Planetary and Space Science 149 (2017) 45–55

Contents lists available at ScienceDirect

Planetary and Space Sciencejournal homepage: www.elsevier.com/locate/pss

Dust evolution with active galactic nucleus feedback in elliptical galaxies
Hiroyuki Hirashita a, *, Takaya Nozawa b
ab

Institute of Astronomy and Astrophysics, Academia Sinica, P.O. Box 23-141, Taipei 10617, Taiwan
National Astronomical Observatory of Japan, Mitaka, Tokyo 181-8588, JapanA R T I C L E I N F O

A B S T R A C T

Keywords:
Active galactic nuclei
Dust
Elliptical galaxies
Galaxy evolution
Interstellar medium

We have recently suggested that dust growth in the cold gas phase dominates the dust abundance in ellipticalgalaxies while dust is efﬁciently destroyed in the hot X-ray emitting plasma (hot gas). In order to understand thedust evolution in elliptical galaxies, we construct a simple model that includes dust growth in the cold gas anddust destruction in the hot gas. We also take into account the effect of mass exchange between these two gas
components induced by active galactic nucleus (AGN) feedback. We survey reasonable ranges of the relevant
parameters in the model and ﬁnd that AGN feedback cycles actually produce a variety in cold gas mass and dustto-gas ratio. By comparing with an observational sample of nearby elliptical galaxies, we ﬁnd that, although thedust-to-gas ratio varies by an order of magnitude in our model, the entire range of the observed dust-to-gas ratios
is difﬁcult to be reproduced under a single parameter set. Variation of the dust growth efﬁciency is the mostprobable solution to explain the large variety in dust-to-gas ratio of the observational sample. Therefore, dust
growth can play a central role in creating the variation in dust-to-gas ratio through the AGN feedback cycle andthrough the variation in dust growth efﬁciency.

1. Introduction

by supernovae. However, dust destruction by sputtering in the X-ray
emitting plasma is so efﬁcient that the observed dust mass cannot be
explained by the balance between the supply from AGB stars and thedestruction (e.g., Patil et al., 2007). Thus, some authors argue that the
dust existing in elliptical galaxies is possibly injected from outside via themerging or accretion of external galaxies (Forbes, 1991; Temi et al.,
2004; Fujita et al., 2013). The lack of correlation between dust FIR luminosity and stellar luminosity is also taken as evidence of external
origin of dust (Temi et al., 2007); however, this argument may not hold if
dust is processed by mechanisms unrelated to stars.
Recently, Hirashita et al. (2015) have proposed that the existence ofdust in elliptical galaxies can be explained by dust growth by the accretion of gas phase metals in the cold interstellar medium (ISM). They alsosuggest that the presence of dust growth also explains the extinction
curves observed in elliptical galaxies. The dust-to-gas ratio could become
as high as ≳103 by accretion, explaining the high dust abundance insome elliptical galaxies. However, dust growth in the cold gas has notbeen considered as a major source of dust in the context of dust evolution
in elliptical galaxies. Dust growth has already been noted as a majormechanism of dust mass increase in a wide context of galaxy evolution(e.g., Dwek, 1998; Hirashita, 1999; Inoue, 2003; Zhukovska et al., 2008,2016; Valiante et al., 2011; Mattsson and Andersen, 2012; Mancini et al.,In the nearby Universe, elliptical galaxies are known to have less gas,dust, and ongoing star formation activity than spiral galaxies. Yet, they
still have some amount of interstellar gas in the form of hot X-ray-emitting halo gas (e.g., O’Sullivan et al., 2001) and cold gas (e.g., Wiklind
et al., 1995). Moreover, dust is detected for a signiﬁcant fraction of
elliptical galaxies by optical extinction (e.g., Goudfrooij et al., 1994; van
Dokkum and Franx, 1995; Ferrari et al., 1999; Tran et al., 2001) or
far-infrared (FIR) emission (e.g., Knapp et al., 1989; Smith et al., 2012;
di Serego Alighieri et al., 2013). Dust mass is estimated from thereddening in the optical or from FIR dust emission, and ranges from 
104 to  107 M⊙ (e.g., Goudfrooij et al., 1994; Leeuw et al., 2004). Since
the existence of dust could affect the cooling and chemical processes(Dwek, 1987; Fabian et al., 1994; Voit and Donahue, 1995; Seok et al.,2015; Hirashita et al., 2015), the understanding of the origin and evolution of dust in elliptical galaxies is important in clarifying
their evolution.
Because the stellar population is dominated by old stars whose ages
are comparable to the cosmic age, the dust in elliptical galaxies is predominantly supplied by asymptotic giant branch (AGB) stars rather than

* Corresponding author.
E-mail address: hirashita@asiaa.sinica.edu.tw (H. Hirashita).
https://doi.org/10.1016/j.pss.2017.01.009
Received 24 November 2016; Received in revised form 19 January 2017; Accepted 23 January 2017
Available online 25 January 20170032-0633/© 2017 Elsevier Ltd. All rights reserved.

H. Hirashita, T. Nozawa

Planetary and Space Science 149 (2017) 45–55

galaxy. For dust sources, in addition to AGB stars considered in previous
studies (Mathews and Brighenti, 2003; Patil et al., 2007), we also
consider dust supply from the cold gas where dust grows by the accretionof gas-phase metals. The dust in the cold gas is injected into the hot gas by
AGN feedback together with the cold gas. The dust injected into the hot
gas is destroyed by sputtering. The hot component ð 107 KÞ is the gas
whose temperature is comparable to the virial temperature determinedby the global gravitational potential of the elliptical galaxy while the cold
component is cold and dense enough to host dust growth (≲100 K; Hirashita et al., 2015). To make the model as simple as possible, we treat
each gas component as a single zone and consider the mass exchange
between the two components. Dust growth and destruction are treatedconsistently with the evolution of each gas component as
explained below.

2015; Popping et al., 2016; Hou et al., 2016), and some experimental
studies have also shown that dust grains could grow by accreting thegas-phase metals (Rouille et al., 2014; but see Ferrara et al., 2016). Thus,
constructing a dust evolution model that includes this dust growthmechanism would contribute to the understanding of dust evolution in
elliptical galaxies.
The overall evolution of dust should be considered in relation to thegas evolution, especially because gas and dust are usually dynamicallycoupled on galactic scales. Recent studies have proposed that the gas
cooling in galaxies is strongly regulated by the energy input from active
galactic nuclei (AGNs). The energy input from AGN winds (Silk and Rees,
1998; Fabian, 1999; King, 2005) or AGN jets (Wagner and Bicknell,
2011; Mukherjee et al., 2016) prevents cooling ﬂows from occurring
and/or makes cold gas evaporate (see also Ciotti and Ostriker, 2001;
Fabian, 2012). These kinds of energy input are called AGN feedback, andare considered to play an important role in galaxy formation and evolution (Croton et al., 2006; Booth and Schaye, 2009).
Temi et al. (2007) showed the existence of a dust emission component
extended over 5–10 kpc in elliptical galaxies using the Spitzer 70 µm banddata. They suggest that this cold dust component was originally contained in the cold gas, which was then heated by AGN feedback andeventually mixed with the hot gas. In their scenario, the heated gas istransported into the hot gas by buoyant force, and the time-scale of thetransport is around 107 yr. Kaneda et al. (2011) also showed in an
elliptical galaxy (NGC 4125) a dust emission component whose extension
is similar to the distribution of the hot X-ray emitting halo. The
multi-phase structures and irregular morphologies of X-ray emitting hot
plasmas could be explained by bubbles created by AGN feedback (Buoteet al., 2003).
A part of the hot gas may cool down to reform the cold gas, which
could contribute to the fueling of AGN (Werner et al., 2014). AGN
feedback may compress the surrounding gas and enhance gas coolinglocally (Valentini and Brighenti, 2015). Because dust grains can grow inthe cold gas as mentioned above, the cold gas injected into the hot gas by
AGN feedback would supply the dust to the hot gas. This dust supply
could be dominant over the dust production by AGB stars. If so, formationof cold gas and the subsequent AGN fueling leading to AGN feedback playa dominant role in the dust evolution in elliptical galaxies.
If the dust evolution is affected by episodic AGN activities, whichappear as a result of a cycle of gas ejection and cooling, the statisticalproperties of the dust abundances in elliptical galaxies are determined by
the time-scales of dust processing relative to the period of an AGN cycle.
Lauer et al. (2005) inferred the period of an AGN cycle in early-typegalaxies based on the dust lifetime against sputtering in the hot gas
and the fraction of dust detection for a sample, obtaining a period of 108 yr. The dust contained in the cold gas may be injected into the hot
gas in an episodic way associated with the AGN cycle, if AGN feedback
efﬁciently heats the cold gas (Mathews et al., 2013).
In this paper, we make a theoretical model of dust evolution in AGN
feedback cycles by including important physical processes such as themass exchange between the hot and cold gas components and the dust
evolution in those gases. For dust processing, we consider dust destruction by sputtering in the hot gas and dust growth by the accretion of gasphase metals in the cold gas. This modeling enables us to examine how
AGN feedback cycles affect the dust abundances in elliptical galaxies. We
can also examine the effect of dust growth on the dust abundance inelliptical galaxies for the ﬁrst time.
The paper is organized as follows: we formulate the model of dust
evolution in an elliptical galaxy in Section 2. We show the results in
Section 3. We discuss the model predictions, and compare them withobservational data in Section 4. Finally we conclude in Section 5.

2.1. Basic equations
We consider the mass exchange between the hot and cold phases. The
evolution of the cold gas mass Mg;c as a function of time t is written as

dMg;c_ in  M_ ret ;
¼M
dt

(1)

_ in is the infall rate of the cooled gas and M_ ret is the gas return rate
where M
from the cold to the hot phase by AGN feedback. These two terms aremodeled below.
The hot gas is treated as a constant reservoir of gas for simplicity; thatis, we assume that the mass of hot gas, Mg;h is constant ðdMg;h =dt ¼ 0Þ.
This treatment neglects the complication arising from the possibility that
there could be a supply/loss of hot gas from/to outside. Because the hot
gas basically acts as an efﬁcient destroyer of dust regardless of the choiceof Mg;h , the value of Mg;h has a minor inﬂuence on the results comparedwith other parameters. However, we should note that the dust-to-gas
ratio in the hot gas is directly affected by Mg;h since it directly enters
the dust-to-gas ratio in the hot gas. We discuss the value of Mg;h again in
Section 2.3.
The time evolution of the dust mass in the cold phase, Md;c , is written as

dMd;c_ in  D c M_ ret þ Md;c ;¼ D hM
dt
τgrow

(2)

where D h ≡Md;h =Mg;h and D c ≡Md;c =Mg;c are the dust-to-gas ratios in the
hot and cold phases, respectively (Md;h and Md;c are the dust mass in the
hot and cold gas, respectively), and τgrow is the time-scale of dust growthby the accretion of gas-phase metals in the cold gas. The dust growthtimescale τgrow is given in Section 2.3 (Eq. (9)), and is treated as afunction of D c . The time evolution of the dust mass in the hot phase,
Mh;c , on the other hand, is written as

dMd;h_ in þ D c M_ ret  Md;h þ D AGB αM ;¼ D h M
dt
τsput

(3)

where τsput is the dust destruction time-scale by sputtering in the hot gas,
D AGB is the dust-to-gas ratio in AGB star winds, α is the mass loss rates of
AGB stars per stellar mass, and M  is the total stellar mass (αM is thetotal mass loss rate of AGB stars). Using Md;c ¼ D c Mg;c , Md;h ¼ D h Mg;h ,and Eq. (1), we rewite Eqs. (2) and (3) as the following equations for the
dust-to-gas ratios:

2. ModelWe construct a model that describes the dust evolution in an elliptical
46

_ in
M
dD c
Dc
¼
þ ðD h  D c Þ
;
dt
τgrow
Mg;c

(4)

_ in D h
_ ret
dD h
αM
M
M
¼ D hþDcþ D AGB:dt
Mg;h τsput
Mg;h
Mg;h

(5)

H. Hirashita, T. Nozawa

Planetary and Space Science 149 (2017) 45–55

Thus, we adopt τtr  107 yr, and also examine an order-of-magnitude
range for τtr .

Table 1
Parameters in the model.
Parameter

Unit

Fiduciala

Rangeb_ in;0
M
τtr
τAGN
fret
τacc
τsput
Z
D AGB
α
M

M⊙ yr1

3

1–10

yr
yr
–
yr
yr
–
–
yr1
M⊙

107
108
0.3
107
107
0.02
0.01
1:6  10121010:5(0.3–3)107
ﬁxed
0.1–0.5
106–108
106–108
ﬁxed
ﬁxed
ﬁxed
1010–1011

2.3. Parameters for dust evolution
We have introduced two time-scale parameters that govern the dust
evolution: dust growth time-scale ðτgrow Þ and dust destruction (sputtering) time-scale ðτsput Þ.
We adopt the following estimate of the time-scale of grain growth(Asano et al., 2013):

1
1=2 anH;c 1 Tgas
Zyr;
0:1 μm 103 cm3
0:02
50 K


τacc ¼ 2  106a

Fiducial value.
b
Range of values investigated unless the parameter value is ﬁxed.

(8)
We solve Eqs. (1), (4) and (5). Below we formulate some undetermined terms and estimate a reasonable range for each parameter (Table 1).

where a is the grain radius, nH;c is the hydrogen number density in thecold gas, Tgas is the gas temperature, and Z is the metallicity (e.g., Inoue,
2011; Asano et al., 2013). Because of some poorly constrained parameters such as a and nH;c , we treat τacc as a given constant parameter for
simplicity, but investigate a wide range in τacc . Moreover, since accretionis efﬁcient only in the dense medium, it depends on the mass fraction ofdense gas in the cold gas, which is denoted as fdense . The dust growthtime-scale is effectively estimated as τacc =fdense . Based on the above estimate, we examine τacc ¼ 106 –108 yr (107 yr for the ﬁducial case),
allowing for a small value for fdense or variation in a and nH;c (Kuo et al.,2013; Schneider et al., 2016; Aoyama et al., 2017). In reality, the accretion time-scale is also affected by grain size distribution (Kuo andHirashita, 2012); thus, the above a represents the appropriate average ofthe grain size.1 Considering the uncertainties in grain size distribution,
τacc may be out of the range above (106–108 yr). If τacc ≲106 yr, the grain
growth is so efﬁcient that the dust-to-gas ratio in the cold gas stays at a
maximum value given below ðD sat Þ for most of the time regardless of thevalue of τacc ð≲106 yrÞ. If τacc ≳108 yr, in contrast, dust growth is not
efﬁcient enough to raise the dust-to-gas ratio above 104. Therefore, therange of τacc ¼ 106 –108 yr covers all the resulting behavior of interest for
D c , i.e., covers all the interesting range of D c as we show below.
Using a given value of τacc , the dust growth time-scale is given by

2.2. Mass exchange between the phases
The mass exchange between the cold and hot phases is described by_ in (inﬂow of cooled hot gas to the cold gas) and M_ ret (return of cold gas
Mto the hot phase by AGN feedback). For simplicity, we assume that AGN
feedback occurs periodically with a period of τAGN . During an episode of
AGN feedback, the cold gas is transported to the hot gas, and thistransportation time-scale is parameterized by τtr . This transport (or the
return of cold gas to the hot gas) lasts for a fraction of τAGN , and thisfraction is parameterized by fret . That is, the duration of an AGN feedback_ ret Þ of the cold gas is on
episode is fret τAGN . We assume that the outﬂow ðM
during the AGN feedback as_ ret ðtÞ ¼M
Mg;c τtr0

if 0  t=τAGN  ½t=τAGN   fret ;otherwise;(6)

where ½x is the ﬂoor function, which indicates the largest integer thatsatisﬁes ½x  x. This equation indicates that the outﬂow is periodicallyturned on every τAGN with a duration of fret τAGN .
The inﬂow of cooled hot gas is assumed to occur only when there is no
outﬂow activity (i.e., when Mret ¼ 0):_ in ðtÞ ¼
M0_ in;0M

if 0  t=τAGN  ½t=τAGN   fret ;otherwise;τgrow ¼τacc;
1  D c =D sat(9)where the denominator on the right-hand side means that accretion issaturated as D c approaches D sat , which is the abundance of the metals
available for dust formation. We assume D sat ¼ 0:01 in this paper, since
we are considering solar metallicity environment (i.e., D sat  Z⊙ ). The
abundance of available metals for dust formation may be correlated withthe stellar mass because of the stellar mass–metallicity relation (Gallazzi
et al., 2005). However, this relation has a large scatter, and it is alsosuggested that the velocity dispersion (or the virial mass) is more tightly
related to the stellar metallicity (Smith et al., 2009). Moreover, it is notclear how tightly the stellar metallicity is related to the gas metallicity
because of accretion of external gas (Su and Irwin, 2013). Thus, we
simply adopt a constant D sat , but we also note that increasing/decreasing D sat has broadly the same effect of short/long τacc .
The time-scale of dust destruction by sputtering is estimated as (Tsaiand Mathews, 1995; Nozawa et al., 2006; Hirashita et al., 2015)(7)_ in;0 as a constant free parameter.
where we treat M
Based on the inferred dust lifetime and dynamical time in the centerof an elliptical galaxy and the rate of dust detection for elliptical galaxies,
Lauer et al. (2005) suggested that the cycle of dust appearance anddisappearance is  108 yr. We can regard this time as τAGN if that dust
cycle is induced by the AGN feedback cycle. Thus, we adopt
τAGN ¼ 108 yr. Since the time evolution of gas and dust is determined by
the time-scale relative to τAGN , we ﬁx τAGN and change other time-scales
as described below. The maximum cold gas mass is roughly estimated as_ in;0 τAGN ð1  fret Þ, which should be comparable to the observed gas massM
 a few  108 M⊙ (e.g., Wiklind et al., 1995). This means that
_ in;0  a few  ð1  fret Þ1 M⊙ yr1 . Thus, we investigate a range ofManH;h 1yr;
0:1 μm 102 cm3

 1–10 M⊙ yr1 . Since cold gas is detected in a signiﬁcant fraction of
elliptical galaxies, fret cannot be very near to 1. Thus, we focus on a rangeof 0 < fret  0:5.
For τtr , it may be reasonable to adopt the dynamical time. As
mentioned in the Introduction, Temi et al. (2007) suggested dust transport by buoyancy acting on the heated cold gas in order to explain theorigin of extended dust FIR emission component. They estimated thetime-scale of transport as  107 yr based on the dynamical time-scale.

τsput ¼ 7:1  106(10)

where nH;h is the number density of hydrogen nuclei in the hot gas. As we

1
More precisely, a is the ratio of the mean a3 to the mean a2 (Hirashita and Kuo, 2011).
As shown in Hirashita and Kuo (2011), the time variation of a could be effectively
incorporated in the deﬁnition of τacc so that τacc could still be treated as constant.

47

H. Hirashita, T. Nozawa

Planetary and Space Science 149 (2017) 45–55

Fig. 1. Time evolutions of relevant quantities. (a) Dust-to-gas ratio in the cold ðD c Þ andhot gas ðD h Þ (solid and dotted lines, respectively). (b) Cold gas mass ðMg;c Þ (solid line),and dust masses in the cold gas ðMd;c Þ (dashed line) and in the hot gas ðMh;c Þ (dotted line).

Fig. 2. Time evolutions of relevant quantities. (a) Dust-to-gas ratio in the hot gas ðD h Þ.
(b) Dust-to-gas ratio in the cold gas ðD c Þ. (c) Cold gas mass ðMg;c Þ. The solid, dotted, and_ in;0 ¼ 3 (ﬁducial), 1, and 10 M⊙ , respectively, in alldashed lines show the results for M
the panels.

did for τacc above, we treat τsput as a given constant parameter. Based on
this estimation, we adopt τsput ¼ 107 yr for the ﬁducial case and examinea range of 106–108 yr considering the variety in a and nH;h . Note thatﬁxing τacc and τsput implicitly assumes a ﬁxed grain size (or grain size
distribution). In reality, the grain size distribution itself is determined asa result of the cycle of dust destruction and growth. Therefore, aconsistent treatment of those time-scales and the grain size distribution
would be necessary. Hirashita et al. (2015) considered the evolution ofgrain size distribution by dust destruction and subsequent dust growthand showed that the resulting grain size distribution is consistent withthe optical extinction curves observed by Patil et al. (2007), although
they did not consider a full cycle of AGN feedback. At the same time, theyalso showed that the resulting grain size distribution depends on the size
distribution of dust grains produced by AGB stars. To avoid such acomplication, we treat τacc and τsput as given constant parameters andconcentrate on the total dust mass. The grain size distribution realized
after AGN feedback cycles will be investigated in the future work.
We adopt D AGB ¼ 0:01, α ¼ 1:6  1012 yr1 , and M ¼
1010 –1011 M⊙ (Tsai and Mathews, 1995). However, the precise values ofthese quantities do not affect the dust abundance in the cold gas as longas the dust formed in AGB stars is efﬁciently destroyed by the hot gas. We
ﬁx D AGB and α, and only focus on the variation of M  .
As explained in Section 2.1, we ﬁx the hot gas mass Mg;hfor simplicity. The hot gas mass in the central a few kpc, which could
directly exchange the gas mass with the central cold component, isestimated as 108 –109 M⊙ (Tsai and Mathews, 1995). Thus, we adopt
Mg;h ¼ 3  108 M⊙ . The dust-to-gas ratio in the hot gas (D h ) is inversely
proportional to Mg;h by deﬁnition; however, because dust in the hot gas is
efﬁciently destroyed by sputtering, as shown below, D h ≪D c is satisﬁed
when the hot gas is actively accreted on to the cold gas, except for thecase where the sputtering time-scale is as long as the AGN feedback cycleðτsput ≳τAGN Þ. Therefore, the inﬂow is practically a “dust-free” gas for thecold gas, so that the value of D h does not inﬂuence D c . This means thatthe choice of Mg;h , which could affect D h , does not have a signiﬁcant
inﬂuence on D c .
We assume the following initial conditions: D c ¼ D h ¼ 106 , andMg;c ¼ 107 M⊙ . As seen later, the initial condition is not important, since
the system “forgets” the initial condition in  τAGN .
3. Results
3.1. Fiducial caseFirst of all, we show the time evolution of relevant quantities underthe ﬁducial parameter values listed in Table 1. In Fig. 1, we show theevolutions of the dust-to-gas ratios in the hot and cold gas, the cold gas
mass, and the dust masses in the cold and hot gas. Here we describe howeach of these quantities evolves as a function of time.
All the quantities have almost periodic behaviors with a period given
by τAGN . In association with the onset of AGN feedback, the dust grown inthe cold gas is injected into the hot gas, so that the dust-to-gas ratio in the
hot gas increases. However, the dust supplied to the hot gas is quickly
destroyed by sputtering, and the dust-to-gas in the hot gas tends toconverge to the value determined by the balance between dust supply
from stars and dust destruction by sputtering. After AGN feedback stops,
the cold gas increases its mass by gas infall. In this phase, because thedust-to-gas ratio in the infalling gas, which is equal to the dust-to-gas
ratio in the hot gas, is smaller than that in the cold gas, the dust-to-gas
ratio in the cold gas decreases as a result of dilution.
The above general behavior does not change by the choice ofparameter values. Thus, for the purpose of simpliﬁcation, we hereafterconcentrate on the dust-to-gas ratios in the cold and hot gas (D c andD h ), and the cold gas mass ðMg;c Þ, since the dust masses in the hot andcold gas just trace the evolution of the corresponding dust-to-gas ratios.
Below we show the dependence on each parameter listed in Table 1.
3.2. Mass inﬂow rate
We consider the mass accretion onto the cold gas when AGN feedback_ in;0 . In Fig. 2,
is off. The mass inﬂow rate is regulated by the parameter M_
we show the time evolution of D c , D h , and Mg;c for M in;0 ¼ 3 (ﬁducial),48

H. Hirashita, T. Nozawa

Planetary and Space Science 149 (2017) 45–55

Fig. 3. Same as Fig. 2 but for various mass transport times ðτtr Þ. The solid, dotted, anddashed lines show the results for τtr ¼ 107 (ﬁducial), 3  106 , and 3  107 M⊙ , respectively, in all the panels.

Fig. 5. Same as Fig. 2 but for various time-scales of dust growth by accretion ðτacc Þ. The
solid, dotted, dashed, and dot-dashed lines show the results for τacc ¼ 107 (ﬁducial), 106,3  107 and 108 yr, respectively, in all the panels.

_ in;0 .
1, and 10 M⊙ yr1 . Below we describe how the results depend on M
The dust-to-gas ratio in the hot gas has a larger amplitude for a larger_ in;0 . This is because more dust is accumulated in the cold gas. When thisMbecause the inﬂow transports the dust from the hot gas to the cold gas inour model. However, the lowest level of the dust-to-gas ratio in the hot
gas is not very sensitive to Min;0 since it is determined by the balance
between dust supply from AGB stars and dust destruction by sputtering.
In terms of the dust-to-gas ratio in the cold gas, the periodic decrease isdue to the inﬂow of dust-poor gas. However, since dust growth is efﬁcientenough, the original high dust-to-gas ratio is recovered as soon as thecold gas attains enough mass by the inﬂow. As expected, the cold gas_ in;0 is larger, but the logarithmic amplitude of the coldmass is larger if M

dusty cold gas is injected into the hot gas by AGN feedback, the hot gas isenriched with dust. The dust injected into the hot gas is readily destroyedby sputtering; thus, the hot gas is dust-poor for most of the time. The dustto-gas ratio in the hot gas drops slightly more in the case of a higher Min;0_ in;0 , since we ﬁx the time-scales of AGN
gas mass does not depend on M
feedback and mass transport.
3.3. Mass transport time-scale in AGN feedback

The mass transport time-scale of AGN feedback, τtr , regulates the massloss rate of the cold gas when AGN feedback is on (Eq. (6)). In Fig. 3, weshow the time evolution of the quantities of interest for τtr ¼ 107 (ﬁducial), 3  106 , and 3  107 yr.
The increase and decrease of the dust-to-gas ratio in the hot gas is
sharper if τtr is shorter just because the effect of mass transport from thecold to hot gas occurs on a shorter time-scale. The amplitudes of all thequantities shown in Fig. 3 are larger for shorter τtr because larger mass is
exchanged between the cold and hot phases. In particular, the amplitudeof the cold gas mass is sensitive to τtr . Accordingly, the dust-to-gas ratio in
the cold gas drops more for shorter τtr because the effect of dilution by theinﬂow is more signiﬁcant. In contrast, the dust-to-gas ratio in the hot gas
drops to the value insensitive to τtr when the AGN feedback is off (i.e.,
when there is no supply of dust from the cold gas) because of sputtering.
The level of the lowest D h is determined by the balance between dust
formation by AGB stars and dust destruction by sputtering.
3.4. Duration of AGN feedback
Fig. 4. Same as Fig. 2 but for various ratios of the AGN feedback duration to the AGN
feedback duty cycle time ðfret Þ. The solid, dotted, and dashed lines show the results forfret ¼ 0:3 (ﬁducial), 0.1, and 0.5, respectively, in all the panels.

The duration of AGN feedback relative to the AGN duty cycle isparametrized by fret , so that an episode of AGN feedback lasts for fret τAGN .
In Fig. 4, we show the time evolution of the quantities of interest for fret ¼
49

H. Hirashita, T. Nozawa

Planetary and Space Science 149 (2017) 45–55

Fig. 7. Same as Fig. 2 but for various stellar masses ðM  Þ. The solid, dotted, and dashedlines show the results for M ¼ 1010:5 (ﬁducial), 1010, and 1011 M⊙ , respectively, in all
the panels.

Fig. 6. Same as Fig. 2 but for various time-scales of dust destruction by sputtering ðτsput Þ.
The solid, dotted, and dashed lines show the results for τsput ¼ 107 (ﬁducial), 106, and108 yr, respectively, in all the panels.

0:3 (ﬁducial), 0.1, and 0.5.
Comparing Figs. 3 and 4, we ﬁnd that the duration of AGN feedback
has an effect similar to the mass transport time in terms of the amplitudes: a larger fret makes the amplitudes of the cold gas mass and the dustto-gas ratio in the cold gas larger. The cold gas naturally decreases more if
AGN feedback lasts longer, and the subsequent dilution of dust abundance by inﬂow becomes more signiﬁcant. The dust-to-gas ratio in the
hot gas has a larger amplitude for a smaller fret since the cold gas mass islarger (i.e., the dust mass supplied from the cold gas is larger).

Naturally, the cold gas mass, which is not related to dust, is notaffected by τsput . As expected, the dust-to-gas ratio in the hot gas is largely
affected by the sputtering time-scale, with longer τsput predicting higher
D h . The dust-to-gas ratio in the hot gas is roughly proportional to τsput(i.e., inversely proportional to the dust destruction efﬁciency). The dustto-gas ratio in the cold gas is also kept high for τsput ¼ 108 yr: if D h remains as high as D c , the dust-to-gas ratio in the cold gas is kept highbecause the dust-to-gas ratio in the infalling gas is high (i.e., the dust
abundance in the cold gas is not diluted by the infall). This effect issigniﬁcant only if τsput ≳τAGN .

3.5. Dust growth time-scale
The accretion time-scale τacc regulates the dust growth in the cold gas.
In Fig. 5, we show the time evolution of the quantities of interest for
τacc ¼ 107 (ﬁducial), 106, 3  107 , and 108 yr.
Naturally, the cold gas mass, which is not related to dust, is notaffected by τacc . As expected, the dust-to-gas ratio in the cold gas becomes
higher for shorter τacc . Moreover, if τacc is as long as τAGN , the overall levelof dust-to-gas ratio is suppressed because dust does not grow sufﬁciently
within an AGN feedback cycle. The dust-to-gas ratio in the hot gas is also
affected, since the major source of dust in the hot gas is the dust grown inthe cold gas. We observe a secular increase of D c for τacc ¼ 3  107 yr.
This indicates that, if τacc is smaller than τAGN , the dust-to-gas ratio in thecold gas tends to increase unless it reaches the saturation limit ðD sat Þ.
Therefore, we observe a bifurcation for the value of D c : if τacc < τAGN , thedust-to-gas ratio increases while if τacc > τAGN , the dust-to-gas ratio issuppressed and D c  D h . In the latter case, dust growth has little inﬂuence on the dust budget and the dust-to-gas ratio is simply determinedby the balance between dust supply from AGB stars and dust destructionin the hot gas.

3.7. Stellar mass
The total stellar mass affects the dust evolution through dust production by AGB stars. In Fig. 7, we show the time evolution of the relevant quantities for M ¼ 1010:5 (ﬁducial), 1010, and 1011 M⊙ .
The stellar mass does not affect the cold gas mass in our model since it
only contributes to the dust production. Because the dust supply from
AGB stars to the hot gas is proportional to the stellar mass, the lowest
level of dust-to-gas ratio which is determined by the balance between
dust supply and dust destruction is proportional to the stellar mass. The
maximum level of the dust-to-gas ratio in the hot gas is insensitive to thestellar mass, because it is determined by the dust injection from the coldgas. The dust-to-gas ratio in the cold gas is not sensitive to the stellar mass
as long as dust growth is efﬁcient enough.
4. Discussion
In this section, we mainly compare the theoretical calculations withobservational data. Here we utilize the observational data for dust andgas in elliptical galaxies. Because of the general deﬁciency of gas and dustin elliptical galaxies, data is limited, while the stellar mass is relatively
easy to be determined in these systems using optical photometric observations. Thus, we also adopt the stellar mass and utilize it (mainly fornormalization).

3.6. Dust destruction time-scale
Dust in the hot gas is destroyed by sputtering. The destruction timescale is regulated by τsput . In Fig. 6, we show the time evolution of therelevant quantities for τsput ¼ 107 (ﬁducial), 106, and 108 yr.
50

H. Hirashita, T. Nozawa

Planetary and Space Science 149 (2017) 45–55

Table 2Elliptical galaxy sample adopted from Smith et al. (2012) and di Serego Alighieri et al. (2013).
Name

Other name

logM
ðM⊙ Þ

logMdustðM⊙ Þ

logMHIðM⊙ Þ

logMH2
ðM⊙ Þ

logD

Ref.a

VCC 763
HRS 150
HRS 186
HRS 241
VCC 345
VCC 881C
VCC 1226
VCC 1619

NGC 4374, M84
NGC 4406, M86
NGC 4494
NGC 4636
NGC 4261
NGC 4406
NGC 4472, M49
NGC 4550

11.18
11.22
10.88
10.98
11.32
11.22
11.39
10.03

5.05b
6.63
5.08
5.06
5.81
5.47
5.49
5.41

8.96
7.95
8.26
9.0
< 8:45
7.95< 7:90< 7:90< 7:23< 7:4< 7:35< 7:02< 7:70–< 7:267.20

3.91c1.43c3.23c3.94c>  2:71d
2.48e>  2:50d>  2:57d

1, 2, 3
1, 3
1, 3
1, 3
2, 3
2, 3
2, 3
2, 3

HRS 3
HRS 43
HRS 49
HRS 125
HRS 135
HRS 179
HRS 181
HRS 211
HRS 214
HRS 218
HRS 236
HRS 245
HRS 248
HRS 258
HRS 312
HRS 316
VCC 1316
VCC 1327

NGC 3226
NGC 3608
NGC 3640
NGC 4339
NGC 4365
NGC 4473
NGC 4478
NGC 4552, M89
NGC 4564
NGC 4570
NGC 4621, M59
NGC 4649, M60
NGC 4660
NGC 4697
NGC 5576
NGC 5638
NGC 4486, M87
NGC 4486A

10.21
10.27
10.70
10.30
11.48
10.71
10.09
10.80
10.25
10.48
10.99
11.34
10.05
11.10
10.60
10.52
11.24
10.05

5.96
< 4:88< 5:20< 5:17< 6:17< 5:19< 4:85< 5:67< 5:30< 5:67< 5:76< 5:40< 4:85
5.46< 5:51< 5:23
5.34
4.92

–
–
–
< 7:84< 8:18< 7:92–< 7:92< 7:79< 7:31< 7:92< 7:92< 7:92–––––< 7:13< 7:28< 7:25< 7:2< 7:62< 7:16< 7:31< 7:36< 7:33< 7:47< 7:24< 7:59< 7:30< 7:25< 7:46< 7:54< 7:18
–

–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–

1, 3
1, 3
1, 3
1, 3
1, 3
1, 3
1, 3
1, 3
1, 3
1, 3
1, 3
1, 3
1, 3
1, 3
1, 3
1, 3
2, 3
2, 3

a

References: (1) Smith et al. (2012); (2) di Serego Alighieri et al. (2013); (3) Cortese et al. (2012).
Adopted from Ref. 1. Ref. 2 gives 5.30 with the same mass absorption coefﬁcient.
The upper limit of H2 mass is used, but this does not affect the estimated dust-to-gas ratio since the gas mass is dominated by H I gas mass.
d
We use the upper limits of gas mass to derive the lower limits of dust-to-gas ratio.
e
We neglect the H2 mass for the gas mass.
bcpart of the sample galaxies is consistent with even the most extreme caseof τtr ¼ 3  106 yr or fret ¼ 0:5. This means that it is difﬁcult to constrain
the lower bound for τtr and the upper bound for fret .

4.1. Sample
One of the newest systematic dust observations in nearby ellipticalgalaxies is carried out by Herschel. We adopt the sample from Smith et al.
(2012), di Serego Alighieri et al. (2013). The sample galaxies adopted arelisted in Table 2. We selected galaxies with a morphological type of
elliptical galaxies (E) and excluded objects with stellar mass with< 109:5 M⊙ . NGC 4374 is common for both samples. The stellar mass istaken from Cortese et al. (2012). The gas masses are traced by HI and H2(CO); therefore, the observed gas masses are compared with the cold gas
mass in our models. We only compare the observed dust mass with thedust mass in the cold gas in our models, because the observational
sensitivity to the diffuse component in the hot gas depends on the spatial
extension, which is not known. In any case, since the dust mass in thecold gas is much larger than that in the hot gas in most of the time, adding
the dust mass in the hot gas does not signiﬁcantly change the comparison below.

4.3. Dust mass
The dust mass in the cold gas varies between  105 and  106 M⊙ inthe ﬁducial model (Fig. 1). The maximum of the dust mass is achieved
when the cold gas mass becomes the largest (i.e., just before AGN feedback). In this phase, the dust-to-gas ratio is almost saturated if τacc issigniﬁcantly shorter than τAGN . If we adopt the maximum value of thedust-to-gas ratio ðD sat ¼ 0:01Þ, we obtain the maximum dust mass in thecase of the largest cold gas mass (109 M⊙ ; see above) as  107 M⊙ . The
observed dust mass is indeed smaller than this value. Because the logarithmic variation of the dust-to-gas ratio is smaller than that of the coldgas mass, the time evolution of the dust mass is dominated by the changeof the cold gas mass in our models.

4.2. Cold gas mass

4.4. Dust-to-stellar mass ratio

The variation of the cold gas mass in our models in Section 3 isbroadly in the range of the observed gas masses shown in Table 2( 109 M⊙ down to  107 M⊙ or less). Therefore, we conﬁrm that the
choices of parameter values in Section 2 are reasonable as far as the coldgas mass is concerned. The largest cold gas mass is realized if we adopt_ in;0 ¼ 10 M⊙ yr1 ; Fig. 2). Therefore, we
the largest inﬂow rate (MTo cancel out the size effects of elliptical galaxies, it is useful tonormalize the dust mass to an indicator of total mass scale. Here we use
the stellar mass for the normalization; that is, we use the dust-to-stellar
mass ratio for the indicator of the richness of dust. As an indicator of
AGN feedback, we also show the ratio of the cold gas mass to the stellar
mass, and examine the relation between Md;c =M and Mg;c =M . For thedata points, we exclude the objects without any constraint on the H I
mass, since it is impossible to constrain the gas mass in such a case. If H I
is detected, we sum the H I mass and the H2 mass to obtain the total coldgas mass (if H2 is not detected, we add the upper limit of H2 gas mass to
the H I gas mass).
In Fig. 8, we show the relation between Md;c =M and Mg;c =M . We
only show the dependence on the parameters which affect the relative

conﬁrm that the maximum inﬂow rate by the accretion of the cooled gas
is ≲10 M⊙ yr1 . The amplitude of the cold gas mass is, on the other hand,determined by the time-scale of gas transport in AGN feedback (Fig. 3)
and the duration of AGN feedback (Fig. 4). If the variation of the gas massin the sample is interpreted as due to time evolution, τtr ≳3  107 yr or
fret ≲0:1 is not favored because the variation of the cold gas is smaller thanan order of magnitude. The non-detection of H I and H2 gas for a large
51

H. Hirashita, T. Nozawa

Planetary and Space Science 149 (2017) 45–55

Fig. 8. Relation between dust-to-stellar mass ratio ðMd;c =M Þ and gas-to-stellar mass ratio ðMg;c =M Þ. (a) Dependence on τtr . The thick (green), medium (blue) and thin (red) lines represent
the trajectory for τtr ¼ 107 (ﬁducial), 3  106 , and 3  107 yr, respectively. (b) Dependence on fret . The thick (green), medium (blue), and thin (red) lines show the trajectory for fret ¼ 0:3(ﬁducial), 0.5, and 0.1, respectively. (c) Dependence on τacc . The thick (green), medium thick (blue), medium thin (red), and thin (brown) lines represent the trajectory for τacc ¼ 107(ﬁducial) 106, 3  107 , and 108 yr, respectively. (d) Dependence on τsput . The thick (green), medium (blue), and thin (red) lines show the trajectory for τsput ¼ 107 (ﬁducial), 106, and108 yr, respectively. These three lines are almost overlapped. We also show observational data points in all the panels listed in Table 2: The diamonds show the galaxies for which both dust
mass and gas mass are detected, while the crosses with arrows present the data points for which either dust mass or gas mass is not detected (only an upper limit is obtained). The cross on
the right lower corner shows the typical error for the observational data points. (For interpretation of the references to color in this ﬁgure legend, the reader is referred to the web version ofthis article.)abundance of dust to gas (i.e., dust-to-gas ratio). Those parameters are τtr ,fret , τacc and τsput . The same ranges for the parameters as above (i.e., theranges in Table 1) are investigated. We only plot the relation att > 2  108 yr, when the trajectory almost converges to a limit cycle (by“forgetting the initial condition”) except for the case with τacc ¼ 3 
107 yr in Panel (c). In this case, there is a secular drift toward high dust
abundance as shown in Fig. 5.
Overall, we observe in Fig. 8 that the variation is dominated by thechange of the gas mass because the variation is mostly in the diagonal
direction on the diagram. If the gas mass changes, both Md;c =M andMg;c =M moves on the diagonal line under a constant D c . In other words,
the variation of the dust-to-gas ratio can be seen in off-diagonal behavior.
Indeed, such off-diagonal behavior is seen clearly for a short τtr in Fig. 8a

and a large fret in Fig. 8b. In both cases, the cold gas mass is lost drastically in the epoch of AGN feedback, so that the dilution of dust abundance by the inﬂow of dust-poor gas has a large impact on the dust-to-gas
ratio in the cold gas (Sections 3.2 and 3.4).
We observe in Fig. 8 that a single model does not cover an area wide
enough to explain all the data points. In particular, the data points at highMg;c =M and low Md;c =M are difﬁcult to be reproduced. As shown above,the dilution effect appears just after the epoch of AGN feedback, when
the cold gas mass is low. Therefore, it is difﬁcult to reproduce the low
dust content at the high gas mass. In our scenario, the only way toreproduce such a dust-poor and gas-rich data point is to change the efﬁciency of accretion as shown in Fig. 8c. The same effect is also realized
by lowering D sat (Eq. (9)). Therefore, the large dispersion of dust mass athigh gas mass can be interpreted as various dust growth efﬁciencies. A
52

H. Hirashita, T. Nozawa

Planetary and Space Science 149 (2017) 45–55

Fig. 9. Same as Fig. 8 but showing the relation between dust-to-gas ratio ðD c ¼ Md;c =Mg;c Þ and gas-to-stellar mass ratio ðMg;c =M Þ. We also show observational data points listed in Table 2(but only the objects with dust detection are shown): The diamonds show the galaxies for which gas is detected, while the crosses with arrows present the data points without gas detection(only an upper limit is obtained for the gas mass). The cross on the right lower corner shows the typical error.

dominated by the overall oscillation of the cold gas mass. To examine theeffect of dust abundance variation more clearly, it is useful to consider aquantity normalized to the gas mass. In this way, we can cancel the effectof oscillatory behavior of the cold gas mass, and concentrate on thevariation of dust abundance. We still use the gas-to-stellar mass ratio,
Mg;c =M , for the horizontal axis to show the cycle of AGN feedback. Thus,
we consider the D c –Mg;c =M diagram here. The same observational
sample as in Section 4.4 is chosen for comparison but we excluded galaxies without detection of dust emission.
In Fig. 9, we show the relation between D c and Mg;c =M . We only plot
the relation at t > 2  108 yr as also done in Fig. 8. We examine thevariations of the same parameters as in Section 4.4. The horizontal axis
shows the “phase” of AGN feedback with high and low phases of Mg;c =M
showing the timings when AGN feedback is turned on and off, respectively. The upper limit of D c is determined by the saturation of dust
growth (D sat ). After AGN feedback, D c becomes low by the dilution as aresult of the inﬂow of dust-poor gas. As the cold gas mass increases, dust
growth raises the dust-to-gas ratio.

variety in dust growth efﬁciency could be caused by a variety in dense gas
fraction, cold gas density, metallicity, or grain size distribution (Section 2.3).
Some studies argue that the dust-to-stellar mass ratio changes as thesystem is enriched with dust (e.g., Remy-Ruyer et al., 2015). Dustenrichment is indeed the most important factor of changing thedust-to-stellar mass ratio in gas-rich star-forming galaxies, since dust
production by stars and dust growth in the cold dense ISM are actively
occurring. In this paper, we have shown that, in elliptical galaxies, thedust-to-stellar mass ratio is still varied by dust growth, although it isdriven by a cycle of AGN feedback, not by chemical enrichment. Therefore, our results imply that, if AGN feedback affects the galaxy evolution,
we also need to consider the variation of dust abundance by
AGN feedback.
4.5. Dust-to-gas ratio
As shown above, the behavior on the Md;c =M –Mg;c =M diagram is53

H. Hirashita, T. Nozawa

Planetary and Space Science 149 (2017) 45–55

ratio through the AGN feedback cycle and through the variation in dust
growth efﬁciency.

As concluded in Section 4.4, it is difﬁcult to reproduce the dust-poor
objects at high gas mass, and the only way to reproduce them in ourmodel is to assume inefﬁcient dust growth. However, it should beemphasized that our model is capable of reproducing an order ofmagnitude variation in dust-to-gas ratio if AGN feedback efﬁciently
evaporates the cold gas into the hot gas (τtr ¼ 3  106 yr in Fig. 9a andfret ¼ 0:5 in Fig. 9b).

Acknowledgment
We are grateful to T. Kokusho and H. Kaneda for their useful comments and discussions, and to the anonymous referees for their careful
reviews of the paper. HH is supported by the Ministry of Science andTechnology (MoST) grant 102-2119-M-001-006-MY3. TN is supported inpart by the JSPS Grant-in-Aid for Scientiﬁc Research (26400223).

5. Conclusion
In this paper, we modeled the evolution of dust in elliptical galaxies
and investigated the dust formation and evolution in the cold and hot gas
components. We also considered the mass exchange between the two gas
components by including AGN feedback, which heats the cold gas andconverts it to hot gas, and also by considering cooling of the hot gas,
which is accreted on to the cold gas. We considered a new dust formation
path through dust growth by the accretion of gas-phase metals in addition to dust formation by AGB stars. Thus, the injection of the cold gas
into the hot gas by AGN feedback acts as a dust supplying mechanism tothe hot gas. We also included sputtering in the hot gas following previous
papers. Since sputtering is efﬁcient enough to make the dust-to-gas ratio
in the hot gas much lower than that in the cold gas, the mass inﬂow to thecold gas dilutes the dust abundance there.
We surveyed reasonable ranges of the relevant parameters in themodel and clariﬁed how each process affects the evolution of dust andgas in elliptical galaxies. (i) The mass inﬂow rate into the cold gas
naturally affects the cold gas mass, although it has a minor inﬂuence on
the dust-to-gas ratio in the cold gas. Therefore, the role of mass inﬂow is
to characterize the total mass scale of the cold gas and dust. (ii) The
mass transport time-scale from the cold gas to the hot gas in AGN
feedback affects the amplitudes of the cold gas mass and the dust-to-gas
ratio in the cold gas. If this time-scale is shorter, the cold gas loses alarger fraction of its mass in AGN feedback. As a result, the subsequentinﬂow of dust-poor gas dilutes the dust abundance in the cold gas more.
Therefore, the variation of dust-to-gas ratio in the cold gas is larger for ashorter mass transport time-scale. (iii) The duration of AGN feedback
also regulates the cold gas lost in an AGN feedback cycle. Therefore, its
effect is similar to that of the mass transport time-scale, and theamplitude of the dust-to-gas ratio in the cold gas is larger for a longer
duration of AGN feedback. (iv) The dust growth time-scale in the cold
gas has the largest impact on the dust-to-gas ratio there. It affects theabsolute level of dust-to-gas ratio rather than the amplitude of dust-togas ratio. The low dust-to-gas ratios in some relatively gas-rich ellipticalgalaxies could be most naturally explained by a large variation in dust
growth time-scale among the sample. Such a variation can be aconsequence of a variety in dense gas fraction, grain size distribution,
metallicity, or gas density. (v) As long as the sputtering time-scale issigniﬁcantly shorter than the AGN feedback cycle, dust in the hot gas is
destroyed efﬁciently so that the infall from the hot to the cold gas phasealways works as dilution of the dust abundance in the cold gas. However, if the sputtering time-scale is comparable or longer than the AGN
feedback cycle, the dilution of the dust abundance in the cold gas does
not occur efﬁciently (i.e., the dust-to-gas ratio in the hot gas remainshigh), so that the dust-to-gas ratio in the cold gas does not drop after theinﬂow. (vi) Because the major source of dust is dust growth in the coldgas, dust production by AGB stars does not affect the evolution of thedust-to-gas ratio in the cold gas.
By comparing with observational data of nearby elliptical galaxies,
we showed that the variety in gas mass is nicely explained by our models
and that the variety in the dust-to-gas ratio can also be reproduced tosome extent. However, the full range of the observed dust-to-gas ratio is
difﬁcult to be reproduced unless we vary the dust growth time-scale (ordust growth efﬁciency). In our framework, the low dust-to-gas ratios in
relatively gas-rich objects are only reproduced with inefﬁcient dust
growth (or long dust growth time-scales). Therefore, we conclude that
dust growth can play a central role in creating the variation in dust-to-gas

References
Aoyama, S., Hou, K.-C., Shimizu, I., Hirashita, H., Todoroki, K., Choi, J.-H., Nagamine, K.,
2017. Galaxy simulation with dust formation and destruction. Mon. Not. R. Astron.
Soc. 466, 105–121.
Asano, R.S., Takeuchi, T.T., Hirashita, H., Inoue, A.K., 2013. Dust formation history ofgalaxies a critical role of metallicity for the dust mass growth by accreting materials
in the interstellar medium. Earth, Planets Space 65, 213–222.
Booth, C.M., Schaye, J., 2009. Cosmological simulations of the growth of supermassive
black holes and feedback from active galactic nuclei method and tests. Mon. Not. R.
Astron. Soc. 398, 53–74.
Buote, D.A., Lewis, A.D., Brighenti, F., Mathews, W.G., 2003. XMM-Newton and Chandra
Observations of the Galaxy Group NGC 5044. I. Evidence for Limited Multiphase Hot
Gas. Astrophys. J. 594, 741–757.
Ciotti, L., Ostriker, J.P., 2001. Cooling Flows and Quasars. II. Detailed Models of
Feedback-modulated Accretion Flows. Astrophys. J. 551, 131–152.
Cortese, L., Boissier, S., Boselli, A., Bendo, G.J., Buat, V., Davies, J.I., Eales, S., Heinis, S.,
Isaak, K.G., Madden, S.C., 2012. The GALEX view of the Herschel Reference Survey
Ultraviolet structural properties of nearby galaxies. Astron. Astrophys. 544, A101.
Croton, D.J., Springel, V., White, S.D.M., De Lucia, G., Frenk, C.S., Gao, L., Jenkins, A.,
Kauffmann, G., Navarro, J.F., Yoshida, N., 2006. The many lives of active galactic
nuclei: cooling ﬂows, black holes and the luminosities and colours of galaxies. Mon.
Not. R. Astron. Soc. 365, 11–28.
di Serego Alighieri, S., Bianchi, S., Pappalardo, C., Zibetti, S., Auld, R., Baes, M.,
Bendo, G., Corbelli, E., Davies, J.I., Davis, T., DeLooze, I., Fritz, J., Gavazzi, G.,
Giovanardi, C., Grossi, M., Hunt, L.K., Magrini, L., Pierini, D., Xilouris, E.M., 2013.
The Herschel Virgo Cluster Survey. XIII. Dust in early-type galaxies. Astron.
Astrophys. 552, A8.
Dwek, E., 1987. The infrared diagnostic of a dusty plasma with applications to supernova
remnants. Astrophys. J. 322, 812–821.
Dwek, E., 1998. The evolution of the elemental abundances in the gas and dust phases of
the galaxy. Astrophys. J. 501, 643.
Fabian, A.C., 1999. The obscured growth of massive black holes. Mon. Not. R. Astron. Soc.
308, L39–L43.
Fabian, A.C., 2012. Observational evidence of active galactic nuclei feedback. Ann. Rev.
Astron. Astrophys. 50, 455–489.
Fabian, A.C., Johnstone, R.M., Daines, S.J., 1994. The effects of dust in cold clouds
embedded in cooling ﬂows. Mon. Not. R. Astron. Soc. 271, 737.
Ferrara, A., Viti, S., Ceccarelli, C., 2016. The problematic growth of dust in high-redshift
galaxies. Mon. Not. R. Astron. Soc. 463, L112–L116.
Ferrari, F., Pastoriza, M.G., Macchetto, F., Caon, N., 1999. A survey of the ISM in earlytype galaxies. II. The dust. Astron. Astrophys. Suppl. 136, 269–284.
Forbes, D.A., 1991. On the external origin for dust in elliptical galaxies. Mon. Not. R.
Astron. Soc. 249, 779–787.
Fujita, Y., Okabe, N., Sato, K., Tamura, T., Matsushita, S., Hirashita, H., Nakamura, M.,
Matsushita, K., Nakazawa, K., Takizawa, M., 2013. Discovery of an outstanding disk
in the cD galaxy of the Hydra A Cluster. Publ. Astron. Soc. Jpn. 65, L15.
Gallazzi, A., Charlot, S., Brinchmann, J., White, S.D.M., Tremonti, C.A., 2005. The ages
and metallicities of galaxies in the local universe. Mon. Not. R. Astron. Soc. 362,
41–58.
Goudfrooij, P., Hansen, L., Jorgensen, H.E., Norgaard-Nielsen, H.U., 1994. Interstellar
matter in Shapley-Ames elliptical galaxies. II. The distribution of dust and ionizedgas. Astron. Astrophys. Suppl. 105.
Hirashita, H., 1999. Global law for the dust-to-gas ratio of spiral galaxies. Astrophys. J.
510 (January), L99–L102.
Hirashita, H., Kuo, T.-M., 2011. Effects of grain size distribution on the interstellar dust
mass growth. Mon. Not. R. Astron. Soc. 416, 1340–1353.
Hirashita, H., Nozawa, T., Villaume, A., Srinivasan, S., 2015. Dust processing in ellipticalgalaxies. Mon. Not. R. Astron. Soc. 454, 1620–1633.
Hou, K.-C., Hirashita, H., Michałowski, M.J., 2016. Dust evolution processes constrainedby extinction curves in nearby galaxies. Publ. Astron. Soc. Jpn. 68, 94.
Inoue, A.K., 2003. Evolution of dust-to-metal ratio in galaxies. Publ. Astron. Soc. Jpn. 55,
901–909.
Inoue, A.K., 2011. The origin of dust in galaxies revisited the mechanism determining
dust content. Earth, Planets, Space 63, 1027–1039.
Kaneda, H., Ishihara, D., Onaka, T., Suzuki, T., Mori, T., Oyabu, S., Yamagishi, M., 2011.
Properties of dust and PAHs in the hot plasma of the elliptical galaxy NGC 4125
revealed with AKARI and Spitzer Space Telescope. Publ. Astron. Soc. Jpn. 63,
601–615.
King, A., 2005. The AGN-Starburst Connection, Galactic Superwinds, and MBH-σ.
Astrophys. J. 635, L121–L123.
54

H. Hirashita, T. Nozawa

Planetary and Space Science 149 (2017) 45–55
Silk, J., Rees, M.J., 1998. Quasars and galaxy formation. Astron. Astrophys. 331,
L1–L4.
Smith, M.W.L., Gomez, H.L., Eales, S.A., Ciesla, L., Boselli, A., Cortese, L., Bendo, G.J.,
Baes, M., Bianchi, S., Clemens, M., Clements, D.L., Cooray, A.R., Davies, J.I., De
Looze, I., di Serego Alighieri, S., Fritz, J., Gavazzi, G., Gear, W.K., Madden, S.,
Mentuch, E., Panuzzo, P., Pohlen, M., Spinoglio, L., Verstappen, J., Vlahakis, C.,
Wilson, C.D., Xilouris, E.M., 2012. The Herschel Reference Survey dust in Early-type
Galaxies and across the Hubble Sequence. Astrophys. J. 748, 123.
Smith, R.J., Lucey, J.R., Hudson, M.J., 2009. Ages and metallicities for quiescent galaxies
in the Shapley supercluster driving parameters of the stellar populations. Mon. Not.
R. Astron. Soc. 400, 1690–1705.
Su, Y., Irwin, J.A., 2013. Investigating the Potential Dilution of the Metal Content of Hot
Gas in Early-type Galaxies by Accreted Cold Gas. Astrophys. J. 766, 61.
Temi, P., Brighenti, F., Mathews, W.G., 2007. Far-Infrared Spitzer Observations ofElliptical Galaxies evidence for Extended Diffuse Dust. Astrophys. J. 660, 1215–1231.
Temi, P., Brighenti, F., Mathews, W.G., Bregman, J.D., 2004. Cold dust in early-typegalaxies. i. observations. Astrophys. J. Suppl. 151, 237–269.
Tran, H.D., Tsvetanov, Z., Ford, H.C., Davies, J., Jaffe, W., van den Bosch, F.C., Rest, A.,
2001. Dusty Nuclear Disks and Filaments in Early-Type Galaxies. Astron. J. 121,
2928–2942.
Tsai, J.C., Mathews, W.G., 1995. Interstellar grains in elliptical galaxies grain evolution.
Astrophys. J. 448, 84.
Valentini, M., Brighenti, F., 2015. AGN-stimulated cooling of hot gas in elliptical galaxies.
Mon. Not. R. Astron. Soc. 448, 1979–1998.
Valiante, R., Schneider, R., Salvadori, S., Bianchi, S., 2011. The origin of the dust in highredshift quasars the case of SDSS J1148þ5251. Mon. Not. R. Astron. Soc. 416,
1916–1935.
van Dokkum, P.G., Franx, M., 1995. Dust in the Cores of Early-Type Galaxies. Astron. J.
110, 2027.
Voit, G.M., Donahue, M., 1995. Problems with cold clouds and cooling ﬂows. Astrophys.
J. 452, 164.
Wagner, A.Y., Bicknell, G.V., 2011. Relativistic Jet Feedback in Evolving Galaxies.
Astrophys. J. 728, 29.
Werner, N., Oonk, J.B.R., Sun, M., Nulsen, P.E.J., Allen, S.W., Canning, R.E.A.,
Simionescu, A., Hoffer, A., Connor, T., Donahue, M., Edge, A.C., Fabian, A.C., von der
Linden, A., Reynolds, C.S., Ruszkowski, M., 2014. The origin of cold gas in giant
elliptical galaxies and its role in fuelling radio-mode AGN feedback. Mon. Not. R.
Astron. Soc. 439, 2291–2306.
Wiklind, T., Combes, F., Henkel, C., 1995. The molecular cloud content of early-typegalaxies. V. CO in elliptical galaxies. Astron. Astrophys. 297, 643.
Zhukovska, S., Dobbs, C., Jenkins, E.B., Klessen, R.S., 2016. Modeling dust evolution ingalaxies with a multiphase, inhomogeneous ISM. Astrophys. J. 831, 147.
Zhukovska, S., Gail, H.-P., Trieloff, M., 2008. Evolution of interstellar dust and stardust in
the solar neighbourhood. Astron. Astrophys. 479, 453–480.

Knapp, G.R., Guhathakurta, P., Kim, D.-W., Jura, M.A., 1989. Interstellar matter in earlytype galaxies. I - IRAS ﬂux densities. Astrophys. J. Suppl. 70, 329–387.
Kuo, T.-M., Hirashita, H., 2012. Impact of grain size distributions on the dust enrichment
in high-redshift quasars. Mon. Not. R. Astron. Soc. 424 (July), L34–L38.
Kuo, T.-M., Hirashita, H., Zafar, T., 2013. Evolution of dust content in galaxies probed by
gamma-ray burst afterglows. Mon. Not. R. Astron. Soc. 436 (December), 1238–1244.
Lauer, T.R., Faber, S.M., Gebhardt, K., Richstone, D., Tremaine, S., Ajhar, E.A., Aller, M.C.,
Bender, R., Dressler, A., Filippenko, A.V., Green, R., Grillmair, C.J., Ho, L.C.,
Kormendy, J., Magorrian, J., Pinkney, J., Siopis, C., 2005. The Centers of Early-Type
Galaxies with Hubble Space Telescope. V. New WFPC2 Photometry. Astron. J. 129,
2138–2185.
Leeuw, L.L., Sansom, A.E., Robson, E.I., Haas, M., Kuno, N., 2004. Observations of cold
dust in nearby elliptical galaxies. Astrophys. J. 612, 837–847.
Mancini, M., Schneider, R., Graziani, L., Valiante, R., Dayal, P., Maio, U., Ciardi, B.,
Hunt, L.K., 2015. The dust mass in z > 6 normal star-forming galaxies. Mon. Not. R.
Astron. Soc. 451, L70–L74.
Mathews, W.G., Brighenti, F., 2003. Rapid cooling of dusty gas in elliptical galaxies.
Astrophys. J. 590, L5–L8.
Mathews, W.G., Temi, P., Brighenti, F., Amblard, A., 2013. Variations of Mid- and Farinfrared Luminosities among Early-type Galaxies relation to Stellar Metallicity andCold Dust. Astrophys. J. 768, 28.
Mattsson, L., Andersen, A.C., 2012. On the dust abundance gradients in late-type galaxies- II. Analytical models as evidence for massive interstellar dust growth in SINGS
galaxies. Mon. Not. R. Astron. Soc. 423, 38–48.
Mukherjee, D., Bicknell, G.V., Sutherland, R., Wagner, A., 2016. Relativistic jet feedback
in high-redshift galaxies - I. Dynamics. Mon. Not. R. Astron. Soc. 461, 967–983.
Nozawa, T., Kozasa, T., Habe, A., 2006. Dust Destruction in the High-Velocity Shocks
Driven by Supernovae in the Early Universe. Astrophys. J. 648, 435–451.
O’Sullivan, E., Forbes, D.A., Ponman, T.J., 2001. A catalogue and analysis of X-ray
luminosities of early-type galaxies. Mon. Not. R. Astron. Soc. 328, 461–484.
Patil, M.K., Pandey, S.K., Sahu, D.K., Kembhavi, A., 2007. Properties of dust in early-typegalaxies. Astron. Astrophys. 461, 103–113.
Popping, G., Somerville, R.S., Galametz, M., 2016. The dust content of galaxies from z¼0
to z¼9. ArXiv e-prints.
R
emy-Ruyer, A., Madden, S.C., Galliano, F., Lebouteiller, V., Baes, M., Bendo, G.J.,
Boselli, A., Ciesla, L., Cormier, D., Cooray, A., Cortese, L., DeLooze, I., DoublierPritchard, V., Galametz, M., Jones, A.P., Karczewski, O.Ł., Lu, N., Spinoglio, L., 2015.
Linking dust emission to fundamental properties in galaxies the low-metallicity
picture. Astron. Astrophys. 582, A121.
Rouille, G., J€ager, C., Krasnokutski, S.A., Krebsz, M., Henning, T., 2014. Cold
condensation of dust in the ISM. Faraday Discuss. 168, 449.
Schneider, R., Hunt, L., Valiante, R., 2016. The dust content of the most metal-poor starforming galaxies. Mon. Not. R. Astron. Soc. 457, 1842–1850.
Seok, J.Y., Koo, B.-C., Hirashita, H., 2015. Dust Cooling in Supernova Remnants in the
Large Magellanic Cloud. Astrophys. J. 807 (July), 100.

55