[Eternal Student (OP)]

Hi.

    How do you determine if a galaxy has S0 morphology (but is seen head on) and not E0 morphology (seen from most angles)?   
    Presumably, it's not in our power to spin the galaxy around and check if you're just seeing it from certain angle.
   
My best guess:   S0 or    "Lenticular" galaxies tend to have bright central bulges but E0 galaxies less so.    Anyway, I don't know and would be grateful for anyone's gudiance or opinion.

Best Wishes.

[Halc]

Your best guess would be mine as well.
Many S0 galaxies are classified thus due to being edge-on, obscuring any bars and other structure.
But the ones seen face-on all seem to have a concentrated central bulge and a thinner disk: a fried egg.
The E0 ones are fat spheres, bright almost all the way out, with a halo of thin stuff almost like a planet atmosphere, a poached egg maybe.
We'll not get into the scrambled-egg ones:

(Image credit: Judy Schmidt/NASA/ESA)

[Eternal Student (OP)]

Thanks @Halc

[evan_au]

I suspect that looking at the red shift across the width of the galaxy would tell you a lot.
- Spiral galaxies have a well-ordered red-shift on one side, and well-ordered blue shift on the other.
- I get the impression that elliptical galaxies are like a swarm of angry bees, with red and blue-shifted stars when viewed on any axis.

See: https://en.wikipedia.org/wiki/Galaxy_morphological_classification

[Eternal Student (OP)]

Hi.

Thanks @evan_au ,

Spiral galaxies have a well-ordered red-shift on one side, and well-ordered blue shift on the other.

    Definitely true when viewed from the side.   Not so obvious when viewed from the top.  ("Top" is an imprecise way of describing a viewing angle.... I'm using it as if the galaxy is a like a child's spinning top and you are watching it from above).   
     If a S0 galaxy is viewed directly from the top then stars are now moving almost perfectly tangentially to the observer and not directly towards and away from them.  So there's no conventional (non-relativistic) Doppler shift at all.  Using the relativistic formula for red-shift there is still some red-shift but it is negligible unless stars are whizzing around the centre of the galaxy at speeds ~ c.

I get the impression that elliptical galaxies are like a swarm of angry bees, with red and blue-shifted stars when viewed on any axis.

    When I first read that comment I would have dismissed it as being something you had no hope of detecting.   There would be no net red-shift or blue-shift.  However, you weren't entirely wrong, looking at spectral lines can still help....
     It's not possible to focus in on one star and observe a clear and individual red-shift or blue-shift.   Instead it's only possible to collect light from a volume which had multiple stars and gas clouds moving in all sorts of directions.   My first thought was that the Doppler shift is then too weak and too confused to be measured or useful. Assuming random motion of objects in the volume under study there would be no net red shift or blue shift detected.   That part is true, so I wasn't entirely wrong either.  There certainly is no net shift and for exactly those reasons as stated.
     However, I've read a bit more about it.   You just don't need to pick up a net red-shift or blue-shift.  When both things happen it's not the same as if neither happens.  There's something you can detect, there's a broadening of the spectral lines.   (OK... it's obvious now but completely escaped me at first).   Anyway, apparently the effect is significant enough to be measured and it can be used to help identify elliptical galaxies.   

Best Wishes.

[evan_au]

Doppler shift is then too weak and too confused to be measured or useful

Measuring the spectrum across the visible disk of a galaxy is an established technique - in fact, it was one of the early indications of the presence of Dark Matter. This technique was applied as long ago as 1939, but in the 1960s, Vera Rubin, with a much better spectrograph, was able to improve on the measurements.

See: https://en.wikipedia.org/wiki/Galaxy_rotation_curve

[Eternal Student (OP)]

Hi.

     Thanks, I've scanned through the Wikipedia link given.   

     It looks like Vera Ruben was working with spiral galaxies not elliptical galaxies and was viewing them side-on or "edge-on" as Wiki describes it.   However, I'm sure the techniques are good and probably much better now if that's what you meant.

Best Wishes.