Episodic accretion, radiative feedback, and their role in low-mass star formation
aa r X i v : . [ a s t r o - ph . GA ] S e p **Volume Title**ASP Conference Series, Vol. **Volume Number****Author** c (cid:13) **Copyright Year** Astronomical Society of the Pacific Episodic accretion, radiative feedback, and their role in low-massstar formation
Dimitris Stamatellos , David Hubber , , and Anthony Whitworth School of Physics & Astronomy, Cardi ff University, 5 The Parade, Cardi ff CF24 3AA, UK Department of Physics & Astronomy, University of She ffi eld, HounsfieldRoad, She ffi eld S3 7RH, UK School of Physics and Astronomy, University of Leeds, Leeds LS2 9JT, UK
Abstract.
It is speculated that the accretion of material onto young protostars isepisodic. We present a computational method to include the e ff ects of episodic ac-cretion in radiation hydrodynamic simulations of star formation. We find that duringaccretion events protostars are “switched on”, heating and stabilising the discs aroundthem. However, these events typically last only a few hundred years, whereas the in-tervals in between them may last for a few thousand years. During these intervals theprotostars are e ff ectively “switched o ff ”, allowing gravitational instabilities to developin their discs and induce fragmentation. Thus, episodic accretion promotes disc frag-mentation, enabling the formation of low-mass stars, brown dwarfs and planetary-massobjects. The frequency and the duration of episodic accretion events may be responsiblefor the low-mass end of the IMF, i.e. for more than 60% of all stars.
1. Introduction
Young protostars grow in mass mainly by accreting material from their surroundingdiscs. The accretion is speculated to be episodic (Herbig 1977; Dopita 1978; Reipurth1989; Kenyon et al. 1990; Evans et al. 2009; Dunham et al. 2010), as e.g. in FU Ori-type outbursts in which a large fraction of the star’s mass is delivered within a fewhundred years (Hartmann & Kenyon 1996; Zhu et al. 2010). The estimated accretionrates during these bursts are up to ∼ × − M ⊙ yr − , so each burst can deliver afew 10 − M ⊙ onto the protostar. Further evidence for episodic accretion comes fromthe periodically spaced knots seen in bipolar jets (e.g. Reipurth 1989). Bipolar jets aredriven o ff along the protostellar rotation axis by the energy released as material spiralsin and accretes onto the protostar; periodically spaced knots therefore imply episodicaccretion. Finally, the luminosity problem provides indirect observational support forepisodic accretion. By the end of the Class 0 phase ( ∼ yr), half the protostar’s finalmass has been accumulated. Thus for a final mass of 1 M ⊙ , the mean accretion rate ontothe protostar must be ∼ × − M ⊙ yr − , and the mean accretion luminosity must be ∼
25 L ⊙ . This is much larger than the observed bolometric luminosities of typical solar-type protostars (Kenyon et al. 1990; Evans et al. 2009). Episodic accretion mitigatesthis problem, as the luminosity is only large intermittently, and most protostars areobserved between bursts (Dunham et al. 2010; O ff ner & McKee 2011).1 Stamatellos, Hubber, and WhitworthAccretion of material onto a young protostar results in large amounts of accre-tion luminosity which may e ff ect the evolution of the protostar’s surrounding disc(Krumholz 2006; Bate 2009; O ff ner et al. 2009; Urban et al. 2010; Krumholz et al. 2010;O ff ner et al. 2010). This is particularly important for the low-mass end of the IMF (e.g.for low-mass stars and brown dwarfs) as gravitational fragmentation of massive ex-tended discs is considered to be one of the main ways of producing these objects (e.g.Whitworth & Stamatellos 2006; Stamatellos & Whitworth 2009a,b; Boley et al. 2010;Kratter & Murray-Clay 2011). Thus, in order to determine the full e ff ect of radiativefeedback in low-mass star formation, it is important to describe in detail the role ofepisodic accretion.
2. An episodic accretion model for hydrodynamic simulations
Material spirals from the outer disc region towards the young protostar due to the workof the gravitational instabilities in transporting angular momentum outwards in the disc.Once this material reaches within a few AU from the protostar the GIs becomes inef-fective as the disc is hotter there. The material is then deposited on a notional inneraccretion disc (IAD), where it piles up until it becomes hot enough that thermal ion-isation couples the matter to the magnetic field. At this point the magneto-rotationalinstability (MRI) is activated, transporting angular momentum outwards, and therebyallowing the matter accumulated in the IAD to spiral inwards and onto the central pro-tostar.Simulations of self-gravitating hydrodynamics on the scale of molecular cloudcores (i.e. sizes from 10 to 10 AU and masses from 0 . ⊙ ) can achieve suf-ficient resolution to capture the formation of discs around young protostars, and thee ff ects of GIs in the outer regions of such discs. However, such simulations cannotcapture what happens in the inner disc region, where sinks are invoked. Contrary toprevious studies (e.g. Attwood et al. 2009), we assume that the matter which enters asink is not instantly accreted onto to protostar but it is accumulated on the IAD, withinthe sink radius. We adapt the model of Zhu et al. (2010) to phenomenologically de-scribe the properties of episodic accretion. The details of the model are discussed inStamatellos et al. (2011b). An episodic accretion event is initiated when M IAD > M MRI (1)which is presumed to correspond to an IAD temperature of T M = M MRI ≃ .
13 M ⊙ M ⋆ . ⊙ ! / ˙ M IAD − M ⊙ yr − ! / , (2)is the mass accreted onto the protostar in an outburst event. The duration of the eventis set as ∆ t MRI ≃
250 yr (cid:18) α MRI . (cid:19) − M MRI .
13 M ⊙ ! , (3)where α MRI is the viscosity parameter provided by the MRI. To match observations ofFU Ori stars, we assume an exponential decay of the accretion rate˙ M ⋆, EA = M MRI ∆ t MRI e − ( t − t ∆ t MRI , t < t < t + ∆ t MRI . (4)pisodic accretion and low-mass star formation 3Once the accretion rate of the protostar has been determined using the abovemodel, its luminosity at any time is given by L = M M ⊙ ! L ⊙ + f GM ˙ MR , (5)where M is the mass of the protostar, R its radius, and ˙ M is the accretion rate ontoit. The first term on the righthand side is the intrinsic luminosity of the protostar (dueto contraction and nuclear reactions in its interior). The second term is the accretionluminosity. f = .
75 is the fraction of the accretion energy that is radiated away atthe photosphere of the protostar, rather than being expended driving jets and / or winds(O ff ner et al. 2009). We assume R = ⊙ is the typical radius of a young protostar(Palla & Stahler 1993). At the initial stages of star formation the accretion luminositydominates over the intrinsic luminosity of the protostar.The above model describes macroscopically the e ff ects of episodic accretion, whichin turn regulates the radiative feedback from the protostar.
3. The role of episodic accretion in low-mass star formation
To evaluate the consequences of episodic accretion for disc fragmentation and low-mass star formation, we perform radiation hydrodynamic simulations of a collapsingturbulent molecular core. We use the SPH code SEREN (Hubber et al. 2011), in whichthe radiative transfer is treated with the di ff usion approximation of Stamatellos et al.(2007b). The outer envelope of the core extends to 5 × AU, and the total coremass is 5.4 M ⊙ . We perform three simulations, all with the same initial conditions, anddi ff ering only in their treatments of the luminosities of protostars (see Stamatellos et al.2011b, for details). In all three simulations the initial collapse leads to the formation ofa primary protostar (i.e. a first sink) at t ∼
77 kyr, and this quickly acquires an extendedaccretion disc (Figs. 1-3). The simulations only diverge after this juncture.
No radiative feedback from protostars.
In the first simulation there is no radiativefeedback from the protostar, and the gas in the disc is only heated by compression andby viscous dissipation in shocks. The disc stays cool and fragments resulting in theformation of 7 secondary protostars, with masses from 0.008 M ⊙ to 0.24 M ⊙ . This isillustrated in Fig. 1. Continuous accretion / continuous radiative feedback from protostars. In the sec-ond simulation, we assume that the matter entering a sink is immediately accreted ontothe protostar at its centre. The accretion of material onto the protostar is continuous(see. Fig. 4, top, blue line). This results in an accretion luminosity which is typically10 to 100 L ⊙ (see Fig. 4, bottom, blue line). It therefore heats the surrounding disc,entirely suppressing disc fragmentation, at all radii, as it is illustrated in Fig. 2. Episodic accretion / episodic radiative feedback from protostars. In the third sim-ulation, the accretion rate into the protostar during the MRI-driven accretion bursts isvery high (see Fig. 4, top, black line), resulting in high luminosity (see Fig. 4, bottom,black line). This heats and stabilises the disc against fragmentation. However, as the Stamatellos, Hubber, and Whitworth
Figure 1. Evolution of the accretion disc around the primary protostar formingin a collapsing turbulent molecular cloud core, without radiative feedback from theprotostar. The disc around the primary protostar increases in mass, becomes grav-itationally unstable, and fragments to form 3 low-mass stars, 2 brown dwarfs and2 planetary-mass objects. The colour encodes the logarithm of column density, ing cm − .Figure 2. Evolution of the accretion disc around the primary protostar with con-tinuous accretion, continuous radiative feedback from the protostar. The disc growsin mass, but radiative feedback makes it so hot that it does not fragment.Figure 3. Evolution of the accretion disc around the primary protostar withepisodic accretion and episodic radiative feedback from the protostar. The discbecomes gravitationally unstable (first and second column) but fragmentation isdamped by heating due to an accretion burst (third column); however, after this burstthe disc cools su ffi ciently to undergo gravitational fragmentation; 2 low-mass starsform in the disc. pisodic accretion and low-mass star formation 5 Figure 4. The evolution of the accretion rate and the luminosity of primary proto-star. Blue lines correspond to the the case with continuous accretion and feedback,and black lines for the case with episodic accretion and feedback. (a) shows the ac-cretion rate onto the primary protostar amd (b) shows the accretion luminosities, forthe cases with continuous (blue) and episodic (black) accretion. mass of the protostar builds up, the mass that is required to activate MRI also goes up,and at the same time the accretion rate into the sink goes down, so that the intervalsbetween bursts become longer. During these intervals the luminosity of the protostaris relatively low, hence the disc cools down. Within a few kyr of the formation ofthe primary protostar, the interval between successive accretion bursts has increased to ∼ ffi cient time to allow the outer disc at R ∼ −
150 AU, to undergogravitational fragmentation. This is illustrated on Fig. 3. In the first two frames, at 82and 83 kyr, the disc is unstable and tries to fragment, but then at 84 kyr it is heatedby an accretion outburst and stabilised. Once the outburst is over, the disc cools backdown fast, and fragments to produce 2 low-mass hydrogen-burning secondaries.
4. Conclusions
If episodic accretion is a common phenomenon among young protostars as observa-tional and theoretical evidence suggests (Herbig 1977; Dopita 1978; Reipurth 1989;Hartmann & Kenyon 1996; Greene et al. 2008; Evans et al. 2009; Peneva et al. 2010;Dunham et al. 2010), it may limit the e ff ect of the luminosity of a protostar on its en-vironment and create favourable conditions for disc fragmentation to occur. As discfragmentation is predominantly a mechanism for forming low-mass stars and brown-dwarfs, episodic accretion may then have a significant influence on the lower end of theIMF (Stamatellos et al. 2007a; Stamatellos & Whitworth 2009a,b; Stamatellos et al. 2011a). Stamatellos, Hubber, and Whitworth References
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