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This research (see press article and technical paper), conducted on 3000 elliptical galaxies (which are typically galaxy merger results), reports finding "distinct relationship between the mass of the dark matter halo and the black hole mass - a relationship stronger than that between a black hole and the galaxy's stars alone".

Does such relationship exist in spiral or irregular galaxies ?

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    $\begingroup$ This question is probably better qualified to be incorporated as a comment to appropriate already existing open active question, but I don't have the required reputation value to place comments. $\endgroup$ – Alex Sep 6 '15 at 14:04
  • $\begingroup$ There's no additional class of galaxy called a "spherical galaxy". Perhaps you meant an irregular galaxy? $\endgroup$ – HDE 226868 Sep 6 '15 at 16:33
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    $\begingroup$ @HDE226868 - yes, you are right - I have corrected this, per your comment $\endgroup$ – Alex Sep 6 '15 at 16:52
  • $\begingroup$ I don't see a specific question here. $\endgroup$ – Rob Jeffries Sep 6 '15 at 20:12
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    $\begingroup$ I reformulated my question for better clarity $\endgroup$ – Alex Sep 7 '15 at 18:35
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The relationship they're claiming is a little more subtle than what comes across in the press article:

  • The black hole masses are not directly measured. They are inferred from the $M-\sigma$ relation for black holes, which says that the larger the central velocity dispersion of stars in a galaxy, the larger the black hole. The velocity dispersion is the (RMS) spread in the velocities. A high $\sigma$ generally indicates a high density, but it's important to note that this measurement is made on scales orders of magnitude larger than the size of the central black hole. The relation is calibrated from a few (~30) more direct measurements of black hole mass. The calibrated relation was applied in the research you link to >3000 galaxies to estimate the black hole masses.
  • The total "virial" masses of the galaxies are also not measured directly, they are inferred from the temperature of hot gas in the galaxy, which is measured from the energy of x-ray photons coming from the gas. A more massive system heats its gas more due to its deeper potential well. This relation is reasonably well understood, I'd say it's much more robust than the $M-\sigma$ relation.
  • The stellar masses are not measured directly either, they're estimated from the luminosity in different filters (i.e. different wavelength bandpasses). This, however, is something astronomers have been doing for a very long time and are rather good at, so that usually it's safe to think of stellar mass as a "measured" quantity rather than a derived one.

So what the paper is claiming directly is that the central velocity dispersion correlates more strongly with the x-ray temperature than with the stellar mass. If you make a couple of assumptions, this can be interpreted as a correlation between dark matter mass and black hole mass.

To get to your precise question, yes one could do something very similar for spiral galaxies, and perhaps also irregulars. The $M-\sigma$ relation also applies to spirals and S0s (lenticulars):

the M-sigma relation

The graphic is from this paper. Notice that the scatter in the relation is rather large, so that the uncertainty in the black hole mass inferred from the velocity dispersion is something like an order of magnitude. Getting the x-ray temperatures to estimate the total masses for spirals is a bit tricky, since most spirals are not massive enough to have a hot gas halo that emits in the x-ray. Other estimates of the total mass (e.g. rotation curve maxima) might work, though.

The trouble with irregulars is that I don't know of any with observed BH masses, so applying the $M-\sigma$ relation in this case would be pure speculation.

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