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Both targets are too faint for us to reach the stability limit of HARPS within realistic integration times. and dispensing with the simultaneous thorium light produces cleaner stellar spectra. more easily amenable to quantitative spectroscopic analysis. | Both targets are too faint for us to reach the stability limit of HARPS within realistic integration times, and dispensing with the simultaneous thorium light produces cleaner stellar spectra, more easily amenable to quantitative spectroscopic analysis. |
The two stars were observed as part of the volume-limited HARPS search for planets (e.g.??).. | The two stars were observed as part of the volume-limited HARPS search for planets \citep[e.g.][]{Moutou2009,LoCurto2010}. |
While generally refered to as F-G-K stars. for the sake of concision. the targets of that program actually include MO dwarfs (?).. | While generally refered to as F-G-K stars, for the sake of concision, the targets of that program actually include M0 dwarfs \citep[][]{LoCurto2010}. |
We used 15 mn exposures for both stars. obtaining median S/N ratios (per pixel at 550 nm) of 53 for the V=9.58 GI 676A. and 49 for the V=10.31 HIP 12961. | We used 15 mn exposures for both stars, obtaining median S/N ratios (per pixel at 550 nm) of 53 for the V=9.58 Gl 676A, and 49 for the V=10.31 HIP 12961. |
The 69 and 46 radial velocities of Gl 676A and HIP 12961 (Tables 3. and 4. | The 69 and 46 radial velocities of Gl 676A and HIP 12961 (Tables \ref{TableRV_Gl676} and \ref{TableRV_HIP12961}, , |
between average Ayo densities of the ISO models from Group A and D with those expected in à ACDAI universe. | between average $\Delta_{V/2}$ densities of the ISO models from Group A and B with those expected in a $\Lambda$ CDM universe. |
Galaxies in Groups A and D are indicated separately. | Galaxies in Groups A and B are indicated separately. |
In the L104 interpretation the ISO halos from Group À are consistent with CDM in terms of shape and average density. while group D is consistent in terms of shape but not density. even though Groups A and D both consist of pure ISO haloes. with easily detectable shallow slopes. | In the H04 interpretation the ISO halos from Group A are consistent with CDM in terms of shape and average density, while group B is consistent in terms of shape but not density, even though Groups A and B both consist of pure ISO haloes, with easily detectable shallow slopes. |
The CDM constraints (i)-(iv) fail to take this into account and are (hus insufficient to distinguish between CDM ancl non-CDM models. | The CDM constraints (i)-(iv) fail to take this into account and are thus insufficient to distinguish between CDM and non-CDM models. |
They cannot exclude (he possibility that LSB galaxies have shallow inner mass-densitv slopes. even ad r=Peony. | They cannot exclude the possibility that LSB galaxies have shallow inner mass-density slopes, even at $r=r_{\rm conv}$. |
Additional constraints are needed {ο make a unique identification of galaxies compatible with CDM. | Additional constraints are needed to make a unique identification of galaxies compatible with CDM. |
Now that it is established that constraints (i)-(iv) are not sufficient to uniquely identilv CDAM-compatible galaxies. (he next step is to identily additional conditions (hat can. | Now that it is established that constraints (i)-(iv) are not sufficient to uniquely identify CDM-compatible galaxies, the next step is to identify additional conditions that can. |
Figures and 5 show that the inner slope and therefore the shape of the rotation curve do not depend on alone. but that there is an equally strong dependence on ο. | Figures \ref{fig:courslope} and \ref{fig:gammartfits} show that the inner slope and therefore the shape of the rotation curve do not depend on $\gamma$ alone, but that there is an equally strong dependence on $r_t$. |
These Figures also explain why LIO4 came to the conclusion that their four constraints were sullicient: implicit in (heir analvsis is the assumption that the shape of the rotation curve depends on > alone. | These Figures also explain why H04 came to the conclusion that their four constraints were sufficient: implicit in their analysis is the assumption that the shape of the rotation curve depends on $\gamma$ alone. |
While ib is (rue that for r;Z0.6 kpe a smaller > implies a steeper slope. this does not ensure a steep slope in an absolute sense. | While it is true that for $r_t \ga 0.6$ kpc a smaller $\gamma$ implies a steeper slope, this does not ensure a steep slope in an absolute sense. |
For >«1. depending on (he value of rj. slopes as shallow as à=—0.2 are still possible. | For $\gamma <1$, depending on the value of $r_t$, slopes as shallow as $\alpha =-0.2$ are still possible. |
Furthermore. it is shown above that the ΠΟ method does not lake (hese shallow slopes into account. and thus allows models with easily detectable ancl prominent shallow slopes purpose-built in (o pass the CDM test with fIying colours. | Furthermore, it is shown above that the H04 method does not take these shallow slopes into account, and thus allows models with easily detectable and prominent shallow slopes purpose-built in to pass the CDM test with flying colours. |
In order to identify galaxies (hat are really compatible with CDM. an additional constraint is needed. in such away that only (5.77) combinations are allowed that vield a steep slope [as well as pass conditions (i)-Gv)]. | In order to identify galaxies that are really compatible with CDM, an additional constraint is needed, in such a way that only $(\gamma,r_t)$ combinations are allowed that yield a steep slope [as well as pass conditions (i)-(iv)]. |
In practice this means that (5.77) parameter space needs to be searched for (he minimum 4? value that still results in a steepslope!. | In practice this means that $(\gamma, r_t)$ parameter space needs to be searched for the minimum $\chi^2$ value that still results in a steep. |
. In order to compare directly with the simulations the slopes are again evaluated al r=0.4 kpe. | In order to compare directly with the simulations the slopes are again evaluated at $r=0.4$ kpc. |
At Chis radius the LO4 simulations show slopes —1.3σαS—1. and strictly speaking one ought to restrict the search of (5.7;) space to slopes a<—1. | At this radius the H04 simulations show slopes $-1.3 \la \alpha \la -1$, and strictly speaking one ought to restrict the search of $(\gamma,
r_t)$ space to slopes $\alpha < -1$. |
However. to take into account uncertainties in data ancl simulations. aud give the CDM models as much leeway as possible. a more liberal range of a«—0.8 will be used. | However, to take into account uncertainties in data and simulations, and give the CDM models as much leeway as possible, a more liberal range of $\alpha < -0.8$ will be used. |
Eig. | Fig. |
4 shows that (liis is the steepest slope we can expect al | \ref{fig:slopeonly} shows that this is the steepest slope we can expect at |
pairs ancl triplets in dependence of their isolation degree (in dillerent environment). | pairs and triplets in dependence of their isolation degree (in different environment). |
Our main conclusions. | Our main conclusions. |
Compact pairs (22,« 150 kpc) and triplets (22),< 200 kpe) are more isolated in average than systems in geometric samples. thus they are characterized. by different: isolation degree. | Compact pairs $R_{h} <$ 150 kpc) and triplets $R_{h} <$ 200 kpc) are more isolated in average than systems in geometric samples, thus they are characterized by different isolation degree. |
The wider pair (triplet). the smaller isolation degree is observed. | The wider pair (triplet), the smaller isolation degree is observed. |
Small values of parameters p, and ἐν, are the evidence of loose environment. of these systems (they have not a “free space” to be the isolated. groups). | Small values of parameters $p_{e}$ and $t_{e}$ are the evidence of loose environment of these systems (they have not a "free space" to be the isolated groups). |
‘Thus. we consider wide geometric pairs and triplets as accidental ones in the common field. | Thus, we consider wide geometric pairs and triplets as accidental ones in the common field. |
We compared the luminosities of single galaxies aud galaxies in geometric pairs ancl triplets. | We compared the luminosities of single galaxies and galaxies in geometric pairs and triplets. |
I0 was shown that galaxics in isolated pairs ancl triplets are. two imes more luminous than isolated. galaxies. | It was shown that galaxies in isolated pairs and triplets are two times more luminous than isolated galaxies. |
On one hand it is the evidence of our gcometric method accuracy. | On one hand it is the evidence of our geometric method accuracy. |
On the other hand. we can conclude that in such small groups as pairs and. triplets the Iuminositv-density relation is observed. | On the other hand, we can conclude that in such small groups as pairs and triplets the luminosity-density relation is observed. |
We considered dark matter content in our groups. | We considered dark matter content in our groups. |
The meclian values of Alo;/£ for our samples limited by cdilleren criteria are 12 Al./L. for isolated pairs. 44 M.fL. for isolated triplets. 7 (8) M./L. for most compact pairs (triplets) with 2« 50 (100) kpe. | The median values of $M_{vir}/L$ for our samples limited by different criteria are 12 $M_{\odot}/L_{\odot}$ for isolated pairs, 44 $M_{\odot}/L_{\odot}$ for isolated triplets, 7 (8) $M_{\odot}/L_{\odot}$ for most compact pairs (triplets) with $R <$ 50 (100) kpc. |
Note. that. for. mos compact (close or interacting) syslenis is not very large dillerence in dark matter content for pairs and triplets. bu for isolated triplets the AM;/L is larger in 3 times than for pairs. | Note, that for most compact (close or interacting) systems is not very large difference in dark matter content for pairs and triplets, but for isolated triplets the $M_{vir}/L$ is larger in 3 times than for pairs. |
These results are in agreement with works of other auhors. | These results are in agreement with works of other authors. |
We also found that the pair/triplet is less isolate system (in denser environment). when Al.;,/L greater. | We also found that the pair/triplet is less isolated system (in denser environment), when $M_{vir}/L$ greater. |
This relation testifies that galaxy systems in denser environmen have greater rms velocity. (because of. Mj,Szn at fixe⋅ distance between galaxies). | This relation testifies that galaxy systems in denser environment have greater rms velocity (because of $M_{vir} \sim S_{v}^{2}$ at fixed distance between galaxies). |
“Phe p./-. ο, dependences are observed only for compact svstems (up to 150-200 kpc for pairs and up to 250-300 kpe for triplets). | The $p, t$ - $M_{vir}/L$ dependences are observed only for compact systems (up to 150-200 kpc for pairs and up to 250-300 kpc for triplets). |
We concluded that 3D Voronoi high-order tessellation method is the elfective tool for small groups identification and studying their properties in dependence on environment. | We concluded that 3D Voronoi high-order tessellation method is the effective tool for small groups identification and studying their properties in dependence on environment. |
In the next paper we will present results on morphological content ancl colour indices of galaxies in pairs and triplets in comparison with isolated. galaxies and their environment. | In the next paper we will present results on morphological content and colour indices of galaxies in pairs and triplets in comparison with isolated galaxies and their environment. |
This work was partially supported by the Cosmonmicrophvsics— Program of— the NAS) of— Ukraine. | This work was partially supported by the Cosmomicrophysics Program of the NAS of Ukraine. |
We are also grateful to Ukrainian Virtual Rocnteen ancl Canuna-Ray Observatory VIBGO.UA and computing cluster of Bogolvuboy Institute for Theoretical Physics. for using their computing resources. | We are also grateful to Ukrainian Virtual Roentgen and Gamma-Ray Observatory VIRGO.UA and computing cluster of Bogolyubov Institute for Theoretical Physics, for using their computing resources. |
where lanbidaIiplugomnega? The real parts of the roots of the equation are:field where and the Theimaginary part ofzc for these roots is =1nqdes and frequentyaq associated The modes 2. 3 have the same growth rate in the limit taken here. where only the first order in 1/À and T, 15 kept. | where H The real parts of the roots of the equation are:, where and _0 The imaginary part of $\tilde\omega$ for these roots is = and q _0] The modes 2, 3 have the same growth rate in the limit taken here, where only the first order in $1/\tilde \lambda$ and $\tilde T_{\rm m0}$ is kept. |
The growth rates of the three modes (65. 66) are all proportional to the magnetic torque. | The growth rates of the three modes (65, 66) are all proportional to the magnetic torque. |
Hence they all quality as instabilities caused by the coupling between the disk and the outflow. if their 2; are negative. | Hence they all qualify as instabilities caused by the coupling between the disk and the outflow, if their $\omega_{\rm i}$ are negative. |
The first mode. cc, is neutral. in the absence of diffusion and magnetic torques. | The first mode, $\omega_1$ is neutral, in the absence of diffusion and magnetic torques. |
If only magnetic diffusion is included (section 5.2.1). it is a damped mode. | If only magnetic diffusion is included (section 5.2.1), it is a damped mode. |
Thus. low frequency perturbations are stabilized by magnetic diffusion. in the absence of a magnetic torque. | Thus, low frequency perturbations are stabilized by magnetic diffusion, in the absence of a magnetic torque. |
When a magnetic torque is present (section 5.2.2) the sign of the growth rate is determined [see eq (65)] by the quantity 240|pilO°). | When a magnetic torque is present (section 5.2.2) the sign of the growth rate is determined [see eq (65)] by the quantity $2q\tilde\Omega^2+ p(1-\tilde\Omega^2)$. |
For low field strength. the second term is small. and instability is determined by the sign of q. the rate of change of the magnetic torque with inclination of the field line. | For low field strength, the second term is small, and instability is determined by the sign of $q$, the rate of change of the magnetic torque with inclination of the field line. |
As Fig. | As Fig. |
| shows. the magnetic torque increases with decreasing inclination (field lines bent further away from the vertical). | 1 shows, the magnetic torque increases with decreasing inclination (field lines bent further away from the vertical). |
This reflects the fact that the centrifugal effect is stronger on field lines that are bent further away from the vertical. increasing the mass flux and magnetic torque. | This reflects the fact that the centrifugal effect is stronger on field lines that are bent further away from the vertical, increasing the mass flux and magnetic torque. |
Thus 4 1s negative in the cases of interest. and the growth rate, positive. | Thus $q$ is negative in the cases of interest, and the growth rate $-\omega_{\rm i}$ positive. |
The term involving p. the dependence of the wind torque on rotation rate. is stabilizing since p>0 (cf Fig.l). | The term involving $p$, the dependence of the wind torque on rotation rate, is stabilizing since $p>0$ (cf Fig.1). |
In dimensional terms. the approximate condition for instability in the absence of magnetic diffusion and in the limit of a weak magnetic wind torque is thus: - . where g,=(Oi—Q3DD,f/(2zX) is the acceleration due to magnetie support of the disk against gravity. ( | In dimensional terms, the approximate condition for instability in the absence of magnetic diffusion and in the limit of a weak magnetic wind torque is thus: > -, where $g_{\rm m} = (\Omega_{\rm K}^2-\Omega^2)r_0 = B_r^{\rm S}B_z/(2\pi\Sigma)$ is the acceleration due to magnetic support of the disk against gravity. ( |
the minus signs are included because the derivatives are A»negative 1 the cases of interest). | the minus signs are included because the derivatives are negative in the cases of interest). |
This mode evidently represents the sought instability. associated with the dependence of magnetic torque on field line inclination. | This mode evidently represents the sought instability, associated with the dependence of magnetic torque on field line inclination. |
The result shows. however. that the instability is not governed only by the dependence of the torque on inclination, | The result shows, however, that the instability is not governed only by the dependence of the torque on inclination. |
ont.Ape, magnébic is strong enough to change the rotation rate by providineSupportMI against gravity. the second term in (65) is important. and its effect stabilizing. | If the magnetic field is strong enough to change the rotation rate by providing support against gravity, the second term in (65) is important, and its effect stabilizing. |
This represents the fact that a lower rotation rate increases the height of the potential d=“barrier. that the wind. has to overcome (cf- discussion.η inη sectionη 3). which decreases the magnetic torque (Ogilvie and Livio. 2001). | This represents the fact that a lower rotation rate increases the height of the potential barrier that the wind has to overcome (cf discussion in section 3), which decreases the magnetic torque (Ogilvie and Livio, 2001). |
OHICYGEWe brieflyπα, discussOne 4 πο σας modes. | We briefly discuss the two oscillatory modes. |
Since. p70 and q«0 for the cases of interest (Fig.1). eq. | Since $p>0$ and $q<0$ for the cases of interest (Fig.1), eq. |
eq. ( | eq. ( |
66) shows that these modes are stable. | 66) shows that these modes are stable. |
In the limit of 77=0 and Tj,=0. the two hoe ths, Same, freaygnWy (af, | In the limit of $\tilde\eta=0$ and $\tilde T_{\rm m0}=0$, the two modes have the same frequency (cf. |
Ecgei ( | Eqs. ( |
54) (64)) | 54) (64)). |
228%μπαμ...σοι Be12 is the epicyclicnté$.QR) with the stable angular momentum gradient. | $[2\tilde\Omega_0(2\tilde\Omega_0+\tilde S)]^{1/2}$ is the epicyclic frequency associated with the stable angular momentum gradient. |
The second [on represents the restoring force due to the change of inclination of the field lines by the perturbations (note that 107xD.D.). | The second term represents the restoring force due to the change of inclination of the field lines by the perturbations (note that $1-\tilde\Omega_0^2\propto B_r B_z$ ). |
On its own. this magnetic restoring force would yield a wave with frequency wxAο5, like a surface wave. | On its own, this magnetic restoring force would yield a wave with frequency $\omega\propto
\lambda^{-1/2}$, like a surface wave. |
This is the result of the long-range nature of the magnetic perturbations of the potential field outside the disk. | This is the result of the long-range nature of the magnetic perturbations of the potential field outside the disk. |
These magnetic waves have been analyzed before (Spruit Taam 1990; Tagger etal. | These magnetic waves have been analyzed before (Spruit Taam 1990; Tagger etal. |
1990). | 1990). |
We obtain the growth rate of the instabilities by solving Eq. ( | We obtain the growth rate of the instabilities by solving Eq. ( |
40) numerically. | 40) numerically. |
For the shear rate 5 we take the Keplerian value S=—23/2. | For the shear rate $\tilde S$ we take the Keplerian value $S=-3/2$. |
The problemis described by the dimensionless disk scale-height /7. the angular velocity of accretion flow Oy which is a measure of the magnetic field strength. the inclination of magnetic field ayDB./D, at the disk surface. and the dimensionless magnetic. diffusivity 7. | The problem is described by the dimensionless disk scale-height $\tilde H$, the angular velocity of accretion flow $\tilde \Omega_0$ which is a measure of the magnetic field strength, the inclination of magnetic field $\kappa_0=B_z/B_r$ at the disk surface, and the dimensionless magnetic diffusivity $\tilde\eta$. |
The inclination turns out to influence the stability mainly through its effeet on the wind torque. which depends sensitively on it (Figs.1. 2). | The inclination turns out to influence the stability mainly through its effect on the wind torque, which depends sensitively on it (Figs.1, 2). |
The second main parameter determining the stability is the strength of the magnetic field. which we have expressed throughout this paper by its effect on the rotation rate (relative to the Keplerian rate) and the angular velocity of accretion flow. Qu=QO/fOgy. | The second main parameter determining the stability is the strength of the magnetic field, which we have expressed throughout this paper by its effect on the rotation rate (relative to the Keplerian rate) and the angular velocity of accretion flow, $\tilde\Omega_0=
\Omega/\Omega_{\rm K}$. |
With increasing field strength. the magnetic stresses start contributing to the support of the disk against gravity. decreasing the rotation rate. | With increasing field strength, the magnetic stresses start contributing to the support of the disk against gravity, decreasing the rotation rate. |
We take the self-similar index © of the magnetic field shape to be I in the following. | We take the self-similar index $\alpha$ of the magnetic field shape to be $4$ in the following. |
In Figs. | In Figs. |
1 and 2. the magnetic torque as functions of fy and Qu is plotted for different values of the dimensionless disk scale-height II. | 1 and 2, the magnetic torque as functions of $\kappa_0$ and $\tilde\Omega_0$ is plotted for different values of the dimensionless disk scale-height $\tilde H$ . |
For small disk scale- te.. if the temperature of gas in the aceretion disk | For small disk scale-height, i.e., if the temperature of gas in the accretion disk |
1n the new coordinate svstem we can now evaluate 5(i7): In ((B13)). all terms with non-zero m vanish alter integration over o: only the term with m=0 contributes to the integral. | In the new coordinate system we can now evaluate $b(\vec{r})$: In \ref{b11}) ), all terms with non-zero $m$ vanish after integration over $\phi$; only the term with $m=0$ contributes to the integral. |
Integrating the remaining terni. we get Substituting ((DI1)) into. ((D13)). and evaluating the fifth time derivative. we get Lore css=26M(a)Εμμμα. | Integrating the remaining term, we get Substituting \ref{psinew}) ) into \ref{b12}) ), and evaluating the fifth time derivative, we get Here $\epsilon_{\rm grav}=2GM/(c^2a)=R_{\rm Schwarzschild}/a$. |
Equations (B3)) and (D14)) are equivalent to Equations (47)). (48)). (49)). (50)). (51)mrot) | Equations \ref{bnr}) ) and \ref{brr}) ) are equivalent to Equations \ref{gravmag}) ), \ref{bgmrot}) ), \ref{blmgrav}) \ref{chi1grav}) \ref{chigrav2}) |
Equations (B3)) and (D14)) are equivalent to Equations (47)). (48)). (49)). (50)). (51)mrot). | Equations \ref{bnr}) ) and \ref{brr}) ) are equivalent to Equations \ref{gravmag}) ), \ref{bgmrot}) ), \ref{blmgrav}) \ref{chi1grav}) \ref{chigrav2}) |
bv previous authors (ee.7) πο fud a siguificautlv lower imean saturation level for the hiehest-auass stars in our saniple (F-tvpe stars). though we will show iu Section 1. that these stars are not in fact saturated. but are supersaturated and we therefore conclude that the N-rav saturation level is iudependeut of spectral type. | by previous authors \citep[e.g.][]{pizz03} we find a significantly lower mean saturation level for the highest-mass stars in our sample (F-type stars), though we will show in Section \ref{s-evolution} that these stars are not in fact saturated, but are super-saturated and we therefore conclude that the X-ray saturation level is independent of spectral type. |
To understand the physical origin of coronal saturation. the threshold for saturation can be converted from one in terms of the Rossby muuber (though effectivelv the rotation period aud the spectral type) to age uxing kuowledec of the rotational evolution of stars. | To understand the physical origin of coronal saturation, the threshold for saturation can be converted from one in terms of the Rossby number (though effectively the rotation period and the spectral type) to age using knowledge of the rotational evolution of stars. |
7) outlined an empirical formulation of the rotation period evolution of solar and late-type stars based on open cluster aud field star data. characterizing two sequences in the Pog(D.V) plane: theeonvectiec (C) sequence of voung. fast rotators. aud theinterface (1) sequence of slow rotators. | \citet{barn03} outlined an empirical formulation of the rotation period evolution of solar and late-type stars based on open cluster and field star data, characterizing two sequences in the $P_{rot} - (B-V)$ plane: the (C) sequence of young, fast rotators, and the (I) sequence of slow rotators. |
This empirical characterization allows ages to be derived frou rotation periods for stars ou the I sequence. a method known as evroclronoloey. | This empirical characterization allows ages to be derived from rotation periods for stars on the I sequence, a method known as gyrochronology. |
This technique results iu a precision of £0.05 dex iu og r/wr (excludingabsoluteuncertaintiesintheclus-cragescale. ?).. | This technique results in a precision of $\pm 0.05$ dex in log $\tau$ /yr \citep[excluding absolute uncertainties in the cluster age scale,][]{mama08}. |
Stars on the C sequence are harder ο date accurately due to star-to-star variations in the ZANIS arrival time aud effects such as disk-lockiug in tle wre-lnain sequence phase. | Stars on the C sequence are harder to date accurately due to star-to-star variations in the ZAMS arrival time and effects such as disk-locking in the pre-main sequence phase. |
Tere the recent evrochronology yaralueterization of 7) las been used to couvert the clupirical threshold for saturation. Ro>0.13. iuto a hnresholl iu massage space. as shown iu Figure L. | Here the recent gyrochronology parameterization of \citet{mama08} has been used to convert the empirical threshold for saturation, $Ro > 0.13$, into a threshold in mass–age space, as shown in Figure \ref{regimes2}. |
It is worth noting that. at the ages cousidered here. differeuces between the exrochronological parameters of 7). ?)., and 7). are too small to be cüsceruible in this figure. | It is worth noting that, at the ages considered here, differences between the gyrochronological parameters of \citet{barn03}, \citet{mama08}, and \citet{meib09} are too small to be discernible in this figure. |
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