking at it from the graph ? $\endgroup$ Feb 11 at 5:39
  • $\begingroup$ Yes and no. I put the answer to your question above. $\endgroup$
    – eshaya
    Feb 11 at 18:57
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Just to add an example to what has already been said by eshaya and Larz.Astro. Here is the spectrum of the Black Hole binary Cygnus X-1 in its hard and its soft state. The plot is taken from Gierlinski et al. 1999 .

enter image description here

You see that the soft state consist of mostly thermal emission below 10 keV, while the hard state is dominated by non-thermal (comtonized) emission above that. Or as the paper puts it:

The resulting Xγ spectrum consists of blackbody photons emitted by the disc (at low energies) and a component due to Compton upscattering of the disc photons by both thermal and nonthermal electrons in the corona.

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