ReadingTimeMachine/rtm-sgt-ocr-v1 · Datasets at Hugging Face

source stringlengths 1 2.05k ⌀	target stringlengths 1 11.7k
For small amplitude libration about L4/L5 and circular orbits. the transit timing perturbation is given by NMGS)/(8). where NM(f) is the angular displacement of the Trojan from L4/L5 at the time of the /th transit.	For small amplitude libration about L4/L5 and circular orbits, the transit timing perturbation is given by $\delta t_i \simeq \epsilon P_s \Delta M(t_i) / (2\pi)$ , where $\Delta M(t_i)$ is the angular displacement of the Trojan from L4/L5 at the time of the $i$ th transit.
The TTVs can be modeled by a sinusoid. 07/;=Aqsin(2x(1—14)(Peppy+6). where Aq is the aaplitude of the transit timing variations and Pp744.	The TTVs can be modeled by a sinusoid, $\delta t_i = K_{\rm tt} \sin\left(2\pi\left(t-t_0\right)/P_{\rm TTV}+\phi\right)$, where $K_{\rm tt}$ is the amplitude of the transit timing variations and $P_{\rm TTV}\sim\tau_{\rm slow}$.
L the dominant periodicity of the transit timing variations (Jj) is well determined. then the remaining parameters can be determined via linear least squares fitting to the observed (ransil times.	If the dominant periodicity of the transit timing variations $P_{\rm TTV}$ ) is well determined, then the remaining parameters can be determined via linear least squares fitting to the observed transit times.
The transit timing variations will have an amplitiucle ens (o ge where A4, is the amplitude of the Trojans angular displacement from (he Lagrange point.	The transit timing variations will have an amplitude 60s ) ) ) ), where $K_{\Delta M}$ is the amplitude of the Trojan's angular displacement from the Lagrange point.
For small amplitude libration. A4;&max\|AAS and rms(0/;)cWy/V2 (see Fig.	For small amplitude libration, $K_{\Delta M}\simeq\mathrm{max}\left\|\Delta M\right\|$ and $\mathrm{rms}(\delta t_i)\simeq K_{\rm tt} / \sqrt{2}$ (see Fig.
1) Libration amplitudes of A4;~5—25 are common for Trojans orbiting near the sun-Jupiter Lagrange points (Murray Dermott 2000).	1) Libration amplitudes of $K_{\Delta M}\sim~5-25^\circ$ are common for Trojans orbiting near the Sun-Jupiter Lagrange points (Murray Dermott 2000).
The Lomb-Scargle5 periocogram5 can be easily adapted to efficiently scan a range5 of putative periods aud identily any signilicant periodicities (Cumming 2004).	The Lomb-Scargle periodogram can be easily adapted to efficiently scan a range of putative periods and identify any significant periodicities (Cumming 2004).
If we assume that ihere are many V4) transit (aiming observations with uncorrelated Gaussian unicertainties σι=Gg. that the transit timing5 observations are evenly distributed. and the duration of observations (2,,,) is greater than than P. (en a periodogram-stvle analvsis results in a chance of detecting a Trojan 1 Ny,>Nyeoy,(atlog\|Tin./(2FTD.i) (Cumming 2004). where F is the false alarm probability. which we set to 107.	If we assume that there are many $N_{\rm tt}$ ) transit timing observations with uncorrelated Gaussian uncertainties $\sigma_{t_i}=\sigma_{tt}$, that the transit timing observations are evenly distributed, and the duration of observations $T_{\rm obs}$ ) is greater than than $P_{\rm TTV}$, then a periodogram-style analysis results in a chance of detecting a Trojan if $K_{tt}\ge K_{1/2} \simeq \sigma_{tt}\left(\frac{4}{N_{\rm tt}} \log\left[T_{\rm obs} / \left(2 F P_s\right) \right] \right)^{1/2}$ (Cumming 2004), where $F$ is the false alarm probability, which we set to $10^{-3}$.
For Vay=L/P.40. Nyyc04. so sub-Earth-mass Trojans could be reaclily detected.	For $N_{\rm tt} = T_{\rm obs}/P_s = 40$, $K_{1/2} \simeq \sigma_{tt}$, so sub-Earth-mass Trojans could be readily detected.
We note that all published transit timing data sets have Ay<20. which results in a significantly reduced sensitvitv. if [ιν is unknown p	We note that all published transit timing data sets have $N_{\rm tt}<20$, which results in a significantly reduced sensitvity, if $P_{\rm TTV}$ is unknown .
riori ln this small-Nq regime. a simple 4? test of the null hypothesis (0/;= 0) is more sensitive for detecting transit timing variations.	In this $N_{\rm tt}$ regime, a simple $\chi^2$ test of the null hypothesis $\delta t_i=0$ ) is more sensitive for detecting transit timing variations.
However. if only a single periodicity (e.g.. 744) is lo be tested. then even a modest number of observations can be quite sensitive (e.g... Ayo22.504even lor Nyy= 13).	However, if only a single periodicity (e.g., $\tau_{\rm slow}$ ) is to be tested, then even a modest number of observations can be quite sensitive (e.g., $K_{1/2}\simeq 2.5\sigma_{\rm tt}$even for $N_{\rm tt}=13$ ).
rotation curve of the receding half drops in the outer parts.	rotation curve of the receding half drops in the outer parts.
The masini rotation speed. leaving out the bump at110".. occurs around a radius of (1.87 ΚΡΟ) at a speed of 25\|.	The maximum rotation speed, leaving out the bump at, occurs around a radius of (1.87 kpc) at a speed of 25.
.. Stil Israel (2002) give a rotation speed Vsini of 17.543.9 aat a radius of {for DDO 43.	Stil Israel (2002) give a rotation speed $V \sin i$ of $\pm$ 3.9 at a radius of for DDO 43.
At that radius our Vsin/ would be the same at 17.60.58 !.	At that radius our $V \sin i$ would be the same at $\pm$ 0.8.
. To examine the quality of the lit. we made a model of the velocity field. (hen subtracted it from the observed. velocity Ποια.	To examine the quality of the fit, we made a model of the velocity field, then subtracted it from the observed velocity field.
The resilual map is shown in Figure 24..	The residual map is shown in Figure \ref{fig:resid}.
The values of the residuals range [rom -6.6 to 7.1!.. so in general. the fit seems quite good.	The values of the residuals range from -6.6 to 7.1, so in general, the fit seems quite good.
We have plotted. contours Irom the model velocity [field on the residual map in Figure 25. and the observed. velocity [field contours on (he residual map in Figure 26..	We have plotted contours from the model velocity field on the residual map in Figure \ref{fig:modelonresid} and the observed velocity field contours on the residual map in Figure \ref{fig:m1onresid}.
The model successfully recreates (he weak turnover in each side of the velocity field. but the residual map shows (hat it had. difficulty with the receding half turnover in the sense that it underestimates it and shifts it slightly north.	The model successfully recreates the weak turnover in each side of the velocity field, but the residual map shows that it had difficulty with the receding half turnover in the sense that it underestimates it and shifts it slightly north.
There is another region of higher-than-average residuals just south of the center of the galaxy: (his area slightly overlaps the west sides of the large hole and knot in the “Thhis is also near (he region of hiehest velocity dispersion in the galaxy. so perhaps it is nol surprising that the velocity residuals are larger here as well.	There is another region of higher-than-average residuals just south of the center of the galaxy; this area slightly overlaps the west sides of the large hole and knot in the \\.Thhis is also near the region of highest velocity dispersion in the galaxy, so perhaps it is not surprising that the velocity residuals are larger here as well.
From Figure 26.. it can be seen that most of the regions of larger residuals (especially negative residuals) coincide with the kinks in the isovels that may be representative of a warp.	From Figure \ref{fig:m1onresid}, it can be seen that most of the regions of larger residuals (especially negative residuals) coincide with the kinks in the isovels that may be representative of a warp.
The residuals are still small however. indicating (hal its not a significant warp.	The residuals are still small however, indicating that it's not a significant warp.
The original listing of DDO 43 as a candidate tidal dwarf by Hunter ((2000) was based on a suggested rotation speed of order 9\|.	The original listing of DDO 43 as a candidate tidal dwarf by Hunter (2000) was based on a suggested rotation speed of order 9.
.. As a result. on a plot of Mg; versus the masini rotation speed (Figure 1 of IIunter al.)) DDO 43 stood oul as unusually huninous for its rotation speed.	As a result, on a plot of $_B$ versus the maximum rotation speed (Figure 1 of Hunter ) DDO 43 stood out as unusually luminous for its rotation speed.
This could imply a deficit of dark matter. a characteristic of dal dwarls (Barnes Hernequist 1992).	This could imply a deficit of dark matter, a characteristic of tidal dwarfs (Barnes Hernquist 1992).
However. with a maximum rotation speed of 25s... found here. DDO 43 now lies close to (he mean of the relationship defined bv other Im galaxies ancl spirals in (hat plot.	However, with a maximum rotation speed of 25, found here, DDO 43 now lies close to the mean of the relationship defined by other Im galaxies and spirals in that plot.
Thus. DDO 43 is unlikely to be without dark matter. and unlikely to be a tidal dwarl.	Thus, DDO 43 is unlikely to be without dark matter, and unlikely to be a tidal dwarf.
This is comforting since there was no obvious nearby postnerger object to have been the parent of DDO 43 if il were a tidal dwarl.	This is comforting since there was no obvious nearby post-merger object to have been the parent of DDO 43 if it were a tidal dwarf.
A erev-scale display of the velocity dispersion map from the ddata is shown in Figure 27 with contours of the integrated ssuperposed.	A grey-scale display of the velocity dispersion map from the data is shown in Figure \ref{fig:veldisp} with contours of the integrated superposed.
Within the optical body of the galaxy. the velocity dispersion is around LOτ	Within the optical body of the galaxy, the velocity dispersion is around 10.
ν, This is the value found in most quiescent gas disks.	This is the value found in most quiescent gas disks.
There are a few spots with higher	There are a few spots with higher
the absorption features at 71.47 keV and ~2.71 keV. now both appear as a resolved line pair. with the energy spacing of the respective Lee and. Lye resonance lines of Mg aid 5. Furthermore. additional narrow absorption features are seen to mateh with same Ix-shell resonance Lines of Ne. οἱ and. possibly Ar.	the absorption features at $\sim$ 1.47 keV and $\sim$ 2.71 keV now both appear as a resolved line pair, with the energy spacing of the respective $\alpha$ and $\alpha$ resonance lines of Mg and S. Furthermore, additional narrow absorption features are seen to match with same K-shell resonance lines of Ne, Si and possibly Ar.
To quantify these absorption features we explored. the ALOS data with Nspec.	To quantify these absorption features we explored the MOS data with Xspec.
. We first. fitted the MOS data at 1-5 keV with a power law to provide a baseline: below l keV the spectrum rises steeplv due to strong soft. X-rav emission (Pounds. and. Reeves 2006).	We first fitted the MOS data at 1-5 keV with a power law to provide a baseline; below 1 keV the spectrum rises steeply due to strong soft X-ray emission (Pounds and Reeves 2006).
Several narrow features clearly visible in the data-to-power-law-mocdel ratio plot (figure 3.2 upper panel) contributed to à poor statistical fit (\7=351266).	Several narrow features clearly visible in the data-to-power-law-model ratio plot (figure 3, upper panel) contributed to a poor statistical fit $\chi^{2}$ =351/266).
Fitting gaussians to the visible features. with a fixed width of a= 10eV. found 6 significant negative (absorption) lines.	Fitting gaussians to the visible features, with a fixed width of $\sigma$ = 10eV, found 6 significant negative (absorption) lines.
Ehe overall improvement to the fit was very significant with X7 reduced to 270/254.	The overall improvement to the fit was very significant with $\chi^{2}$ reduced to 270/254.
The fitted line energies and I[uxes are listed in Table 1 where the observe line energy is in each case compared: with the most likely identification. chosen as the nearest resonance transition of an abundant ion.	The fitted line energies and fluxes are listed in Table 1 where the observed line energy is in each case compared with the most likely identification, chosen as the nearest resonance transition of an abundant ion.
Crucially. α 6 line energies exhibit a "blue shift in the range ~5-7 %..	Crucially, all 6 line energies exhibit a `blue shift' in the range $\sim$ 5-7.
Assuming the same ratio for the absorption line observed at 731.07 keV. gives a preferrec identification with Llea of FeXXV. (figure 2).	Assuming the same ratio for the absorption line observed at $\sim$ 7.07 keV gives a preferred identification with $\alpha$ of FeXXV (figure 2).
In the res frame o£ tthe revised. identification of the absorption spectrum now vields an increased. outllow velocity in the range vo 0.13-0.15c.	In the rest frame of the revised identification of the absorption spectrum now yields an increased outflow velocity in the range $\sim$ 0.13-0.15c.
To test the compatibility of the visual absorption line set with a physical absorber we then compared the MOS data with a photoionised. gas modelled using the NSTAIU code (Kallman et al 1996).	To test the compatibility of the visual absorption line set with a physical absorber we then compared the MOS data with a photoionised gas modelled using the XSTAR code (Kallman et al 1996).
Free. parameters of the absorber in this comparison were the column density and. ionisation parameter. with outflow (or inflow) velocities included as an adjustment to the apparent. redshift of the absorbing gas.	Free parameters of the absorber in this comparison were the column density and ionisation parameter, with outflow (or inflow) velocities included as an adjustment to the apparent redshift of the absorbing gas.
Alb relevant abundant elements from Ne to Fe were include with the relative abundances constrained to within a factor 2 of solar.	All relevant abundant elements from Ne to Fe were included with the relative abundances constrained to within a factor 2 of solar.
Since our primary aim was to check the energies an relative strength of the principal absorption lines identifiec in the visual spectral fit shown in figure 2. the mocdel clic not attempt to match the broad. excess Lux near 6 keV: it therefore consisted only of a power law with photolonisec absorber.	Since our primary aim was to check the energies and relative strength of the principal absorption lines identified in the visual spectral fit shown in figure 2, the model did not attempt to match the broad excess flux near $\sim$ 6 keV; it therefore consisted only of a power law with photoionised absorber.
Fitting over the 1-10. keV band. the addition of he photoionisec absorber improved the spectral fit. [rom v of 522 for 358 degrees of freedom to 465/345.	Fitting over the 1-10 keV band the addition of the photoionised absorber improved the spectral fit from $\chi^{2}$ of 522 for 358 degrees of freedom to 465/345.
The vest-fit column density was Ny21077 em with an ionisation parameter of logé=2.9-+0.4 and nominal relative abundances of Ne. Mg. Si. S. Ar and Fe of 0.5. 1. 0.5. 1. 1.5 and 0.5.	The best-fit column density was $_{H}$$\sim$$2\times 10^{22}$ $^{-2}$, with an ionisation parameter of $\xi$ $\pm$ 0.4 and nominal relative abundances of Ne, Mg, Si, S, Ar and Fe of 0.5, 1, 0.5, 1, 0.5 and 0.5.
Figure 3 (mid. panel) reproduces this absorbed power Law model. with the strongest. predicted: absorption ines (in order of increasing energy) corresponding to Ix-shell resonance transitions of Ne. Me. Si. S. Ar and Fe. supporting he visual assessment of figure 2.	Figure 3 (mid panel) reproduces this absorbed power law model, with the strongest predicted absorption lines (in order of increasing energy) corresponding to K-shell resonance transitions of Ne, Mg, Si, S, Ar and Fe, supporting the visual assessment of figure 2.
Additionally. we note the Ly? line of Μο would occur at 1.83 keV. sugeesting	Additionally, we note the $\beta$ line of MgXII would occur at $\sim$ 1.83 keV, suggesting
V405 Xurigae. 0558.015353) was discovered. in the Al-Sky Survey ancl identified as απ intermediate polar (a cataclysmic variable with a magnetic white-cwarl primary) by Llaberl (1994).	V405 Aurigae J0558.0+5353) was discovered in the All-Sky Survey and identified as an intermediate polar (a cataclysmic variable with a magnetic white-dwarf primary) by Haberl (1994).
lt is notable. firstly. for showing a soft blackbocdvy component in the X-ray spectrum. one of a number of such objects discovered. withZosal.	It is notable, firstly, for showing a soft blackbody component in the X-ray spectrum, one of a number of such objects discovered with.
. Secondly. its soft-N-ray and optical emission shows a double-pealked. modulation at the white-dwarl spin period AAllan 11996). whereas most of these stars show a single-peakecl moculation (see. ce.g.. Patterson 1994 or Hellier 2001 for reviews of this class).	Secondly, its soft-X-ray and optical emission shows a double-peaked modulation at the white-dwarf spin period Allan 1996), whereas most of these stars show a single-peaked modulation (see, e.g., Patterson 1994 or Hellier 2001 for reviews of this class).
The hard X-ray. emission in intermediate polars (LPs) originates below a. stanc-oll aceretion shock near the magnetic poles of the white dwarf.	The hard X-ray emission in intermediate polars (IPs) originates below a stand-off accretion shock near the magnetic poles of the white dwarf.
The soft. blackhocky emission is then understood. as arising from heated: white-dwarf surface around the accretion footprints.	The soft blackbody emission is then understood as arising from heated white-dwarf surface around the accretion footprints.
his is nearly always seen in the AM Ller class of cataclysmic variable. but it is seen only in some LPs. for which the reason is unclear.	This is nearly always seen in the AM Her class of cataclysmic variable, but it is seen only in some IPs, for which the reason is unclear.
The issue of why some LPs show a single-peaked pulsation. whereas others show a clouble-peakecl pulsation. is also unclear.	The issue of why some IPs show a single-peaked pulsation, whereas others show a double-peaked pulsation, is also unclear.
One idea Lblellier 1996: Allan 11996: Norton 1999) notes that LPs with shorter spin periods will have smaller magnetospheres in which the accretion clises are disrupted nearer the white cwarf.	One idea Hellier 1996; Allan 1996; Norton 1999) notes that IPs with shorter spin periods will have smaller magnetospheres in which the accretion discs are disrupted nearer the white dwarf.
This could result in shorter. fatter ‘accretion curtains’ of material which might have lower opacity in the vertical direction. thus. preferentially beaming X-ravs along magnetic field lines.	This could result in shorter, fatter `accretion curtains' of material which might have lower opacity in the vertical direction, thus preferentially beaming X-rays along magnetic field lines.
The two magnetic poles would combine to. produce a double-peaked pulsation.	The two magnetic poles would combine to produce a double-peaked pulsation.
With longer spin periods. where disc clisruption occurs further out. the opposite might hold. with tall. thin accretion curtains preferentially bcaming rays out of the sides.	With longer spin periods, where disc disruption occurs further out, the opposite might hold, with tall, thin accretion curtains preferentially beaming X-rays out of the sides.
Phe two poles would then act in phase. producing a single-peakecl pulsation.	The two poles would then act in phase, producing a single-peaked pulsation.
The X-ray satellite has a larger collecting area ancl better spectral resolution thanfosef.. allowing us to return to V405 Aur with better N-rav. cata than previously obtained.	The X-ray satellite has a larger collecting area and better spectral resolution than, allowing us to return to V405 Aur with better X-ray data than previously obtained.
We report here on a 30-ks. observation aimed at understanding the pulsation at the 545-8 spin period of V405 Aur.	We report here on a 30-ks observation aimed at understanding the pulsation at the 545-s spin period of V405 Aur.
(SAIBLL masses for our sample are estimated. from. stellar velocity clispersions: see Section 4.3 for further details: see Column 7 o£ Table 1). e(0.2 20)«107eres1M.lt the luminosity completeness linit (Lxz107ergs +) and assuming a similar distribution in bExddington ratios. the smallest SAIBLLE which could conceivably be in our sample is Mag=510M.: this is a factor z10 below the lowest mass Compton-thick ΑΝ identified here (Albu=5OPAL. ).	(SMBH masses for our sample are estimated from stellar velocity dispersions; see Section 4.3 for further details; see Column 7 of Table 1), $\approx (0.2$ $20) \times 10^{35} \ergps \Msun^{-1}$, at the luminosity completeness limit $L_{\rm X} \goa 10^{42} \ergps$ ) and assuming a similar distribution in Eddington ratios, the smallest SMBH which could conceivably be in our sample is $\Mbh \approx 5 \times 10^5 \Msun$; this is a factor $\approx 10$ below the lowest mass Compton-thick AGN identified here $\Mbh \approx 5 \times 10^6 \Msun$ ).
We may now estimate how many Conpton-thick AGNs may contain SAIBLIs in the mass region Myg25(0.5 5)«I0"M.. and hence constrain the number of Compton-hick .ACGNs not included in our space-density estimate clue o the lower mass limit of the SDSS.	We may now estimate how many Compton-thick AGNs may contain SMBHs in the mass region $\Mbh \approx (0.5$ $5) \times 10^6 \Msun$, and hence constrain the number of Compton-thick AGNs not included in our space-density estimate due to the lower mass limit of the SDSS.
Η the five most conservatively identified Compton-thick ACGNs with Mpg estimates contained SMDlIISs which were a factor z10 smaller in mass but had the same Lx/Mpg ratio. our (=SO percent) would still have Lyz1072eres+ and would therefore be included in our estimate of the space density of Compton-thick ACGNs as shown in Fig. 6..	If the five most conservatively identified Compton-thick AGNs with $\Mbh$ estimates contained SMBHs which were a factor $\approx 10$ smaller in mass but had the same $L_{\rm X} / \Mbh$ ratio, four $\approx 80$ percent) would still have $L_{\rm X} \goa 10^{42} \ergps$ and would therefore be included in our estimate of the space density of Compton-thick AGNs as shown in Fig. \ref{fig:space_dens}. .
Based on a simple extrapolation of the SMDII mass function of 7.. AGNs hosting SAIBIIs with Alpyz(0.5 5)10"M. are a factor &1.5 more abundant than those with Mig25(0.5 5)-10AL..	Based on a simple extrapolation of the SMBH mass function of \citet{marconi04}, AGNs hosting SMBHs with $\Mbh \approx (0.5$ $5) \times 10^{6} \Msun$ are a factor $\approx 1.5$ more abundant than those with $\Mbh \approx (0.5$ $5) \times 10^{7} \Msun$.
Hence. based on this simplistic formalisim. we estimate that approximately half of all Compton-thick AGNs with Lyz1077ergs may contain SAIBLIs with Mayzm(0.5 5)10"AL. which are not included in our parent sample.	Hence, based on this simplistic formalism, we estimate that approximately half of all Compton-thick AGNs with $L_{\rm X} \goa 10^{42} \ergps$ may contain SMBHs with $\Mbh \approx (0.5$ $5) \times 10^{6} \Msun$ which are not included in our parent sample.
Obscuration and host-ealaxy contamination may further prevent us from identifving all Compton-thick ACGNs in our considered. volume.	Obscuration and host-galaxy contamination may further prevent us from identifying all Compton-thick AGNs in our considered volume.
Obscured AGNsS can be mis-classified whenthe host-ealaxy over-shines the nuclear emission.	Obscured AGNs can be mis-classified whenthe host-galaxy over-shines the nuclear emission.
In the absence of extinction. a NL-AGN with Lx21077ergs can be almost totally eluted by a star-Lormation rate of I0M. 1 (Le. z95r percent of the observed. 41:23 emission is produced in regions: e.g. 7).	In the absence of extinction, a NL-AGN with $L_{\rm X} \approx 2 \times 10^{42} \ergps$ can be almost totally diluted by a star-formation rate of $10 \Msun$ $^{-1}$ (i.e., $\goa 95$ percent of the observed $H \beta$ emission is produced in regions; e.g., \citealt{yan10}) ).
The contribution of these sources to our observed space density is dillicult to quantify.	The contribution of these sources to our observed space density is difficult to quantify.
However. it is predicted that as many z50 percent of AGNs may. show no evidence for AGN activity in their optical spectroscopy (eg. ?:: Goulding Alexander 2009). anc would therefore not be included in our optically selected AGN sample.	However, it is predicted that as many $\approx 50$ percent of AGNs may show no evidence for AGN activity in their optical spectroscopy (e.g., \citealt{maiolino03}; Goulding Alexander 2009), and would therefore not be included in our optically selected AGN sample.
Allowing for the incompleteness within our optical parent sample and the possibility that many more of the AGNs studied here may be Compton thick. we suggest that our derived space density can be broadly consistent with the ΧΙ models.	Allowing for the incompleteness within our optical parent sample and the possibility that many more of the AGNs studied here may be Compton thick, we suggest that our derived space density can be broadly consistent with the XRB models.
Some theoretical models predict that Compton-thick ACGNs may harbour SAIBLIs which are undergoing an evolutionary phase of rapid growth (c.g.. ??2)).	Some theoretical models predict that Compton-thick AGNs may harbour SMBHs which are undergoing an evolutionary phase of rapid growth (e.g., \citealt{Fabian99,Granato06,Hopkins08}) ).
In this section we consider the implied. Ecllington ratios Gp~Laon/Leaa: where Leam126«lo(AlbuΔΙ.Jeres 13 for the Compton-thick ACGNs identified in our sample with publicly available black-hole mass (Alby) estimates.	In this section we consider the implied Eddington ratios $\eta \sim L_{\rm AGN} / L_{\rm Edd}$; where $ L_{\rm Edd} \approx 1.26 \times 10^{38} (\Mbh / \Msun) \ergps$ ) for the Compton-thick AGNs identified in our sample with publicly available black-hole mass $\Mbh$ ) estimates.
Stellar velocity dispersion measurements have been computed for 13 of the LE ΑΝ» in our sample. at least five of whieh we conservatively identify as Compton-thick AGNs.	Stellar velocity dispersion measurements have been computed for 13 of the 14 AGNs in our sample, at least five of which we conservatively identify as Compton-thick AGNs.
These measurements are publicly available in the MDPA-JIEU release of SDSS-DIU and ave derived. [rom the fitting of stellar population synthesis models to the SDSS 1-D Using the A o relation of 2? we convert the stellar velocity dispersions to Alby (sec Column 7 of Table 1)) in order to calculate Leap for these sources.	These measurements are publicly available in the MPA-JHU release of SDSS-DR7 and are derived from the fitting of stellar population synthesis models to the SDSS 1-D Using the $M$ $\sigma$ relation of \citet{gebhardt00} we convert the stellar velocity dispersions to $\Mbh$ (see Column 7 of Table \ref{tab:srce_props}) ) in order to calculate $L_{\rm Edd}$ for these sources.
The median SALBLL mass for our sample is AlpymA105M.(ic. these AGNs host SMDLI which are similar to those identified in the optical studs of Heckman et al.	The median SMBH mass for our sample is $\Mbh \approx 3 \times 10^7 \Msun$(i.e., these AGNs host SMBHs which are similar to those identified in the optical study of Heckman et al.
2004).	2004).
In order to estimate η for our Compton-thick ACGNs. we use Loy, as a proxy [or Lage and we assume the bolometric corrections of ?..	In order to estimate $\eta$ for our Compton-thick AGNs, we use $L_{6 \mu m}$ as a proxy for $L_{\rm AGN}$ and we assume the bolometric corrections of \citet{marconi04}.
Phe use of the 6pum continuum emission to infer £Lxcoy bas the advantage that it is an independent measure of the intrinsic luminosity of the AGN. whilst the NL emission arises from a similar region to that of Oru] which was used for the selection of the sources considered. here.	The use of the $6 \um$ continuum emission to infer $L_{\rm AGN}$ has the advantage that it is an independent measure of the intrinsic luminosity of the AGN, whilst the NL emission arises from a similar region to that of ] which was used for the selection of the sources considered here.
Twelve of our 14 sources have both Alby estimates and 6tum measurements.	Twelve of our 14 sources have both $\Mbh$ estimates and $6 \um$ measurements.
We find that our sample of AGNs are spread: over a wide-range of Edclington ratio. ye0.002 0.3 (median =0.014: see Column Ll of Table 2): the five Compton-thick ACiNs are at systematically higher Eddington ratios. rjz0.01 0.3 (median z0.2). Similarly. we find that the wellestucdied local Compton-thick AGNs (Circinus. Mrk 3. NGC LOGS and NGC 6240) have a similar range in Ecdclineton ratio. 4s0.002 1 (median z 0.2).	We find that our sample of AGNs are spread over a wide-range of Eddington ratio, $\eta \approx 0.002$ –0.3 (median $\approx 0.014$; see Column 11 of Table 2); the five Compton-thick AGNs are at systematically higher Eddington ratios, $\eta \approx 0.01$ $0.3$ (median $\approx 0.2$ Similarly, we find that the well-studied local Compton-thick AGNs (Circinus, Mrk 3, NGC 1068 and NGC 6240) have a similar range in Eddington ratio, $\eta \approx 0.002$ –1 (median $\approx 0.2$ ).
Lt is important to note the large uncertainties involved. with caleulating bolometric luminosities and subsequent LEclclington ratios: the large scatter in the 6pum relation combined with a possible LEcclineton ratio dependent bolometric correction (e.g... 2)) could vield an uncertainty [actor of the order z10 for the highest Iddington ratio sources.	It is important to note the large uncertainties involved with calculating bolometric luminosities and subsequent Eddington ratios; the large scatter in the $6 \um$ relation combined with a possible Eddington ratio dependent bolometric correction (e.g., \citealt{vasudevan07}) ) could yield an uncertainty factor of the order $\goa 10$ for the highest Eddington ratio sources.
None of the AGNs in our sample appear to be Ededington-limited on the basis of the 6tun luminosity. and any uncertainties would apply equally to all of the AGNs considered. bere. hence. our. [finding of systematically higher Exldington ratios for Compton-thick AGNs. to first-order. appears to be relatively robust.	None of the AGNs in our sample appear to be Eddington-limited on the basis of the $6 \um$ luminosity, and any uncertainties would apply equally to all of the AGNs considered here, hence our finding of systematically higher Eddington ratios for Compton-thick AGNs, to first-order, appears to be relatively robust.
Llowever. we suggest that this result may be driven by our selection of Oiu]-bright AGNsas well as our sensitivity towards the identification of Compton-thick ACNs.	However, we suggest that this result may be driven by our selection of ]-bright AGNsas well as our sensitivity towards the identification of Compton-thick AGNs.
For example. with deeper X-ray. data we may icentily further Compton-thick ACiNs in our sample which have lower values of η, and hence reducing the median Eddington ratio for the Compton-thick ACN subsample.	For example, with deeper X-ray data we may identify further Compton-thick AGNs in our sample which have lower values of $\eta$, and hence reducing the median Eddington ratio for the Compton-thick AGN subsample.
ὃν comparison. for the total population of Typc-2 ACGNSs identified from optical emission-line diagnostics in the SDSS. ? find that basedon the use of Ori] emission. to infer Lycoy. <0.5 percent of Evpe-2 AGNs hosting SMDIIS with Migz3OAL. are accreting above 4j;8 0.1: by contrast. we find that z30 percent of our sample have ne 0.1.	By comparison, for the total population of Type-2 AGNs identified from optical emission-line diagnostics in the SDSS, \citet{heckman04} find that basedon the use of ] emission to infer $L_{\rm AGN}$ , $< 0.5$ percent of Type-2 AGNs hosting SMBHs with $\Mbh \approx 3 \times 10^7 \Msun$ are accreting above $\eta \approx 0.1$ ; by contrast, we find that $\goa 30$ percent of our sample have $\eta \goa 0.1$ .
A particular advantage to a direct comparison with the study of Leckman et al. (	A particular advantage to a direct comparison with the study of Heckman et al. (
2004) is that selection processes ancl biases are likely to be identical between both studies.	2004) is that selection processes and biases are likely to be identical between both studies.
7 tuclicates that: 1) brown dwarfs in the ONC dorofl depart Grom the £x - mass relationship we observe for higher mass stars. and 2) the mean BD N-ray luminosity is of the order of 107 eres. F.	\ref{fig:BD} indicates that: 1) brown dwarfs in the ONC do depart from the $L_X$ - mass relationship we observe for higher mass stars, and 2) the mean BD X-ray luminosity is of the order of $10^{28.5}$ $\cdot$ $^{-1}$.
Ou average this is higher than the recent. results obtained for BDs in IC 318 by (2001).. but lower than the £x reported by Imanishietal.(2001) for oue detected BD and one BD caudidate in the voung p Ophiuchi cloud.	On average this is higher than the recent results obtained for BDs in IC 348 by \citet{pre01}, , but lower than the $L_X$ reported by \citet{ima01} for one detected BD and one BD candidate in the young $\rho$ Ophiuchi cloud.
Although the relationship with mass explains a good deal of the scatter in activity levels of our sample. the deviations from this treuc are still siguificant.	Although the relationship with mass explains a good deal of the scatter in activity levels of our sample, the deviations from this trend are still significant.
The next stellar parameter we investigate in order to uuderstaud this residual scatter is the age. as iuferred from the SDF evolutiouary tracks.	The next stellar parameter we investigate in order to understand this residual scatter is the age, as inferred from the SDF evolutionary tracks.
Figure 8. shows the Log(Lx) vs. Log(.Age) plot Dor stars iu our sample with mass between 0.2 aud 1.0 M..	Figure \ref{fig:LXvsA0a} shows the $Log(L_X)$ vs. $Log(Age)$ plot for stars in our sample with mass between 0.5 and 1.0 $M_{\odot}$.
The median Ly appears to decrease with increaslug age. but we must exercise special care in the tuterpretation of this treud: there is a widespread coucern that the age spread iudicated yy the position of low mass stars still ou the Hayashi tracks may be largely. or even eutirely. due ο an artificial spread in the heometric luminosities (cf.Hartimann2001).	The median $L_X$ appears to decrease with increasing age, but we must exercise special care in the interpretation of this trend: there is a widespread concern that the age spread indicated by the position of low mass stars still on the Hayashi tracks may be largely, or even entirely, due to an artificial spread in the bolometric luminosities \citep[cf.][]{har01}.

For small amplitude libration about L4/L5 and circular orbits. the transit timing perturbation is given by NMGS)/(8). where NM(f) is the angular displacement of the Trojan from L4/L5 at the time of the /th transit.

For small amplitude libration about L4/L5 and circular orbits, the transit timing perturbation is given by $\delta t_i \simeq \epsilon P_s \Delta M(t_i) / (2\pi)$ , where $\Delta M(t_i)$ is the angular displacement of the Trojan from L4/L5 at the time of the $i$ th transit.

The TTVs can be modeled by a sinusoid. 07/;=Aqsin(2x(1—14)(Peppy+6). where Aq is the aaplitude of the transit timing variations and Pp744.

The TTVs can be modeled by a sinusoid, $\delta t_i = K_{\rm tt} \sin\left(2\pi\left(t-t_0\right)/P_{\rm TTV}+\phi\right)$, where $K_{\rm tt}$ is the amplitude of the transit timing variations and $P_{\rm TTV}\sim\tau_{\rm slow}$.

L the dominant periodicity of the transit timing variations (Jj) is well determined. then the remaining parameters can be determined via linear least squares fitting to the observed (ransil times.

If the dominant periodicity of the transit timing variations $P_{\rm TTV}$ ) is well determined, then the remaining parameters can be determined via linear least squares fitting to the observed transit times.

The transit timing variations will have an amplitiucle ens (o ge where A4, is the amplitude of the Trojans angular displacement from (he Lagrange point.

The transit timing variations will have an amplitude 60s ) ) ) ), where $K_{\Delta M}$ is the amplitude of the Trojan's angular displacement from the Lagrange point.

For small amplitude libration. A4;&max|AAS and rms(0/;)cWy/V2 (see Fig.

For small amplitude libration, $K_{\Delta M}\simeq\mathrm{max}\left|\Delta M\right|$ and $\mathrm{rms}(\delta t_i)\simeq K_{\rm tt} / \sqrt{2}$ (see Fig.

1) Libration amplitudes of A4;~5—25 are common for Trojans orbiting near the sun-Jupiter Lagrange points (Murray Dermott 2000).

1) Libration amplitudes of $K_{\Delta M}\sim~5-25^\circ$ are common for Trojans orbiting near the Sun-Jupiter Lagrange points (Murray Dermott 2000).

The Lomb-Scargle5 periocogram5 can be easily adapted to efficiently scan a range5 of putative periods aud identily any signilicant periodicities (Cumming 2004).

The Lomb-Scargle periodogram can be easily adapted to efficiently scan a range of putative periods and identify any significant periodicities (Cumming 2004).

If we assume that ihere are many V4) transit (aiming observations with uncorrelated Gaussian unicertainties σι=Gg. that the transit timing5 observations are evenly distributed. and the duration of observations (2,,,) is greater than than P. (en a periodogram-stvle analvsis results in a chance of detecting a Trojan 1 Ny,>Nyeoy,(atlog|Tin./(2FTD.i) (Cumming 2004). where F is the false alarm probability. which we set to 107.

If we assume that there are many $N_{\rm tt}$ ) transit timing observations with uncorrelated Gaussian uncertainties $\sigma_{t_i}=\sigma_{tt}$, that the transit timing observations are evenly distributed, and the duration of observations $T_{\rm obs}$ ) is greater than than $P_{\rm TTV}$, then a periodogram-style analysis results in a chance of detecting a Trojan if $K_{tt}\ge K_{1/2} \simeq \sigma_{tt}\left(\frac{4}{N_{\rm tt}} \log\left[T_{\rm obs} / \left(2 F P_s\right) \right] \right)^{1/2}$ (Cumming 2004), where $F$ is the false alarm probability, which we set to $10^{-3}$.

For Vay=L/P.40. Nyyc04. so sub-Earth-mass Trojans could be reaclily detected.

For $N_{\rm tt} = T_{\rm obs}/P_s = 40$, $K_{1/2} \simeq \sigma_{tt}$, so sub-Earth-mass Trojans could be readily detected.

We note that all published transit timing data sets have Ay<20. which results in a significantly reduced sensitvitv. if [ιν is unknown p

We note that all published transit timing data sets have $N_{\rm tt}<20$, which results in a significantly reduced sensitvity, if $P_{\rm TTV}$ is unknown .

riori ln this small-Nq regime. a simple 4? test of the null hypothesis (0/;= 0) is more sensitive for detecting transit timing variations.

In this $N_{\rm tt}$ regime, a simple $\chi^2$ test of the null hypothesis $\delta t_i=0$ ) is more sensitive for detecting transit timing variations.

However. if only a single periodicity (e.g.. 744) is lo be tested. then even a modest number of observations can be quite sensitive (e.g... Ayo22.504even lor Nyy= 13).

However, if only a single periodicity (e.g., $\tau_{\rm slow}$ ) is to be tested, then even a modest number of observations can be quite sensitive (e.g., $K_{1/2}\simeq 2.5\sigma_{\rm tt}$even for $N_{\rm tt}=13$ ).

rotation curve of the receding half drops in the outer parts.

The masini rotation speed. leaving out the bump at110".. occurs around a radius of (1.87 ΚΡΟ) at a speed of 25|.

The maximum rotation speed, leaving out the bump at, occurs around a radius of (1.87 kpc) at a speed of 25.

.. Stil Israel (2002) give a rotation speed Vsini of 17.543.9 aat a radius of {for DDO 43.

Stil Israel (2002) give a rotation speed $V \sin i$ of $\pm$ 3.9 at a radius of for DDO 43.

At that radius our Vsin/ would be the same at 17.60.58 !.

At that radius our $V \sin i$ would be the same at $\pm$ 0.8.

. To examine the quality of the lit. we made a model of the velocity field. (hen subtracted it from the observed. velocity Ποια.

To examine the quality of the fit, we made a model of the velocity field, then subtracted it from the observed velocity field.

The resilual map is shown in Figure 24..

The residual map is shown in Figure \ref{fig:resid}.

The values of the residuals range [rom -6.6 to 7.1!.. so in general. the fit seems quite good.

The values of the residuals range from -6.6 to 7.1, so in general, the fit seems quite good.

We have plotted. contours Irom the model velocity [field on the residual map in Figure 25. and the observed. velocity [field contours on (he residual map in Figure 26..

We have plotted contours from the model velocity field on the residual map in Figure \ref{fig:modelonresid} and the observed velocity field contours on the residual map in Figure \ref{fig:m1onresid}.

The model successfully recreates (he weak turnover in each side of the velocity field. but the residual map shows (hat it had. difficulty with the receding half turnover in the sense that it underestimates it and shifts it slightly north.

The model successfully recreates the weak turnover in each side of the velocity field, but the residual map shows that it had difficulty with the receding half turnover in the sense that it underestimates it and shifts it slightly north.

There is another region of higher-than-average residuals just south of the center of the galaxy: (his area slightly overlaps the west sides of the large hole and knot in the “Thhis is also near (he region of hiehest velocity dispersion in the galaxy. so perhaps it is nol surprising that the velocity residuals are larger here as well.

There is another region of higher-than-average residuals just south of the center of the galaxy; this area slightly overlaps the west sides of the large hole and knot in the \\.Thhis is also near the region of highest velocity dispersion in the galaxy, so perhaps it is not surprising that the velocity residuals are larger here as well.

From Figure 26.. it can be seen that most of the regions of larger residuals (especially negative residuals) coincide with the kinks in the isovels that may be representative of a warp.

From Figure \ref{fig:m1onresid}, it can be seen that most of the regions of larger residuals (especially negative residuals) coincide with the kinks in the isovels that may be representative of a warp.

The residuals are still small however. indicating (hal its not a significant warp.

The residuals are still small however, indicating that it's not a significant warp.

The original listing of DDO 43 as a candidate tidal dwarf by Hunter ((2000) was based on a suggested rotation speed of order 9|.

The original listing of DDO 43 as a candidate tidal dwarf by Hunter (2000) was based on a suggested rotation speed of order 9.

.. As a result. on a plot of Mg; versus the masini rotation speed (Figure 1 of IIunter al.)) DDO 43 stood oul as unusually huninous for its rotation speed.

As a result, on a plot of $_B$ versus the maximum rotation speed (Figure 1 of Hunter ) DDO 43 stood out as unusually luminous for its rotation speed.

This could imply a deficit of dark matter. a characteristic of dal dwarls (Barnes Hernequist 1992).

This could imply a deficit of dark matter, a characteristic of tidal dwarfs (Barnes Hernquist 1992).

However. with a maximum rotation speed of 25s... found here. DDO 43 now lies close to (he mean of the relationship defined bv other Im galaxies ancl spirals in (hat plot.

However, with a maximum rotation speed of 25, found here, DDO 43 now lies close to the mean of the relationship defined by other Im galaxies and spirals in that plot.

Thus. DDO 43 is unlikely to be without dark matter. and unlikely to be a tidal dwarl.

Thus, DDO 43 is unlikely to be without dark matter, and unlikely to be a tidal dwarf.

This is comforting since there was no obvious nearby postnerger object to have been the parent of DDO 43 if il were a tidal dwarl.

This is comforting since there was no obvious nearby post-merger object to have been the parent of DDO 43 if it were a tidal dwarf.

A erev-scale display of the velocity dispersion map from the ddata is shown in Figure 27 with contours of the integrated ssuperposed.

A grey-scale display of the velocity dispersion map from the data is shown in Figure \ref{fig:veldisp} with contours of the integrated superposed.

Within the optical body of the galaxy. the velocity dispersion is around LOτ

Within the optical body of the galaxy, the velocity dispersion is around 10.

ν, This is the value found in most quiescent gas disks.

This is the value found in most quiescent gas disks.

There are a few spots with higher

the absorption features at 71.47 keV and ~2.71 keV. now both appear as a resolved line pair. with the energy spacing of the respective Lee and. Lye resonance lines of Mg aid 5. Furthermore. additional narrow absorption features are seen to mateh with same Ix-shell resonance Lines of Ne. οἱ and. possibly Ar.

the absorption features at $\sim$ 1.47 keV and $\sim$ 2.71 keV now both appear as a resolved line pair, with the energy spacing of the respective $\alpha$ and $\alpha$ resonance lines of Mg and S. Furthermore, additional narrow absorption features are seen to match with same K-shell resonance lines of Ne, Si and possibly Ar.

To quantify these absorption features we explored. the ALOS data with Nspec.

To quantify these absorption features we explored the MOS data with Xspec.

. We first. fitted the MOS data at 1-5 keV with a power law to provide a baseline: below l keV the spectrum rises steeplv due to strong soft. X-rav emission (Pounds. and. Reeves 2006).

We first fitted the MOS data at 1-5 keV with a power law to provide a baseline; below 1 keV the spectrum rises steeply due to strong soft X-ray emission (Pounds and Reeves 2006).

Several narrow features clearly visible in the data-to-power-law-mocdel ratio plot (figure 3.2 upper panel) contributed to à poor statistical fit (\7=351266).

Several narrow features clearly visible in the data-to-power-law-model ratio plot (figure 3, upper panel) contributed to a poor statistical fit $\chi^{2}$ =351/266).

Fitting gaussians to the visible features. with a fixed width of a= 10eV. found 6 significant negative (absorption) lines.

Fitting gaussians to the visible features, with a fixed width of $\sigma$ = 10eV, found 6 significant negative (absorption) lines.

Ehe overall improvement to the fit was very significant with X7 reduced to 270/254.

The overall improvement to the fit was very significant with $\chi^{2}$ reduced to 270/254.

The fitted line energies and I[uxes are listed in Table 1 where the observe line energy is in each case compared: with the most likely identification. chosen as the nearest resonance transition of an abundant ion.

The fitted line energies and fluxes are listed in Table 1 where the observed line energy is in each case compared with the most likely identification, chosen as the nearest resonance transition of an abundant ion.

Crucially. α 6 line energies exhibit a "blue shift in the range ~5-7 %..

Crucially, all 6 line energies exhibit a `blue shift' in the range $\sim$ 5-7.

Assuming the same ratio for the absorption line observed at 731.07 keV. gives a preferrec identification with Llea of FeXXV. (figure 2).

Assuming the same ratio for the absorption line observed at $\sim$ 7.07 keV gives a preferred identification with $\alpha$ of FeXXV (figure 2).

In the res frame o£ tthe revised. identification of the absorption spectrum now vields an increased. outllow velocity in the range vo 0.13-0.15c.

In the rest frame of the revised identification of the absorption spectrum now yields an increased outflow velocity in the range $\sim$ 0.13-0.15c.

To test the compatibility of the visual absorption line set with a physical absorber we then compared the MOS data with a photoionised. gas modelled using the NSTAIU code (Kallman et al 1996).

To test the compatibility of the visual absorption line set with a physical absorber we then compared the MOS data with a photoionised gas modelled using the XSTAR code (Kallman et al 1996).

Free. parameters of the absorber in this comparison were the column density and. ionisation parameter. with outflow (or inflow) velocities included as an adjustment to the apparent. redshift of the absorbing gas.

Free parameters of the absorber in this comparison were the column density and ionisation parameter, with outflow (or inflow) velocities included as an adjustment to the apparent redshift of the absorbing gas.

Alb relevant abundant elements from Ne to Fe were include with the relative abundances constrained to within a factor 2 of solar.

All relevant abundant elements from Ne to Fe were included with the relative abundances constrained to within a factor 2 of solar.

Since our primary aim was to check the energies an relative strength of the principal absorption lines identifiec in the visual spectral fit shown in figure 2. the mocdel clic not attempt to match the broad. excess Lux near 6 keV: it therefore consisted only of a power law with photolonisec absorber.

Since our primary aim was to check the energies and relative strength of the principal absorption lines identified in the visual spectral fit shown in figure 2, the model did not attempt to match the broad excess flux near $\sim$ 6 keV; it therefore consisted only of a power law with photoionised absorber.

Fitting over the 1-10. keV band. the addition of he photoionisec absorber improved the spectral fit. [rom v of 522 for 358 degrees of freedom to 465/345.

Fitting over the 1-10 keV band the addition of the photoionised absorber improved the spectral fit from $\chi^{2}$ of 522 for 358 degrees of freedom to 465/345.

The vest-fit column density was Ny21077 em with an ionisation parameter of logé=2.9-+0.4 and nominal relative abundances of Ne. Mg. Si. S. Ar and Fe of 0.5. 1. 0.5. 1. 1.5 and 0.5.

The best-fit column density was $_{H}$$\sim$$2\times 10^{22}$ $^{-2}$, with an ionisation parameter of $\xi$ $\pm$ 0.4 and nominal relative abundances of Ne, Mg, Si, S, Ar and Fe of 0.5, 1, 0.5, 1, 0.5 and 0.5.

Figure 3 (mid. panel) reproduces this absorbed power Law model. with the strongest. predicted: absorption ines (in order of increasing energy) corresponding to Ix-shell resonance transitions of Ne. Me. Si. S. Ar and Fe. supporting he visual assessment of figure 2.

Figure 3 (mid panel) reproduces this absorbed power law model, with the strongest predicted absorption lines (in order of increasing energy) corresponding to K-shell resonance transitions of Ne, Mg, Si, S, Ar and Fe, supporting the visual assessment of figure 2.

Additionally. we note the Ly? line of Μο would occur at 1.83 keV. sugeesting

Additionally, we note the $\beta$ line of MgXII would occur at $\sim$ 1.83 keV, suggesting

V405 Xurigae. 0558.015353) was discovered. in the Al-Sky Survey ancl identified as απ intermediate polar (a cataclysmic variable with a magnetic white-cwarl primary) by Llaberl (1994).

V405 Aurigae J0558.0+5353) was discovered in the All-Sky Survey and identified as an intermediate polar (a cataclysmic variable with a magnetic white-dwarf primary) by Haberl (1994).

lt is notable. firstly. for showing a soft blackbocdvy component in the X-ray spectrum. one of a number of such objects discovered. withZosal.

It is notable, firstly, for showing a soft blackbody component in the X-ray spectrum, one of a number of such objects discovered with.

. Secondly. its soft-N-ray and optical emission shows a double-pealked. modulation at the white-dwarl spin period AAllan 11996). whereas most of these stars show a single-peakecl moculation (see. ce.g.. Patterson 1994 or Hellier 2001 for reviews of this class).

Secondly, its soft-X-ray and optical emission shows a double-peaked modulation at the white-dwarf spin period Allan 1996), whereas most of these stars show a single-peaked modulation (see, e.g., Patterson 1994 or Hellier 2001 for reviews of this class).

The hard X-ray. emission in intermediate polars (LPs) originates below a. stanc-oll aceretion shock near the magnetic poles of the white dwarf.

The hard X-ray emission in intermediate polars (IPs) originates below a stand-off accretion shock near the magnetic poles of the white dwarf.

The soft. blackhocky emission is then understood. as arising from heated: white-dwarf surface around the accretion footprints.

The soft blackbody emission is then understood as arising from heated white-dwarf surface around the accretion footprints.

his is nearly always seen in the AM Ller class of cataclysmic variable. but it is seen only in some LPs. for which the reason is unclear.

This is nearly always seen in the AM Her class of cataclysmic variable, but it is seen only in some IPs, for which the reason is unclear.

The issue of why some LPs show a single-peaked pulsation. whereas others show a clouble-peakecl pulsation. is also unclear.

The issue of why some IPs show a single-peaked pulsation, whereas others show a double-peaked pulsation, is also unclear.

One idea Lblellier 1996: Allan 11996: Norton 1999) notes that LPs with shorter spin periods will have smaller magnetospheres in which the accretion clises are disrupted nearer the white cwarf.

One idea Hellier 1996; Allan 1996; Norton 1999) notes that IPs with shorter spin periods will have smaller magnetospheres in which the accretion discs are disrupted nearer the white dwarf.

This could result in shorter. fatter ‘accretion curtains’ of material which might have lower opacity in the vertical direction. thus. preferentially beaming X-ravs along magnetic field lines.

This could result in shorter, fatter `accretion curtains' of material which might have lower opacity in the vertical direction, thus preferentially beaming X-rays along magnetic field lines.

The two magnetic poles would combine to. produce a double-peaked pulsation.

The two magnetic poles would combine to produce a double-peaked pulsation.

With longer spin periods. where disc clisruption occurs further out. the opposite might hold. with tall. thin accretion curtains preferentially bcaming rays out of the sides.

With longer spin periods, where disc disruption occurs further out, the opposite might hold, with tall, thin accretion curtains preferentially beaming X-rays out of the sides.

Phe two poles would then act in phase. producing a single-peakecl pulsation.

The two poles would then act in phase, producing a single-peaked pulsation.

The X-ray satellite has a larger collecting area ancl better spectral resolution thanfosef.. allowing us to return to V405 Aur with better N-rav. cata than previously obtained.

The X-ray satellite has a larger collecting area and better spectral resolution than, allowing us to return to V405 Aur with better X-ray data than previously obtained.

We report here on a 30-ks. observation aimed at understanding the pulsation at the 545-8 spin period of V405 Aur.

We report here on a 30-ks observation aimed at understanding the pulsation at the 545-s spin period of V405 Aur.

(SAIBLL masses for our sample are estimated. from. stellar velocity clispersions: see Section 4.3 for further details: see Column 7 o£ Table 1). e(0.2 20)«107eres1M.lt the luminosity completeness linit (Lxz107ergs +) and assuming a similar distribution in bExddington ratios. the smallest SAIBLLE which could conceivably be in our sample is Mag=510M.: this is a factor z10 below the lowest mass Compton-thick ΑΝ identified here (Albu=5OPAL. ).

(SMBH masses for our sample are estimated from stellar velocity dispersions; see Section 4.3 for further details; see Column 7 of Table 1), $\approx (0.2$ $20) \times 10^{35} \ergps \Msun^{-1}$, at the luminosity completeness limit $L_{\rm X} \goa 10^{42} \ergps$ ) and assuming a similar distribution in Eddington ratios, the smallest SMBH which could conceivably be in our sample is $\Mbh \approx 5 \times 10^5 \Msun$; this is a factor $\approx 10$ below the lowest mass Compton-thick AGN identified here $\Mbh \approx 5 \times 10^6 \Msun$ ).

We may now estimate how many Conpton-thick AGNs may contain SAIBLIs in the mass region Myg25(0.5 5)«I0"M.. and hence constrain the number of Compton-hick .ACGNs not included in our space-density estimate clue o the lower mass limit of the SDSS.

We may now estimate how many Compton-thick AGNs may contain SMBHs in the mass region $\Mbh \approx (0.5$ $5) \times 10^6 \Msun$, and hence constrain the number of Compton-thick AGNs not included in our space-density estimate due to the lower mass limit of the SDSS.

Η the five most conservatively identified Compton-thick ACGNs with Mpg estimates contained SMDlIISs which were a factor z10 smaller in mass but had the same Lx/Mpg ratio. our (=SO percent) would still have Lyz1072eres+ and would therefore be included in our estimate of the space density of Compton-thick ACGNs as shown in Fig. 6..

If the five most conservatively identified Compton-thick AGNs with $\Mbh$ estimates contained SMBHs which were a factor $\approx 10$ smaller in mass but had the same $L_{\rm X} / \Mbh$ ratio, four $\approx 80$ percent) would still have $L_{\rm X} \goa 10^{42} \ergps$ and would therefore be included in our estimate of the space density of Compton-thick AGNs as shown in Fig. \ref{fig:space_dens}. .

Based on a simple extrapolation of the SMDII mass function of 7.. AGNs hosting SAIBIIs with Alpyz(0.5 5)10"M. are a factor &1.5 more abundant than those with Mig25(0.5 5)-10AL..

Based on a simple extrapolation of the SMBH mass function of \citet{marconi04}, AGNs hosting SMBHs with $\Mbh \approx (0.5$ $5) \times 10^{6} \Msun$ are a factor $\approx 1.5$ more abundant than those with $\Mbh \approx (0.5$ $5) \times 10^{7} \Msun$.

Hence. based on this simplistic formalisim. we estimate that approximately half of all Compton-thick AGNs with Lyz1077ergs may contain SAIBLIs with Mayzm(0.5 5)10"AL. which are not included in our parent sample.

Hence, based on this simplistic formalism, we estimate that approximately half of all Compton-thick AGNs with $L_{\rm X} \goa 10^{42} \ergps$ may contain SMBHs with $\Mbh \approx (0.5$ $5) \times 10^{6} \Msun$ which are not included in our parent sample.

Obscuration and host-ealaxy contamination may further prevent us from identifving all Compton-thick ACGNs in our considered. volume.

Obscuration and host-galaxy contamination may further prevent us from identifying all Compton-thick AGNs in our considered volume.

Obscured AGNsS can be mis-classified whenthe host-ealaxy over-shines the nuclear emission.

Obscured AGNs can be mis-classified whenthe host-galaxy over-shines the nuclear emission.

In the absence of extinction. a NL-AGN with Lx21077ergs can be almost totally eluted by a star-Lormation rate of I0M. 1 (Le. z95r percent of the observed. 41:23 emission is produced in regions: e.g. 7).

In the absence of extinction, a NL-AGN with $L_{\rm X} \approx 2 \times 10^{42} \ergps$ can be almost totally diluted by a star-formation rate of $10 \Msun$ $^{-1}$ (i.e., $\goa 95$ percent of the observed $H \beta$ emission is produced in regions; e.g., \citealt{yan10}) ).

The contribution of these sources to our observed space density is dillicult to quantify.

The contribution of these sources to our observed space density is difficult to quantify.

However. it is predicted that as many z50 percent of AGNs may. show no evidence for AGN activity in their optical spectroscopy (eg. ?:: Goulding Alexander 2009). anc would therefore not be included in our optically selected AGN sample.

However, it is predicted that as many $\approx 50$ percent of AGNs may show no evidence for AGN activity in their optical spectroscopy (e.g., \citealt{maiolino03}; Goulding Alexander 2009), and would therefore not be included in our optically selected AGN sample.

Allowing for the incompleteness within our optical parent sample and the possibility that many more of the AGNs studied here may be Compton thick. we suggest that our derived space density can be broadly consistent with the ΧΙ models.

Allowing for the incompleteness within our optical parent sample and the possibility that many more of the AGNs studied here may be Compton thick, we suggest that our derived space density can be broadly consistent with the XRB models.

Some theoretical models predict that Compton-thick ACGNs may harbour SAIBLIs which are undergoing an evolutionary phase of rapid growth (c.g.. ??2)).

Some theoretical models predict that Compton-thick AGNs may harbour SMBHs which are undergoing an evolutionary phase of rapid growth (e.g., \citealt{Fabian99,Granato06,Hopkins08}) ).

In this section we consider the implied. Ecllington ratios Gp~Laon/Leaa: where Leam126«lo(AlbuΔΙ.Jeres 13 for the Compton-thick ACGNs identified in our sample with publicly available black-hole mass (Alby) estimates.

In this section we consider the implied Eddington ratios $\eta \sim L_{\rm AGN} / L_{\rm Edd}$; where $ L_{\rm Edd} \approx 1.26 \times 10^{38} (\Mbh / \Msun) \ergps$ ) for the Compton-thick AGNs identified in our sample with publicly available black-hole mass $\Mbh$ ) estimates.

Stellar velocity dispersion measurements have been computed for 13 of the LE ΑΝ» in our sample. at least five of whieh we conservatively identify as Compton-thick AGNs.

Stellar velocity dispersion measurements have been computed for 13 of the 14 AGNs in our sample, at least five of which we conservatively identify as Compton-thick AGNs.

These measurements are publicly available in the MDPA-JIEU release of SDSS-DIU and ave derived. [rom the fitting of stellar population synthesis models to the SDSS 1-D Using the A o relation of 2? we convert the stellar velocity dispersions to Alby (sec Column 7 of Table 1)) in order to calculate Leap for these sources.

These measurements are publicly available in the MPA-JHU release of SDSS-DR7 and are derived from the fitting of stellar population synthesis models to the SDSS 1-D Using the $M$ $\sigma$ relation of \citet{gebhardt00} we convert the stellar velocity dispersions to $\Mbh$ (see Column 7 of Table \ref{tab:srce_props}) ) in order to calculate $L_{\rm Edd}$ for these sources.

The median SALBLL mass for our sample is AlpymA105M.(ic. these AGNs host SMDLI which are similar to those identified in the optical studs of Heckman et al.

The median SMBH mass for our sample is $\Mbh \approx 3 \times 10^7 \Msun$(i.e., these AGNs host SMBHs which are similar to those identified in the optical study of Heckman et al.

2004).

In order to estimate η for our Compton-thick ACGNs. we use Loy, as a proxy [or Lage and we assume the bolometric corrections of ?..

In order to estimate $\eta$ for our Compton-thick AGNs, we use $L_{6 \mu m}$ as a proxy for $L_{\rm AGN}$ and we assume the bolometric corrections of \citet{marconi04}.

Phe use of the 6pum continuum emission to infer £Lxcoy bas the advantage that it is an independent measure of the intrinsic luminosity of the AGN. whilst the NL emission arises from a similar region to that of Oru] which was used for the selection of the sources considered. here.

The use of the $6 \um$ continuum emission to infer $L_{\rm AGN}$ has the advantage that it is an independent measure of the intrinsic luminosity of the AGN, whilst the NL emission arises from a similar region to that of ] which was used for the selection of the sources considered here.

Twelve of our 14 sources have both Alby estimates and 6tum measurements.

Twelve of our 14 sources have both $\Mbh$ estimates and $6 \um$ measurements.

We find that our sample of AGNs are spread: over a wide-range of Edclington ratio. ye0.002 0.3 (median =0.014: see Column Ll of Table 2): the five Compton-thick ACiNs are at systematically higher Eddington ratios. rjz0.01 0.3 (median z0.2). Similarly. we find that the wellestucdied local Compton-thick AGNs (Circinus. Mrk 3. NGC LOGS and NGC 6240) have a similar range in Ecdclineton ratio. 4s0.002 1 (median z 0.2).

We find that our sample of AGNs are spread over a wide-range of Eddington ratio, $\eta \approx 0.002$ –0.3 (median $\approx 0.014$; see Column 11 of Table 2); the five Compton-thick AGNs are at systematically higher Eddington ratios, $\eta \approx 0.01$ $0.3$ (median $\approx 0.2$ Similarly, we find that the well-studied local Compton-thick AGNs (Circinus, Mrk 3, NGC 1068 and NGC 6240) have a similar range in Eddington ratio, $\eta \approx 0.002$ –1 (median $\approx 0.2$ ).

Lt is important to note the large uncertainties involved. with caleulating bolometric luminosities and subsequent LEclclington ratios: the large scatter in the 6pum relation combined with a possible LEcclineton ratio dependent bolometric correction (e.g... 2)) could vield an uncertainty [actor of the order z10 for the highest Iddington ratio sources.

It is important to note the large uncertainties involved with calculating bolometric luminosities and subsequent Eddington ratios; the large scatter in the $6 \um$ relation combined with a possible Eddington ratio dependent bolometric correction (e.g., \citealt{vasudevan07}) ) could yield an uncertainty factor of the order $\goa 10$ for the highest Eddington ratio sources.

None of the AGNs in our sample appear to be Ededington-limited on the basis of the 6tun luminosity. and any uncertainties would apply equally to all of the AGNs considered. bere. hence. our. [finding of systematically higher Exldington ratios for Compton-thick AGNs. to first-order. appears to be relatively robust.

None of the AGNs in our sample appear to be Eddington-limited on the basis of the $6 \um$ luminosity, and any uncertainties would apply equally to all of the AGNs considered here, hence our finding of systematically higher Eddington ratios for Compton-thick AGNs, to first-order, appears to be relatively robust.

Llowever. we suggest that this result may be driven by our selection of Oiu]-bright AGNsas well as our sensitivity towards the identification of Compton-thick ACNs.

However, we suggest that this result may be driven by our selection of ]-bright AGNsas well as our sensitivity towards the identification of Compton-thick AGNs.

For example. with deeper X-ray. data we may icentily further Compton-thick ACiNs in our sample which have lower values of η, and hence reducing the median Eddington ratio for the Compton-thick ACN subsample.

For example, with deeper X-ray data we may identify further Compton-thick AGNs in our sample which have lower values of $\eta$, and hence reducing the median Eddington ratio for the Compton-thick AGN subsample.

ὃν comparison. for the total population of Typc-2 ACGNSs identified from optical emission-line diagnostics in the SDSS. ? find that basedon the use of Ori] emission. to infer Lycoy. <0.5 percent of Evpe-2 AGNs hosting SMDIIS with Migz3OAL. are accreting above 4j;8 0.1: by contrast. we find that z30 percent of our sample have ne 0.1.

By comparison, for the total population of Type-2 AGNs identified from optical emission-line diagnostics in the SDSS, \citet{heckman04} find that basedon the use of ] emission to infer $L_{\rm AGN}$ , $< 0.5$ percent of Type-2 AGNs hosting SMBHs with $\Mbh \approx 3 \times 10^7 \Msun$ are accreting above $\eta \approx 0.1$ ; by contrast, we find that $\goa 30$ percent of our sample have $\eta \goa 0.1$ .

A particular advantage to a direct comparison with the study of Leckman et al. (

A particular advantage to a direct comparison with the study of Heckman et al. (

2004) is that selection processes ancl biases are likely to be identical between both studies.

2004) is that selection processes and biases are likely to be identical between both studies.

7 tuclicates that: 1) brown dwarfs in the ONC dorofl depart Grom the £x - mass relationship we observe for higher mass stars. and 2) the mean BD N-ray luminosity is of the order of 107 eres. F.

\ref{fig:BD} indicates that: 1) brown dwarfs in the ONC do depart from the $L_X$ - mass relationship we observe for higher mass stars, and 2) the mean BD X-ray luminosity is of the order of $10^{28.5}$ $\cdot$ $^{-1}$.

Ou average this is higher than the recent. results obtained for BDs in IC 318 by (2001).. but lower than the £x reported by Imanishietal.(2001) for oue detected BD and one BD caudidate in the voung p Ophiuchi cloud.

On average this is higher than the recent results obtained for BDs in IC 348 by \citet{pre01}, , but lower than the $L_X$ reported by \citet{ima01} for one detected BD and one BD candidate in the young $\rho$ Ophiuchi cloud.

Although the relationship with mass explains a good deal of the scatter in activity levels of our sample. the deviations from this treuc are still siguificant.

Although the relationship with mass explains a good deal of the scatter in activity levels of our sample, the deviations from this trend are still significant.

The next stellar parameter we investigate in order to uuderstaud this residual scatter is the age. as iuferred from the SDF evolutiouary tracks.

The next stellar parameter we investigate in order to understand this residual scatter is the age, as inferred from the SDF evolutionary tracks.

Figure 8. shows the Log(Lx) vs. Log(.Age) plot Dor stars iu our sample with mass between 0.2 aud 1.0 M..

Figure \ref{fig:LXvsA0a} shows the $Log(L_X)$ vs. $Log(Age)$ plot for stars in our sample with mass between 0.5 and 1.0 $M_{\odot}$.

The median Ly appears to decrease with increaslug age. but we must exercise special care in the tuterpretation of this treud: there is a widespread coucern that the age spread iudicated yy the position of low mass stars still ou the Hayashi tracks may be largely. or even eutirely. due ο an artificial spread in the heometric luminosities (cf.Hartimann2001).

The median $L_X$ appears to decrease with increasing age, but we must exercise special care in the interpretation of this trend: there is a widespread concern that the age spread indicated by the position of low mass stars still on the Hayashi tracks may be largely, or even entirely, due to an artificial spread in the bolometric luminosities \citep[cf.][]{har01}.