Accretion Variability Research Articles

Multiepoch Ultraviolet HST Observations of Accreting Low-mass Stars

Abstract Variability is a defining characteristic of young low-mass stars that are still accreting material from their primordial protoplanetary disk. Here we present the largest Hubble Space Telescope (HST) variability study of classical T Tauri stars (CTTS) to date. For five of these objects, we obtained a total of 25 spectra with the Space Telescope Imaging Spectrograph. Mass accretion rates and the fraction of the star covered by accretion columns (i.e., filling factors) were inferred using 1D NLTE physical models whose parameters were fit within a Bayesian framework. On week-long timescales, typical changes in the mass accretion rates range up to a factor of about two, while changes of up to a factor of about five are inferred for the filling factors. In addition to this, we observed a possible accretion burst in the transitional disk system GM Aur, and an incident we interpret as a chance alignment of an accretion column and the undisturbed photosphere along our line of sight in the full disk system VW Cha. We also measure correlations between mass accretion rate and line luminosities for use as secondary tracers of accretion. We place our objects in context with recent high-cadence photometric surveys of low-mass star formation regions and highlight the need for more broad-wavelength, contemporaneous data to better understand the physical mechanisms behind accretion variability in CTTS.

Spatiotemporal variability of erosion and accretion in Ganges River using GIS and RS: a comparative study overlapping Rennell’s map of 1760s

Bangladesh has predominantly four major river systems. Ganges (Padma) River is one of the prominent rivers which support the life and livelihoods of millions of people in Bangladesh. The riverine area of Bangladesh has always faced some changing stages for radical accretion and erosion of lands. Areas of erosion and deposition were determined from successive changes in the bankline positions. Erosion is more active in course line and deposition in sandbar of river. In this research, the area which is eroded and deposited during 1760–2015 (more than 250 years) was analyzed. Erosion and accretion are measured by using Rennell’s map and Landsat MSS, TM and ETM+ satellite imagery with an average duration of 20 years. Processing of image analysis such as layer stack, image enhancement, mosaic and re-projection is done by different tools of image processing software. The Raster and spatial data have been analyzed by image analysis approaches and geo-processing techniques, while quantitative data have been analyzed by using some other statistical computer software program. It was analyzed through the spatial and temporal variation in the study reaches. These are identified by geo-processing techniques of riverbanks. The highest amount of erosional area occurred during 1760–1975 is 38,633 ha, depositional area is 55,140, and therefore, difference is 16,507, with the lowest amount of erosion occurring during 1995–2015. On the other hand, highest amount of deposition occurred during 1760–2015 is 57,605 ha, erosional land is 33,320 ha and there difference is 24,285 ha, with the lowest amount of deposition occurring during 1975–2015. The erosion and deposition has been comparatively low during 1975–1995 and 1995–2015. Finally it is identified that deposition is more active than erosion in Ganges–Padma River in a long period of time (during 1760–2015).

Burst occurrence in young massive stellar objects

Episodic accretion-driven outbursts are an extreme manifestation of accretion variability. It has been proposed that the development of gravitational instabilities in the proto-circumstellar medium of massive young stellar objects (MYSOs) can lead to such luminous bursts, when clumps of fragmented accretion discs migrate onto the star. We simulate the early evolution of MYSOs formed by the gravitational collapse of rotating 100 M pre-stellar cores and analyze the characteristics of the bursts that episodically accompany their strongly time-variable protostellar lightcurve. We predict that MYSOs spend ~ 10^3 yr (~ 1.7\%) of their modelled early 60 kyr experiencing eruptive phases, during which the peak luminosity exceeds the quiescent pre-burst values by factors from 2.5 to more than 40. Throughout these short time periods, they can acquire a substential fraction (up to ~ 50 \%) of their zero-age-main sequence mass. Our findings show that fainter bursts are more common than brighter ones. We discuss our results in the context of the known bursting MYSOs, e.g. NGC6334I-MM1 and S255IR-NIRS3, and propose that these monitored bursts are part of a long-time ongoing series of eruptions, which might, in the future, be followed by other luminous flares.

Low angular momentum accretion of fractal medium on to Kerr black holes and the emergence of the acoustic manifold

For three different geometric configurations of matter and two different thermodynamic equations of state, low angular momentum, multi-transonic, axially symmetric accretion flow of matter having fractional dimension of mass distribution onto a rotating black hole has been studied by employing certain post-Newtonian pseudo-Kerr black hole potential. Such task has been accomplished mathematically by mapping the fractal nature of accreted medium onto its continuum counterpart. The difference between spin dependence of accretion dynamics of the fractal medium and the continuous medium has been highlighted. By employing a time dependent linear perturbation scheme, it has been demonstrated that accretion of matter with fractional dimension of density distribution can be considered as a natural example of classical analogue model. The corresponding acoustic surface gravity has been estimated in terms of accretion variables. The value of the surface gravity changes as the accreted matter makes a transition from its fractal nature to the corresponding continuum distribution.

An Unusual Transient in the Extremely Metal-Poor Galaxy SDSS J094332.35+332657.6 (Leoncino Dwarf)

We have serendipitously discovered that Leoncino Dwarf, an ultra-faint, low-metallicity record-holder dwarf galaxy, may have hosted a transient source, and possibly exhibited a change in morphology, a shift in the center of brightness, and peak variability of the main (host) source in images taken approximately 40 yr apart; it is highly likely that these phenomena are related. Scenarios involving a Solar System object, a stellar cluster, dust enshrouding, and accretion variability have been considered, and discarded, as the origin of the transient. Although a combination of time-varying strong and weak lensing effects, induced by an intermediate mass black hole (10$^4$ - 5 $\times$ 10$^{5}$ M$_{\odot}$) moving within the Milky Way halo (0.1 -- 4 kpc), can conceivably explain all of the observed variable galaxy properties, it is statistically highly unlikely according to current theoretical predictions, and, therefore, also discarded. A cataclysmic event such as a supernova/hypernova could have occurred, as long as the event was observed towards the later/late-stage descent of the light curve, but this scenario fails to explain the absence of a post-explosion source and/or host HII region in recent optical images. An episode related to the giant eruption of a luminous blue variable star, a stellar merger or a nova, observed at, or near, peak magnitude may explain the transient source and possibly the change in morphology/center of brightness, but can not justify the main source peak variability, unless stellar variability is evoked.

The 2016–2017 peak luminosity of the pre-main sequence variable V2492 Cygni

Context. V2492 Cyg is a young pre-main sequence star presenting repetitive brightness variations of significant amplitude (ΔR ≥ 5 mag) whose physical origin has been ascribed to both extinction (UXor-type) and accretion (EXor-type) variability, although their mutual proportion has not been clarified yet. Recently, V2492 Cyg has reached a level of brightness ever registered in the period of its documented activity.Aim. We aim to derive the variation of the mass accretion rate between low- and high-state and to get new insights on the origin of the variability of V2492 Cyg.Methods. Optical and near-infrared (NIR) photometry and spectroscopy have been obtained in October 2016 and between March and July 2017. The source has remained bright until the end of May 2017, then it started to rapidly fade since the beginning of June at a rate of ~0.08 mag/day. On mid-July 2017 the source has reached the same low-brightness level as two years before. Extinction and mass accretion rate were derived by means of the luminosity of the brightest lines, in particular Hα and Hβ. A couple of optical high-resolution spectra are also presented to derive information on the gas kinematics.Results. Visual extinction variations do not exceed a few magnitudes, while the mass accretion rate is estimated to vary from less than 10−8 up to a few 10−7 M⊙ yr−1. This latter is comparable to that estimated on the previous high-state in 2010, likely occurred under more severe extinction conditions.Conclusions. The combined analysis of the optical and NIR observations extends to the present event the original suggestion that the V2492 Cyg variability is a combination of changing extinction and accretion.

Relativistic sonic geometry for isothermal accretion in the Kerr metric

We linearly perturb advective isothermal transonic accretion onto rotating astrophysical black holes to study the emergence of the relativistic acoustic spacetime and to investigate how the salient features of this spacetime is influenced by the spin angular momentum of the black hole. We have perturbed three different quantities—the velocity potential, the mass accretion rate and the relativistic Bernoulli’s constant to show that the acoustic metric obtained for these three cases are the same up to a conformal factor. By constructing the required causal structures, it has been demonstrated that the acoustic black holes are formed at the transonic points of the flow and the acoustic white holes are formed at the shock location. The corresponding acoustic surface gravity has been computed in terms of the relevant accretion variables and the background metric elements. We have performed a linear stability analysis of the background stationary flow.

How Do Stars Gain Their Mass? A JCMT/SCUBA-2 Transient Survey of Protostars in Nearby Star-forming Regions

Abstract Most protostars have luminosities that are fainter than expected from steady accretion over the protostellar lifetime. The solution to this problem may lie in episodic mass accretion—prolonged periods of very low accretion punctuated by short bursts of rapid accretion. However, the timescale and amplitude for variability at the protostellar phase is almost entirely unconstrained. In A James Clerk Maxwell Telescope/SCUBA-2 Transient Survey of Protostars in Nearby Star-forming Regions, we are monitoring monthly with SCUBA-2 the submillimeter emission in eight fields within nearby ( < 500 pc) star-forming regions to measure the accretion variability of protostars. The total survey area of ∼1.6 deg2 includes ∼105 peaks with peaks brighter than 0.5 Jy/beam (43 associated with embedded protostars or disks) and 237 peaks of 0.125–0.5 Jy/beam (50 with embedded protostars or disks). Each field has enough bright peaks for flux calibration relative to other peaks in the same field, which improves upon the nominal flux calibration uncertainties of submillimeter observations to reach a precision of ∼2%–3% rms, and also provides quantified confidence in any measured variability. The timescales and amplitudes of any submillimeter variation will then be converted into variations in accretion rate and subsequently used to infer the physical causes of the variability. This survey is the first dedicated survey for submillimeter variability and complements other transient surveys at optical and near-IR wavelengths, which are not sensitive to accretion variability of deeply embedded protostars.

Magnetorotational instability and dynamo action in gravito-turbulent astrophysical discs

Though usually treated in isolation, the magnetorotational and gravitational instabilities (MRI and GI) may coincide at certain radii and evolutionary stages of protoplanetary discs and active galactic nuclei. Their mutual interactions could profoundly influence several important processes, such as accretion variability and outbursts, fragmentation and disc truncation, or large-scale magnetic field production. Direct numerical simulations of both instabilities are computationally challenging and remain relatively unexplored. In this paper, we aim to redress this neglect via a set of 3D vertically stratified shearing-box simulations, combining self-gravity and magnetic fields. We show that gravito-turbulence greatly weakens the zero-net-flux MRI. In the limit of efficient cooling (and thus enhanced GI), the MRI is completely suppressed, and yet strong magnetic fields are sustained by the gravito-turbulence. This turbulent ‘spiral wave’ dynamo may have widespread application, especially in galactic discs. Finally, we present preliminary work showing that a strong net-vertical-flux revives the MRI and supports a magnetically dominated state in which the GI is secondary.

Protostellar accretion traced with chemistry

Context. Understanding how accretion proceeds is a key question of star formation, with important implications for both the physical and chemical evolution of young stellar objects. In particular, very little is known about the accretion variability in the earliest stages of star formation.

Violent environment of the inner disk of RW Aurigae A probed by the 2010 and 2015 dimming events

RW Aur is a young binary system showing strong signatures of a recent tidal encounter between the circumprimary disk and the secondary star. The primary star has recently undergone two major dimming events ($\Delta$mag $\approx$ 2 in V-band), whose origin is still under debate. To shed light on the mechanism leading to the dimming events, we study the extinction properties, accretion variability, and gas kinematics using absorption lines from the material obscuring star RW Aur A. We compare our moderate resolution X-Shooter spectra of the dim state of RW Aur A with other spectral observations. In particular, we analyse archival high resolution UVES spectra obtained during the bright state of the system, in order to track the evolution of the spectral properties across the second dimming event. The spectrum obtained during the dim state shows narrow absorption lines in the Na and K optical doublets, where the former is saturated. With a velocity of -60 km/s these lines indicate that during the dim state the disk wind is either enhanced, or significantly displaced into the line of sight. The photometric evolution across the dimming event shows a gray extinction, and is correlated with a significant reduction of the EW of all photospheric lines. Emission lines tracing accretion do not vary significantly across the dimming. We conclude that the dimming event is related to a major perturbation on the inner disk. We suggest that the inner disk is occulting (most of) the star, and thus its photosphere, but is not occulting the accretion regions within a few stellar radii. Since observations of the outer disk indicate that the disk is modestly inclined (45 - 60 deg), we propose that the inner disk might be warped by a yet unseen (sub-)stellar companion, which may also explain the 2.77 day periodic variability of the spectral lines.

Precession and accretion in circumbinary discs: the case of HD 104237

We present the results of smoothed particle hydrodynamics (SPH) simulations of the disc around the young, eccentric stellar binary HD 104237. We find that the binary clears out a large cavity in the disc, driving a significant eccentricity at the cavity edge. This then precesses around the binary at a rate of $\dot{\varpi} = 0.48^{\circ}T_{\mathrm{b}}^{-1}$, which for HD 104237 corresponds to 40 years. We find that the accretion pattern into the cavity and onto the binary changes with this precession, resulting in a periodic accretion variability driven purely by the physical parameters of the binary and its orbit. For each star we find that this results in order of magnitude changes in the accretion rate. We also find that the accretion variability allows the primary to accrete gas at a higher rate than the secondary for approximately half of each precession period. Using a large number of 3-body integrations of test particles orbiting different binaries, we find good agreement between the precession rate of a test particle and our SPH disc precession. These rates also agree very well with the precession rates predicted by the analytic theory of Leung & Lee (2013), showing that their prescription can be accurately used to predict long-term accretion variability timescales for eccentric binaries accreting from a disc. We discuss the implications of our result, and suggest that this process provides a viable way of preserving unequal mass ratios in accreting eccentric binaries in both the stellar and supermassive black hole regimes

TORQUE-LIMITED GROWTH OF MASSIVE BLACK HOLES IN GALAXIES ACROSS COSMIC TIME

We combine cosmological hydrodynamic simulations with analytic models to evaluate the role of galaxy-scale gravitational torques on the evolution of massive black holes at the centers of star-forming galaxies. We confirm and extend our earlier results to show that torque-limited growth yields black holes and host galaxies evolving on average along the Mbh-Mbulge relation from early times down to z = 0 and that convergence onto the scaling relation occurs independent of the initial conditions and with no need for mass averaging through mergers or additional self-regulation processes. Smooth accretion dominates the long-term evolution, with black hole mergers with mass ratios >1:5 representing typically a small fraction of the total growth. Winds from the accretion disk are required to eject significant mass to suppress black hole growth, but there is no need for coupling this wind to galactic-scale gas to regulate black holes in a non-linear feedback loop. Torque-limited growth yields a close-to-linear relation for the star formation rate and the black hole accretion rate averaged over galaxy evolution time scales. However, the SFR-AGN connection has significant scatter owing to strong variability of black hole accretion at all resolved time scales. Eddington ratios can be described by a broad lognormal distribution with median value evolving roughly as (1 + z)^1.9, suggesting a main sequence for black hole growth similar to the cosmic evolution of specific SFRs. Our results offer an attractive scenario consistent with available observations in which cosmological gas infall and transport of angular momentum in the galaxy by gravitational instabilities regulate the long-term co-evolution of black holes and star-forming galaxies.

Temporal variability of carbon and nutrient burial, sediment accretion, and mass accumulation over the past century in a carbonate platform mangrove forest of the Florida Everglades

AbstractThe objective of this research was to measure temporal variability in accretion and mass sedimentation rates (including organic carbon (OC), total nitrogen (TN), and total phosphorous (TP)) from the past century in a mangrove forest on the Shark River in Everglades National Park, USA. The 210Pb Constant Rate of Supply model was applied to six soil cores to calculate annual rates over the most recent 10, 50, and 100 year time spans. Our results show that rates integrated over longer timeframes are lower than those for shorter, recent periods of observation. Additionally, the substantial spatial variability between cores over the 10 year period is diminished over the 100 year record, raising two important implications. First, a multiple‐decade assessment of soil accretion and OC burial provides a more conservative estimate and is likely to be most relevant for forecasting these rates relative to long‐term processes of sea level rise and climate change mitigation. Second, a small number of sampling locations are better able to account for spatial variability over the longer periods than for the shorter periods. The site average 100 year OC burial rate, 123 ± 19 (standard deviation) g m−2 yr−1, is low compared with global mangrove values. High TN and TP burial rates in recent decades may lead to increased soil carbon remineralization, contributing to the low carbon burial rates. Finally, the strong correlation between OC burial and accretion across this site signals the substantial contribution of OC to soil building in addition to the ecosystem service of CO2 sequestration.

Spatio-temporal variability in accretion and erosion of coastal foredunes in the Netherlands: regional climate and local topography.

Depending on the amount of aeolian sediment input and dune erosion, dune size and morphology change over time. Since coastal foredunes play an important role in the Dutch coastal defence, it is important to have good insight in the main factors that control these changes. In this paper the temporal variations in foredune erosion and accretion were studied in relation to proxies for aeolian transport potential and storminess using yearly elevation measurements from 1965 to 2012 for six sections of the Dutch coast. Longshore differences in the relative impacts of erosion and accretion were examined in relation to local beach width. The results show that temporal variability in foredune accretion and erosion is highest in narrow beach sections. Here, dune erosion alternates with accretion, with variability displaying strong correlations with yearly values of storminess (maximum sea levels). In wider beach sections, dune erosion is less frequent, with lower temporal variability and stronger correlations with time series of transport potential. In erosion dominated years, eroded volumes decrease from narrow to wider beaches. When accretion dominates, dune-volume changes are relatively constant alongshore. Dune erosion is therefore suggested to control spatial variability in dune-volume changes. On a scale of decades, the volume of foredunes tends to increase more on wider beaches. However, where widths exceed 200 to 300 m, this trend is no longer observed.

Relating jet structure to photometric variability: the Herbig Ae star HD 163296

Herbig Ae/Be stars are intermediate-mass pre-main sequence stars surrounded by circumstellar dust disks. Some are observed to produce jets, whose appearance as a sequence of shock fronts (knots) suggests a past episodic outflow variability. This "jet fossil record" can be used to reconstruct the outflow history. We present the first optical to near-infrared (NIR) VLT/X-shooter spectra of the jet from the Herbig Ae star HD 163296. We determine physical conditions in the knots, as well as their kinematic "launch epochs". Knots are formed simultaneously on either side of the disk, with a regular interval of ~16 yr. The velocity dispersion versus jet velocity and the energy input are comparable in both lobes. However, the mass loss rate, velocity, and shock conditions are asymmetric. We find Mjet/Macc ~ 0.01-0.1, consistent with magneto-centrifugal jet launching models. No evidence for dust is found in the high-velocity jet, suggesting it is launched within the sublimation radius (<0.5 au). The jet inclination measured from proper motions and radial velocities confirms it is perpendicular to the disk. A tentative relation is found between the structure of the jet and the photometric variability of the source. Episodes of NIR brightening were previously detected and attributed to a dusty disk wind. We report for the first time significant optical fadings lasting from a few days up to a year, coinciding with the NIR brightenings. These are likely caused by dust lifted high above the disk plane; this supports the disk wind scenario. The disk wind is launched at a larger radius than the high-velocity atomic jet, although their outflow variability may have a common origin. No significant relation between outflow and accretion variability could be established. Our findings confirm that this source undergoes periodic ejection events, which may be coupled with dust ejections above the disk plane.

YOUNG STELLAR OBJECTS IN LYNDS 1641: DISKS, ACCRETION, AND STAR FORMATION HISTORY

We investigate the young stellar objects (YSOs) in the Lynds~1641 (L1641) cloud using multi-wavelength data including Spitzer, WISE, 2MASS, and XMM covering ~1390 YSOs across a range of evolutionary stages. In addition, we targeted a sub-sample of YSOs for optical spectroscopy. We use this data, along with archival photometric data, to derive spectral types, extinction values, masses, ages, as well as accretion rates. We obtain a disk fraction of ~50% in L1641. The disk frequency is almost constant as a function of stellar mass with a slight peak at log(M_*/M_sun)\approx-0.25. The analysis of multi-epoch spectroscopic data indicates that the accretion variability of YSOs cannot explain the two orders of magnitude of scatter for YSOs with similar masses. Forty-six new transition disk (TD) objects are confirmed in this work, and we find that the fraction of accreting TDs is lower than for optically thick disks (40--45% vs. 77--79% respectively). We confirm our previous result that the accreting TDs have a similar median accretion rate to normal optically thick disks. We confirm that two star formation modes (isolated vs. clustered) exist in L1641. We find that the diskless YSOs are statistically older than the YSOs with optically-thick disks and the transition disk objects have a median age which is intermediate between the two populations. We tentatively study the star formation history in L1641 based on the age distribution and find that star formation started to be active 2--3 Myr ago.

Pulsed accretion in a variable protostar

Periodic increases in luminosity arising from variable accretion rates have been predicted for some pre-main-sequence close binary stars as they grow from circumbinary disks. The phenomenon is known as pulsed accretion and can affect the orbital evolution and mass distribution of young binaries, as well as the potential for planet formation. Accretion variability is a common feature of young stars, with a large range of amplitudes and timescales as measured from multi-epoch observations at optical and infrared wavelengths. Periodic variations consistent with pulsed accretion have been seen in only a few young binaries via optical accretion tracers, albeit intermittently with accretion luminosity variations ranging from zero to 50 per cent from orbit to orbit. Here we report that the infrared luminosity of a young protostar (of age about 10(5) years) increases by a factor of ten in roughly one week every 25.34 days. We attribute this to pulsed accretion associated with an unseen binary companion. The strength and regularity of this accretion signal is surprising; it may be related to the very young age of the system, which is a factor of ten younger than the other pulsed accretors previously studied.

LAMP: the long-term accretion monitoring programme of T Tauri stars in Chamaeleon I

We present the results of a variability study of accreting young stellar objects in the Chameleon I star-forming region, based on ∼300 high-resolution optical spectra from the Fibre Large Area Multi-Element Spectrograph (FLAMES) at the European Southern Observatory (ESO) Very Large Telescope (VLT). 25 objects with spectral types from G2–M5.75 were observed 12 times over the course of 15 months. Using the emission lines Hα (6562.81 Å) and Ca ii (8662.1 Å) as accretion indicators, we found 10 accreting and 15 non-accreting objects. We derived accretion rates for all accretors in the sample using the Hα equivalent width, Hα 10 per cent width and Ca ii (8662.1 Å) equivalent width. We found that the Hα equivalent widths of accretors varied by ∼7–100 Å over the 15-month period. This corresponds to a mean amplitude of variations in the derived accretion rate of ∼0.37 dex. The amplitudes of variations in the derived accretion rate from Ca ii equivalent width were ∼0.83 dex and those from Hα 10 per cent width were ∼1.11 dex. Based on the large amplitudes of variations in accretion rate derived from the Hα 10 per cent width with respect to the other diagnostics, we do not consider it to be a reliable accretion rate estimator. Assuming the variations in Hα and Ca ii equivalent width accretion rates to be closer to the true value, these suggest that the spread that was found around the accretion rate to stellar-mass relation is not due to the variability of individual objects on time-scales of weeks to ∼1 year. From these variations, we can also infer that the accretion rates are stable within <0.37 dex over time-scales of less than 15 months. A major portion of the accretion variability was found to occur over periods shorter than the shortest time-scales in our observations, 8–25 days, which are comparable with the rotation periods of these young stellar objects. This could be an indication that what we are probing is spatial structure in the accretion flows and it also suggests that observations on time-scales of ∼a couple of weeks are sufficient to limit the total extent of accretion-rate variations in typical young stars. No episodic accretion was observed: all 10 accretors accreted continuously for the entire period of observations and, though they may have undetected low accretion rates, the non-accretors never showed any large changes in their emission that would imply a jump in accretion rate.

RESOLVING THE LUMINOSITY PROBLEM IN LOW-MASS STAR FORMATION

We determine the observational signatures of protostellar cores by coupling two-dimensional radiative transfer calculations with numerical hydrodynamical simulations that predict accretion rates that both decline with time and feature short-term variability and episodic bursts caused by disk gravitational instability and fragmentation. We calculate the radiative transfer of the collapsing cores throughout the full duration of the collapse, using as inputs the core, disk, and protostellar masses, radii, and mass accretion rates predicted by the hydrodynamical simulations. From the resulting spectral energy distributions, we calculate standard observational signatures (bolometric luminosity, bolometric temperature, ratio of bolometric to submillimeter luminosity) to directly compare to observations. We show that the accretion process predicted by these models reproduces the full spread of observed protostars in both Lbol - Tbol and Lbol - core mass space, including very low luminosity objects, provides a reasonable match to the observed protostellar luminosity distribution, and resolves the long-standing luminosity problem. These models predict an embedded phase duration shorter than recent observationally determined estimates (0.12 Myr vs. 0.44 Myr), and a fraction of total time spent in Stage 0 of 23%, consistent with the range of values determined by observations. On average, the models spend 1.3% of their total time in accretion bursts, during which 5.3% of the final stellar mass accretes, with maximum values being 11.8% and 35.5% for the total time and accreted stellar mass, respectively. Time-averaged models that filter out the accretion variability and bursts do not provide as good of a match to the observed luminosity problem, suggesting that the bursts are required.