### Toomre Q parameter

**(Q, Q parameter)**
(stability criterion for differentially rotating disks)

The **Toomre Q parameter** (**Q parameter**) is a value used
as part of a criterion for the stability of differentially rotating disks,
and constructed so that Q < 1 implies instability.
The instability in this case is a tendency for the higher-density
locations on the disk to gain density.
The letter *Q* is certainly used in analogy to an oscillator's
Q factor, i.e., **quality factor**.
The Toomre Q parameter was originally devised for disks of stars,
such as in a disk galaxy, but has since found use for modeling
accretion disks and protoplanetary disks.
Form for the latter:

*c*_{s}κ
*Q = ———*
*πGΣ*

The condition of Q > 1 is known as **Toomre's stability criteria**,
analogous to the Jeans criterion but including the effects of
the disk's rotation.
It specifically includes the effects of self-gravity
of the disk material.
For a gaseous disk, it is often labeled **Q**_{gas},
and for molecular clouds, the assumption is that
>1 means no star formation, i.e., a stable disk,
and <1 means star formation.

The parameter and criteria are based upon the assumption that the
disk is of a homogeneous substance. Stability criteria can be more
complex given more than one substance, e.g., a disk of both a gas
an dust. In such cases, sometimes a higher Q threshold
(e.g., 3) is used to accommodate this.

(*fluid dynamics,mathematics,measure,limit,rotation*)
**Further reading:**

http://en.wikipedia.org/wiki/Toomre%27s_stability_criterion

https://ui.adsabs.harvard.edu/abs/1964ApJ...139.1217T/

http://ui.adsabs.harvard.edu/abs/1997AstL...23..483P/

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