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Our sample, in contrast, contains four times as many irregular dwarf galaxies. | Our sample, in contrast, contains four times as many irregular dwarf galaxies. |
Therefore, when interpreting the color vs morphology plot, it must be noted that our sample dominates the morphological bin of irregular galaxies and the literature data dominates the larger galaxies. | Therefore, when interpreting the color vs morphology plot, it must be noted that our sample dominates the morphological bin of irregular galaxies and the literature data dominates the larger galaxies. |
'The comparison of morphology to the B—H colour shows that the early-type galaxies are redder than the late-type, irregular and dwarf galaxies. | The comparison of morphology to the $B - H$ colour shows that the early-type galaxies are redder than the late-type, irregular and dwarf galaxies. |
A similiar study by ? for galaxies in the 2MASS Large Galaxy Atlas also showed this trend. | A similiar study by \cite{jarrett03} for galaxies in the 2MASS Large Galaxy Atlas also showed this trend. |
In Figure we plot the mean effective surface brightness of our sample galaxies as afunction of absolute magnitude. | In Figure \ref{fig:lsp} we plot the mean effective surface brightness of our sample galaxies as afunction of absolute magnitude. |
In addition to our H-band data, we include 560 late-type Virgo cluster galaxies (obtained from the Goldmine database; ?)). | In addition to our $H$ -band data, we include 560 late-type Virgo cluster galaxies (obtained from the Goldmine database; \citealt{gavazzi03}) ). |
The mean effective surface brightness for Virgo cluster galaxies was calculated as and the data was corrected for extinction using Ay=0.01 mmag. | The mean effective surface brightness for Virgo cluster galaxies was calculated as and the data was corrected for extinction using $A_H=0.01$ mag. |
The morphologies of Virgo cluster galaxies included in the sample range from SO to Sd, Irr and BCD (listed as types 1 to 18 in the Goldmine database). | The morphologies of Virgo cluster galaxies included in the sample range from S0 to Sd, Irr and BCD (listed as types 1 to 18 in the Goldmine database). |
As previously discussed in ?,, the relationship between the two photometric parameters provides an important link to the underlying physical parameters of a galaxy, namely its total mass M;,; and total angular momentum. | As previously discussed in \cite{dejong00}, the relationship between the two photometric parameters provides an important link to the underlying physical parameters of a galaxy, namely its total mass ${\cal M}_{tot}$ and total angular momentum. |
The total angular momentum of a galaxy, expressed as the dimensionless spin parameter A=J|E[2MLPαι (?),, is related to the scale length of its disk ? | The total angular momentum of a galaxy, expressed as the dimensionless spin parameter $\lambda=J|E|^{1/2}{\cal M}_{tot}^{-5/2}G^{-1}$ \citep{peebles69}, is related to the scale length of its disk \citep{fall80, dalcanton97,mao98}. |
showed that A can be transformed into observable (???)..quantities. | \cite{dejong00} showed that $\lambda$ can be transformed into observable quantities. |
The authors presented a model of a singular isothermal sphere with EοςJV(;,,V2 from the virial theorem and perfect exponential disk with angular momentum αι,ac (assuming Vaiss= Vc). | The authors presented a model of a singular isothermal sphere with $E\propto {\cal M}_{tot}V_c^2$ from the virial theorem and a perfect exponential disk with angular momentum $J_{disk}\propto {\cal M}_{disk}r_{eff}V_c$ (assuming $V_{disk}=V_c$ ). |
They showed that if Maiskrep¢VeJajsk/JMlaiskοJ/Mot and MagaiskοςMio: then λοςrepfVo/Madisk- | They showed that if $J_{disk}/{\cal M}_{disk}\propto J/{\cal M}_{tot}$ and ${\cal M}_{disk}\propto {\cal M}_{tot}$ then $\lambda\propto r_{eff}V_c^2/{\cal M}_{disk}$. |
Furthermore, using the relation Mio:οςv3 predicted for dark matter halos, de Jong and Lacey showed that λοςreyn 3, where Y is the mass-to-light ratio for the disk. | Furthermore, using the relation ${\cal M}_{tot}\propto V_c^3$ predicted for dark matter halos, de Jong and Lacey showed that $\lambda\propto r_{eff} L^{\Upsilon /3}$ , where $\Upsilon$ is the mass-to-light ratio for the disk. |
This can be transformed into an expression between surface brightness and total magnitude by invoking which results in: | This can be transformed into an expression between surface brightness and total magnitude by invoking which results in: |
Cataclysmic Variable (CV). stars are. interacting binary systems in which a late-tvpe secondary star overllows. its Roche lobe and aceretes matter onto a compact. primary. | Cataclysmic Variable (CV) stars are interacting binary systems in which a late-type secondary star overflows its Roche lobe and accretes matter onto a compact primary. |
Amonest these. the nova-like variables are defined as those that persist in a high mass-accretion rate. | Amongst these, the nova-like variables are defined as those that persist in a high mass-accretion rate. |
(X result. of such a heterogeneous label is that. amongst. the nova-like variables. there are many objects that. displaying similarities to members of other CV classes. sit. uneasily with their classification. | A result of such a heterogeneous label is that, amongst the nova-like variables, there are many objects that, displaying similarities to members of other CV classes, sit uneasily with their classification. |
In this paper we present high time-resolution UN spectroscopy of one such example QU Car. | In this paper we present high time-resolution UV spectroscopy of one such example – QU Car. |
Atom.=λε QU Car is one of the brightest known CV. so it is rather surprising that until now it has been mostly ignored. in observational studies. | At $m_{\rm v}=11.4$, QU Car is one of the brightest known CV, so it is rather surprising that until now it has been mostly ignored in observational studies. |
From among the small number of hitherto published: studies. Cülliland. Phillips (1982) examined optical spectra | From among the small number of hitherto published studies, Gilliland Phillips \shortcite{82gilliland} examined optical spectra |
The stars that make up galaxies exist in a six-dimensional phase space of positions and velocities. which offers a large amount of freedom in the possible configurations of stellar populations. and hence the morphologies and dynamics of the galaxies that they combine to form. | The stars that make up galaxies exist in a six-dimensional phase space of positions and velocities, which offers a large amount of freedom in the possible configurations of stellar populations, and hence the morphologies and dynamics of the galaxies that they combine to form. |
However. because stars do not move instantaneously from one place to another. and similarly their velocities only change smoothly via finite gravitational accelerations. the evolution of their configuration obeys the simple collisionless Boltzmann equation. which requires that the phase density f. the number of stars per unit volume in both space and velocity. remains constant around any given star as it travels through space (?).. | However, because stars do not move instantaneously from one place to another, and similarly their velocities only change smoothly via finite gravitational accelerations, the evolution of their configuration obeys the simple collisionless Boltzmann equation, which requires that the phase density $f$, the number of stars per unit volume in both space and velocity, remains constant around any given star as it travels through space \citep{BinneyTremaine08}. |
In principle. this equation places a very strong constraint on the manner in which a stellar system's properties can evolve with time. | In principle, this equation places a very strong constraint on the manner in which a stellar system's properties can evolve with time. |
However. there is one significant complication in that although Eq. (1)) | However, there is one significant complication in that although Eq. \ref{eq:CBE}) ) |
guarantees that the number of stars within any region of phase space remains constant. the shape of that region can become grossly distorted over time. wrapping itself around in a serpentine fashion. | guarantees that the number of stars within any region of phase space remains constant, the shape of that region can become grossly distorted over time, wrapping itself around in a serpentine fashion. |
Just as a confectionery chef lightens the density of toffee by repeatedly pulling it into strands and wrapping them around. thus trapping ar between the layers of toffee. so the phase wrapping of a stellar system will create a complex tangle of the original phase density distribution and empty space. | Just as a confectionery chef lightens the density of toffee by repeatedly pulling it into strands and wrapping them around, thus trapping air between the layers of toffee, so the phase wrapping of a stellar system will create a complex tangle of the original phase density distribution and empty space. |
In practice. one can only hope to measure the phase space density over a finite region: even in principle. since stars are intrinsically a discretized sampling of phase space density. it may not be possible to resolve the complex phase-wrapped structure. | In practice, one can only hope to measure the phase space density over a finite region; even in principle, since stars are intrinsically a discretized sampling of phase space density, it may not be possible to resolve the complex phase-wrapped structure. |
Instead. one measures an average that combines both the phase density from potentially many original locations and the mixed-in empty space. creating à "coarse grained” distribution function that will always tend to be diluted down from the original maximum phase density. and thus doesnot obey Eq. (1)). | Instead, one measures an average that combines both the phase density from potentially many original locations and the mixed-in empty space, creating a “coarse grained” distribution function that will always tend to be diluted down from the original maximum phase density, and thus doesnot obey Eq. \ref{eq:CBE}) ). |
However. the tendency of this evolution to always dilute the maximum phase density still places a strong constraint on the possible ways in which a stellar system can evolve. irrespective of the details of its evolution. | However, the tendency of this evolution to always dilute the maximum phase density still places a strong constraint on the possible ways in which a stellar system can evolve, irrespective of the details of its evolution. |
For example. ? pointed out that the maximum phase space density m an elliptical galaxy of comparable mass to the Milky Way is significantly higher than that found in a disk of similar mass. | For example, \citet{Carlberg86} pointed out that the maximum phase space density in an elliptical galaxy of comparable mass to the Milky Way is significantly higher than that found in a disk of similar mass. |
It is therefore fundamentally impossible for such a disk system to be converted into an elliptical through collisionless processes since there is no way of generating the high phase density at the centre of the elliptical by mixing the lower phase densities of a disk. | It is therefore fundamentally impossible for such a disk system to be converted into an elliptical through collisionless processes since there is no way of generating the high phase density at the centre of the elliptical by mixing the lower phase densities of a disk. |
Although intriguing. this seemingly-fundamental challenge to the current paradigm in which ellipticals form from mergers of disk systems has not generally been viewed as a matter of great concern. | Although intriguing, this seemingly-fundamental challenge to the current paradigm in which ellipticals form from mergers of disk systems has not generally been viewed as a matter of great concern. |
As pointed out by ?.. the controversial region of high-density phase space represents a tiny fraction of the stellar distribution right at the extreme maximum of phase density. so that a relatively minor change to the properties of the initial disk. such as modestly decreasing its scale-height at large radit. can produce adequate numbers of stars at high phase density to populate this small region. | As pointed out by \citet{Lake89}, the controversial region of high-density phase space represents a tiny fraction of the stellar distribution right at the extreme maximum of phase density, so that a relatively minor change to the properties of the initial disk, such as modestly decreasing its scale-height at large radii, can produce adequate numbers of stars at high phase density to populate this small region. |
Alternatively. as noted by ? and as we will also see below. the denser bulge component of a typical disk galaxy ean straightforwardly fill this gap. | Alternatively, as noted by \citet{Hernquist93} and as we will also see below, the denser bulge component of a typical disk galaxy can straightforwardly fill this gap. |
Finally. a small amount of star formation triggered by the transformation process could easily produce the requisite component at high stellar densities. since the gas-dynamie processes of star formation are highly collisional and therefore not subject to this collisionless constraint. | Finally, a small amount of star formation triggered by the transformation process could easily produce the requisite component at high stellar densities, since the gas-dynamic processes of star formation are highly collisional and therefore not subject to this collisionless constraint. |
So. there are a variety of ways to explain away such a violation of the mixing constraint at this extreme end of the distribution of phase densities. without any fine tuning of the processes. and thus there is no compelling reason to throw out the entire paradigm of merger-driven galaxy evolution on the basis of such an argument. | So, there are a variety of ways to explain away such a violation of the mixing constraint at this extreme end of the distribution of phase densities, without any fine tuning of the processes, and thus there is no compelling reason to throw out the entire paradigm of merger-driven galaxy evolution on the basis of such an argument. |
However. the physics of phase mixing also places limits on possible evolutionary paths followed by stars that do not lie in this extreme region of high-density phase space. | However, the physics of phase mixing also places limits on possible evolutionary paths followed by stars that do not lie in this extreme region of high-density phase space. |
The more general criterion was derived by ?.. who proved the following theorem. | The more general criterion was derived by \citet{Tremaineetal86}, who proved the following theorem. |
Define the mass of stars within a galaxy that find themselves in regions of phase space where the density i5 greater than f to be M(f). and the volume in phase space that these stars occupy to be V(f). | Define the mass of stars within a galaxy that find themselves in regions of phase space where the density is greater than $f$ to be $M(f)$, and the volume in phase space that these stars occupy to be $V(f)$. |
Since both of these quantities vary monotonically with f£. one can construct a function M(V) for the system. | Since both of these quantities vary monotonically with $f$, one can construct a function $M(V)$ for the system. |
For a galaxy to evolve from an initial form MV) to a final state M (V). it is a necessary condition that | For a galaxy to evolve from an initial form $M_i(V)$ to a final state $M_f(V)$ , it is a necessary condition that |
1.2. our cevolution law is eiven by At 2=0 our fit vields a local oof (1.00£0.21)«10FALoxy!Mpe5 for (2002).. which corresponds to oof (1.65£0.32)«102AZ.r.!Mpe7 for a Salpeter(19055) IMFE. | , our evolution law is given by At $z = 0$ our fit yields a local of $(1.09 \pm 0.21) \times
10^{-2} M_{\odot} {\rm yr}^{-1}{\rm Mpc}^{-3}$ for \citet{Kroupa02}, which corresponds to of $(1.65 \pm 0.32) \times 10^{-2}
M_{\odot} {\rm yr}^{-1}{\rm Mpc}^{-3}$ for a \citet{Salpeter55}
IMF. |
Our estimate agrees with previous works ou the local tthat have properly accounted for the iuterual extinction of the galaxy. | Our estimate agrees with previous works on the local that have properly accounted for the internal extinction of the galaxy. |
Without such corrections tle wwill be underestimated by 50 70% (Callegoal. 2007). | Without such corrections the will be underestimated by 50 $-$ 70 \citep{Gallego95, TresseMad98, Hanish06, Salim07}. |
. The agreeimeut between cestimates corrected for internal extinction aud our dderived from 21 jan luminosity suggests that ~half of the local star formation is obscured and the MIB provides a direct and reliable 1ueaus for SFR measurcinenut. | The agreement between estimates corrected for internal extinction and our derived from 24 $\micron$ luminosity suggests that $\sim$ half of the local star formation is obscured and the MIR provides a direct and reliable means for SFR measurement. |
Fiewe 9 illustrates the eood aegrecment of the normalization of our cestimates aud those derived frou the UV. observation corrected for the effects of intrinsic extinction of the target galaxies (normalization corrections can be as large as O.7-dex: c.e.. Fieure 5 of Schiminovichetal.(2005) illustrates the extent of the required correction for the UV observations). | Figure \ref{SFR_Madauplot} illustrates the good agreement of the normalization of our estimates and those derived from the UV observation corrected for the effects of intrinsic extinction of the target galaxies (normalization corrections can be as large as 0.7-dex; e.g., Figure 5 of \citet{Schimi05} illustrates the extent of the required correction for the UV observations). |
Hopkius(2001). reports the it to a compilation of the tthat has been corrected for extinction of the tarect ealaxies with au assumption of a huninosity-depeudeut obscuration. | \citet{Hopkins04} reports the fit to a compilation of the that has been corrected for extinction of the target galaxies with an assumption of a luminosity-dependent obscuration. |
The resulting best fit is given by log(.)(3.2940.26)loe(1]2)1.980.01 (assumingthe I&roupa(2002) INE). which also agrees well with our evolution determined from the combination of the NDWES aud the FIDEL results. | The resulting best fit is given by ${\rm log}(\SFRD) =
(3.29 \pm 0.26){\rm log}(1+z) - 1.98 \pm 0.04$ (assuming the \citet{Kroupa02} IMF), which also agrees well with our evolution determined from the combination of the NDWFS and the FIDEL results. |
Again. this aerecment coufirxuis that star formation at redshift 0.0<2«1.2 occurs in obscured euvirounients and can be traced directly with 21 jan observations given a proper classification aud exclusion of ACNs. | Again, this agreement confirms that star formation at redshift $0.0 < z < 1.2$ occurs in obscured environments and can be traced directly with 24 $\micron$ observations given a proper classification and exclusion of AGNs. |
It should be noted that our result is cousisteut with fiudines of Takeuchietal.(2005)...which slow au evolution of the fraction of obseured star formation from locally to >SOC at z~1. | It should be noted that our result is consistent with findings of \citet{Takeuchi05},which show an evolution of the fraction of obscured star formation from locally to $> 80$ at $z \sim 1$. |
We study the evolution of 21 jnu-solected. galaxies by constructing thei 21 juu (rest-frame) hnunuinositv functions (LE). | We study the evolution of 24 $\micron$ -selected galaxies by constructing their 24 $\micron$ (rest-frame) luminosity functions (LF). |
Our suuple contains LOI? ealaxics with spectroscopic redshifts at 0.0x20.65 in the feld of the NOAO Decp-Wide Field Survey (NDWES). | Our sample contains 4,047 galaxies with spectroscopic redshifts at $0.0 \leq z \leq 0.65$ in the field of the NOAO Deep-Wide Field Survey (NDWFS). |
The 21 uu data and spectroscopic redshifts were obtained withSpitzer aud with the ACN and Galaxies Evolution Survey (AGES). respectively. | The 24 $\micron$ data and spectroscopic redshifts were obtained with and with the AGN and Galaxies Evolution Survey (AGES), respectively. |
Our sample is a uique combination of wide field. spectroscopic redshifts. and 2| nu imaging that is ideal for iuterinediate redshitts where AUR ealaxy evolution has not beeu woell-studied. | Our sample is a unique combination of wide field, spectroscopic redshifts, and 24 $\micron$ imaging that is ideal for intermediate redshifts where MIR galaxy evolution has not been well-studied. |
The large area (9 sq. | The large area (9 sq. |
deg.) | deg.) |
of the field helps mütisate cosmic variance. which otherwise can be a serious issue at low aud intermediate redshifts. | of the field helps mitigate cosmic variance, which otherwise can be a serious issue at low and intermediate redshifts. |
Theoretically. the cosmic variance in our study d$ less than at i:>0.2. | Theoretically, the cosmic variance in our study is less than at $z > 0.2$. |
Spectroscopic redshifts reduce cross-talk between redshift bins aud faint/bright cud slope biases and provide an accurate nunber deusity contribution for cach object. | Spectroscopic redshifts reduce cross-talk between redshift bins and faint/bright end slope biases and provide an accurate number density contribution for each object. |
Galaxies exhibiting ACN activities characterized by A-rav ciuission and iuid-IR power-law are exclhucdec from our star-forming sample. | Galaxies exhibiting AGN activities characterized by X-ray emission and mid-IR power-law are excluded from our star-forming sample. |
We find that the optica line diagnostics (the BPT iunethod) are not suitable for identifviug ACN dominant at mid-IR waveleuetls because the ΙΤ cussion frou, opticallv-selectec AGNs is often dominated bv stay formation. | We find that the optical line diagnostics (the BPT method) are not suitable for identifying AGN dominant at mid-IR wavelengths because the mid-IR emission from optically-selected AGNs is often dominated by star formation. |
We identified 288 objects with 21 jan emission likely to be dominated by ACN. | We identified 288 objects with 24 $\micron$ emission likely to be dominated by AGN. |
Excluding them leaves a sample of 3.759 star-forming galaxies. | Excluding them leaves a sample of 3,759 star-forming galaxies. |
We derive the 21 juu huninositv using calibrations derived from the most recent SED library of the iiid-IR spectra frouSpitzer (Rickeetal.2009).. | We derive the 24 $\micron$ luminosity using calibrations derived from the most recent SED library of the mid-IR spectra from \citep{Rieke09}. . |
Our sample is colmprised inaiulv of normal star-forming galaxies have L(TIR)<10H L,)) and LIRGs have tot! LocLOTIR)«10272 £4). | Our sample is comprised mainly of normal star-forming galaxies have $\LTIR < 10^{11}$ ) and LIRGs have $10^{11}$ $< \LTIR < 10^{12}$ ). |
Ouly ave ULIRGSs (L(TIR)—1072 £L.) aud we found that most of the ULIRGs contain ACN. | Only are ULIRGs $\LTIR > 10^{12}$ ) and we found that most of the ULIRGs contain AGN. |
We construct the local 21 jan lunünositv function (LLF) as a template to study evolution of the LE. | We construct the local 24 $\micron$ luminosity function (LLF) as a template to study evolution of the LF. |
Our LLF was constructed at 0.05<2<0.25 and evolved yack to 2=0 simultancously with the ft to constrain he elobal evolution of our suuple. | Our LLF was constructed at $0.05 \leq z \leq 0.25$ and evolved back to $z = 0$ simultaneously with the fit to constrain the global evolution of our sample. |
The LLF template for our star-forming sample is given bv a double power-aw with faint-cnd slope. a=0.357+0.0L. bright-eud slope, j=2.36d0.11. characteristic Iuninositv. L.(:= LOL. and deusitv normalization. C—(124308)«10?Mpc5 | The LLF template for our star-forming sample is given by a double power-law with faint-end slope, $\alpha = 0.37 \pm 0.04$, bright-end slope, $\beta = 2.36 \pm 0.41$, characteristic luminosity, $_*(z=0) = (4.27
\pm 0.71) \times 10^9 \Lsun$ , and density normalization, $C = (1.2 \pm
0.8) \times 10^{-3}{\rm Mpc}^{-3}$. |
Qur major results are as ollows. | Our major results are as follows. |
1l. | 1. |
The evolution of the LE at :<0.65 can ο represented by pure luminosity evolution with the characteristic 21 421 Iuninosity of star-forming galaxies evolving as LGm)x(0|)*9?, | The evolution of the LF at $z \leq 0.65$ can be represented by pure luminosity evolution with the characteristic 24 $\micron$ luminosity of star-forming galaxies evolving as $_*(24~\micron) \propto
(1+z)^{3.8 \pm 0.3}$. |
We demonstrate » the construction of the bivariate Lband aud 21 jan luminosity function that the fraction of missing 21 iaa-Iuninous. optically-faint galaxies due to our bau nagnitude limit for spectroscopic tarecting is very small. | We demonstrate by the construction of the bivariate I-band and 24 $\micron$ luminosity function that the fraction of missing 24 $\micron$ -luminous, optically-faint galaxies due to our I-band magnitude limit for spectroscopic targeting is very small. |
2. | 2. |
We extend the constraint ou the evolution of to Do1.2 by combining our results with the higher redshift results from AMaeuellietal.(2009) based on the FIDEL survey. | We extend the constraint on the evolution of $_*$ to $z \sim 1.2$ by combining our results with the higher redshift results from \citet{Magnelli09} based on the FIDEL survey. |
The combined sample gives a slightly shallower huninosity evolution of L.(21san)x(1|το | The combined sample gives a slightly shallower luminosity evolution of $_*(24~\micron)
\propto (1+z)^{3.4 \pm 0.2}$. |
The shallower evolution law derived by including the FIDEL saluple at redshifts of +=0.85 aud 1.15 sueeests that the evolution in nuuav beein to slow compared to lower redshifts. | The shallower evolution law derived by including the FIDEL sample at redshifts of $z = 0.85$ and $1.15$ suggests that the evolution in may begin to slow compared to lower redshifts. |
3. | 3. |
The local star formation rate density based ou our 21 pau data is oof (1.00+(0.21)«10237.vr!Mpe.P assuming the Iroupa(2002) ΤΝΤ, which correspouds to oof (1.65£0.32)«102AZ.r.2Mpeο for a Salpeter(1955) IME. | The local star formation rate density based on our 24 $\micron$ data is of $(1.09 \pm 0.21) \times 10^{-2} M_{\odot} {\rm
yr}^{-1}{\rm Mpc}^{-3}$ assuming the \citet{Kroupa02} IMF, which corresponds to of $(1.65 \pm 0.32) \times 10^{-2} M_{\odot} {\rm
yr}^{-1}{\rm Mpc}^{-3}$ for a \citet{Salpeter55} IMF. |
The combined evolution constraint for the LF at 2<1.2 indicates that eevolves as ῥxCL|το ο, | The combined evolution constraint for the LF at $z \leq 1.2$ indicates that evolves as $\SFRD \propto (1+z)^{3.5 \pm 0.2}$ . |
Our normalization aud evolution measurements agree well with the :=1 extinction-corrected fudiugsfrom other studies. which confirms that most of star formation is obscured aud that 2| pau serves as a direct aud reliable indicator in these cases. | Our normalization and evolution measurements agree well with the $z
\lesssim 1$ extinction-corrected findingsfrom other studies, which confirms that most of star formation is obscured and that 24 $\micron$ serves as a direct and reliable indicator in these cases. |
We thank Denujuni Weiner. Benjamin Magnelli. Clhiristopher Willner. aud Pablo Pérrez-Gonzállez for invaluable discussions. | We thank Benjamin Weiner, Benjamin Magnelli, Christopher Willmer, and Pablo Pérrez-Gonzállez for invaluable discussions. |
W.B. thauks Andrew Topkins for supplying lis | W.R. thanks Andrew Hopkins for supplying his |
em MEVdg(Oj—JN e | ^2] A_0 = - a = -, ^2] a = - } . |
llere. angular brackets denote the average over (he statisties of NV: in the first equation. the term V2.4, was neglected due tothe large-scale variation of Ag: in the last equation. the term v:Va—(v:Va) was dropped (quasi linear approximation). | Here, angular brackets denote the average over the statistics of $N$; in the first equation, the term ${\nabla}^2 A_0$ was neglected due tothe large-scale variation of $A_0$; in the last equation, the term $ {\bf v}
\cdot {\bf \nabla} a - \langle {\bf v} \cdot {\bf \nabla}
a \rangle$ was dropped (quasi linear approximation). |
G=(va) is the flux of magnetic potential. which determines the evolution (effective diffusion) of Ay. | ${\bf G} = \langle {\bf v} a \rangle$ is the flux of magnetic potential, which determines the evolution (effective diffusion) of $A_0$. |
To obtain G in terms of mean quantities. we rewrile il as: dO. (pasci +. | To obtain ${\bf G}$ in terms of mean quantities, we rewrite it as: dt _t a + dt _t a = +. |
. llere. Gy is a kinematic part while Gs comes Irom the back reaction of the flow onto the magnetic potential. | Here, ${\bf G}_1$ is a kinematic part while ${\bf G}_2$ comes from the back reaction of the flow onto the magnetic potential. |
It is easy to check G4=—£(7) Vy. by using 7 approximation (Giuzinov&Diamond1994.1996).. namely by replacing the time derivative bv i, | It is easy to check ${\bf G}_1 = - \frac{\tau}{2}
\langle {v}^2 \rangle {\bf \nabla} A_0$ , by using $\tau$ approximation \citep{Gruzinov94,Gruzinov96}, namely by replacing the time derivative by $\frac{1}{\tau}$. |
The expression lor Gy is just the standard beta effect in 2D. It is interesting to express Gy in terms of N since the statisties of the latter can be prescribed. | The expression for ${\bf G}_1$ is just the standard beta effect in 2D. It is interesting to express ${\bf G}_1$ in terms of $N$ since the statistics of the latter can be prescribed. |
For simplicity. we assume the statisties of N to be stationary with a delta-Iuiction power spectrin around &—fy as follows: ENG Kurs) By taking spatial Fourier transform of the first equation of ((2)) without the Lorentz force term. and by using ((2)). we obtain | For simplicity, we assume the statistics of $N$ to be stationary with a delta-function power spectrum around $k=k_0$ as follows: ,t) By taking spatial Fourier transform of the first equation of \ref{Systeme}) ) without the Lorentz force term, and by using \ref{statistics}) ), we obtain ^2 =. |
Therefore. the effective diffusion coefficient in the kinematic limit is given by qQ84£N2)iz | Therefore, the effective diffusion coefficient in the kinematic limit is given by $\beta_0= - \frac{{\bf G_1}}{{\bf \nabla} A_0}= \frac{\tau}{2} [\frac{\tau
\gamma}{1+\tau \gamma}]^2 \frac{\langle N^2 \rangle}{k_0^2}$ . |
Notey- that 9) takes its− maximum.− value when neutrals and ions− are stronglv coupled with 57c 1. | Note that $\beta_0$ takes its maximum value when neutrals and ions are strongly coupled with $\gamma \tau \gg 1$ . |
This is a natural consequence of the assumption (hations obtain their kinetic energy through frictional coupling to neutrals. | This is a natural consequence of the assumption thations obtain their kinetic energy through frictional coupling to neutrals. |
Thus. crudely put. id is | Thus, crudely put, $\beta_0$ is |
correlations. bolometer time constants) which are more casily represeuted in the time or frequency domain. | correlations, bolometer time constants) which are more easily represented in the time or frequency domain. |
Iu passing. we mention a clever alternative method proposed bw 2. where the asvuuuetric-heam-imediuced anisotropy of the observed noisy CAIB field is compared in Fourier space to statistically isotropic noise realizations to deduce the beam asviunuetry. but not the complete beam function. | In passing, we mention a clever alternative method proposed by , where the asymmetric-beam-induced anisotropy of the observed noisy CMB field is compared in Fourier space to statistically isotropic noise realizations to deduce the beam asymmetry, but not the complete beam function. |
We «esigned and implemented a software pipeline to rapkvy simulate planet crossing in the time domain. and then recoistiruct the beam. | We designed and implemented a software pipeline to rapidly simulate planet crossing in the time domain, and then reconstruct the beam. |
The CCoaboration has 1uplemieuted an exteusive software iufrastructure to VAnuulate time-ordered data ΤΗ. oit tjose tools are. by desig1 aud optimization. intende [Snulae large survevs. | The Collaboration has implemented an extensive software infrastructure to simulate time-ordered data , but these tools are, by design and optimization, intended to simulate large surveys. |
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