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Feedback by Massive Black Holes in Dwarf Galaxies

Could there be intermediate mass black holes in essentially all old dwarf galaxies? I argue that current observations of Active Galactic Nuclei in dwarfs allow such a radical hypothesis which provides early feedback and potentially provides a unifying explanation for many if not all of the apparent dwarf galaxy anomalies, such as the abundance, core-cusp,"too big to fail", ultra-faint and baryon-fraction issues. I describe the supporting arguments, which are largely circumstantial in nature, and discuss a number of tests. There is no strong motivation for modifying the nature of cold dark matter in order to explain any of the dwarf galaxy"problems".


INTRODUCTION
There are two types of observed astrophysical black holes, stellar mass and supermassive. Stellar mass black holes that originate in the deaths of stars in the ∼ 20 − 100M ⊙ range are observed directly via gravitational waves. Supermassive black holes (SMBH) are observed via kinematic signatures at the centers of galaxies, with most accuracy for the MWG and for nearby disks with orbiting circumnuclear masers. However broad emission line signatures provide compelling evidence for SMBH to high redshift in the cores of massive galaxies. The observed mass range of SMBH is ∼ 10 6 − 10 10 M ⊙ .
Logically, there is no reason not to expect a population of intermediate mass black holes in the mass range ∼ 10 2 − 10 5 M ⊙ that are too massive to be formed directly by stellar collapse in the recent universe. Indeed, the formation of SMBH is believed to be a combination of dynamical merging of smaller black holes and gas accretion. The latter process is observed via x-ray and optical emission line studies.
Gravity wave experiments, most notably LISA, will enable us to directly observe IMBH mergers. The gas accretion contribution to the SMBH masses is constrained by the Soltan radiative argument (Soltan 1982). Seed black holes of mass∼ 10 3 − 10 4 M ⊙ are usually required at high redshift in order to account for the existence and growth via accretion of SMBH in the mass range ∼ 10 9 −10 10 M ⊙ at z > ∼ 6, unless super-Eddington growth is invoked. IMBH are observed in dwarf galaxies, although the occupation fraction in uncertain. Early-forming dwarfs are generally the building blocks of massive galaxies. Were they to universally contain IMBH, this would provide a reservoir for seeding growth of SMBH by tidal disruption of stars and gas accretion, as well as possibly by IMBH mergers. It is expected that many IMBH are left behind in the course of hierarchical merging (Rashkov & Madau 2014) and should be present in many satellite dwarfs at z = 0 (van Wassenhove et al. 2010) as well as be detectable as outliers on the black-hole scaling relations, especially at high redshift (Volonteri & Natarajan 2009).
The best evidence for IMBH in dwarf galaxies comes from x-ray (Kormendy & Ho 2013;Pardo et al. 2016) as well as optical emission line studies. Active galactic nuclei are found in about 1% of dwarfs, with the x-ray luminosities well in excess of an x-ray binary contribution as predicted from the star formation rate (Baldassare et al. 2016). For any reasonable duty cycle, there must be IMBH in at least 10% of dwarfs, and one cannot exclude a larger fraction because of the special circumstances required for the shallow gravitational potentials of dwarfs to retain gas as effectively as their massive counterparts. Moreover a NUSTAR survey suggests that because of heavy x-ray absorption, a significant number of dwarfs with AGN may be missed both in optical spectroscopic surveys and in X-ray surveys below 10 keV (Chen et al. 2017). Of course theoretical studies show that not all dwarfs necessarily host IMBH (Volonteri et al. 2008).
Near IR studies of nearby dwarfs also suggest the presence of obscured IMBH, but the data remains ambiguous (Hainline et al. 2016). Optical studies of emission lines from central nuclei find a similar fraction of IMBH in dwarfs to that found in x-ray surveys (Moran et al. 2014).
An interesting indirect argument for AGN feedback in dwarfs comes from the possibility of IMBH quenching of star formation in dwarfs. The handful of identified dwarf IMBH lie on the usual M BH − σ scaling relation, where M BH is the black hole mass and σ is the dwarf stellar velocity dispersion. However these same dwarfs fall below the M BH −M * scaling relation where M * is the stellar mass (Baldassare et al. 2015;Reines & Volonteri 2015). One can possibly interpret this as IMBH-induced suppression of star formation in dwarfs that occurred in the early gas-rich phase of dwarf evolution.
IMBH are generically predicted to form in the course of Population III evolution. There is competition with fragmentation into Population III stars. Fragmentation dominates in the first generation of clouds unless there are special circumstances in which H 2 cooling is suppressed. However, clouds of mass ∼ 10 7 − 10 8 M ⊙ that form at z ∼ 10 collapse at virial temperatures ∼ 10 4 K where H 2 formation indeed is suppressed. IMBH plausibly form in these clouds, as fragmentation is inhibited (Spaans & Silk 2006). These systems are the precursors of many of today's dwarf galaxies, which with measured or inferred halo masses of ∼ 10 8 − 10 9 M ⊙ must have formed with baryon masses in the ∼ 10 7 − 10 8 M ⊙ range. Unless the clouds are contaminated by metal-injection from the smaller clouds at a level above Z ∼ 10 −3 Z ⊙ , a process such as Lyman alpha photon trapping and associated H − photo-detachment (Johnson & Dijkstra 2016) will guarantee high central cooling and accretion rates leading to IMBH formation. However the efficiency of the IMBH production process is highly uncertain, particularly with regard to heavy element production by the first stars, followed by diffusion and mixing, as in Ferrara et al. (2014).
In what follows, I will assume that the IMBH occupation fraction in dwarf galaxies is anywhere between 10% and 100%. There are a number of enigmas surrounding dwarf galaxies. Most but not all of these have relatively conventional explanations in terms of baryonic feedback. However in several cases, the modeling seems fine-tuned, and this has motivated many discussions of modified dark matter as an alternative explanation. These modifications include appeals to warm (Bose et al. 2017), fuzzy (Marsh & Silk 2014) and selfinteracting dark matter (Elbert et al. 2015), to name the most popular.
In this note, I will reconsider baryonic feedback in the light of the possible presence of IMBHs. First, I discuss the theoretical case for IMBH feedback in dwarfs. I then make the case that the presence of IMBH potentially provides a unifying explanation for essentially all of the dwarf galaxy anomalies. I conclude with several predictions that may help underpin and clarify the IMBH-dwarf galaxy connection.

THE CASE FOR IMBH FEEDBACK IN DWARFS
A major question concerning the efficiency of AGN feedback is the efficiency of coupling relativistic jets and ultrafast nuclear outflows with the ambient interstellar medium. An example of efficient coupling is given by jet-driven backflows that lose enough angular momentum to feed and self-regulate the central AGN (Cielo et al. 2014). The efficiency problem may be ameliorated in dwarfs which form at high redshift with high central density. Outflows are more readily trapped and this seems likely to lead to more coherent coupling of the central source with the ambient medium.
These questions need to be explored in more detail. Here I will assume similar AGN jet or ouflow coupling to that normally adopted for massive galaxies, and only comment on the gross energetics, comparing supernova and AGN-driven feedback in gas-rich dwarf galaxies.
Consider a cloud of mass M c /10 8 M ⊙ . This forms stars at ∼ 1% efficiency and produces 10 4 SNe in a star cluster of 10 6 M ⊙ . These supernovae generate 10 55 ergs.
Compare this to the IMBH case, where the energy produced by the AGN is ηM BH c 2 or 10 56 M 3 ergs. Here the energy ejection efficiency η = 0.1 and M 3 = M BH /10 3 M ⊙ . Now consider superbubbles, which allow for the coherent explosions of supernovae, thereby enhancing their feedback efficiency into the surrounding galaxy. The luminosity in mechanical energy production due to super-novae in a massive young star cluster is L SN = 10 40 ergs/s(E SN /10 51 ergs)(ǫ sfr /0.01)(M c /10 8 M ⊙ ) over 40.10 6 yr, the typical lifetime of an OB association.
An AGN also produces a superbubble. Its luminosity is Even at an Eddington efficiency of 10%, the AGN power gain amounts to an order of magnitude over that of supernovae. This will be aggravated by the fact that the denser interstellar medium in young dwarf galaxies will generate enhanced cooling and the efficiency will be correspondingly reduced, as well as possibly limiting central BH growth (Prieto et al. 2017). The opposite effect is expected for AGN where the denser ISM reduces the porosity of the shocked medium. These effects need to be modeled in detail.

IMBH IN THE CENTERS OF DWARFS
Theoretical reasoning aside, the main point I wish to make is that there is strong empirical but circumstantial evidence for AGN feedback in dwarfs. I review 10 observations of problems which confront the standard ΛCDM model of structure formation on dwarf galaxy scales. None of these can be said to be rigorously resolved. However most can be accounted for by supernova-driven feedback in combination with other plausible environmental processes such as ram pressure and tidal stripping. But at the very least, considerable fine-tuning is required. Some problems, previously thought to be understood, even resurface as simulation resolution, interstellar physics and observational diagnostics are improved.
The net effect is that a large community has seized on the notion that additional physics is needed that can only come from modifying the nature of dark matter in a drastic way. However modifying the nature of dark matter should be the last resort. Bringing in fundamental physics to solve astrophysical problems demands castiron evidence. Einstein struck gold, because the advance of Mercury's precession fell into this category. However the dwarf galaxy evidence is far removed from such a degree of robustness.
In fact, I will show here that a new astrophysical ingredient, IMBH feedback, provides a unifying theme that can account for most, if not all, of the dwarf galaxy issues. No single example is robust, since most of the details have yet to be explored. However I will argue that the circumstantial evidence is overwhelming for some 10 key dwarf galaxy issues that may be explained in terms of a single unifying hypothesis. I will then present several potential tests of this hypothesis.
I begin by remarking that IMBH, which I postulate to be ubiquitously present in essentially all early-forming dwarfs, are mostly passive today but were active in their gas-rich past.  (2015) and Trujillo-Gomez et al. (2016) take the opposite view for the case of a more realistic multiphase ISM. The situation is equally unclear even for massive disk galaxies in so far as whether SNe are effective in driving gas fountains from the disk vis superbubbles, but compare Kim et al. (2016) and Keller et al. (2016), the latter arguing for the need for additional AGN feedback.
2. Discoveries of ultrafaint dwarfs in our galactic halo and that of M31 are usually attributed to the success of supernova feedback. The recent discovery of ultradiffuse massive dwarf galaxies poses more of a challenge (van Dokkum et al. 2015). The feedback has clearly been dramatic in the past, and seems beyond the reach of supernovae, as is also the case for the "too-big-to-fail" problem, see below. A closely related phenomenon is the prevalence, at the ∼ 30% level, of bulgeless disks often found outside rich clusters (Kormendy 2016). These have formed their stellar disks more efficiently, presumably via late infall of gas, but early bulge formation, long thought to be generic in CDM modelling of galaxy formation, must have somehow been avoided. Again, effective SMBH or IMBH feedback is a plausible culprit, assuming that IMBH formation precedes the bulk of star formation.
3. Numerical simulations predict more massive dwarfs than are observed, the so-called too-big-to-fail problem (Boylan-Kolchin et al. 2011), whereby SNe are commonly believed to be incapable of inhibiting star formation in massive dwarfs (Garrison-Kimmel et al. 2013). One preferred solution is to modify dwarf kinematics by SNe physics, as below, in combination with environmental evolution, notably tidal and ram pressure stripping (Brooks & Zolotov 2014) 4. Supernova momentum input drives bulk gas motions in gas-rich dwarfs. The resulting dynamical heating of the dark matter generates cores in dwarfs (Pontzen & Governato 2014).
In fact, AGN are equally capable of driving bulk gas motions (Peirani et al. 2008). Episodes of such motions dynamically heat the dark matter. This occurs either via mechanically-driven winds or by jet-driven bow shocks via gas cloud interactions, as observed in nearby radio galaxies such as 3C293 (Mahony et al. 2016) and IC5063 (Morganti et al. 2015). Modified dark matter in the form of WDM fails to generate large enough cores, but both fuzzy and self-interacting dark matter have been advocated as alternative solutions of the cusp/core problem ).

5.
A fraction ∼30 percent of baryons is missing within the virial radius of massive disk galaxies (Bregman et al. 2015). It is non-trivial to reduce baryon fraction in Milky Way-type galaxies, that is galaxies of Type Sb or later. SNe fail to eject enough baryons: at best, they drive a fountain since the central SMBH is too small to induce strong global feedback. IMBH feedback in gas-rich dwarfs provides an attractive solution, as the AGN operate in the hierarchical assembly phase of disk galaxies (Peirani et al. 2012 7. Early chemical evolution generally occurs by bursts of star formation and accompanying supernovae in dwarf galaxies that disperse much of the enriched debris into successive generations of subhalos and halos. The extreme low surface brightness MWG dwarf Reticulum II with only ∼1000 stars presents an interesting exception, being self-enriched in rprocess elements such as europium (Ji et al. 2016).
Reticulum II must have retained the enriched debris from an early binary neutron star merger. Such retention requires both a dense ISM and an initially deeper potential well. Here one can imagine that early SNe must have failed to cause significant gas ejection, reminiscent of the "too-big-tofail" problem. The intervention of an AGN might have plausibly provided the new ingredient that heated the dark matter potential well and triggered delayed escape both of gas directly and of stars via tidal disruption.
8. Formation of SMBH at high redshift, z > ∼ 6, in the mass range > ∼ 10 9 M ⊙ , may require the presence of seed IMBH (Johnson et al. 2013 (Bicknell et al. 2000) and NCG 5643 (Cresci et al. 2015). Positive feedback could in principle occur in dwarfs that harbor IMBH. One example is the compact starburst galaxy Henize 2-10 ( Reines et al. 2016). A signature of early episodes of positive feedback would be enhanced star formation. Some of the lowest mass dwarfs have enhanced stellar mass fractions (Oman et al. 2016), for which there is no conventional (i.e. stellar physics) explanation other than the possibility of systematic measurement error due to inclination.
10. ULXs are often found in the outskirts of galaxies. This is also the domain of accreted ultrafaint dwarf galaxies. While some ULXs are almost certainly neutron stars accreting at super-Eddington rates, some are considered as likely IMBH candidates accreting from a close companion star (Bachetti 2016). An IMBH has been reported in the inner MWG (Oka et al. 2016) as well as in the massive globular cluster 47 Tuc (Kızıltan et al. 2017).

PREDICTIONS
I now provide a few predictions that potentially provide a test of whether IMBH indeed inhabit dwarf galaxies.

Kinematic imprints on stellar orbits
AGN feedback may leave a unique signature on stellar orbits. Indeed SN feedback drives potential irregularities that are unveiled by stellar kinematics (El-Badry et al. 2016). However the imprint of AGN feedback is more coherent, especially in the presence of positive feedback (Dugan et al. 2014). Early AGN feedback in nearby dwarf galaxies should leave long-lived kinematic signatures on old stars that formed during the feedback phase. Quenched jets or winds are similarly expected to perturb velocities of newly forming stars. Low power jets (as well as outflows) from the AGN are especially promising as they result from minor accretion events, should greatly outnumber strong jets and are trapped in the interstellar medium for a longer time (Mukherjee et al. 2016).
A simple estimate of the perturbed stellar kinematics is as follows. I assume the AGN outflow is described by a spherically symmetric wind-blown interstellar bubble, the pressure-driven snowplow model of Weaver et al. (1977), and applied to triggered star formation by McCray & Kafatos (1987). For AGN triggering, the injected power isṖ = ηL Edd /c, where η ∼ 0.1η 0.1 is the mechanical efficiency and f Edd L Edd is the AGN luminosity relative to Eddington of the accreting IMBH of mass M IMBH = 1000M ⊙ M IMBH,3 . The analytical solution for the shock velocity is v sh = (3Ṗ /8πρ a δ) 1/2 r −1 for a cloud of density contrast δ = 100δ 100 at distance r from the IMBH. Assuming an isothermal profile for gas and dark matter, the cloud and stars formed therein receives an impulsive kick of velocity contrast relative to the dwarf circular velocity of for a dwarf of mass 10 7 M d,7 M ⊙ that formed at redshift 10z gf,10 . This velocity perturbation will be long-lived, radially directed and potentially measurable as blue asymmetries in stellar absorption line widths via IFU-type spectroscopy for compact dwarfs. A similar effect has been detected in stacked SDSS star-forming galaxies (Cicone et al. 2016). Dynamical detection via stellar kinematical signatures in nearby compact dwarfs must await the next generation of ELT-like telescopes (Volonteri 2010).

Tidal disruption events
IMBH can tidally disrupt white dwarfs, unlike their SMBH counterparts. The main difference with TDEs of main sequence stars is that a similar amount of mass is accreted on a much more rapid timescale. This leads to luminous flares, especially via tidal disruption of the hydrogen-rich envelopes often surrounding white dwarfs and observed as nuclear transients on short time-scales (Law-Smith et al. 2017). Tidal decompression can trigger SNe with possible implications for acceleration of cosmic rays to ultrahigh energies, and in particular, an intermediate/heavy composition for the observed UHE-CRs that is independent of specific acceleration models (Alves Batista & Silk 2017). The debris of magnetized white dwarfs is subject to MRI-driven dynamo amplification of magnetic fields that produces radio jets (Shcherbakov et al. 2012) In a flux-limited survey of TDEs, white dwarf disruptions should account for ∼ 10% of the events, and possibly more if IMBH are as numerous as our dwarf hypothesis implies. Jetted tidal disruption events of main sequence stars by binary IMBH in dwarf galaxies, discussed by Fialkov & Loeb (2016), are likely to be outnumbered by the more luminous TDE signatures of white dwarfs (Krolik & Piran 2012), which also provide a prime mechanism for growing the IMBH (Baumgardt et al. 2006). Gravitational microlensing against extended radio sources is a direct way of imaging IMBH. One proposal requires mapping strongly lensed radio-loud QSOs at 10µs resolution with a VLBI space observatory (Inoue & Chiba 2003). Another approach at much higher frequencies requires the next generation of submillimeter telescopes (Inoue et al. 2013).
Gravitational waves from IMBH mergers are a primary goal for LISA, expected to be launched in 2034 (Tinto & de Araujo 2016).
The dwarf galaxy ansatz augments the number of IMBH by of order M SMBH /M IMBH > ∼ 100 − 1000, with potentially important implications for the predicted frequency of extreme-mass-ratio inspiral merger events that can probe the IMBH mass function in the range 10 4 − 10 7 M ⊙ .
Tidal stripping of dwarfs containing relic IMBH in halos such as M31 can leave morphologically distinct stellar debris signatures that survive for hundreds of millions of years (Miki et al. 2014). High resolution simulations are required to study the signatures of wandering IMBH, as might also be produced by infall of bulgeless disks (Kormendy & Ho 2013).
The source of reionization in the early universe is unknown, because of the large uncertainty in escape frac-tion of ionizing photons from star-forming galaxies, although dwarf galaxies are generally believed to be the dominant contributor given current optical depth measurements (Planck Collaboration et al. 2016). However AGN are expected to have a high ionizing photon escape fraction, and SMBH alone, including their growth phase, are believed to contribute significantly to the ionizing photon budget ). If IMBH form early and are sufficiently numerous, as motivated by the present hypothesis, they can reionise the universe by production of hard photons. The mass in IMBH expected is of order the mass in low metallicity stars at [Z] < ∼ −3, and hence potentially of comparable efficiency to dwarf galaxies in reionization of the universe. The 21cm dark ages absorption signature against the CMB is more pronounced for soft photons than for hard photons with much longer mean free paths (Cohen et al. 2016).

SUMMARY
SMBH scaling relations have been extended to the IMBH regime. As previously noted, comparison of the M SMBH − σ and M SMBH − M * relations shows that IMBH tend to lie below the extrapolated scaling relation (Baldassare et al. 2015), and possibly also in the prototypical example of Henize 2-10 (Kormendy & Ho 2013). The fact that M * is effectively reduced in dwarfs as inferred from the scaling relation, admittedly with sparse data, strengthens the case for suppression of star formation in dwarfs, and tends to confirm our hypothesis that gas ejection may have played a greater role in dwarfs than in massive galaxies.
This might suggest that while SMBH may form contemporaneously with the old stellar population, IMBH could well have formed first. Confirmation of this trend would strengthen the case for AGN feedback playing an important role in early dwarf evolution. The IMBH black hole occupation fraction inferred from x-ray observations of dwarfs is likely to be significant for any reasonable duty cycle: possible issues of black hole recoils will be considered elsewhere.
Dwarf galaxies continue to play a central role in cosmology. For example, the most recent example is of the only known repeating fast radio burst (FRB), recently localized by VLBI/VLBA observations at sub-arc sec resolution (Chatterjee et al. 2017) to be in a dwarf galaxy host. This supports the inference that FRBs are extragalactic, one leading interpretation being that these highly luminous and short-duration events involve tidal disruption of a neutron star by a central IMBH (Romero et al. 2016). Localization of more FRBs, and especially detection of x-ray and optical emission line signatures, will lead to confirmation of the involvement of low luminosity AGN in dwarfs as a central hypothesis for understanding the inferred high frequency of FRBs.
In summary, dwarf galaxies pose problems that are not easily resolved unless complicated and diverse types of baryonic feedback are introduced. This has motivated many authors to invent dark matter modifications to explain such properties of dwarf galaxies as their frequency, structure and surface brightness. I argue that the rationale for such extreme measures, namely modifying fundamental physics, is lacking when plausible astrophysical explanations remain to be explored. I provide one of these, which goes beyond the usual discussions of stellar feedback by appealing to a population of central IMBH that formed in the earliest gas-rich phase of dwarf galaxy evolution.
The work of JS has been supported in part by ERC Project No. 267117 (DARK) hosted by the Pierre and Marie Curie University-Paris VI, Sorbonne Universities and CEA-Saclay. I thank P. Behroozi, M. Volonteri and A. Wagner for illuminating discussions of these topics.