DICTIONARY OF GEOPHYSICS, ASTROPHYSICS, and ASTRONOMY

initial condition
time. Different regions of the universe may be
of different age.
2. The curvature index k of the Robertson–
Walker models is, in general, not a constant, but
a function of position. Hence, some parts of the
universe may go on expanding forever, while
some regions may collapse in a finite time to the
final singularity.
3. The spatially homogeneous and isotropic
models (see homogeneity, isotropy) are
unstable with respect to the formation of condensations
and voids. Hence, the formation of
clusters of galaxies and voids is a natural phenomenon
rather than a problem.
4. An arbitrarily small electric charge will
prevent the collapse to the final singularity. This
also applies to the initial singularity — the
model with charge, extended backward in time,
has no Big Bang. The charge may be spread
over all matter (then it has to be sufficiently
small compared to the matter density) or concentrated
in a small volume; the result holds
in both cases. Reference: A. Krasiński, Inhomogeneous
Cosmological Models. Cambridge
University Press, 1997.
initial condition A boundary condition appliedtohyperbolicsystemsataninitialinstantof
time; or for ordinary differential equations (one
independent variable) applied at one end of the
domain. For more complicated situations, for
instance, in theories like general relativity one
may specify the state of the gravitational field
and its derivative (which must also satisfy some
consistency conditions) at one instant of time.
These are the initial conditions. One obtains the
later behavior by integrating forward in time.
initial data In general relativity, see constraint
equations.
initial mass function (IMF) The distribution
of newly formed stars as a function of mass. The
initial mass function is estimated from the photometric
and spectroscopic properties of stars
in open clusters and associations of stars. Ideally,
the IMF can be measured counting the stars
of each spectral type in an association of stars
so young that the shortest-lived massive stars
are still in the main sequence. The initial mass
function is usually assumed to be of the form
© 2001 by CRC Press LLC
244
(m) ∝ m −Ɣ , where m is the mass of the star.
The index Ɣ may vary for different mass ranges,
but it is always positive, implying that high mass
stars are formed less frequently than low mass
stars. According to E.E. Salpeter, (m) ∝
m −2.35 , for all masses. From this law, we expect
that for one star of 20 solar masses (M⊙) ≈ 1000
stars of 1M⊙ are formed. According to G.E.
Miller and J.M. Scalo, the IMF valid for the solar
neighborhood can be approximated as (m) ∝
m −1.4 , for 0.1 < ∼ m < ∼ 1M⊙ , (m) ∝ m −2.5 ,
for 1 < ∼ m < ∼ 10M⊙, and (m) ∝ m −3.5 , for
m > ∼ 10M⊙. This law predicts fewer high mass
stars (m > ∼ 10M⊙) for a given number of solar
mass stars than Salpeter’s law.
injection boundary A line in the nightside
equatorial magnetosphere along which dispersionless
plasma injections appear to be generated.
inner core The Earth’s inner core has a radius
of 1215 km, and is solid. The inner core is primarily
iron and its radius is growing as the Earth
cools. As the outer core solidifies to join the inner
core, elements dissolved in the outer core are
exsolved. The heat of fusion from the solidification
of the inner core provides a temperature
gradient, and convection, and the ascent of these
light exsolved components are major sources of
energy to drive the geodynamo.
inner radiation belt A region of trapped
protons in the Earth’s magnetosphere, typically
crossing the equator at a geocentric distance of
1.2 to 1.8 RE (Earth radii), with energies around
5 to 50 MeV. The inner belt is dense enough
to cause radiation damage to satellites that pass
through it, gradually degrading their solar cells.
Manned space flights stay below the belt.
The 1958 discovery of the inner belt was the
first major achievement of Earth satellites. The
belt seems to originate in the neutron albedo, in
secondary neutrons from the collisions between
cosmic ray ions and nuclei in the high atmosphere.
The trapping of its particles seems very
stable, enabling them to accumulate over many
years. The planet Saturn also seems to have an
inner belt, with the neutrons coming from cosmic
ray collisions with the planet’s rings.