1981MNRAS.196..597W
Downloaded from https://academic.oup.com/mnras/article-abstract/196/3/597/1014264 by California Institute of Technology user on 19 May 2020
Mon.
Not.
R.
astr.
Soc.
(1981)
196,
597-610
Models
ofradio
source
evolution
-
II.
The
2700-MHz
source
count
J.
V.
Wall*,
T.
J.
Pearsont
and
M.
S.
Longair:t:
Mullard
Radio
Astronomy
Observatory,
Cavendish
Laboratory,
Madingley
Road,
Cambridge
CB3
OHE
Received
1981
January
9;
in
original
form
1980
July
28
Summary.
Our
technique
for
deriving
cosmological
evolution
from
source
counts
and
identifications
is
applied
to
data
at
2700
MHz.
The
analysis
is
carried
out
on
the
assumption
that
two
populations
with
different
evolution-
ary
behaviours
appear
in
surveys
at
this
frequency:
'steep-spectrum'
sources
with
extended
radio
structures,
and
'non-steep-spectrum'
sources
with
compact
structures,
the
majority
of
which
are
identified
with
QSOs.
The
2700-MHz
data
add
constraints
to
the
evolution
deduced
for
the
'steep-
spectrum'
sources
from
low-frequency
data;
in
particular,
of
the
two
types
of
model
obtained
in
our
analysis
of
the
408-MHz
data,
only
one
now
appears
tenable.
The
present
results
for
'non-steep-spectrum'
sources
agree
with
the
results
from
luminosity
- volume
tests
on
samples
of
'flat-spectrum'
QSOs
-
the
change
in
space
density
with
epoch
appears
less
dramatic
than
for
the
powerful
radio
sources
with
steep
spectra
and
extended
radio
structures.
1 Introduction
In
Paper
I
(Wall,
Pearson
&
Longair
1980)
we
described
a self-consistent
technique
for
deriving
the
cosmological
evolution
of
extragalactic
radio
sources
from
source
counts,
identi-
fication
and
redshift
data
for
the
brighter
sources.
The
scheme
was
applied
to
data
at
408
MHz.
In
the
present
paper
we
employ
the
technique
in
a preliminary
investigation
of
the
cosmological
implications
of
source
counts
and
identifications
at
2700
MHz.
Surveys
at
frequencies
of
408
MHz
and
lower
are
dominated
by
'steep-spectrum'
(SS)
sources
with
extended
radio
structures.
As
the
survey
frequency
is
raised,
the
proportion
of
'centimetre-excess'
or
'flat-spectrum'
sources
increases.
The
latter term
is
a misnomer,
and
is
used
to
describe
collectively
the
sources
whose
spectra
are
'not
steep',
i.e.
whose
spectra
are
not
power
laws
of
spectral
index
a>
0.5
(So::
v-a)
or
power
laws
with
such
indices
which
bend
to
steeper
power
laws
at
higher
frequencies.
The
so-called
'flat-spectrum'
sources
have
*Present
address:
Royal
Greenwich
Observatory,
Herstmonceux
Castle,
Hailsham,
East
Sussex
BN27
lRP.
t
Present
address:
Owens
Valley
Radio
Observatory,
California
Institute
of
Technology,
Pasadena,
Cali-
fornia
91125,
USA.
tPresent
address:
Royal
Observatory,
Blackford
Hill,
Edinburgh
EH9
3HJ.
©
Royal
Astronomical
Society
• Provided
by
the
NASA Astrophysics
Data
System
1981MNRAS.196..597W
Downloaded from https://academic.oup.com/mnras/article-abstract/196/3/597/1014264 by California Institute of Technology user on 19 May 2020
598
J.
V.
Wall,
T.
J.
Pearson
and
M
S.
Longair
1 ·0
/
/
/
/
/
/
,.
/
/
.·
,
.·
,
.
,
,.
·01....._~~~---~~~~~~~~~~~~~~~~~
.
001
.
01
0·1
1 ·0
10
52700
{
Jy)
Figure
1.
The
total
source
count
at
2 700
MHz.
In
this
relative
differential
form,
AN
is
the
number
of
sources
with
flux
density
between
Sand
S
+AS,
and
AN
0
is
the
number
computed
from
the
'Euclidean'
law,
i.e.
AN
0
=
100
(s-
1
•
5
-
(S
+ t:i.St
1
•
5
].
The
error
box
at
the
faint
flux
densities
represents the
estimate
of
the
source-count
from
P(D)
(background
deflection)
analysis.
The
smooth
curves
show
total
(model)
counts
formed
by
adding
sub-counts
computed
for
the
'steep-spectrum'
(SS)
sources
and
the
'non-steep-
spectrum'
(NSS)
sources.
Dotted
curve:
SS
source
evolution
model
4b
(parameters
in
the
caption
of
Fig.
2)
+
NSS
source
evolution
model
of
'exponential'
type
with
exponent
M
=
7.
Dashed
curve:
SS
evolution
model
4 b +
NSS
'exponential' model
with
M
=
S.
spectra
which
show
flattening
or
inversion
at
the
higher
frequencies
and/or
cutoffs
to
the
lower
frequencies;
the
assortment
of
forms
(which
are
anything
but
flat)
is
shown
in
Figs
2
to
12
of
Wall
(1972).
To
avoid
the
term
'flat-spectrum',
we
shall
refer
to
these
sources
as
'non-steep-spectrum'
(NSS).
The
structures
of
these
sources
are
dominated
by
one
or
more
compact
components
whose
self-absorption
gives
rise
to
the
cutoffs
and
inversions
in
the
integrated
spectra;
some
of
the
components
are
highly
variable
both
in
flux
density
and
structure
on
time-scales
as
short
as
weeks.
Most
of
the
identified
sources
of
this
spectral
type
have
QSOs
as
their
optical
counterparts
(e.g.
Peterson
&
Bolton
1973),
and
a few
are
iden-
tified
with
elliptical
galaxies
with
active
nuclei
(e.g.
Heeschen
1970;
Klihr
1977).
The
mapping
of
the
cosmological
evolution
of
NSS
sources
is
essential
in
any
attempt
to
understand
the
cosmic
behaviour
of
radio
sources
in
general,
and
this
can
be
provided
by
systematic
analyses
of
high-frequency
source
counts.
There
is
some
evidence
that
their
radial
distribution
differs
significantly
from
that
of
the
powerful
radio
sources
of
the
steep-spectrum
type:
V/V
max
(luminosity-volume)
analyses
of
samples
of
QSOs
selected
at
high
frequencies
suggest
a more
uniform
distribution
(Schmidt
1976;
Masson
&
Wall
1977).
The
consequences
for
general
schemes
of
cosmological
evolution
(e.g.
Grueff
&
Vigotti
1977)
remain
largely
unexplored.
The
frequency
of
2700
MHz
is
optimum
for
a preliminary
investigation.
Some
60
per
cent
of
the
sources
detected
at
this
frequency
are
still
of
the
SS
variety,
whose
evolutionary
properties
should
be
comprehensible
from
our
investigation
of
the
408-MHz
data.
The
remaining
40
per
cent
of
NSS
sources
constitute
a large
enough
proportion
to
yield
signifi-
cant
conclusions.
There
exists
a well-defined
source
count,
obtained
from
the
Parkes
survey
at
2700
MHz
(Fig.
1 ). Flux
variability
at
this
frequency
is
less
than
at
higher
frequencies,
and
does
n
1
bt
give
rise
to
serious
epoch-dependence
of
the
counts
and
complete
samples.
More-
over,
accurate
positions
(±
2 arcsec)
from
the
RRE-Malvem
interferometer
have
yielded
optical
identifications
for
a
sample
which
are
based
on
positional
coincidence
alone
(McEwan,
Browne
&
Crowther
197
5, hereafter
MBC).
©
Royal
Astronomical
Society
•
Provided
by
the
NASA
Astrophysics
Data
System
1981MNRAS.196..597W
Downloaded from https://academic.oup.com/mnras/article-abstract/196/3/597/1014264 by California Institute of Technology user on 19 May 2020
Models
of
radio
source
evolution
-II
599
In
the
analysis
of
the
408-MHz
count
in
Paper
I,
we
assumed
that
all
sources
belonged
to
a single
(SS)
population.
Here
we
assume
that
the
counts
at
2700
MHz
consist
of
two
populations,
the
SS
and
NSS
sources.
We
allow
the
NSS
sources
to
evolve
independently
of
the
SS
population,
and
carry
out
the
exploration
of
the
2700-MHz
data
separately
for
each.
2
The
scheme
at
2700
MHz
The
extension
of
the
scheme
described
in
Paper
I to
two
populations
is
straightforward.
For
each
radio
source
population,
we
want
to
know
p
(P,
z),
the
radio
luminosity
function
and
its
dependence
on
epoch.
As
in
Paper
I, the
dependence
of
each
population
on
epoch
may
be
described
explicitly
with
an
evolution
function
F,
i.e.
p
(P,
z)
=
F(P,
z)
Po
(P),
(1)
where
Po
is
the
local
luminosity
function
p
(P,
z
= 0).
For
known
F
and
p
0
,
the
count
may
be
computed
from
1
°"
(z(S)
N(>S)=
0
dPj
0
p
0
(P)·F(P,z)·dV(z),
(2)
where
d V
(z)
is
the
volume
element
in
the
adopted
geometry,
and
z
(S)
is
the
redshift
at
which
a source
of
power
P
has
a flux
density
S,
obtained
from
(3)
The
procedure
for
finding
evolution
functions
consists
of
constructing
a complete
lumino-
sity
distribution
n
(P)
from
the
optical
data
for
a sample
of
sources
with
S;:;;.
S
0
,
and
using
this
to
obtain
Po
for
each
evolution
function
via
/(z(S
0
)
p
0
(P)dP
=
n (P)
dP
/Jo
F(P,
z)
·
d
V(z).
(4)
The
count
computed
via
equation
(2)
can
then
be
tested
statistically
against
the
observed
count.
Thus
the
scheme
requires
(a)
a luminosity
distribution
and
(b)
a source
count,
for
each
population
at
the
frequency
in
question.
To
construct
the
two
luminosity
distributions
for
the
SS
and
NSS
populations,
we
adopted
S
0
(2700
MHz)=
1.0
Jy;
at
this
level
the
MBC
sample
yields
48
sources
(Table
1)
in
0 .514
sr
of
the
±
4
°
dee
zone
which
is
free
of
obscura-
tion.
Of
these
sources,
42
are
identified,
and
25
have
redshift
measurements.
The
sample
provides
luminosity
distributions
which
suffer
from
serious
statistical
uncertainty,
but
a
deeper
sample
from
the
zone
cannot
help
because
the
proportion
with
redshift
measurements
falls
rapidly
with
flux
density.
There
is
a great
urgency
for
much
larger
complete
samples
of
identified
sources
selected
from
high-frequency
surveys;
the
sample
of
Peacock
&
Wall
(1981),
compiled
after
the
present
work
was
completed,
goes
some
way
to
fulfilling
this
requirement.
The
classification
of
the
sample
of
Table
1 into
SS
and
NSS
sources
is
straight-
forward
because
extensive
spectral
data
are
available
(Wall
1972).
To
obtain
a source
count
for
each
of
the
two
populations
we
proceeded
as
follows.
Most
sources
from
the
Parkes
2700-MHz
surveys
have
been
observed
at
5000
MHz,
and
high-frequency
spectral
indices
a
(2700-5000
MHz)
are
therefore
available.
Inspec-
tion
of
the
spectra
over
the
frequency
range
178-5000
MHz
(Wall
1972)
indicates
that,
if
a
(2700-
5000
MHz)<
0.5,
the
source
is
invariably
of
the
NSS
type.
The
converse
holds
to
a first
approximation
- a small
proportion
of
NSS
sources
have
a
(2700-5000
MHz)>
0.5,
©
Royal
Astronomical
Society
• Provided
by
the
NASA
Astrophysics
Data
System
1981MNRAS.196..597W
Downloaded from https://academic.oup.com/mnras/article-abstract/196/3/597/1014264 by California Institute of Technology user on 19 May 2020
600
J.
V
Wall,
T.
J.
Pearson
and
M
S.
Longair
Table
1.
A
complete
sample
of
sources
with
S
2100
~
1.0
Jy.
(
1)
(2)
(3)
(4)
(5)
(6)
(7)
(
8)
(9)
SOURCE
3C
S2700
"HF
IDE
NT
mpg
z
log
Ppoo*
Spectrum+
PKS
Jy
W
Hz-
sr-1
SS
NSS
0003-00
2
2.41
o.
77
QSO
21.4
1.037
27.
02
I
0019-00
1.90
0.84
G
21.1
(
o.
48)
26.23
./
0034-0l
15
2.56
o.75
EO
17.6
o.
0733
24.68
I
0035-02
17
4.
04
o.68
E
19.6
o.
2201
25.84
I
0036+03
1.10
0.84
E2
14
.5
o.
0145
22.90
./
0051-03
26
1.11
1.03
EO
18.9
o.
2106
25.27
I
0055-01
29
3.46
o.56
EO
15.9
o.
0450
24.38
I
0056-00
1.80
o.47
QSO
17.6
o.
717
26.48
I
0106+01
1.88
-0.67
QSO
19.1
2.
099
26.84
I
0112-017
1.38
-0.23
QSO
18.4
1.366
26.65
I
0122-00
1.43
0.25
QSO
17.
0
1.
070
26.66
I
0123-01
40
2.75
o.91
db
13.
7
o.
0180
23.49
I
0137+012
1.07
o.48
QSO
17.
0
0.262
25.40
./
0218-02
63
1.68
1.14
E
20.6
(
o.
3
7)
25.98
I
024(}-00
71
3.12
o.76
Sey
9.7
o.
00344
22.10
I
0305+03
78
5.33
0.54
D
15.3
o.
0289
24.18
I
0325+02
88
3.18
o.
70
D
15.7
o.
0302
24.00
I
0421+00
LOO
o.84
(
o.
5)
25.99
I
0422+00
1.29
-0.32
BSO
16.6
(1.
0)
26.38
I
0431-02
1.06
o.91
G
21.1
c
o.48)
25.98
I
044(}-00
3.53
o.08
QSO
19.1
o.848
26.82
I
0457+024
1.63
0.18
QSO
19.3
2.383
27.29
I
0458-02
1.99
0.16
QSO
19.6
2.286
27.34
I
0723-008
3.
01
0.21
NSO
18.4
(1.
5)
27.23
I
0724-01
180
1.56
o.92
G
20.0
(
o.
28)
25.66
I
0736+01
2.42
0.09
QSO
17.7
0.191
25.45
I
0743-006
1.40
-0.43
NSO
17.6
(1.5)
26.64
./
0812+02
1.18
o.69
QSO
17
.6
o.402
25.84
./
0906+01
1.20
0.23
QSO
17.6
1.021
26.54
I
0949+00
230
1.53
1.35
-
(
o.
5)
26.26
I
1039+02
1.66
0.82
(
o.
5)
26.20
I
1055+01
3.02
o.oo
QSO
18.7
o.888
26.76
I
1059-01
249
1.34
1.10
(
o.
5)
26.16
I
1138+01
1.57
o.
72
(
o.5)
26.16
I
1148-00
2.56
o.39
QSO
17.6
1.982
27
.45
I
1215+03
1.21
1.33
E,D
18.0
0.076
24.40
I
1226+02
273
43.4
o.04
QSO
13
.o
0.158
26.54
I
122
9-02
1.33
o.45
QSO
17.1
1.043
26.66
I
133o+02
287.1
1.91
o.50
N
18.9
0.2156
25.48
I
2044-02
1.38
0.60
G
20.5
(
o.
35)
25.
77
I
2131-021
1.91
-0.15
QSO
19.1
0.557
26.18
I
2134+004
7.59
-1.02
QSO
17.7
1.935
27.25
./
22lo+01
1.
79
0.79
(
o.
5)
26.23
I
2216-03
1.04
-0.30
QSO
16.2
0.901
26.23
I
2221-02
445
3.46
0.81
N
17.3
o.
0568
24.59
I
2313+03
459
2.38
o.94
N
18.2
o.
2205
25.63
I
2324-02
1.56
0.75
EO
18.9
(0.17)
25.20
I
2349-01
1.01
0.74
N
17.1
0.174
25.
04
I
*H
0
=
50
km
s-l
Mpc-
1
;
(l
=
1.0.
t
SS
=
'steep-spectrum';
NSS
=
'not-steep-spectrum',
or
'flat-spectrum'.
namely
those
with
single
spectral
peaks
in
the
frequency
range
200-2000
MHz.
Ignoring
this
detail,
we
constructed
the
separate
counts
for
SS
and
NSS
sources,
using
the
sources
from
the
survey
for
which
a
(2700-5000
MHz)
exists,
and
adopting
the
criterion
that
the
source
is
classified
as
SS
if
a>
0.5
and
NSS
if
a.;;;;
0.5.
The
two
counts
(Table
2)
were
constructed
from
the
zones
of
the
survey
with
differing
completeness
limits
at
2700
MHz,
the
total
area
being
much
smaller
for
the
fainter
sources.
Bolton,
Savage
&
Wright
(1979)
give
references
for
the
15
parts
of
the
survey
now
completed.
The
faint
end
of
the
total
count
(Fig.
1)
is defined
by
statistical
(P(D))
methods
(Wall
&
©
Royal
Astronomical
Society
• Provided
by
the
NASA
Astrophysics
Data
System