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In case of the dust disc. all raclii are at this limit gaimultaneously. since eq. (39))
In case of the dust disc, all radii are at this limit simultaneously, since eq. \ref{mslimit}) )
is exactly the hydrostatic quation for a pressure-less disc.
is exactly the hydrostatic equation for a pressure-less disc.
It should. be noted. that 1e angular velocity reached in these strongerrelativistic cases exceeds the value of thepressure-Free case (Q= O,) or the same central redshift.
It should be noted that the angular velocity reached in these strongerrelativistic cases exceeds the value of thepressure-free case $\Omega=\Omega_c$ ) for the same central redshift.
This effect. is caused by 1f non-linearity of the Einstein-equations.
This effect is caused by the non-linearity of the Einstein-equations.
Through. the eravitational action of the internal pressure. the potential
Through the gravitational action of the internal pressure, the potential
ideal MHD. they evolve according to corresponding to the advection of magnetic field lines by Lagrangian particles (2)..
ideal MHD, they evolve according to corresponding to the advection of magnetic field lines by Lagrangian particles \citep{stern66}.
We extend the Euler potentials method to non-ideal MHD by incorporating shock-capturing dissipation terms. the form of which is given. using a simple generalisation of the terms derived in ?.. by where the summation is over neighbouring particles. e. is a maximum signal velocity between the particle pair as in PMOS. the mean density p=0.5(p;|pj). VM refers to the magnitude of the mean kernel gradient VM;;|=0.5;j|(hi)VWithj)] and a? is a time-variable co-efficient for each particle that is evolved as described in PMOS.
We extend the Euler potentials method to non-ideal MHD by incorporating shock-capturing dissipation terms, the form of which is given, using a simple generalisation of the terms derived in \citet{pm04b}, by where the summation is over neighbouring particles, $v_{\rm sig}$ is a maximum signal velocity between the particle pair as in PM05, the mean density $\bar{\rho} = 0.5(\rho_i + \rho_{j})$, $\vert \overline{\nabla W_{ij}} \vert$ refers to the magnitude of the mean kernel gradient $\overline{\nabla W_{ij}} = 0.5[\nabla W_{ij}(h_{i}) + \nabla W_{ij}(h_{j})]$ and $\alpha^{\rm B}$ is a time-variable co-efficient for each particle that is evolved as described in PM05.
The magnetic force is computed using the ?— formalism discussed in PMOS (using the B computed from equation 51) which ensures stability of the SPMHD formalism against particle-clumping instabilities in the regime where gas pressure is dominant over magnetic pressure.
The magnetic force is computed using the \citet{morris96} formalism discussed in PM05 (using the ${\bf B}$ computed from equation \ref{eq:eulerpots}) ) which ensures stability of the SPMHD formalism against particle-clumping instabilities in the regime where gas pressure is dominant over magnetic pressure.
The MHD part of the force equation (that is. apart from the gravitational and artificial viscosity forces) reads where ¢;.p;.P; and D; refer to the density. pressure and magnetic field of particle { and O is a normalisation term related to the gradient of the smoothing length (as in. e.g. 22»).
The MHD part of the force equation (that is, apart from the gravitational and artificial viscosity forces) reads where $v_{i}, \rho_{i}, P_{i}$ and $B_{i}$ refer to the density, pressure and magnetic field of particle $i$ and $\Omega$ is a normalisation term related to the gradient of the smoothing length (as in, e.g. \citealt{monaghan02,pm06}) ).
The first term in (I2)) is the isotropic hydrodynamic + magnetic pressure force and the second term is the magnetic tension force.
The first term in \ref{eq:morrisforce}) ) is the isotropic hydrodynamic + magnetic pressure force and the second term is the magnetic tension force.
For simulations “without magnetic tension” we do not include the latter term.
For simulations “without magnetic tension” we do not include the latter term.
A detailed summary of the recent changes to the hydrodynamic method (including details of the implementation of the variable smoothing length SPH formalisms in both the pressure and gravity terms) and the implementation of the Euler potentials into the numerical code (including test problems comparing the use of them to the "standard SPMHD formalism of PMOS) are discussed in detail in 2. and we refer the reader to this paper for an up-to-date summary of the present numerical code (the specitic code described differs fromthat used here but the algorithms implemented in each are identical).
A detailed summary of the recent changes to the hydrodynamic method (including details of the implementation of the variable smoothing length SPH formalisms in both the pressure and gravity terms) and the implementation of the Euler potentials into the numerical code (including test problems comparing the use of them to the `standard' SPMHD formalism of PM05) are discussed in detail in \citet{pr07} and we refer the reader to this paper for an up-to-date summary of the present numerical code (the specific code described differs fromthat used here but the algorithms implemented in each are identical).
The initial cloud is a sphere of radius 2=4«107 em (0.013 pe) and mass AJ=LAZ. with mean density 10 ο .
The initial cloud is a sphere of radius $R= 4\times 10^{16}$ cm (0.013 pc) and mass $M= 1M_{\odot}$ with mean density $\rho_{0} = 7.43\times 10^{-18}$ g $^{-3}$.
The free-fall time of the cloud is --2.4107 years.
The free-fall time of the cloud is $t_{\rm ff} = 2.4\times 10^{4}$ years.
We assume. for simplicity. that an initially uniform magnetic flux threads the cloud and connects it to the surrounding interstellar medium.
We assume, for simplicity, that an initially uniform magnetic flux threads the cloud and connects it to the surrounding interstellar medium.
However. a key factor in the problems studied here is the angular momentum transfer introduced by the magnetic field in the form of magnetic braking of the rotating core.
However, a key factor in the problems studied here is the angular momentum transfer introduced by the magnetic field in the form of magnetic braking of the rotating core.
Thus careful attention must be paid to the boundary condition at r= 11.
Thus careful attention must be paid to the boundary condition at $r=R$ .
Experiments with simple boundary conditions for SPH (for example. using pressure boundaries Or ghost partices) proved somewhat constantunsatisfactory. particularly because. in the higher magnetic field strength runs. significant material is flung outwards (12hy the cloud along the magnetic field lines into the surrounding medium.
Experiments with simple boundary conditions for SPH (for example, using constant pressure boundaries or ghost particles) proved somewhat unsatisfactory, particularly because, in the higher magnetic field strength runs, significant material is flung outwards by the cloud along the magnetic field lines into the surrounding medium.
Toa: Weτ thereforeM model the boundaries: self-consistently: by placing the eloud within a uniform. low density box of surrounding material in pressure equilibrium with the cloud (seealso.27)..
We therefore model the boundaries self-consistently by placing the cloud within a uniform, low density box of surrounding material in pressure equilibrium with the cloud \citep[see also ][]{hosking02,bp06}.
To ensure regularity of the particle distributions at the box boundaries. we use quasi-periodic boundary conditions at the box edge (that is. particles within 2 smoothing lengths of the boundary are "ghosted' to the opposite boundary. with no self gravity between SPH particles and ghost particles).
To ensure regularity of the particle distributions at the box boundaries, we use quasi-periodic boundary conditions at the box edge (that is, particles within $2$ smoothing lengths of the boundary are `ghosted' to the opposite boundary, with no self gravity between SPH particles and ghost particles).
Since a uniform magnetic field necessarily implies a linear gradient in the Euler potentials. continuity of the magnetic field across the box boundary is ensured by adding an offset to the values of à and «2 copied to the ghosted particles corresponding to an extrapolation of the linear gradients outside the box boundaries.
Since a uniform magnetic field necessarily implies a linear gradient in the Euler potentials, continuity of the magnetic field across the box boundary is ensured by adding an offset to the values of $\alpha$ and $\beta$ copied to the ghosted particles corresponding to an extrapolation of the linear gradients outside the box boundaries.
We tind that satisfactory results are obtained using a box size of 8.IO "em «c.g.zSI0! em (that is. twice the cloud radius in each direction) and a density ratio of 30:1 between the cloud and the surrounding medium.
We find that satisfactory results are obtained using a box size of $-8 \times 10^{16}$ cm $< x,y,z < 8 \times 10^{16} $ cm (that is, twice the cloud radius in each direction) and a density ratio of $30:1$ between the cloud and the surrounding medium.
This density ratio was chosen simply to ensure that the surrounding medium is sufficiently hot so as not to contribute significantly to the self-gravity of the cloud (that is c22GAL/ 2).
This density ratio was chosen simply to ensure that the surrounding medium is sufficiently hot so as not to contribute significantly to the self-gravity of the cloud (that is, $c_{\rm s}^{2} > GM/R$ ).
The initial setup is shown in Figure I. showing a cross-section slice of density at y=0 with overlaid magnetic field lines for a field initially oriented in the : direction.
The initial setup is shown in Figure \ref{fig:setup}, showing a cross-section slice of density at $y=0$ with overlaid magnetic field lines for a field initially oriented in the $z-$ direction.
Both the spherical cloud and the surrounding medium are set up by placing the particles in a regular close-packed lattice arrangement (e.g.2?) which is a stable arrangement for the particles (2)..
Both the spherical cloud and the surrounding medium are set up by placing the particles in a regular close-packed lattice arrangement \citep[e.g.][]{hosking02} which is a stable arrangement for the particles \citep{morrisphd}. .
Whilst such> regularity introduces some undesirable side effects due to the lattice regularity in the initial collapse phase. these small and transient effects are largely eliminated by the time
Whilst such regularity introduces some undesirable side effects due to the lattice regularity in the initial collapse phase, these small and transient effects are largely eliminated by the time
colour band excess on LLJD 3524 and in the carly phase of the secondary outburst at JD. 3546.
colour band excess on HJD 3524 and in the early phase of the secondary outburst at HJD 3546.
On the night of 2005. June 5 the band measurement at 1LJD 37.1449. revealed a ~0.45 magnitude excess above the trend. from. previous and succeeding nights.
On the night of 2005, June 5 the band measurement at HJD 3527.1449 revealed a $\sim 0.45$ magnitude excess above the trend from previous and succeeding nights.
Phere was no evidence of any excess above the trend-lines for any of the other colours all of which were measured within ~2 hrs of the band.
There was no evidence of any excess above the trend-lines for any of the other colours all of which were measured within $\sim 2$ hrs of the band.
The existence of an band: excess is also obvious in the broadband spectrum for the night as shown in bie.
The existence of an band excess is also obvious in the broadband spectrum for the night as shown in Fig.
4.
4.
The absence of any perceptible increase in or indicates that the enhanced radiation in was sharply cut-olf in waveleneth or was of cluration less than 32 minutes when the next measurement (in V) was mace.
The absence of any perceptible increase in or indicates that the enhanced radiation in was sharply cut-off in wavelength or was of duration less than 32 minutes when the next measurement (in ) was made.
An enhanced orbital modulation can be ruled. out since there was no increase in or measured one orbital evele alter4.
An enhanced orbital modulation can be ruled out since there was no increase in or measured one orbital cycle after.
RATE Proportional Counter Array (PCA) measurements show that a typical Type L N-ray burst occurred. almost in the micelle of our 300 see band integration (private communication. Wijnands Ixlein-Wolt).
Proportional Counter Array (PCA) measurements show that a typical Type I X-ray burst occurred almost in the middle of our 300 sec band integration (private communication, Wijnands Klein-Wolt).
The peak amplitude was 40 times the baseline flux and the duration (to 5% of baseline) was 35 s. The associated. optical burst. generated. by reprocessing of the burst X-rays undoubtedly contributed to the increase in4.
The peak amplitude was $\sim 40$ times the baseline flux and the duration (to $ 5\% $ of baseline) was $\sim 35$ s. The associated optical burst generated by reprocessing of the burst X-rays undoubtedly contributed to the increase in.
Type PE X-ray bursts have been observed. from. many neutron star binaries and typically last LO20 sec although a few have lasted. up to 150 seconds ( Wong et al.
Type I X-ray bursts have been observed from many neutron star binaries and typically last 10–20 sec although a few have lasted up to 150 seconds ( Kong et al.
2000).
2000).
For the fe examples available with simultaneous X-ray and optical data. mostly from 4U 163653 (Pedersen et al.
For the few examples available with simultaneous X-ray and optical data, mostly from 4U 1636–53 (Pedersen et al.
1982: Lawrence et al.
1982; Lawrence et al.
1983: Matsuoka ct al.
1983; Matsuoka et al.
1984) and GS 182624 ( Ίνοις et al.
1984) and GS 1826--24 ( Kong et al.
2000). the optical and X-ray. profiles are similar in shape and duration “Phere is usually evidence for an optical lag of a few seconds corresponding to the leh travel time to the reprocessing site.
2000), the optical and X-ray profiles are similar in shape and duration There is usually evidence for an optical lag of a few seconds corresponding to the light travel time to the reprocessing site.
Preliminary calculations suggest that reprocesscc radiation contributed only a small fraction of the increase seen in the banc.
Preliminary calculations suggest that reprocessed radiation contributed only a small fraction of the increase seen in the band.
A paper on this event. combining the A-ray. optical and radio data. is in preparation.
A paper on this event, combining the X-ray, optical and radio data, is in preparation.
This wil include detailed: calculations setting limits on the optica Hux expected. from reprocessed radiation.
This will include detailed calculations setting limits on the optical flux expected from reprocessed radiation.
For now we rely on nsoximate approximateestimates based on scaling areargumentsnts using published: simultaneous optical ancl X-ray. observations of the A-rav burst source 4U. 1636.53.
For now we rely on approximate estimates based on scaling arguments using published simultaneous optical and X-ray observations of the X-ray burst source 4U 1636–53.
Phe peak amplitudes of the bursts were 40 times the baseline N-rav. lux. in both svstems although the duration of the SAX JISOS.43658 burst was about twice as long as typical bursts seen in 4U 163653,
The peak amplitudes of the bursts were $\sim 40 $ times the baseline X-ray flux in both systems although the duration of the SAX J1808.4--3658 burst was about twice as long as typical bursts seen in 4U 1636–53.
Optical bursts are generated by reprocessing of burst X-ravs incident on the disc and the companion.
Optical bursts are generated by reprocessing of burst X-rays incident on the disc and the companion.
The fraction observed from the disc is expected to be strongly dependent on the inclination of the svstem.
The fraction observed from the disc is expected to be strongly dependent on the inclination of the system.
The component coming [rom the companion star will also be dependent on on the inclination (though not so strongly) and will be proportional to the solid angle subtended by the companion Roche lobe ab the burst source.
The component coming from the companion star will also be dependent on on the inclination (though not so strongly) and will be proportional to the solid angle subtended by the companion Roche lobe at the burst source.
Lts amplitude. will depend. on the orbital phase at which the burst occurred.
Its amplitude will depend on the orbital phase at which the burst occurred.
We assume in the calculations below that the fraction. arising from the companion is equal to the fractional. orbital modulation observed during transient outbursts.
We assume in the calculations below that the fraction arising from the companion is equal to the fractional orbital modulation observed during transient outbursts.
The inclination angles are poorly known in both SAX JIsO0S.43658 and 4U 163653 but are believed to be ~60! in both systems (Chakrabarty Morgan. 1998: Homer et al.
The inclination angles are poorly known in both SAX J1808.4–3658 and 4U 1636–53 but are believed to be $\sim 60 \degr $ in both systems (Chakrabarty Morgan 1998; Homer et al.
2002: Frank. Wine Lasota LOST).
2002; Frank, King Lasota 1987).
The X-ray burst occurred at binary phase ©=0.08 (phase zero corresponds to the time when the companion star is at its maximum distance from the observer). almost optimum time for observing reprocessed radiation from the companion.
The X-ray burst occurred at binary phase $\phi = 0.08$ (phase zero corresponds to the time when the companion star is at its maximum distance from the observer), almost optimum time for observing reprocessed radiation from the companion.
Using the estimated dimensions of the two systems (Frank. lxing Lasota LOST: Chakrabarty Morgan 1998) we find that the solid angle of the Roche lobe in the 4U 163653 system is 4times that in SAX JISOS4.3658.
Using the estimated dimensions of the two systems (Frank, King Lasota 1987; Chakrabarty Morgan 1998) we find that the solid angle of the Roche lobe in the 4U 1636–53 system is $\sim 4$ times that in SAX J1808.4–3658.
Hence the peak optical burst [ux from the companion in 4U 163653 will be 4 times that in SAN JLSOS.43658 assuming that the X-ray bursts are similar in peak llux.
Hence the peak optical burst flux from the companion in 4U 1636–53 will be 4 times that in SAX J1808.4–3658 assuming that the X-ray bursts are similar in peak flux.
Orbital modulation measurements show. however. that the fraction of radiation reprocessed on the companion to 4U 163653 is ~25 per cent (Giles et al.
Orbital modulation measurements show, however, that the fraction of radiation reprocessed on the companion to 4U 1636–53 is $ \sim 25$ per cent (Giles et al.
2002) which is only twice that in SAN JISOS.43658 (Giles et al.
2002) which is only twice that in SAX J1808.4–3658 (Giles et al.
1999).
1999).
Llenee. for the same peak X-ray. burst flux. the observed. reprocessed. radiation from the disc is also larger in 4U 163653 than in S.XX JISOS.43658.
Hence, for the same peak X-ray burst flux, the observed reprocessed radiation from the disc is also larger in 4U 1636–53 than in SAX J1808.4–3658.
This mav be a consequence of a larger disc size or perhaps of a smaller inclination angle for 4U 163653.
This may be a consequence of a larger disc size or perhaps of a smaller inclination angle for 4U 1636–53.
The two conditions above are satisfied if we assume that. for the same peak A-ray burst Hux. optical bursts in 4U 163653 are twice as large as those in SAN JLSOSA3658.
The two conditions above are satisfied if we assume that, for the same peak X-ray burst flux, optical bursts in 4U 1636–53 are twice as large as those in SAX J1808.4–3658.
The typical peak optical burst. Εαν to baseline. ratio in 4U 163653 is ~1.5 (Pedersen ct al.
The typical peak optical burst flux to baseline ratio in 4U 1636–53 is $\sim 1.5$ (Pedersen et al.
1982: Lawrence et al.
1982; Lawrence et al.
1983).
1983).
Bursts in GS 182624 are much longer in duration but the ratio of optical to X-ray burst. height. is less (Ixong et al.
Bursts in GS 1826–24 are much longer in duration but the ratio of optical to X-ray burst height is less (Kong et al.
2000).
2000).
Given that the X-ray bursts in SAX JISQS.43658 and 4U 163653 are of similar peak amplitude we expect the optical burst in SAX JISQOS.43658 to have half the relative amplitude (~0.75r times baseline).
Given that the X-ray bursts in SAX J1808.4–3658 and 4U 1636–53 are of similar peak amplitude we expect the optical burst in SAX J1808.4–3658 to have half the relative amplitude $\sim 0.75$ times baseline).
The total band integration time (300 s) was much longer than the burst duration and this will reduce the amplitude of the reprocessing signal bv the ratio of the integrated optical burst flux to the "normal. optical flux.
The total band integration time (300 s) was much longer than the burst duration and this will reduce the amplitude of the reprocessing signal by the ratio of the integrated optical burst flux to the 'normal' optical flux.
‘Vhis ratio is ~0.5«|20/300 assuming the optical burst. profile was triangular with effective duration 20 s. Hence the increase in the integrated. band Lux due to reprocessing would be 2.5 per cont above baseline.
This ratio is $\sim 0.5\times20/300$ assuming the optical burst profile was triangular with effective duration $ \sim 20$ s. Hence the increase in the integrated band flux due to reprocessing would be $\sim 2.5$ per cent above baseline.
This is a factor 20 less than the observed. ~50 per cent increase in7.
This is a factor 20 less than the observed $\sim 50 $ per cent increase in.
There are many uncertainties in the above argument but it seems. unlikely that all the band excess can be due to reprocessed) X-ray burst emission.
There are many uncertainties in the above argument but it seems unlikely that all the band excess can be due to reprocessed X-ray burst emission.
The burst may have been the trigger for an on-going svnchrotron emission event.
The burst may have been the trigger for an on-going synchrotron emission event.
ltupen et al. (
Rupen et al. (
2005) detected: weak 4.86 and 8.46 Ciz radio emission [rom SAN JISOS.4.3658 on 2005 June 7. 11 &116 (LLJD 3529. 3533. 538) and suggested it was due to svnchrotron emission.
2005) detected weak 4.86 and 8.46 GHz radio emission from SAX J1808.4–3658 on 2005 June 7, 11 16 (HJD 3529, 3533 3538) and suggested it was due to synchrotron emission.
Rea et al. (
Rea et al. (
2005) measured magnitudes on 2005 June 5 (LID — 3526.5) and. set ade upper limit of 16.5 on band LR emission.
2005) measured magnitudes on 2005 June 5 (HJD $ \sim 3526.5 $ ) and set a $5\sigma$ upper limit of 16.5 on band IR emission.
Their measurements of the optical magnitudes are of low precision but are more consistent with our normal. spectrum of June 3 than with the anomalous. data of June 5.
Their measurements of the optical magnitudes are of low precision but are more consistent with our 'normal' spectrum of June 3 than with the 'anomalous' data of June 5.
Their band upper Limit is slightly above an extrapolation of the ‘normal’ spectrum but is more consistent with it than with the "anomalous! one.
Their band upper limit is slightly above an extrapolation of the 'normal' spectrum but is more consistent with it than with the 'anomalous' one.
The measurements by Rea et al. (
The measurements by Rea et al. (
2005) were made 12 hrs before our observations of June 5.
2005) were made $\sim 12$ hrs before our observations of June 5.
It seems likely that the LR excess was not present at that time ancl we note also that no radio emission was detected on 2005
It seems likely that the IR excess was not present at that time and we note also that no radio emission was detected on 2005
models in the M-Rin plane.
models in the $\dot{M}$ $R_{in}$ plane.
The symbols represent a sample of observations of solar-type objects classified as ‘transition’ discs by Espaillat et al. (
The symbols represent a sample of observations of solar-type objects classified as `transition' discs by Espaillat et al. (
2007a,b,2008,2010) - Red Circles, Hughes et al. (
2007a,b,2008,2010) - Red Circles, Hughes et al. (
2009,2010) - Red Squares, Kim et al. (
2009,2010) - Red Squares, Kim et al. (
2009) - Red Diamonds, Calvet et al. (
2009) - Red Diamonds, Calvet et al. (
2005) - Black Diamonds, Merin et al. (
2005) - Black Diamonds, n et al. (
2010) - Black Squares and Cieza et al. (
2010) - Black Squares and Cieza et al. (
2010) - Black Triangles (Although Cieza et al.
2010) - Black Triangles (Although Cieza et al.
2010 do not fit for the inner-hole radius they list as transitional sources those discs that have a deficit of emission in theSpitzer IRAC bands; therefore we conservatively estimate an inner hole radius of « 10AU for all their sources).
2010 do not fit for the inner-hole radius they list as transitional sources those discs that have a deficit of emission in the IRAC bands; therefore we conservatively estimate an inner hole radius of $<10$ AU for all their sources).
It is immediately clear from the figure that there is a population of large inner hole, strongly accreting transition discs that cannot have been created by XPE.
It is immediately clear from the figure that there is a population of large inner hole, strongly accreting transition discs that cannot have been created by XPE.
Gap opening by a giant planet or grain growth is perhaps the most plausible explanation for these objects.
Gap opening by a giant planet or grain growth is perhaps the most plausible explanation for these objects.
However, there is a significant number of discs with inner holes that are consistent with an XPE origin.
However, there is a significant number of discs with inner holes that are consistent with an XPE origin.
Furthermore we note the lack of observations of non-accreting ‘transition’ discs with holes at radii greater than 20AU, where our model predicts a significant populations (although several non-accreting discs with large holes have been detected in different mass ranges e.g. Merín et al.
Furthermore we note the lack of observations of non-accreting `transition' discs with holes at radii greater than 20AU, where our model predicts a significant populations (although several non-accreting discs with large holes have been detected in different mass ranges e.g. n et al.
2010, where the observations probe different radial scales).
2010, where the observations probe different radial scales).
The observations are still rather sparse and it is currently not possible to say whether the observed population of transition discs is a true representation or an artifact of observational selection effects.
The observations are still rather sparse and it is currently not possible to say whether the observed population of transition discs is a true representation or an artifact of observational selection effects.
One obvious consequence of an X-ray photoevaporation mechanism is that the properties of transition discs should be correlated with the X-ray luminosity, something no other model of photoevaporation or ‘transition’ disc origin would predict.
One obvious consequence of an X-ray photoevaporation mechanism is that the properties of transition discs should be correlated with the X-ray luminosity, something no other model of photoevaporation or `transition' disc origin would predict.
In Figure 14,, we show two such correlations namely the inner hole radius (left panel) and accretion rate (right panel) against X-ray luminosity, considering only accreting ‘transition’ discs (i.e. those with an accretion rate >1x10!'Ms !))
In Figure \ref{fig:inner_corr}, we show two such correlations namely the inner hole radius (left panel) and accretion rate (right panel) against X-ray luminosity, considering only accreting `transition' discs (i.e. those with an accretion rate $>1\times 10^{-11}$ ).