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Global Preventive Feedback of Powerful Radio
Jets on Galaxy Formation
Renyue Cena,1,2
This manuscript was compiled on August 23, 2024
Firmly anchored on observational data, giant radio lobes from massive galaxies hosting
supermassive black holes can exert a major negative feedback effect, by endowing the
intergalactic gas with significant magnetic pressure hence retarding or preventing gas
accretion onto less massive halos in the vicinity. Since massive galaxies that are largely
responsible for producing the giant radio lobes, this effect is expected to be stronger in more
overdense large-scale environments, such as proto-clusters, than in underdense regions, such
as voids. We show that by redshift
z
= 2 halos with masses up to (10
11−12,
10
12−13
)
M⊙
are significantly hindered from accreting gas due to this effect for radio bubble volume filling
fraction of (1
.
0
,
0
.
2), respectively. Since the vast majority of the stars in the universe at
z <
2
−
3form precisely in those halos, this negative feedback process is likely one major
culprit for causing the global downturn in star formation in the universe since. It also provides
a natural explanation for the rather sudden flattening of the slope of the galaxy rest-frame UV
luminosity function around
z∼
2. A cross-correlation between proto-clusters and Faraday
rotation measures may test the predicted magnetic field. Inclusion of this external feedback
process in the next generation of cosmological simulations may be imperative.
Cosmology |large-scale structure of universe |intergalactic medium |observations |
C
osmological hydrodynamic simulations have entered its fourth decade since the
pioneering works in the late eighties and early nineties of the last century (e.g.,
1
–
4
).
In the first two decades, the focus was largely on the evolution of the intergalactic medium,
regions significantly removed from star formation in galaxies, with a number of notable
successes, including the finding of the fluctuating nonlinear Gunn-Peterson cosmological
density field as the origin of the Lyman alpha forest (
5
–
8
), a successful account of the
missing baryons in the universe at zero redshift (
9
,
10
) and the discovery of two modes of
gas accretion into galaxies (
11
). In the most recent two decades, driven in part by the
availability of large computing power, we witnessed large-scale cosmological simulations
with increasingly high numerical resolutions and ever more sophisticated implementations
for feedback processes from stellar evolution and growth of supermassive black holes
(e.g.,
12
–
23
). On the feedback processes from AGN, the mainstream implementations of
various modes (QSO or radio mode) can be classified as internal feedback processes by
pushing entered gas away from galaxies.
In the article we put forth an important AGN energy source,
namely, the powerful FR II radio jets, for regulating the thermo-
dynamic state of the cosmic gas, especially in the low-density
intergalactic medium (IGM). FR II jets are observed to transport
a large amount of energy to megaparsec scale, deep into the
low-density IGM (e.g.,
24
). Preferentially affecting low-density gas
is economical energetically by maximizing entropy generation.
In contrast to internal feedback processes currently employed
in cosmological simulations, this new feedback process is of
global, collective and multi-generational nature, where radio
lobes generated by earlier galaxies will retard, reduce or prevent
subsequent gas accretion onto galaxies in the neighborhood.
Suppression of Galactic Gas Accretion due to Inter-
galactic Magnetic Field
We consider the simplest case that powerful AGN radio jets send
magnetic fields permeating the entire universe but will discuss
later if filling fraction is less than unity, the likely case. Let us
denote the mean magnetic field of the universe due to AGN jets
as
Bi
at certain redshift. Then under the adiabatic assumption,
Significance Statement
Negative feedback processes from
the growth of supermassive black
holes are believed to play a cen-
tral role to the formation of galax-
ies. Internal feedback processes by
essentially driving gas away from
galaxies have been widely used in
cosmological simulations. In this
article, we investigate a new type of
negative feedback process, termed
external negative feedback, due to
powerful radio jets by energizing
intergalactic medium. The inter-
galactic medium endowed with sig-
nificant magnetic fields is retarded
or prevented from entering subse-
quent halos. This external feedback
process is in a sense pro-active
and preventative, in contrast to the
case of interval feedback processes.
Inclusion of this external feedback
process in the next generation of
cosmological simulations may be
imperative.
Author affiliations:
a
Center for Cosmology and Compu-
tational Astrophysics, Institute for Advanced Study in
Physics, and Institute of Astronomy, School of Physics,
Zhejiang University, Hangzhou 310027, China; renyue-
cen@zju.edu.cn
Please provide details of author contributions here.
The authors declare no conflict of interest.
1
Author contributions: R.C. designed, performed
research and wrote the paper.
2
To whom correspondence should be addressed. E-
mail: renyuecen@zju.edu.cn
www.pnas.org/cgi/doi/10.1073/pnas.XXXXXXXXXX PNAS | August 23, 2024 | vol. XXX | no. XX | 1–7
arXiv:2408.12040v1 [astro-ph.GA] 21 Aug 2024
-2 -1.5 -1 -0.5 0
log Bi ( Gauss)
9
10
11
12
13
14
15
z=2
z=3
Fig. 1. shows the magnetic Jeans mass,
MB
, as a function of the magnetic field in
the mean density of the universe,
Bi
, at
z
= 2 (black solid curve) and
z
= 3 (red
dashed curve).
when a small gas parcel is eventually brought to the virial surface
of a halo with a density equal to the virial overdensity
δv
, the
magnetic field would have increased to Bv,
Bv=Biδ2/3
v.[1]
Can this gas parcel enter this virial radius? To answer this
question, let us make a most conservative assumption that this
gas has completely lost its thermal pressure when arriving at the
virial surface of the halo. Under a likely valid assumption that it is
not self-gravitating (because otherwise it would have entered
a halo already), the magnetic pressure force is dynamically
analagous to thermal pressure force in terms of retarding the
gas from accreting onto the halo. When the magnetic pressure
force exceeds gravitational force due to the dark matter halo at the
virial radius, or equivalently, the magnetic temperature, defined
as
TB≡B2
v/
8
πnvkB
, where
nv
is gas number density at the
virial radius and
kB
the Boltzmann’s constant, exceeds the virial
temperature of the halo, the gas parcel will be prevented from
entering the halo. This statement can be expressed in terms of a
threshold Alfv´
en velocity vA=pB2
v/4πρv(where ρv=mpnv)
vA=√2σv,[2]
where σvis the 1-d velocity dispersion of the halo.
Combining Eq (1) and (2), along with the relation between halo
mass and
σv
, we obtain the results shown in Figure (1). A more
precise formulation may be quantified with detailed simulations, in
a way similar to the Jeans filtering effect demonstrated insightfully
in (
25
) and is reserved for a future study. Nevertheless, we
see that, if an initial mean field
Bi
of order 0
.
1
µ
G is reached,
gas accretion onto halos as massive as
Mh∼
10
12 M⊙
will be
significantly affected. In the next section, we examine whether
such a field may be injected into the intergalactic medium by
powerful radio jets.
Intergalactic Magnetic Field Due to Powerful Radio Jets
To estimate the energetics of powerful radio jets, we introduce
a few variables. We denote the global ratio of supermassive
black hole (SMBH) mass to stellar mass as
β
adopting 0
.
002
-2.5 -2 -1.5 -1 -0.5 0
log J
10
11
12
13
14
z=2, f=0.2
z=3, f=0.2
z=2, f=1.0
z=3, f=1.0
PDF( J) of FR II
Fig. 2. shows the magnetic Jeans mass,
MB
, as a function of
ηJ
, the fraction of
the SMBH rest mass energy released in the form of powerful radio jets in radio-loud
galaxies, at
z
= 2 (dot-dashed lines) and
z
= 3 (dashed lines). Two cases of filling
factor
f
are shown: the two red lines are for
f
= 0
.
2, whereas the two black lines
are for
f
= 1
.
0. Other relevant parameters are as follows. The observed mean
stellar mass density of 5
.
7
×
10
7M⊙Mpc−3
and 3
.
6
×
10
7M⊙Mpc−3
at
z
= 2 and
z
= 3, respectively, are from (
28
). For the fraction of all relevant galaxies
classified as radio loud galaxies,
ηR
= 0
.
2is adopted (
29
). The fraction of original
jet magnetic energy remaining in the form of magnetic energy in the final giant radio
bubbles is assumed to be
ηB
= 7
.
5%, estimated from simulations. Also shown as
solid blue curve is the observed probability density distributions of
ηJ
for the classic
FR II sources (30).
measured locally (e.g.,
26
), although there is preliminary evidence
that this ratio may increase with increasing redshift (e.g.,
27
).
We denote the fraction of SMBH rest mass energy (
MSMBHc2
)
released in the form of powerful radio jets as
ηJ
for the radio loud
galaxy population, and
ηR
as the fraction of all relevant galaxies
classified as radio loud galaxies. To obtain the fraction of jet
energy in the form of magnetic energy,
ηB
, we have performed
MHD simulations of magnetic energy powered explosion and find
that for a point injection of 10
61
erg magnetic energy,
ηB
retains
a value of 15%(0
.
5
Mpc/RB
)at late stages, where
RB
is the
bubble radius. The universal stellar mass density formed by a
redshift of interest in units of the total baryonic density is denoted
as
η∗
. With these variables and assuming that the radio jets send
magnetic fields to large distances to fill a volume fraction of the
universe, f, we obtain the mean magnetic field energy density
B2
i
8π= 3 ×10−4ηM
0.002 ηB
0.15 ηR
0.2 f
0.2−1
η∗ηJc2ρb(z)
= 2.8×10−15(µG)2ηM
0.002 ηB
0.15 ηR
0.2 f
0.2−1
η∗
0.018 ηJ
0.05 1 + z
33
,
[3]
where
c
is the speed of light,
ρb
(
z
)the mean baryonic density at
the redshift in question.
Let us now go through the numerical values of various vari-
ables, based solely on observational data. We adopt the universal
stellar density of (5
.
7
×
10
7M⊙Mpc−3
,3
.
6
×
10
7M⊙Mpc−3
) (in
comoving volume) at
z
= (2
,
3), respectively, from (
28
) converted
to values corresponding to the Salpeter initial mass function,
yielding
η∗
= (0
.
018
,
0
.
011). From Figure 10 of (
29
) we find
radio loud fraction
ηR
= (0
.
19
,
0
.
24) at
z
= (3
,
2), respectively;
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given the uncertainties involved, we shall adopt a single value of
ηR
= 0
.
2, which is a good approximation for the entire redshift
range of
z
= 0
−
4. The distribution of
ηJ
for the classic FR II
sources (shown as blue solid curve) is from (
30
). If
f
= 1, we find
Bi
= 0
.
12
µ
G at
z
= 2, which is the mean magnetic field strength
over the entire universe.
We express the threshold halo mass
MB
due to magnetic
pressure, as a function of
ηJ
, shown in Figure (2), where
ηB
=
0
.
075 is adopted. The observed distribution of
ηJ
for the FR
II sources shown as the blue solid curve has the
±
1
σ
range
indicated by the two vertical dotted blue lines.
MB
values at
the two crossing points between an inclined line and the two
vertical dotted blue lines indicate the
±
1
σ
range of
MB
for that
line. We find
±
1
σ
range of [2
.
2
×
10
10,
4
.
0
×
10
11
]
M⊙
and [1
.
0
×
10
11,
1
.
3
×
10
12
]
M⊙
at
z
= 3 and
z
= 2, respectively, assuming
f
= 1
.
0;
±
1
σ
range becomes [3
.
5
×
10
11,
4
.
5
×
10
12
]
M⊙
and
[1
.
1
×
10
12,
1
.
4
×
10
13
]
M⊙
at
z
= 3 and
z
= 2, respectively, if
f= 0.2.
Discussion and Predictions
We have shown that, with a set of parameters anchored firmly
on observational data, the magnetic pressure of accreting gas
infused with magnetic fields originating from giant radio lobes
exerts significant retarding effects on gas accretion into halos as
massive as 10
12−12.5M⊙
. Here we discuss possible other effects
and tests of this physical process.
Effect of Parker Instability. For a dark matter halo the density
profile near the virial radius
rv
has a local slope
α∼ −
2
.
3.
Then, it can be shown that the minimum wavelength of the
planar undular instability at the virial radius
rv
is
λmin
=
4
p2/(−1−α)
(
vA/√2σv
)
rv
= 5
.
0(
vA/√2σv
)
rv
. Since
vA/√2σv
(see Eq 2) is about unity or larger for the magnetic
suppression to be significant, we see that the perturbation with
the minimal wavelength, which is also the fastest growing mode,
grows on a time scale of order five times the dynamic time of
the halo at the virial radius. Hence, the induced RT instability, if
it exists, will unlikely be very important, since the relevant time
scale close a halo is its dynamical time. In other words, if the
gas eventually becomes unstable, the long waiting time of five
dynamical times is already a significant retarding effect. Moreover,
λmin
is much larger than
rv
and in fact larger than one half of the
circumference, such a planar undular instability then would not
exist in the first place. Thus, we expect the RT instability due to
magnetic buoyancy is unlikely to significantly alter the proposed
magnetic pressure based gas accretion suppression onto eligible
halos.
Magnetic Reconnection. In our model, the initial magnetic field
that we focus on is on large scales, of order 1Mpc, larger than
affected halos of virial radius of 300kpc or smaller. Hence the
magnetic field reaching a halo is on the scale of the halo size
or larger. Given the normalized reconnection rate of order 0.1,
inferred from observations and from theoretical calculations, it
implies that the magnetic reconnection time is about ten times
the system time (i.e., halo dynamical time), which is on the order
of Hubble time at any redshift. Moreover, when the gas is en
route to the halo, the reconnection time scale is still longer. This
indicates that magnetic reconnection, which may take place to
perhaps cancel some of the smaller scale stressed magnetic field
on relatively shorter time scales, is unlikely to reduce significantly
the overall magnetic energetics of gas endowed with large-scale
magnetic field with vA=√2σor larger.
Volume Filling Fraction of Radio Bubbles. We now return to
the issue of volume filling fraction of the magnetic bubbles,
f
.
We can only give a very rough estimate given uncertainties.
Let us assume that the radio AGNs are dominated by massive
galaxies, based on available observational evidence (e.g.,
30
). To
facilitate an estimation, let us assume that 0
.
5
L∗
galaxies and
above are responsible for making the giant radio lobes; the mean
separation of 0
.
5
L∗
galaxies is about 4
h−1
Mpc. For a Schechter
function with a low-end slope of
−
1, one half of the galaxy mass is
contributed by galaxies above 0
.
5
L∗
. Thus, if radio bubbles each
have a mean radius of 0
.
5Mpc for the galaxies considered, we
have
f
= 2
×
4
π
(0
.
5
proper Mpc
)
3/
3
/
(4
h−1
(1 +
z
)
−3Mpc
)
3∼
14% at = 2, assuming that there is one occurrence of radio bubble
event per 0
.
5
L∗
galaxy. Adopting the peak value of
ηJ
shown in
Figure (2), and assuming the average SMBH mass of the radio
lobe launching AGNs is 10
8M⊙
, corresponding to
L∗
galaxies
(
31
), we obtain the number of pairs of radio lobes per galaxy
Np
= 0
.
9
E−1
60
, where
E60
=
ER/
10
60
erg with
ER
being the
mean energy of each radio lobe; the observed radio lobe total
energy is in the range of a few times 10
59 −
10
61
erg (e.g.,
32
,
33
).
It thus seems that the overall volume filling fraction
f
may fall
in the range of order 10-20 percent. In terms of galaxies, these
regions around radio jet sources are likely highly biased. But the
fraction of halos contained in these regions are likely substantially
higher than
f
. Therefore, we expect that the suppression effect
due to magnetic pressure of accretion onto relevant halos will
be substantial. More importantly, the suppression effect will
be spatially dependent, potentially giving rise to a new kind of
modulation of galaxy formation across different environments.
On the Global Downturn of Star Formation below
z
= 2
−
3.
The observation that this feedback effect strength due to magnetic
pressure becomes strong enough by
z
= 2
−
3to have crossed
a halo mass threshold of about
MB∼
10
12 −
10
12.5M⊙
is
significant. This threshold halo mass is similar to the halo mass
which separates cold and hot accretion modes (
11
). This implies
that, while the halos more massive than about
MB∼
10
12.5M⊙
will be self-quenched due to lack of cooling, the smaller halos
where cold accretion mode would otherwise operate are now
hindered from accreting gas due to magnetic pressure. Conse-
quently, star formation across the entire halo mass spectrum is
now suppressed. This may be a major culprit causing the global
downturn of star formation in the universe from
z
= 2
−
3to the
present.
At this point, it is perhaps useful to clarify one point. This
external, preventive feedback proposed here is not exclusive and
does not rule out any possible internal feedback from AGN or
from supernovae, both of which are undoubtedly present and
important. In fact, in galaxies with sufficient cooling flows, internal
AGN feedback has been demonstrated by many authors (
34
–
36
)
to be able to counter or delay cooling of the hot gaseous halo to
significantly reduce star formation.
On the Flattening of Schechter Luminosity Function below
z
= 2
−
3.Another significant point to note is the rather prompt
change in the observed slope of the galaxy rest-frame UV
luminosity function around
z
= 2
−
3, from
α
=
−
1
.
94 at
z
= 2
−
3
to
α
=
−
1
.
56 at
z
= 1
.
0
−
1
.
6(
37
). The traditional conjecture
that supernovae exert negative feedback on low mass galaxies
Cen PNAS | August 23, 2024 | vol. XXX | no. XX | 3
would be in stark contradiction to this observed change in galaxy
luminosity function slope. The argument goes as follows. Star
formation is the most vigorous at
z >
2
−
3(
38
). Therefore,
if supernova feedback were responsible for suppressing star
formation in progressively lower mass galaxies, the slope of
the galaxy luminosity function at
z >
2
−
3would have been
flatter than at lower redshift, when star formation is less vigorous
and hence suppressing effect on low-mass galaxies relatively
less severe. The negative effect due to magnetic pressure
proposed here, however, provides a natural explanation in timing.
Gas accretion suppression due to magnetic pressure becomes
important only at
z <
2or so and the suppression is increasingly
more severe on smaller mass halos, leading to a flattening of the
galaxy luminosity function at
z <
2. As to how flattened the slope
is due to this effect can not be easily estimated without detailed
cosmological simulations.
An Argument For Preventive Feedback Processes. Observa-
tions show a peak value of about 20% of the global baryon to total
mass ratio around galaxies of halo mass
∼
10
12
in the SDSS
galaxy sample (e.g.,
39
). This is tentalizing. This is perhaps
a direct piece of evidence against interval feedback as being
the primary actor for driving gas away, simply because there is
not an amount of gas that corresponds to the global ratio to be
driven away in the first place, at least at relatively low redshift. In
other words, there is no widespread evidence of the existence
of galaxies whose baryon to total mass ratios are close to what
the global ratio would indicate. If our model bears the truth, one
expects that such a "deficiency" of baryons should persist to
z∼
2and then start to shift to more baryon rich galaxies at
higher redshift, but the shift will be halo mass dependent with
lower mass halos remaining deficient longer. Presently, most
observational data at high redshift are presented as the gas to
stellar mass ratio as a function of galaxy stellar mass (e.g., 40).
Seeding Magnetic Field in Galaxies and Damped Lyman
Alpha Systems. If a significant volume of the intergalactic space
can attain a magnetic field of a strength of 0
.
1
µ
G or so, observed
large magnetic field in some damped Lyman alpha systems
at moderate redshift may be accounted for; for example, a
simple contraction from the mean intergalactic gas density of
∼
10
−5cm−3
to a typical interstellar medium density of 1
cm−3
would amplify a 0
.
1
µ
G field to an amplitude of 200
µ
G, readily
explaining an amplitude of 84
µ
G in a galaxy at
z
= 0
.
7(
41
).
Simulations have shown that damped Lyman alpha systems
at moderate redshift of
z
= 2
−
3are largely caused by
circumgalactic filaments and sheets with a typical volumetric
density in the range of 10
−3−
10
−1cm−3
(
42
). Contraction
alone from the mean intergalactic gas density of
∼
10
−5cm−3
would result in a field in the range 2
−
50
µ
G for DLAs, consistent
with the observed values of typically a few micro Gauss (43).
Magnetic Field in the WHIM and Clusters. In the preceding
subsection, we discuss the overall magnetic field in the IGM that
a Faraday rotation measure based on line-of-sight integrals may
yield. An estimate of the magnetic field in filaments, i.e., the
warm-hot intergalactic medium (WHIM) at zero redshift (
9
). which
make up a large portion of the missing baryons, may be made.
Assuming that the magnetic field has largely been seeded due
to the peak AGN activities at
z
= 2, then the magnetic field in
filaments of density neat z= 0 is
BWHIM(ne) = 0.66µG¯
B
0.1µGne
10−4cm−32/3
,[4]
assuming no further dynamo or other amplification. With a 0
.
1
−
1
µ
Gmagnetic field expected in WHIM filaments, if converging
shocks compressing and forming filaments can accelerate or re-
energize electrons, filaments may be detected in synchrotron
radiation by the next generation radio facilities, such as SKA.
Current observations have already begun to detect such emission
from filaments even assuming magnetic fields weaker than our
estimates (e.g.,
44
), The expected field strength is roughly
consistent with synchrotron radiation observations, estimated
based on energy equipartition assumption, of the magnetic field
in local filaments (e.g., 45).
In the cores of clusters of density
ne∼
10
−3−
10
−2cm−3
a field strength of several microGauss or tens of microGauss is
expected, even in the absence of any further amplification. This
is in line with observations (e.g.,
46
). What is perhaps more
significant to note is that, if the cluster center is anchored by a
field strength of several microGauss or tens of microGauss, a field
strength of several 0
.
1
µ
Gto several microGauss may exist in the
outskirts of clusters of galaxies in our model, which appears to be
observed (e.g., 46,47).
Cross-Correlations Between Faraday Rotation Measure and
Others. In our model, we expect that magnetic field injected
into the IGM is most concentrated in proto-clusters. As such,
a significant cross-correlation signal is expected between proto-
clusters and Faraday RM along a same line of sight. To enhance
the signal of this measure, one may denominate the cross-
correlation between proto-clusters and RM along the lines of
sight through proto-cluster by the cross-correlation between proto-
clusters and RM along random lines of sight. This may allow
one to pick out the line-of-signt magnetic field strength in the
proto-clusters fairly easily.
In addition to cross-correlating proto-clusters with Faraday RM
to pick out the magnetic field strength in the proto-clusters, one
may also compute the cross-correlation between Lyman alpha
forest transmitted flux and RM. The premise behind this method
is that the Lyman forest transmission in proto-clusters of galaxies
is substantially different from the Lyman forest transmission in
typical, average lines of sights. This method shall yield RM
measure as a function of Lyman alpha transmission flux. As
long as there is a difference in Lyman alpha transmission flux
between proto-cluster regions and non-proto-cluster regions, one
may be able to teased out RM in proto-clusters in the future
facilitated by SKA observations.
Deposition of Thermal Energy in IGM due to Expanding Lobe
Shock Heating. The amount of thermal energy deposited in the
IGM or proto-cluster regions or whereever can be calculated. We
consider two regimes. If the cooling time of the heated postshock
regions due to the expanding lobe is longer than the Hubble time
at the redshift in question, then all thermalized energy is counted.
On the other hand, if the cooling time of the heated postshock
regions is shorter than the Hubble time, the apparent amount of
all thermalized energy will be reduced by the ratio of the former
to the latter, when one does a time averaging. Assuming zero
metallicity for the ambient gas into which the radio lobe driven
shocks are propagating, the results are shown in Figure (3), where
4| www.pnas.org/cgi/doi/10.1073/pnas.XXXXXXXXXX Cen
10 11 12 13 14
4
4.5
5
5.5
6
7
log <T> (K)
z=2 if all IGM heated
z=2 if only overdensity 5.5 regions heated
obs upper limit if bias=1 at z=2 (Chen+2023)
obs upper limit if bias=5.5 at z=2 (Chen+2023)
Fig. 3. shows the expected mean temperature per baryon in the entire universe as
a function of the magnetic Jeans mass
MB
at redshift
z
= 2, for two cases, one
assuming that the entire IGM is heated (black solid line) and the other assuming
that only regions with overdensity of 5.5 is heated (red dashed line). Also shown
are upper limits observationally derived at
z
= 2 (
48
) for two cases, one assuming
that the entire IGM is heated with a bias factor equal to unity (blue arrow), and the
other assuming that only regions that have turned around from universal expansion
are heated with a bias factor equal to 5.5 (red arrow). In shock propagation, zero
metallicity for the ambient gas is assumed.
the amount of energy shown in the y axis is expressed as the
mean temperature of the IGM as a function of the magnetic Jeans
mass
MB
. Two cases are shown, one assuming that the entire
IGM is heated with a bias factor equal to unity (black solid line),
and the other assuming that only regions that have turned around
from universal expansion are heated with a bias factor equal to
5.5 (red dashed line). In the latter case, the mean temperature is
still averaged over all gas in the universe. Also shown are upper
limits observationally derived at
z
= 2 (
48
) for two cases, one
assuming that the entire IGM is heated with a bias factor equal
to unity (blue arrow), the other assuming that only regions that
have turned around from universal expansion are heated with a
bias factor equal to 5.5 (red arrow), because the observationally
derived upper limits depend on the bias factor of the heated region.
We see that, so long as
MB≤
10
12 −
10
12.5M⊙
, the thermal
energy injected by expanding giant radio lobes is consistent with
current observational limit.
Magnetic Field At Virial Radius as a function of Halo Mass.
For halos less massive than the magnetic Jeans mass
MB
, we
expect that accreting gas will be prevented from entering the virial
radius. As a result, the field may accumulate outside the virial
radius of such a halo. Consequently, we expect that the magnetic
field strength at the virial radius (assuming overdensity of 100)
will be just at the threshold level for each halo at lower redshift at
Bh(σv) = p600πΩBρc,0(1 + z)3σv,[5]
where
σv
is the 1-d velocity dispersion of the halo,
ρc
is the critical
density of the universe at
z
= 0, and Ω
B
baryon density. This
prediction is potentially testable by SKA in the future.
Suggestion on How to Implement This MHD Effect. A simple
version of how to implement this MHD effect may be described
as follows, although more sophisticated implementation may be
devised. First, one runs radio jet expansion simulation not in a
cosmological simulation box but in an isolated box before hand to
produce a standard mold of magnetic field structures in a bubble of
size 1 proper Mpc, to be inserted into the cosmological simulation.
One may inject a prescribed amount of magnetic energy into
the center over 100Myr to mimic FR II sources. Second, one
runs a cosmological MHD simulation of a sufficiently large box
to contain one cluster of galaxies by
z
= 0. One then retraces
back to the starting redshift to identify a region that contains
the proto-cluster of the cluster found at
z
= 0. Then, one re-
runs the simulation with static meshrefinement in the zoom-in
region that contain the proto-cluster from the starting redshift. At
z
= 2, one adds a pair of radio bubbles of radius 1 proper Mpc
for each of the masssive galaxies at a distance of 1Mpc from that
galaxy in the proto-cluster using the mold in the first step with
appropriate adjustments in velocity and density field based on the
local values in the cosmological simulation box, and then re-starts
the simulation from z= 2 to run to z= 0.
Conclusions
Utilizing a set of parameters fully anchored on observational data,
we show that giant radio lobes from supermassive black holes
residing in massive galaxies can inject enough magnetic energy
so as to exert a major negative feedback effect, by significantly
retarding or preventing gas accretion onto halos as massive as
MB
= 10
13 M⊙
by
z
= 2, depending on the volume filling fraction
of the radio bubbles in the universe, thanks to the magnetic
pressure of the accreting gas. The accretion suppression effect
increases with decreasing halo mass. We shall call
MB
the
magnetic Jeans mass.
The implication is profound. That is, by
z
= 2
−
3, halos where
cold accretion mode would otherwise operate are now significantly
prevented from accreting gas due to magnetic pressure. This
negative feedback process may be the culprit for causing the
global downturn in star formation in the universe from
z
= 2
−
3
to the present. This feedback mechanism also provides a natural
explanation for the rather prompt change in the slope of the galaxy
rest-frame UV luminosity function around
z
= 2
−
3, from
α
=
−1.94 at z= 2.2−3to α=−1.56 at z= 1.0−1.6(37).
Finally, a number of ramifications and predictions due to this
process are given. First, magnetic fields for a host of systems,
such as galaxies and damped Lyman alpha systems at moderate
redshift, and extragalactic filaments and clusters of galaxies low
redshift, may be accounted for. Second, the thermal energy
injected by shocks due to supersonically expanding magnetic
bubbles is significant but in agreement with current observational
upper limits. Third, cross-correlations between proto-clusters and
Faraday rotation measures should be able to test the predicted
magnetic field directly. Cross-correlations between Faraday
rotation measure and Lyman alpha forest flux spectrum can
provide additional information on this.
Materials and Methods
A combination of empirical observational data and bubble evolution
analytics is used to quantify a potentially significant preventive effect on
the dynamics of intergalactic gas accretion onto dark matter halos. We
make use of the observed abundance of radio galaxies, the observed
fractional energy released in the form of large radio jets in terms of
supermassive black rest mass energy and the total amount of mass
in supermassive black holes in units of the stellar mass formed in the
Cen PNAS | August 23, 2024 | vol. XXX | no. XX | 5
universe. We deduce the total amount of magnetic energy in giant radio
lobes based on these observational data, in combination with results
obtained based on MHD radio bubble expansion simulations that estimate
the surviving magnetic energy when realistic bubbles reach a radius of
order 1Mpc. Combining these results, we estimate the magnetic pressure
of gas accreting into dark matter halos and show that it could provide
a significant hinderance for gas accretion, thus potentially preventing or
slowing or retarding gas accretion onto dark matter halos as massive as
10
12 M⊙
at
z <
2
−
3. Uncertainties and spatial variations of this effect
is discussed, depending the volume filling factor of the radio bubbles.
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