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We approximate theprior clistribution of parameter values bya Gaussian distribution with covariance matrix (T. so the covariance matrix ofparameter.values including prior information is given by Ixnox 1995). where F is the Fisher matrix (1)). | We approximate theprior distribution of parameter values bya Gaussian distribution with covariance matrix ${\bf T}$ , so the covariance matrix ofparametervalues including prior information is given by Knox 1995), where ${\bf F}$ is the Fisher matrix \ref{eq:fishmat}) ). |
b.10) Ag. 10.1 AD. ουν, 109AL, 0.530ML. Τον TF "nEu à, 77/7, | $5-10$ $M_H$ $10^{-4}
M_H$ $M_H$ $ 10 \, \msun < M_{\pbh} < \, 10^6 \msun$ $\sim 10^4 \msun$ $10^6 \msun$ $0.3-30 \msun$ $T_c$ $\sim M_{\pbh}$ $T_c$ $n_{0,\pbh}$ $\delta_p$ $T/T_c$ |
The San Pedro. Márrtir (SPM) observatory ds. located: at 31702/39"N. ποτ’) and at an altitude of 2830 nn. inside the Parque NacionalW Sierra de San Pedro. Márrtir. | The San Pedro Márrtir (SPM) observatory is located at $31^{\circ} 02^{\prime} 39^{\prime \prime}$ N, $115^{\circ} 27^{\prime} 49^{\prime \prime}$ W and at an altitude of 2830 m, inside the Parque Nacional Sierra de San Pedro Márrtir. |
SPAL is ~65 km E of the Pacific Coast anc ~55 km Woto the Gulf. of California. | SPM is $\sim$ 65 km E of the Pacific Coast and $\sim$ 55 km W to the Gulf of California. |
The. largest. telescope at the site is a 2.1-m. Büitehev-Clhréttien.. operational since 1981. | The largest telescope at the site is a 2.1-m Ritchey-Chréttien, operational since 1981. |
Astroclimatological characterization studies at SPM are reviewed in Tapia.Hiriart&Cruz-Gonzalez(2007). | Astroclimatological characterization studies at SPM are reviewed in \citet{Tapia07}. |
. Compilations of one and two continuous decades of weather and observing statistics of OXN-SPM have been reported bv Tapia(1992). ancl Tapia(2003). | Compilations of one and two continuous decades of weather and observing statistics of OAN-SPM have been reported by \citet{Tapia92} and \citet{Tapia03}. |
. Phe vearly fractions of photometric and spectroscopic nights from. 1984 to 2006 is presented. on Table 3 of Tapia.Hiriart&Cruz-Conzalez (2007). | The yearly fractions of photometric and spectroscopic nights from 1984 to 2006 is presented on Table 3 of \citet{Tapia07}. |
. Other aspects of the site characterization have been reported by several authors e.g. and Cruz-González.etal.(2007). | Other aspects of the site characterization have been reported by several authors e.g. and \citet{CruzGlez07}. |
. Nevertheless. this is the first study on the radiation cata measured in situ. | Nevertheless, this is the first study on the radiation data measured in situ. |
The data were recorded. by the Thirty. Meter Telescope CENE). site-testing team from 2004 to 2008: see Schocketal.(2009) for an overview of the PM project and its main results. | The data were recorded by the Thirty Meter Telescope (TMT) site-testing team from 2004 to 2008; see \citet{Schock09} for an overview of the TMT project and its main results. |
Cloud cover is one of the most important considerations to characterize a ground-based astronomical observatory. | Cloud cover is one of the most important considerations to characterize a ground-based astronomical observatory. |
Only for low-frequency racio observations cloucliness is of little importance. | Only for low-frequency radio observations cloudiness is of little importance. |
Given a site. statistics of daytime cloud cover are indicative of the usable portion. of the time for optical and. near-infrared) observations ancl bring kev information for the potentiality of that site for millimeter and sub-millimeter astronomy. | Given a site, statistics of daytime cloud cover are indicative of the usable portion of the time for optical and near-infrared observations and bring key information for the potentiality of that site for millimeter and sub-millimeter astronomy. |
Phe relationship between diurnal and. nocturnal cloudiness is strongly. dependent on the location of the site. | The relationship between diurnal and nocturnal cloudiness is strongly dependent on the location of the site. |
Erasmus&VanStaden(2002). give a detailed discussion on that topic. | \citet{Erasmus02} give a detailed discussion on that topic. |
For the case of SPM these authors conclude that the cay versus night. variation of the cloud cover is less than 5 per cent. | For the case of SPM these authors conclude that the day versus night variation of the cloud cover is less than 5 per cent. |
Therefore. davtime cloud cover statistics at. SPM is a useful indicator of nighttime | Therefore, daytime cloud cover statistics at SPM is a useful indicator of nighttime |
accelerated region (i.e. that of patch (B) in Fig. 2)) | accelerated region (i.e. that of patch $B$ ) in Fig. \ref{fig:pvel}) ) |
ranges between 50 Mpc aud 1000 Mpe. | ranges between 50 Mpc and 1000 Mpc. |
Within these scales q lies in the (-0.1.00) range. taking its minima value in small-scale regious of low density aud approaching zero as we move on to larger lengths. | Within these scales $\tilde{q}$ lies in the 0) range, taking its minimum value in small-scale regions of low density and approaching zero as we move on to larger lengths. |
These estimates are not far frou those inferred by the supernovae data. which value the cleceleration parameter close to -0.5 and put the transition to deceleration near z=0.9 (Turner&Riess2002:etal2001). | These estimates are not far from those inferred by the supernovae data, which value the deceleration parameter close to -0.5 and put the transition to deceleration near $z=0.5$ \citep{TR,Retal2}. |
.. The picture does not change much when we adopt the results of Li&Schwarz(2008).. the surveys ol Watkinsetal(2009) auc Feldiianetal (2009).. or those of Iashliuskyetal(2008.2009a.)).. | The picture does not change much when we adopt the results of \cite{LS}, the surveys of \cite{WFH} and \cite{FWH}, , or those of \cite{KA-BKE1,KA-BKE2,KA-BEEK}. |
Substituted, into expressious (8)) aud (9)). the former give —0.2«q<0 in regions of 50 Mpc when Q<0.5 there. | Substituted into expressions \ref{eq:ltq1}) ) and \ref{eq:con1}) ), the former give $-0.2<\tilde{q}<0$ in regions of 50 Mpc when $\Omega<0.5$ there. |
Similarly. close to 150 Mpe. the measurements of Watkinsetal(2009) and put d in the range 00). provided Q<0.2 there. | Similarly, close to 150 Mpc, the measurements of \cite{WFH} and \cite{FWH} put $\tilde{q}$ in the range 0), provided $\Omega<0.2$ there. |
Finally on leneths of 150 aud 800 Mpc. the results of Ixashliuskyetal(2008.2009a.b) suggest that q varies tle range 00) auc 00) respectively. when ο<0.15 aud Q<0.07 on the corresponding scales. | Finally on lengths of 450 and 800 Mpc, the results of \cite{KA-BKE1,KA-BKE2,KA-BEEK} suggest that $\tilde{q}$ varies the range 0) and 0) respectively, when $\Omega<0.15$ and $\Omega<0.07$ on the corresponding scales. |
Note that the same survey indicates bulk flows of 1500 km/sec on scales close to 150 Mpe. | Note that the same survey indicates bulk flows of 1500 km/sec on scales close to 150 Mpc. |
Inserted into Eqs. (8)). (9)) | Inserted into Eqs. \ref{eq:ltq1}) ), \ref{eq:con1}) ) |
these values lead to —0.3)<q2«0 when ϱ«0.5. | these values lead to $-0.3<\tilde{q}<0$ when $\Omega<0.8$. |
One should keep in mind. however. that ou relatively small scales the peculiar-velocity errorbars are large (see Ixashlinskyetal(2008))). | One should keep in mind, however, that on relatively small scales the peculiar-velocity errorbars are large (see \cite{KA-BKE1}) ). |
Let us now turn to the last term of Eq. (7)). | Let us now turn to the last term of Eq. \ref{eq:tq2}) ). |
Qualitatively speaking. a positive / will assist the acceleration. relax the above given conditions and lead to lower values of q. | Qualitatively speaking, a positive $\dot{\vartheta}$ will assist the acceleration, relax the above given conditions and lead to lower values of $\tilde{q}$. |
So. here. we will assume that 7 is negative. | So, here, we will assume that $\dot{\vartheta}$ is negative. |
We will also demand that 2/0!c7/0<1. to ensure that both J aud ave small perturbations relative to their background. associates. | We will also demand that $\dot{\vartheta}/\Theta^{\prime}\simeq\vartheta/\Theta\ll1$, to ensure that both $\vartheta$ and $\dot{\vartheta}$ are small perturbations relative to their background associates. |
The next step is to recast Raychaudbtui's formula (see Eq. | The next step is to recast Raychaudhuri's formula (see Eq. |
(3aa)) in the form with Of< 0. | \ref{eq:Rays1}a a)) in the form with $\Theta^{\prime}<0$ . |
Solving the above lor O7. substituting into Eq. (7)) | Solving the above for $\Theta^2$, substituting into Eq. \ref{eq:tq2}) ) |
aud emploving some straightforward algebra we arrive at Using the previous values of 4Ο. we find that negative gs on 50 Mpc scales need Q«0.5. | and employing some straightforward algebra we arrive at Using the previous values of $\vartheta/\Theta$, we find that negative $\tilde{q}$ s on $\sim50$ Mpc scales need $\Omega<0.5$. |
Sunilarlv. expression (11)) translates iuto Q<0.2 close to 100 Mpe and into €<0.02 uear the 1000 Mpe mark. if d is to become negative there. | Similarly, expression \ref{eq:ltq2}) ) translates into $\Omega<0.2$ close to 100 Mpc and into $\Omega<0.02$ near the 1000 Mpc mark, if $\tilde{q}$ is to become negative there. |
Under these conditions. tlie accelerated patel extends from 50 Mpe to 1000 Mpe. with q varying within (-0.2.00). | Under these conditions, the accelerated patch extends from 50 Mpc to 1000 Mpc, with $\tilde{q}$ varying within 0). |
So. even with the last term of (7)) accounted for (aud iu an unfavourable way). negative values for d are still possible. | So, even with the last term of \ref{eq:tq2}) ) accounted for (and in an unfavourable way), negative values for $\tilde{q}$ are still possible. |
Conventional alinost-FRW= kinematics can acconunodate accelerated expansion. | Conventional almost-FRW kinematics can accommodate accelerated expansion. |
To sumiuarise. suppose that in a clust-dominated FRW universe a sulliciently large region CA) is endowed with a weakbulk peculiar velocity of positive divergence (Le. J> O). | To summarise, suppose that in a dust-dominated FRW universe a sufficiently large region$A$ ) is endowed with a weakbulk peculiar velocity of positive divergence (i.e. $\vartheta>0$ ). |
When the | When the |
1154showsemullicolourtighleurve forV 1154€'C'yg. | shows a multicolour light curve for Cyg. |
IcontaimsI14- 120pointsincach filleroblainedwith fourdi f[erentlelescopesasdeseribedinspelion 22. | It contains $114-120$ points in each filter obtained with four different telescopes as described in \ref{mulcol}. |
Fheampliludesandamplituderaliosareconsistentwilh As a check. | The amplitudes and amplitude ratios are consistent with Cyg being a Cepheid, e.g. the ratio of the $I$ and $V$ amplitude is 0.6, which is exactly what is expected. |
the colours of VII54CCve | \ref{fps} shows that the average Fourier parameters of Cyg fit well all the progressions, although in each case they are slightly lower than the main progression. |
were compared o other Galactic C'epheidsin relPC.. | As a check, the colours of Cyg were compared to other Galactic Cepheidsin \\ref{PC}. |
Phe observed colours of (21)=(0865 and (V.1)=1.021 were derived from the DVRL. light curves. | The observed colours of $(B-V)=0.865$ and $(V-I)=1.021$ were derived from the $BVR_cI_c$ light curves. |
To correct for extinction. we adopted the colour excess from Fernieetal.(1995) (after. removing the systematic rend in Fernie system using the prescription given in lTamnnmannetal. 2003)). | To correct for extinction, we adopted the colour excess from \citet{feb95} (after removing the systematic trend in Fernie system using the prescription given in \citealt{tsr03}) ). |
The extinetion-free colours are (DY),20.546 and (V.D),=0.612. | The extinction-free colours are $(B-V)_0=0.546$ and $(V-I)_0=0.612$. |
As shown in ref[PC.. these colours. fit well within the periocd-colour relations defined by the Galactic Cepheids. | As shown in \\ref{PC}, these colours fit well within the period-colour relations defined by the Galactic Cepheids. |
With almost a vear of continuous data. it is in. principle xossible to study the stability of the light curve of a classical Cepheid over. several dozen pulsation evcles. | With almost a year of continuous data, it is in principle possible to study the stability of the light curve of a classical Cepheid over several dozen pulsation cycles. |
. However. »ecause instrumental elfeets are still present in the data. it is oo early to perform such an analysis at least until pixel-Ievel data becomoe available. which would allow the data reduction o be optimized for this particular tvpe of star. | However, because instrumental effects are still present in the data, it is too early to perform such an analysis at least until pixel-level data become available, which would allow the data reduction to be optimized for this particular type of star. |
The frequeney content of the light curve of V1154€€ve was investigated with standard Fourier transform micthocls ον applying well-tested software packages:SIGSPEC (Iteegen 2007).. (Lenz&Breeer2005). anc (Ixolláth1990). | The frequency content of the light curve of Cyg was investigated with standard Fourier transform methods by applying well-tested software packages: \citep{reg07}, \citep{lb05} and \citep{kol90}. |
. The distorted parts of the LC light curves iive been omitted. because their presence causes spurious requencey peaks around the main frequencies. | The distorted parts of the LC light curves have been omitted, because their presence causes spurious frequency peaks around the main frequencies. |
The alfected parts are the entire QO and BJD=2455054.0 2454094.24] in Q2. | The affected parts are the entire Q0 and ${\rm BJD}=[2455054.0-2454094.24]$ in Q2. |
The frequeney spectrum shows the main pulsation requency at fo=O.208ded and many harmonics. | The frequency spectrum shows the main pulsation frequency at $f_0=0.203$ $^{-1}$ and many harmonics. |
Two iwmonics (2fy and 3f5) are clearly visible in the upper duel of 12.. | Two harmonics $2f_0$ and $3f_0$ ) are clearly visible in the upper panel of \ref{w4}. |
Prewhitening with these peaks reveals ‘urther harmonies up to the 107 order with very low amplitudes. | Prewhitening with these peaks reveals further harmonics up to the $10^{\rm th}$ order with very low amplitudes. |
This is the first time that. such. high-order iwmonics have been detected. underlining the accuracy of he observations. | This is the first time that such high-order harmonics have been detected, underlining the accuracy of the observations. |
The clleet of instrumental artefacts (trends. amplitude variation) is clearly seen in the remaining »ower around. fo. | The effect of instrumental artefacts (trends, amplitude variation) is clearly seen in the remaining power around $f_0$. |
Apart from that the frequency spectrum is completely free of additional power at the significance level up to the Nyquist frequeney as shown in the lower two panels of refw4.. | Apart from that the frequency spectrum is completely free of additional power at the significance level up to the Nyquist frequency as shown in the lower two panels of \\ref{w4}. |
3elore finishing this paper. Q5 SC data became available for V1I54CCve. | Before finishing this paper, Q5 SC data became available for Cyg. |
To investigate the high-frequcney range we used this dd long data set ane the dd long SC data taken in Ql. | To investigate the high-frequency range we used this d long data set and the d long SC data taken in Q1. |
The two data sets have a very similar frequeney content. and we chose to plot the Q5 SC frequeney spectrum in panel d of refw4.. because the longer timebase ensures better frequency resolution and higher SNR. | The two data sets have a very similar frequency content, and we chose to plot the Q5 SC frequency spectrum in panel d of \\ref{w4}, , because the longer timebase ensures better frequency resolution and higher SNR. |
The top of the grass of the remaining spectrum. is imag. while the average is ymmag in the spectrum up to 5. | The top of the grass of the remaining spectrum is $\mu$ mag, while the average is $\mu$ mag in the spectrum up to $^{-1}$. |
Above that the top of the grass of the remaining spectrum decreases to L5ymmag. and [rom ! it remains constant. | Above that the top of the grass of the remaining spectrum decreases to $\mu$ mag, and from $^{-1}$ it remains constant. |
Phe average of the remaining peaks is below lgmag in this high-frequency. range. | The average of the remaining peaks is below $\mu$ mag in this high-frequency range. |
The. residual spectrum shows no signal of any shorter period. nonraclia pulsation moces or solar-like oscillations. | The residual spectrum shows no signal of any shorter period nonradial pulsation modes or solar-like oscillations. |
The frequencies. amplitudes and. phases of the detecte ancl identified peaks based on Q4 LC data are listed in reftabfreq.. | The frequencies, amplitudes and phases of the detected and identified peaks based on $-$ Q4 LC data are listed in \\ref{tabfreq}. |
The zero epoch was chosen close to momen of the first data point. i.c. BJD= 2454954.0. | The zero epoch was chosen close to moment of the first data point, i.e. ${\rm BJD}=2454954.0$ . |
The errors have been estimated. from PeriodO4. | The errors have been estimated from Period04. |
Searching for only one frequeney of thehighest amplitude at a time ane prewhitening for it and then repeating the procecure gave practically the same results as searching for all the harmonics simultancously. | Searching for only one frequency of thehighest amplitude at a time and prewhitening for it and then repeating the procedure gave practically the same results as searching for all the harmonics simultaneously. |
that case. the algorithm is not confident in its accuracy and stops. | that case, the algorithm is not confident in its accuracy and stops. |
When the difference between two frequencies is larger than twice the frequency associated with the length of the total time interval. the determination of each fundamental frequency is not perturbed by the other ones. | When the difference between two frequencies is larger than twice the frequency associated with the length of the total time interval, the determination of each fundamental frequency is not perturbed by the other ones. |
Although the iterative method suggested by Champenois(1998) allows to reduce this distance. some difficulties remain when the frequencies are too close to each other. | Although the iterative method suggested by \citet{c98} allows to reduce this distance, some difficulties remain when the frequencies are too close to each other. |
In order to deliver theories of rotation that can be easily compared with observations. we chose to express our results in the following vartables: There are at least two ways to define the longitudinal librations. | In order to deliver theories of rotation that can be easily compared with observations, we chose to express our results in the following variables: There are at least two ways to define the longitudinal librations. |
We can for instance consider the librations about the exact synchronous rotation. Le. p-«n>f. usually calledlibrations. | We can for instance consider the librations about the exact synchronous rotation, i.e. $p-<n>t$, usually called. |
. In this case. we have used for «n> the frequency associated with the proper model. 1.8. Mimas? mean longitude. | In this case, we have used for $<n>$ the frequency associated with the proper mode $\lambda$, i.e. Mimas' mean longitude. |
Another way to consider the longitudinal librations is to work on the librations about the Mimas-Saturn direction. | Another way to consider the longitudinal librations is to work on the librations about the Mimas-Saturn direction. |
We will call these librations because they represent the misalignment of the tidal bulge of the satellite. | We will call these librations because they represent the misalignment of the tidal bulge of the satellite. |
The difference between these two librations is known aslibrations.. only due to the orbital motion of Mimas around Saturn. | The difference between these two librations is known as, only due to the orbital motion of Mimas around Saturn. |
The reader can find graphical descriptions of these librations in Murray&Dermott(1999).. Fig.5.16. | The reader can find graphical descriptions of these librations in \citet{md99}, Fig.5.16. |
The latitudinal librations are the North-South librations of the large axis of the considered body in the saturnocentric reference frame that follows the orbital motion of the body. | The latitudinal librations are the North-South librations of the large axis of the considered body in the saturnocentric reference frame that follows the orbital motion of the body. |
They are analogous to the tidal librations that are the East-West librations. | They are analogous to the tidal librations that are the East-West librations. |
In order to get the tidal longitudinal librations and the latitudinal librations. we first should express the unit vector f| Bo.(ie. the directionη. of3 Mimas?η. long axis)η in. the inertialη. frame3 (σι.65.EJ63). | In order to get the tidal longitudinal librations and the latitudinal librations, we first should express the unit vector $\vec{f_1}$ (i.e. the direction of Mimas' long axis) in the inertial frame $(\vec{e_1},\vec{e_2},\vec{e_3})$. |
From (Eq.22)) and the definitions of the Andoyer modified variables 15)). we get: The tidal longitudinal librations v and the latitudinal ones 7 are found this way: and ff is=. the unit vector. normal to the orbit plane.2 and { thewhere tangent to the trajectory. | From \ref{equ:passage}) ) and the definitions of the Andoyer modified variables \ref{equ:modified}) ), we get: The tidal longitudinal librations $\psi$ and the latitudinal ones $\eta$ are found this way: and where $\vec{n}$ is the unit vector normal to the orbit plane, and $\vec{t}$ the tangent to the trajectory. |
We get these last two vectors by: and where ¥ is the position vector of the body. and v its velocity. | We get these last two vectors by: and where $\vec{x}$ is the position vector of the body, and $\vec{v}$ its velocity. |
Finally. the motion of the rotation axis about thepole is derived from the wobble J. it is given by the two variables Qj and Q» defined as: = they are the first two components of the unit vector pointing at the instantaneous North Pole of Mimas! rotation axis. in the body frame of Mimas. | Finally, the motion of the rotation axis about thepole is derived from the wobble $J$, it is given by the two variables $Q_1$ and $Q_2$ defined as: and they are the first two components of the unit vector pointing at the instantaneous North Pole of Mimas' rotation axis, in the body frame of Mimas. |
These quantities are finally multiplied by the polar radius of the satellite. i.e. 190.6 km 2010) to get a deviation in meters. | These quantities are finally multiplied by the polar radius of the satellite, i.e. $190.6$ km \citep{t10} to get a deviation in meters. |
We here present the outputs of our numerical study of the rotation of Mimas. | We here present the outputs of our numerical study of the rotation of Mimas. |
We first give the example of a non-hydrostatic model of Mimas based on its observed shape. then we compare the results with the rotational response of the first 22 models of Tab.2.. obtained in considering Mimas to be in hydrostatic equilibrium. | We first give the example of a non-hydrostatic model of Mimas based on its observed shape, then we compare the results with the rotational response of the first 22 models of \ref{tab:lescas}, obtained in considering Mimas to be in hydrostatic equilibrium. |
As already mentioned. this case is unique. because changes in the size of the core do not affect the ratios of the moments of inertia A/C. and B/C. and the coefficients y, and ys (Eq.17 and 18)). | As already mentioned, this case is unique, because changes in the size of the core do not affect the ratios of the moments of inertia $A/C$, and $B/C$, and the coefficients $\gamma_1$ and $\gamma_2$ \ref{equ:gama1} and \ref{equ:gama2}) ). |
As a consequence. there is a unique rotational behavior of Mimas for any homogenous or 2-layermodel using this specific model based on the observed shape. | As a consequence, there is a unique rotational behavior of Mimas for any homogenous or 2-layermodel using this specific model based on the observed shape. |
The free librations around the equilibrium are assumed to be damped. it is anyway important to know their frequencies Gy. ων and w, (or periods T,. T, and 7,) because they characterize the way the system reacts to external sinusoidal | The free librations around the equilibrium are assumed to be damped, it is anyway important to know their frequencies $\omega_u$ , $\omega_v$ and $\omega_w$ (or periods $T_u$ , $T_v$ and $T_w$ ) because they characterize the way the system reacts to external sinusoidal |
ol 46 davs and then it [aded by 2 mag within 94 davs in all four bancs. | of 46 days and then it faded by $>$ 2 mag within 94 days in all four bands. |
3 outburst state in Jan 2007 was reported by Gupta et ne(0005ο) with Raney 14 Ν being the peak during their run. | An outburst state in Jan 2007 was reported by Gupta et (2008c) with $_{mag}$ $\sim$ 14.98 being the peak during their observing run. |
In our observation span the source reaches a maximum brightness of It — 15.18 mag and then fades to I5 — 17.4 mag. so it seems likely that we have caught this BL Lac in a post-outburst phase. | In our observation span the source reaches a maximum brightness of R = 15.18 mag and then fades to R = 17.4 mag, so it seems likely that we have caught this BL Lac in a post-outburst phase. |
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