Long duration radio transients lacking optical counterparts are possibly Galactic Neutron Stars

Abstract

(abridged) Recently, a new class of radio transients in the 5-GHz band was detected by Bower et al. We present new deep near-Infrared (IR) observations of the field containing these transients, and find no counterparts down to a limiting magnitude of K=20.4 mag. We argue that the bright (>1 Jy) radio transients recently reported by Kida et al. are consistent with being additional examples of the Bower et al. transients. We refer to these groups of events as "long-duration radio transients". The main characteristics of this population are: time scales longer than 30 minute but shorter than several days; rate, ~10^3 deg^-2 yr^-1; progenitors sky surface density of >60 deg^-2 (95% C.L.) at Galactic latitude ~40 deg; 1.4-5 GHz spectral slopes, f_\nu ~ \nu^alpha, with alpha>0; and most notably the lack of any counterparts in quiescence in any wavelength. We rule out an association with many types of objects. Galactic brown-dwarfs or some sort of exotic explosions remain plausible options. We argue that an attractive progenitor candidate for these radio transients is the class of Galactic isolated old neutron stars (NS). We confront this hypothesis with Monte-Carlo simulations of the space distribution of old NSs, and find satisfactory agreement for the large areal density. Furthermore, the lack of quiescent counterparts is explained quite naturally. In this framework we find: the mean distance to events in the Bower et al. sample is of order kpc; the typical distance to the Kida et al. transients are constrained to be between 30 pc and 900 pc (95% C.L.); these events should repeat with a time scale of order several months; and sub-mJy level bursts should exhibit Galactic latitude dependence. We discuss possible mechanisms giving rise to the observed radio emission. Comment: Submitted to ApJ, 17 pages, 10 figures

Full text

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arXiv:0910.3676v1 [astro-ph.HE] 19 Oct 2009
Draft of October 19, 2009
Preprint typeset using LATEX style emulateapj v. 08/22/09
LONG DURATION RADIO TRANSIENTS LACKING OPTICAL COUNTERPARTS ARE POSSIBLY
GALACTIC NEUTRON STARS
E. O. Ofek1,2, B. Breslauer3,4, A. Gal-Yam5, D. Frail4, M. M. Kasliwal1, S. R. Kulkarni1& E. Waxman5
Draft of October 19, 2009
ABSTRACT
Recently, a new class of radio transients in the 5-GHz band and with durations of the order of
hours to days, lacking any visible-light counterparts, was detected by Bower and collaborators. We
present new deep near-Infrared (IR) observations of the field containing these transients, and find no
counterparts down to a limiting magnitude of K = 20.4mag. We argue that the bright (> 1Jy) radio
transients recently reported by Kida et al. are consistent with being additional examples of the Bower
et al. transients. We refer to these groups of events as “long-duration radio transients”. The main
characteristics of this population are: time scales longer than 30minute but shorter than several days;
very large rate, ∼ 103deg−2yr−1; progenitors sky surface density of > 60deg−2(at 95% confidence)
at Galactic latitude ∼ 40◦; 1.4–5GHz spectral slopes, fν ∝ να, with α>∼0; and most notably the
lack of any X-ray, visible-light, near-IR, and radio counterparts in quiescence. We discuss putative
known astrophysical objects that may be related to these transients and rule out an association with
many types of objects including supernovae, gamma-ray bursts, quasars, pulsars, and M-dwarf flare
stars. Galactic brown-dwarfs or some sort of exotic explosions in the intergalactic medium remain
plausible (though speculative) options. We argue that an attractive progenitor candidate for these
radio transients is the class of Galactic isolated old neutron stars (NS). We confront this hypothesis
with Monte-Carlo simulations of the space distribution of old NSs, and find satisfactory agreement for
the large areal density. Furthermore, the lack of quiescent counterparts is explained quite naturally.
In this framework we find: the mean distance to events in the Bower et al. sample is of order kpc; the
typical distance to the Kida et al. transients are constrained to be between 30pc and 900pc (at the
95% confidence level); these events should repeat with a time scale of order several months; and sub-
mJy level bursts should exhibit Galactic latitude dependence. We discuss two possible mechanisms
giving rise to the observed radio emission: incoherent synchrotron emission and coherent emission.
We speculate that if the latter is correct, the long duration radio transients are sputtering ancient
pulsars or magnetars and will exhibit pulsed emission.
Subject headings: radio continuum: general — stars: neutron — stars: low-mass, brown dwarfs —
galaxies: high-redshift — Galaxy: kinematics and dynamics
1. INTRODUCTION
Large field-of-view radio telescope facilities such as
the Parks multi-beam facility, the Arecibo multi-beam
instrument, the Allen Telescope Array (DeBoer et al.
2004), and the Low Frequency Array (Falcke et al. 2007)
have reinvigorated the radio-frequency time domain fron-
tier. First signs of this “revolution” are indicated by the
discoveries of new classes of radio transients. Examples
include: several Galactic center sources (e.g., Hyman et
al. 2005; 2009); Rotating Radio Anomalous Transients
(RRATs; McLaughlin et al. 2006) which represent a pre-
viously unknown class of radio pulsars, probably twice
as abundant as their “normal” cousins; and the powerful
(∼ 30 Jy) radio “Sparker”, with a time scale of several
milliseconds (Lorimer et al. 2007; Kulkarni et al. 2009).
Here, we focus on yet another emerging class of myste-
rious radio transients. In a novel approach, Bower et
1Division of Physics, Mathematics and Astronomy, California
Institute of Technology, Pasadena, CA 91125, USA
2Einstein fellow
3Department of Physics and Astronomy, Oberlin College, Ober-
lin, Ohio 44074-1088
4National Radio Astronomy Observatory, P.O. Box O, Socorro,
NM 87801
5Benoziyo Center for Astrophysics, Weizmann Institute of Sci-
ence, 76100 Rehovot, Israel
al.
ray6(VLA) observations, taken about once per week for
twenty two years, of a single calibration field.
authors discovered a total of ten transients, nine in the
5-GHz band and one in the 8-GHz band. These tran-
sients can be divided into two groups: “single-epoch” and
“multi-epoch” transients. The eight single-epoch tran-
sients, as can be gathered by their names, were detected
in only one epoch. Given a single epoch detection, one
can only constrain the duration of the transient by the
epochs preceding and succeeding the time at which the
transient was detected (approximately one week). The
lower limit could be as small as the typical integration
time (about 20minute). The two multi-epoch transients
were detected after averaging over two months of data.
Thus, the duration of these two events can be taken to
be about two months.
Bower et al. (2007) split the data for each epoch, con-
sisting of 20 minutes, into five segments and looked for
variability on four-minute time scale. They did not find
any evidence for variability on these time scales. How-
(2007) re-analyzed 944 epochs of Very Large Ar-
These
6The Very Large Array is operated by the National Radio As-
tronomy Observatory, a facility of the National Science Foundation
operated under cooperative agreement by Associated Universities,
Inc.

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2Ofek et al.
ever, the total S/N of these detections was <∼7, and
therefore the limits on variability within these 20-minute
windows are appropriately weak. More importantly, the
authors find the circular polarization is less than ∼ 30%.
Separately, Kuniyoshi et al. (2006), Niinuma et al.
(2007), and Kida et al. (2008) reported on a search
for radio transients using an East-West interferometer
of the Nasu Pulsar Observatory (located in Tochigi Pre-
fecture, Japan) of Waseda University. The program con-
sists of daily drift scanning of the sky towards the local
zenith.These authors reported six bright radio tran-
sients (and several other were mentioned but without
details), with flux density above 1Jy in the 1.4-GHz
band. Five were single epoch transients while one was
detected on two successive days with flux densities of 1.7
and 3.2Jy, respectively (Niinuma et al. 2007). In each
epoch the transients were detected for about 4minutes,
which is the drift scanning time, and did not exhibit
any significant variation within the observation. Unfor-
tunately, these events are not well localized and have po-
sitional uncertainties of the order of 0.4◦in declination,
and 0.04◦in right ascension. Kida et al. (2008) stated
that the 2-σ upper limit for the rate of these transients
is 0.0049deg−2yr−1. Arguably, these events also have
time scales somewhere in the range of a few minutes to a
few days. Therefore, later we consider the framework in
which both the VLA and the Nasu events have a common
origin.
Another relevant survey was conducted by Levinson et
al. (2002) who compared the NRAO VLA Sky Survey
(NVSS; Condon et al. 1998) and the “Faint Images of
the Radio Sky at Twenty centimeters” survey (FIRST;
Becker et al.1995; White et al.
surveys were undertaken in the 1.4-GHz band and their
5-σ limits are 3.5 and 1mJy, respectively. Levinson et al.
(2002) identified nine radio transient candidates with flux
densities greater than 6mJy. Followup observations of
these radio transients (Gal-Yam et al. 2006) showed that
seven were spurious and the remaining two were plausible
transients7: an optically extincted SN in NGC 4216 from
which the radio emission lasted for several years; and
VLA J172059.9+385229 (discussed in §2).
Bower et al. (2007) obtained deep visible light images
of their transients.They found that the multi-epoch
event RT819870422 was 1.′′5 from a z = 0.249, R =
20.2mag galaxy. The peak luminosity of RT19870422,
assuming that the transient is related to this galaxy, is
consistent (to an order of a magnitude) with an ener-
getic supernova (SN) similar to SN1998bw (GRB980425;
Kulkarni et al. 1998) and SN2006aj (Soderberg et al.
2006). We note that the rate of these events is marginally
consistent with the rate of low-luminosity GRBs derived
by Soderberg et al. (2006). In contrast, the other multi-
epoch transient RT20010331 has no optical counterpart
to a limiting magnitude of g ≈ 27.6mag, R ≈ 26.5mag,
and K ≈ 19.2mag (this paper) to within 5′′of the radio
source. The great offset between a putative host galaxy
and the radio transient make this an unusual source. We
1997).Both these
7The term “transient” is used here in the sense that we do not
detected emission in quiescence.
8Here RT stands for radio transient and the succeeding eight
digits are yyyymmdd where yyyy is the year, mm is the month and
dd is the day.
note that Cenko et al. (2008) presented an example of a
GRB in a galaxy halo environment. However, only about
1% of all GRBs occures in such environments.
The single-epoch radio transient RT19840613 falls
within the optical boundary of a z = 0.040 spiral galaxy,
but clearly lying outside the nucleus of the galaxy. On
the basis of the radio luminosity (assuming association
with the galaxy) and the nature of the putative host
galaxy this transient is consistent with an origin similar
to that of RT19870422 (i.e., a low luminosity GRB).
The remaining seven single-epoch transients (one de-
tected in 8GHz and six at 5GHz) do not have astro-
metrically coincident optical, near-IR, or radio counter-
parts and have a point source appearance (see Table 1).
This is a major clue in that a large fraction of gamma
ray bursts (GRBs) and most SNe have detectable optical
host galaxies at R ∼ 26mag level (e.g., Ovaldsen et al.
2007).
In order to separate the events discussed above from
Sparkers (Lorimer et al. 2007; Kulkarni et al. 2009),
which have very short time scales, we refer to these events
as “long-duration radio transients”.
In Table 1 we summarize the observational properties
of all the long-duration radio transients. We define this
class as events with no optical identification and dura-
tions between hours to days.
seven known sources from Bower et al. (2007) that are
not associated with any optical counterpart and have
time scales shorter than about one week; RT19870422
(see above); and the six bright transients reported by
Kida et al. (2008).
The structure of this paper is as follows. In §2 we re-
examine the case of VLAJ172059.9+385229(Levinson et
al. 2002) and show it is a spurious event. In §3 we present
new near-IR observations of the Bower et al. field. In
§4 we review the basic properties (areal density, annual
rate) of the long-duration radio transients. Next, in §5
we use the observational clues to refute several plausible
explanations regarding the nature of the long-duration
radio transients. In §6 we argue that the most attractive
explanation is that these radio transients are associated
with Galactic isolated old Neutron Stars (NS). Finally,
we discuss and summarize the results in §7.
This group include the
2. VLAJ172059.9+385226.6: A RE-ANALYSIS
VLAJ172059.9+385226.6 was identified as a 9-mJy
source in the FIRST survey but was undetected in the
NVSS (S<∼3.5mJy). Each image in the FIRST survey
is made from data taken several days apart (R. Becker,
personal communication). Searching the VLA archive,
we have found this field was observed three times on
1994, August 8, 13 and 14.
shows that this source was present only in the last 10-
s integration out of the 2.5-minute scan taken on Au-
gust 8th, and had 370-mJy flux density.
closer look at the data showed that this event was due
to a previously unknown bug in the VLA recording sys-
tem; this bug affected the FIRST survey. Specifically,
the telescopes were repointed, but the header informa-
tion was not updated. VLAJ172059.9+385226.6 is, in
fact, a genuine source at a different sky position (α =
17h24m00.s50, δ = +38◦52
VLAJ172059.9+385226.6 is not a real transient source.
Re-analysis of the data
However, a
′26.
′′6, J2000.0). Therefore,

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Radio transients3
TABLE 1
List of candidate long-duration radio transients
Transient
Band
GHz
Lim. mag.
g
mag
EpochR.A.
J2000
Dec.
J2000
Sδta
day
Snextb
µJy
Sdeepc
µJy
S/Sdeep
Xd
cts
RKRef.
µJymag mag
1984 05 02
1986 01 15
1986 01 22
1992 08 26
1997 05 28e
1999 05 04
1997 02 05
2005 01 10
2005 03 27
2005 03 04
2005 01 02
2005 02 13f
2004 03 20
2001 10 31g
15 02 24.61
15 02 26.40
15 00 50.15
15 02 59.89
15 00 23.55
14 59 46.42
15 01 29.35
04 45 17
06 45 15
10 39 43
10 43 06
14 43 22
17 37 17
15 03 46.18
+78 16 10.1
+78 17 32.4
+78 15 39.4
+78 16 10.8
+78 13 01.4
+78 20 29.0
+78 19 49.2
+41 30
+32 00
+32 00
+41 00
+34 39
+38 08
+78 15 41.7
5.0
5.0
5.0
5.0
5.0
5.0
8.4
1.4
1.4
1.4
1.4
1.4
1.4
4.0
448 ± 74
370 ± 67
1586 ± 248
642 ± 101
1731 ± 232
7042 ± 963
2234 ± 288
1.8 × 106
1.2 × 106
1.7 × 106
1.7 × 106
3.2 × 106
1.0 × 106
697 ± 94
7
7
7
56
7
21
5
1
1
1
1
1
1
59
−10 ± 68
199 ± 121
−59 ± 164
37 ± 83
90 ± 206
−313 ± 1020
857 ± 323
<
∼3 × 105
<
∼3 × 105
<
∼3 × 105
<
∼3 × 105
<
∼3 × 105
<
∼3 × 105
85 ± 85
< 8
< 8
< 15
< 9
< 36
< 117
< 646
<
∼9 × 103
<
∼6 × 103
<
∼7 × 103
<
∼1 × 103
<
∼2 × 103
<
∼6 × 103
< 37
56
46
106
71
48
60
3.5
200
200
240
1700
1600
170
19
0.08
0.07
0.08
0.08
0.07
0.05
0.08
0.02
0.02
0.04
0.02
0.02
0.02
0.08
27.6
27.6
27.6
27.6
27.6
27.6
27.6
26.5
26.5
26.5
26.5
26.5
26.5
26.5
20.4
20.4
20.2
19.6
20.0
19.2
20.4
1
1
1
1
1
1
1
2
2
2
2
2
2
127.626.519.2
Note. — A list of candidate long-duration radio transients and their properties. Transients detected in different frequencies or instru-
ments are separated by horizontal lines. The first (second) block lists the six (one) single-epoch transients detected by Bower et al. (2007)
at 5GHz (8GHz) with no optical counterpart. The third block lists the Kida et al. (2008) events, and the fourth block lists the two-months
5GHz event detected by Bower et al. (2007). This last event is shown here for completeness. References: (1) Bower et al. (2007); (2) Kida
et al. (2008). We note that the Kida et al. (2008) transients have positional uncertainties of order 0.4◦in declination, and 0.04◦in right
ascension.
aTime to next observation.
bFlux limit in the next observation.
cSpecific flux limit on radio emission at quiescence. For the Bower et al. transients this limit is obtained from the non detection in the
combined image of the Bower et al. field. For the Kida et al. (2008) transients we list the flux of the brightest FIRST or NVSS radio
source (or detection limit if no source) in the transient positional error region.
dROSAT 3-σ upper limit (in counts−1) in the 0.12-2.48keV band. For the Kida et al. (2008) transients we list the count rate of the
brightest ROSAT source (or detection limit if no source) in the transient positional error region. We obtained these limits by calculating
the 3-σ noise level due to the background in the ROSAT X-ray images at the location of each transient.
eA galaxy with R = 19.6mag and z = 0.245, 5′′away, probably due to chance coincidence.
fDetected on two epochs, separated by one day, with fluxes of 1.7Jy and 3.2Jy on the first and second epochs, respectively.
gRT20011031 had a time scale of two months and is listed here for completeness.
Unfortunately, follow up visible-light Hubble Space Tele-
scope and near-IR Keck-II observations were undertaken
before this realization.
We note that Bower et al. (2007) did not find evidence
for variability in their transients, within the 20-minute
integration interval. Therefore, the Bower et al. tran-
sients cannot be spurious sources of the same kind (see
also a detailed discussion in Bower et al. 2007). How-
ever, given the uncertain nature of other radio transients
(e.g., Lorimer et al. 2007; Deneva et al. 2008), we think
that some caution is warranted.
3. NEAR-IR OBSERVATIONS OF THE BOWER ET
AL. FIELD
On UTC 2008 April 28.4 we obtained a 7500-s exposure
in Ks-band of the Bower et al. field, with the Hale 5.08-m
telescope at Palomar observatory (P200) equipped with
the Wide-field IR Camera (WIRC). The field-of-view of
WIRC contains all the eight radio transients found by
Bower et al. which do not have any visible-light counter-
parts.
An astrometric solution was obtained using the ASC-
fit package (Jørgensen et al. 2002) and the images were
combined using SWarp9. Cutouts from the combined
image, around the position of the eight transients, are
presented in Figure 1. We do not detect any Ks-band
counterparts to each of these eight transients (see Ta-
ble 1).
9Written by E. Bertin; http://terapix.iap.fr/
Also listed in Table 1 are the flux limits, at the position
of the transients, from the ROSAT-PSPC all-sky survey
in the 0.12–2.48keV band (Voges et al. 1999).
4. OBSERVATIONAL PROPERTIES OF THE
LONG-DURATION RADIO TRANSIENTS
In the following we analyze the observational proper-
ties of the long-duration radio transients. Specifically, we
discuss their rate (§4.1), sky surface density (§4.2), and
source count function (§4.3).
4.1. Rate
Bower et al. (2007) found that the observed areal den-
sity of events at 5GHz and 8GHz (dominated by the
5GHz events), with flux density above 370µJy at a two-
epoch survey, is 1.5 ± 0.4deg−2. Thus, the single epoch
areal density of events with flux greater than 370µJy, is
0.75+0.40,+0.81
1- and 2-σ confidence (using the formulation of Gehrels
1986). This is translated to a 5GHz rate of events with
flux density above 370µJy of
−0.28,−0.45deg−2, where the errors are given at the
ℜ5GHz,>0.37mJy= 540+290,+590
−200,−330
?
tdur
0.5day
?−1
deg−2yr−1,
(1)
where tdur is the (unknown) typical duration of these
events and the errors are given at the 1- and 2-σ confi-
dence. tdur can be a function of frequency. Therefore,
comparison of this rate with rates at other frequencies

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4 Ofek et al.
Fig. 1.— P200/WIRC cutouts around the locations of the eight radio transients lacking optical counterparts found by Bower et al. (2007).
The position of each transient is marked by a circle with 3′′radius. The spatial radio position uncertainty of these transients is about 0.3′′
(Bower et al. 2007). The tie between the optical and radio coordinates frame is usually better than 1′′(e.g. Gal-Yam et al. 2006). The
transients names are noted at top-left of each cutout and are shown by their position East to West, upper row from left to right and than
the lower row from left to right. The effective exposure times for the cutouts are: 1530s, 3030s, 7500s, 7500s, 7500s, 5940s, 4440s, and
1530s, respectively.
should be treated with care. We are aware that our 5-
GHz rate (Eq. 1) is much larger than the rate computed
by Bower et al. (2007). However, the latter estimate was
the result of an arithmetic error which once corrected
yields the estimate given in Equation 1.
As can be gathered from Equation 1, the minimum
rate is achieved for the largest value of tdurwhich is seven
days. Assuming a constant event rate, this minimum rate
is > 9 × 1015(at the 95% confidence level [CL]) events
over the Hubble time. For comparison, this estimate is
several orders of magnitude larger than the population
of any known Galactic class of sources.
long-duration radio transients are Galactic, they must
be repeaters. On the other hand, if the events are catas-
trophic (i.e., single-shot, not repeaters) then the mean
time between events is<∼100s (and possibly as small as
∼ 1s). The only known cosmological population with
such high rate is supernovae (∼ 1s−1; see §5.1).
Next we look into the rates of these events in the 1.4-
GHz band. As noted earlier (§2) the FIRST-NVSS analy-
sis did not result in a firm detection of any long-duration
transient. The total survey area of the FIRST-NVSS
search, after correcting it for point-source incomplete-
ness, source confusion due to the poor resolution of the
NVSS and missing NVSS data, is 2500deg2(see Levin-
son et al. 2002 for details). We place an upper limit
to the sky density (i.e., density of sources observed in
a single epoch) of transient sources (flux density above
6mJy in the 1.4 GHz band) of 1.5 × 10−3deg−2and
2.6 × 10−3deg−2, at the 95% and 99.73% CL, respec-
tively. We note that this sky density is consistent with
the upper limit derived by Carilli, Ivison & Frail (2003).
Therefore, the 95% confidence upper limit on the 1.4GHz
rate, ℜ, of long duration radio transients with flux den-
Therefore, if
sity above 6mJy is:
ℜ1.4GHz,>6mJy< 1.1
?
tdur
0.5day
?−1
deg−2yr−1.(2)
4.2. Sky Surface Density
Another interesting quantity is the areal density of
the transients, Σ.We obtain a lower limit by divid-
ing the number of unique sources by the angular area
of the VLA field. All the Bower et al. transients were
found within 9′(twice the half-power radius at 5GHz)
from the center of a single VLA field (α = 15h02m20.53s,
δ = +78◦16′14.905′′; J2000.0). Within the half-power ra-
dius of 4.5′(corresponding to a solid angle of 0.018deg2)
there are four detections (see Fig. 2 in Bower et al. 2007).
At 95% CL the smallest number of sources is > 1.1 (using
the formulation of Gehrels 1986). Therefore, at Galactic
latitude b ∼ 40◦, Σ > 60deg−2(95% CL).
We note that the lack of any repeater events in the
Bower et al. (2007) sample can be used to improve this
limit. This can be done by calculating the probability of
choosing seven events out of N with no repetition. How-
ever, the resulting areal density is only increased by 40%
(to the same 95% CL). We therefore retain the simpler
estimate.
Assuming a constant surface density as a function of
Galactic latitude the all-sky surface density of radio tran-
sient progenitors is Σall−sky> 3.5×106. We note that if
the long duration radio transients are Galactic then their
sky surface density toward the Galactic plane should be
higher, and therefore the total all-sky number could be
larger.
4.3. Source number count function

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Radio transients5
The source number count function, N(> S), where N
is the number of events brighter than a peak flux density
S, may provide some hints regarding the nature of the ra-
dio transient population. We consider a power-lawsource
count function, N(> S) ∝ Sn, where n is the power-law
index. For a homogeneous population of sources residing
in an Euclidean Universe we expect n = −3/2, while for
Galactic thin disk population n ≈ −1.
Assuming that tdurdoes not depend on the frequency,
we can use the transient rates given in §4.1 to put limits
on the power-law index, n, of the source number count
function. For each expected value of the number of events
detected in the Bower et al. (2007) survey, λb, and the
Levinson et al. (2002) search, λl, we calculate the prob-
ability that kb= 6 events will be detected in the Bower
et al. search and kl= 0 in the Levinson et al. survey:
P =
1
kl!kb!λkb
be−λbλkl
le−λl.(3)
The power-law index, n relates to λb/λlthrough:
λb
λl
=Ab
Al
?νb
νl
?n?Sb
Sl
?α
,(4)
where Ab = 9.33deg2is the effective10(single epoch)
search area of the Bower et al. survey. This was es-
timated by dividing the number of transients found by
Bower et al. (7), by the one epoch search areal density
(0.75deg−2). Al= 2500deg2is the area of the Levinson
et al. search, νb= 5GHz and νl= 1.4GHz are the sur-
veys frequencies, Sb= 0.37mJy and Sl= 6mJy are their
specific flux limits, and α is the spectral power law in-
dex of the sources (Sν∝ να). Equation 4 contains three
parameters: n, λland λb. However λlis a function of n
and λb. Thus we need only explore the phase space of
two of these (e.g., n and λb).
We calculated the probability in Equation 3 as a func-
tion of n and λb. In Figure 2 we show the log likelihood
contours as a function of n and λbfor α = 5/2 and for
α = 0. The contours are for the 1, 2 and 3-σ, assuming
two degrees of freedom (Press et al. 1992).
For α = 0, we find n < −1.8 at the 3-σ CL. Since such
a steep number count index is unlikely for astrophysical
sources, we conclude that most probably α >∼0. The
highest α possible for continuum emission is α = 5/2
(synchrotron self absorption; Rybicki & Lightman 1979,
p. 186). For such α we find that n < −0.7 (−1.0) at the
3 (2)-σ CL.
There are at least two caveats in our analysis. First,
we assumes that the source luminosity function does not
depend on distance. Second, the Levinson et al. (2002)
and Bower et al. (2007) rates were measured at different
celestial positions. Therefore, if the long-duration radio
transients are Galactic sources, then their sky distribu-
tion is probably not uniform, and this may affect the
results presented in this section (however, see discussion
in §6.1).
5. THE PROGENITORS OF LONG-DURATION
RADIO TRANSIENTS
10This is the area of a single epoch observation multiplied by
the number of epochs.
−2.2−2−1.8−1.6−1.4
n
−1.2−1−0.8−0.6
0
2
4
6
8
10
12
14
16
18
20
λb


3σ
2σ
1σ
3σ
2σ
α=5/2
α=0
0
200
400
600
800
1000
1200
1400
1600
1800
ℜ5 GHz,>0.37 mJy (tdur/0.5 day)
Fig. 2.— Confidence interval contours (as calculated from the
log-likelihood) as a function of the expected value of the number
of events in the Bower et al. (2007) search, λb, and the power-law
index n, of the source number count function (see Eq. 3). The
gray lines show the 2- and 3-σ contours for spectral index α = 0,
while the black lines show the 1-, 2- and 3-σ contours for α = 5/2.
The right-hand y-axis is the corresponding transients rate assuming
tdur= 0.5day.
In this section we list astrophysical sources and phe-
nomenon that may be responsible for the long-duration
radio transients. Some of these possibilities were already
presented by Bower et al. (2007). We first discuss the
extragalactic hypothesis (§5.1) followed by Galactic pro-
genitors (§5.2).
5.1. Extragalactic sources
When observing the error boxes of known types of ex-
tragalactic explosions (e.g., GRBs and supernovae), we
usually detect the host galaxy (e.g., Fruchter et al. 2006;
Ovaldsen et al. 2007; Perley et al. 2009). In Figure 3 we
present a histogram of the R-band magnitude (or limiting
magnitude) for host galaxies of a sample of Swift (Gehrels
et al. 2004) detected GRBs (Ovaldsen et al. 2007). A
high fraction (∼ 50%) of the Swift GRBs are associated
with galaxies brighter than about R ∼ 25mag. For op-
tically identified supernovae (SNe) in blind surveys the
fraction is almost 100%. We note that we still do not have
deep images, and therefore constraints on the hosts, of
the new class of bright supernovae (Barbary et al. 2009;
Quimby et al. 2009).
We find it significant that only one of the Bower et al.
transients has an optical counterpart (see §1). It is fur-
thermore curious that this counterpart is a low redshift
galaxy (RT19840613; z∼= 0.04). Note the absence of any
intermediate redshift counterparts.
Another way to quantify this curious absence of host
galaxies is by using the observed star formation rate in
the Universe. In Figure 4 we show the probability that
the minimum redshift in a sample of seven sources ran-
domly selected from the observed star formation rate dis-
tribution in the Universe (Hopkins & Beacom 2006) will
be smaller than a given redshift. From Figure 4 we con-
clude that at least one of the seven radio transients will
have z < 1.5, at the 99.73% CL. The luminosity function
of galaxies at high redshift is not well known. However,
the GRB host galaxies sample of Ovaldsen et al. (2007;
Fig. 3) which probe typical redshifts of>∼2 suggest that

Page 6

6Ofek et al.
202122
R−band magnitude
23242526
0
1
2
3
4
5
6
7
8
9
10
Number


Measurements
limiting mag.
Fig. 3.— R-band magnitude (black bars) or 2-σ limiting mag-
nitude (gray bars) distribution of GRB host galaxies (Ovaldsen et
al. 2007). In some cases the observations were done in a different
band than R-band, in these cases, we converted the host galaxies
magnitude to R-band by assuming it is an Sc-type galaxy at red-
shift of 2, based on the galaxy spectral templates of Kinney et al.
(1996).
00.511.5
0
0.2
0.4
0.6
0.8
1
Redshift
P(<zmin)
Fig. 4.— The cumulative probability that the minimum redshift
out of seven sources, randomly selected from the star formation
distribution will be smaller than a given redshift. We used the
star formation distribution compiled by Hopkins & Beacom (2006)
using the parametrization of Cole et al. (2001) and assuming a
modified Salpeter IMF. We divided this star formation distribution
by (1+z) to account for the decreasing transients rate due to time
dilation.
if the radio transients residing in hosts similar to those
of GRBs then Bower et al. should have detected optical
counterparts to most of those transients.
The above discussion not withstanding we now con-
sider the usual suspects in the extragalactic framework.
GRBs: Gamma-Ray Bursts (GRBs) are often de-
tected in radio frequencies for periods of days to weeks
(e.g., Frail et al. 1997; Chandra et al. 2008). How-
ever, as graphically demonstrated by Figure 3 the GRB
hypothesis can be excluded. Furthermore, the observed
all-sky rate of GRBs is 2 day−1, while the all-sky rate of
long-duration radio transients is>∼103day−1(§4.1).
Orphan GRBs: Observational evidences suggest that
GRB emission is beamed and highly anisotropic (e.g.,
Harrison et al. 1999; Levinson et al. 2002). Therefore,
the actual rate of orphan GRB explosions is f−1
larger than the observed rate. Here, f−1
b
times
b
is the inverse
00.511.522.533.5
2
2.5
3
3.5
4
z
Color [mag]


R−K
g−K
Fig. 5.— The RVega−KVega(solid line), and gAB−KVega(dashed
line) colors, of quasars, as a function of redshift z.
are based on synthetic photometry of quasar spectral templates
(Brotherton et al. 2001; Glikman, Helfand & White 2006). Syn-
thetic photometry is calculated using the code of Poznanski et al.
(2002). The minimum g−K in the range z = 0 to z = 3.7 is about
2.5mag. However, at z > 3.7 the g−K color will be larger since
the Lyman α line is found at wavelength redder than that of the
g-band.
The colors
of the beaming factor, and it is probably in the range
50–500 (e.g., Guetta, Piran & Waxman 2005; Gal-Yam
et al. 2006). However, orphan GRB radio afterglows are
expected to have time scales of years rather than days,
which is not in line with the time scales of long-duration
radio transients. More importantly, such orphans are ex-
pected to be at redshifts lower than that of GRBs (which
are beamed and thus seen at higher redshift) making the
host-galaxy non detections even more problematic (see
Levinson et al. 2002).
Quasars and Active Galactic Nuclei: To a lim-
iting magnitude of i ≈ 26 mag, the faintest quasars11
can be detected to a redshift of about 5. The lack of
optical counterparts associated with these transients is
not consistent with a quasar connection. Low luminosity
quasars (i.e., Active Galactic Nuclei; AGN), are fainter,
but if their abundance roughly follows the star formation
rate in the Universe, then as shown in Figure 4, the host
galaxies should have been found in visible light.
Obscured quasars, also known as type-II quasars are
faint in visible light frequencies. However, these sources
may reveal themselves in near-IR (e.g., Gregg et al. 2002;
Reyes et al. 2008). Figure 5 shows the g−K and R−K
color of “normal” quasars as a function of redshift. The
minimum g−K color of quasars is about 2.5mag. The
non-detection of AGNs down to Ks-band magnitude of
20.4 (§3) corresponds to a non detection of a quasar
with intrinsic g-band magnitude fainter than 23. This
is based on the assumption that type-II quasars and nor-
mal quasars have similar K-band luminosity functions,
To this magnitude level, the faintest quasars can be
detected up to z ≈ 2.
do not detect any near-IR sources associated with the
long-duration radio transients disfavors association with
reddened quasars.
Supernovae: There are two known variants of bright
radio SNe:type-II radio SNe, for which SN1979C
(Weiler et al. 1991) is the prototype, and Type-Ic ra-
dio SN (e.g., SN1998bw; Kulkarni et al. 1998).
Therefore, the fact that we
11The taxonomic definition of quasars is nuclear absolute magni-
tude MB< −21.5+5log10h0, where h0is the present day Hubble
parameter in units of 100 km s−1Mpc−1(Peterson 1997).

Page 7

Radio transients7
Type-II radio SNe, have long time scales (years) and
are detectable in nearby galaxies (z ∼ 0.01). On the
other hand, type-Ic radio SNe are detected to somewhat
larger distances (z ∼ 0.1), and last a few weeks. There-
fore, based on the lack of optical counterparts we can
rule out association with type-II or type-Ic radio SNe.
Extragalactic Microlensing: When considering mi-
crolensing events we should discuss the population of
sources and lenses. While the lenses can be “unseen”
objects, the sources should be radiant. Most sub-mJy
sources, which are the potential sources for microlens-
ing, are starburst galaxies. These galaxies have spatial
size several orders of magnitude larger than the Ein-
stein radius of stellar-mass lenses. Therefore, microlens-
ing by extragalactic or Galactic objects cannot explain
the high amplitude of the radio transients discussed here
(Table 1).
We note that the small number of background sources
and the high amplitude of the transients also rules out
scintillation events.
ExtragalacticSoftGamma-Ray
(SGRs): There are only eight12SGRs known in the
Milky Way galaxy and the Magellanic Clouds. However,
extragalactic SGRs (e.g., Eichler 2002; Nakar et al. 2006;
Popov & Stern 2006; Ofek et al. 2006, 2008; Ofek 2007)
may be detected to larger distances. Currently, the radio
emission from giant flares of SGRs is not well constrained
(see Cameron et al. 2005). Assuming a fraction of 10−4
of the energy released in hard X-rays/γ-rays is emitted
in radio over one hour, a giant X-ray flare with lumi-
nosity LX ∼ 1046erg can be observed to a distance of
a about 100Mpc. However, the rate of SGR giant flares
with such energy is about 10−4−10−5Mpc−3yr−1(Ofek
2007). Therefore, the expected observed rate of Galac-
tic and extragalactic SGRs is at least three orders of
magnitude smaller than the rate of long-duration radio
transients.
New unknown explosions: Explosions taking place
outside galaxies (“naked”) may explain the lack of optical
counterparts. In general we can not rule out putative
extra-Galactic sources, which have not been discovered
yet.
We discuss several examples of such putative sources,
showing that they are unlikely sources for the long-
duration radio transients.
that primordial black holes of mass<∼1015g will evap-
orate within the Hubble time, and eventually emit a
burst of energetic photons and particles. Such explosions
are expected to manifest as a short-duration (≪ 1s) ra-
dio pulse as the ambient magnetic field is altered by an
expanding conducting shell (Rees 1977). However, to
date such events were not found (e.g., Phinney & Taylor
1979). Moreover, they are expected to have very short
time scales, in contrary to long-duration radio transients.
Following the suggestion by Kulkarni et al. (2009),
Vachaspati (2008) presented a model in which grand uni-
fication scale superconducting cosmic strings are emit-
ting short (< 1s) radio flares. Vachaspati (2008) predicts
that the source number count function of such events
will be N(> S) ∝ S−1/2, which is not consistent with
the long-duration radio transients source count function
(§4.3).
12http://www.physics.mcgill.ca/∼pulsar/magnetar/main.html
Repeaters
Hawking (1974) suggested
Strong radio emission from supernovae was suggested
by Colgate & Noerdlinger (1971) and Colgate (1975).
In their scenario, the expanding core of the supernova
“combs” the star’s intrinsic dipole field, and the gener-
ated current sheet produce coherent radio emission. The
maximum energy emitted in such a radio pulse, assum-
ing no attenuation, is of the order of 1046erg. However,
the expected pulse is very short (≪ 1s) in comparison to
the observed time scale of long-duration radio transients.
Of course, the lack of detectable host galaxies makes any
such suggestion untenable.
The lack of optical counterparts cannot rule out as-
sociation with high redshift sources (e.g., population-III
stars). Assuming a large cosmological distance, the rest-
frame energy of such events is approximately:
Ef,cos≈3 × 1048
Sν
0.4mJy
?
erg;
∆ν
1010Hz
tdur
0.5day
?
dL
5 × 1010pc
?2
×
?1 + z
6
(5)
here, dLis the luminosity distance (normalized to 1+z =
6), z is the redshift, and Sν, ∆ν, and tdurare given in
the observed frame.
The rest-frame brightness temperature (normalize at
1 + z = 6) of such events is:
TB,cos=Sν,restd2
≈7 × 1016
lum(c/νrest)2(2πkBR2
Sν
0.4mJy
?−2?Rrest
200au
rest)−1
?1 + z
6
?−1?
?−2
dL
5 × 1010pc
?2
×
?
ν
5GHz
K,(6)
where we set the size of the emission region, Rrest, to
200au which is the light crossing time in the rest frame,
ctdur,rest= ctdur(1 + z)−1, for tdur= 7day. Again, Sν,
∆ν, and tdurare given in the observer frame, while the
subscript “rest” indicate quantities at the rest frame.
As tdur<∼7day, this is a lower limit on the bright-
ness temperature.The huge brightness temperature,
relative to the minimum energy or equipartition tem-
perature (Readhead 1994), requires a coherent emission
mechanism or alternatively a Lorentz factor of >∼102.
However, if the beaming factor is large, then the rate of
long-duration radio transients will exceed the SN rate in
the Universe.
5.2. Galactic
Stellar sources: Several types of Galactic sources,
which are known to flare at radio wavebands were dis-
cussed by Bower et al. (2007). Specifically, RS CVn
stars, FK Com stars, Algol class binaries and X-ray bi-
naries are ruled out by the lack of optical counterparts.
Other possibilities, like T Tau stars, are associated with
star forming regions typically found at low Galactic lat-
itude.
Late-type stars are known to flare in radio wavebands
(see G¨ udel 2002 for review). However, the lack of R- and
K-band optical/near-IR counterparts rules out an associ-
ation with late-type M-dwarfs up to a distance of 2kpc,
which is the median distance of Galactic M-dwarfs at
the direction of the Bower et al. field (Gould, Bahcall, &
Flynn 1996). Moreover, flares from M dwarfs (and brown
dwarfs) are known to exhibit strong circular polarization

Page 8

8Ofek et al.
(∼ 100%; e.g., Hallinan et al. 2007; Berger 2006). How-
ever, as summarized in §1, Bower et al. (2007) did not
find evidence for circular polarization above 30% in any
of their radio transients.
Brown dwarfs: In recent years, it was found that at
least some brown-dwarfs are active, and show bursts in
radio and X-ray wavebands (e.g., Burgasser et al. 2000;
Berger et al.2001; Berger et al.
Putman 2005). In the radio regime, these flares peaks
around 5GHz (spectral slopes α>∼0; Berger et al. 2001;
2005; 2008a;b).
Brown dwarfs are potentially very faint sources. Our
near-IR search of the Bower et al. (2007) field can detect
a T5-type brown dwarf up to distances of about 250pc .
However, our observations cannot rule out an association
of the Bower et al. transients with older, or less massive,
and hence cooler and fainter brown-dwarfs (e.g., Y-class
brown-dwarfs; see Burrows et al. 1997; Baraffe et al.
2003 for evolutionary models).
For cooler brown-dwarfs which are undetectable by our
K-band search, based on the minimum surface density
of radio transient progenitors derived in §4.2, we can put
a rough lower limit on the distance. We assume that
the local density of brown dwarfs with effective temper-
ature above 200K is ρBD≈ 0.1pc−3(Reid et al. 1999;
Burgasser et al. 2004) and that at small distances the
distribution can be regarded as isotropic. Agreement be-
tween the areal density of the radio transients (§4.2) to
that of old brown dwarfs is obtained by having the brown
dwarfs at a typical distance of d>∼200pc.
At such distances, the energy needed to produce a sin-
gle long-duration radio transient burst will be about:
2002; Burgasser &
Ef,BD≈8 × 1030
Sν
0.4mJy
?
d
200pc
?2
∆ν
1010Hz
×
tdur
0.5dayerg.(7)
Should the Bower et al. radio transients arise from
brown dwarfs then they must repeat. The flare repeti-
tion time scale is Σ/ℜ. For the minimum sky surface
density of Σ ∼ 60deg−2(§4.2), and assuming a rate
ℜ ≈ 500yr−1deg−2, the repetition time scale is>∼50day.
For a typical distance of 200pc, the total energy emit-
ted over the Hubble time from a single active Brown-
dwarf will be ∼ 1042erg. For comparison, the magnetic
energy of active late-type M-dwarfs is:
EB=4
3πR3
∼=5.1 × 1035?
∗
B2
8π
r∗
70000km
?3?B
3kG
?2
erg,(8)
where R∗is the star radius, and B is its magnetic field.
We note that magnetic fields in the most magnetically
active M-dwarfs reach several kG (e.g., Valenti, Marcy,
& Basri 1995; Johns-Krull & Valenti 1996; Berger et al.
2008b). This is several orders of magnitude smaller than
the total energy output of a long-duration radio tran-
sient. Therefore, this scenario requires that the magnetic
field of brown-dwarfs will be replenished from an inter-
nal energy source. This is not an implausible sugges-
tion. For example, 1042erg is only a small fraction of the
brown dwarf thermal or rotational energy. The strongest
argument against the association of long-duration radio
transients with brown dwarfs is the lack of circular po-
larization observed in the Bower et al. (2007) events.
Reflected solar flares: As discussed by Bower et al.
(2007), a solar flare reflected by a solar system object
will have a flux of:
Sref=6.6S⊙,flare
108Jy
?r
1au
A
0.6
?
d
100km
?−2
?2
×
?−2?∆
1au
µJy, (9)
where S⊙,flare is the solar flare flux density, r and ∆
are the distance of the asteroid from the Sun and Earth,
respectively, and A is its albedo13. Strong X-class solar
flares may have flux densities of 108Jy, although they
typically last less than 20 minute (Bastian, Benz, & Gary
1998). Moreover, in order to explain the long-duration
radio transients using such reflected events, we need a
population of huge asteroids (d > 100 km), at near Earth
orbits, which do not exist. More importantly, the motion
of such objects will be detectable by the VLA in A array
whereas the Bower et al. transients are point sources.
Pulsars: Most of the Galactic pulsars are young ob-
jects (up to 108yr), and found near the Galactic plane.
Moreover, with the exception of magnetars, known pul-
sars have radio spectrum with α ≈ −2 (e.g., Camilo et
al.2006). Based on the catalogue of simulated NSs
(Ofek 2009), the expected surface density of NSs with
age smaller than 10 (100)Myr, at the direction of the
Bower et al. field, is about 0.3 (8)deg−2, assuming 109
NSs in the Galaxy. We note that the number of NSs in
the direction of the Bower et al. field (b∼= 37◦) rises
faster than linearly with age, since NSs are born in the
Galactic plane and ejected (mostly) to high Galactic lat-
itudes.
Isolated old neutron stars: The Galaxy may host
about 109old isolated NSs (see §6.1). This is a plausible
hypothesis and we discuss this in the next section.
To conclude, the analysis of Bower et al. (2007) and
our own analysis does not favor association of the long-
duration radio transients with many types of astrophys-
ical sources. However, we cannot rule out association of
the long-duration radio transients with Galactic isolated
NSs, Galactic cool brown-dwarfs, or some sort of exotic
explosion. Although cool brown dwarfs are interesting
candidates, they require an emission mechanism which
does not produce circularly polarized radiation like that
observed in flare stars.
6. ISOLATED-OLD NEUTRON STARS AS
PROGENITORS OF THE LONG-DURATION
RADIO TRANSIENTS
The organization of this section is as follows. In §6.1
we give a brief introduction to old neutron stars. Based
on Monte-Carlo orbital simulations of NSs we estimate
their sky surface density, distances and source number
counts function (§6.2). In §6.3 we discuss the energetics
of long-duration radio transients in the context of Galac-
tic NS. In §6.4 we present a simple synchrotron emission
model for such radio flares, while in §6.5 we discuss the
13The radar albedo of asteroids ranges from 0.05 for carbona-
ceous chondrites to 0.6 for high-density nickel-iron. Typical value
is 0.15.

Page 9

Radio transients9
possibility that these are some kind of intermittent pul-
sars. Finally, we derive a lower and upper limits on the
distance scale to the Kida et al. transients assuming they
are originating from Galactic NSs (§6.6).
6.1. Introduction to Galactic isolated old NS
Based on the metal content of the Milky Way galaxy,
Arnett, Schramm & Truran (1989) estimated that about
109SNe exploded in the Milky Way and hence similar
number of NSs were born in our Galaxy. The observed
SN rate in the Galaxy suggests a number which is smaller
by a factor of 3–10. Thus it is expected that there are
about 108to 109NS in the Galaxy.
NSs cool on relatively short time scales (∼106yr; e.g.,
Yakovlev & Pethick 2004). Therefore, they are expected
to be intrinsically dim and extremely hard to detect.
However, Ostriker et al.
may be heated through accretion of inter-stellar mat-
ter (ISM). This novel suggestion raised many hopes that
NSs may be detected as soft X-ray sources (e.g., Helfand,
Chanan & Novick 1980; Treves & Colpi 1991; Blaes &
Madau 1993). These predictions were followed by inten-
sive searches for such objects (e.g., Motch et al. 1997;
Maoz, Ofek, & Shemi 1997; Haberl, Motch, & Pietsch
1998; Rutledge et al. 2003; Ag¨ ueros et al. 2006). How-
ever, the several candidates that were found (e.g., Haberl,
Motch, & Pietsch 1998) are young cooling NSs (e.g.,
Neuh¨ auser & Tr¨ umper 1999; Popov et al. 2000; Treves
et al. 2001).
Among the usual explanations for the observational
paucity of isolated accreting old NSs in the ROSAT all-
sky survey (Voges et al. 1999) are the fact that the ve-
locity distribution of NSs is much higher than the early
estimates (e.g., Narayan & Ostriker [1990] vs. Cordes
& Chernoff [1998]) or the suggestion that magnetized
NSs cannot accrete matter efficiently at the Bondi-Hoyle
rate14(e.g., Colpi et al. 1998; Perna et al. 2003).
(1970) suggested that NSs
6.2. Surface density and distance
In order to estimate the surface density we need a
model for isolated old NS space distribution at the cur-
rent epoch. Ofek (2009) integrated the orbits of sim-
ulated NSs in the Galactic gravitational potential, us-
ing two different natal velocity distributions and vertical
scale height distributions of the progenitor populations
suggested by Arzoumanian et al. (2002) and Faucher-
Gigu` ere & Kaspi (2006). These simulations assume that
60% of the Galactic NSs were born in the Galactic bulge
12Gyr ago, while 40% were born continuously, with a
constant rate, in the disk over the past 12Gyr.
Based on this catalog, and using the Arzoumanian et
al. initial conditions, in Figure 6 we show the theoretical
sky surface density of all Galactic NSs, and NSs within
1kpc from the Sun. Towards the direction of the Bower
et al. (2007) field, the total surface density of isolated
old NSs is about 104deg−2. The mean surface density
of old NSs at Galactic latitude b > 30◦, which roughly
corresponds to the FIRST survey footprint, is about 5%
larger. The small difference between the two surface den-
sities suggests that if indeed long-duration radio tran-
sients are associated with isolated old NSs then the com-
parison between the 1.4GHz and 5GHz rates presented
14Bondi & Hoyle (1944).
Fig. 6.— Sky surface density distribution of all NSs (panel a) and
NSs at distance < 1kpc from the Sun (panel b). The maps are pre-
sented in the Galactic coordinate system and using the Aitoff equal
area projection. The sky surface density are calculated using the
catalog of simulated old NSs presented in Ofek (2009) including
both populations of bulge-born and disk-born NSs, and using the
natal velocity distribution of Arzoumanian et al. (2002) and as-
suming 109NSs. The plus sign marks the position of the Bower
et al. (2007) field at l = 115◦, b = 37◦. The lines mark the decli-
nation zone of 32◦to 42◦, in which the survey for radio transients
described by Kida et al. (2008) was conducted. The six circles
mark the position of the bright (flux at 1.4GHz greater than 1Jy)
transients reported by Kida et al. (2008).
in §4.3 is not affected by the different sky positions at
which these surveys were conducted.
In Figure 7 we show the cumulative surface density
of NSs, at the Bower et al. (2007) field direction, as a
function of distance from the observer (i.e., the Sun).
The plots assume that the Sun is located 8kpc from
the Galactic center (Ghez et al.
we also mark, by a dotted horizontal line, the minimal
sky surface density of long-duration radio transients (i.e.,
Σ > 60deg−2) that we derived in §4.2. This Figure sug-
gests that if isolated old NSs are indeed related to the
sub-mJy level Bower et al. transients then their typical
distance scale is at least ∼ 1kpc. Otherwise the pre-
dicted sky surface density will not be consistent with the
minimum sky surface density of NS at the direction of
the Bower et al. field (see §4.2). On the other hand, the
typical distance is presumably not greater than about
5kpc, otherwise the slope of the cumulative distribution
will be too shallow relative to the steep power-law index,
n, of the number count distribution derived in §4.3. We
note that the luminosity function of these hypothetical
events may depend on the age (and therefore distance)
to the NSs. Therefore, we do not attempt to quantify
the upper limit on the distance mentioned above.
A possibility that we should consider is that only a
fraction of the Galactic NSs are the progenitors of the
long-duration radio transients (e.g., only “young” NSs).
Based on the NSs orbital simulations, we find that all the
NSs with ages smaller than at least 1Gyr are required as
progenitors of the radio transients. Thus, the sub-mJy
long duration radio transients cannot arise from pulsars.
2008). In Figure 7

Page 10

10Ofek et al.
10
−1
10
0
10
1
10
2
10
3
10
4
10
−1
10
0
10
1
10
2
10
3
10
4
d [kpc]
Cumulative density [deg−2]


At direction: l=115o b=37o (Bower et al. field)
Uniform distribution, n=−3/2
n=−0.7
All
disk
bulge
Fig. 7.— Cumulative number of simulated NSs per deg2at the
direction of the Bower et al.(2007) field as a function of dis-
tance.The thick solid line shows the distribution of the entire
NS population of which 60% (40%) are assumed to be of bulge
(disk) origin, the thin solid line is for the disk-born NSs, while
the dashed line is for the bulge-born NSs. The three distributions
give a rough idea regarding the uncertainties that may arise from
our ignorance regarding the birth locations of NSs along Galactic
history. The dotted horizontal line marks the minimum surface
density required (60deg−2; see §4.2). The thick solid gray lines
show the expected slopes for a population with a homogeneous
distribution (n = −3/2), and n = −0.7, which corresponds to our
3-σ upper limit (see however text).
A simple test for the hypothesis that long-duration ra-
dio transients are associated with Galactic isolated old
NSs (or for that matter any Galactic population with ra-
dial scale length of a kpc or so) is to look for excess of
sub-mJy radio transients near the Galactic center, rela-
tive to high Galactic latitude. In Figure 8 we therefore
show the cumulative distribution of isolated old NSs as
a function of distance, but towards the direction of the
Galactic center.
There are several marked differences between Figures 7
and 8. The total sky surface density in the direction
of the Galactic center is about two orders of magnitude
larger than the sky surface density at the direction of the
Bower et al. field. Next, if we consider only NSs with
distances up to 1kpc, then the sky surface density in
the direction of the Galactic center is about seven times
larger than that in the Bower et al. field. Finally, the
source count function in the direction of the Galactic
center is steeper than that in the direction of the Bower
et al. (2007) field.
6.3. Energetics and time scales
In the old-NS framework the typical energy release
from a single flare is:
Ef≈2 × 1032
Sν
0.4mJy
tdur
0.5dayerg.
?
d
1kpc
?2
×
∆ν
1010Hz
(10)
The rate of the sub-mJy long-duration radio transients is
in the range of ℜ ≈ 20deg−2yr−1to 2 × 104deg−2yr−1
(Eq. 1).Adopting a representative rate of ℜ
500deg−2yr−1, and tdur ∼ 0.5day we find that over
≈
10
−1
10
0
10
1
10
2
10
3
10
4
10
−1
10
0
10
1
10
2
10
3
10
4
10
5
10
6
d [kpc]
Cumulative density [deg−2]


At direction: l=0o b=0o (Galactic center)
Uniform distribution, n=−3/2
All
disk
bulge
Fig. 8.— Like Fig. 7, but towards the direction of the Galactic
center.
the Hubble time the all-sky number of events is larger
by several orders of magnitude than that of any known
Galactic stellar population. Therefore, any hypothesis
involving Galactic stars would require that the sources
be repeaters. The mean time scale between bursts, ∆tb,
is given by:
∆tb=Σ
ℜ
∼=0.2
Σ
102deg−2
Σ
102deg−2
?ℜ
500
tdur
0.5dayyr,
?−1
yr
∼=0.2
(11)
where Σ is the sky surface density of sources in the di-
rection of the Bower et al. (2007) field. In that case the
flares duty cycle is of order of D = tdur/∆tb≈ 7 × 10−3.
An immediate prediction is that if long-duration radio
transients are associated with Galactic NSs, then the
repetition time scale for bursts is relatively short, of the
order of several months.
Multiplying Equation 10 by the expected number of
flares within the Hubble time (tH/∆tb∼ 5×1010, where
tH is the Hubble time), we find that the total energy
emitted by a single object over its life time is:
Etot≈1 × 1043
Sν
0.4mJy
Σ
102deg−2
?
d
1kpc
?2
∆ν
1010Hz
×
?
?−1
erg,(12)
Dividing Equation 10 by Equation 11, the mean lumi-
nosity over time required in order to power these bursts
is:
Sν
0.4mJy
?
102deg−2
?˙E?≈3 × 1025
?
d
1kpc
ergs−1.
?2
∆ν
1010Hz
×
Σ
?−1
(13)
Note that this quantity is independent of ∆tb.
Next, we consider the energy reservoir of isolated old
NSs, and check whether it is consistent with the mean

Page 11

Radio transients11
luminosity given by Equation 13. Isolated old NSs have
several sources of available energy. Among these are:
(i) spin energy; (ii) magnetic energy; and (iii) accretion,
from the ISM, energy.
The rotational kinetic energy of NSs is:
Erot=1
2Iω2
∼=2.2 × 1044?P
10s
?−2 MNS
1.4M⊙
?RNS
10km
?2
erg,(14)
where MNS is the NS mass, I is the moment of iner-
tia (assuming I = 0.4MNSR2
angular speed, and P (= 2π/ω) is its rotation period.
The energy-loss rate available from the rotational energy
reservoir is:
NS), ω is the NS rotational
˙Erot=Iω ˙ ω = 4π2IP−3˙P
∼=4.4 × 1026MNS
?P
10s
1.4M⊙
?−3
?RNS
10km
?2
×
˙P
10−17ergs−1,(15)
where ˙ ω is the time derivative of the NS angular fre-
quency, and˙P is defined as minus of its period derivative.
Typical values for˙P are in the range of 10−10s ˙ s for mag-
netars, 10−17s ˙ s to 10−12s ˙ s for normal radio pulsars, and
10−21s ˙ s to 10−18s ˙ s for millisecond pulsars (Srinivasan
1989).
A large fraction of NSs may have high surface magnetic
field in excess of 1014G (e.g., Magnetars). The energy
stored in the magnetic field of such objects is about:
EB≈4
≈1.7 × 1045?rNS
3πR3
NS
B2
8π
10km
?3?
B
1014G
?2
erg,(16)
where RNSis the NS radius, and B is its interior mean
magnetic field. We note that the internal magnetic field
may be higher, and therefore, Equation 16 is a lower
limit on the magnetic energy reservoir.
which the magnetic field of NSs is decaying is debated
both theoretically and observationally (e.g., Urpin &
Muslimov 1992; Chanmugam 1992; Phinney & Kulka-
rni 1994; Sengupta 1997; Sun & Han 2002). Assuming
the magnetic field is uniformly decaying on the Hubble
time scale, this will provide, on average, energy loss rate
of˙E ≈ 4 × 1027ergs−1.
Another possible source of energy is heating of the NS
by accretion from the ISM (e.g., Ostriker et al. 1970).
Assuming NSs accrete at the Bondi-Hoyle rate (Bondi &
Hoyle 1944), the energy-loss rate will be:
The rate at
˙Eacc=4πG3M3
RNS(v2+ c2
≈5 × 1026?MNS
nISM
0.1cm−3
NSρISM
s)3/2
1.4M⊙
?
300kms−1
?3?RNS
10km
v
?−1
×
?−3
ergs−1,(17)
where v is the velocity of the NS relative to an ISM with
a mass (number) density ρISM (nISM). cs is the sound
speed in the ISM, which is of the order of 10kms−1and
is therefore neglected15. We note, however, that magneto
hydrodynamic simulations suggest that in the presence
of a strong magnetic field the accretion rate will be sup-
pressed relative to the Bondi rate (e.g., Toropina et al.
2001, 2003, 2005; see however Arons & Lea 1976, 1980).
To conclude, the combination of NSs energy sources
may provide enough energy to explain long-duration ra-
dio transients. Specifically, the rotation energy of NSs
and the energy available for NSs from accretion from
the ISM is at least an order of magnitude larger than
needed for generating the long-duration radio transients
(Eq. 13). However, unless additional energy sources are
invoked, this implies that the outbursts can not emit
much higher energy at other frequencies.
6.4. Incoherent synchrotron radiation from an
afterglow
Now we address the mechanism of radio emission.
There are two possibilities: (i) incoherent synchrotron
emission (the afterglow model); and (ii) coherent emis-
sion. We discuss the first possibility in this section and
the second possibility in §6.5.
In the afterglow model, the source undergoes an ex-
plosive event and ejects relativistic particles and may
generate magnetic field (hereafter relativistic plasma).
Some sort of pressure confinement is needed to prevent
rapid expansion of the relativistic plasma.
the expansion or adiabatic losses vastly increase the en-
ergy budget which would be inconsistent with the old
NS framework. In the case of GRBs, the afterglow is
confined by the dynamic pressure of the blast wave. We
return to this critical issue towards the end of the subsec-
tion. We proceed by computing the (quasi)static proper-
ties of the (approximately) confined relativistic plasma.
We note that the parameters derived from this model are
estimated to within an order of magnitude.
Our simple model involves four free parameters: the ra-
dius of the emitting region, R; the mean electron density,
ne; the magnetic field, B; and the characteristic electron
Lorentz factor, γe= (1−β2
electron speed in units of the speed of light. The large
value of the 5GHz rate (Eq. 1) relative to that at 1.4GHz
rate (Eq. 2) suggests that the synchrotron self absorption
frequency is above 5GHz (see §4.3). Therefore, we as-
sume νs>∼5GHz, and that the optical depth at 5GHz,
τ5> 1. Furthermore, we assume that the optical depth
at the synchrotron frequency τs<∼1.
In order to estimate these parameters, we use the fol-
lowing relations:
(i) The characteristic synchrotron frequency:
Otherwise
e)−1/2, where βeis the typical
νs=γ2
∼=2.8 × 106γ2
e
eB
2πmec
eB Hz,(18)
where e is the elementary (electron) charge, me is the
electron mass, and B the magnetic field in cgs units (i.e.,
Gauss).
15The sound speed is given by cs = (γkBT/µm)1/2, where γ
is the adiabatic index, kB is the Boltzmann constant, T is the
temperature, and µm is the mean weight of the ISM particles. For
γ = 5/3 and T = 104K the sound speed is 11 and 15kms−1for
neutral and ionized gas, respectively.

Page 12

12Ofek et al.
(ii) The power emitted by a relativistic single electron
due to synchrotron radiation (e.g., Rybicki & Lightman
1979) is:
Ps=4
∼=1.1 × 10−15β2γ2
3σTcβ2γ2
eUB
eB2ergs−1,(19)
where σT is the Thomson cross-section, and UB =
B2/(8π) is the magnetic field energy density. The syn-
chrotron cooling time scale, assuming τs<∼1, is given
by
tsyn=γemec2
∼=7.7 × 108γ−1
Ps
e β−2B−2s.(20)
(iii) The brightness temperature, TB(essentially a con-
veniently chosen surrogate for distance) is:
TB=Sνd2(c/ν)2(2πkBR2)−1
∼=1.6 × 1021
?
5GHz
where ν is the frequency at which we observe (i.e.,
5GHz). For optical depth larger than unity the bright-
ness temperature is related to the electrons energy:
Sν
0.4mJy
?−2?
?
d
1kpc
?−2
?2
×
ν
R
10km
K,(21)
kBTB≈ γemec2.(22)
(iv) Finally, in order to get a self absorption spectrum
(see §4.3) the optical depth at 5GHz should be larger
than unity. This holds if and only if at 5GHz the thermal
emission is smaller than the optically thin emission:
2πkBTB
?ν
c
?2
<1
3RnePs
νs
?ν
νs
?1/3
(23)
Next, we can solve equations 18–23 for the free pa-
rameters B, γe, and R and we can put a lower limit on
the value of ne. Since we do not know the exact value
of tdur, νs and d we solve for the free parameters as a
function of these arguments. For completeness, we also
state the dependency on Sν. We normalized the solu-
tions for Sν= 0.4mJy, d = 1kpc, tsyn≈ tdur= 0.5day,
and νs = 2 × 1011Hz (the choice for νs is to minimize
the total energy; see below). We note that tdur ≈ tsyn
means that there is no energy injection into the emis-
sion region after the initial burst (i.e., the duration of
the events is dominated by the synchrotron cooling time
scale). However, if energy is injected then tdur>∼tsyn.
The following solution holds for τ5>∼1 and τs<∼1:
B ≈ 17
2 × 1011Hz
?
2 × 1011Hz
?
νs
?−1/3?
tsyn
0.5day
?−2/3
G,(24)
γe≈ 66
νs
?2/3?
tsyn
0.5day
?1/3
, (25)
R≈6 × 1010?
?
νs
2 × 1011Hz
?1/2?
?−1/3?
tsyn
0.5day
?−1/6
×
Sν
0.4mJy
d
1kpc
?
cm,(26)
and the lower limit on Rneis
Rne> 2 × 1016?
νs
2 × 1011Hz
?4/3
tsyn
0.5daycm−2.(27)
We note that in order to minimize the energy, neshould
be around the lower limit implied by Equation 27. For
convenient we also give the brightness temperature:
TB≈4 × 1011?
?
νs
2 × 1011Hz
?1/3
K.
?2/3
×
tsyn
0.5day
(28)
Next, we can derive the ratio between the magnetic
energy and electron energy densities:
UB/Ue=B2/(8π)
neγemec2
?
2 × 1011Hz
×
0.4mJy
<∼1
νs
?−3?
tsyn
0.5day
d
1kpc
?−17/6
?
Sν
?1/2??
,(29)
where Ue= neγemec2is the electrons energy density. We
note that UB/Ueis very sensitive to both the duration,
tsyn, and the synchrotron frequency, νs, whose values are
not well known. Therefore, a small change in these un-
known parameters will change UB/Uedramatically (see
also Readhead 1994).
We note that by setting UB/Ue∼ 1, we have ensured
that TBis equal to the equipartition brightness temper-
ature (Readhead 1994) and minimized the energy re-
quirement. Next we test if these parameters are below
the inverse-Compton catastrophe limit (Kellermann &
Pauliny-Toth 1969). The inverse-Compton catastrophe
is relevant if Urad/UB>∼1. Assuming τs<∼1:
Urad≈RUe
ctsyn.(30)
Since R/(ctsyn) ≪ 1 we get Urad≪ Ue∼ UB. Therefore,
inverse-Compton effects can be neglected.
Assuming the electron density is close to the minimum
density implied by Equation 27, the total energy in a sin-
gle burst (i.e., in both the electrons and magnetic field)
is given by:
E =4
3πR3(Ue+ UB)
∼=1 × 1034??
?
0.4mJy
+1 × 1034??
?
0.4mJy
νs
2 × 1011Hz
??
1kpc
?4/3?
?2?
tsyn
0.5day
?
×
Sν
d
νs
2 × 1011Hz
?3/2?
1kpc
?−5/3?
?3?
erg.
tsyn
0.5day
?−11/6
×
Sν
d
(31)
The specific values we have selected, νs= 2×1011Hz and
tsyn= 0.5day, give a solution which is near equipartition
and therefore minimizes the energy. For ne close to its
minimum implied by Equation 27, the total energy in a
burst, and UB/Ueas a function of νsand tsynare shown
in Figure 9.This Figure suggests that the minimum

Page 13

Radio transients 13
UB/Ue=100
UB/Ue=0.01
E=2×1034 erg
E=1035 erg
E=1036 erg
νs [Hz]
tsyn [s]
10
9
10
10
10
11
10
12
10
13
10
3
10
4
10
5
10
6
10
−1
10
0
10
1
tsyn [day]
Fig. 9.— UB/Ue (black contours) and total energy (gray con-
tours), E = 4/3πR3(Ue+ UB), as a function of νs and tsyn, and
assuming d = 1kpc, and Sν = 0.4mJy. The equal UB/Ue lines are
100, 10, 1, 0.1, and 0.01 from left to right.
energy required per burst is around 1034erg. This energy
per burst multiplied by the expected number of bursts
over the Hubble time (∼ 5 × 1010) is of the same order
of magnitude of the energy reservoir of NSs identified in
§6.3.
So far we have assumed that the duration of the
events is set by the synchrotron cooling timescale. We
now explore the consequences of decreasing the cooling
timescale and letting the duration be determined by the
plasma injection timescale. In this case Equation 31 rep-
resent the total energy of a flare within the synchrotron
cooling time scale. Therefore, in order to get the total
energy we need to multiply Equation 31 by tdur/tsyn. As
can be gathered from Figure 9 the energy is minimized
by setting the cooling time equal to the duration time.
It is interesting to compare the derived radius, R ≈ 6×
1010cm, with some typical radii dominating NS physical
processes. The light-cylinder radius is:
Rlc=
c
2πP∼= 4.8 × 1010P
10scm.(32)
The co-rotation radius of a NS is:
Rcor=
?GMNS
ω2
∼=7.8 × 108?MNS
?1/3
1.4M⊙
?1/3?P
10s
?2/3
cm.(33)
Assuming a Bondi-Hoyle accretion rate:
˙M =4πG2M2
NSmpnISM
(V2+ c2
s)3/2
,(34)
where mp is the proton mass, then the Magnetosphere
radius is:
µ2
˙M√2GMNS
∼=2.1 × 1011?
4 × 1030
×
1.4M⊙
Rm=
?
?2/7
µ
?4/7?
˙M
2 × 108grs−1
?−2/7
?MNS
?−1/7
cm,(35)
where µ is the magnetic dipole moment of the NS. Fi-
nally, the accretion radius is:
Racc≈2GMNS
≈1.7 × 1012MNS
V2
1.4M⊙
?
V
150kms−1
?−2
cm. (36)
As noted at the beginning of the sub-section rapid ex-
pansion of the radiating plasma would vastly increase the
energy budget. For this reason, an integral requirement
of the incoherent model is that the plasma must be con-
fined (in which case the duration of the event is set by
the cooling time or by the duration of the injection of en-
ergy by the source). We note that the confinement radius
should probably be smaller than the light cylinder radius.
Otherwise, the energy requirement will be larger due to
the inertia of the electrons. The equipartition radius we
find (Eq. 26) is a little bit larger than the plausible con-
finement radius (e.g., Eq. 32). However, our calculation
provides only an order of a magnitude estimate to the
fireball parameters and the equipartition radius in par-
ticular. Therefore, we cannot rule out the incoherent
synchrotron model based on the small inconsistency be-
tween the equipartition radius and light cylinder radius.
Assuming a dipole magnetic field, decaying as R−3(in-
side the light cylinder radius; Eq. 32), and B = 17G at
R = 6×1010cm, the extrapolated magnetic field strength
on the surface of a 10km radius NS will be about:
R
10km
≈4 × 1015?
2 × 1011Hz
×
0.4mJy
B(10km)≈B
?
?3
νs
?−4/3?
?3
tsyn
0.5day
?−7/6
?
Sν
?3/2?
d
1kpc
G. (37)
This is higher than the typical estimated surface mag-
netic fields of pulsars and Magnetars. However, for some-
what larger νsor tsynthe discrepancy is smaller. More-
over, the events may be related to the release of magnetic
energy stored in the NS interior. Therefore, we conclude
that the incoherent synchrotron model cannot be ruled
out.
Finally, we note that the total mass of matter within
the emission radius is 4/3πnempR3∼ 4 × 1014gr. In-
terestingly, this mass is similar to the total amount of
matter that a NS with a space velocity of 150kms−1
will accrete from the ISM (assuming n = 0.1cm−3and
Bondi-Hoyle accretion) within several months, which is
the typical time interval between bursts that we found
in §6.3. We note that Treves, Colpi & Lipunov (1993)
suggested that accreted matter from the ISM is piled up
near the Alfv´ en radius, followed by infall of the piled up
matter on the NS. They estimated that these episodic
infalls may occur every several months.
6.5. Flares from intermittent pulsars
In recent years, several types of pulsars with small
duty cycles have been discovered.
RRATs (McLaughlin et al. 2006), and intermittent pul-
sars (Kramer et al. 2006). Several models were suggested
to explain such episodic pulsars (e.g., Treves et al 1993;
Zhang, Gil & Dyks 2006; Cordes & Shannon 2008). How-
ever, their evolutionary status is still unclear.
This includes the

Page 14

14Ofek et al.
Known intermittent pulsars and RRATs have charac-
teristic ages similar to those of “normal” pulsars (i.e.,
<∼107yr). However, as we discussed in §6.2, the long-
duration radio transients cannot be associated exclu-
sively with pulsars younger than about 1Gyr, otherwise
their predicted surface density will not be consistent with
the observations (§4.2).
As shown in §6.3, in the framework of Galactic NSs,
the duty cycle of the long-duration radio transients is
∼ 7 × 10−3. Such a small duty cycle will make it hard
to detect them as repeaters in current pulsars searches.
In addition, most pulsar searches are conducted at low
frequencies (<∼1.4GHz), in which the rate of the long-
duration radio transients seems to be low. Thus, a pre-
diction of this model is that high frequency (say 5GHz)
searches should find a much larger rate of long duration
radio transients.
The flat spectrum (α>∼0) of the long duration tran-
sients is reminiscent of the radio spectrum of magnetars
in their “active state” (cf. Camilo et al. 2006). Thus, a
plausible model is that the long duration transients are
ancient magnetars in short lived high states.
6.6. The distance scale to the Kida et al. transients
Next we derive a physical distance to the bright events
discussed by Kida et al. (2008). We remind the reader
that these events are about a thousand times brighter
than the VLA events. We use a modified Rayleigh test
(see Fisher et al. 1987) to compare the sky distribution of
the Kida et al. (2008) transients with that of the celestial
positions of simulated NSs:
(
6
?
i=1
sin[bi])2≡ Σ2b,(38)
for the sample of six radio transients found by Kida et
al. (2008); here b is the Galactic latitude.
Next, we selected from the Heliocentric catalog of sim-
ulated isolated-old NSs of Ofek (2009), six random NSs
within the footprints of the Kida et al. search zone, found
up to a distance d from the Sun and calculated their
Σ2b. We assume that the survey described in Kida et al.
(2008) covers the entire declination zone δ = 32◦− 42◦
equally. For each distance d, in the range of 100pc to
10kpc, we repeated this process 10,000 times. In Fig-
ure 10, we show the mean expected value, and the 68,
95 and 99.73 percentiles, for the distribution of Σ2b of
simulated NSs as a function of distance. As can be gath-
ered from Figure 10 the typical distance to these events
is below 150pc (900pc), at the 68% (95%) CL.
Kida et al. reported six events in their survey which
covers about 7% of the celestial sphere. Therefore, the
all-sky surface density of the Kida et al. transients is
>∼30 sources at the 95% confidence. Ofek (2009) found
that the density of NSs in the solar neighborhood is
2×10−4pc−3assuming 109NS in the Galaxy and the Ar-
zoumanian et al. (2002) initial velocity distribution. At
small distances (<∼100pc) the distribution of NSs around
the Sun is near isotropic. Therefore, by comparing the
density from the simulations with the observed surface
density of the Kida et al. (2008) events, we put a lower
limit on the distance to the Kida et al. (2008) event,
assuming they originate from Galactic NSs, of >∼30pc
at the 95% CL.
10
−1
10
0
10
1
0
5
10
15
20
25
30
35
Distance [kpc]
(ΣZ)2
Mean
68%
95%
99.73%
Fig. 10.— The sky uniformity of the Kida et al. transients (de-
scribed by Σ2b; Eq. 38) as a function of the distance to the tran-
sients. The gray-thick dashed line shows the value calculated for
the observed sample. The black line shows the mean value calcu-
lated for the simulated NSs, while the gray-thin dashed lines show
the upper 68, 95 and 99.73 percentiles (from bottom up) of the
distribution of the uniformity criterion Σ2b of the simulated NSs.
The lines fluctuates due to the limited statistics.
7. SUMMARY
We review several recent discoveries of radio transients
with durations between minutes to days (Kuniyoshi et
al.2006; Bower et al.2007; Niinuma et al.
Kida et al. 2008). We suggest that these radio tran-
sients may be generated by a single class of progenitors.
The main characteristics of these “long duration radio
transients” are: (i) a very high occurrence rate of about
∼ 103deg−2yr−1in the 5-GHz band; (ii) common at
intermediate Galactic latitude, with progenitors sky sur-
face density of>∼60deg−2at Galactic latitude, b ∼ 40◦;
(iii) lacking any X-ray (>∼10−13ergcm−2s−1), visible
light (g < 27.6, R < 26.5mag), near-IR (K < 20.4mag)
and radio (S5 GHz>∼10µJy) counterparts; and (iv) more
abundant in the 5-GHz band as compared to that in the
1.4-GHz band; From the rates in the two bands we infer
the spectral index between the two bands is α>∼0 where
the flux density, fν∝ να.
These events are most probably not associated with the
usual culprits like GRBs, SGRs, AGNs, SNe, flare stars,
pulsars and interacting binaries (§5). We find that sev-
eral other hypothesis including Galactic isolated old NS;
brown dwarfs and some sort of a new kind of explosions
cannot be ruled out. Among these, we find that the asso-
ciation with isolated old NSs is especially attractive. We
explore this hypothesis in details and show that it is con-
sistent with the current observations. In the framework
of Galactic isolated old NSs we show that: (i) the typical
distance to the Bower et al. sample (mJy events) is be-
tween 1kpc and ∼ 5kpc; (ii) the typical distance to the
Kida et al. Jy-level events is less than about 0.9kpc and
more than 30pc at the 95% CL; and (iii) they will have a
burst repetition time scale of about several months and
duty cycle of ∼ 7 × 10−3.
A possible association with isolated old NS is exciting.
If correct, this may prove to be the most practical way,
so far, to find old NSs in our Galaxy and explore their
2007;

Page 15

Radio transients15
demographics. Specifically, the demography of old NSs
constitute an excellent probe of the star formation his-
tory and metal enrichment of the Galaxy, and the grav-
itational potential of the Galaxy.
Our analysis naturally suggests several tests that can
be used to rule out this hypothesis. First, if indeed long-
duration radio transients are associated with isolated old
NSs, then we expect them to be distributed inhomoge-
neously on the celestial sphere. Specifically, this hypoth-
esis predicts that faint sub-mJy long-duration radio tran-
sients will be at least a few times more common in the
Galactic center than in high Galactic latitude. The ex-
act ratio, however, depends on the distance scale to these
events. This is illustrated in Figure 6 which shows the
expected approximate distribution of isolated old NSs
on the celestial sphere, for the entire NS population and
NS which are at distance smaller than 1kpc from the
Sun. Finally, we note that if the radio emission from such
sources is pulsating, then pulsars searches conducted at
5GHz will find these objects. The fact that such “pul-
sars” were not found in existing surveys may be due to
the fact that the majority of pulsars searches are carried
on in low frequencies in which the rate of these transients
is low.
We thank Re’em Sari, Orly Gnat, Ehud Nakar, Peter
Goldreich, Stel Phinney, Dovi Poznanski and Nat Butler
for many discussions and for Robert Becker for valuable
information regarding the strategy of the FIRST survey
and information regarding VLAJ172059.90+385226.6.
Support for program number HST-GO-11104.01-A was
provided by NASA through a grant from the Space Tele-
scope Science Institute, which is operated by the Asso-
ciation of Universities for Research in Astronomy, Incor-
porated, under NASA contract NAS5-26555. A.G. ac-
knowledges support by the Israeli Science Foundation, an
EU Seventh Framework Programme Marie Curie IRG fel-
lowship, and the Benoziyo Center for Astrophysics, a re-
search grant from the Peter and Patricia Gruber Awards,
and the William Z. and Eda Bess Novick New Scientists
Fund at the Weizmann Institute.
REFERENCES
Ag¨ ueros, M. A., et al. 2006, AJ, 131, 1740
Arnett, W. D., Schramm, D. N., & Truran, J. W. 1989, ApJL,
339, L25
Arons, J., & Lea, S. M. 1976, ApJ, 207, 914
Arons, J., & Lea, S. M. 1980, ApJ, 235, 1016
Arzoumanian, Z., Chernoff, D. F., & Cordes, J. M. 2002, ApJ,
568, 289
Baraffe, I., Chabrier, G., Barman, T. S., Allard, F., & Hauschildt,
P. H. 2003, A&A, 402, 701
Barbary, K., et al. 2009, ApJ, 690, 1358
Bastian, T. S., Benz, A. O., & Gary, D. E. 1998, ARA&A, 36, 131
Becker, R. H., White, R. L., & Helfand, D. J. 1995, ApJ, 450, 559
Berger, E., et al. 2001, Nature, 410, 338
Berger, E. 2002, ApJ, 572, 503
Berger, E., et al. 2005, ApJ, 627, 960
Berger, E. 2006, ApJ, 648, 629
Berger, E., et al. 2008a, ApJ, 673, 1080
Berger, E., et al. 2008b, ApJ, 676, 1307
Blaes, O., & Madau, P. 1993, ApJ, 403, 690
Bondi, H., & Hoyle, F. 1944, MNRAS, 104, 273
Bower, G. C., Saul, D., Bloom, J. S., Bolatto, A., Filippenko,
A. V., Foley, R. J., & Perley, D. 2007, ApJ, 666, 346
Burgasser, A. J., Kirkpatrick, J. D., Reid, I. N., Liebert, J., Gizis,
J. E., & Brown, M. E. 2000, AJ, 120, 473
Burgasser, A. J. 2004, ApJS, 155, 191
Burgasser, A. J., & Putman, M. E. 2005, ApJ, 626, 486
Burrows, A., et al. 1997, ApJ, 491, 856
Cameron, P. B., et al. 2005, Nature, 434, 1112
Camilo, F., Ransom, S. M., Halpern, J. P., Reynolds, J., Helfand,
D. J., Zimmerman, N., & Sarkissian, J. 2006, Nature, 442, 892
Carilli, C. L., Ivison, R. J., & Frail, D. A. 2003, ApJ, 590, 192
Cenko, S. B., et al. 2008, ApJ, 677, 441
Chandra, P., et al. 2008, ApJ, 683, 924
Chanmugam, G. 1992, ARA&A, 30, 143
Cole, S., et al. 2001, MNRAS, 326, 255
Colgate, S. A. 1975, ApJ, 198, 439
Colgate, S. A., & Noerdlinger, P. D. 1971, ApJ, 165, 509
Colpi, M., Turolla, R., Zane, S., & Treves, A. 1998, ApJ, 501, 252
Condon, J. J., Cotton, W. D., Greisen, E. W., Yin, Q. F., Perley,
R. A., Taylor, G. B., & Broderick, J. J. 1998, AJ, 115, 1693
Cordes, J. M., & Chernoff, D. F. 1998, ApJ, 505, 315
Cordes, J. M., & Shannon, R. M. 2008, ApJ, 682, 1152
Deneva, J. S., et al. 2008, arXiv:0811.2532
DeBoer, D. R., et al. 2004, Proc. SPIE, 5489, 1021
Eichler, D. 2002, MNRAS, 335, 883
Falcke, H. D., et al. 2007, Highlights of Astronomy, 14, 386
Faucher-Gigu` ere, C.-A., & Kaspi, V. M. 2006, ApJ, 643, 332
Fisher, N. I., Lewis, T., & Embleton, B. J. J. 1987, Cambridge:
University Press, 1987,
Frail, D. A., et al. 1997, ApJL, 483, L91
Fruchter, A. S., et al. 2006, Nature, 441, 463
Galama, T. J., de Bruyn, A. G., van Paradijs, J., Hanlon, L., &
Bennett, K. 1997, A&A, 325, 631
Gal-Yam, A., et al. 2006, ApJ, 639, 331
Gehrels, N. 1986, ApJ, 303, 336
Gehrels, N., et al. 2004, ApJ, 611, 1005
Ghez, A. M., et al. 2008, ApJ, 689, 1044
Goldreich, P., & Julian, W. H. 1969, ApJ, 157, 869
Gould, A., Bahcall, J. N., & Flynn, C. 1996, ApJ, 465, 759
Gregg, M. D., Lacy, M., White, R. L., Glikman, E., Helfand, D.,
Becker, R. H., & Brotherton, M. S. 2002, ApJ, 564, 133
G¨ udel, M. 2002, ARA&A, 40, 217
Guetta, D., Piran, T., & Waxman, E. 2005, ApJ, 619, 412
Haberl, F., Motch, C., & Pietsch, W. 1998, Astronomische
Nachrichten, 319, 97
Hallinan, G., et al. 2007, ApJL, 663, L25
Harrison, F. A., et al. 1999, ApJL, 523, L121
Hawking, S. W. 1974, Nature, 248, 30
Helfand, D. J., Chanan, G. A., & Novick, R. 1980, Nature, 283,
337
Hopkins, A. M., & Beacom, J. F. 2006, ApJ, 651, 142
Hyman, S. D., Lazio, T. J. W., Kassim, N. E., Ray, P. S.,
Markwardt, C. B., & Yusef-Zadeh, F. 2005, Nature, 434, 50
Hyman, S. D., Wijnands, R., Lazio, T. J. W., Pal, S., Starling,
R., Kassim, N. E., & Ray, P. S. 2009, ApJ, 696, 280
Ikhsanov, N. R. 2007, Ap&SS, 308, 137
Johns-Krull, C. M., & Valenti, J. A. 1996, ApJL, 459, L95
Jørgensen, P. S., Riis, T., Betto, M., & Pickles, A. 2002,
Astronomical Data Analysis Software and Systems XI, 281, 207
Kellermann, K. I., & Pauliny-Toth, I. I. K. 1969, ApJL, 155, L71
Kida, S., et al. 2008, New Astronomy, 13, 519
Kinney, A. L., Calzetti, D., Bohlin, R. C., McQuade, K.,
Storchi-Bergmann, T., & Schmitt, H. R. 1996, ApJ, 467, 38
Kramer, M., Lyne, A. G., O’Brien, J. T., Jordan, C. A., &
Lorimer, D. R. 2006, Science, 312, 549
Kulkarni, S. R., et al. 1998, Nature, 395, 663
Kulkarni, S. R., Ofek, E. O., Neill, D., Juric, M., Zheng, Z., in
prep.
Kuniyoshi, M., et al. 2006, PASP, 118, 901
Levinson, A., Ofek, E. O., Waxman, E., & Gal-Yam, A. 2002,
ApJ, 576, 923
Lorimer, D. R., Bailes, M., McLaughlin, M. A., Narkevic, D. J.,
& Crawford, F. 2007, Science, 318, 777
Maoz, D., Ofek, E. O., & Shemi, A. 1997, MNRAS, 287, 293
McLaughlin, M. A., et al. 2006, Nature, 439, 817
Motch, C., Guillout, P., Haberl, F., Pakull, M., Pietsch, W., &
Reinsch, K. 1997, A&A, 318, 111
Nakar, E., Gal-Yam, A., Piran, T., & Fox, D. B. 2006, ApJ, 640,
849
Narayan, R., & Ostriker, J. P. 1990, ApJ, 352, 222
Niinuma, K., et al. 2007, ApJL, 657, L37
Ofek, E. O. 2007, ApJ, 659, 339
Ofek, E. O., et al. 2006, ApJ, 652, 507
Ofek, E. O., et al. 2008, ApJ, 681, 1464
Ofek, E. O. 2009, PASP, 121, 814
Ostriker, J. P., Rees, M. J., & Silk, J. 1970, ApL, 6, 179
Ovaldsen, J.-E., et al. 2007, ApJ, 662, 294
Perley, D. A., et al. 2009, arXiv:0905.0001
Perna, R., Narayan, R., Rybicki, G., Stella, L., & Treves, A. 2003,
ApJ, 594, 936