Synthetic extinction maps around intermediate-mass black holes in Galactic globular clusters
MMNRAS , 1– ?? (0000) Preprint 6 May 2016 Compiled using MNRAS L A TEX style file v3.0
Synthetic extinction maps around intermediate-mass blackholes in Galactic globular clusters
C. Pepe , ⋆ and L. J. Pellizza , Instituto de Astronom(cid:19)(cid:16)a y F(cid:19)(cid:16)sica del Espacio, Av. Int. Guiraldes s/n, Ciudad Aut(cid:19)onoma de Buenos Aires, Argentina Consejo Nacional de Investigaciones Cient(cid:19)(cid:16)(cid:12)cas y T(cid:19)ecnicas, Av. Rivadavia 1917, Ciudad Aut(cid:19)onoma de Buenos Aires, Argentina Instituto Argentino de Radioastronom(cid:19)(cid:16)a, Camino Gral. Belgrano Km 40, Villa Elisa, Buenos Aires, Argentina
ABSTRACT
During the last decades, much effort has been devoted to explain the discrepancybetween the amount of intracluster medium (ICM) estimated from stellar evolutiontheories and that emerging from observations in globular clusters (GCs). One possiblescenario is the accretion of this medium by an intermediate-mass black hole (IMBH)at the centre of the cluster. In this work, we aim at modelling the cluster colour-excessprofile as a tracer of the ICM density, both with and without an IMBH. Comparing theprofiles with observations allows us to test the existence of IMBHs and their possiblerole in the cleansing of the ICM. We derive the intracluster density profiles fromhydrodynamical models of accretion onto a central IMBH in a GC and we determinethe corresponding dust density. This model is applied to a list of 25 Galactic GCs.We find that central IMBHs decrease the ICM by several orders of magnitude. In asubset of 9 clusters, the absence of the black hole combined with a low intraclustermedium temperature would be at odds with present gas mass content estimations. Asa result, we conclude that IMBHs are an effective cleansing mechanism of the ICM ofGCs. We construct synthetic extinction maps for M 62 and ω Cen, two clusters in thesmall subset of 9 with observed 2D extinction maps. We find that under reasonableassumptions regarding the model parameters, if the gas temperature in M 62 is closeto 8000 K, an IMBH needs to be invoked. Further ICM observations regarding boththe gas and dust in GCs could help to settle this issue.
Key words:
Globular clusters: general – Radiative transfer – ISM: general – dust,extinction – Stars: black holes
The fate of interstellar medium (ISM) in globular clusters(GCs) is still an unresolved issue. Although stellar evolu-tion theories predict between 10–100 M ⊙ of ISM, observa-tions have failed to detect such quantities and they onlyhave succeeded at placing upper limits well below the pre-dicted values. For instance, van Loon et al. (2006) estimatedupper-limits for a small sample of GCs and detected 0 : M ⊙ of atomic hydrogen in M 15 while Freire et al. (2001) esti-mated a similar amount (0 : M ⊙ ) of ionized hydrogen in theparticular case of 47 Tuc. Later, van Loon et al. (2009b) de-termined additional, more stringent upper limits for anothersample of GCs. In addition, sub-millimetric and infrared ob-servations have been performed in the search for dust, yield- ⋆ Currently at Instituto Argentino de Radioastronom´ıa. e-mail:[email protected] ing upper limits of ∼ − –10 − M ⊙ (Barmby et al. 2009,see Priestley 2011 for a rather comprehensive review on thesubject). In the particular case of M 15, Evans et al. (2003)reported a first detection of 5 10 − M ⊙ . This result was laterrefined by Boyer et al. (2006) who estimated ∼ − M ⊙ ofdust in this cluster. Thus, a cleansing mechanism that re-moves the ISM of GCs needs to be invoked.Models intending to explain the discrepancy betweenstellar evolution theories and observations have been de-veloped since the middle 1970s. Scott & Rose (1975) andFaulkner & Freeman (1977) studied an intrinsic cleansingmechanism by solving the steady-state flow equations inone dimension. In both cases the authors assume that themost evolved stars contribute to the ISM by means of theirwinds. However, Scott & Rose (1975) assume that there issufficient stellar ultraviolet radiation to maintain hydrogenfully ionized and that this is the unique energy input to thegas system while Faulkner & Freeman (1977) consider the c ⃝ C. Pepe et al. corresponding injection of energy and the consequent colli-sional ionization by electrons along with the associated ra-diative cooling of the gas. Under the same physical assump-tions, the work of Faulkner & Freeman (1977) was later re-fined by VandenBerg & Faulkner (1977), who investigatedthe time-dependent equations. Finally, McDonald & Zijlstra(2015) showed that UV radiation from white dwarfs can ef-ficiently clear the intracluster medium Yet, extrinsic mecha-nisms arising from the GC environment have also been con-sidered. Frank & Geisler (1976) studied an analytical modelconcerning the effect of the GC moving through the Galac-tic halo medium as a sweeping mechanism. More recently,Priestley et al. (2011) developed the first 3D hydrodynami-cal simulation of such scenario. Accretion flows have also be-come an appealing scenario. Krause et al. (2012) stated thatthe power required to expel the gas from the GC can be pro-vided by a coherent onset of accretion onto the stellar rem-nants of supernovae. Similarly, Scott & Durisen (1978) andMoore & Bildsten (2010) investigated the input of energyby hydrogen-rich explosions on accreting white dwarfs. Fur-ther, Leigh et al. (2013) argue that accretion onto stellar-mass black holes is an effective mechanism for rapid gas de-pletion. Finally, we (Pepe & Pellizza 2013, hereafter PaperI) developed a numerical model for the steady-state isother-mal flow resulting from the constant injection of mass bythe red giants in the cluster in the presence of an accret-ing intermediate-mass black hole (IMBH). We showed thata significant fraction of the ISM can be removed from theGC either via accretion onto the black hole in the inner re-gions or winds in the external regions. It is clear that effortshave been devoted to explain the cited discrepancy betweentheory and observations. However, due to the lack of mea-surements, little has been done in testing the density profilespredicted by the models, as an evaluation of the main hy-potheses of the model under consideration. One goal of thiswork is to develop a method to this aim.All of the cited works focused on the gaseous compo-nent of the ISM. However, the dusty component is cou-pled to the gas in the ISM with a density two–five ordersof magnitude lower, according to the cluster metallicity.This dust introduces differential reddening in the light ofGC stars. Some authors have developed new techniques toderedden the CMDs and obtain high-precision maps of theobserved differential reddening of a vast sample of GCs.Alonso Garc´ıa et al. (2011) developed a method in whichthey use photometric studies of main sequence, subgiantbranch and red giant branch stars but, unlike other authors(see Piotto et al. 1999, for example), the extinction is calcu-lated not on a predetermined grid but on a star by star basis.McDonald et al. (2009) and van Loon et al. (2009) also con-structed reddening maps on a star by star basis fow ! Cen,exclusively. As a result, these authors obtain differential ex-tinction maps which could be used to detect the ISM andtrace its density profile. This would provide us with a newobservable to test different cleansing mechanisms, in partic-ular that involving an IMBH, since the existence of theseobjects is still a topic of debate.Different kinds of observations and theoretical workshave suggested that black holes with masses in the range10 − M ⊙ exist in the Universe (Fabbiano 2006;Feng & Soria 2011; Magorrian et al. 1998). According tothem, globular clusters are the main candidates to host these IMBHs. For this reason, GCs have become the main targetof observations that search for these elusive compact objects.Up to date, two different approaches have been usedto constrain the presence as well as the mass of IMBHs inGalactic globular clusters. The first one relies on the dy-namical effects of the putative IMBH on the surroundingstars. From the combinations of different dynamical modelswith both surface brightness and velocity dispersion pro-files, several authors have managed to place constraints onthe hypothetical IMBH mass. However, there is no consen-sus about the masses measured. The reader is referred tothe references in Feldmeier et al. (2013) for an extensive listof observations and results. Not only different dynamicalmodels have led to very conflicting results, but also, giventhe spatial resolution of current telescopes, these methodsdo not allow to distinguish between one single object and acollection of smaller objects.The second approach used to detect IMBHs in GCsis related to the study of the emission due to the ac-cretion process. The most significant observation was re-ported by Nucita et al. (2008) who claim the detection ofan X-ray source (using Chandra and
XMM-Newton ) lo-cated in the centre of NGC 6388 with spectral proper-ties consistent with an accreting IMBH. However,
Chan-dra was not able to detect any source in the core ofM 15 (Ho, Terashima & Okajima 2003). Also, radio ob-servations have been performed since Maccarone (2004)stated that IMBHs would be more easily detected in ra-dio. Maccarone, Fender & Tzioumis (2005) reported the de-tection of an IMBH of ≲ M ⊙ in M 15 (using VeryLarge Array , VLA) while no central sources have been de-tected in the core of ! Cen (from
Australia Telescope Com-pact Array , ATCA, observations). The result for M 15 waslater challenged by Bash et al. (2008) who failed to detectthe core of this GC. Further, different upper limits on theIMBH mass have been reported by several authors for allof these GCs (e.g. Maccarone & Servillat 2010; Lu & Kong2011; Strader et al. 2012; Cseh et al. 2010). The dependenceof these results on the model used to describe how accretiononto the IMBH proceeds is discussed in Paper I.It is clear that the state-of-the-art of this topic is com-plex and efforts should be made in order to resolve this issue.In this work, we present synthetic extinction maps of glob-ular clusters from density profiles of models with and with-out IMBHs This allows us to investigate the reliability ofthe physical hypotheses underlying this particular cleansingmechanism. We choose the density profiles emerging fromthe model presented in Paper I, aiming at establishing thepresence of an IMBH from observations of the gas contentand extinction in globular clusters. In Sect. 2 we state thebasic equations and describe the construction method indetail. Our sample consists of the 25 Galactic GCs wheresearches of IMBHs have been performed so far (see Table1). In Sect. 3, we present our results for the density profiles,gas mass and extinction maps for different ISM parametersin our sample. Finally, in Sect. 4 we discuss the relevance ofour results and the implementation of this method to otherISM models while in Sect. 5 we present our conclusions.
MNRAS , 1– ?? (0000) xtinction maps around IMBHs Table 1.
List of globular clusters where IMBHs have beensearched for, according to the literature, ordered by increasing (cid:27) . The maps of this work were constructed for this sample. Thecluster parameters r and (cid:26) were taken from Harris (1996) while (cid:27) = √ (cid:25)G(cid:26) r was calculated using the former parameters.ID r (pc) (cid:26) ( M ⊙ pc − ) (cid:27) (km s − )NGC 6535 0.712 2.19E+2 0.82NGC 6397 0.03345 5.75E+5 1.99NGC 6652 0.2908 3.02E+4 3.98NGC 5694 0.6108 8.91E+3 4.54M 10 0.9855 3.47E+3 4.57NGC 5694 0.6186 8.91E+3 4.60NGC 6752 0.1978 1.10E+5 5.16M 79 0.6003 1.20E+4 5.18M 13 1.2804 3.55E+3 6.09M 5 0.9599 7.59E+3 6.58NGC 6402 2.1371 2.29E+3 8.05M 28 0.3839 7.24E+4 8.14NGC 5286 0.9594 1.26E+4 8.48M 80 0.4363 6.18E+4 8.54NGC 1851 0.3167 1.23E+5 8.75NGC 5824 0.5602 4.07E+4 8.9047 Tuc 0.4712 7.59E+4 10.22 ! Cen 3.5849 1.41E+3 10.61M15 0.4235 1.12E+5 11.17NGC 6440 0.3461 1.74E+5 11.36NGC 2808 0.6981 4.57E+4 11.76M 54 0.6937 4.90E+4 12.09M 62 0.4351 1.45E+5 13.03NGC 6388 0.3455 2.34E+5 13.18NGC 6441 0.4386 1.82E+5 14.74
In this Section we describe the basic equations underlyingthe method. It has been designed so as to calculate the red-dening value for every single star in the cluster. The de-tails concerning the binning and building of the map areexplained in the forthcoming section.The reddening maps constructed in this work show thedistribution of the colour excess E B − V = ( B − B ) − ( V − V ) = A B − A V : (1)where A B and A V are the absorption values for the B andV bands, respectively and were chosen in order to obtainmaps comparable to those of Alonso Garc´ıa et al. (2011).Following Cardelli, Clayton & Mathis (1989), we assume astandard reddening law with R V = 3 :
1, according to obser-vational fits.Here, we study the emission of each single star in thecluster and assume that there are no sources of radiationother than the star itself. Then, from the classic transportequation dI ν ds = − (cid:20) ν I ν ; (2)where I ν is the radiation intensity and (cid:20) ν the extinctioncoefficient, s the distance travelled by the stellar light withinthe GC and the emission coefficient was already set to zero. Assuming pure absorption, we obtain the absorption law I ν ( s ∗ ) = I ν, exp ( − ∫ s ∗ s min (cid:20) ν ds ) : (3)where s ∗ is the position of the star and s min the edge of thecluster closest to the observer, both along the line of sight.The extinction coefficient can be modeled as (cid:20) ν = n(cid:27) νe ; (4)where n = (cid:26)=m p is the particle density of the dust distri-bution and (cid:27) νe is the cross section of the extinction process.Only absorption effects are considered whereas scatteringprocesses are neglected.Since the radiation intensity and the observed magni-tude m are related through m = − : I (cid:23) + C ν , theabsorption A B can be written as A B = 1 : (cid:27) Be ∫ s ∗ s min n ( s ) ds: (5)Therefore, Eq. 1 can be written in terms of the integralof the particle density profiles E B − V = 1 : (cid:27) Ve ( A B A V − ) ∫ s ∗ s min n ( s ) ds; (6)where Eq. 5 has been used to replace the ratio (cid:27) Be =(cid:27) Ve . Thecoefficient A B =A V is taken from Cardelli, Clayton & Mathis(1989), who found a correlation between ⟨ A ( (cid:21) ) =A ( V ) ⟩ and R V (the reader is referred to that article for the complete ex-pressions). The cross section (cid:27) Ve = q(cid:25)a is assumed to be ageometrical parameter, where a , lying in the range 1˚A − (cid:22) m(Weingartner & Draine 2001) is the radius of a dust particleand the factor q ∼ : a with the mean density of dust particles ( (cid:26) p ∼ − ,Draine 2004), the particle mass can be calculated. A remark-able fact is that, given the dependence of (cid:27) νe and m p on theradius of the particle a , the colour excess E B − V dependsonly on the ratio q=a .Thus, given the position s ∗ of a star in the cluster wecan obtain an excess colour estimate E B − V by integratingthe dust density profile up to s ∗ as stated in Eq. 6. Theconstruction details of the maps are stated below. We used a Monte Carlo (MC) simulation to generate thesynthetic stellar distribution of a given globular cluster. AMiocchi (2007) model was assumed for the potential of thecluster. The integration of such model leads to the radialstellar distribution used in the MC model. Once the tridi-mensional position of every single star is known, we projectit on the plane of the sky and characterize its position withits transversal distance to the cluster centre R T and thedepth s ∗ , which is the distance to the plane of the sky thatindicates whether the star lies on the close or distant halfof the cluster. The integral of Eq. 6 is calculated up to the s ∗ value in order to obtain the colour excess for each star.The projection of the cluster in the sky plane is divided intosquare bins (see Figure 1 for a sketch of the geometry) ofsize 0 : r × : r . For each bin, the colour excess of all thestars in the column is averaged. The mean value is chosento represent the colour excess in the bin. MNRAS , 1– ????
1, according to obser-vational fits.Here, we study the emission of each single star in thecluster and assume that there are no sources of radiationother than the star itself. Then, from the classic transportequation dI ν ds = − (cid:20) ν I ν ; (2)where I ν is the radiation intensity and (cid:20) ν the extinctioncoefficient, s the distance travelled by the stellar light withinthe GC and the emission coefficient was already set to zero. Assuming pure absorption, we obtain the absorption law I ν ( s ∗ ) = I ν, exp ( − ∫ s ∗ s min (cid:20) ν ds ) : (3)where s ∗ is the position of the star and s min the edge of thecluster closest to the observer, both along the line of sight.The extinction coefficient can be modeled as (cid:20) ν = n(cid:27) νe ; (4)where n = (cid:26)=m p is the particle density of the dust distri-bution and (cid:27) νe is the cross section of the extinction process.Only absorption effects are considered whereas scatteringprocesses are neglected.Since the radiation intensity and the observed magni-tude m are related through m = − : I (cid:23) + C ν , theabsorption A B can be written as A B = 1 : (cid:27) Be ∫ s ∗ s min n ( s ) ds: (5)Therefore, Eq. 1 can be written in terms of the integralof the particle density profiles E B − V = 1 : (cid:27) Ve ( A B A V − ) ∫ s ∗ s min n ( s ) ds; (6)where Eq. 5 has been used to replace the ratio (cid:27) Be =(cid:27) Ve . Thecoefficient A B =A V is taken from Cardelli, Clayton & Mathis(1989), who found a correlation between ⟨ A ( (cid:21) ) =A ( V ) ⟩ and R V (the reader is referred to that article for the complete ex-pressions). The cross section (cid:27) Ve = q(cid:25)a is assumed to be ageometrical parameter, where a , lying in the range 1˚A − (cid:22) m(Weingartner & Draine 2001) is the radius of a dust particleand the factor q ∼ : a with the mean density of dust particles ( (cid:26) p ∼ − ,Draine 2004), the particle mass can be calculated. A remark-able fact is that, given the dependence of (cid:27) νe and m p on theradius of the particle a , the colour excess E B − V dependsonly on the ratio q=a .Thus, given the position s ∗ of a star in the cluster wecan obtain an excess colour estimate E B − V by integratingthe dust density profile up to s ∗ as stated in Eq. 6. Theconstruction details of the maps are stated below. We used a Monte Carlo (MC) simulation to generate thesynthetic stellar distribution of a given globular cluster. AMiocchi (2007) model was assumed for the potential of thecluster. The integration of such model leads to the radialstellar distribution used in the MC model. Once the tridi-mensional position of every single star is known, we projectit on the plane of the sky and characterize its position withits transversal distance to the cluster centre R T and thedepth s ∗ , which is the distance to the plane of the sky thatindicates whether the star lies on the close or distant halfof the cluster. The integral of Eq. 6 is calculated up to the s ∗ value in order to obtain the colour excess for each star.The projection of the cluster in the sky plane is divided intosquare bins (see Figure 1 for a sketch of the geometry) ofsize 0 : r × : r . For each bin, the colour excess of all thestars in the column is averaged. The mean value is chosento represent the colour excess in the bin. MNRAS , 1– ???? (0000) C. Pepe et al.
Figure 1.
Some relevant geometrical parameters. Each star islabeled with its distance to the centre of the cluster R T and itsposition s ∗ that indicates if the star is located in the close ordistant half of the cluster. All stars contained in a 0 : r × : r bin in the sky plane contribute to the colour excess in that bin. Computing the reddening requires a known dust density pro-file. In order to derive it, we assume that dust grains followthe gas distribution with a density (cid:26) gas . The dust-to-gasratio is metallicity-dependent and it is taken from Eq. 3in McDonald et al. (2011). The model for the gas densitywas set forth in Paper I. There it was shown that, when as-suming an IMBH at the centre of the cluster, two differentaccretion regimes (high-accretion rate regime – HAR, andlow-accretion rate regime – LAR) can be found accordingto the value of the parameter c s =(cid:27) , where c s is the soundspeed in the medium and (cid:27) is the velocity dispersion of thecluster. Here, we briefly recall the assumptions and summa-rize the main results of this model as follows:(i) The gravitational pull of the stars in the cluster isconsidered as well as the black hole at the centre.(ii) Winds from red giant stars act as a source of ISM.(iii) ISM can be described as an isothermal, stationary,perfect fluid with spherical symmetry.(iv) As a result, we find that a stagnation radius separatesthe inner-accretion region from the outer region, where theISM escapes as a wind.(v) Also, a clear correlation between the location of thestagnation radius and the black hole mass is found for thoseclusters in the LAR regime.In Paper I we studied the dependence of the accretionrate on the relevant parameters, the black hole mass M BH and the gas temperature T . Although several combinationsof these two parameters were explored, in this work we onlyshow the results for T = 5000 and 10000 K , in combinationwith three different black hole masses ( M BH = 0 ;
100 and1000 M ⊙ ) as representative values of the possible masses ofIMBHs according to observations. In this work, we present Intermediate and higher values of the temperature were alsoexplored but we show only two temperatures for simplicity inFigure 2. −4−2024681012 l og ( g as p a r t i c l e d e n s i t y / c m − ) −3 −2 −1 0 1 2−20−18−16−14−12−10−8−6−3 −2 −1 0 1 2−20−18−16−14−12−10−8−6−3 −2 −1 0 1 2−20−18−16−14−12−10−8−6log (r/ r ) l og ( du s t p a r t i c l e d e n s i t y / c m − ) M = 0M = 100M = 1000 −4−20246 l og ( g as p a r t i c l e d e n s i t y / c m − ) −3 −2 −1 0 1 2−20−18−16−14−12−3 −2 −1 0 1 2−20−18−16−14−12−3 −2 −1 0 1 2−20−18−16−14−12log (r/ r ) l og ( du s t p a r t i c l e d e n s i t y / c m − ) M = 0M = 100M = 1000
Figure 2.
Gas and dust particle densities for M 62 from the modelpresented in Paper I. Top: the gas temperature is T = 5000K.The density obtained from the no-IMBH scenario is a few ordersof magnitude higher for r ≲ r . Bottom: the gas temperature is T = 10000K. The value of the density in the central areas in theno-IMBH scenario is comparable to that obtained when includingthe IMBH. the resulting gas density profiles for the first time. In addi-tion, dust particle density profiles are calculated assuming adust particle radius of a = 0 : (cid:22) m (see Discussion below).Note that the equilibrium temperature of dust particlesexposed to the radiation of three blackbodies of T star = 3000,4000 and 7500 K , is ∼ −
20 K, depending on grain size(Draine & Lee 1984). Further, given the gas temperature T and the grain size a , the time it takes the dust to couple tothe gas can be calculated as t ∼ m dust =K s , where K s = 43 (cid:25)(cid:26) gas a √ k B T(cid:25)(cid:22) ; (7)is the drag coefficient, k B is the Boltzmann constant and (cid:22) isthe mean-molecular weight (Booth, Sijacki & Clarke 2015).This stopping time needs to be smaller than the crossingtime of the fluid in the GC in order to obtain a dynamicalcoupling between dust and gas. This condition is satisfied These temperature values are in range with the surface tem-perature of main sequence and red giant stars in GCs.MNRAS , 1– ?? (0000) xtinction maps around IMBHs inside the core radius, where most of the extinction takesplace, for all models. Further, Laki´cevi´c et al. (2012) haveshown that the detachment occurs when (cid:26) gas falls below10 cm − . This is the case for all the models for which ac-tually compute the reddening in Section 3.3.Figure 2 shows the gas and dust particle density for theparticular case of M 62. The fractional mass injection rate of the red giants has been set to 10 − yr − (see Paper I fora discussion on the impact of such a choice). We find thatthe density profile changes qualitatively from flat to steepwhen we consider the IMBH. Additionally, we find that forthose GCs with the highest velocity dispersion parameter,such as M 62 (along with 47 Tuc, ! Cen, M 15, NGC 6440,NGC 2808, M 54, NGC 6388 and NGC 6441), if the gastemperature T is low enough, the central values of the den-sity are 2–3 orders of magnitude higher than in the IMBHscenario and this has a remarkable impact, as we shall showbelow. From the gas densities predicted by the model in PaperI, we can estimate the gas mass content in each cluster.This allows us to place constraints on the parameter spaceto explore, for a given cluster. In Fig. 3, we show the gasmass fraction (relative to the total cluster stellar mass) inthe cluster core as a function of both, the black hole mass M BH and T . Given that stars are injecting gas at a frac-tional rate (cid:11) = 10 − yr − and considering 10 yr forthe time in between passages through the Galactic plane(Odenkirchen et al. 1997), it implies 10 M ⊙ of gas fora typical cluster of 10 M ⊙ . This value is in agreementwith the predictions of stellar evolution theories (see e.g.Tayler & Wood 1975). We assume this fractional content ofgas M gas =M GC = 10 − as an upper limit to this parameter.It can be seen that for 47 Tuc, ! Cen, M 15, NGC 6440,NGC 2808, M 54, M 62, NGC 6388 and NGC 6441, certaincombination of parameters lead to unrealistic values of themass since they require comparable (or even higher) massesto the cluster mass itself and/or it takes the system morethan 10 yr to inject that amount of gas into the medium.Recall that our modelling of the gas is stationary and, assuch, it requires an infinite amount of mass which is notphysically acceptable. Hence, this model is only reliable fora certain combination of parameters, which we constrainhere. Those combinations of parameters that lead to unre-alistic physical predictions are disregarded in the followinganalysis. Additionally, there are observational estimations ofthe gas content in some of the clusters in 3. These are shownas a dashed-dotted line, when available.As a result of our gas modelling we can place evenstronger constraints on the parameters. We find a criticaltemperature T crit for all clusters ranging from ∼ ∼ T crit can be explained by one of the following scenarios: eitherthe ISM thermalized at temperatures higher than T crit or, The mass injection rate is defined such that dM cluster =dt = (cid:11)M cluster . if it is cooler, only scenarios including an IMBH are com-patible with the current estimations of the gas mass contentin globular clusters. The extreme is NGC 6441, where evenhigher temperatures ( T crit ∼ Extinction maps for the GCs listed in Table 1 were con-structed following the procedure described in the previoussection. This selection corresponds to the list of GCs forwhich searches of IMBHs have been reported. In Figure 4and 5 we show the constructed extinction and dispersionmaps, respectively, for M 62. The blank bins indicate theabsence of stars in that bin and the colour code correspondsto log(E(B − V)). The top panels correspond to a gas tem-perature of T = 8000 K while T = 12500 K is assumedin the bottom figures. The corresponding IMBH masses are M BH = 0 ;
100 and 1000 M ⊙ , from left to right. These arerepresentative values of the mass range emerging from obser-vations . Although we show a small subset of the M BH − T parameter space, intermediate and higher values were alsoexplored.We find that, if the temperature is close to the criticalvalue T crit ∼ − V)) ∼ − :
7) from their zero-point reddeningvalue, E(B-V) = 0.42 mag. Considering that this estimationalso includes foreground reddening, it is not straightforwardto compare our maps with theirs. Further, the authors statethat the increase in the extincion in the east-west directionsouth from the cluster centre is due to material (cloud) lyingalong the line of sight but outside the cluster. However, notethat their zero-point reddeing value is located almost coin-cident with the cluster centre and that there seems to existsome radial symmetry (decreasing outwards), if the cloud isneglected. Our results for the model with T crit ∼ Although the observations in ! Cen have led to much highermasses, those high values can only be considered for such a mas-sive GC as this one.MNRAS , 1– ????
7) from their zero-point reddeningvalue, E(B-V) = 0.42 mag. Considering that this estimationalso includes foreground reddening, it is not straightforwardto compare our maps with theirs. Further, the authors statethat the increase in the extincion in the east-west directionsouth from the cluster centre is due to material (cloud) lyingalong the line of sight but outside the cluster. However, notethat their zero-point reddeing value is located almost coin-cident with the cluster centre and that there seems to existsome radial symmetry (decreasing outwards), if the cloud isneglected. Our results for the model with T crit ∼ Although the observations in ! Cen have led to much highermasses, those high values can only be considered for such a mas-sive GC as this one.MNRAS , 1– ???? (0000) C. Pepe et al. T gas (K) l og ( M ( r ) / M G C )
47 Tuc M BH = 0M ⊙ M BH = 100M ⊙ M BH = 1000M ⊙ T gas (K) l og ( M ( r ) / M G C ) M 15 M BH = 0M ⊙ M BH = 100M ⊙ M BH = 1000M ⊙ T gas (K) l og ( M ( r ) / M G C ) NGC 6440 M BH = 0M ⊙ M BH = 100M ⊙ M BH = 1000M ⊙ T gas (K) l og ( M ( r ) / M ⊙ ) NGC 2808 M BH = 0M ⊙ M BH = 100M ⊙ M BH = 1000M ⊙ T gas (K) l og ( M ( r ) / M G C ) M 54 M BH = 0M ⊙ M BH = 100M ⊙ M BH = 1000M ⊙ T gas (K) l og ( M ( r ) / M ⊙ ) M 62 M BH = 0M ⊙ M BH = 100M ⊙ M BH = 1000M ⊙ Figure 3.
Gas mass–fraction inside the core radius for a subset of our sample of GCs. For low temperatures, if the black hole is notpresent the predicted values are above the 10 − limit (dashed line) derived from stellar evolution theories. Dashed-dotted line shows theobservational limit, when available. The corresponding references are: Freire et al. (2001) for 47 Tuc, van Loon et al. (2006) for M 15,Lynch et al. (1989) for NGC 6388, Bowers et al. (1979) for NGC 6441 and McDonald et al. (2009) for ! Cen. rule out these models. Hence, if gas temperature is close to8000 K only models including an IMBH are not in contradic-tion with the observations, favouring the IMBH hypothesis.As gas temperature increases, the gas and dust content de-crease and so does the extinction in M 62. We find that atemperature only 1000 K higher, reduces the core densityenough to avoid discrepancies between our predictions andobservations. The lower pannel of Fig. 4 shows the maps for T = 10000 K for reference. For these hotter temperatures,both scenarios, with and without an IMBH seem plausible.The same kind of maps were constructed for ! Cen (seeFig. 6). For this cluster, the smallest dust particles are con-sidered, with ∼ : T crit ∼ all masses, placing strong constraints on the gas tempera-ture in this cluster. Additionally, we find that if T ⩾ T crit MNRAS , 1– ?? (0000) xtinction maps around IMBHs T gas (K) l og ( M ( r ) / M G C ) NGC 6388 M BH = 0M ⊙ M BH = 100M ⊙ M BH = 1000M ⊙ T gas (K) l og ( M ( r ) / M G C ) NGC 6441 M BH = 0M ⊙ M BH = 100M ⊙ M BH = 1000M ⊙ T gas (K) l og ( M ( r ) / M G C ) ω Cen M BH = 0M ⊙ M BH = 100M ⊙ M BH = 1000M ⊙ Figure 3.
Cont. there is no efficient accretion onto the black hole and mod-els with and without the black hole lead to similar gas den-sity profiles and mass content. Therefore, the dust distribu-tion and, consequently, the extinction, is the same for allmasses. van Loon et al. (2009) constructed 2-D maps of theextinction in ! Cen. They found a cloud in the periphery ofthe cluster and a curious dust cloud near the centre. Thisexcess of reddening towards the centre (of ∼ :
024 mag,log(E(B − V)) ∼ − :
6) due to a foreground cloud domi-nates the colour excess and it hinders the analysis of theintracluster extinction. Further, our predictions are below the sensitivity of the observed map and the model can notbe discarded nor supported.For the rest of the clusters, we only have available thereddening towards the cluster centre, obtained from inte-grated colours and colour-magnitude diagrams where thelight is dominated by the central stars (Harris 1996). How-ever, this is not useful to our aims, since we are interestedin studying the extinction inside the cluster and we needspatial variations of the reddening to make predictions withour modelling. We did check for all clusters that the meanvalue of the extinction of the stars inside the core radius isbelow the estimations of Harris (1996). Unfortunately, nofurther analysis is possible in these cases. The question ”What happened to intracluster medium?”still does not have a satisfactory answer. While different sce-narios have been proposed by several authors, still none ofthem prevail over the others. The only consensus is that theintracluster medium is being removed from the cluster. Inthis work we explore the possibility that the ISM is beingaccreted by an IMBH. Although its presence at the centreof GCs is still under debate, observational works have ledto place constraints on the mass of the putative black holein certain GCs, by means of stellar dynamics or accretiondetection. However, little has been done investigating theireffects on the surrounding media. This was the main pur-pose of the model developed in Paper I. In this work wecombine these two issues. On one hand, a new mechanismfor the removal of the ISM is proposed. On the other, theresults obtained allow us to decide whether the model con-taining the IMBH or not suits better the observations. Thisis our main goal: to make predictions about the presenceof an IMBH. If the results suggest the need to invoke anIMBH, this strengthens the hypothesis that accretion ontoan IMBH is a possible and valid cleansing mechanism inGCs.Our main conclusion is that, for some GCs (namely,M 62, NGC 2808, M 15, 47 Tuc, ! Cen, M 54, NGC 6440,NGC 6441 and NGC 6388), if the gas temperature is belowa critical value T crit , the gas mass content is orders of magni-tude above the observational estimation if the IMBH is notpresent at the centre of the cluster. However, for the sametemperature, adding an IMBH reduces the density value andthe total gas mass can be reconciled with the observations.This feature can be well understood in terms of the gas en-ergetics: for lower temperatures, in abscense of an accretingIMBH, the gas lacks the required energy to escape as a windand is retained in the cluster potential. As the temperaturegoes up, the gas avoids its retention in the cluster potentialand, hence, the density decreases and this explains the dif-ferences in the total gas mass in the cluster. As discussed inthe previous section, this subset of clusters corresponds tothose with velocity dispersion (cid:27) >
10 km s − . Clearly, thedetection of the ISM and the determination of its tempera-ture would be crucial to confirm the existence of an IMBH Actually, our estimations are at least 2 orders of magnitudebelow that limit.MNRAS , 1– ????
10 km s − . Clearly, thedetection of the ISM and the determination of its tempera-ture would be crucial to confirm the existence of an IMBH Actually, our estimations are at least 2 orders of magnitudebelow that limit.MNRAS , 1– ???? (0000) C. Pepe et al. −2 −1 0 1 2−2−1.5−1−0.500.511.52
Rt (r0) z ( r ) l og ( E ( B − V )) −2.5−2−1.5−1 −2 −1 0 1 2−2−1.5−1−0.500.511.52 Rt (r0) z ( r ) l og ( E ( B − V )) −4−3.5−3−2.5 −2 −1 0 1 2−2−1.5−1−0.500.511.52 Rt (r0) z ( r ) l og ( E ( B − V )) −6−5.5−5−4.5−2 −1 0 1 2−2−1.5−1−0.500.511.52 Rt (r0) z ( r ) l og ( E ( B − V )) −4−3.5−3−2.5 −2 −1 0 1 2−2−1.5−1−0.500.511.52 Rt (r0) z ( r ) l og ( E ( B − V )) −4−3.5−3−2.5 −2 −1 0 1 2−2−1.5−1−0.500.511.52 Rt (r0) z ( r ) l og ( E ( B − V )) −5.5−5−4.5−4 Figure 4.
Extinction maps for M 62 from the model presented in Paper I. In both upper and lower panels the corresponding masses are M BH = 0 ;
100 and 1000 M ⊙ , from left to right. Top: the gas temperature is T ∼ T = 10000K.Note the different colour scaling through the plots. −2 −1 0 1 2−2−1.5−1−0.500.511.52 Rt (r0) z ( r ) l og ( ∆ E ( B − V )) −4−3.5−3−2.5 −2 −1 0 1 2−2−1.5−1−0.500.511.52 Rt (r0) z ( r ) l og ( ∆ E ( B − V )) −6−5.5−5−4.5 −2 −1 0 1 2−2−1.5−1−0.500.511.52 Rt (r0) z ( r ) l og ( ∆ E ( B − V )) −8.5−8−7.5−7−6.5−6−5.5−5−2 −1 0 1 2−2−1.5−1−0.500.511.52 Rt (r0) z ( r ) l og ( ∆ E ( B − V )) −6−5.5−5−4.5 −2 −1 0 1 2−2−1.5−1−0.500.511.52 Rt (r0) z ( r ) l og ( ∆ E ( B − V )) −6−5.5−5−4.5 −2 −1 0 1 2−2−1.5−1−0.500.511.52 Rt (r0) z ( r ) l og ( ∆ E ( B − V )) −7−6.5−6−5.5 Figure 5.
Dispersion of the extinction maps for M 62 from the model presented in Paper I. In both upper and lower panels thecorresponding masses are M BH = 0 ;
100 and 1000 M ⊙ , from left to right. Top: the gas temperature is T ∼ T = 10000K. Note the different colour scaling through the plots. MNRAS , 1– ?? (0000) xtinction maps around IMBHs −2 −1 0 1 2−2−1.5−1−0.500.511.52 Rt (r0) z ( r ) l og ( E ( B − V )) −4−3.5−3−2.5−2 −1 0 1 2−2−1.5−1−0.500.511.52 Rt (r0) z ( r ) l og ( ∆ E ( B − V )) −8.5−8−7.5−7 Figure 6.
Extinction and dispersion map for ! Cen from themodel presented in Paper I. It corresponds to a model with noIMBH and T = 10000 K. For temperatures T ≳ K addingthe black hole does not change the mass distribution. in these GCs and, therefore, to support the hypothesis ofaccretion as an efficient cleansing mechanism. However, aspointed out by different authors (e.g., Scott & Rose 1975,and references therein), the gas temperature should dependonly on the properties of the radiation field of the cluster.The ISM of GCs with an important source of UV radia-tion is expected to be ionized at T ≳ K. From the GCslisted above, only four (47 Tuc, NGC 2808, M 15 and M 62)have stars hot enough to provide a wealth of UV radiation(log T > :
3) (O’Connell et al. 1997; Miocchi 2007) . Therest of them (M 54, NGC 6388, NGC 6440 and NGC 6441)lack these stars and, hence, become the best candidatesto search for an IMBH. NGC 6441 is the most appealingone as our models predict a high critical temperature, near12500 K. For a detailed list of sources in 47 Tuc and an estimation ofthe flux needed to ionize its medium, see McDonald & Zijlstra(2015). McDonald et al. (2015) present another approach aboutthe effect of UV radiation on the 47 Tuc medium.
In Paper I, we have discussed the impact of the frac-tional mass injection rate, (cid:11) on our results. Since the gasmass depends linearly on this parameter, a brief discus-sion on this dependence seems relevant. The value of (cid:11) hasbeen constrained to the range 10 − − − yr − from ob-servational works (Scott & Rose 1975; Fusi Pecci & Renzini1975; Dupree et al. 1994; Mauas et al. 2006; Priestley et al.2011). In Paper I, we managed to estimate (cid:11) by means ofcomparing our model with the traditional Bondi & Hoyle(1944) model and using the current observational constrainton the ISM obtained by Freire et al. (2001) in 47 Tuc. Thisyielded (cid:11) values in agreement with the range stated before.Nonetheless, even if (cid:11) was lower, it would not suffice to rec-oncile the estimated gas mass with the observational con-straints since, in most cases, the difference is greater thanthe 3 orders of magnitude of span in (cid:11) .We also constructed synthetic exctinction maps assum-ing the dusty component of the ISM couples to the gaseouscomponent, with a density times lower, depending onthe cluster metallicity. It is worth pointing out that anyspherical density distribution can be tested by means of thismethod. The maps were constructed on a star-by-star basisand consider only the extinction produced by the dust within the cluster. van Loon et al. (2009) and Alonso Garc´ıa et al.(2012) constructed 2-D extinction maps for ! Cen and M 62,respectively. In the case of ! Cen, we can draw no con-clusions about the accuracy of our extinction modelling inthis cluster, given the current observational precision in ex-tinction maps. On the other hand, our map for M 62 with T = 8000 K and no black hole, reproduces the spatial distri-bution observed by Alonso Garc´ıa et al. (2012), although itoverpredicts the difference in magnitudes between the cen-tral area of the cluster and the periphery. This result sug-gests that a model with an IMBH suits better the observa-tions of the reddening in this cluster, if gas temperature isclose to 8000 K. Of course, this result depends on the dustparticle size; note that Eq. 6 scales as ∼ a − . Recall thatfor M 62 we adopted a value of a ∼ : (cid:22) m. In Fig. 7 weshow 1D cuts of the upper-panel maps in Fig. 4 as dashed-coloured lines. The shaded regions account for the spread inthe grain size. It can be seen that for smallest particles, theextinction can be enhanced a few orders of magnitude. Con-straining the dust grain sizes as well as the gas temperaturewould be of great relevance to the study of IMBHs via dustextinction mapping. In this work we have developed a method that allow us to de-cide whether the presence of an IMBH at the centre of a GCis compatible with current estimations of the colour excess, E ( B − V ). As stated before, the construction method of themaps is independent of the density profile used. Hence, thisprocedure can be applied to any density distribution of in-terest. Unfortunately, observational techniques still includethe reddening produced along the path between the observerand the cluster while our method only estimates the redden-ing due to intracluster dust. This avoids a detailed compar-ison between our maps and the observational maps of eithervan Loon et al. (2009) or Alonso Garc´ıa et al. (2011). Thiscomparison would be useful, for example, to constrain the MNRAS , 1– ????
In Paper I, we have discussed the impact of the frac-tional mass injection rate, (cid:11) on our results. Since the gasmass depends linearly on this parameter, a brief discus-sion on this dependence seems relevant. The value of (cid:11) hasbeen constrained to the range 10 − − − yr − from ob-servational works (Scott & Rose 1975; Fusi Pecci & Renzini1975; Dupree et al. 1994; Mauas et al. 2006; Priestley et al.2011). In Paper I, we managed to estimate (cid:11) by means ofcomparing our model with the traditional Bondi & Hoyle(1944) model and using the current observational constrainton the ISM obtained by Freire et al. (2001) in 47 Tuc. Thisyielded (cid:11) values in agreement with the range stated before.Nonetheless, even if (cid:11) was lower, it would not suffice to rec-oncile the estimated gas mass with the observational con-straints since, in most cases, the difference is greater thanthe 3 orders of magnitude of span in (cid:11) .We also constructed synthetic exctinction maps assum-ing the dusty component of the ISM couples to the gaseouscomponent, with a density times lower, depending onthe cluster metallicity. It is worth pointing out that anyspherical density distribution can be tested by means of thismethod. The maps were constructed on a star-by-star basisand consider only the extinction produced by the dust within the cluster. van Loon et al. (2009) and Alonso Garc´ıa et al.(2012) constructed 2-D extinction maps for ! Cen and M 62,respectively. In the case of ! Cen, we can draw no con-clusions about the accuracy of our extinction modelling inthis cluster, given the current observational precision in ex-tinction maps. On the other hand, our map for M 62 with T = 8000 K and no black hole, reproduces the spatial distri-bution observed by Alonso Garc´ıa et al. (2012), although itoverpredicts the difference in magnitudes between the cen-tral area of the cluster and the periphery. This result sug-gests that a model with an IMBH suits better the observa-tions of the reddening in this cluster, if gas temperature isclose to 8000 K. Of course, this result depends on the dustparticle size; note that Eq. 6 scales as ∼ a − . Recall thatfor M 62 we adopted a value of a ∼ : (cid:22) m. In Fig. 7 weshow 1D cuts of the upper-panel maps in Fig. 4 as dashed-coloured lines. The shaded regions account for the spread inthe grain size. It can be seen that for smallest particles, theextinction can be enhanced a few orders of magnitude. Con-straining the dust grain sizes as well as the gas temperaturewould be of great relevance to the study of IMBHs via dustextinction mapping. In this work we have developed a method that allow us to de-cide whether the presence of an IMBH at the centre of a GCis compatible with current estimations of the colour excess, E ( B − V ). As stated before, the construction method of themaps is independent of the density profile used. Hence, thisprocedure can be applied to any density distribution of in-terest. Unfortunately, observational techniques still includethe reddening produced along the path between the observerand the cluster while our method only estimates the redden-ing due to intracluster dust. This avoids a detailed compar-ison between our maps and the observational maps of eithervan Loon et al. (2009) or Alonso Garc´ıa et al. (2011). Thiscomparison would be useful, for example, to constrain the MNRAS , 1– ???? (0000) C. Pepe et al.
Figure 7. T ∼ M BH = 0 ;
100 and 1000 M ⊙ , from left to right. The shaded areas cover theuncertainty in the extinction value due to the dispersion in the dust grain size. The horizontal dashed black line shows the ∼ : mass of the IMBH. However, we can explain the spatial sym-metry observed by these authors in M 62 and ! Cen, undercertain natural assumptions about the model parameters.Furthermore, in M 62, if gas temperature is close to 8000 K,our results suggest that an IMBH needs to be invoked, giventhe current observations of the extinction in this cluster.Finally, the cluster sample of Alonso Garc´ıa et al. (2012)corresponds to GCs with low Galactic latitude, where fore-ground extinction is highly variable and might obliteratethe effect due to intracluster dust (M. Catel´an, private com-munication). To overcome this issue, high-latitude clustersextinction maps should be measured and, if that is the case,the study of the extinction in GCs could be an extra obser-vational method to search for IMBHs that complements thecurrent ones based on star dynamics and accretion emission.
ACKNOWLEDGEMENTS
C.P. wants to express her gratitude to the referee, Jacco vanLoon, for such a detailed evaluation of the manuscript. Allthe suggestions only improved our work.
REFERENCES
Alonso Garc´ıa, J., Mateo, M., Sen, B., Banerjee, M. & von Braun,K., 2011, AJ, 141, 146Alonso-Garc´ıa, J., Mateo, M., Sen, B., Banerjee, M., Catelan, M.,Minniti, D. & von Braun, K., 2012, AJ, 143, 70Barmby P., et al., 2009, AJ, 137, 207Bash F. N., Gebhardt K., Goss W. M. & Vanden Bout, P. A.,2008, AJ, 135, 182Bondi H., Hoyle F., 2008, MNRAS, 104, 273Booth R., Sijacki D. & Clarke C., 2015, MNRAS, 452, 3932Bowers P. F., Kerr F. J., Knapp G. R., Gallagher J. S. & Hunter,D. A., 1979, AJ, 233, 553Boyer M. L., Woodward C. E., van Loon J. Th., et al., 2006, AJ,132, 1415Cardelli J. A., Clayton, G. C. & Mathis J. S., 1989, ApJ, 345,245Cseh D., Kaaret P., Corbel S., Kording E., Coriat M.,TzioumisA., Lanzoni B., 2010, MNRAS, 406, 1049Draine B. T. & Lee H. M, 1984, AJ, 285, 89Draine B. T., 2004, ASPC, 309, 691 Dupree A. K., Hartmann L., Smith G. H, et al., 1994, ApJ, 421,542Evans A., Stickel M., van Loon J. Th. , et al., 2003, A&A, 2003,408, L9Fabbiano G., 2006, ARA&A, 44, 323Frank J., Gisler G., 1976, MNRAS, 176, 533Faulkner D. J. & Freeman K. C., 1977, ApJ, 211, 77Feldmeier A., L¨utzgendorf N., Neumayer N., et al., 2013, A&A,554, 63Feng H. & Soria R., 2011, NewAr, 55, 166Freire, P. C., Kramer, M., Lyne, A. G., Camilo F., ManchesterR. N., D’Amico, N. ApJ, 557, L105Fusi Pecci F., Renzini A., 1975, A&A, 39, 413Harris, W.E. 1996, AJ, 112, 1487Ho, L. C., Terashima, Y. & Okajima,(2003) T., 2003, ApJ, 587,35Jalali B., Baumgardt H., Kissler-Patig M., et al., 2012, 538, 19Krause M., Charbonnel C., Decressin T., Meynet G., Prantzos N.& Diehl R., A&A, 546, L5Lakievi M., van Loon J. Th., Stanke T., De Breuck C. & PatatF., 2012, 541, L1Leigh N. W. C, B¨oker T., Maccarone T. J. & Perets H. B., MN-RAS, 2013, 429, L2997Lu T. & Kong A. K. H., 2011, AJ, 729, L25L¨utzgendorf N., Kissler-Patig M., Gebhardt K., et al., 2013, A&A,552, 49Lynch D. K. , Bowers P. F. & Whiteoak J. B., 1989, AJ, 97, 1708Maccarone T. J., 2004, MNRAS, 351, 1049Maccarone T. J., Fender R. P. & Tzioumis A. K., 2005, MNRAS,356, L17Maccarone T. J. & Servillat M., 2010, MNRAS, 408, 2511Magorrian J., et al., 1998, AJ, 115, 285Mauas P. J. D., Cacciari C., Pasquini L., 2006, A&A, 454, 609McDonald I., van Loon J. Th. , Decin L. et al., 2009, MNRAS,394, 831McDonald I., Boyer M. L., van Loon J. Th. & Zijlstra A. A., 2011,ApJ, 730, 71McDonald I., Zijlstra A. A., 2015, MNRAS, 446, 2226McDonald I., Zijlstra A. A., Lagadec E. et al., 2015, MNRAS,453, 4324Miocchi P., 2007, MNRAS, 381, 103Miocchi P., 2010, A&A, 514, 52Moore, K. & Bildsten, L., 2010, ApJ, 728, 81Naiman, J. P.; Ramirez-Ruiz, E.; Lin, D. N. C., 2011, ApJ, 735,25Noyola, E. & Gebhardt, G., AJ, 132, 447 (2006)Noyola E., Gebhardt K., Kissler-Patig M., et al., 2010, ApJ, 719,MNRAS , 1– ?? (0000) xtinction maps around IMBHs L60Nucita A. A., De Paolis F., Ingrosso G., Carpano S., GuainazziM., 2008, A&A, 478, 763O’Connell R. W., 1997, AJ, 114, 1982Odenkirchen M., Brosche P., Geffert M. & Tucholke H.-J., 1997,New Astronomy, 2, 477Pepe, C. & Pellizza, L. J., 2010, Star clusters: basic galactic build-ing blocks throughout time and space, Proceedings of theInternational Astronomical Union, IAU Symposium, Volume266, p. 491Pepe, C., & Pellizza, L. J. 2013, MNRAS, 430, 2789Piotto, G., Zoccali, M., King. I. R., et al., 1999, AJ, 118, 1727Priestley W., Ruffert M., Salaris M., 2011, MNRAS, 411, 1935Roberts, M. S., 1960, AJ, 65, 457Schlegel, D., Finkbeiner, D., & Davis, M. 1998, ApJ, 500, 525Scott, E. H. & Rose, W. K., 1975, ApJ, 197, 147Scott, E. H. & Durisen, R. H., 1978, AJ, 222, 612Strader J., Chomiuk L., Maccarone T. J., et al., 2012, ApJ, 750,L27Tayler R. J. & Wood P. R., 1975, MNRAS, 171, 467VandenBerg D. A. & Faulkner D. J., 1977, ApJ, 218, 415Van den Bosch, R., et al., 2006, ApJ, 641, 852van Loon J. T., Stanimirovi´c S., Evans A. & Muller E., 2006,MNRAS, 365, 1277van Loon J. T., Smith K. T., McDonald I., et al., 2009, MNRAS,399, 195van Loon J. T., Stanimirovi´c S., Putman M., et al., 2009, MN-RAS, 396, 1096Weingartner J. C. & Draine B. T., 2001, AJ, 548, 296MNRAS , 1– ????