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In anv case. if iu Eq. (21)) | In any case, if in Eq. \ref{eq:Cei}) ) |
matrix Cy is substituted for Cy aud one sets then it is a trivial matter to decorrelate 7,5 aud LN,je by aneaus of Eqs. (26))-(27)) | matrix $C_{\xb}$ is substituted for $\Cb_{\chib}$ and one sets then it is a trivial matter to decorrelate $\zh_k$ and $\zh_{N_{\dag} + k}$ by means of Eqs. \ref{eq:norm}) \ref{eq:step3}) ) |
aud to compute the periodograin through Eq. (28)). | and to compute the periodogram through Eq. \ref{eq:step1}) ). |
This result cau be casily exteud to the case where. because of measurement errors. each entry of a has its own variance ση, aud a weighted mica is subtracted from the data sequence Xj=UÜUjS2,uteiNu gie with yy= 1o. | This result can be easily extend to the case where, because of measurement errors, each entry of $\xb$ has its own variance $\sigma^2_{x_j}$ and a weighted mean is subtracted from the data sequence $\chi_j = x_j - \sum _l
\eta_j x_l / \sum_l \eta_l$ , with $\eta_l = 1/
\sigma^2_{x_l}$ . |
Indeed. it is sufficient to substitute Cy as given by Eq. (29)) | Indeed, it is sufficient to substitute $\Cb_{\chib}$ as given by Eq. \ref{eq:chib}) ) |
with ο...σιJL. | with where $\sigmab^2=[\sigma^2_{x_0}, \sigma^2_{x_1}, \ldots, \sigma^2_{x_{N-1}}]^T$. |
The rest of the procedure remains uuniodified. | The rest of the procedure remains unmodified. |
The second cxample consists of zeroaneun colored noise. | The second example consists of zero-mean colored noise. |
The improvement in the quality of the results obtainable with the approach presented in the previous section is visible in Fig. l.. | The improvement in the quality of the results obtainable with the approach presented in the previous section is visible in Fig. \ref{fig:color}. |
The top left panel shows a discrete sigual vj=0.5in(2xfj)|nj. f=0.121. siuulated ou a regular erid of 120 time instauts but with missing data iu the ranges [3170| aud [76115]. | The top left panel shows a discrete signal $x_j
= 0.5 \sin{(2 \pi f j)} + n_j$, $f=0.127$, simulated on a regular grid of $120$ time instants but with missing data in the ranges $[31~70]$ and $[76~115]$. |
Uere. nis the realization of a discrete. zeroanean. colored Loise process Whose autocovariance function ix elven iu he top right panel. | Here, $\nb$ is the realization of a discrete, zero-mean, colored noise process whose autocovariance function is given in the top right panel. |
From the bottom left paucl. it is evideut that periodogram of the original sequence a provides rather ambienous results concerning he presence of a sinusoidal component. | From the bottom left panel, it is evident that periodogram of the original sequence $\xb$ provides rather ambiguous results concerning the presence of a sinusoidal component. |
Ou the other rand. such componeut is well visible in the bottom right ul that shows the periodogran of the sequence| y=CTL1/2X. | On the other hand, such component is well visible in the bottom right panel that shows the periodogram of the sequence $\yb = \Cb_{\nb}^{-1/2} \xb$. |
The formalisua proposed here is also useful iu the context of luore theoretical questions (but with nuportaut practical inplications). | The formalism proposed here is also useful in the context of more theoretical questions (but with important practical implications). |
For example. a point often overlooked in the astronomical literature is the relationship between the periodogram aud the least-squares fit of sine functions. | For example, a point often overlooked in the astronomical literature is the relationship between the periodogram and the least-squares fit of sine functions. |
Often these two methods are believed to be equivalent. | Often these two methods are believed to be equivalent. |
Actually. this is true only when the sampling is regular and the frequencies of the sinusoids are given by theFourier oucs. | Actually, this is true only when the sampling is regular and the frequencies of the sinusoids are given by the ones. |
Indeed. if f;=1j aud fy,=hin. bh=O01...egN—I. then Eq. (13) | Indeed, if $t_j = \tilde{t}_j$ and $f_k = k / N$, $k=0, 1,
\ldots, N-1$, then Eq. \ref{eq:model}) ) |
can be written in the form with and @=[ag.03.....ayyblusu.byil’. | can be written in the form with and $\ab = [a_0, a_1, \ldots, a_{N-1}, b_0, b_1, \ldots, b_{N-1}]^T$. |
The least-squares solution à of svete (32)) is eiven by where πο denotespscudo-inverse (Byorck1996). | The least-squares solution $\bar{\ab}$ of system \ref{eq:ls}) ) is given by where ${}^+$ ” denotes \citep{bjo96}. |
. Iu the case of even suupling. wwhen Fy= aud Fr=Επ. it happens that Iu other words. coefficients [a4] and (bi). as given by the least-squares approach. cau be obtained through the DET of a. because. as shown by means of Eqs. (11)). (S8)8=F | In the case of even sampling, when $\Fmatcb_{\Rmatc} = \Fb_{\Rmatc}$ and $\Fmatcb_{\Imatc} = \Fb_{\Imatc}$, it happens that In other words, coefficients $\{ a_k \}$ and $\{ b_k \}$, as given by the least-squares approach, can be obtained through the DFT of $\xb$, because, as shown by means of Eqs. \ref{eq:orth}) ), $(\Fmatfb \Fmatfb^T)^+ \Fmatfb = \Fmatfb$. |
In the case of uneven saupline. this identitv is not fulfilled. | In the case of uneven sampling, this identity is not fulfilled. |
Αν kind of periodogram coniputed hrough Eq. (22)) | Any kind of periodogram computed through Eq. \ref{eq:irr4}) ) |
and the least-squares fit of sine functions has to be expected to eive different results. | and the least-squares fit of sine functions has to be expected to give different results. |
Moreover. as only uuder the two above-mentioned couditious do the sine fictions constitute au orthonormal basis. the least-squares fit of a single sine fiction per time does not iu general provide the same result as the sinultauecous ft of all the sinusoids as in Eq. (31)) (6.8.SCC1973.page 150).. | Moreover, as only under the two above-mentioned conditions do the sine functions constitute an orthonormal basis, the least-squares fit of a single sine function per time does not in general provide the same result as the simultaneous fit of all the sinusoids as in Eq. \ref{eq:lsfit}) ) \citep[e.g. see][page 450]{ham73}. |
Iu particulu. if an uneveulv- signal is eiven by the contribution of two or mere sa.imsoids. the one-at-a-time fit of a sinele sine functiou provides biased results. | In particular, if an unevenly-sampled signal is given by the contribution of two or more sinusoids, the one-at-a-time fit of a single sine function provides biased results. |
This also holds for the poriodogrsun. which is equivalent to the least-squares fit of a single sinusoid with a specifice frequelcy. with the coustraint that the correspouding cocfiicicuts "a7 and "hb are uncorrelated (Scarele1982:Zeclun | This also holds for the periodogram, which is equivalent to the least-squares fit of a single sinusoid with a specified frequency, with the constraint that the corresponding coefficients $a$ ” and $b$ ” are uncorrelated \citep{sca82, zec09}. |
cisterI&ürster 2009)... As cemoustrated in Sec. 3 | As demonstrated in Sec. \ref{sec:generalization}, |
. when noise has arbitrary statistical characteristics. the commutation of the periodogrami of an unevenulbv-saupled signal requires two steps: The first step. unavoidable even in the case of regular saluplue. is a computationally expensive operation. | when noise has arbitrary statistical characteristics, the computation of the periodogram of an unevenly-sampled signal requires two steps: The first step, unavoidable even in the case of regular sampling, is a computationally expensive operation. |
Therefore. for tine series containing more than a few housand data points. dedicated algorithnis exploitiug he specific structure of C, ooften this matrix is of banded type} have to be developed for implementing Eq. (21 jn | Therefore, for time series containing more than a few thousand data points, dedicated algorithms exploiting the specific structure of $\Cb_{\nb}$ often this matrix is of banded type) have to be developed for implementing Eq. \ref{eq:whitey}) ). |
Tlowever. this problem is bevoud the aim of he present paper. | However, this problem is beyond the aim of the present paper. |
The secoud step is much less time consuuing. | The second step is much less time consuming. |
Indeed. iu the caseof time series containing sole thousands of poiuts and when the periodogram has o be computed on a simular nuuber of frequencies. the direct inipleiieutation of Eqs. (22))-(28)) | Indeed, in the caseof time series containing some thousands of points and when the periodogram has to be computed on a similar number of frequencies, the direct implementation of Eqs. \ref{eq:irr4})\ref{eq:step1}) ) |
results ina few seconds of computation time onlv. | results in a few seconds of computation time only. |
Iu other words. iu uany practical situations. no dedicated aleoritlini is really | In other words, in many practical situations, no dedicated algorithm is really |
html The Balbus-Tawley instability is the most seenerallv applicable iiechanisni known to initiate turbulence aud outward augular momoeutun transport m accretion disks (Balbus Hawley 1991). | The Balbus-Hawley instability is the most generally applicable mechanism known to initiate turbulence and outward angular momentum transport in accretion disks (Balbus Hawley 1991). |
This is a line. local iustabilitv that exists for rotating flows threaded by a weal magnetic field with dO?/dre«0. conditions. satisfied in disks (for earlier discussions see Velikhov 1959. Chandrasekhar 1961). | This is a linear, local instability that exists for rotating flows threaded by a weak magnetic field with ${\rm d} \Omega^2 / {\rm d} r < 0$, conditions satisfied in disks (for earlier discussions see Velikhov 1959, Chandrasekhar 1961). |
A vigorous erowth rate is obtained for a wide variety of initial magnetic Ποια coufiguratious (Balbus Tawleyv 1992: Oevilvie Pringle 1996: Terquem Papaloizou 1996). iuiplving that the instability is inescapable for ionized disks where the field is wellkcoupled to the gas. | A vigorous growth rate is obtained for a wide variety of initial magnetic field configurations (Balbus Hawley 1992; Ogilvie Pringle 1996; Terquem Papaloizou 1996), implying that the instability is inescapable for ionized disks where the field is well-coupled to the gas. |
Extensive nuuerical simulations have explored the 1onlinear development of the iustabilitv within the local. shearing box approxination (for a review. sce e.c. Came 1998). | Extensive numerical simulations have explored the nonlinear development of the instability within the local, shearing box approximation (for a review, see e.g. Gammie 1998). |
Such sunulatious lave couvincingly established hat the nonlinear development of the Balbus-Tawley instability leads to sustained turbulence aud significant aneular moment trausport. typically finding a Shakura-Sunvacy (1973) azm10? Cawley, Gamunie Balbus 1995. 1996: Stone cet al 1996: Braudenbure et al. | Such simulations have convincingly established that the nonlinear development of the Balbus-Hawley instability leads to sustained turbulence and significant angular momentum transport, typically finding a Shakura-Sunyaev (1973) $\alpha \approx 10^{-2}$ (Hawley, Gammie Balbus 1995, 1996; Stone et al 1996; Brandenburg et al. |
1995). | 1995). |
There is some evidence for cvclic behavior that might have iuportaut nuplicatious for disk variability (Draudeuburg oet al. | There is some evidence for cyclic behavior that might have important implications for disk variability (Brandenburg et al. |
1996). | 1996). |
Equally müportaut has been the funal cliniuation of convection (Stone Balbus 1996). aud the rear-clinunation of nonlinear lyvcodvuamic turbulence (Balbus. Tlawley Stone 1996). as plausible rival nechanisias for angular momentum transport in accretion disks. | Equally important has been the final elimination of convection (Stone Balbus 1996), and the near-elimination of nonlinear hydrodynamic turbulence (Balbus, Hawley Stone 1996), as plausible rival mechanisms for angular momentum transport in accretion disks. |
Progress has also been made in tryiug to understand row the rich. phenomenology of accretion disk variability can arise within a dynamo driven disk model (Armitage. Livio Pringle 1996: Game Moenou 1998). although uuch more remaius to be done in this area. | Progress has also been made in trying to understand how the rich phenomenology of accretion disk variability can arise within a dynamo driven disk model (Armitage, Livio Pringle 1996; Gammie Menou 1998), although much more remains to be done in this area. |
There are many further questions that one may hope simulations will address. aud not all of them are amcuable to a local treatiment. | There are many further questions that one may hope simulations will address, and not all of them are amenable to a local treatment. |
Most obvioush. is the angular mionentun transport in a disk locally determined? | Most obviously, is the angular momentum transport in a disk locally determined? |
What is the structure of the spatial and time variability of the disk fields. aud are they suitable for launchius a magnetically driven disk wind or jet? | What is the structure of the spatial and time variability of the disk fields, and are they suitable for launching a magnetically driven disk wind or jet? |
Uusurprisinely. the elobal calculations needed to investigate these issues are extremely demanding. both as a consequence of the larecr conrutational domain aud. especially, because of the ueed to simulate regions of low density where the high Alfvéun speed severely hits the timestep of explicit umuerical codes. | Unsurprisingly, the global calculations needed to investigate these issues are extremely demanding, both as a consequence of the larger computational domain and, especially, because of the need to simulate regions of low density where the high Alfvénn speed severely limits the timestep of explicit numerical codes. |
Tn this paper. results are presented from a vertically uustratified global simulation of accretion disk turbulence. | In this paper, results are presented from a vertically unstratified global simulation of accretion disk turbulence. |
Such a calculation is evideutly missing esseutial plivsics. | Such a calculation is evidently missing essential physics. |
There is no buovancy. no possibility of Parker instability (Parker 1979). and no magnetically dominated disk corona all features that are expected to arise iu a full disk model and which may be crucial for the disk dynamo problem (Tout Pringle 1992). | There is no buoyancy, no possibility of Parker instability (Parker 1979), and no magnetically dominated disk corona – all features that are expected to arise in a full disk model and which may be crucial for the disk dynamo problem (Tout Pringle 1992). |
ITowever the lesser computational demands pernut a preliminary investigation of some of the inportant questions raised by previous. local. simulations. | However the lesser computational demands permit a preliminary investigation of some of the important questions raised by previous, local, simulations. |
The equations of ideal maguetolhydrodvuamics (MIID) are solved. uxiug the ZEUS-3D code developed by the Laboratory for Computational Astrophysics (Clarke. Norman Fiedler 1991: Stone Norman 1992a. 1992h). | The equations of ideal magnetohydrodynamics (MHD) are solved using the ZEUS-3D code developed by the Laboratory for Computational Astrophysics (Clarke, Norman Fiedler 1994; Stone Norman 1992a, 1992b). |
ZEUS is a time explicit culerian finite difference code that uses the method of characteristics (MoC') constrained transport scheme to evolve the magnetic fields (Lawley Stone 1995: Stone Norman L992). | ZEUS is a time explicit eulerian finite difference code that uses the method of characteristics (MoC) – constrained transport scheme to evolve the magnetic fields (Hawley Stone 1995; Stone Norman 1992b). |
For this simulation an isothermal equation of state Po=pe? replaces the internal energv equation. so the remaining equations are: | For this simulation an isothermal equation of state $P = \rho c_s^2$ replaces the internal energy equation, so the remaining equations are: |
including the models with lower T, and lower logg that seem to be preferred by the photometry¢¢ (right panel of Figure 4)). | including the models with lower $T_{eff}$ and lower $\log{g}$ that seem to be preferred by the photometry (right panel of Figure \ref{fig-4}) ). |
Since we have already ruled out a DA WD companion of similar temperature, we expect the shape of the higher order Balmer lines to be a reliable probe of the mass of12574-5428,, even if the underlying continuum is somewhat distorted. | Since we have already ruled out a DA WD companion of similar temperature, we expect the shape of the higher order Balmer lines to be a reliable probe of the mass of, even if the underlying continuum is somewhat distorted. |
'The spectral models shown in Figure 7 translate into masses between 0.60 and 1.20Mo, which we will adopt as conservative lower and upper limits to My. | The spectral models shown in Figure \ref{fig-7} translate into masses between $0.60$ and $1.20\,\mathrm{M_{\odot}}$, which we will adopt as conservative lower and upper limits to $M_{A}$. |
It is unfortunate that the poor performance of the spectral models in this temperature range does not allow for a more accurate measurement of MA, but we believe that our estimate is reasonable, and probably the best that can be done with current tools. | It is unfortunate that the poor performance of the spectral models in this temperature range does not allow for a more accurate measurement of $M_{A}$, but we believe that our estimate is reasonable, and probably the best that can be done with current tools. |
We note that the models we contemplate here span a range of logg values around the best-fit solution that is comfortably larger than the reported increase (30.5)for T,;;«12000 K (~0.2,Kepleretal.2007;Bergeron 2007).. | We note that the models we contemplate here span a range of $\log{g}$ values around the best-fit solution $\pm 0.5$ ) that is comfortably larger than the reported increase for $T_{eff}<12000$ K \citep[$\sim
0.2$,][]{kepler07:WD_mass_distribution,bergeron07:mass_distribution_WDS}. |
Also, ourlower limit to MA is close to the mean mass of DA WDs with Tepe212000 K (0.58Mo,2007), which would be the best guess for the mass of a WD in absence of any spectral or photometric information. | Also, ourlower limit to $M_{A}$ is close to the mean mass of DA WDs with $T_{eff} \geq 12000$ K \citep[$0.58\,\mathrm{M_{\odot}}$, which would be the best guess for the mass of a WD in absence of any spectral or photometric information. |
For all these reasons, we are confident that the true mass of llies within the range of values that we propose here. | For all these reasons, we are confident that the true mass of lies within the range of values that we propose here. |
For comparison purposes, the best-fit hot spectral model (Tegg=35000 K, logg= translates into a value of 0.45Mefor My. | For comparison purposes, the best-fit hot spectral model $T_{eff}=35000$ K, $\log{g}=7.5$ ) translates into a value of $0.45\,\mathrm{M_{\odot}}$for $M_{A}$. |
With the set 7.5)of limiting spectral models around the best-fit cold solution shown in Figure 4,, the Holberg&Bergeron curves yield a cooling age of 2.0+1.0 Gyr. | With the set of limiting spectral models around the best-fit cold solution shown in Figure \ref{fig-4}, the \citeauthor{holberg06:WD_models_photometry} curves yield a cooling age of $2.0\pm1.0$ Gyr. |
The absolute g magnitude is 19.4104, which results in a distance of D=48719 pc for1257+5428.. | The absolute $g$ magnitude is $13.4^{+1.1}_{-0.4}$, which results in a distance of $D=48^{+10}_{-19}$ pc for. |
Combining our estimate for the mass of ((Ma=0.924035 Mo) with the values of P (4.5550+0.0007 hr) and X4 (322.74-6.3km s) derived in Section 3.2, we obtain Mpsin(i)=1.62*029Mo for its unseen companion, with Mg and the inclination angle { being degenerate as in all single-lined binaries. | Combining our estimate for the mass of $M_{A}=0.92^{+0.28}_{-0.32}\,\mathrm{M_{\odot}}$ ) with the values of $P$ $4.5550 \pm 0.0007$ hr) and $K_{A}$ $322.7 \pm 6.3\,\mathrm{km\,s^{-1}}$ ) derived in Section \ref{subsec:orbit}, , we obtain $M_{B}\sin(i)=1.62^{+0.20}_{-0.25}\,\mathrm{M_{\odot}}$ for its unseen companion, with $M_{B}$ and the inclination angle $i$ being degenerate as in all single-lined binaries. |
A plot of the companion mass as a function of cos(i) is shown in Figure 8.. | A plot of the companion mass as a function of $\cos(i)$ is shown in Figure \ref{fig-8}. |
We stress that the properties of the RV curve alone require a massive companion, regardless of the estimated value for M4: Mg must be more massive than 0.66Mo even for M4=0 (ie, assuming the value of MA is negligible for the dynamics of the system), and more massive than 1.08M, for M4=0.3Mo. | We stress that the properties of the RV curve alone require a massive companion, regardless of the estimated value for $M_{A}$: $M_{B}$ must be more massive than $0.66 \,
\mathrm{M_{\odot}}$ even for $M_{A}=0$ (i.e., assuming the value of $M_{A}$ is negligible for the dynamics of the system), and more massive than $1.08 \, \mathrm{M_{\odot}}$ for $M_{A}=0.3 \, \mathrm{M_{\odot}}$. |
With any reasonable range of masses for the primary, a nondegenerate stellar companion would have a spectral type G or earlier, which is clearly incompatible with the observations of1257+5428. | With any reasonable range of masses for the primary, a nondegenerate stellar companion would have a spectral type G or earlier, which is clearly incompatible with the observations of. |
. The companion must therefore be a compact object, either another WD, a NS or a BH. | The companion must therefore be a compact object, either another WD, a NS or a BH. |
Could the companion be a WD? | Could the companion be a WD? |
We have not been able to discard this possibility from the point of view of the optical spectrum alone, but the properties of the RV curve make it very unlikely. | We have not been able to discard this possibility from the point of view of the optical spectrum alone, but the properties of the RV curve make it very unlikely. |
The companion could only be a WD if our mass estimate for M4 was completely off, and even then, it would have to be a very massive object 1.0Μς for any reasonable value of MA), cool object, (abovewithout any prominent absorption lines (see discussion in Section 3.3.0)). | The companion could only be a WD if our mass estimate for $M_{A}$ was completely off, and even then, it would have to be a very massive object (above $1.0 \,
\mathrm{M_{\odot}}$ for any reasonable value of $M_{A}$ ), cool object, without any prominent absorption lines (see discussion in Section \ref{subsubsec:poorfits}) ). |
Such massive WDs are extremely rare. | Such massive WDs are extremely rare. |
But we have found no evidence to indicate that the shape of the Balmer lines in the spectrum of iis distorted in any way, so there is no reason to doubt our conservative estimate for M4. | But we have found no evidence to indicate that the shape of the Balmer lines in the spectrum of is distorted in any way, so there is no reason to doubt our conservative estimate for $M_{A}$. |
If this estimate holds, assuming the smallest possible value of M4 (0.6 Mo), the orbit would have to be nearly edge-on (i> 82°) for Mg to be below the Chandrasekhar limit Mg. | If this estimate holds, assuming the smallest possible value of $M_{A}$ $0.6\,\mathrm{M_{\odot}}$ ), the orbit would have to be nearly edge-on $i \geq 82^\circ$ ) for $M_{B}$ to be below the Chandrasekhar limit $M_{Ch}$ . |
This inclination is expected to happen randomly in only 1496of binary systems, but ddoes have a strong observational bias towards finding high inclination systems. | This inclination is expected to happen randomly in only $14\%$of binary systems, but does have a strong observational bias towards finding high inclination systems. |
Even then, the companion would be more massive than the largest known WDs(1.33to Mo, 1995). | Even then, the companion would be more massive than the largest known WDs\citep[$1.33$ to $1.35\,\mathrm{M_{\odot}}$ , . |
In this unlikely circumstance, the | In this unlikely circumstance, the |
confined iu size aud uever reach the overlap phase that defines the epoch of reiouization. | confined in size and never reach the overlap phase that defines the epoch of reionization. |
The simulation data shown in this paper is the higher resolution ruu in ROSO2b. evolved further to redshift z=8.0 after the introduction of a bright source of ionizing radiation tliat completes relouization al z9 (see RGOS lor details). | The simulation data shown in this paper is the higher resolution run in RGS02b, evolved further to redshift $z=8.0$ after the introduction of a bright source of ionizing radiation that completes reionization at $z \sim 9$ (see RG05 for details). |
The ueed for introduciug a bright ionizatiou source is dictated by the simall volume of the simulation (1.5° MNpc*): otherwise the volume would be reionized too late. | The need for introducing a bright ionization source is dictated by the small volume of the simulation $1.5^3$ $^3$ ); otherwise the volume would be reionized too late. |
The ionizing source removes all the remaining gas from halos with ve<20 kimi and shuts down star formation. | The ionizing source removes all the remaining gas from halos with $v_c<20$ km $^{-1}$ and shuts down star formation. |
Here we compare the RC» predictions for tlie fossils of primordial galaxies to the observed properties (see Table 1)) of the new Milky Way aud M31 dwarls. | Here we compare the RG05 predictions for the fossils of primordial galaxies to the observed properties (see Table \ref{tab:one}) ) of the new Milky Way and M31 dwarfs. |
The symbols aud lines in Figs. 1- | The symbols and lines in Figs. \ref{Kor}- |
-6 have the following meanings. | \ref{ZS} have the following meanings. |
All known Milky Way dSphs are shown by circles: Ancromecda’s dSplis satellites are shown by triangles: simulated fossils are shown by the small solid squares. | All known Milky Way dSphs are shown by circles; Andromeda's dSphs satellites are shown by triangles; simulated fossils are shown by the small solid squares. |
The solic auc open symbols refer to previously kuowu aud new cdSplis. respectively. | The solid and open symbols refer to previously known and new dSphs, respectively. |
The trausition betwee fossils and non-fossil galaxies is gradual. | The transition between fossils and non-fossil galaxies is gradual. |
La order to illustrate the different. statistical treuds of "non-[fossil galaxies we show dwarf irregulars (dlrrs) with asterisks aud the dwarf ellipticals (dE as Crosses. and we show the statistical trends for more luminous galaxies as thick dashedlines oi the right side of each panel. | In order to illustrate the different statistical trends of “non-fossil” galaxies we show dwarf irregulars (dIrrs) with asterisks and the dwarf ellipticals (dE) as crosses, and we show the statistical trends for more luminous galaxies as thick dashedlines on the right side of each panel. |
Figure 1 shows how the surface brightuess (top panel) and half light radius (bottom pauel) of all known Milky Way and Audromeca satellites as a function of V-baud luminosity compares to the simulated fossils. | Figure \ref{Kor} shows how the surface brightness (top panel) and half light radius (bottom panel) of all known Milky Way and Andromeda satellites as a function of V-band luminosity compares to the simulated fossils. |
The surface brightness limit of the SDSS is shown by the thin solid lines in botl pauels of the figure. | The surface brightness limit of the SDSS is shown by the thin solid lines in both panels of the figure. |
The new dwarfs agree with the predictious up to this tlireshold. suggesting the possible existence of an uudetected population of dwarls with X4: below the SDSS seusitivity limit. | The new dwarfs agree with the predictions up to this threshold, suggesting the possible existence of an undetected population of dwarfs with $\Sigma_{V}$ below the SDSS sensitivity limit. |
The new M31 satellites have properties similar to their previously known Milky Way counterparts(e.g... Ursa Minor aud Draco). | The new M31 satellites have properties similar to their previously known Milky Way counterparts, Ursa Minor and Draco). |
Given the similar lost masses anc environments. is reasonable to assume a similar [formation history [or the halos of M31 aud the Milky Way. | Given the similar host masses and environments, is reasonable to assume a similar formation history for the halos of M31 and the Milky Way. |
This suggestsMOD the existence of au undiscovered population dwarls orbiting M31 equivalent to the new SDSS clwarts. | This suggests the existence of an undiscovered population dwarfs orbiting M31 equivalent to the new SDSS dwarfs. |
The large mass outflows due to photo-heatiug by massive stars and the consequeut suppression oL star formation after an initial burst. make reiouization [ossils among the most dark matter dominated objects in the universe. with predicted M/L ratios as high as 10! and Ly~10*—10! L.. . | The large mass outflows due to photo-heating by massive stars and the consequent suppression of star formation after an initial burst, make reionization fossils among the most dark matter dominated objects in the universe, with predicted M/L ratios as high as $10^4$ and $L_V \sim
10^3-10^4$ $_{\odot}$ . |
distributions as described in Minton&Malhotra(2009)... | distributions as described in \cite{Minton:2009p280}. |
This is likely due to the effects of (he sweeping r4; inclination-longitude of ascending node secular resonance. analogous to the sweeping 5j eccentricitv-pericenter secular resonance (hat we analvzed in the present studs; | This is likely due to the effects of the sweeping $\nu_{16}$ inclination-longitude of ascending node secular resonance, analogous to the sweeping $\nu_6$ eccentricity-pericenter secular resonance that we analyzed in the present study. |
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