The formation of UCDs and massive GCs: Quasar-like objects for testing for a variable stellar initial mass function (IMF)
Tereza Jerabkova, Pavel Kroupa, Joerg Dabringhausen, Michael Hilker, Kenji Bekki
AAstronomy & Astrophysics manuscript no. 31240_corr c (cid:13)
ESO 2018October 16, 2018
The formation of UCDs and massive GCs:
Quasar-like objects to test for a variable stellar initial mass function
T. Jeˇrábková , (cid:63) , P. Kroupa , (cid:63)(cid:63) , J. Dabringhausen , M. Hilker , and K. Bekki Astronomical Institute, Charles University in Prague, V Holešoviˇckách 2, CZ-180 00 Praha 8, Czech Republic Helmholtz Institut für Strahlen und Kernphysik, Universität Bonn, Nussallee 14–16, 53115 Bonn, Germany European Southern Observatory, Karl-Schwarzschild-Str. 2, D-85748, Garching bei München, Germany ICRAR,The University of Western Australia 35 Stirling Hwy, Crawley Western Australia 6009, AustraliaReceived 24.05. 2017; accepted 21.08. 2017
ABSTRACT
The stellar initial mass function (IMF) has been described as being invariant, bottom-heavy, or top-heavy in extremely dense star-burst conditions. To provide usable observable diagnostics, we calculate redshift dependent spectral energy distributions of stellarpopulations in extreme star-burst clusters, which are likely to have been the precursors of present day massive globular clusters (GCs)and of ultra compact dwarf galaxies (UCDs). The retention fraction of stellar remnants is taken into account to assess the mass to lightratios of the ageing star-burst. Their redshift dependent photometric properties are calculated as predictions for James Webb SpaceTelescope (JWST) observations. While the present day GCs and UCDs are largely degenerate concerning bottom-heavy or top-heavyIMFs, a metallicity- and density-dependent top-heavy IMF implies the most massive UCDs, at ages <
100 Myr, to appear as objectswith quasar-like luminosities with a 0.1-10% variability on a monthly timescale due to core collapse supernovae.
Key words. galaxies: formation – galaxies: star clusters: general – galaxies: high-redshift – stars: luminosity function, mass function– galaxies: dwarf – (galaxies) quasars: general
1. Introduction
The question of whether the stellar initial mass function (IMF)varies systematically with the physical conditions is a centralproblem of modern astrophysics (Elmegreen 2004; Bastian et al.2010; Kroupa et al. 2013). If it does vary, we would expect thelargest di ff erences compared to nearby star forming regions inthe most extreme star-burst conditions (e.g. Larson 1998). Whereare the most extreme star-burst conditions in terms of star for-mation rate densities to be found, with the constraint that theirpresent-day remnants are observable allowing detailed observa-tional scrutiny of their present-day stellar populations? Given thepresent-day masses ( > M (cid:12) ) and present-day half-light radii(1 −
50 pc), globular clusters (GCs) and in particular ultra com-pact dwarf galaxies (UCDs) are promising candidates (Mieskeet al. 2002; Chilingarian et al. 2008; Brodie et al. 2011, present-day half mass radius). For example a 10 M (cid:12) present-day UCDwith a half-light radius of 20 pc would likely have had a mass of10 M (cid:12) and a radius of a few pc when it was 1 Myr old (Dabring-hausen et al. 2010).Ultra compact dwarf galaxies (UCDs) were discovered byHilker et al. (1999) and Drinkwater et al. (2000). There is nounique definition of what a UCD is, but it is generally taken tomean a stellar system with a radius between a few and 100 pc,and a dynamical mass of 10 M (cid:12) (cid:47) M d y n (cid:47) M (cid:12) . Absolutemagnitudes of UCDs lie roughly between − (cid:39) M V (cid:39) −
16 M V ,where the higher value corresponds to an old and low mass UCD(similar to ω Cen), while the lower value is more characteristicfor a fairly young and / or massive UCDs (like W3). The most (cid:63) [email protected] (cid:63)(cid:63) [email protected] massive known old UCDs have magnitudes of M V ≈ −
14. Thepresence of UCDs has been reported also in other galaxy clus-ters, for example Virgo (Drinkwater et al. 2004), Coma (Priceet al. 2009), Centaurus (Mieske et al. 2007), Hydra I (Misgeldet al. 2011), and Perseus (Penny et al. 2012), or in massiveintermediate-redshift clusters (e.g. Zhang & Bell 2017). The ex-istence of systems with properties of UCDs was discussed al-ready by Kroupa (1998) based on the observations of star clustercomplexes in the Antennae galaxies.
The origin and evolution of UCDs is still a matter of debate (e.g.Côté et al. 2006; Hilker 2009; Brodie et al. 2011) and up untiltoday several possible formation scenarios have been proposed:(A) UCDs are the massive end of the distribution of GCs (e.g.Mieske et al. 2002; Forbes et al. 2008; Murray 2009; Dabring-hausen et al. 2009; Chiboucas et al. 2011; Mieske et al. 2012;Renaud et al. 2015), (B) UCDs are merged star cluster com-plexes (Kroupa 1998; Fellhauer & Kroupa 2002b,a; Brüns et al.2011), (C) UCDs are the tidally stripped nuclei of dwarf galaxies(Oh et al. 1995; Bekki et al. 2001, 2003; Drinkwater et al. 2003;Goerdt et al. 2008; Pfe ff er & Baumgardt 2013), and (D) UCDsare remnants of primordial compact galaxies (Drinkwater et al.2004).Murray (2009) showed that the distribution and kinematicsof the visible matter is not consistent with UCDs being objectsdominated by non-baryonic dark matter halos. This is supportedby a detailed study of one of the most massive UCDs (Frank et al.2011). Based on the Millenium II cosmological simulation, Pf-e ff er et al. (2014) show that the formation of UCDs as tidally Article number, page 1 of 18 a r X i v : . [ a s t r o - ph . GA ] O c t & A proofs: manuscript no. 31240_corr stripped nuclei of dwarf galaxies can account only for about 50per cent of observed objects with mass > M (cid:12) ; for masses > M (cid:12) this drops to approximately 20 per cent (Pfe ff er et al.2016). Furthermore, earlier Thomas et al. (2008) showed thatthe tidally stripped nucleus scenario fails to reproduce UCDs lo-cated in the outer parts of the Fornax cluster. Based on theseresults we focus on scenarios (A) and (B), which both suggestthat UCDs are the high-mass end of star cluster-like objects,formed most likely during massive starbursts (Weidner et al.2004; Schulz et al. 2015, 2016) at higher redshift, where compactstar-bursts are indeed observed (Vanzella et al. 2017; Glazebrooket al. 2017). In this contribution we aim to quantify how extreme star for-mation environments may appear at high redshifts, where themost intense star-bursts are likely to have occurred. We there-fore concentrate on the progenitors of present-day UCDs andGCs (i.e. their young counterparts at high redshift). We con-struct stellar population models using the PEGASE (Fioc &Rocca-Volmerange 1997) code to suggest possible photometricdiagnostics to provide observational predictions for upcomingmissions such as the James Webb Space Telescope (JWST). Theunderlying question for this work is: Can a systematic variationof the stellar IMF be confirmed by observations of the likelyhigh-redshift precursors of present-day GCs and UCDs using theJWST?This paper is structured as follows: The first section is de-voted to the introduction of the topic. Section 2 describes themethods we use. Section 3 focuses on results and Sections 4 and5 contain the discussion and conclusion, respectively.
2. Methods
We compute properties of UCDs and UCD progenitors assum-ing that they have formed according to scenario (A), that is bymonolithic collapse. In such a case we expect that the first UCDswere formed alongside the formation of early massive galaxies( ≈ . For quantifying our approach, we consider UCDs with the fol-lowing properties: the UCD’s initial stellar mass, M UCD ∈ [10 , ] M (cid:12) , red-shift, z ∈ , , ,
9, corresponding, respec-tively, to ages from the Big-Bang ≈ Λ cold dark matter ( Λ CDM) cosmologywith Planck estimates, Ω m ≈ . Ω Λ ≈ . H ≈ . − Mpc − (Planck Collaboration et al. 2016b,a). Otherparameters are metallicity, [Fe / H] = − / pegase. We describe the stellar IMF as a multi-power law, ξ ( m (cid:63) ) = k m − α . ≤ m (cid:63) / M (cid:12) < . , k m − α . ≤ m (cid:63) / M (cid:12) < . , k m − α . ≤ m (cid:63) / M (cid:12) ≤ , (1)where ξ ( m (cid:63) ) = d N / d m (cid:63) (2)is the number of stars per unit of mass and k i are normalizationconstants which also ensure continuity of the IMF function. Asa benchmark we use the IMF α values derived from the Galacticstar forming regions by Kroupa (2001), where α = . α = α = .
3, here denoted as CAN IMF (canonical IMF).A larger α than the canonical value leads to a bottom-heavyIMF. A bottom-heavy IMF is also described by a single Salpeterslope α = α = α = α = .
3, which has been shown to leadto slightly elevated M / L V values (Dabringhausen et al. 2008;Mieske & Kroupa 2008) relative to the CAN IMF. Throughoutthis paper we will call this IMF the SAL IMF (Salpeter IMF).An even more bottom-heavy IMF, which might be necessary forexplaining the observed M / L V values around ten and higher, wassuggested by van Dokkum & Conroy (2010) for massive ellip-tical galaxies, due to features observed in their spectra (but seeSmith & Lucey 2013). This IMF is here referred to as the vDCIMF, and is characterized by an IMF slope α = α = α = α = .
0. A dependency of α on star-cluster-scale star-formation den-sity and metallicity is currently not known. Chabrier et al. (2014)suggest increased turbulence to account for a bottom-heavy IMFin dense star forming regions. However, further theoretical work(Bertelli Motta et al. 2016; Liptai et al. 2017) casts doubts onthis. This issue clearly needs further research.The other option of how to explain the observed M / L V ratiosis a top-heavy IMF (Dabringhausen et al. 2009). The top-heavyIMF has an empirical prescription, which establishes the slope ofthe heavy-mass end, α , over the interval of masses (1 , (cid:12) as a function of metallicity [Fe / H] and birth density of the em-bedded star cluster, (cid:37) cl . The lower stellar masses ( < . (cid:12) ) arein our formulation here distributed according to the CAN IMF.The relation for α by Marks et al. (2012) is, α = (cid:40) . x < − . , − . x + .
94 if x ≥ − . , (3)where x = − . Fe / H ] + .
99 log (cid:32) (cid:37) cl M (cid:12) pc − (cid:33) . (4)These relations have been obtained from a multi-dimensional re-gression of GC and UCD data. To calculate the birth density, (cid:37) cl , we use the empirical relation from Marks & Kroupa (2012),where the half-mass radii of embedded clusters follow R cl / pc = . M ecl / M (cid:12) ) . , (5)where M ecl is the stellar mass. The total density (gas + star) , (cid:37) cl ,for a star formation e ffi ciency, (cid:15) , is given by (cid:37) cl = M ecl (cid:15)π R cl . (6)Further on, we assume a star formation e ffi ciency (cid:15) = .
33 (e.g.Megeath et al. 2016; Banerjee 2017) and refer to the IMF derived
Article number, page 2 of 18. Jeˇrábková et al.: The formation of UCDs: Testing for a variable stellar IMF
IMF Top-heavy Canonical Bott.-heavy Bott.-heavyMKDP CAN SAL vDC α α α Table 1.
Summary of IMF variations used in this paper. The α -coe ffi cients are defined by Equation 1. The MKDP IMF depends onthe initial stellar mass of the system according to Equation 3. using these relation as the MKDP IMF. The α and half-massradii R cl are listed in Table 2. Theoretical arguments for the IMFbecoming top-heavy with increasing density, temperature, anddecreasing metallicity of the star-forming gas cloud have beendescribed by e.g. Larson (1998), Adams & Laughlin (1996), Dibet al. (2007), Papadopoulos (2010) and Romano et al. (2017).All the IMFs considered here are summarized in Table 1. The above parametrizations are used as input values to the PÉ-GASE time-dependent stellar population synthesis code (Fioc& Rocca-Volmerange 1997) and we compute the time evolutionof various quantities, such as the total luminosity, L UCD , numberof massive stars ( m (cid:63) > (cid:12) ), N mass , and also observable prop-erties: the redshifted time evolution of the spectral energy distri-bution (SED), and colour-magnitude diagrams. Furthermore weinvestigate in detail the M / L V values. Besides the values con-sidered here for the initial stellar mass, metallicity, and redshiftof the UCDs ( M UCD , [Fe / H], z ), we use the following values tocompute the PÉGASE models: a conservative value η = . η ∈ (0 . , . M / L V ratios To evaluate the dynamical mass, M , and luminosity in the V band, L V , several assumptions are made: (i) We assume that theUCDs are gas free during the whole period of their evolution,which means that our predictions are only valid for pure stel-lar populations. (ii) Mass loss from the UCDs is only throughstellar evolution in the form of ejected gas. We assume that allstars are kept in the system and no stars are lost by dynamicalevolution of the UCDs. Stellar loss due to dynamical evolutionis an important process (e.g. Balbinot & Gieles 2017) which is,however, significant only for systems with initial stellar mass (cid:47) M (cid:12) (Lamers et al. 2005; Schulz et al. 2016; Brinkmannet al. 2017). The reason is that for large stellar mass, (cid:39) M (cid:12) , / pegase. the tidal radius in a Milky-Way galaxy potential is (cid:39)
100 pc forGalactocentric distances (cid:39) few kpc such that the vast majorityof stars remain bound. This is consistent with using Equation (5)from Lamers et al. (2005) which, after integration, gives an upperlimit for tidal stellar mass loss over a Hubble time ≈ M (cid:12) in-dependent of initial mass. (iii) The e ff ect of loss of dark remnants(neutron stars and black holes) on the estimate of the dynamicalmass for the vDC, SAL, and CAN IMF is negligible to the valueof the M / L V ratio (for the CAN IMF dark remnants contributeonly few per cent of the UCD mass). However, in the MKDPIMF case, where dark remnants contribute a substantial fractionto the total mass of the system, the amount of dark remnants keptis no longer negligible. The actual fraction of dark remnants keptin a system is still being discussed mainly because to study rem-nant ejections, close dynamical encounters in a system are im-portant on a Hubble timescale (Banerjee 2017). Such studies areextremely computationally intensive for systems as massive asUCDs. On the other hand, Peuten et al. (2016) and Baumgardt &Sollima (2017), constrain the retention fraction of dark remnantsin lower mass GCs, which allows us to deduce implications forUCDs. The mass-to-light ratios of UCDs depend on the retention frac-tion of stellar remnants within the system once the progenitorstars die. In order to assess the possible range of retention frac-tions, we assume that white dwarfs (WDs) receive no kicks uponthe death of their progenitor stars such that all WDs remainbound to the system. A star more massive than 8 M (cid:12) explodesas a type II supernova or implodes leaving either a neutron staror a stellar black hole. The kicks these receive during such vio-lent events due to the asymmetry of the explosion or implosionare uncertain. Large natal kicks will lead to the loss of most suchremnants from the system.We estimate the retention fraction by assuming that10 per cent of all neutron stars and black holes are retainedin a globular cluster with a mass of 10 M (cid:12) . This is a conser-vative assumption as Baumgardt & Sollima (2017) and Peutenet al. (2016) constrain the retention fraction to be less than about50 per cent for globular clusters (GCs) based on a detailed studyof their observed mass segregation. With this normalisation con-dition, and assuming two possible radius-mass relations for GCsand for UCDs, we can estimate the likely values of the retentionfraction of stellar remnants (neutron stars and black holes) as afunction of birth system mass, M . One possibility for the R ( M )relation is to assume the observed radii of clusters (typicallyabout 3 pc) and of UCDs (Eq. (4) in Dabringhausen et al. 2008).The other possibility is to assume that the stars die in their birthsystems before these expand (Dabringhausen et al. 2010) dueto residual gas expulsion and stellar-evolution-driven mass losswith the R ( M ) relation constrained by Marks & Kroupa (2012,their Eq. 7). Given the R ( M ) relation, we assume that remnantsare lost if their speed after the kick is larger than the central es-cape velocity. We assume the systems to be Plummer models andthat the kick velocities follow a Maxwell-Boltzmann distribution(MBD) with velocity dispersion σ kick .Figure 1 shows the resulting MBD for the two assumed R ( M )relations. The adopted normalization condition forces the MBDto be narrow, with a small kick, σ kick =
24 km / s, for the present-day radii of clusters and UCDs, while applying the birth radiiresults in a larger kick, σ kick =
61 km / s. Despite the two dif-ferent values, the resulting retention fractions, defined for thepresent purpose as the fraction of remnants with a speed smaller Article number, page 3 of 18 & A proofs: manuscript no. 31240_corr
MKDP IMF CAN IMF[Fe / H] = -2 [Fe / H] = M UCD [M (cid:12) ] R cl [pc] α N ( m (cid:63) > M (cid:12) ) α N ( m (cid:63) > M (cid:12) ) α N ( m (cid:63) > M (cid:12) )10 . .
61 0 . .
73 0 . . . . .
37 2 . .
48 2 . . . .
12 23 . .
23 23 . . . .
87 213 . .
99 222 . . . .
62 1943 . .
74 2032 . . Table 2.
Values of the initial radii of the embedded star clusters, R cl , (Marks & Kroupa 2012), α values (see Eq. (3)), and the number of massivestars N ( m (cid:63) > M (cid:12) ) computed as a function of initial stellar mass, M UCD = M ecl , and metallicity. For comparison, we also show N ( m (cid:63) > M (cid:12) ) forthe CAN IMF. The predicted values of the embedded cluster / UCD initial radii, R cl , are small. However, due to stellar and dynamical evolution,UCDs expand by approximately a factor of ten (Dabringhausen et al. 2010). We use the R cl values as an empirical extrapolation from GCs andtherefore at UCD scales departures are possible. than the central escape speed, are very similar. This is shownin Fig. 2, from which it also follows that the retention fractionincreases steeply with system mass such that for M > M (cid:12) the retention fraction can be assumed to be near to 100 per cent,if the normalization condition applied here holds. We also plotthe retention fraction for distributions with larger σ kick values,namely 100, 300 , and 500 km / s. Given these results it is rea-sonable to assume that the retention fraction of UCDs with birthmasses larger than 10 M (cid:12) is close to 100%. Indirect evidencesuggesting a possible large retention fraction in UCDs are re-cent findings of super massive black holes (SMBHs) in UCDs(e.g. Seth et al. 2014; Ahn et al. 2017, see Sec. 4.3). Neverthe-less, we still investigate the e ff ect of smaller retention fractionson the M / L V values to allow us to see the maximum impact theassumed IMF can potentially have. v [km / s]0 . . . . . . p r o p a b ili t y d e n s i t y / s σ kick = 61.0 km / s v esc = 45.9 km / s33.9 km / s σ kick = 24.0 km / s v esc = 17.7 km / s Fig. 1.
Distribution function of speeds of dark stellar remnants. We usethe conservative estimate that only 10 per cent of dark remnants are keptin 10 M (cid:12) system due to SN kicks. We constrain the SN kick velocitydistribution assuming it has a Maxwell-Boltzman shape for birth radius(Marks & Kroupa 2012, red curve) and for present day radius, 3 pc forGCs and for the UCDs we use the mass-radius relation from Dabring-hausen et al. (2008) (their Eq. 4, blue curve). The peak velocity, σ kick ,and v esc values are stated. We note here three possible limitations to the models introducedabove: M UCD [M (cid:12) ])0 . . . . . . b l a c k h o l e s r e t e n t i o n f r a c t i o n b i r t h r a d i u s o b s e r v e d r a d i u s σ k i c k = k m / s σ k i c k = k m / s σ k i c k = k m / s Fig. 2.
Retention fraction of dark remnants as a function of system massif we assume that the main mechanism of dark remnants ejection areSN kicks with a Maxwell-Boltzman kick velocity distribution shown inFig. 1. We assumed two di ff erent mass-radius relations (red and bluecurves, as in Fig. 1), radii for each mass being written next to the cor-responding points and a normalization described in the text. In blackand grey we plot retention fractions if larger kick velocity dispersionsare assumed. In this case we use the mass-radius relation from Marks &Kroupa (2012).
1. E ff ects of binariesThe majority of stars form in binaries (e.g. Marks et al. 2011;Thies et al. 2015). Mass transfer and mergers can rejuvenatestellar populations leading to significantly more UV radia-tion even after a few Gyr (Stanway et al. 2016, BPASS code).Since here we focus on the IR region mostly and on systemsyounger than 100 Myr, it is likely that our conclusions arenot a ff ected strongly if binary-star evolution is taken into ac-count, but it is nevertheless important to check this factor inthe future.2. Multiple populationsIt is well established that GCs have multiple stellar popula-tions (e.g Renzini et al. 2015, review). This may be true forUCDs as well. Future SED modelling has the potential to ad-dress how and if these can be observed in young systems athigh redshift. However, we caution that binary stellar evolu-tion (Item 1 above) may lead to degeneracies.3. Statistical importanceLarge statistical samples may be needed to ascertain asystematic variation of the IMF with physical conditions Article number, page 4 of 18. Jeˇrábková et al.: The formation of UCDs: Testing for a variable stellar IMF
QSO z M V M I RQ / RL0923 +
201 0.193 -24.6 -24.28 RQ2344 +
184 0.138 -23.6 -23.80 RQ1635 +
119 0.147 -23.1 -22.39 RQ1012 +
008 0.185 -24.3 -25.39 RQ1004 +
130 0.241 -25.7 -24.90 RL1020-103 0.197 -24.2 -24.35 RL2355-082 0.211 -23.0 -23.71 RL
Table 3.
Quasar (QSO) data. The first column is the QSO identification, z is the redshift, M V and M I are absolute magnitudes, and RQ / RL labelsthe QSO as being radio quiet (RQ) or radio loud (RL). We have notfound any publication or catalogue presenting both the absolute magni-tudes in the V filter, M V , and I filter, M I . Therefore, the data in the tableuse the catalogue by Souchay et al. (2015) containing the M I values.The M V values are taken from Dunlop et al. (1993) and Dunlop et al.(2003). (Dabringhausen et al. (2008); Dabringhausen et al. (2009);Dabringhausen et al. (2012)).
3. Results
For the grid of chosen parameters we construct a time grid (1-10 Myr with 1 Myr step, 10-100 Myr with 10 Myr steps, 100-1000 Myr with 100 Myr steps, and 1-13 Gyr with 1 Gyr steps)of SEDs, which contain all the light information from the sourcenecessary for the construction of other observables. Further de-tails (e.g comparison of the PEGASE code and the StarBurst99–code (Leitherer et al. 1999) with description of the evolution ofSEDs with time and dependency on redshift) can be found inAppendix A.
To demonstrate how luminous progenitors of UCDs could havebeen, we compute the bolometric luminosity, L bol , as a functionof time. The L bol ( t ) dependency is shown in Fig. 3. The bench-mark initial mass is M UCD = M (cid:12) . For the cases of the CAN,SAL, and vDC IMF, the L bol values are proportional to M UCD .The MKDP IMF is a function of M UCD and therefore we plot L bol ( t ) also for M UCD = and 10 M (cid:12) . The main di ff erencebetween di ff erent MKDP IMFs (for di ff erent M UCD ) is the slopeof the luminosity as a function of time. For a more top-heavyIMF, the decrease of the luminosity with time is steeper.There are several noticeable features in this figure: (i) for theMKDP IMF, UCDs with initial stellar mass M UCD (cid:39) M (cid:12) areas bright as quasars (Dunlop et al. 1993, 2003; Souchay et al.2015) for the first few 10 yr. We use low-redshift quasars be-cause for these we were able to find bolometric luminosities, butalso absolute magnitudes in the V and I band. We note, however,that high redshift quasars show very comparable luminosities asshown for example by Mortlock et al. (2011). This is mainly dueto the presence of a large number of O and B stars (10 − )in the system. Due to stellar evolution and core-collapse super-nova explosions, these UCDs will be variable on a timescale ofmonths. As already suggested by Terlevich & Boyle (1993), suchobjects might be confused with quasars, especially for examplein large photometric surveys. (ii) After less than a 100 Myr, astrong degeneracy between the IMF and M UCD appears. That is,for di ff erent M UCD and di ff erent IMFs, similar luminosities com-parable to those of observed UCDs occur. (iii) The metallicity isa second-order e ff ect. M / L V ratio The PEGASE output allows us to evaluate the mass-to-light() M / L V ) ratios in arbitrary photometric filters since with the timeevolution the code keeps information about the current stellarmass, mass in black holes and neutron stars, and also about thegas (non-consumed initial gas and the gas ejected by stars). Sincethe vDC or SAL (bottom-heavy) IMFs do not depend on the ini-tial UCD mass, neither does the M / L V ratio. The situation isdi ff erent for the MKDP IMF and we therefore plot the time evo-lution of the M / L V ratio for di ff erent initial masses in Fig. 4. M / L V ratio variations The results show that the largest di ff erences in M / L V ratios areevident in the first ≈
100 Myr, which is the age corresponding tothe time when the most massive stars evolve into dark remnants(see Fig. 4 where we can also see the e ff ect of the retention frac-tion of remnants on the M / L V values). For later times ( > M / L V ratios might become indistinguishable at timesolder than ≈
100 Myr for di ff erent IMFs within the observationaland metallicity uncertainties.Using the same models, we construct the dependence of M / L V on L V for di ff erent evolutionary times (Fig. 5). To con-struct these plots, we assumed the set of initial UCD masses to be10 , , M (cid:12) . As is clear from the comparison of the panelsin Fig. 5, the metallicity has a large e ff ect on the M / L V values. The supernovae (SNe) II rate (Lonsdale et al. 2006; Andersonet al. 2011) can be a very good indicator of the IMF as onecan see in Fig. 6. According to the standard stellar evolution-ary tracks employed here, every star more massive than 8 M (cid:12) ends as a supernova explosion. However, this may not always bethe case. As the metallicity varies it may happen that a star of agiven mass may implode and create a black hole directly withoutany explosion (see e.g. Pejcha & Thompson 2015) and thereforeour theoretical prediction represents the upper limit to the SN IIrate.It is important to point out that the SN rate depends on thestar formation history of a system. If the whole system is formedduring an instantaneous starburst, the peak SN II rate might bya factor of ten higher than in the case of constant star formationover a period of 5 Myr. On the other hand, if the star formationis more extended then the period of high SN II rate lasts longer.Considering the luminosities of SNe (Gal-Yam 2012; Lymanet al. 2016), in Fig. 3 we show that at the later phases, > M (cid:12) initial mass (for smallerinitial masses, SN II explosions will be more pronounced) andtherefore might be detectable as photometric fluctuations on thescale of months.To compute the SN Ia, rate we adopt a conservative frac-tion, η = .
05, of intermediate-mass stars that eventually ex-plode as SNe Ia. According to Maoz (2008), η = . − .
4. Weuse η = .
05 also because it is a default value of this parame-ter and therefore our results will probably be comparable withother studies. The η value a ff ects the estimates of the number ofSNe Ia and also of the ejecta (Thielemann et al. 1986; Greggio &Renzini 1983; Matteucci & Greggio 1986). The computed rates Article number, page 5 of 18 & A proofs: manuscript no. 31240_corr time [Myr]10 L b o l [ L (cid:12) ] M UCD = 10 M (cid:12) L bol ∝ M UCD (NOT for MKDP) M (cid:12) M (cid:12) M (cid:12) [Fe/H]= − − . − . − . − . − . − . − . − . M b o l [ m ag ] U C DD A T A QUASARS S U PE R N O VA E Fig. 3.
Time evolution of the bolometric luminosity for di ff erent IMFs. The MKDP IMF changes with the initial mass of the UCD and does notscale linearly with its mass. In contrast, the vDC, SAL, and CAN IMFs have UCD-mass-independent slopes and scale proportionally with M UCD .The grey panel shows the typical luminosities of quasars (Dunlop et al. 1993, 2003; Souchay et al. 2015) and the brown panel shows the luminosityspan for the peak luminosities supernovae (Gal-Yam 2012; Lyman et al. 2016), which might cause luminosity variations in L bol of UCDs youngerthan about 50 Myr according to SNe rates. are plotted in Fig. 7. Using a value as large as η = . M / L V values, arenot a ff ected by the value of η , since di ff erent values of η do notchange the mass distribution of stars. β UV slope The β UV slope is defined here as the slope of the fitted linearfunction to the logarithmically scaled SED, expressed in unitsof ergs − cm − Å − , in a wavelength interval (1350,3500)Å in therest frame of the observed object, as shown in Fig. A.7 in theAppendix. We computed β UV for the complete set of our SEDs(Fig. 8). The β UV values have been determined for objects downto 10 M (cid:12) (for a top-heavy IMF this may be 10 M (cid:12) ) at high red-shifts (up to z =
6) (Vanzella et al. 2017) and therefore mightallow very useful additional constraints on the IMF and the ageestimates. The β UV values are metallicity sensitive and have agenerally increasing trend with age. The dependence on the IMFis stronger for objects younger than 10 Myr and at low metal-licity, β MKDPUV ≈ − . β v DCUV ≈ − . / H] = -2.At an age of 200 Myr, these values evolve to β MKDPUV ≈ − . β v DCUV ≈ − .
1. At a high redshift it may not always be possible to obtain aspectrum of a UCD. In such a case we can obtain photometricfluxes in at least two filters and use these to approximate the β UV slope. For z = z = z = Other observables, which can be computed from the SED andfor standard filters and which are provided by PEGASE, are var-ious colours and magnitudes. The time evolution of our objectsis shown in the V versus V − I c diagram for comparison withother work (e.g. Evstigneeva et al. 2008). This is done for theCAN, SAL, and vDC IMFs in Fig. 10, and for the MKDP IMFin Fig. 9. As expected we can see the increasingly strong degen-eracy with time that makes it hard to distinguish the metallicity,initial mass, or the IMF.The colour-colour diagram has the advantage of having dif-ferences in magnitudes on both axis and therefore in a way sub-dues the information about the absolute values and enhancesthe di ff erences in spectral shapes and features. As is shown inFig. A.8, we chose to use the standard filters J, K, and N. The N Article number, page 6 of 18. Jeˇrábková et al.: The formation of UCDs: Testing for a variable stellar IMF time [Myr]10 − − − − M / L V NO remnants10% remnants100% remnants M (cid:12) M (cid:12) M (cid:12) [Fe/H]=-2 M B H ↑ vDC IMFSAL IMFCAN IMFMKDP IMF time [Myr]10 − − − − M / L V NO remnants10% remnants100% remnants M (cid:12) M (cid:12) M (cid:12) [Fe/H]=0 M B H ↑ vDC IMFSAL IMFCAN IMFMKDP IMF Fig. 4.
Time evolution of M / L V for all IMFs considered (vDC, SAL, CAN, MKDP). We assume that the system is gas free and that neither starsnor remnants are leaving (the dashed lines show the change of the M / L V value if only certain fractions of remnants are kept). The upwards-pointingblue arrow demonstrates that if we would assume more massive remnants (e.g. due to implosion directly to a BH without a SN explosion), thenthis would lead to larger values of M / L V . The models are computed for the case of M UCD = M (cid:12) , however, results are mass independent. Theonly exception is the MKDP IMF, which depends on initial object mass, M UCD , and also contains a large fraction of mass in high mass stars, and isplotted for M UCD = (10 , , M (cid:12) , bottom to top) and di ff erent fractions of remnants retained (100%,10%,0%). Left panel:
The evolution for[Fe / H] = -2. Right panel:
The evolution for [Fe / H] =
0. The grey band indicates the span of the observed present-day M / L V values, approximatelyfive to ten for the majority of UCDs (Mieske et al. 2008; Dabringhausen et al. 2009). The scales are identical for both panels. L V [L V (cid:12) ]510152025 M / L V M V [mag] 10 L V [L V (cid:12) ]510152025 M / L V [Fe/H]= 0-10.17 -12.67 -15.17 M V [mag] Fig. 5.
Values of the M / L V ratio as a function of L V for three di ff erent times 5 , ,
13 Gyr. The case of the MKDP IMF is not constant since theMKDP IMF is a function of initial mass. The plotted curves assume all remnants are kept; if only a fraction are kept, the M / L V values wouldbecome smaller accordingly. There are two horizontal axes, the one on the top of the plots shows corresponding values of the absolute magnitudein the rest-frame V band. The observed values of M / L V for UCDs are in the interval from approximately five to ten, with few values spanning upto 15 (Mieske et al. 2002), which are shown by the grey band. The points plotted on the curves mark luminosities and M / L V values for UCDsstarting with initial mass of 10 , , and 10 M (cid:12) . Left panel: [Fe / H] = -2. Right panel: [Fe / H] = filter is almost identical to F1000W on the mid-infrared instru-ment (MIRI) on the JWST. The J and K filters cover a similarrange as the F115W and F200W filters on near infrared cam-era (NIRCam) on the JWST. The results presented here assumetransmission functions corresponding to their filters to be givenby the rectangular regions shown in Fig. A.4. These filters pos-sess several useful characteristics: (i) even for a redshift of valuenine, they are still in the spectral range covered by the PEGASESEDs and therefore we do not introduce any additional errors byusing the extrapolated range of the SEDs, (ii) J, K, and N cover large parts of the SEDs and therefore are good representatives ofan overall shape, and (iii) the N filter is still in the well-describedregion where we do not expect large discrepancies from modelto model and therefore also in real measurements as can be seenin Fig. A.2. The first question which we need to ask is whether UCD progen-itors are bright enough to be detected and if so up to which red-
Article number, page 7 of 18 & A proofs: manuscript no. 31240_corr
10 20 30 40 50time [Myr]10 − − − − S N e II r a t e [ y r − ] M UCD = 10 M (cid:12) ∝ M UCD (NOT for MKDP) [Fe/H]= − M (cid:12) M (cid:12) shorter SF history MKDP IMFvDC IMFSAL IMFCAN IMF
Fig. 6.
SNe II rate as a function of time for a constant star formationhistory over a period of 5 Myr. In the instantaneous star-burst case, theSNeII rate may be10 × higher at ages <
10 Myr. We show the case of thevDC, SAL, CAN, and MKDP IMFs. Since only the MKDP IMF doesnot scale linearly with initial stellar mass, M UCD , we show also the linesfor M UCD = M (cid:12) and 10 M (cid:12) ; for the other IMFs we chose to plotonly 10 M (cid:12) . The arrow indicates that the peak of the SN II rate shiftsto the left and upwards for a star formation history which is shorter than5 Myr. time [Myr]10 − − − − − − S N e I a r a t e [ y r − ] M UCD = 10 M (cid:12) M (cid:12) M (cid:12) [Fe/H]= − ∝ M UCD (NOT for MKDP) vDC IMFSAL IMFCAN IMFMKDP IMF
Fig. 7.
SNe Ia rate as a function of time. We show the case of the vDC,SAL, CAN, and MKDP IMFs. Since only the MKDP IMF does notscale linearly with initial stellar mass, M UCD , we show also the lines for M UCD = M (cid:12) and 10 M (cid:12) ; for the other IMFs we chose to plot only10 M (cid:12) . The text gives more details. shift. To quantify this we use the upcoming James Webb SpaceTelescope (JWST) as a benchmark. To cover the wavelength re-gion computed here by PEGASE, the most suitable instrumentis NIRCam in imaging mode, in total covering the region from0.6 to 5 µ m. To probe longer wavelengths, we also compute pre-dictions for the MIRI instrument in imaging mode.All predictions we make are for the UCDs with an initialstellar mass of 10 M (cid:12) ; we use the CAN IMF as the standardand consider also the MKDP IMF. For the NIRCam instrumentwe use as a setup sub arrays FULL, readout DEEP8, groups 10,integration 1, and exposures 5. This results in a total exposuretime of 10149 s. For the MIRI instrument the parameters are: instr. filter z S / N CAN S / N MKDPNIRCam F115W 3 47 194NIRCam F200W 3 47 215NIRCam F480M 3 7 52MIRI F1000W 3 0.4 4NIRCam F115W 6 14 76NIRCam F200W 6 15 83NIRCam F480M 6 2 16MIRI F1000W 6 0.1 1NIRCam F115W 9 6 36NIRCam F200W 9 7 42NIRCam F480M 9 1 7MIRI F1000W 9 0.06 0.5
Table 4.
Predictions for di ff erent filters of the JWST telescope. All val-ues are computed for an initial stellar mass of 10 M (cid:12) and for referencethe CAN IMF and the MKDP IMF are considered. The S / N values canbe reached within a total integration time of ≈ subarrays FULL, readout FAST, groups 100, integration 1, ex-posures 36, resulting in a similar exposure time of 10090 s. Thepredictions for the JWST telescope are summarized in Table 4.The general conclusion is that UCD progenitors are detectableusing JWST photometry with a ≈
3h exposure time with promis-ing values of S / N , as already suggested for GCs progenitors byRenzini (2017).
4. Discussion
The star-formation-rate density typically peaks near the centre ofa galaxy. This is evident in interacting galaxies (Joseph & Wright1985; Norman 1987; Wright et al. 1988; Dabringhausen et al.2012), while in self-regulated galaxies the distribution of star-formation-rate density may be more complex as a result of con-verging gas flows, for example at the intersection points betweena disc and bar. Generally though, central regions are the most ac-tive in star formation activity in star forming galaxies. That themost massive clusters form near the centres of galaxies where theSFR-density is highest is evident in various star-bursting galax-ies (Ferrarese & Merritt 2002; Dabringhausen et al. 2012), in ourGalaxy (Stolte et al. 2014), and also in young-cluster surveysof individual galaxies (Pflamm-Altenburg et al. 2013). Simula-tions of star forming galaxies lead to the same result (Li et al.2017). Observationally it has been shown that the most massiveclusters form preferentially in galaxies with the highest star for-mation rate (SFR) (Weidner et al. 2004; Randriamanakoto et al.2013). We can therefore consider the following overall process:in the process of the formation of massive galaxies, star for-mation would have been spread throughout the merging proto-galactic gas clumps. The most massive clusters, the proto-UCDs,would be forming in the deepest potential wells of these, butwould decouple from the hydrodynamics once they became stel-lar systems. As the proto-galaxies merge to form the massivecentral galaxies of galaxy clusters, many of such formed UCDswould end up on orbits about the central galaxy, possibly withthe most massive UCDs within and near the centre of the galaxy.We can therefore expect that the most massive UCDs, thosethat formed monolithically (i.e. according to formation sce-nario A), are to be found in the innermost regions of formingcentral-dominant galaxies at a high redshift. Such galaxies have
Article number, page 8 of 18. Jeˇrábková et al.: The formation of UCDs: Testing for a variable stellar IMF − . − . − . β U V [Fe/H]= − M (cid:12) M (cid:12) MKDP IMFSAL IMFvDC IMF − . − . − . − . − . β U V zoom plot [Fe/H]= − M (cid:12) M (cid:12) Fig. 8.
Time evolution of the β UV values fitted over the wavelength interval (1350,3500)Å to the SEDs in the rest frame of the observed object inunits ergs − cm − Å − . The β UV slope is M UCD -independent, but not for the case of the MKDP IMF for which we plot the case of M UCD = M (cid:12) and 10 M (cid:12) . Left panel:
The time evolution of the β UV slope over the time period of 200 Myr. Right panel:
The zoom-in plot covers the first 50Myr. The grey band shows the measurement from Vanzella et al. (2017) for their object GC1. − . . . . . M V − M I c − . − . − . − . − . − . − . − . M V QUASARS U C D d a t a MKDP IMF10 M (cid:12) M (cid:12) M (cid:12) [Fe/H]=0 [Fe/H]= − t i m e Fig. 9.
Colour-magnitude diagram showing M V as a function of V − I c (in the UCD rest frame). These latter are photometric filters directlycomputed by PEGASE. We consider 10 , , M (cid:12) as initial stellar masses, and metallicity values [ Fe / H ] = − ,
0. Here we show only theresults for the MKDP IMF plotted together with the quasar data (black cross and plus markers, cross for radio quiet and plus for radio loud quasars)from Dunlop et al. (1993, 2003); Souchay et al. (2015). The data are compiled in Table 3. The CAN IMF, SAL IMF and vDC IMF are shown inFig. 10. The arrow indicates the time evolution for the UCD models; the black filled circles and squares mark evolutionary time, from left to right:100 Myr, 500 Myr, 1 Gyr, 5 Gyr, 10 Gyr for [Fe / H] = -2 and 0 dex. The rectangular region indicates where the majority of observed UCDs arelocated (e.g. Evstigneeva et al. 2008). Since UCDs have a di ff erent metallicity, we do not plot individual data points. Article number, page 9 of 18 & A proofs: manuscript no. 31240_corr − . . . . . M V − M I c − − − − M V U C D d a t a CAN IMFQUASARS10 M (cid:12) M (cid:12) M (cid:12) [Fe/H]=0 [Fe/H]= − t i m e − . . . . . M V − M I c − − − − M V QUASARSSAL IMF10 M (cid:12) M (cid:12) M (cid:12) [Fe/H]=0 [Fe/H]= − U C D d a t a t i m e − . . . . . M V − M I c − − − − M V vDC IMF10 M (cid:12) M (cid:12) M (cid:12) [Fe/H]=0 [Fe/H]= − QUASARS t i m e Fig. 10.
As Fig. 9 but for the CAN IMF (MIRI
Top panel) , the SALIMF ( middle panel), and the vDC IMF (bottom panel) . been deduced to form on a timescale of and within less thana Gyr of the Big Bang with SFRs larger than a few 10 M (cid:12) / yr(Recchi et al. 2009). Under more benign conditions, that is whenthe system-wide SFR is smaller as in later interacting galax-ies or the formation of less massive elliptical galaxies within afew Gyr of the Big Bang, UCDs may form also but are morelikely to be the mergers of star-cluster complexes. Cases in pointare the Antennae galaxies, where such young complexes are evi-dent (Kroupa 1998; Fellhauer & Kroupa 2002b), and the Tadpolegalaxy Kroupa (2015).Therefore, the best place to search for very massive UCDs isin the inner regions of extreme star-bursts at very high redshift.Elliptical galaxies and bulges in formation may also host youngmassive UCDs. If it were possible to observationally remove thegas and dust obscuration, then such systems are likely to looklike brilliantly lit Christmas trees. If monolithic collapse (scenario A) applies, then according toMarks et al. (2012); Dabringhausen et al. (2012) top-heavyMKDP IMFs are expected, which in turn lead to larger M / L V values at older ages (Figs. 4 and 5). At young ages, such objectscan be as bright as quasars (Fig. 3).In the case of the formation of UCDs from merged clustercomplexes (scenario B), the IMF in each sub-cluster would becloser to the canonical IMF. The IMF of a whole object wouldthus be less top-heavy (e.g. Pflamm-Altenburg et al. 2009; Wei-dner et al. 2013; Fontanot et al. 2017; Yan et al. 2017), leading tosmaller M / L V ratios at older ages (Figs. 4 and 5). They are sig-nificantly less luminous than monolithically-formed objects withMKDP IMFs (Fig. 3). Therefore the realization of both scenarios(A) and (B) in reality may lead to a spread of M / L V values forpresent-day UCDs, which may be comparable to the observedspread.In the case of a bottom-heavy IMF, one might expect similarbehaviour; that is, if a UCD is created by a monolithic star-burstthe IMF may be more bottom-heavy than in the case of mergedcluster complexes. Thus, for monolithically-formed objects, the M / L V ratios are large at all ages (Fig. 4), while they would besub-luminous for their mass (Fig. 3).All these di ff erent IMF cases can be distinguished best whenthe objects are younger than 100 Myr as their luminosities andcolours will be most di ff erent (Fig. 9, Fig. 10). Particularly usefulobservable diagnostics are provided by the colour-colour plots(Fig. A.8) and the slope of the SED (Fig. 8). M / L V –ratios The elevated M / L V ratios observed for some UCDs can becaused by three, partially interconnected scenarios: (1) a vari-ation of the IMF (top-heavy or bottom-heavy), (2) the presenceof a super-massive black hole (SMBH), and (3) the presence ofnon-baryonic dark matter. Point (3) is directly connected to for-mation scenario (D), which is, as already mentioned, disfavouredfor UCDs. As shown above, the variable IMF (scenario (1))can explain the observed elevated M / L V values. The mass of aSMBH in scenario (2) required to explain the observed M / L V values, needs typically to be 10-15 per cent of the present-dayUCD mass (Mieske et al. 2013). The presence of SMBHs withsuch masses is indeed suggested or observationally confirmed at Article number, page 10 of 18. Jeˇrábková et al.: The formation of UCDs: Testing for a variable stellar IMF least for a few UCDs (e.g. Seth et al. 2014; Janz et al. 2015; Ahnet al. 2017).To address which scenario (variation of IMF, (1), or presenceof SMBH, (2)) is responsible for the elevated M / L V values indi ff erent formation scenarios is not straightforward. In the caseof formation scenario (C), where UCDs are tidally stripped nu-clei, there is an observational connection with the presence ofSMBHs. Graham & Spitler (2009) found that the existence ofa SMBH in a galactic nuclear cluster is indeed frequently thecase. However, since the exact formation mechanism of SMBHsis still discussed, it is not possible to constrain the IMF of UCDsformed by scenario (C). On the other hand, even though in for-mation scenarios (A) and (B), where UCDs are cluster-like ob-jects and where the variable IMF is introduced to explain ob-served M / L V values, the existence of a SMBH cannot be ex-cluded. The SMBH can potentially be formed as a merger ofdark remnants (Giersz et al. 2015, Kroupa, et al, in prep.). If astandard IMF is assumed, the mass of dark remnants (BHs andneutron stars) represents approximately only 2 per cent of thepresent-day mass of a system. For a top-heavy IMF this fractioncan be significantly higher.
5. Conclusions
We investigated if observations with upcoming observatories,with an emphasis on predictions for the JWST, may be able todiscern the formation and evolution of UCDs assuming that theyare cluster-like objects which form by (A) single monolithic col-lapse or (and) (B) by the merging of cluster complexes. The pri-mary area of interest is to find observable diagnostics that mayallow us to assess how the stellar IMF varies with physical con-ditions. The extreme star-bursts, which massive GCs and UCDsmust have been at a high redshift, may be excellent test beds forthis goal. For this purpose we compute the time-dependent evo-lution of SEDs for di ff erent physical parameters and mainly fordi ff erent IMFs. We test the top-heavy IMF, as parametrized byMarks et al. (2012), which predicts a top-heavy IMF for the caseof scenario (A) and an IMF closer to the canonical IMF in thecase of scenario (B). The bottom-heavy IMFs are implementedas a single power law function with a slope − . − – The retention fraction of stellar remnants is near to 100% forsystems with birth masses larger than 10 M (cid:12) . – We show that if UCD progenitors younger than ≈
100 Myrare observed, their stellar IMF can be constrained and there-fore also the formation scenario can be constrained by ob-taining achievable measurements (e.g. absolute luminosityand supernova rate or an appropriate combination of coloursand the value of β UV ). UCD progenitors most likely locatedat redshifts 3-9 have not been observed yet, however, ac-cording to our predictions we should be able to detect themeven with current telescopes as they would appear like pointsources with high, quasar-like luminosities. Computed expo-sure times for chosen JWST MIRI and NIRCam instrumentsare presented. – We also discuss degeneracies, which start appearing at ages >
50 Myr as massive stars and evolve into dark remnants,and we reveal which information and constraints we can ob-tain from present-day UCDs. That is, the object’s luminositywith a top-heavy IMF starts to be comparable with a UCD of the same (or even smaller) initial mass but with a canonicalor bottom-heavy IMF. Therefore, within observational un-certainties, these cases might be indistinguishable on colour-magnitude or colour-colour diagrams. Even M / L V becomesdegenerate, however, for the majority of cases we should beable to separate a vDC IMF from the rest if the metallicity ofthe UCD is constrained reasonably well. – If UCDs were formed with a top-heavy IMF ( α < . α = . ff erent from Galactic star forma-tion regions. The UCD progenitors with initial stellar massesof ≈ M (cid:12) would contain ≈ O stars in a region span-ning not more than a few pc. This drives a tremendous lu-minosity, very high SN II rates, and also poses the furtherquestion as to how the strong radiation field influences thestate and evolution of other stars and thus the IMF especiallyat the low-mass end (e.g. Kroupa & Bouvier 2003). – Interestingly, we have found evidence that some of the ob-served quasars have photometric properties of very youngUCD models with top-heavy IMFs. This may suggest thatsome quasars at high redshift may actually be very massiveUCDs with ages <
10 Myr. This needs further study though,for example by quantifications of SEDs. One method to helpidentify true UCDs with top-heavy IMFs would be to moni-tor their luminosities. Since core-collapse supernovae will becommon in such systems, exploding at a rate of more thanone per year, the luminosity of such a UCD ought to showincreases by ≈ . −
10 per cent (depending on star forma-tion history, IMF, and initial stellar mass) over a timescale ofa few months up to a few dozen times a year. Young UCDsshould thus be time-variable. – Groups of very young UCDs, if found at high redshift, maybe indicating the assembly of the inner regions of galaxyclusters (see also Schulz et al. 2016): the assembly timescaleis 10 Myr, being of the order of the dynamical timescale.The seeds of the most massive galaxies in the centre ofgalaxy clusters probably had a very clustered formation ofUCD-mass objects that created today’s giant ellipticals andbrightest cluster galaxies. Thus, during the assembly of theinner region of galaxy clusters, we would expect generationsof quasar-like UCDs, each with a high luminosity and life-time of about 10 Myr, forming such that the overall lifetimeof the UCD-active epoch would be about 10 Myr. This iscomparable to the lifetime of quasars, adding to the similar-ity in photometric properties noted above. – The majority of ultra-massive very young UCDs, which lookcomparable to quasars, are therefore likely to form in thecentral region of the star-bursts from which the present-daycentral dominant elliptical galaxies emerge. But such UCDswill not be observable today as they are likely to sink to thecentres of the elliptical galaxies through dynamical frictionBekki (2010).To gain more firm conclusions, individual cases of observedUCDs need to be considered taking all observational constraintsinto account. To disentangle degeneracies that arise mainly withage, new data reporting UCDs younger than ≈
100 Myr areneeded. We would like to emphasize here that no such objectshave been observationally confirmed yet.
Acknowledgements.
We thank the referee and Holger Baumgardt for useful com-ments that helped to improve this manuscript. TJ was supported by Charles Uni-versity in Prague through grant SVV-260441 and through a stipend from theSPODYR group at the University of Bonn. TJ, PK, and KB thank the DAAD(grant 57212729 "Galaxy formation with a variable stellar initial mass function”)for funding exchange visits. We would like to acknowledge the use of Python
Article number, page 11 of 18 & A proofs: manuscript no. 31240_corr (G. van Rossum, Python tutorial, Technical Report CS-R9526, Centrum voorWiskunde en Informatica (CWI), Amsterdam, May 1995). Apart from standardPython libraries, we used pyPegase from Colin Jacobs. We also acknowledgediscussions with Christopher Tout and many useful contributions seen duringthe ImBaSe 2017 conference in Garching.
References
Adams, F. C. & Laughlin, G. 1996, ApJ, 468, 586 3Ahn, C. P., Seth, A. C., den Brok, M., et al. 2017, The Astrophysical Journal,839, 72 4, 11Anderson, J. P., Habergham, S. M., & James, P. A. 2011, MNRAS, 416, 567 5Balbinot, E. & Gieles, M. 2017, arXiv.org, arXiv:1702.02543 3Banerjee, S. 2017, MNRAS, 467, 524 2, 3Bastian, N., Covey, K. R., & Meyer, M. R. 2010, ARA&A, 48, 339 1Bastian, N. & Strader, J. 2014, MNRAS, 443, 3594 3Baumgardt, H. & Sollima, A. 2017, arXiv.org, arXiv:1708.09530 3Bekki, K. 2010, MNRAS, 401, 2753 11Bekki, K., Couch, W. J., & Drinkwater, M. J. 2001, ApJ, 552, L105 1Bekki, K., Couch, W. J., Drinkwater, M. J., & Shioya, Y. 2003, MNRAS, 344,399 1Bertelli Motta, C., Clark, P. C., Glover, S. C. O., Klessen, R. S., & Pasquali, A.2016, MNRAS, 462, 4171 2Brinkmann, N., Banerjee, S., Motwani, B., & Kroupa, P. 2017, Astronomy &Astrophysics, 600, A49 3Brodie, J. P., Romanowsky, A. J., Strader, J., & Forbes, D. A. 2011, AJ, 142, 1991Brüns, R. C., Kroupa, P., Fellhauer, M., Metz, M., & Assmann, P. 2011, A&A,529, A138 1Chabrier, G., Hennebelle, P., & Charlot, S. 2014, ApJ, 796, 75 2Chiboucas, K., Tully, R. B., Marzke, R. O., et al. 2011, ApJ, 737, 86 1Chilingarian, I. V., Cayatte, V., & Bergond, G. 2008, MNRAS, 390, 906 1Côté, P., Piatek, S., Ferrarese, L., et al. 2006, ApJS, 165, 57 1Dabringhausen, J., Fellhauer, M., & Kroupa, P. 2010, MNRAS, 403, 1054 1, 3,4Dabringhausen, J., Hilker, M., & Kroupa, P. 2008, MNRAS, 386, 864 2, 3, 4, 5Dabringhausen, J., Kroupa, P., & Baumgardt, H. 2009, Monthly Notices of theRoyal Astronomical Society, 394, 1529 1, 2, 5, 7Dabringhausen, J., Kroupa, P., Pflamm-Altenburg, J., & Mieske, S. 2012, ApJ,747, 72 5, 8, 10Dib, S., Kim, J., & Shadmehri, M. 2007, Monthly Notices of the Royal Astro-nomical Society: Letters, 381, L40 3Drinkwater, M. J., Gregg, M. D., Couch, W. J., et al. 2004, PASA, 21, 375 1Drinkwater, M. J., Gregg, M. D., Hilker, M., et al. 2003, Nature, 423, 519 1Drinkwater, M. J., Jones, J. B., Gregg, M. D., & Phillipps, S. 2000, PASA, 17,227 1Dunlop, J. S., McLure, R. J., Kukula, M. J., et al. 2003, MNRAS, 340, 1095 5,6, 9Dunlop, J. S., Taylor, G. L., Hughes, D. H., & Robson, E. I. 1993, MNRAS, 264,455 5, 6, 9Elmegreen, B. G. 2004, MNRAS, 354, 367 1Evstigneeva, E. A., Drinkwater, M. J., Peng, C. Y., et al. 2008, AJ, 136, 461 6, 9Fellhauer, M. & Kroupa, P. 2002a, Ap&SS, 281, 355 1Fellhauer, M. & Kroupa, P. 2002b, MNRAS, 330, 642 1, 10Ferrarese, L. & Merritt, D. 2002, Phys. World, 15N6, 41 8Fioc, M. & Rocca-Volmerange, B. 1997, A&A, 326, 950 2, 3Fontanot, F., De Lucia, G., Hirschmann, M., et al. 2017, MNRAS, 464, 3812 10Forbes, D. A., Lasky, P., Graham, A. W., & Spitler, L. 2008, MNRAS, 389, 19241Frank, M. J., Hilker, M., Mieske, S., et al. 2011, MNRAS, 414, L70 1Gal-Yam, A. 2012, Science, 337, 927 5, 6Giersz, M., Leigh, N., Hypki, A., Lützgendorf, N., & Askar, A. 2015, MNRAS,454, 3150 11Glazebrook, K., Schreiber, C., Labbé, I., et al. 2017, Nature, 544, 71 2Goerdt, T., Moore, B., Kazantzidis, S., et al. 2008, MNRAS, 385, 2136 1Graham, A. W. & Spitler, L. R. 2009, MNRAS, 397, 2148 11Greggio, L. & Renzini, A. 1983, A&A, 118, 217 5Hilker, M. 2009, UCDs - A Mixed Bag of Objects, ed. T. Richtler & S. Larsen,51 1Hilker, M., Infante, L., Vieira, G., Kissler-Patig, M., & Richtler, T. 1999, A&AS,134, 75 1Janz, J., Forbes, D. A., Norris, M. A., et al. 2015, MNRAS, 449, 1716 11Joseph, R. D. & Wright, G. S. 1985, MNRAS, 214, 87 8Kroupa, P. 1998, MNRAS, 300, 200 1, 10Kroupa, P. 2001, MNRAS, 322, 231 2Kroupa, P. 2015, Canadian Journal of Physics, 93, 169 10Kroupa, P. & Bouvier, J. 2003, MNRAS, 346, 369 11 Kroupa, P., Weidner, C., Pflamm-Altenburg, J., et al. 2013, The Stellar and Sub-Stellar Initial Mass Function of Simple and Composite Populations, 115 1Lamers, H. J. G. L. M., Gieles, M., Bastian, N., et al. 2005, A&A, 441, 117 3Larson, R. B. 1998, MNRAS, 301, 569 1, 3Leitherer, C., Schaerer, D., Goldader, J. D., et al. 1999, ApJS, 123, 3 5, 13Li, H., Gnedin, O. Y., Gnedin, N. Y., et al. 2017, The Astrophysical Journal, 834,69 8Liptai, D., Price, D. J., Wurster, J., & Bate, M. R. 2017, MNRAS, 465, 105 2Longmore, S. N. 2015, MNRAS, 448, L62 3Lonsdale, C. J., Diamond, P. J., Thrall, H., Smith, H. E., & Lonsdale, C. J. 2006,ApJ, 647, 185 5Lyman, J. D., Bersier, D., James, P. A., et al. 2016, Monthly Notices of the RoyalAstronomical Society, 457, 328 5, 6Maoz, D. 2008, MNRAS, 384, 267 3, 5, 6Marks, M. & Kroupa, P. 2012, A&A, 543, A8 2, 4Marks, M., Kroupa, P., Dabringhausen, J., & Pawlowski, M. S. 2012, MNRAS,422, 2246 2, 10, 11Marks, M., Kroupa, P., & Oh, S. 2011, MNRAS, 417, 1684 4Matteucci, F. & Greggio, L. 1986, A&A, 154, 279 5Megeath, S. T., Gutermuth, R., Muzerolle, J., et al. 2016, AJ, 151, 5 2Mieske, S., Dabringhausen, J., Kroupa, P., Hilker, M., & Baumgardt, H. 2008,Astronomische Nachrichten, 329, 964 7Mieske, S., Frank, M. J., Baumgardt, H., et al. 2013, A&A, 558, A14 10Mieske, S., Hilker, M., & Infante, L. 2002, A&A, 383, 823 1, 7Mieske, S., Hilker, M., Jordán, A., Infante, L., & Kissler-Patig, M. 2007, A&A,472, 111 1Mieske, S., Hilker, M., & Misgeld, I. 2012, A&A, 537, A3 1Mieske, S. & Kroupa, P. 2008, ApJ, 677, 276 2Misgeld, I., Mieske, S., Hilker, M., et al. 2011, A&A, 531, A4 1Mortlock, D. J., Warren, S. J., Venemans, B. P., et al. 2011, Nature, 474, 616 5Murray, N. 2009, ApJ, 691, 946 1Norman, C. A. 1987, in NASA Conference Publication, Vol. 2466, NASA Con-ference Publication, ed. C. J. Lonsdale Persson 8Oh, K. S., Lin, D. N. C., & Aarseth, S. J. 1995, ApJ, 442, 142 1Papadopoulos, P. P. 2010, ApJ, 720, 226 3Pejcha, O. & Thompson, T. A. 2015, ApJ, 801, 90 5Penny, S. J., Forbes, D. A., & Conselice, C. J. 2012, MNRAS, 422, 885 1Peuten, M., Zocchi, A., Gieles, M., Gualandris, A., & Hénault-Brunet, V. 2016,MNRAS, 462, 2333 3Pfe ff er, J. & Baumgardt, H. 2013, MNRAS, 433, 1997 1Pfe ff er, J., Gri ff en, B. F., Baumgardt, H., & Hilker, M. 2014, MNRAS, 444, 36701Pfe ff er, J., Hilker, M., Baumgardt, H., & Gri ff en, B. F. 2016, MNRAS, 458, 24922Pflamm-Altenburg, J., González-Lópezlira, R. A., & Kroupa, P. 2013, MNRAS,435, 2604 8Pflamm-Altenburg, J., Weidner, C., & Kroupa, P. 2009, MNRAS, 395, 394 10Planck Collaboration, Adam, R., Aghanim, N., et al. 2016a, A&A, 596, A108 2Planck Collaboration, Ade, P. A. R., Aghanim, N., et al. 2016b, A&A, 594, A132Price, J., Phillipps, S., Huxor, A., et al. 2009, MNRAS, 397, 1816 1Randriamanakoto, Z., Escala, A., Väisänen, P., et al. 2013, ApJ, 775, L38 8Recchi, S., Calura, F., & Kroupa, P. 2009, A&A, 499, 711 10Renaud, F., Bournaud, F., & Duc, P.-A. 2015, MNRAS, 446, 2038 1Renzini, A. 2017, Monthly Notices of the Royal Astronomical Society: Letters,469, L63 8Renzini, A., D’Antona, F., Cassisi, S., et al. 2015, Monthly Notices of the RoyalAstronomical Society, 454, 4197 4Romano, D., Matteucci, F., Zhang, Z. Y., Papadopoulos, P. P., & Ivison, R. J.2017, Monthly Notices of the Royal Astronomical Society, 470, 401 3Schulz, C., Hilker, M., Kroupa, P., & Pflamm-Altenburg, J. 2016, A&A, 594,A119 2, 3, 11Schulz, C., Pflamm-Altenburg, J., & Kroupa, P. 2015, A&A, 582, A93 2Seth, A. C., van den Bosch, R., Mieske, S., et al. 2014, Nature, 513, 398 4, 11Smith, R. J. & Lucey, J. R. 2013, MNRAS, 434, 1964 2Souchay, J., Andrei, A. H., Barache, C., et al. 2015, A&A, 583, A75 5, 6, 9Stanway, E. R., Eldridge, J. J., & Becker, G. D. 2016, MNRAS, 456, 485 4Stolte, A., Hußmann, B., Morris, M. R., et al. 2014, ApJ, 789, 115 8Terlevich, R. J. & Boyle, B. J. 1993, MNRAS, 262, 491 5Thielemann, F.-K., Nomoto, K., & Yokoi, K. 1986, A&A, 158, 17 5Thies, I., Pflamm-Altenburg, J., Kroupa, P., & Marks, M. 2015, The Astrophysi-cal Journal, 800, 72 4Thomas, P. A., Drinkwater, M. J., & Evstigneeva, E. 2008, MNRAS, 389, 102 2van Dokkum, P. G. & Conroy, C. 2010, Nature, 468, 940 2, 11Vanzella, E., Calura, F., Meneghetti, M., et al. 2017, Monthly Notices of theRoyal Astronomical Society, 467, 4304 2, 6, 9Weidner, C., Kroupa, P., & Larsen, S. S. 2004, MNRAS, 350, 1503 2, 8Weidner, C., Kroupa, P., Pflamm-Altenburg, J., & Vazdekis, A. 2013, MNRAS,436, 3309 10Wright, G. S., Joseph, R. D., Robertson, N. A. and. James, P. A., & Meikle,W. P. S. 1988, MNRAS, 233, 1 8Yan, Z., Jerabkova, T., & Kroupa, P. 2017, arXiv.org, arXiv:1707.04260 10Zhang, Y. & Bell, E. F. 2017, ApJ, 835, L2 1 Article number, page 12 of 18. Jeˇrábková et al.: The formation of UCDs: Testing for a variable stellar IMF
Appendix A: Additional figures and procedures
To make the text of the main paper more continuous, we presenta part of the figures in this Appendix. At first we would like topresent here redshift as a function of time from the Big-Bang.Even though this plot is elementary, it is not straightforward tofind it in other literature in this format. We marked the redshift-time points that are relevant for this study. . . . . . . r e d s h i f t z z = 10 . z = 4 . z = 2 . t = . G y r t = . G y r t = . G y r Fig. A.1.
Redshift z as a function of time from the Big-Bang (age of theUniverse) adopting for this study the standard Λ CDM cosmology withPlanck parameters (see Sec. 2.1).
In addition, since the PEGASE SED’s minimal wavelengthis ≈ z (cid:39)
6) this re-gion contributes to the standard optical filters, we extrapolatethe computed SEDs at smaller wavelengths using a black-bodyapproximation. To avoid adding an additional uncertainty to ourresults, we do not use the extrapolations to make any predictionsor conclusions, but strictly as a demonstration of an approximatetrend.As a consistency check and also as a basic estimation of thedi ff erence between di ff erent stellar population codes, we com-puted the same set of SEDs with the StarBurst99–code (Leithereret al. 1999) online library. The results are plotted in Fig. A.2showing agreement in the general characteristic of the SED andin the time evolution. The maximum di ff erences in the SEDs,estimated only in the region which is computed by PEGASEwithout extrapolating, reach a factor of a few and are expectedsince di ff erent stellar evolutionary tracks are used in both codes.These di ff erences represent the minimal uncertainty that needsto be considered if our results are compared with observations.The time evolution of SEDs for the MKDP IMF is plottedin Fig. A.3 in comparison to the CAN IMF. The same time evo-lution for the vDC and SAL IMFs is plotted in Figs. A.5 andA.6. The wavelength shift and fainting proportional to the in-verse square of luminosity distance with redshift is shown inFig. A.4. Article number, page 13 of 18 & A proofs: manuscript no. 31240_corr λ [˚A]10 − − F ν [ ( e r g s − c m − H z − ) ] λ [˚A]3Myr 10 λ [˚A]5Myr 10 λ [˚A]7MyrPEGASESB99 10 λ [˚A]10Myr Fig. A.2.
Time evolution of SEDs for a 10 M (cid:12) system normalized to the distance of 10 pc for the Salpeter IMF slope α = .
35 within the massrange (1,100) M (cid:12) and metallicity Z = . λ [˚A]10 − − F ν [ ( e r g s − c m − H z − ) ] ? λ [˚A] 6Myr7Myr8Myr9Myr10Myr20Myr CAN IMF Fig. A.3.
PEGASE time evolution of SEDs for [Fe / H] = -2 and a representative initial stellar mass of 10 M (cid:12) as if it is at a distance of 10 pc. Sincewe assume that the star formation lasts for 5 Myr, we start with the SED at 6 Myr to avoid overlapping of lines. Left panel:
The evolution for theMKDP IMF.
Right panel:
The evolution for the CAN IMF. The region below a wavelength of ≈ λ [˚A]10 − − − − F ν [ ( e r g s − c m − H z − ) ] z = z = z = top-heavy IMF8 Myr J fi l t . N fi l t . K fi l t . λ [˚A] z = z = z = canonical IMF 8 Myr J fi l t . N fi l t . K fi l t . CAN IMF
Fig. A.4.
SEDs of 8-Myr-old UCDs at di ff erent redshifts. For this purpose, we arbitrarily chose the SED of an 8-Myr -old stellar population withmetallicity [Fe / H] = -2 and corrected the spectrum for the wavelength shift and luminosity fainting with luminosity distance for redshifts 3, 6, and9. Left panel:
SEDs of the MKDP IMF.
Right panel:
SEDs of the CAN IMF. The photometric filters, here approximated by rectangular profilesas shaded vertical regions, are shown. The J, K, and N filters are used in the colour analysis of the data. λ [˚A]10 − − − F ν [ ( e r g s − c m − H z − ) ] ? λ [˚A] 6Myr7Myr8Myr9Myr10Myr20Myr CAN IMF Fig. A.5.
As Fig. A.3 but for the vDC IMF ( left panel ), with the CAN IMF ( right panel , identical to Fig. A.3) shown here as a benchmark.Article number, page 15 of 18 & A proofs: manuscript no. 31240_corr λ [˚A]10 − − F ν [ ( e r g s − c m − H z − ) ] ? λ [˚A] 6Myr7Myr8Myr9Myr10Myr20Myr CAN IMF Fig. A.6.
As Fig. A.3 but for the SAL IMF ( left panel ), with the CAN IMF ( right panel , identical to Fig. A.3) shown here as a benchmark.Article number, page 16 of 18. Jeˇrábková et al.: The formation of UCDs: Testing for a variable stellar IMF λ [˚A]10 − − − F λ [ ( e r g s − c m − ˚A − ) ] MKD IMF 10 M (cid:12) [Fe/H]=0, age=20 MyrvDC IMF[Fe/H]= −
2, age=8 Myrfitted interval β UV slope fit Fig. A.7.
Fit to a SED in the grey shaded region shows the slope β UV for two di ff erent UCDs with di ff erent age, the same mass 10 M (cid:12) , anddi ff erent metallicity. We can see that in the grey region the spectra havea smooth shape and therefore it is possible to fit this part by a linearfunction to obtain a good estimate of β UV . Section 3.4 gives more de-tails. Article number, page 17 of 18 & A proofs: manuscript no. 31240_corr − .
25 0 .
00 0 .
25 0 . m J − m K m K − m N z=0 t max | z =0 ≈ . M (cid:12) M (cid:12) M (cid:12) vDC MKD . . . . . . . . . l og (t i m e [ M y r ] ) − . . m J − m K . . . . m K − m N z=0zoomed plot t max | z =0 ≈ . . . . . . . . . . l og (t i m e [ M y r ] ) m J − m K . . . . m K − m N z=3 t max | z =3 ≈ . . G y r . . . . . . . . . l og (t i m e [ M y r ] ) . . . . m J − m K m K − m N z=6 t max | z =6 ≈ . . . . . . . . . . l og (t i m e [ M y r ] ) . . . m J − m K m K − m N z=9 t max | z =9 ≈ . . . . . . . . . . l og (t i m e [ M y r ] ) . . . m J − m K . . . . m K − m N z=9zoomed plot t max | z =9 ≈ . . . . . . . . . . l og (t i m e [ M y r ] ) Fig. A.8.
Colour-colour diagram made for standard filters J, K, and N approximated here by rectangular boxes in Fig. A.4 showing the comparisonof the vDC IMF and the MKDP IMF for di ff erent initial UCD masses, M UCD . Since according to the Λ CDM cosmological model the upper limitto the age of the universe is t max ≈ ..