K. Orphan Afterglows
Orphan afterglows arise as a natural prediction of GRB jets. The
realization that GRBs are collimated with rather narrow opening
angles, while the following afterglow could be observed over a
wider angular range, led immediately to the search for orphan
afterglows: afterglows which are not associated with observed
prompt GRB emission. While the GRB and the early afterglow are
collimated to within the original opening angle,
j, the
afterglow can be observed, after the jet break, from a viewing
angle of
-1.
The Lorentz factor,
, is a rapidly
decreasing function of time. This means that an observer at
obs >
j couldn't
see the burst but could detect an afterglow once
-1 =
obs. As the
typical emission
frequency and the flux decrease with time, while the jet opening
angle
increases, this
implies that observers at larger
viewing angles will detect weaker and softer afterglows. X-ray
orphan afterglows can be observed several hours or at most a few
days after the burst (depending of course on the sensitivity of
the detector). Optical afterglows (brighter than 25th mag ) can be
detected in R band for a week from small (~ 10°) angles
away from the GRB jet axis. On the other hand, at very late
times, after the Newtonian break, radio afterglows could be
detected by observers at all viewing angles.
The search for orphan afterglows is an observational challenge. One has to search for a 10-12 ergs/sec/cm2 signal in the X-ray, a 23th or higher magnitude in the optical or a mJy in radio (at GHz) transients. Unlike afterglow searches that are triggered by a well located GRB for the orphan afterglow itself there is no information where to search and confusion with other transients is rather easy. So far there was no detection of any orphan afterglow in any wavelength.
Rhoads
[343]
was the first to suggest that observations of
orphan afterglows would enable us to estimate the opening angles
and the true rate of GRBs. Dalal et al.
[69]
have pointed out that as the post jet-break afterglow light curves
decay quickly, most orphan afterglows will be dim and hence
undetectable. They point out that if the maximal observing angle,
max, of an
orphan afterglow will be a constant factor
times
j the
ratio of observed orphan afterglows,
Rorphobs, to that of GRBs,
RGRBobs, will not tell
us much about the opening angles of GRBs and the true rate of
GRBs, RGRBtrue
fb
RGRBobs. However as we see
below this assumption is inconsistent with the constant energy of
GRBs that suggests that all GRBs will be detected to up to a fixed
angle which is independent of their jet opening angle.
Optical orphan afterglow is emitted at a stage when the outflow
is still relativistic. The observation that GRBs have a roughly
constant total energy
[105,
291,
310]
and that the observed variability in the apparent luminosity
arises mostly from variation in the jet opening angles leads to a
remarkable result: The post jet-break afterglow light curve is
universal [139].
Fig. 31
depicts this universal light curve. This implies that for a given
redshift, z, and a given limiting magnitude, m, there will be
a fixed
max(z,
m) (independent of
j, for
j <
max) from
within which orphan afterglow can be detected.
This universal post jet-break light curve can be estimated from
the observations [409]
or alternatively from first principles
[273] .
An observer at
obs >
j will
(practically) observe the afterglow emission only at
t
when
=
obs-1.
Using Eq. 104 and the fact that
t-1/2
after the jet break (Eq. 106) one can estimate the time,
t
when
a emission from a jet would be detected at
obs:
![]() |
(109) |
where A is a factor of order unity, and tjet is the time of the jet break (given by Eq. 104). The flux at this time is estimated by substitution of this value into the post-jet-break light curve (see Nakar et al. [273] for details):
![]() |
(110) |
where F0 is a constant and
f (z) = (1 + z)1+
DL28-2
includes all the cosmological effects and DL28 is the
luminosity distance in units of 1028 cm. One notices here a
very strong dependence on
obs. The peak
flux drops quickly when the observer moves away from the axis. Note also
that this maximal flux is independent of the opening angle of the
jet,
j. The
observations of the afterglows with a clear jet break (GRB 990510
[159,
394],
and GRB 000926
[160])
can be used to calibrate F0.
Now, using Eq. 110, one can estimate
max(z,
m) and more generally the time,
(tobs(z,
, m) that a burst
at a redshift, z, can be seen from an angle
above a limiting
magnitude, m:
![]() |
(111) |
One can then proceed and integrate over the cosmological distribution of bursts (assuming that this follows the star formation rate) and obtain an estimate of the number of orphan afterglows that would appear in a single snapshot of a given survey with a limiting sensitivity Flim:
![]() |
(112) |
where n(z) is the rate of GRBs per unit volume and unit proper time and dV(z) is the differential volume element at redshift z. Note that modifications of this simple model may arise with more refined models of the jet propagation [139, 273].
The results of the intergration of Eq. 112 are depicted in
Fig. 32. Clearly the rate of a single detection
with a given limiting
magnitude increases with a larger magnitude. However, one should
ask what will be the optimal strategy for a given observational
facility: short and shallow exposures that cover a larger solid
angle or long and deep ones over a smaller area. The exposure time
that is required in order to reach a given limiting flux,
Flim, is proportional to
Flim-2. Dividing the number
density of observed orphan afterglows (shown in
Fig. 32) by this time factor results in the rate
per square degree per hour of observational facility. This rate
increases for a shallow surveys that cover a large area. This
result can be understood as follows. Multiplying Eq. 112
by Flim2 shows that the rate per square
degree per hour of observational facility
Flim2-2/p. For p > 1 the
exponent is positive and a shallow survey is preferred. The
limiting magnitude should not be, however, lower than ~ 23rd
as in this case more transients from on-axis GRBs will be
discovered than orphan afterglows.
![]() |
Figure 32. The number of
observed orphan afterglows per square degree (left vertical scale)
and in the entire sky (right vertical scale), in a single
exposure, as a function of the limiting magnitude for detection.
The thick lines are for model A with three different sets
of parameters: i) Our "canonical" normalization
F0 = 0.003 µJy,
zpeak = 1,
|
Using these estimates Nakar et al. [273] find that with their most optimistic parameters 15 orphan afterglows will be recorded in the Sloan Digital Sky Survey (SDSS) (that covers 104 square degrees at 23rd mag) and 35 transients will be recorded in a dedicated 2m class telescope operating full time for a year in an orphan afterglow search. Totani and Panaitescu [409] find a somewhat higher rate (a factor ~ 10 above the optimistic rate). About 15% of the transients could be discovered with a second exposure of the same area provided that it follows after 3, 4 and 8 days for mlim = 23, 25 and 27. This estimate does not tackle the challenging problem of identifying the afterglows within the collected data. Rhoads [345] suggested to identify afterglow candidates by comparing the multi-color SDSS data to an afterglow template. One orphan afterglow candidate was indeed identified using this technique [420]. However, it turned out that it has been a variable AGN [118]. This event demonstrates the remarkable observational challenge involved in this project.
After the Newtonian transition the afterglow is expanding spherical. The velocities are at most mildly relativistic so there are no relativistic beaming effects and the afterglow will be observed from all viewing angles. This implies that observations of the rate of orphan GRB afterglows at this stage will give a direct measure of the beaming factor of GRBs. Upper limits on the rate of orphan afterglows will provide a limit on the beaming of GRBs [298]. However, as I discuss shortly, somewhat surprisingly, upper limits on the rate of orphan radio afterglow (no detection of orphan radio afterglow) provide a lower (and not upper) limit on GRB beaming [215].
Frail et al.
[107]
estimate the radio emission at
this stage using the Sedov-Taylor solution for the hydrodynamics
(see Section VIID). They find that the radio
emission at
GHz will be around 1 mJy at the time of the Newtonian transition
(typically three month after the burst) and it will decrease like
t-3(p-1)/2+3/5 (see Eq. 97). Using this limit
one can estimate the rate of observed orphan radio afterglow
within a given limiting flux. The beaming factor
f-1b arises
in two places in this calculations. First, the overall rate of
GRBs: RGRBtrue
fb
RGRBobs, increases with
fb. Second the total energy is proportional to
fb-1 hence
the flux will decrease when fB increases. The first factor
implies that the rate of orphan radio afterglows will increase
like fb. To estimate the effect of the second factor
Levinson et al.
[215]
use the fact that (for a fixed observed
energy) the time that a radio afterglow is above a given flux is
proportional to E10/9 in units of the NR transition time
which itself is proportional to E1/3. Overall this is
proportional to E13/9 and hence to
fb-13/9. To obtain
the overall effect of fb Levinson et al.
[215] integrate
over the redshift distribution and obtain the total number of
orphan radio afterglow as a function of fb. For a
simple limit
of a shallow survey (which is applicable to current surveys)
typical distances are rather "small", i.e. less than 1 Gpc and
cosmological corrections can be neglected. In this case it is
straight forwards to carry the integration analytically and obtain
the number of radio orphan afterglows in the sky at any given
moment [215]:
![]() |
(113) |
where R is the observed rate of GRBs per Gpc3 per year, and ti is the time in which the radio afterglow becomes isotropic.
Levinson et al. [215] search the FIRST and NVSS surveys for point-like radio transients with flux densities greater than 6 mJy. They find 9 orphan candidates. However, they argue that the possibility that most of these candidates are radio loud AGNs cannot be ruled out without further observations. This analysis sets an upper limit for the all sky number of radio orphans, which corresponds to a lower limit fb-1 > 10 on the beaming factor. Rejection of all candidates found in this search would imply fb-1 > 40 [153].