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What we found. however. was a statistically significant maximum at Af20.—40pes. which. while being ically unexpected from the standpoint of standard cosmic-rav phwsies. is exactlv what had. motivated: the present experiment.
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What we found, however, was a statistically significant maximum at $\Delta t \approx 20-40\,\mks$, which, while being totally unexpected from the standpoint of standard cosmic-ray physics, is exactly what had motivated the present experiment.
|
I is due to signals from the bottom PM tubes. which arrive after the signals from the top (leading) PAL tubes triggering the measurement. svstem.
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It is due to signals from the bottom PM tubes, which arrive after the signals from the top (leading) PM tubes triggering the measurement system.
|
One can infer also an existence of a leading maximun. Le. à maximuni with Af<0.
|
One can infer also an existence of a leading maximum, i.e. a maximum with $\Delta t < 0$.
|
Lt is much less significant. ancl is shifted. by Als(40GO)ps.
|
It is much less significant and is shifted by $\Delta t \approx -(40-60)\,\mks$.
|
Lis such maxima that were anticipated by us based on the daemon hypothesis.
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It is such maxima that were anticipated by us based on the daemon hypothesis.
|
‘These observations. besides indicating the existence of a new type of penetrating cosmic radiation. suggested that the velocity of the discovered. particles is barely ~5189 km/s. which should be characteristic of objects captured into geocentric orbits with a perigee inside the Earth.
|
These observations, besides indicating the existence of a new type of penetrating cosmic radiation, suggested that the velocity of the discovered particles is barely $\sim\!5-10$ km/s, which should be characteristic of objects captured into geocentric orbits with a perigee inside the Earth.
|
Their(ux wough the Earth's surface reaches ~10S'em?s1
|
Their flux through the Earth's surface reaches $\sim\!10^{-8}-10^{-7}\,
{\rm cm^{-2}s^{-1}}$.
|
We are presenting below a description. of further xperiments. which support our preliminary conclusions of 1ο existence of daemons and shed light on some features of wile interaction with matter.
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We are presenting below a description of further experiments, which support our preliminary conclusions of the existence of daemons and shed light on some features of their interaction with matter.
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Llowever prior to going over to these results. we gawil formulate the main postulates which permit a noncontradictorv interpretation. of our experimental data within the daemon concept.
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However prior to going over to these results, we shall formulate the main postulates which permit a noncontradictory interpretation of our experimental data within the daemon concept.
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These postulates have formed to a considerable. extent in the course of an analysis of the results themselves mace on the basis of faily general physical ideas. (
|
These postulates have formed to a considerable extent in the course of an analysis of the results themselves made on the basis of fairly general physical ideas. (
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a) A slowlv-moving (V.zi100 kms) daemon impact neither ionizes nor excites the electronic shells of atoms.
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a) A slowly-moving $V \la 100$ km/s) daemon impact neither ionizes nor excites the electronic shells of atoms.
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Therefore it cannot produce scintillations. (
|
Therefore it cannot produce scintillations. (
|
b) In passing through matter. à daemon can capture an atomic nucleus.
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b) In passing through matter, a daemon can capture an atomic nucleus.
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The ensuing drop of the nucleus to deeper levels in the electric field of the daemon will cause an emission. of electrons which initially. surrounded. the atomic nucleus. (
|
The ensuing drop of the nucleus to deeper levels in the electric field of the daemon will cause an emission of electrons which initially surrounded the atomic nucleus. (
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c) As the daemon continues to propagate through matter. it can capture a heavier nucleus while loosing the old one (or its remnant. see below). again with emission of Auger electrons.
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c) As the daemon continues to propagate through matter, it can capture a heavier nucleus while loosing the old one (or its remnant, see below), again with emission of Auger electrons.
|
The capture of a heavier nucleus is similar to the ellect of charge exchange of ions moving through a gas. which is well known from the physics of eas discharge.
|
The capture of a heavier nucleus is similar to the effect of charge exchange of ions moving through a gas, which is well known from the physics of gas discharge.
|
Therefore as à daemon enters ZnsS(Aeg) [rom air or polvstvrene. one should expect the light nuclei to become replaced by the $8. Zn. ancl Ag nuclei anc excitation of a scintillation.
|
Therefore as a daemon enters ZnS(Ag) from air or polystyrene, one should expect the light nuclei to become replaced by the S, Zn, and Ag nuclei and excitation of a scintillation.
|
In this case the process of "charge exchange’ is more elficient for a arger mass dillerence between the exchanging nuclei. (
|
In this case the process of `charge exchange' is more efficient for a larger mass difference between the exchanging nuclei. (
|
4) HE the nucleus captured earlier by the daemon has a small mass and Zi,xZa. interaction of this complex with another ight nucleus and the capture of the latter may culminate in nuclear fusion.
|
d) If the nucleus captured earlier by the daemon has a small mass and $Z_{\rm n} \le Z_{\rm d}$, interaction of this complex with another light nucleus and the capture of the latter may culminate in nuclear fusion.
|
Because of the internal conversion. the usion energy has a high probability of becoming converted o the kinetic energy of the compouncd-nucleus thus formed. which escapes from the daemon.
|
Because of the internal conversion, the fusion energy has a high probability of becoming converted to the kinetic energy of the compound-nucleus thus formed, which escapes from the daemon.
|
The daemon remains free afterwards for some timo. (
|
The daemon remains free afterwards for some time. (
|
c) Lo the daemon captures a light nucleus in a sulliciently rarelieck (noncondensed) medium. for instance. in air. the ight nucleus will not be able to shed the excess energy aud. hus. may turn out to occupy such a high level as not even o be in contact with the daemon. (
|
e) If the daemon captures a light nucleus in a sufficiently rarefied (noncondensed) medium, for instance, in air, the light nucleus will not be able to shed the excess energy and, thus, may turn out to occupy such a high level as not even to be in contact with the daemon. (
|
Recall that the lowest nucleus-daemon level for Zi=10 Lies within the nucleus with .d&2. and inside the nucleon for Z,z24/Z4.) (
|
Recall that the lowest nucleus-daemon level for $Z_{\rm d} = 10$ lies within the nucleus with $A \ge 2$, and inside the nucleon for $Z_{\rm n} \ge
24/Z_{\rm d}$ .) (
|
D) It appears that the scintillations observed by us are wimarily caused by the Auger electrons. emitted. in. the capture of new atomic nuclei.
|
f) It appears that the scintillations observed by us are primarily caused by the Auger electrons emitted in the capture of new atomic nuclei.
|
We cannot at present maintain with certainty that what we detect are the nuclei released w the daemon ancl representing products of the fusion of ight nuclei or particles produced in the decay. of daemon-containing nucleons (or nuclei). although such events must certainly take place.
|
We cannot at present maintain with certainty that what we detect are the nuclei released by the daemon and representing products of the fusion of light nuclei or particles produced in the decay of daemon-containing nucleons (or nuclei), although such events must certainly take place.
|
Pherefore we believe that as a daemon masses through ai scintillator [aver. the scintillation is »wimarilv excited in the capture of a nucleus from the latter o» the daemon. and by the resultant emission. of Auger electrons.
|
Therefore we believe that as a daemon passes through a scintillator layer, the scintillation is primarily excited in the capture of a nucleus from the latter by the daemon, and by the resultant emission of Auger electrons.
|
Scintillations are also produced in Auger electron emission and in the capture of a nucleus from outside the scintillator. if part of these electrons reaches the scintillator. (
|
Scintillations are also produced in Auger electron emission and in the capture of a nucleus from outside the scintillator, if part of these electrons reaches the scintillator. (
|
e) The caemon-containing heavy nucleus decays apparently not in an explosive manner as we believecl before (Drobvshevski 2000a.b). but rather step by step. nucleon w nucleon.
|
g) The daemon-containing heavy nucleus decays apparently not in an explosive manner as we believed before (Drobyshevski 2000a,b), but rather step by step, nucleon by nucleon.
|
Because a negative daemon should. preferably reside in the protons of a nucleus. the decay most. probably occurs in the proton-hy-proton manner.
|
Because a negative daemon should preferably reside in the protons of a nucleus, the decay most probably occurs in the proton-by-proton manner.
|
The. proton-hy-»oton disintegration should be accompanied by emission of excess neutrons [rom the nucleus.
|
The proton-by-proton disintegration should be accompanied by emission of excess neutrons from the nucleus.
|
This gradual digestion. of he nucleus ends probably either in the decay. (absorption?)
|
This gradual `digestion' of the nucleus ends probably either in the decay (absorption?)
|
of the last proton of the remaining tritium (or even of ΤΗ) or in a capture of an encountered. nucleus which is heavier han the disintegrating>e residual nucleus.
|
of the last proton of the remaining tritium (or even of $^4{\rm H}$ ) or in a capture of an encountered nucleus which is heavier than the disintegrating residual nucleus.
|
Clearly enough.o he nuclear decay time and the recovery by the daemon of its postulated. catalytic properties are. on the whole. woportional to the initial nuclear mass: however in the
|
Clearly enough, the nuclear decay time and the recovery by the daemon of its postulated catalytic properties are, on the whole, proportional to the initial nuclear mass; however in the
|
study, and classified six targets as 6 SSct stars, five stars as 6 SSct-y DDor hybrids, four stars as DDor-ó SSct hybrids, and three stars as pure DDor pulsators (see also Table 5).
|
study, and classified six targets as $\delta$ Sct stars, five stars as $\delta$ $\gamma$ Dor hybrids, four stars as $\gamma$ $\delta$ Sct hybrids, and three stars as pure $\gamma$ Dor pulsators (see also Table 5).
|
Below we discuss the targets that show particularities in their periodogram (Fig. 5)).(HD178875):
|
Below we discuss the targets that show particularities in their periodogram (Fig. \ref{fig:per1}) ).:
|
As noted above, this star shows a >lo difference between the luminosity values derived from the HIPPARCOS parallax and from spectroscopy (see reftab4)).
|
As noted above, this star shows a $> 1\,\sigma$ difference between the luminosity values derived from the HIPPARCOS parallax and from spectroscopy (see \\ref{tab4}) ).
|
Binarity is a possible explanation for this discrepancy.
|
Binarity is a possible explanation for this discrepancy.
|
The frequency spectrum shows two dominant peaks near 10 and 12 d-1.
|
The frequency spectrum shows two dominant peaks near 10 and 12 d-1.
|
A model in terms of óSSct pulsations, rotation and/or binarity needs to be investigated.199-27597):
|
A model in terms of $\delta$ Sct pulsations, rotation and/or binarity needs to be investigated.:
|
This star is the coolest star in the sample and lies outside the instability strip.
|
This star is the coolest star in the sample and lies outside the instability strip.
|
The periodogram shows single strong peak at f=5.302 cc/d. 55296877 is probablya a contact binary with an orbital period of 2/f= 0.38dd. The late spectral type of F4.5IV and the large value vsini= 200kkmss~' suggest that it is a high amplitude ellipsoidal variable.183787):
|
The periodogram shows a single strong peak at $f = 5.302$ c/d. 5296877 is probably a contact binary with an orbital period of $2/f = 0.38$ d. The late spectral type of F4.5IV and the large value $v \sin i = 200$ $^{-1}$ suggest that it is a high amplitude ellipsoidal variable.:
|
this star has been classified as pure y Dor as the frequencies are predominantly in the y Dor range and those in the ó Sct region have low amplitude.
|
this star has been classified as pure $\gamma$ Dor as the frequencies are predominantly in the $\gamma$ Dor range and those in the $\delta$ Sct region have low amplitude.
|
However the star lies in the middle of the ó Sct instability
|
However the star lies in the middle of the $\delta$ Sct instability
|
footprint of SDSS-1 by approximately 3500 deg?. ancl also obtained 2 7 2000 spectroscopy for approximately 240.000 stars over a waveleneth range of 3800—9200A.
|
footprint of SDSS-I by approximately 3500 $^{2}$, and also obtained $R$ $\simeq$ 2000 spectroscopy for approximately 240,000 stars over a wavelength range of $-$.
|
. This included spectra for a collection of Galactic globular and open clusters. which served as calibrators for theZi...g.. and scales for all stars observed. by SD55/SEGUE. as processed bx the SEGUE Stellar Parameter Pipeline
|
This included spectra for a collection of Galactic globular and open clusters, which served as calibrators for the, and scales for all stars observed by SDSS/SEGUE, as processed by the SEGUE Stellar Parameter Pipeline.
|
2003).. Tables | and 2. list the photometric. spectroscopic. and physical properties of the eight GC's in our sample.
|
Tables \ref{tabclusterphotprops} and \ref{tabclusterspecprops} list the photometric, spectroscopic, and physical properties of the eight GCs in our sample.
|
The SSPP produces estimates ofTai.g..|Fe/H].. and radial velocities (RVs). along with the equivalent widths and/or line indices for 85 atomic and molecular absorption lines. by processing (he calibrated spectra generated by (the standard SDSS spectroscopic reduction pipeline2002).
|
The SSPP produces estimates of, and radial velocities (RVs), along with the equivalent widths and/or line indices for 85 atomic and molecular absorption lines, by processing the calibrated spectra generated by the standard SDSS spectroscopic reduction pipeline.
|
. See Lor a detailed discussion of the approaches used by the SSPP: provides details on the most recent updates to (his pipeline. along with additional validations.
|
See for a detailed discussion of the approaches used by the SSPP; provides details on the most recent updates to this pipeline, along with additional validations.
|
Membership selection for the clusters is based on the color-magnitude diagram (CMD) mask algorithm described by(1995).
|
Membership selection for the clusters is based on the color-magnitude diagram (CMD) mask algorithm described by.
|
.. Details on the application of Chis method to our specific clusters are described by and(2011).. aud will only be brielly summarized here.
|
Details on the application of this method to our specific clusters are described by and, and will only be briefly summarized here.
|
The procedure involves a series of cuts. reducing the overall sample to include only those stars for which one can reasonably claim (ane membership.
|
The procedure involves a series of cuts, reducing the overall sample to include only those stars for which one can reasonably claim true membership.
|
First. all stas within the tidal radius of the GC! ave selected.
|
First, all stars within the tidal radius of the GC are selected.
|
Stars with available spectra but with (S/N)<LO (averaged over the entire spectrum). or that lacked estimates of oor RV. are excluded.
|
Stars with available spectra but with $\langle \rm{S/N}\rangle <
10$ (averaged over the entire spectrum), or that lacked estimates of or RV, are excluded.
|
A CAID is then constructed of the remaining stars. along with a CMD ol stars in a concentric annulus designated to represent the field.
|
A CMD is then constructed of the remaining stars, along with a CMD of stars in a concentric annulus designated to represent the field.
|
A measure of the ellective signal-to-noise in regions of the CMD is obtained. where the “signal” in this case constitutes
|
A measure of the effective signal-to-noise in regions of the CMD is obtained, where the “signal” in this case constitutes
|
In Equation (17)). the rate Q at which energy is drained from the AWs equals the energy cascade rate given in Equation. (43)). which is determined by the "large-scale quantities” fs... and Lj.
|
In Equation \ref{eq:dEwdt}) ), the rate $Q$ at which energy is drained from the AWs equals the energy cascade rate given in Equation \ref{eq:Q}) ), which is determined by the “large-scale quantities” $z^+_{\rm rms}$, $z^-_{\rm rms}$, and $L_\perp$.
|
All of the AW energy that cascades to small scales dissipates. contributing to turbulent heating. butthe way that Q is apportioned between Ος. Q|p. and depends upon the mechanisms that dissipate the fluctuationsQj, at length scales «£L,.
|
All of the AW energy that cascades to small scales dissipates, contributing to turbulent heating, butthe way that $Q$ is apportioned between $Q_{\rm e}$, $Q_{\perp \rm p}$, and $Q_{\parallel \rm p}$ depends upon the mechanisms that dissipate the fluctuations at length scales $\ll L_{\perp}$.
|
In this section. we describe how we divide the turbulent heating power between Ο.. and using results from the theories of linear wave dampingQi». and Qj,nonlinear stochastic heating.
|
In this section, we describe how we divide the turbulent heating power between $Q_{\rm e}$, $Q_{\perp \rm p}$, and $Q_{\parallel \rm p}$ using results from the theories of linear wave damping and nonlinear stochastic heating.
|
Nonlinear interactions between counter-propagating AWs cause AWenergy to cascade primarily to larger κι. and only weakly to larger Ly|. where Κι and Ay are wavevector components perpendicular and parallel to By (2222)...
|
Nonlinear interactions between counter-propagating AWs cause AWenergy to cascade primarily to larger $k_\perp$ and only weakly to larger $|k_\parallel|$, where $k_\perp$ and $k_\parallel$ are wavevector components perpendicular and parallel to $\bm{B}_0$ \citep{shebalin83,goldreich95,ng96,galtier00}.
|
This cascade does not transfer AW energy efficiently to higher frequencies(the AW frequency being Ajva). and thus cyclotron damping is not an important dissipation mechanism for the anisotropic AW cascade (??)..
|
This cascade does not transfer AW energy efficiently to higher frequencies(the AW frequency being $k_\parallel v_{\rm A}$ ), and thus cyclotron damping is not an important dissipation mechanism for the anisotropic AW cascade \citep{cranmer03,howes08a}.
|
There may be other mechanisms in the solar wind that generate AWs with sufficiently high frequencies that the AWs undergo cyclotron damping (?2). such as a turbulent cascade involving compressive waves (???) or instabilities driven by proton or alpha-particle beams (??)..
|
There may be other mechanisms in the solar wind that generate AWs with sufficiently high frequencies that the AWs undergo cyclotron damping \citep{leamon98a,hamilton08}, such as a turbulent cascade involving compressive waves \citep{chandran05a,chandran08b,yoon08} or instabilities driven by proton or alpha-particle beams \citep{gomberoff96,hellinger11}.
|
However. we do not account for these possibilities in our model.
|
However, we do not account for these possibilities in our model.
|
When AW energy cascades to kipp=|. the cascade transitions to a kinetic Alfvénn wave (KAW) cascade (2222?).. and the KAW fluctuations undergo Landau damping and transit-time damping (???) απά dissipation via stochastic heating (222)..
|
When AW energy cascades to $k_\perp \rho_{\rm p} \simeq 1$, the cascade transitions to a kinetic Alfvénn wave (KAW) cascade \citep{bale05,howes08a,howes08b,schekochihin09,sahraoui09}, and the KAW fluctuations undergo Landau damping and transit-time damping \citep{quataert98,gruzinov98,leamon99} and dissipation via stochastic heating \citep{mcchesney87,chen01,johnson01}.
|
Some of the turbulent energy dissipates at Kjpy1. and some of the turbulent energy cascades to. and then dissipates at. smaller scales.
|
Some of the turbulent energy dissipates at $k_\perp \rho_{\rm p} \simeq 1$, and some of the turbulent energy cascades to, and then dissipates at, smaller scales.
|
Before describing the details of how we incorporate dissipation into our model. we first summarize our general approach.
|
Before describing the details of how we incorporate dissipation into our model, we first summarize our general approach.
|
We make the approximation that the dissipation occurs in two distinct wavenumber ranges: Kjpp~| and Κιρρ>I.
|
We make the approximation that the dissipation occurs in two distinct wavenumber ranges: $k_\perp \rho_{\rm p} \sim 1$ and $k_\perp \rho_{\rm p} \gg
1$.
|
We divide the total dissipation power between these two wavenumber ranges by comparing the energy cascade time scale and damping time scale at kipy=] (see Equation (53)) below).
|
We divide the total dissipation power between these two wavenumber ranges by comparing the energy cascade time scale and damping time scale at $k_\perp \rho_{\rm p} = 1$ (see Equation \ref{eq:Gamma}) ) below).
|
We divide the power that is dissipated at KiPpp~| between Q.. and by comparing the damping rates at ki;py=| Ορ.associated Qj,withthree different dissipation mechanisms. each of which contributes primarily to either Ος. Ορ. or Ορ.
|
We divide the power that is dissipated at $k_\perp \rho_{\rm p} \sim 1$ between $Q_{\rm e}$, $Q_{\perp \rm p}$, and $Q_{\parallel \rm p}$ by comparing the damping rates at $k_\perp \rho_{\rm p} = 1$ associated withthree different dissipation mechanisms, each of which contributes primarily to either $Q_{\rm e}$, $Q_{\perp \rm p}$, or $Q_{\parallel \rm p}$ .
|
We then assume that all of the power that dissipates at Kj>py! does so via interactions with electrons. thereby contributing to Q,.
|
We then assume that all of the power that dissipates at $k_\perp \gg
\rho_{\rm p}^{-1}$ does so via interactions with electrons, thereby contributing to $Q_{\rm e}$.
|
We define y, and y, to be the electron and proton contributions to the linear damping rate of KAWs at kpy=I. where is the proton gyroradius.
|
We define $\gamma_{\rm e}$ and $\gamma_{\rm p}$ to be the electron and proton contributions to the linear damping rate of KAWs at $k_\perp
\rho_{\rm p} = 1$, where $\rho_{\rm p}$ is the proton gyroradius.
|
Using a numerical code that solvesp, the full hot-plasma "Sdispersion relation (2)... we have calculated y, and for a range of plasma parameters. assuming isotropic protonyy and electron temperatures.
|
Using a numerical code that solves the full hot-plasma dispersion relation \citep{quataert98}, we have calculated $\gamma_{\rm e}$ and $\gamma_{\rm p}$ for a range of plasma parameters, assuming isotropic proton and electron temperatures.
|
For 107«<10. LZT5/T.Z5. £oand [Kpv|Ορ. our results are well Byapproximated by the following formulas: and where Dy=8riikpT;B; and B.=SikgT.Bi.
|
For $10^{-3} < \beta_{\rm p} < 10$, $1 \lesssim T_{\rm p}/T_{\rm e} \lesssim 5$, and $|k_\parallel v_{\rm
A} |\ll \Omega_{\rm p}$, our results are well approximated by the following formulas: and where $\beta_{\rm p} = 8\pi n k_{\rm B} T_{\rm p}/B_0^2$ and $\beta_{\rm e} = 8\pi n k_{\rm B} T_{\rm e}/B_0^2$.
|
In Figure l.. we compare Equations (44)) and (45)) with our numerical solutions for the case in which 75=27).
|
In Figure \ref{fig:gamma_e_p}, , we compare Equations \ref{eq:gammae}) ) and \ref{eq:gammap}) ) with our numerical solutions for the case in which $T_{\rm p } = 2 T_{\rm e}$.
|
At Kip=I. AW/KAW turbulence has a range of ky values.
|
At $k_\perp \rho_{\rm p} \simeq 1$, AW/KAW turbulence has a range of $k_\parallel$ values.
|
However. we approximate the linear proton and electron damping rates by assigning a single effective IK| to the spectrum at &;py=| given by the critical-balance condition (2???) where is the energy cascade time at kipp=I. and ὃνρ is the rms amplitude of AW/KAW velocity fluctuations at KjPp~I.
|
However, we approximate the linear proton and electron damping rates by assigning a single effective $|k_\parallel|$ to the spectrum at $k_\perp \rho_{\rm p} = 1$ given by the critical-balance condition \citep{higdon84,goldreich95,cho04b,boldyrev06}
where is the energy cascade time at $k_{\perp} \rho_{\rm p} = 1$, and $\delta v _{\rm p}$ is the rms amplitude of AW/KAW velocity fluctuations at $k_\perp \rho_{\rm p} \sim 1$.
|
Inwriting Equation (47)). we have taken the total fluctuation energy per unit volume at Kjpp~|to be twice the kinetic energy densityH por,ao?2. and we have assumed that dissipationH πια.0s! does not reduce the cascade power at kipp~| much below the level that is present throughout the inertial range.
|
Inwriting Equation \ref{eq:tc}) ), we have taken the total fluctuation energy per unit volume at $k_\perp \rho_{\rm p} \sim 1$to be twice the kinetic energy density $\rho \delta v_{\rm p}^2/2$, and we have assumed that dissipation at $k_\perp < \rho_{\rm p}^{-1}$ does not reduce the cascade power at $k_\perp \rho_{\rm p} \sim 1$ much below the level that is present throughout the inertial range.
|
There is some evidence that the magnetic fluctuations in the solar wind are consistent with turbulence theories based on critical balance (???)..
|
There is some evidence that the magnetic fluctuations in the solar wind are consistent with turbulence theories based on critical balance \citep{horbury08,podesta09c,forman11}.
|
However. there are conflicting claims in the literature over the validity of Equation (46)) when "rms3h.>7za... vpms* a point to which we return in Section 5.4..
|
However, there are conflicting claims in the literature over the validity of Equation \ref{eq:critbal}) ) when $z^+_{\rm rms} \gg z^-_{\rm rms}$ , a point to which we return in Section \ref{sec:division}. .
|
We assume that for length scales A between py and the perpendicular AW correlation length (outer scale) L,. the rmsamplitude of the AW velocity fluctuations at perpendicular scale A is οςA! asin observations at r=| AU (2?).. direct numerical simulations of AW turbulence in the presence of a strong background magnetic field (????).. and recent theories of strong AW turbulence (??)..
|
We assume that for length scales $\lambda$ between $\rho_{\rm p}$ and the perpendicular AW correlation length (outer scale) $L_{\perp}$ , the rmsamplitude of the AW velocity fluctuations at perpendicular scale $\lambda$ is $\propto \lambda^{1/4}$ asin observations at $r=1
$ AU \citep{podesta07,chen11}, , direct numerical simulations of AW turbulence in the presence of a strong background magnetic field \citep{maron01,muller05,mason06,perez08a}, , and recent theories of strong AW turbulence \citep{boldyrev06,perez09a}. .
|
We thus take
|
We thus take
|
The dispersion relation for the magnetic Rossby waves can be written as The magnetic field causes the splitting of ordinary Rossby waves into last and. slow magnetic. Rossby waves as in. the e<I case.
|
The dispersion relation for the magnetic Rossby waves can be written as The magnetic field causes the splitting of ordinary Rossby waves into fast and slow magnetic Rossby waves as in the $\epsilon \ll 1$ case.
|
I.B ψεαῃL7<1. then we can write. Fast magneticoO Rosshy waves are similar to hydrodvuamic Rosshy waves moclified by the magneticoS field.
|
If $\sqrt {\epsilon}\alpha_0^2 \ll 1$, then we can write Fast magnetic Rossby waves are similar to hydrodynamic Rossby waves modified by the magnetic field.
|
Slow magnetic5 Rosshv waves have a similar dispersion relation as in the e«| case.
|
Slow magnetic Rossby waves have a similar dispersion relation as in the $\epsilon \ll 1$ case.
|
The dispersion diagram lor the s=1 harmonics of magnetic Poincaré and magnetic ]tossby waves according to Eq. (
|
The dispersion diagram for the $s=1$ harmonics of magnetic Poincaré and magnetic Rossby waves according to Eq. (
|
10) is shown in Fig 3.
|
10) is shown in Fig 3.
|
Here e=2700 and ag=0.05.
|
Here $\epsilon = 2700$ and $\alpha_0=0.05$.
|
The behaviour of [ast magnetic Rossby waves (dotted line) is similar to the small € case: the absolute value of their Irequency significantly decreases wilh increasing v (which now plavs the role of the poloidal wave number).
|
The behaviour of fast magnetic Rossby waves (dotted line) is similar to the small $\epsilon$ case: the absolute value of their frequency significantly decreases with increasing $\nu$ (which now plays the role of the poloidal wave number).
|
ILowever. we immediately note that the Irequency now is much smaller than that of the €«1 case.
|
However, we immediately note that the frequency now is much smaller than that of the $\epsilon\ll 1$ case.
|
This is also true for magnetic Poincaré waves (solid lines): their [requency. is sienilicantlv small compared to the case of small e. now being even smaller (han the rotational frequency.
|
This is also true for magnetic Poincaré waves (solid lines): their frequency is significantly small compared to the case of small $\epsilon$, now being even smaller than the rotational frequency.
|
The frequency. of slow magnetic Rossby waves onlyslightly depends on v. but now it decreases wilh increasing v. contrary lo e«&1 case.
|
The frequency of slow magnetic Rossby waves onlyslightly depends on $\nu$, but now it decreases with increasing $\nu$ , contrary to $\epsilon\ll 1$ case.
|
Fie.
|
Fig.
|
4 shows the dependence of the 5=lv2 and s=1.p3 harmonics on € and αμ.
|
4 shows the dependence of the $s=1, \nu=2$ and $s=1, \nu=3$ harmonics on $\epsilon$ and $\alpha_0$.
|
The frequency of magnetic BRossby mode harmonies significantly depends on ag: the frequencies of both last ancl slow magnetic Rosshv modes increase wilh increasing o5.
|
The frequency of magnetic Rossby mode harmonics significantly depends on $\alpha_0$; the frequencies of both fast and slow magnetic Rossby modes increase with increasing $\alpha_0$.
|
On the other hand. it (turis out thatthe frequencies of magnetic Poincaré waves have almost no dependence on απ.
|
On the other hand, it turns out thatthe frequencies of magnetic Poincaré waves have almost no dependence on $\alpha_0$ .
|
However. (μον aresignificantly reduced will increasing e.
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However, they aresignificantly reduced with increasing $\epsilon$ ,
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cosmological times vields eunoush fuel to build up the mass of the SMDIT if the fuel can be efficiently accreted.
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cosmological times yields enough fuel to build up the mass of the SMBH if the fuel can be efficiently accreted.
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The large fluctuations iu the interior σας nias correspond to waves moving through the circiuunuclear disk. which can potentially drive iudividual clumps of anolecular eas into the vicinity. of the SMDII.
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The large fluctuations in the interior gas mass correspond to waves moving through the circumnuclear disk, which can potentially drive individual clumps of molecular gas into the vicinity of the SMBH.
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The fuctuations develop stochastically as shown iu Section 3.. which may ultimately lead to stochastic SMDITI aceretion eveuts.
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The fluctuations develop stochastically, as shown in Section \ref{sec:mass}, which may ultimately lead to stochastic SMBH accretion events.
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If the direction of the angular momentum vector of accreted material with respect to the black hole's spin axis also varies stochastically. some fraction of accretion events will be auti-alieued. loweriue the black holes spin aud cousequeutly its radiative cficiency (227?3..
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If the direction of the angular momentum vector of accreted material with respect to the black hole's spin axis also varies stochastically, some fraction of accretion events will be anti-aligned, lowering the black hole's spin and consequently its radiative efficiency \citep{KingPringle06,KingPringle07,NayakshinKing07,Kingetal08}.
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Tlowever. large amounts of accretion. as mn inergor driven fuchne. will teud to align an SAIBITs spin with that of the circunuuuclear disk. increasing its radiative efficiency (27).
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However, large amounts of accretion, as in merger driven fueling, will tend to align an SMBH's spin with that of the circumnuclear disk, increasing its radiative efficiency \citep{Volonterietal07}.
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