An Etymological Dictionary of Astronomy and Astrophysics
English-French-Persian

The value of the exponent in the → initial mass function as derived by Salpeter (1955) for solar to → intermediate mass stars in the Solar neighborhood: &Gamma = 1.35 or &alpha = 2.35, or x = -1.35. Also known as Sapleter index.

→ Salpeter function; → slope.

1) An inclined surface; deviation from the horizontal or vertical.
2) The tangent of the angle formed by the intersection of a given straight line and the X-axis of a system of Cartesian coordinates.
3) The derivative of the function whose graph is a given curve evaluated at a designated point.
4) The exponent of the → initial mass function . See also → Salpeter slope.
5) → slope parameter.

From M.E. aslope (adv.) "on the incline," from O.E. *aslopen, p.p. of aslupan "to slip away," from a- "away" + slupan "to slip."

Šib "slope, descent, declivity," contraction of nešib, našib "declivity, descent; lowness of ground, slope of any place;" Mid.Pers. nišēp "declivity, (astrology) dejection," Av. *nixšvaēpā-, xšvaēpā- "bottom, rear."

In a → power-law distribution or → regression, the → exponent that represents the effect of the → independent variable, x, on the → dependent variable, y. X has no association with y if the slope parameter = 0 and x has strong association with y if the slope parameter is large.

→ slope; → parameter.