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2.4 Comparison with Bonanos et al. ( 2004 As discussed in section 2.1, our survey of Draco is nearly four times larger in area and twice the number of variable stars as were found than in Bonanos et al. ( 2004 ’s survey. Because of a match up error in preparing their tables, the periods, magnitudes, and the identificat... |
Data Analysis Once the datasets from USNO and WIRO were independently reduced, the data were combined. This increased the number of epochs for 103 variable stars. Using our combined datasets, we present a robust CMD of the Draco dSph galaxy down to a limiting magnitude of [MATH] in figure |
. In this updated CMD, we have identified pulsating and eclipsing stars as well as background QSOs in the Draco field. Our census has yielded 279 stars that are either of the RR Lyrae or Cepheid type of pulsating variable star. We have found 12 variable stars which were not RRL, anomalous Cepheids, or eclipsing stars, ... |
The subsequent analysis was done in four steps: 1) period searching, 2) amplitudes and mean magnitudes calculation, 3) Fourier decomposition of the light curves, and 4) deriving distances from the RRL population. The Fourier decomposition work is discussed in detail in section 4.2. |
For the full dataset, we anticipated minimizing any period alias solutions, specifically any yearly aliases. Our primary period searching method was the date compensated discrete Fourier transform (DCDFT) program (Ferraz-Mello 1981 ; Foster 1995 . This program was particularly useful for datasets that have a patchy dis... |
(Foster 1995 . An updated version of this program is available through Peranso . As a check for the period solutions, the IRAF version of the phase dispersion minimization statistic (PDM) (Stellingwerf 1978 was used as well as the Supersmoother routine (Reimann 1994 . Overall our periods are good to about 0.00001 to 0.... |
Variable Star Census 4.1 RR Lyrae Stars Figure shows the phased [MATH] and [MATH] light curves. The [MATH] light curves have our best spline fit included to aid the eye. Fourier series fits to our light curves were not used because they often give biassed results at rapidly changing phases (rising and maximum light) if... |
The Variable Stars of the Draco Dwarf Spheroidal Galaxy - Revisited lists the RRL positions (RA and DEC J2000.0), the period solutions (column 4), the [MATH] amplitude (column 5), the intensity-weighted mean magnitudes in [MATH] and [MATH] (columns 6 and 7), and the type of RRL with additional notes (column 8). We find... |
Foreground RRL have been found in our survey. Using the surface density for RRL in the SA57 field (Kinman et al. 1994 , and assuming a halo space density of [MATH] , we calculated the volume and RRL per magnitude along our line of sight. From the calculation, we expected 0.9 field RRL in the line of sight, but in actua... |
4.1.1 Double-Mode RR Lyrae Stars Goranskij ( 1982 used the photometry of Baade & Swope ( 1961 to identify three RR Lyrae stars in Draco that were pulsating simultaneously in the first overtone and fundamental radial modes. Also using the Baade & Swope ( 1961 |
observations, Nemec ( 1985a identified seven more of these stars (RRd variables in Nemec’s nomenclature, or RR01 stars in the nomenclature of Clement et al. 2001 Bonanos et al. ( 2004 redetermined periods for six of the RRd stars found by Nemec ( 1985a |
We carried out a search for double-mode behavior among the RR Lyrae stars that had light curves that did not seem to be adequately described by a single period. Using the CLEANest routine (Foster 1995 to prewhiten the V-band observations, we removed the primary frequency and its first four harmonics. A search was then ... |
By this means we found all ten of the RRd stars identified by Goranskij ( 1982 and Nemec ( 1985a . In addition, we have identified 16 probable RRd variables, giving a total of 26. The first overtone mode was the dominant mode in each case. First overtone mode periods, fundamental mode periods, and period ratios for pro... |
In plotting the Petersen diagram (Petersen 1973 of period ratio versus fundamental period, Nemec ( 1985a discovered that V165 had a position in this diagram similar to those seen among RRd stars in Oosterhoff type I globular clusters, but that all of the other stars had properties similar to those of RRd stars in Ooste... |
Figure plots the luminosity weighted mean V magnitude against the primary period for all of the Draco RR Lyrae stars. V165, the sole Oosterhoff type I RRd star, is also the faintest RRd star. This is at least qualitatively consistent with other findings that RR Lyrae stars in Oosterhoff type I clusters are less luminou... |
(e.g., Sandage 1958 ; Sandage et al. 1981 4.1.2 Blazhko Effect The Blazhko effect is a second order modulation most evident in the shape of the RRL light curve. The maximum light phase can be depressed by the Blazhko effect. This effect is also periodic – on the order of tens to hundreds of days. What causes the Blazhk... |
(see Kolenberg et al. 2006 ; Stothers 2006 We do not have enough observations to determine Blazhko periods for those RRL stars in our sample that show the Blazhko effect. We can, however, identify as Blazhko effect candidates those RRL stars that have unusually large scatter in their light curves and which do not seem ... |
The Variable Stars of the Draco Dwarf Spheroidal Galaxy - Revisited by noting “Bl” in the last column. Stars V26, V33, V34, V35, V37, V39, V41, V68, V75, V96, V123, V129, V147, V150, V160, V184, and V196 have already been identified as possible Blazhko variables by |
Nemec ( 1985a and Bonanos et al. ( 2004 . The mean period of the Blazhko effect candidates among the RRab stars is [MATH] days. 4.2 Fourier Decomposition |
The Fourier decomposition of the light curves was done only on the [MATH] data. Using Simon’s MINFIT program (Simon 1979 ; Simon & Teays 1982 , a cosine series up to 8th order was fit to the light curves: |
[EQUATION] Once the amplitude ( [MATH] ) and phase ( [MATH] ) terms were obtained, the Fourier parameters, [MATH] and [MATH] , were calculated up to the 4th order. |
We applied the Jurcsik & Kovacs ( 1996 photometric metallicity relation using the Fourier decomposition parameter [MATH] and the period (their equation 3). The Jurcsik & Kovacs method works best when RRab light curves are fully sampled and where photometric uncertainties are relatively small. The light curves for indiv... |
[MATH] deviation parameter, is calculated. This deviation parameter is determined from a comparison of the observed and predicted Fourier parameters. An updated version of this test is provided in |
Kovacs & Kanbur ( 1998 . In order for a star to be a good candidate for the Jurcsik & Kovacs method, the [MATH] parameter criterion must be met. For our RRab sample, we chose [MATH] (as recommended by Jurcsik & Kovacs) and [MATH] |
(as recommended by Clement & Shelton 1999 . Stars that have passed the criteria are listed in Table with asterisks. Table also lists the Fourier decomposition parameters and photometric metallicities of the Draco RRab stars. All photometric metallicities on are the metallicity scale of the Jurcsik & Kovacs method (Jurc... |
The [Fe/H] values derived from the Jurcsik & Kovacs method may in this case be more useful in deriving a mean [Fe/H] value for Draco than in the determination of metallicities for individual stars. It is quite likely that some of the outlying [Fe/H] values in Table |
, at both the high and low end do not really reflect the metallicities of the stars for which they are derived. The average [Fe/H] for Draco, as determined by the photometric metallicities of the RRab stars, is [MATH] , if we assume the stars are not undergoing the Blazhko effect (see section 4.1.1) and have passed the... |
shows the metallicity distribution of the RRab stars that have passed the [MATH] criterion with respect to period. Using Stromgren photometry, Faria et al. ( 2007 recently obtained a mean [MATH] of [MATH] for Draco and field red giant branch stars, with most stars falling within the limits [MATH] . That result is broad... |
Shetrone et al. ( 2001b and Zinn ( 1978 , although Shetrone et al. did find one red giant star as metal poor as [MATH] Faria et al. ( 2007 calibrated their derived metallicities to the work of |
Hilker ( 2000 , which analyzed the red giants of three globular clusters and spanned a metallicity range of [MATH] to 0.0 dex. Therefore, we must be cautious when comparing out metallicity results to those of other studies since there are dependencies to various metallicity calibrations. However, there is a suggestion ... |
4.3 RRL distance for Draco Since RRL are excellent distance indicators, we calculate the distance to the Draco dwarf galaxy. We use the metal-poor ( [MATH] ) relation from |
Cacciari & Clementini ( 2003 (their equation 4). As with Bonanos et al.’s work, we use an [MATH] from the Schlegel et al. ( 1998 reddening maps, and the corrections for the extinction as suggested by the work of |
Cardelli et al. ( 1989 , thus, [MATH] . From our sample of RRL stars, the intensity-weighted mean V magnitude is [MATH] [MATH] ). For this value, we omitted the magnitudes of the foreground RRL (V276, V321, and V327) and V176 since it is blended with a bright star. The uncertainties given for this mean magnitude accoun... |
If we assume a metallicity for Draco from our Fourier decomposition analysis, [MATH] , and using the Cacciari & Clementini ( 2003 relation, our resultant absolute magnitude is [MATH] Therefore, using the present mean [MATH] magnitude of the RRL stars and accounting for the extinction, we derive a dereddened distance mo... |
Shetrone et al. ( 2001b obtained a mean metallicity of [MATH] from high resolution spectroscopy of Draco red giants, whereas Faria et al. ( 2007 found [MATH] . If we assume the metallicity values of [MATH] and [MATH] , and using the same Cacciari & Clementini relation and the present RRL mean [MATH] magnitude, the resu... |
4.4 Anomalous Cepheids In our study of the Draco dwarf galaxy, we increase the number of known anomalous Cepheids (AC) to nine. Baade & Swope ( 1961 had identified what appeared to be five overly bright RR Lyrae stars in their original survey. Norris & Zinn ( 1975 , followed by |
Zinn & Searle ( 1976 first classified these variables as AC stars (V134, V141, V157, V194, and V204). Nemec et al. ( 1988a reidentified the five stars in Draco as AC, based on a reanalysis of B&S’s photographic survey. These five AC stars were confirmed in our study. We have been able to add four new AC’s: V31, V230, V... |
Of the new anomalous Cepheids, one star, V31, has been reclassified. Originally, it was identified by B&S as an RRL variable star based on eye estimates only. However, it lies only 13” from a bright BD star. The [MATH] and the [MATH] color are particularly uncertain because of scattered light from the nearby bright red... |
Generally, these variable stars are brighter than the RRL population by 0.5 (for shorter period, [MATH] days) to 2 magnitudes (longer period, [MATH] days). These stars are also more massive than the RRL, typically 1.0-2.0 [MATH] |
(Pritzl et al. 2002a , and references therein) , and must be relatively metal-poor in order for the progenitor stars to reach the instability strip. Anomalous Cepheids have been found in all the known dwarf spheroidal galaxies of the Local Group, however, they are not typically found in the Galactic globular clusters. ... |
(Zinn & Dahn 1976 and two candidates in [MATH] Cen (Wallerstein & Cox 1984 . XZ Ceti is a well known field AC. The origins of these stars still remains unsolved, but the leading theories suggest that they are either 1) intermediate aged stars ( [MATH] Gyrs) or 2) primordial binary systems undergoing mass transfer. Thes... |
Recently, Momany et al. ( 2007 investigated the frequency of blue straggler stars in the Local Group dSph population, compared to the frequency of such stars in Galactic globular clusters, open clusters, and the field. They find that, in general, the blue straggler frequency is higher in dSph galaxies than in globular ... |
Anomalous Cepheids of dSph galaxies have also been used to create a period-luminosity (P-L) relation. Recent work by Dall’Ora et al. ( 2003 |
Pritzl et al. ( 2002a , and Nemec et al. ( 1994 have presented empirical anomalous Cepheid P-L relations associated with the pulsational mode. Both empirical and theoretical P-L relations have shown that they are not parallel |
(Pritzl et al. 2002a ; Bono et al. 1997 . However, there is still some question as to whether the two apparent P-L relations are real, due to distinct fundamental and first-overtone mode relations, or whether the results might instead be interpreted as a single P-L relation with large scatter. That scatter might be a r... |
For the Draco AC sample, we applied the empirical P-L relations of Pritzl et al. ( 2002a to see whether the location of the additional Draco stars would support the reality of two distinct P-L relations. We have calculated absolute magnitudes for the Draco AC stars assuming a distance modulus of [MATH] and an |
[MATH] (Pritzl et al. 2002a in order to incorporate our results with their empirical P-L relations. Figure 11 shows the location of the Draco AC stars with respect to the AC stars found in other Local Group dwarf galaxies. We see that most of the Draco ACs (V31, V141, V157, V194, V230, V282, and V312) fall along the P-... |
4.5 Other Variable Stars Three categories of variable stars other than RR Lyraes and Cepheids appear in our data: two eclipsing binaries, 30 “bluish long-period variables”, 12 red semi-regular or irregular variables, and carbon stars have been found and are listed in Tables |
The Variable Stars of the Draco Dwarf Spheroidal Galaxy - Revisited and 10 . The following subsections discusses each of these types of stars. |
4.5.1 Eclipsing Binary Stars A field eclipsing binary star (V296) was found in the survey completed by Bonanos et al. ( 2004 , which we have recovered in our work. We agree with their period solution for this star with a period of 0.2435 days. Figure 12 shows the light curve of V296 phased to this period. Additionally,... |
The Variable Stars of the Draco Dwarf Spheroidal Galaxy - Revisited , we provide two plausible period solutions. However, to truly confirm the nature of this eclipsing binary, a careful follow up will be needed to arrive at the correct period. |
4.5.2 Carbon Stars A population of stars redward of the red giant branch (RGB) have been often identified as carbon stars (Aaronson et al. 1983 . There are six carbon stars known in Draco (C1-C3 Aaronson et al. 1982 |
(C4 Azzopardi et al. 1986 (C5 Armandroff et al. 1995 (C6 Shetrone et al. 2001a . We find the stars C1, C2, and C5 to be variable with [MATH] amplitudes close to 0.2 mag. Stars C3, C4, and C6 do not appear to vary during two seasons of observations at USNO. Shetrone et al. also reported C2 as a definite variable, and C5... |
The unusual nature of star C1 was noted by Aaronson et al. ( 1982 and by Margon et al. ( 2002 from their independent study of the star in a spectrum from the Sloan Digital Sky Survey. The strong emission lines of hydrogen and helium, the blue continuum flux, and the X-ray emission indicate it is a symbiotic carbon star... |
4.5.3 Long Period Variables and QSOs The characteristics of the bluish long-period variables are slow variability, no apparent period, amplitudes typically 0.25 mag, colors blueward of the Draco giant branch, and no clear concentration toward Draco. These characteristics suggest that most of them are background QSOs, a... |
B&S remarked on the lack of red variables found in Draco. Bonanos et al. ( 2004 showed there are variables among the stars near the tip of the giant branch, as is also shown in Figure Our 12 red variables are mostly of low amplitude, and the amplitudes must have been just below the threshold for detection by B&S. We no... |
Distinguishing between background QSOs and red variables in Draco is not always obvious, however, because QSOs sometimes can be red, and some Draco variables might be bluish and without regular periods. For example, UU Her and RV Tauri stars are found in globular clusters and could be confused here with our limited dat... |
(Schneider et al. 2005 . Eight additional variables with similar characteristics are listed in Table 10 as probable QSOs. The prototype of the QSOs behind Draco, V203, was found by B&S and given in their Table VII, and the light curve spanning over six years was shown in their Fig. 8. They did not understand its nature... |
(Schmidt 1963 ; Matthews & Sandage 1963 Draco and the Oosterhoff dichotomy Oosterhoff ( 1939 found that five RR Lyrae-rich globular clusters could be divided into two groups, now known as Oosterhoff groups, on the basis of the properties of their RR Lyrae stars. Subsequent investigations found that almost all of the Mi... |
(see, for example Smith 1995 . However, not all systems show the Oosterhoff dichotomy. In contrast to the Milky Way globular clusters, dwarf spheroidal systems often have Oosterhoff intermediate properties (for recent discussions, see Pritzl et al. 2002a ; Catelan 2004 2005 |
The mean period of RRab stars in Draco found here, [MATH] , seems to confirm its Oosterhoff intermediate nature. However, a detailed inspection of the the properties of its RRL suggests a complicated picture. The Draco period-amplitude (Bailey) diagram (Figure 14 ) is consistent with an Oosterhoff intermediate classifi... |
Cacciari et al. ( 2005 are used instead of those of Clement & Rowe ( 2000 . The Cacciari et al. ( 2005 lines are based on the period-amplitude distribution of RRab, some of which are evolved along the horizontal branch, of M3. In the Milky Way, a metallicity of [MATH] would be typical of globular clusters of Oosterhoff... |
It is plausible that the discordant Oosterhoff properties of the Draco RRL are in some way related to the overall distribution of stars across its horizontal branch. Draco has a HB redder than found among ordinary Oosterhoff II clusters, or among Milky Way globular clusters having |
[MATH] (see for example Catelan 2005 . It has been proposed (Lee et al. 1990 ; Clement & Shelton 1999 ; Clement et al. 2001 that many RRL in Oosterhoff type II systems have evolved into the blue part of the instability strip from ZAHB positions. The paucity of blue HB stars in Draco makes it unlikely that the majority ... |
According to the [MATH] -cold dark matter hierarchical model, the outer halo has been assembled partly due to the accretion of objects like the Local Group dwarf galaxy population. However, almost no globular clusters of the Galaxy have Oosterhoff intermediate properties. Nor does the field RRL population of the halo r... |
Shetrone et al. ( 2001a and Pritzl et al. ( 2005 found that the patterns of elemental abundances in the dwarf spheroidal galaxies were distinct from those in globular clusters and halo field stars. However, Bellazzini et al. ( 2002 |
argue that objects like Draco could still be considered as a building block if we consider that the accretion may have occurred early in the star formation history of the dwarf galaxy or during an early episode of gas stripping by the Galaxy. Our findings with Draco at least imply that objects like this dwarf galaxy co... |
Summary We have presented the latest census of variable stars of the Draco dwarf spheroidal galaxy. We have found 81 new RRab stars, 8 new RRc stars, and 16 probable new RRd stars, thus bringing to 214 RRab, 30 RRc and 26 RRd the total number of RRL stars of the different types known in Draco. We have increased the num... |
The anomalous Cepheids in the Draco dSph galaxy show a possible dual P-L relation stemming from the pulsational modes of the stars. However, with so few stars populating the first-overtone relation, we cannot say with certainty that two P-L relation alternative is the only one capable of describing the relationships of... |
This research used the facilities of the Canadian Astronomy Data Centre operated by the National Research Council of Canada with the support of the Canadian Space Agency. The identification of QSOs is based partly on spectra obtained with the Hydra multifiber spectrograph on the WIYN telescope at Kitt Peak National Obs... |
# Source: arxiv 0808.2611 # Title: The Evolution of L and T Dwarfs in Color-Magnitude Diagrams # Sections: all # Downloaded: 2026-03-02T07:58:13.654799+00:00 |
The Evolution of L and T Dwarfs in Color-Magnitude Diagrams Abstract We present new evolution sequences for very low mass stars, brown dwarfs and giant planets and use them to explore a variety of influences on the evolution of these objects. While the predicted adiabatic evolution of luminosity with time is very simil... |
The L- to T-type ultracool dwarf transition can be accommodated within the Ackerman & Marley ( 2001 cloud model by varying the cloud sedimentation parameter. We develop a simple model for the evolution across the L/T transition. By combining the evolution calculation and our atmosphere models, we generate colors and ma... |
stars: low mass, brown dwarfs — stars: evolution — stars: atmospheres Introduction There are now approximately 450 L dwarfs and 100 T dwarfs known (see Kirkpatrick ( 2005 for a review of these spectral classes). They span effective temperatures from about 2400 to 700 K and exhibit a range of gravities, metallicities, a... |
To enable such comparisons using our own model atmosphere effort and to pursue a more complete analysis of spectroscopic and photometric data, we have developed a code to compute evolution sequences of low mass stars, brown dwarfs and giant planets. These evolution sequences have already been applied extensively to the... |
We discuss several potentially observable features in near-infrared CMDs that would illuminate the evolution of brown dwarfs as well as the nature of L/T transition. |
Evolution model: Assumptions and physical inputs The evolution model assumes adiabatic cooling of spherical, hydrostatic, non-magnetic, non-rotating brown dwarfs. The adiabatic assumption is valid for dense fully convective structures and objects with masses ranging from [MATH] down to Saturn’s mass can be modeled. In ... |
2.1 Electron Conduction The effects of electron conduction on the cooling of old brown dwarfs, pointed out by Chabrier et al. ( 2000a , are not included in our adiabatic calculation. Conduction becomes significant only for the more massive brown dwarfs and at ages greater than about 2 Gyr (Chabrier et al., 2000a Becaus... |
2.2 Thermal Structure and evolution The adiabatic evolution is obtained by solving the mass equation [EQUATION] the equation of hydrostatic equilibrium |
[EQUATION] and the equation of conservation of energy [EQUATION] where the rate of nuclear energy generation is [MATH] and the equation of state (EOS) along an adiabat is [MATH] and [MATH] . In these equations, [MATH] [MATH] [MATH] and |
[MATH] are the density, the pressure, the temperature, and the entropy of the gas, respectively, [MATH] is the luminosity, and [MATH] is the mass interior to radius [MATH] . The equation of conservation of energy controls the evolution time scale as it gives the time step [MATH] between two successive adiabatic structu... |
We use the hydrogen and helium EOSs of Saumon, Chabrier & Van Horn (1995, hereafter SCVH), which was developed specifically for this type of application. This EOS is common to nearly all other evolution and structure calculations of low mass stars, brown dwarfs, extrasolar giant planets, Jupiter and Saturn (e.g. Burrow... |
2.3 Nuclear Energy Generation Nuclear energy generation in low mass stars and brown dwarfs is quite simple and is reduced to one branch of the pp chain (Burrows & Liebert, 1993 |
[EQUATION] and [EQUATION] We use the nuclear reaction cross-sections from the NACRE data base (Angulo et al., 1999 and apply the screening corrections developed by Chabrier which include both ionic and electronic screening (Saumon et al. 1996; Chabrier & Baraffe 1997; Chabrier, priv. comm.). We assume that the composit... |
2.4 Initial State The initial state for the evolution assumes an extended, high entropy, spherical configuration defined by [MATH] K (higher for larger mass). Such an idealized initial condition bears little relation with the actual formation of brown dwarfs. |
Baraffe et al. ( 2002 have shown that the evolution of brown dwarfs is quite sensitive to the choice of initial state for ages under [MATH] Myr. For this reason, we present only the evolution for later times. The early evolution of our models is further limited by the high-temperature limit of the atmosphere grid (see ... |
2.5 Surface Boundary Condition The most significant difference between the BD evolution calculations published over the past decade is in the treatment of the surface boundary condition of the model, which connects the surface properties [MATH] ) to the interior model ( [MATH] [MATH] [MATH] , age). For our adiabatic (i... |
Our atmosphere models have been described previously (McKay et al., 1989 ; Marley et al., 1996 ; Burrows et al., 1997 ; Marley & McKay, 1999 ; Marley et al., 2002 and used in several detailed comparisons with data (Marley et al., 1996 2002 ; Roellig et al., 2004 ; Saumon et al., 2006 2007 ; Leggett et al., 2007b ; Main... |
allowing inclusion of arbitrary Mie scattering particles in the opacity of each layer. Our opacity database, accounting for all important absorbers is described in Freedman et al. ( 2008 Our chemical equilibrium grid of molecular, atomic and ionic abundances as a function of temperature, pressure, and metallicity is ba... |
show generally excellent fits between our model spectra and observations of cloudy L dwarfs. The near infrared colors of brown dwarfs are quite sensitive to the choice of [MATH] a point we will return to in the discussion of color-magnitude diagrams (§4). |
Our grid of atmosphere models covers [MATH] K and [MATH] , which does not provide a boundary condition for the late evolution of low-mass objects and the very early evolution of the more massive ones. To obtain a boundary condition for [MATH] K, we define [MATH] as the temperature at [MATH] bar that gives the same entr... |
(Lunine et al., 1989 . We smoothly interpolate [MATH] quadratically to [MATH] at [MATH] at constant gravity. The interpolated values of [MATH] are then converted back to an equivalent entropy [MATH] for use as the surface boundary condition. For [MATH] K and gravities outside the range of the atmosphere grid, linear ex... |
and [MATH] are used. This gives well-behaved but inaccurate results for the early, warm phase of the evolution and for very-low mass objects ( [MATH] ). |
In the following we present two evolution sequences, one based on a cloudless atmosphere grid and one using a cloudy grid with [MATH] , both with solar metallicity. The two surface boundary conditions (expressed as [MATH] ) are shown in Fig. |
for selected gravities. Clouds play a minor role in high- [MATH] atmospheres and both sequences converge to the same boundary condition. The cloudy surface boundary condition is not as smooth as the cloudless case because of occasional numerical difficulties in the cloudy atmosphere calculation. Cloudy atmospheres have... |
Evolution sequences 3.1 Cloudless and cloudy surface boundary conditions The evolution of the luminosity is shown in Fig. for cloudless models and Fig. for the cloudy models for objects ranging from 0.005 to 0.08 [MATH] . Both show the well-known features of the evolution of very low mass stars, brown dwarfs and giant ... |
(Burrows et al., 1993 ; Burrows & Liebert, 1993 ; Chabrier & Baraffe, 2000 ; Chabrier et al., 2000a and a comparison of the cloudy and cloudless sequences shows the expected trends. The cooling rate is primarily controlled by the slope of the [MATH] relation (Fig. ) and for [MATH] K, the cloudy models are cooler and le... |
For these evolution sequences with solar metallicity atmospheres, the minimum hydrogen-burning mass, defined by objects that reach stable H-burning at an age of 10 Gyr is 0.075 [MATH] where [MATH] K for the cloudless sequence. The main sequence of cloudy models ends at a lower mass of [MATH] and [MATH] K. The latter fa... |
For comparisons with observables, a representation of the evolution in terms of [MATH] and gravity is more transparent (Figure ). The range of [MATH] shown covers all spectral types later than L0, and includes the bottom of the main sequence. The figure also shows isochrones, and lines of constant radius and luminosity... |
brown dwarf at [MATH] K. In the cloudy sequence, the peak gravity occurs at the same mass but [MATH] and [MATH] K. There is a similar weak dependence of the maximum gravity on the metallicity, which increases by 0.023 dex for a decrease of 0.3 dex in [M/H] (for cloudless sequences). More generally, there is an upper ( ... |
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