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Once the (x.y) coordinates have been determined. the parallax and proper motion of ULAS 0034 are determined using the methods adopted in the TOPP (??)..
Once the (x,y) coordinates have been determined, the parallax and proper motion of ULAS 0034 are determined using the methods adopted in the TOPP \citep{Sma03a, 2007AA...464..787S}.
We limit the reference objects used to only those within 5 aremimutes of the target. as these are sufficient for a transformation. and limiting the area of the detector being modeled also limits possible differential astrometric distortion.
We limit the reference objects used to only those within 5 arcminutes of the target, as these are sufficient for a transformation, and limiting the area of the detector being modeled also limits possible differential astrometric distortion.
We have made two significant changes to the procedures used in the (1) As we are observing in the J/-band where the atmospheric refraction is small we expect the differential reddening correction (DCR). to be negligible.
We have made two significant changes to the procedures used in the (1) As we are observing in the $J$ -band where the atmospheric refraction is small we expect the differential reddening correction (DCR), to be negligible.
This is in agreement with ? and hence we do not apply any correction,
This is in agreement with \citet{2003AJ....126..975T} and hence we do not apply any correction.
Once we have data on more targets we will estimate the DCR and quantify the effect this could have on the target (2) Since we have the SDSS colours in this region we use the method of ? to determine photometric parallaxes for the anonymous reference stars and from those we calculate the correction from relative to absolute parallax.
Once we have data on more targets we will estimate the DCR and quantify the effect this could have on the target (2) Since we have the SDSS colours in this region we use the method of \citet{2008ApJ...684..287I} to determine photometric parallaxes for the anonymous reference stars and from those we calculate the correction from relative to absolute parallax.
This correction is typically less than 2 milliareseconds.
This correction is typically less than 2 milliarcseconds.
lightcurve models.
lightcurve models.
This replaces the touchdown measurement used for PRE bursts with a different condition which we use to constrain M and R for1826—24.
This replaces the touchdown measurement used for PRE bursts with a different condition which we use to constrain $M$ and $R$ for.
. In our analysis we take care to include the possible anisotropy 1n. burst and persistent emission and show how that could affect the mass and radius determination.
In our analysis we take care to include the possible anisotropy in burst and persistent emission and show how that could affect the mass and radius determination.
We then compare the spectral evolution during the tail of the burst with spectral models.
We then compare the spectral evolution during the tail of the burst with spectral models.
The good understanding of bursts from ssuggests that they could be a good testing ground for spectral models.
The good understanding of bursts from suggests that they could be a good testing ground for spectral models.
We show that in the initial cooling phase following peak luminosity the spectral evolution agrees well with the models of Suleimanov et al. (
We show that in the initial cooling phase following peak luminosity the spectral evolution agrees well with the models of Suleimanov et al. (
201Ib). and we derive the associated constraints on M and Δ.
2011b), and we derive the associated constraints on $M$ and $R$.
In both cases. we look for constraints that are independent of distance and emission anisotropies since neither are well-constrained for1826—24.
In both cases, we look for constraints that are independent of distance and emission anisotropies since neither are well-constrained for.
. The outline of the paper is as follows.
The outline of the paper is as follows.
The data analysis is described in 82.
The data analysis is described in 2.
In $3. we discuss the possible anisotropy of the burst and persistent emission and review calculations of the expected degree of anisotropy in the literature.
In 3, we discuss the possible anisotropy of the burst and persistent emission and review calculations of the expected degree of anisotropy in the literature.
In S4. we use the model lightcurve from Heger et al. (
In 4, we use the model lightcurve from Heger et al. (
2007) to set the luminosity scale of the observed bursts and show that this gives a distance-independent relation between the redshift and color correction factor f...
2007) to set the luminosity scale of the observed bursts and show that this gives a distance-independent relation between the redshift and color correction factor $f_c$.
Suleimanovy et al. (
Suleimanov et al. (
2011a) argued that rather than using a single measurement of touchdown flux. the entire cooling track of the burst should be fit to spectral models.
2011a) argued that rather than using a single measurement of touchdown flux, the entire cooling track of the burst should be fit to spectral models.
We do this in $5. and show that even though the peak flux is below Eddington. the fits provide a constraint on the value of Fi as well as the normalization of the spectrum.
We do this in 5, and show that even though the peak flux is below Eddington, the fits provide a constraint on the value of $F_{\rm Edd}$ as well as the normalization of the spectrum.
These two measurements translate into a distance independent upper limit on R4
These two measurements translate into a distance independent upper limit on $R_\infty$.
We compare these two different constraints and diseuss their .implications in $6.
We compare these two different constraints and discuss their implications in 6.
We used data taken with the Proportional Counter Array (PCA: Jahoda et al.
We used data taken with the Proportional Counter Array (PCA; Jahoda et al.
1996) onboard the Rossi X-ray Timing Explorer (RXTE). from the catalogue of bursts detected over the mission lifetime (GO8).
1996) onboard the Rossi X-ray Timing Explorer (RXTE), from the catalogue of bursts detected over the mission lifetime (G08).
Where not explicitly stated. the data analysis procedures are as in (005.
Where not explicitly stated, the data analysis procedures are as in G08.
Time-resolved spectra in the range 2-60 keV covering the burst duration were extracted on intervals as short as 0.25 s during the burst rise and peak. with the bin size increasing step-wise into the burst tail to maintain roughly the same signal-to-noise level.
Time-resolved spectra in the range 2-60 keV covering the burst duration were extracted on intervals as short as 0.25 s during the burst rise and peak, with the bin size increasing step-wise into the burst tail to maintain roughly the same signal-to-noise level.
A spectrum taken from a 16-s interval prior to the burst was adopted as the background.
A spectrum taken from a 16-s interval prior to the burst was adopted as the background.
We re-fit the spectra over the energy range 2.5-20 keV using the revised PCA response matrices.v11.7.. anc adopted the recommended systematic. error of0.
We re-fit the spectra over the energy range 2.5-20 keV using the revised PCA response matrices, and adopted the recommended systematic error of.
59c.. The fitting was undertaken using XSPEC version 12.
The fitting was undertaken using XSPEC version 12.
In order to accommodate spectral bins with low count rates. we adoptec Churazov weighting.
In order to accommodate spectral bins with low count rates, we adopted Churazov weighting.
We modelled the effects of interstellar absorption. using a multiplicative model component t XSPEC). with the column density Nj, frozen at 4«107!em (e.g. in "t Zand et al.
We modelled the effects of interstellar absorption, using a multiplicative model component in ), with the column density $N_H$ frozen at $4\times10^{21}\ {\rm cm^{-2}}$ (e.g. in 't Zand et al.
1999).
1999).
In the original analysis carrtec out by GO8. the neutral absorption was determined separately for each burst. from the mean value obtained for spectral fits carried out with the Nj value free to vary.
In the original analysis carried out by G08, the neutral absorption was determined separately for each burst, from the mean value obtained for spectral fits carried out with the $N_H$ value free to vary.
This has a negligible effect on the fluxes. but can introduce spurious burst-to-burst variations in the blackbody normalisation.
This has a negligible effect on the fluxes, but can introduce spurious burst-to-burst variations in the blackbody normalisation.
The burst data used here has been corrected for "deadtime". a short period of inactivity in the detectors following the detection of a X-ray photon.
The burst data used here has been corrected for “deadtime”, a short period of inactivity in the detectors following the detection of a X-ray photon.
There are however concerns regarding the absolute flux calibration of the PCA associated with variations in the flux from the Crab nebula and the effective area of the PCA.
There are however concerns regarding the absolute flux calibration of the PCA associated with variations in the flux from the Crab nebula and the effective area of the PCA.
We will show that such absolute uncertainties will not influence our derived constraints.
We will show that such absolute uncertainties will not influence our derived constraints.
The possibility that the burst or persistent emission is not isotropic has been long discussed (e.g. Lapidus et al.
The possibility that the burst or persistent emission is not isotropic has been long discussed (e.g. Lapidus et al.
1985). but has not always been included in recent work using X-ray bursts to constrain neutron star mass and radius.
1985), but has not always been included in recent work using X-ray bursts to constrain neutron star mass and radius.
For example. in Ozzel (2006). Steiner et al. (
For example, in Özzel (2006), Steiner et al. (
2010). and Suleimanov et al. (
2010), and Suleimanov et al. (
2011a) the burst emission is assumed to be isotropic.
2011a) the burst emission is assumed to be isotropic.
Here. we review the expected size of the anisotropy.
Here, we review the expected size of the anisotropy.
We follow Fujimoto (1988) and define an anisotropy parameter © by the relation 4xdF&=L between the observed flux F and the luminosity of the source L over the whole sky. where d is the distance to the source.
We follow Fujimoto (1988) and define an anisotropy parameter $\xi$ by the relation $4\pi d^2 F \xi = L$ between the observed flux $F$ and the luminosity of the source $L$ over the whole sky, where $d$ is the distance to the source.
When ©«I (>1). the radiation is beamed towards (away from) the observer.
When $\xi<1$ $>1$ ), the radiation is beamed towards (away from) the observer.
We write the anisotropy factor for the burst and persistent emission às ερ and ¢, respectively.
We write the anisotropy factor for the burst and persistent emission as $\xi_b$ and $\xi_p$ respectively.
Lapidus. Sunyaev Titarchuk (1985) showed that 1f the accretion disk extends to the neutron star surface during the flash. it will intercept ~1/4 of the radiation from the burst. reflecting 1t preferentially along the disk axis.
Lapidus, Sunyaev Titarchuk (1985) showed that if the accretion disk extends to the neutron star surface during the flash, it will intercept $\approx 1/4$ of the radiation from the burst, reflecting it preferentially along the disk axis.
They provide the approximate expression where / is the inclination angle (;20° means the system 1s viewed face on. looking down the disk axis). which closely fits their more detailed results derived from solving the radiative transfer equations for a disk geometry (they found à maximum value of 1.39 rather than 1.5).
They provide the approximate expression where $i$ is the inclination angle $i=0^\circ$ means the system is viewed face on, looking down the disk axis), which closely fits their more detailed results derived from solving the radiative transfer equations for a disk geometry (they found a maximum value of 1.39 rather than 1.5).
The range of G! is from 0.5 (edge on) to 1.5 (face on). implying an uncertainty of a factor of 3 depending on inclination angle.
The range of $\xi_b^{-1}$ is from 0.5 (edge on) to 1.5 (face on), implying an uncertainty of a factor of 3 depending on inclination angle.
The anisotropy factor for the persistent emission is perhaps even more uncertain than that for the burst flux. depending on the specific model for the inner accretion disk. boundary layer. and corona ete.
The anisotropy factor for the persistent emission is perhaps even more uncertain than that for the burst flux, depending on the specific model for the inner accretion disk, boundary layer, and corona etc.
Lapidus et al. (
Lapidus et al. (
1985) and Fujimoto (1988) derive opposite behaviors for the factor ¢, as a function of inclination.
1985) and Fujimoto (1988) derive opposite behaviors for the factor $\xi_p$ as a function of inclination.
The model presented in Fujimoto (1988) for the persistent emission assumes that radiation from the boundary layer. which encircles the neutron star in a “belt” about its equator. is largely screened by the inflated inner part of the accretion disk and scattered preferentially in a direction along the disk axis.
The model presented in Fujimoto (1988) for the persistent emission assumes that radiation from the boundary layer, which encircles the neutron star in a “belt” about its equator, is largely screened by the inflated inner part of the accretion disk and scattered preferentially in a direction along the disk axis.
In Lapidus et al. (
In Lapidus et al. (
1985). however. the inner part of the disk is assumed to be thin. and less than one half of the boundary layer radiation falls on the aceretion disk and is re-scattered. again preferentially along the disk axis. while the remainder of the emission is beamed preferentially in the direction ;=90° (along the plane of the disk).
1985), however, the inner part of the disk is assumed to be thin, and less than one half of the boundary layer radiation falls on the accretion disk and is re-scattered, again preferentially along the disk axis, while the remainder of the emission is beamed preferentially in the direction $i=90^\circ$ (along the plane of the disk).
This difference in their modelling of the inner accretion disk is made apparent by fact that. while Fujimoto (1988) predicts no radiation to be emitted in the /290° direction. Lapidus et al. (
This difference in their modelling of the inner accretion disk is made apparent by fact that, while Fujimoto (1988) predicts no radiation to be emitted in the $i=90^\circ$ direction, Lapidus et al. (
1985) find a substantial portion of the persistent emission will be beamed in that direction.
1985) find a substantial portion of the persistent emission will be beamed in that direction.
The ratio varies by up to à factor of ~3 with inclination for both £,/£;models. although while Fujimoto (1988) finds that the ratio is monotonically increasing with inclination. Lapidus et al. (
The ratio $\xi_p/\xi_b$ varies by up to a factor of $\sim$ 3 with inclination for both models, although while Fujimoto (1988) finds that the ratio is monotonically increasing with inclination, Lapidus et al. (
1985) find the opposite trend.
1985) find the opposite trend.
We note that these two models do not considerthe effects of general relativity on the trajectories of photons near the neutron star surface.
We note that these two models do not considerthe effects of general relativity on the trajectories of photons near the neutron star surface.
However. Lapidus et al. (
However, Lapidus et al. (
1985)
1985)
black-body fluxes in the 3.6 and 1.5 micron bands.
black-body fluxes in the 3.6 and 4.5 micron bands.
These indices sugeest that the atmosphere of lis consistent with a non-duverted profile. which is iu agreement with the results of our preseut study.
These indices suggest that the atmosphere of is consistent with a non-inverted profile, which is in agreement with the results of our present study.
This worl is based on observations made withKepler. which was competitively selected as the teuth Discovery mussion.
This work is based on observations made with, which was competitively selected as the tenth Discovery mission.
Funding for this mission is provided by NASA‘s Science. Mission. Directorate.
Funding for this mission is provided by NASA's Science Mission Directorate.
The authors would like to thank the mamy people who eenerously gave so much their time to make this Mission a success.
The authors would like to thank the many people who generously gave so much their time to make this Mission a success.
This work is also based on observations made with theTelescope. which is operated by the Jet Propulsion Laboratory. California Institute of Technology uuder a contract with NASA.
This work is also based on observations made with the, which is operated by the Jet Propulsion Laboratory, California Institute of Technology under a contract with NASA.
Support for this work was provided by NASA through an award issued by JPL/Caltech.
Support for this work was provided by NASA through an award issued by JPL/Caltech.
Some of the data presented lerein were obtained a the WAAL Keck Observatory. which is operated as a scientific partnership among the California Iustitute of "Technology. the University of California aud the Nationa Acronauties aud Space Administration.
Some of the data presented herein were obtained at the W.M. Keck Observatory, which is operated as a scientific partnership among the California Institute of Technology, the University of California and the National Aeronautics and Space Administration.
The Observatory was nde possible by the generous financial support of he W.M. Keck Foundation.
The Observatory was made possible by the generous financial support of the W.M. Keck Foundation.
This work is also based on observations obtaiue with the ILlobbs-Eberlv Telescope (HET). which is a joint project of the University of Texas at Austin. he Pennsylvania State University. Stanford University. Ludwie-Maxiuiliaus-Universitat Munchen. and Ceore-Aueust-Universitat Gottingen.
This work is also based on observations obtained with the Hobby-Eberly Telescope (HET), which is a joint project of the University of Texas at Austin, the Pennsylvania State University, Stanford University, Ludwig-Maximilians-Universitat Munchen, and Georg-August-Universitat Gottingen.
The HET is uamed in 1onor of its principal benefactors. Walliams P. Hobby aud Robert E. Eberly.
The HET is named in honor of its principal benefactors, William P. Hobby and Robert E. Eberly.
We would like to thank the Spitzer staff at IPAC and in articular Nancy Silberman for scheduling the Spitzer observations of this program.
We would like to thank the Spitzer staff at IPAC and in particular Nancy Silbermann for scheduling the Spitzer observations of this program.
AL C. isa FNRS Research Associate.
M. G. is a FNRS Research Associate.
Tagον2500 KIN Gvith redder BV colors at lower [M/TI] values in this Z5 range: note that the trend is opposite at ligher teiiperatures).
$T_{\rm eff}\sim3800$ K (with redder $B-V$ colors at lower $\MoH$ values in this $T_{\rm eff}$ range; note that the trend is opposite at higher temperatures).
The ‘turn-off towards the bluer colors (which sets iu at Tay~3800 IIS at ΑΠ= 0.0)also tends to occur at lower Diy aud redder colors at lower ietallicities;
The `turn-off' towards the bluer colors (which sets in at $T_{\rm eff}\sim3800$ K at $\MoH=0.0$ )also tends to occur at lower $T_{\rm eff}$ and redder colors at lower metallicities.
As the ‘turvot iu the Tig (5.V) plane is caused by the rapidly increasing TiO absorbtion in the V. baud with decreasing Tig (seo Paper ID. au lnereasinely larger yaction of the available Ti is bouud in TiO to produce the same band strength at lower AL/TI].
As the `turn-off' in the $T_{\rm eff}$ $(B-V)$ plane is caused by the rapidly increasing TiO absorbtion in the $V-$ band with decreasing $T_{\rm eff}$ (see Paper I), an increasingly larger fraction of the available Ti is bound in TiO to produce the same band strength at lower $\MoH$.
This causes he turn-off” to shift to lower effective ο with cecreasing moetallicitv. as the efficiency of TiO formation (aud thus he concentration of TiO uolecules) grows raXdlv with decreasii Ta
This causes the `turn-off' to shift to lower effective temperatures with decreasing metallicity, as the efficiency of TiO formation (and thus the concentration of TiO molecules) grows rapidly with decreasing $T_{\rm eff}$.
Au increasing influence of metallicity ou broad-baud photometric colors at lower effective telaperatires can be seen in other Z;g color planes too. with colors becoming πο at lower ΕΠ.
An increasing influence of metallicity on broad-band photometric colors at lower effective temperatures can be seen in other $T_{\rm eff}$ –color planes too, with colors becoming bluer at lower $\MoH$.
Typically. this is duce to the decreasing concentration of various molecules at a given effective temperature with decreasing |MTI].
Typically, this is due to the decreasing concentration of various molecules at a given effective temperature with decreasing $\MoH$.
For instance. he blueward shift in the Diag (VJP) aud Tig (VA) planes at Tigx 1000T&IN is essentiale governed w the decreasing abundance of TiO at lower |MjTI] values (at Tigzx 3700TSIS the effect of lower VO aud IIO concentrations becomes dnuportant in 7 aud A xuids. respectively}.
For instance, the blueward shift in the $T_{\rm eff}$ $(V-I)$ and $T_{\rm eff}$ $(V-K)$ planes at $T_{\rm eff}\la 4000$ K is essentially governed by the decreasing abundance of TiO at lower $\MoH$ values (at $T_{\rm eff} \la 3700$ K the effect of lower VO and ${\rm H}_{2}{\rm O}$ concentrations becomes important in $I$ and $K$ bands, respectively).
The trends seen in the Tig (7Iv) aue are caused by a complex interplay of decreasing concentrations of Ποο. CO and TiO (see Paper I for a discussion on the influence of molecular opacities ou the yhotometric colors).
The trends seen in the $T_{\rm eff}$ $(J-K)$ plane are caused by a complex interplay of decreasing concentrations of ${\rm H}_{2}{\rm O}$, CO and TiO (see Paper I for a discussion on the influence of molecular opacities on the photometric colors).
The trends see rin the color diagrams esseutiallv reflect the behavjour in the corresponding Tey color planes.
The trends seen in the color–color diagrams essentially reflect the behaviour in the corresponding $T_{\rm eff}$ –color planes.
The infiueice of mnctallicity is stroug in the (BVj(WF) pla1ο for V.£2 loa similar effect is seen in the (.JIv)(V.Fv) plane for VKz L0.
The influence of metallicity is strong in the $(B-V)-(V-I)$ plane for $V-I \ga 1.7$; a similar effect is seen in the $(J-K)-(V-K)$ plane for $V-K \ga 4.0$ .
Note that the effects of metallicitv are minor in the (VID)A) plane.
Note that the effects of metallicity are minor in the $(V-I)-(V-K)$ plane.
Interestingly. this color plane is also little affected by eravity aud the choice of mucroturbulent veocity (Paper I).
Interestingly, this color–color plane is also little affected by gravity and the choice of microturbulent velocity (Paper I).
The final spectrum and its various components is shown in the top panel of fig 4..
The final spectrum and its various components is shown in the top panel of fig \ref{fig:TESTspec}.
The accretion rate for the reference model is M/Mgga=0.002 assuming an efficiency of10%,, while the luminosity in the 0.5-10 keV range is Lx/Lgaa=107.
The accretion rate for the reference model is $\dot{M}/\dot{M}_{\rm{Edd}} = 0.002$ assuming an efficiency of, while the luminosity in the 0.5-10 keV range is $L_{\rm{X}}/L_{\rm{Edd}} = 10^{-4}$.
The total spectrum is shown in black.
The total spectrum is shown in black.
The individual components run as follows.
The individual components run as follows.
The green thermal component (dash-double dotted line) shows the spectral contribution from the outer part of the disk where the hot layer is no longer significant (outside R/Rs= 100), while the red long-dashed component shows the rest of the disk and reflection spectrum.
The green thermal component (dash-double dotted line) shows the spectral contribution from the outer part of the disk where the hot layer is no longer significant (outside $R/R_S = 100$ ), while the red long-dashed component shows the rest of the disk and reflection spectrum.
For the reference model the reflection ionization parameter is small enough that the reflection and iron line are not apparent in the final spectrum, although we again stress that we are using a reflection model developed for AGN, so in reality the reflection could be stronger.
For the reference model the reflection ionization parameter is small enough that the reflection and iron line are not apparent in the final spectrum, although we again stress that we are using a reflection model developed for AGN, so in reality the reflection could be stronger.
The blue dotted line shows the Comptonized spectrum from the hot layer, while the orange dash-dotted line shows the Comptonized spectrum from the hot ring.
The blue dotted line shows the Comptonized spectrum from the hot layer, while the orange dash-dotted line shows the Comptonized spectrum from the hot ring.
Fitting the overall spectrum with a photon index I=1.91 in the 10 keV range, we see a small soft excess below 0.5keV, even though the maximum disk temperature is only 0.05keV. The bottom panel of fig 4 shows the total spectrum divided by a power law with Γ=1.91.
Fitting the overall spectrum with a photon index $\Gamma = 1.91$ in the 1-10 keV range, we see a small soft excess below 0.5keV, even though the maximum disk temperature is only 0.05keV. The bottom panel of fig \ref{fig:TESTspec} shows the total spectrum divided by a power law with $\Gamma = 1.91$.
The observed deviation from a single power law in the hard part of the spectrum (which leads to a deficit around 1 keV and a harder power law index above 10 keV) is caused by anisotropic Comptonization resulting from considering a plane-parallel configuration (see e.g. ? and sect.
The observed deviation from a single power law in the hard part of the spectrum (which leads to a deficit around 1 keV and a harder power law index above 10 keV) is caused by anisotropic Comptonization resulting from considering a plane-parallel configuration (see e.g. \cite{1993ApJ...413..680H} and sect.
?? of this paper), and also by the contribution from the hot ring.
\ref{sec:discussion} of this paper), and also by the contribution from the hot ring.
Except for the very low accretion rate, we see a spectrum that is qualitatively similar to those of ? and ?..
Except for the very low accretion rate, we see a spectrum that is qualitatively similar to those of \cite{2006ApJ...652L.113M} and \cite{2006ApJ...653..525M}.