DICTIONARY OF GEOPHYSICS, ASTROPHYSICS, and ASTRONOMY

dog days The time period (July 3 through
August 11) during the northern summer when
Sirius is high in the daytime sky, supposedly
adding to the summer sun’s heat.
doldrums The equatorial zone, characterized
by high temperatures with small seasonal
and diurnal change (and heavy rainfall) and light
winds, so that sailing ships have difficulty sailing
through the region.
domain of dependence LetS be an achronal
set. The future/past domain of dependence
D ± (S) of S is the set of points x such that an
arbitrary past/future endless trip containingx intersects
S. The domain of dependence of S is
D(S) = D + (S) ∩D − (S). See achronal set,
causality relations.
domain of outer communication The region
outside of all black hole surfaces (horizons).
The region of spacetime that is visible
from infinity.
domain wall Cosmological topological defects
arising in phase transitions for which a discrete
symmetry is spontaneously broken: the
phase transition G → H induces a discrete
family of equivalent vacuum states and domains
having a different value for the Higgs field responsible
for the symmetry breaking will form,
separated by a correlation length. At the intersections
between these domains, the Higgs
field will, by continuity, not be able to lie in
the true vacuum (the minimum of the potential),
and thus the region (a wall) will contain
an enormous amount of energy. Any theory predicting
such walls contradicts observational cosmology
as, for instance, they would contribute
to the total energy density of the universe as well
as to the anisotropies of the cosmic microwave
background at a level well over that observed.
See cosmic topological defect, homotopy group,
spontaneous symmetry breaking.
dominant energy condition For all futuredirected
time-like vectors ξ a , the vector −T a b ξ b
is a future-directed time-like or null vector. Here
T a
b is the stress tensor of the matter. This condition
expresses the requirement that the speed
of energy flow is less than the speed of light.
© 2001 by CRC Press LLC
Doppler beaming
Doodson number A set of six integers in the
notation d1d2d3.d4d5d6 defined by A.T. Doodson
in 1921 to uniquely classify tide components.
In this scheme, the tidal band is decomposed
into integer multiples of six astronomical
functions: τ, the mean lunar time; s, the mean
longitude of the moon; h, the mean longitude
of the sun; p, the mean longitude of the lunar
perigee; N ′ , the negative mean longitude of the
ascending lunar mode; and ps, the mean longitude
of the solar perigee. Thus, for each component
j, the tidal frequency, ωj , and phase, βj ,
are decomposed as:
ωj + βj =
d1τ + (d2 − 5) s + (d3 − 5) h +
(d4 − 5) p + (d5 − 5) N ′ + (d6 − 5) ps
The first digit, d1 defines the tidal species and
is always equal to the order of the spherical
harmonic component of the tide potential from
which it originates. Long-period tides have
d1 = 0, diurnal tides have d1 = 1, and semidiurnal
tides have d1 = 2. The combination of
the first two digits d1d2 defines the tidal group
number, and the first three digits d1d2d3 define
the tidal constituent number. For example, the
largest semi-diurnal tide, M2, has a Doodson
number of 255.555, while the largest diurnal
tide, K1, has a Doodson number of 165.555.
Doppler beaming Beaming of radiation due
to the rapid, i.e., close to the speed of light, motion
of an emitting source with respect to an observer.
Light emitted isotropically in the rest
frame of a source is observed greatly enhanced
if the source is moving toward the observer: For
a radiating particle moving at a velocity close to
the speed of light, corresponding to a Lorentz
factor γ ≫ 1(γ is equal to 1 (1 − (v/c) 2 ),
where v is the velocity of the radiating matter,
and c is the speed of light), the observer
would see most light concentrated in a narrow
beacon of half-opening angle 1/γ radians, and
enhanced (or “Doppler boosted”) by a factor that
can be proportional to a large power (3 to 4) of γ .
Doppler beaming is relevant whenever there are
charges moving at a velocity close to the speed
of light (for example, if v = 0.95c then γ = 3),
as in the case of radio jets in radio galaxies and
quasars.