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In both cases. the authors interpret the field stars with second-generation abundances as stars that formed in globular clusters and were later transferred to the halo through nass-loss processes such as tidal stripping by the Galaxy or two-body interactions within the cluster.
In both cases, the authors interpret the field stars with second-generation abundances as stars that formed in globular clusters and were later transferred to the halo through mass-loss processes such as tidal stripping by the Galaxy or two-body interactions within the cluster.
It is also claimed in MGIO that their figure of 2.5% of halo stars having second-generation abundances. seen through the lens of
It is also claimed in MG10 that their figure of $2.5\%$ of halo stars having second-generation abundances, seen through the lens of
is clear that the initially high magnetic energy. decreases as the initially imposed magnetic field undergoes reconnection. and(1/3) reaches a saturated value of (1/3)~0.011 once the turbulence reaches a statistical steady state.
is clear that the initially high magnetic energy decreases as the initially imposed magnetic field undergoes reconnection, and$\langle 1/\beta \rangle$ reaches a saturated value of $\langle 1/\beta \rangle \simeq 0.011$ once the turbulence reaches a statistical steady state.
Figure 16 shows the time evolution of the volume averaged: Shakura-Sunvacy stress parameter a defined: by equation 26..
Figure \ref{fig15} shows the time evolution of the volume averaged Shakura-Sunyaev stress parameter $\alpha$ defined by equation \ref{alpha}.
The solid line represents the Maxwell stress. the dotted. line. represents the Itevnolds stress. and. the dashed. line represents the sum of these.
The solid line represents the Maxwell stress, the dotted line represents the Reynolds stress, and the dashed line represents the sum of these.
It is clear that as the cise becomes unstable to the MIL. the stresses increase initially. but then decrease to a saturated: state corresponding to àστ10
It is clear that as the disc becomes unstable to the MRI, the stresses increase initially, but then decrease to a saturated state corresponding to $\alpha \simeq 7 \times 10^{-3}$.
The racial distribution of a. time averaged for a short period of time (one orbit at i— 1) is shown in figure L7..
The radial distribution of $\alpha$, time averaged for a short period of time (one orbit at $r=1$ ) is shown in figure \ref{fig16}.
As expected this is a rapidly varving quantity às a function of both space and time due to the turbulence (see also paper D.
As expected this is a rapidly varying quantity as a function of both space and time due to the turbulence (see also paper I).
The final state of the dise model shown in figures 15 17 was used as the initial condition for simulations that examine the interaction between turbulent. clises and embedded: protoplancts.
The final state of the disc model shown in figures \ref{fig14} – \ref{fig16} was used as the initial condition for simulations that examine the interaction between turbulent discs and embedded protoplanets.
Models. 1 G4 used. full 2% azimuthal domains that were constructed by patching eight copies of the z/4 turbulent cise model together.
Models G1 – G4 used full $2 \pi$ azimuthal domains that were constructed by patching eight copies of the $\pi/4$ turbulent disc model together.
Model G5. which had a restricted. azimuthal domain of x/2. consisted of two copies of the relaxed. turbulent cise mocdoel patched together. with periodic boundary conditions in the azimuthal direction being emploved.
Model G5, which had a restricted azimuthal domain of $\pi/2$, consisted of two copies of the relaxed, turbulent disc model patched together, with periodic boundary conditions in the azimuthal direction being employed.
These simulations are described below.
These simulations are described below.
In this section we present the results from. simulations labeled as Glo G5 in table 2..
In this section we present the results from simulations labeled as G1 – G5 in table \ref{table2}. .
The aim is to examine how the cise properties change as a function. of. planet
The aim is to examine how the disc properties change as a function of planet
and eruptive binaries: stus wilh active surfaces. rapid rotation: emission-line objects; aud others.
and eruptive binaries; stars with active surfaces, rapid rotation; emission-line objects; and others.
The columns of Table 1 eive the (1-2) star name and its WD number. (3) tvpe of peculiaritv. (4) tvpe of variability [rom the living of the General Catalogue of Variable Stars (GCVS). (5-6) spectral (vpe aud ils source. (7-8) the (D—V)y color aud the Vp magnitude as given in the Tyvceho-2 catalog.
The columns of Table 1 give the (1-2) star name and its HD number, (3) type of peculiarity, (4) type of variability from the living of the General Catalogue of Variable Stars (GCVS), (5-6) spectral type and its source, (7-8) the $(B-V)_T$ color and the $V_T$ magnitude as given in the Tycho-2 catalog.
Η the latter are not available. a twpical V. magnitude [rom other sources is given.
If the latter are not available, a typical $V$ magnitude from other sources is given.
The observations were carried oul with the Echelle spectrograph mounted at the Cassegrain focus of the 1.32 m telescope operated in Asiago by INAF Astronomical Observatory of Padova.
The observations were carried out with the Echelle spectrograph mounted at the Cassegrain focus of the 1.82 m telescope operated in Asiago by INAF Astronomical Observatory of Padova.
The detector was a Thomson TIIN31156 CCD with 1024 x 1024 pixels of 19 san size cooled with liquicl nitrogen.
The detector was a Thomson THX31156 CCD with 1024 $\times$ 1024 pixels of 19 $\micron$ size cooled with liquid nitrogen.
The chip was of the thick type. front illuminated. with Lumigen coating for enhanced blue response ancl presented. πο detectable fringing in the red.
The chip was of the thick type, front illuminated, with Lumigen coating for enhanced blue response and presented no detectable fringing in the red.
The cross-clisperser was a grating. (hus the reddest Echelle orders were contaminated by (he superimposed second order from the cross-clisperser.
The cross-disperser was a grating, thus the reddest Echelle orders were contaminated by the superimposed second order from the cross-disperser.
This contaminalion was suppressed wilh a high-pass OG455 filler with a thickness of 3 mm which was inserted into the optical path.
This contamination was suppressed with a high-pass OG455 filter with a thickness of 3 mm which was inserted into the optical path.
The filter cut the light with wavelengths bluer than 4600A.
The filter cut the light with wavelengths bluer than 4600.
. So it effectively removed the second order contamination up to 9200A.. but il also set the short wavelength limit of our atlas.
So it effectively removed the second order contamination up to 9200, but it also set the short wavelength limit of our atlas.
Great care was taken to keep (he dispersion and the resolving power values constant during the whole observing campaign which started in November 1998 and was completed in August 2002. for à total of 56 different observing nights.
Great care was taken to keep the dispersion and the resolving power values constant during the whole observing campaign which started in November 1998 and was completed in August 2002, for a total of 56 different observing nights.
All observations were carried ont with the spectrograph slit opened to a width of 2 arcsec.
All observations were carried out with the spectrograph slit opened to a width of 2 arcsec.
The slit was aligned with the parallactic angle when the airmass exceeded 1.5.
The slit was aligned with the parallactic angle when the airmass exceeded 1.5.
of the iron edge.
of the iron edge.
Ehe iron line width is actually resolved in the EPIC pn spectrum. with @=3211 eV. corresponding to PWIM=3500100255 Em if produced by. Doppler broadening. thus putting an estimate to the inner radius of the torus. r=0.6TIE|cin?j pe.
The iron line width is actually resolved in the EPIC pn spectrum, with $\sigma=32^{+13}_{-14}$ eV, corresponding to $3\,500^{+1\,400}_{-1\,500}$ km $^{-1}$ if produced by Doppler broadening, thus putting an estimate to the inner radius of the torus, $r=0.6^{+1.3}_{-0.3}\,\sin^2{i}$ pc.
Moreover. a possible variation on a timescale of 7 months of the ionisation stage of iron between the and the observations is fully compatible with the photoionisation time for iron at à clistance of around 1 pe.
Moreover, a possible variation on a timescale of $\simeq7$ months of the ionisation stage of iron between the and the observations is fully compatible with the photoionisation time for iron at a distance of around 1 pc.
The soft) X-ray spectrum. of AIrk 3 is dominated. by emission lines of LE and Lelike from the most abundant metals. superimposed over an unabsorbed powerkuy with re same photon index of the primary continuum.
The soft X-ray spectrum of Mrk 3 is dominated by emission lines of H– and He–like from the most abundant metals, superimposed over an unabsorbed powerlaw with the same photon index of the primary continuum.
[t is important to note that the full resolution of these lines in the RGS spectra was required: before. correctly. fitting us part of the spectrum in the lower resolution pn data. lus preventing the adoption of a much steeper (E2 3) »owerlaw. whose physical interpretation would have been ess straightforward.
It is important to note that the full resolution of these lines in the RGS spectra was required before correctly fitting this part of the spectrum in the lower resolution pn data, thus preventing the adoption of a much steeper $\Gamma\simeq3$ ) powerlaw, whose physical interpretation would have been less straightforward.
From the ratio between the Luxes of 10 rellected component and the primary continuum. a ‘column density. of a few 1077 em7 can be derived. for 10 photoionised material.
From the ratio between the fluxes of the reflected component and the primary continuum, a column density of a few $10^{22}$ $^{-2}$ can be derived for the photoionised material.
However. it must be noted that at least two different ionisecl rellectors are needed. to take into account the emission lines from lighter metals and the
However, it must be noted that at least two different ionised reflectors are needed to take into account the emission lines from lighter metals and the
where He,~2000 is the minimal Revnolds number in the planar limit.
where $Re_p\sim 2000$ is the minimal Reynolds number in the planar limit.
This gives 1/7. which is somewhat larger (han the value of 1/20 shown on Fig.
This gives $\Delta_c\sim 1/7$ , which is somewhat larger than the value of $1/20$ shown on Fig.
G (but closer to the unecducated guess A,~ 1). because of the reduction adopted above of the value of 1ο”.
\ref{fig3} (but closer to the uneducated guess $\Delta_c\sim 1$ ), because of the reduction adopted above of the value of $Re^*$.
Note also that /4;~r/300.
Note also that $l_M\sim r/300$.
One might. wonder why such a small leneth scale arises. whereas one would naively expect fy,~r on dimensional grounds.
One might wonder why such a small length scale arises, whereas one would naively expect $l_M\sim r$ on dimensional grounds.
llowever. (he same dimensional (wpe of argument would also predict that turbulence sets in for Re=1. which is strongly violated by the empirical evidence.
However, the same dimensional type of argument would also predict that turbulence sets in for $Re\gtrsim 1$, which is strongly violated by the empirical evidence.
The two lacts have the same plwsical origin: the (as vet not understood) mechanism which sustains turbulence.
The two facts have the same physical origin: the (as yet not understood) mechanism which sustains turbulence.
Two other explanations of the behavior of the Revnolds ummber with relative gap width have previously been proposed in the literature.
Two other explanations of the behavior of the Reynolds number with relative gap width have previously been proposed in the literature.
Zeldovich(1981). assumed Chat turbulence in these Couette-Tavlor flows is controlled by a competition between the epicyclie (stabilizing) frequency and the shear rate which is the source of the turbulent motions: however his findings are inconsistent with some of the data (see the discussion of this point in the appendix of RichardandZahn 1999)).
\citet{Zel81} assumed that turbulence in these Couette-Taylor flows is controlled by a competition between the epicyclic (stabilizing) frequency and the shear rate which is the source of the turbulent motions; however his findings are inconsistent with some of the data (see the discussion of this point in the appendix of \citealt{RZ99}) ).
Dubrulle(1993) looks for an explanation in terms of finite amplitude instabiliües in the WIXD approximation. but (his is incompatible with the [act that (he scale + plavs a kev role in the problem.
\citet{Bulle93} looks for an explanation in terms of finite amplitude instabilities in the WKB approximation, but this is incompatible with the fact that the scale $r$ plays a key role in the problem.
] conclude this section bx pointing out that the Coriolis lorce appears nowhere in the arguments presented in tliis section. which suggests that it plavs little role in the development of turbulence in suberitical Couette-Tavlor flows. αἱ least for q~1—2.
I conclude this section by pointing out that the Coriolis force appears nowhere in the arguments presented in this section, which suggests that it plays little role in the development of turbulence in subcritical Couette-Taylor flows, at least for $q\sim 1-2$.
Indeed. in opposition to the inerlial (geometric) terms. the Coriolis force does not single out anv length scale.
Indeed, in opposition to the inertial (geometric) terms, the Coriolis force does not single out any length scale.
In particular. the ratio of the advection term (~iw Wie) to the Coriolis one (iQ) in Eq. (3))
In particular, the ratio of the advection term $\sim w\nabla w$ ) to the Coriolis one $\sim w\Omega$ ) in Eq. \ref{NSCT}) )
is l1 both at scale /3; and at scale Ar for the values |g]~1—2 of interest here. and increases wilh decreasing scale in a IxXolmogorov cascade picture.
is $\sim 1$ both at scale $l_M$ and at scale $\Delta r$ for the values $|q|\sim 1-2$ of interest here, and increases with decreasing scale in a Kolmogorov cascade picture.
However. it does play a role in (he loss of turbulence in simulated rotating flows. but this apparent paradox cannot be investigated in (he Iranework of the order of magnitude arguments developed in (his section.
However, it does play a role in the loss of turbulence in simulated rotating flows, but this apparent paradox cannot be investigated in the framework of the order of magnitude arguments developed in this section.
The next section is devoted to a discussion of this point.
The next section is devoted to a discussion of this point.
The question I want to address here is the following: why is turbulence lost in numerical simulations of sheared flows when even a small amount of rotation is added (and the resulting
The question I want to address here is the following: why is turbulence lost in numerical simulations of sheared flows when even a small amount of rotation is added (and the resulting
which any point source is observed for ~70 d (the LAT field of view is 2.4 Therefore during the background-limited regime (whenf is large enough that many background photons are observed) the flux limit scale with ras 4«10° οι” s (/70di7.
which any point source is observed for $\sim$ 70 d (the LAT field of view is 2.4 Therefore during the background-limited regime (when $t$ is large enough that many background photons are observed) the flux limit scale with $t$ as $4 \times 10^{-9}$ $^{-2}$ $^{-1}$ $(t/70~\mathrm{d})^{-1/2}$.
During the photon-count-limited regime (when f 1s so small that less thàn one background photon is expected). in contrast. the detection limit is at a constant fluence.
During the photon-count-limited regime (when $t$ is so small that less than one background photon is expected), in contrast, the detection limit is at a constant fluence.
Therefore the fluence sensitivity of the GLAST-LAT detector is where fo=650 s represents the time when the transition from photon-count-limited to background-limited regime occurs in the LAT case.
Therefore the fluence sensitivity of the -LAT detector is where $t_0 = 650$ s represents the time when the transition from photon-count-limited to background-limited regime occurs in the LAT case.
Note that equation (13)) is for the limitingfleence. the time-1integrated flux. rather than the flux.
Note that equation \ref{eq:GLAST limit}) ) is for the limiting, the time-integrated flux, rather than the flux.
This limit is more natural in the photon-count-limited regime and it is more relevant to EGRET constraints that we derived in the previous section.
This limit is more natural in the photon-count-limited regime and it is more relevant to EGRET constraints that we derived in the previous section.
Detailed derivation of this sensitivity is given in Appendix B..
Detailed derivation of this sensitivity is given in Appendix \ref{app:GLAST}.
In Table 1.. we summarize the values of fo and Fi(£) for a few cases of power law index —o and integration time f.
In Table \ref{table:GLAST}, we summarize the values of $t_0$ and $F_{\rm lim}(t)$ for a few cases of power law index $-\alpha$ and integration time $t$.
The values of FjG) for¢to in the table are determined by erniteria. of five-photon detection. while those forf—fy are by 5o significance.
The values of $F_{\rm lim}(t)$ for $t \ll t_0$ in the table are determined by criteria of five-photon detection, while those for $t > t_0$ are by $5\sigma$ significance.
The fluence we argue here is the one integrated over 30 MeV—30 GeV. in order to compare with the EGRET fluence upper bounds.
The fluence we argue here is the one integrated over 30 MeV–30 GeV, in order to compare with the EGRET fluence upper bounds.
In the case of background-limited regime. it might be more appropriate to use higher energy threshold (instead of 30 MeV) especially for hard source spectrum. because the background spectrum falls steeply with frequency (o~2.1).
In the case of background-limited regime, it might be more appropriate to use higher energy threshold (instead of 30 MeV) especially for hard source spectrum, because the background spectrum falls steeply with frequency $\alpha \simeq 2.1$ ).
We may find optimal low-frequency threshold depending on spectral index of GRB emissions: it is higher for harder spectrum.
We may find optimal low-frequency threshold depending on spectral index of GRB emissions; it is higher for harder spectrum.
Thus. we should be able to improve the fluence sensitivity for background-limited regime. compared with the figures given in Table ]..
Thus, we should be able to improve the fluence sensitivity for background-limited regime, compared with the figures given in Table \ref{table:GLAST}.
In addition. transition from photon-count to background limited regime would occur later than 650 s. For our purpose. however. as time scales we consider (Joo for prompt emission and 200 s after Του for afterglows) are both during photon-count-limited regime. the consideration above does not apply and we can use full energy range (30 MeV-30 GeV for EGRET) to collect as many photons as possible.
In addition, transition from photon-count to background limited regime would occur later than 650 s. For our purpose, however, as time scales we consider $T_{90}$ for prompt emission and 200 s after $T_{90}$ for afterglows) are both during photon-count-limited regime, the consideration above does not apply and we can use full energy range (30 MeV–30 GeV for EGRET) to collect as many photons as possible.
GLAST 1s also equipped with the GLAST Burst Monitor (GBM) instrument. dedicated for the detection of GRBs.
is also equipped with the GLAST Burst Monitor (GBM) instrument, dedicated for the detection of GRBs.
It detects photons of 8 keV to more than 25 MeV and its field of view is ~8 sr.
It detects photons of 8 keV to more than 25 MeV and its field of view is $\sim$ 8 sr.
The expected rate of GRBs that trigger GBM is ~200 vr!2006).. which is almost as high as BATSE rate.
The expected rate of GRBs that trigger GBM is $\sim$ 200 $^{-1}$, which is almost as high as BATSE rate.
Each year. about 70 out of these 7-200 bursts should fall within the LAT field of view.
Each year, about 70 out of these $\sim$ 200 bursts should fall within the LAT field of view.
Given the distribution of fluences (Fig. 4))
Given the distribution of fluences (Fig. \ref{fig:dndf_egret}) )
and the LAT sensitivity (Table 1)). we can estimate the fraction of GRBs that would be detected with LAT.
and the LAT sensitivity (Table \ref{table:GLAST}) ), we can estimate the fraction of GRBs that would be detected with LAT.
In Table 2.. we show the expected LAT detection rate for a=2.3. which is ~20 yr! for the best-fit models of the EGRET data for both the prompt and afterglow emissions.
In Table \ref{table:result}, we show the expected LAT detection rate for $\alpha = 2.3$ , which is $\sim$ 20 $^{-1}$ for the best-fit models of the EGRET data for both the prompt and afterglow emissions.
The prompt phase estimates are for detections of the synchrotron component in the ~100 MeV range.
The prompt phase estimates are for detections of the synchrotron component in the $\sim$ 100 MeV range.
Given the large effective area of the LAT it is expectedalso to detect ο GeV photons from the IC component and identify the spectral break associated with the transition from the synchrotron to 16 component. thereby directly testing the SSC model.
Given the large effective area of the LAT it is expectedalso to detect $\gtrsim$ GeV photons from the IC component and identify the spectral break associated with the transition from the synchrotron to IC component, thereby directly testing the SSC model.
The estimates given in Table 2 are fairly conservative.
The estimates given in Table \ref{table:result} are fairly conservative.
First. while we used five-photon criterion for the detection. even two-photon detection should be quite significant. because the expected background count is much smaller than one photon during Του and the following 200 s that we considered.
First, while we used five-photon criterion for the detection, even two-photon detection should be quite significant, because the expected background count is much smaller than one photon during $T_{90}$ and the following 200 s that we considered.
Second.Swift can find dimmer bursts than GBM.
Second, can find dimmer bursts than GBM.
Although the discovery rate is not as high as that of GBM or BATSE. it would still be able to find tens of new GRBs in the LAT field of view.
Although the discovery rate is not as high as that of GBM or BATSE, it would still be able to find tens of new GRBs in the LAT field of view.
Thus the true rate would likely be larger than the figures given in Table 2..
Thus the true rate would likely be larger than the figures given in Table \ref{table:result}.
All the GRBs except for those detected by EGRET should contribute to the EGB flux to a certain extent2007).
All the GRBs except for those detected by EGRET should contribute to the EGB flux to a certain extent.
. This may be computed as where F is EGRET fluence in 30 MeV—30 GeV. dP/dF is the normalized distribution of EGRET fluence (eq. [12]]
This may be computed as where $F$ is EGRET fluence in 30 MeV–30 GeV, $dP / dF$ is the normalized distribution of EGRET fluence (eq. \ref{eq:fluence distribution}] ]
and Fig. 4)).
and Fig. \ref{fig:dndf_egret}) ),
and Rorp~2 d is the occurrence rate of GRBs from all sky.
and $R_{\rm GRB} \sim 2$ $^{-1}$ is the occurrence rate of GRBs from all sky.
The factor |—e(F) takes into account the fact that very bright GRBs cannot contribute to the EGB because they would be identified as point sources (but see discussions below).
The factor $1 - \epsilon (F)$ takes into account the fact that very bright GRBs cannot contribute to the EGB because they would be identified as point sources (but see discussions below).
Figure 6 shows differential EGB intensity ¢/igp/dlogF that represents contribution from GRBs ofa given fluence. for prompt and afterglow phases.
Figure \ref{fig:egb_dist} shows differential EGB intensity $dI_{\rm EGB} / d\log F$ that represents contribution from GRBs ofa given fluence, for prompt and afterglow phases.
In the third column of Table 2.. we show the EGB intensity
In the third column of Table \ref{table:result}, , we show the EGB intensity
out that the last of these differences may also be amplified by an uuimmocdeled survey selection effectstars hosting planets tend to be observed more frequently. thereby. enhancing the chance to discover additional low-mass planets.
out that the last of these differences may also be amplified by an unmodeled survey selection effect—stars hosting planets tend to be observed more frequently, thereby enhancing the chance to discover additional low-mass planets.
Most of the plots in the lower panels of Figure 1. are mareinally consistent wilh separability. as discussed at the end of re[secisurvev..
Most of the plots in the lower panels of Figure \ref{fig:one} are marginally consistent with separability, as discussed at the end of \\ref{sec:survey}.
The evilence on separability [rom the Kepler survey is more dillicult to interpret. because geometric selection ellects do not preserve separability (see discussion just before relsec:lisher)).
The evidence on separability from the Kepler survey is more difficult to interpret, because geometric selection effects do not preserve separability (see discussion just before \\ref{sec:fisher}) ).
Nevertheless. (he semi-major axis distributions of single- and multiple-tranet svslenms in (he ορίου survey are indistinguishable according to a INS test (p-value 0.20: see also Figure 2)). which is consistent with separability.
Nevertheless, the semi-major axis distributions of single- and multiple-tranet systems in the Kepler survey are indistinguishable according to a KS test $p$ -value 0.20; see also Figure \ref{fig:epsw}) ), which is consistent with separability.
Presumably (he pileup of hot Jupiters al small semi-major axes seen in the RV survevs is less prominent in the lNepler sample because the typical planetary mass is much smaller. and (he jump outside 1AU is not seen because Ixepler is not sensitive to these orbital periods.
Presumably the pileup of hot Jupiters at small semi-major axes seen in the RV surveys is less prominent in the Kepler sample because the typical planetary mass is much smaller, and the jump outside $1\au$ is not seen because Kepler is not sensitive to these orbital periods.
Lathametal.(2011) have shown that Ixepler svstems with multiple tranets are less likely to include a giant planet. Career than. Neptune) than svstems will a single tranet.
\cite{latham11} have shown that Kepler systems with multiple tranets are less likely to include a giant planet (larger than Neptune) than systems with a single tranet.
We confirm using a Ix9 test that the distributions of radii in the single- ancl multiple-tranet svslenms are different (maximum difference in (he cumulative probability distribution of 0.20).
We confirm using a KS test that the distributions of radii in the single- and multiple-tranet systems are different (maximum difference in the cumulative probability distribution of 0.20).
llowever. the results al the end of relfsec:survey show that the numbers of two-. three-. and fonr-tranet svstems as a function of the radius cutoff appear to be consistent wilh separabilitv.
However, the results at the end of \\ref{sec:survey} show that the numbers of two-, three-, and four-tranet systems as a function of the radius cutoff appear to be consistent with separability.
Evidentlv equations such as (11)) that we use to compare the observable multiplicity function between surveys are less sensitive to deviations from separability than statistical tests designed specifically for this purpose.
Evidently equations such as \ref{eq:cccc}) ) that we use to compare the observable multiplicity function between surveys are less sensitive to deviations from separability than statistical tests designed specifically for this purpose.
These comparisons suggest (hat deviations from separability. though present in both the RV and Ixepler planet samples. are not large enough to compromise our method and results.
These comparisons suggest that deviations from separability, though present in both the RV and Kepler planet samples, are not large enough to compromise our method and results.
llowever. further exploration of both the magnitude and the effects of these deviations is neecec.
However, further exploration of both the magnitude and the effects of these deviations is needed.
The Kepler survey has a complex set of survev selection effects. which we do not attempt to model.
The Kepler survey has a complex set of survey selection effects, which we do not attempt to model.
The constraints on the multipliditv function that we derive therefore apply to the
The constraints on the multiplicity function that we derive therefore apply to the
function is well measured in the disk down to the hvdrogen-burning limit ancl in the bulge down to M0.15.V..
function is well measured in the disk down to the hydrogen-burning limit and in the bulge down to $M\sim 0.15\,M_\odot$.
There are. of course. uncertainties in extrapolating (hese mass functions to lower. sub-stellar masses. and to the remnants of the now deceased. stars ad hieher masses.
There are, of course, uncertainties in extrapolating these mass functions to lower, sub-stellar masses, and to the remnants of the now deceased stars at higher masses.