The Faber-Jackson relation in ellipticals. The Faber-Jackson law, Figure , relates the velocity dispersion $ \sigma $ of the stars in an E-type galaxy with the . Psychotherapy, the therapist, and psychopathology as reflected in current fiction and film. Farber, B. A., & Jackson, H. D. (). Developing the therapeutic relationship: Integrating case studies, research, and practice. Find Medicare Therapists, Psychologists and Medicare Counseling in De "In working with clients, I focus on establishing a therapeutic relationship that fosters trust, mutual respect and empathy. Dale Faber, Clinical Social Work/Therapist.
Tully-Fisher, Faber-Jackson and the fundamental plane
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Faber–Jackson relation - Wikipedia
ApJ, finds a value somewhere in between, but closer to the "short" scale: ApJ, However, in some galaxies, the stars move very quickly in their orbits -- these tend to be the massive ones -- and in others, the stars move relatively slowly.
One way to quantify the motions of stars in such systems is by the dispersion of their velocities: In most galaxies, we can't distinguish individual stars. When we take a spectrum, the light of many, many stars is all mixed up, yielding a composite spectrum of the entire population.
Since some of the stars are moving towards us, and others away from us, while some have no radial velocity at all, features in the composite spectrum are smeared out in wavelength space.
The larger the range of motions, the larger the degree of smearing. If the light from those two stars is mixed together, the result is a spectrum in which the features are slightly diluted.
If a system contains stars with a wide range of velocities Faber and Jackson measured the velocity dispersion in their sample of elliptical galaxies by comparing the spectrum of light from the center of each galaxy to a series of synthetic spectra, in which a single template spectrum was broadened in a series of steps: When they compared the velocity dispersion of each galaxy to the absolute magnitude of the galaxy, they found a pretty good correlation: Another connection can be made between velocity dispersion and mass-to-light ratio: Since velocity dispersion is correlated with absolute magnitude, this means that mass-to-light ratio is also correlated with absolute magnitude.
So, let's summarize the findings of FJ We confirm that there is some close connection between several fundamental properties of ordinary elliptical galaxies. FJ76 discussed the first two properties: Sometimes, astronomers pick size -- denoted by the term Dn, which stands for "diameter measured at a particular level of surface brightness" Figure taken from Bernardi et al.
It's obvious, but note that there is quite a bit of scatter around the trend. The relationship looks a little bit tighter if one plots luminosity as a function of size, as shown in the panel at top right. Now, the bottom-left panel shows a rather weak dependence between velocity dispersion and radius: But there might be some sort of systematic skewing: In that case, we could improve the quality of the relationship by throwing all three quantities into a big blender -- if we mix them up in JUST the right proportion, we can find a model which matches the observations better than the simple one.
Look at the bottom-right panel in the figure above. Because there are three variables, not just two, people describe this relationship among the properties of elliptical galaxies as the fundamental plane the term was coined by Djorgovski and Davis in The idea is that we can use any two of the three quantities to predict the value of the third, in some manner equivalent to: There are many different ways that one can express this idea, given that each quantity can be described in several different ways, and on scales with may be linear or logarithmic.
For example, La Barbera et al.
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Bernardi et al, AJuse the same variables, but their notation is a little different. Note that the connection between dynamics, luminosity, and size is seen in passbands across the optical.
What does it mean? The physics behind the relationships Okay, so we observe that luminous spiral galaxies have a large range of HI velocities.