The farthest possible object

kw: observations, cosmology

There was some excitement not long ago, among cosmologists, that a quasar with a redshift parameter Z=10 had been observed. However, this is not yet verified, so the highest redshifts currently accepted are in the range around Z=7.

Z is the wavelength ratio: 1+Z = λobsv/λemit. This is related to relativistic velocity thus: (1+Z)² = [(1+v/c)/(1-v/c)]. By a little algebra, we find: v/c = [(1+Z)²-1]/[(1+Z)²+1]. Now, for an object with Z=10, v/c works out to 120/122, or approximately v=0.984c. That's getting pretty close to the observable limit.

The point I was thinking of, however, is that the actual limit of observation is not much beyond the point where Z=10. This is my reasoning:

• The universe is filled with dilute hydrogen. It forms 99% of the interstellar medium, at densities between 0.1 and 1 atom/cc.
  
• Hydrogen is ionized by radiation with an energy of 13.6eV or greater. That corresponds to a wavelength of 91.2nm (400nm is the bluest light the eye can see).
• Hydrogen thus absorbs all photons with wavelengths shorter than this. It also absorbs selected wavelengths of the Lyman series starting near 122nm. Spectral features with shorter wavelengths will not be observed at any distance greater than a few light years.
• Of the 1% of the interstellar medium that is not hydrogen, much is water, and much is also carbon dioxide. Water, in particular, has a series of broad absorption bands in the infrared beginning about 800nm, and absorbs everything beginning at 11,000nm (11 microns), until the very far infrared with wavelengths of a few mm.
• Over millions of light years, there is enough water to absorb most radiation longer than 800nm, and carbon dioxide will "get" much of what water misses.
• There happens to be a gap in water's absorption bands in the 900-1000nm range.
• For Z=10, you need the wavelength ratio to be 11. 91.2nm times 11 is 1003.
• While it is thus possible to observe light that began as Lyman series emissions, that has been stretched into the 1000nm range, this is the Redshift limit, for practical purposes.
  

My conclusion: cosmological redshifts greater than Z=10 cannot be observed in the optical or near-optical range. They need to be observed at microwave or radio wavelengths, and then in a region of the spectrum for which the entire range of redshifted radiation will not be absorbed on its way to our radio telescopes. I haven't looked into that yet, in enough detail to know if it is possible.