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[However. even that there is rot a systematic eitect. this should not have iuplications on our results as a sample.
However, given that there is not a systematic effect, this should not have implications on our results as a sample.
Column 6 lists the projecxd rotational velocity from the Bright Star Catalogue and roni Uesugi Fikuda (1982).
Column 6 lists the projected rotational velocity from the Bright Star Catalogue and from Uesugi Fukuda (1982).
Colum 7 contains the )olomietric hunuiuositv calculates following Ayres ct al. (
Column 7 contains the bolometric luminosity calculated following Ayres et al. (
1981) and column & lists the ROSAT sequence uuuber of the imaecs.
1981) and column 8 lists the ROSAT sequence number of the images.
The Atype stars already studied in the iterature have been marked wih a note after the ΠΟ uber and the relevant references are reported at the able bottom.
The A–type stars already studied in the literature have been marked with a note after the HD number and the relevant references are reported at the table bottom.
The count rates listed in the WGA catalogue present sole Πταος for our study due to: (1) the automatic detection techuique used. based on an optimuzed sliding cell algorithia has problems in the case of crowded fields. extended sources. ete: (
The count rates listed in the WGA catalogue present some limitations for our study due to: (1) the automatic detection technique used, based on an optimized sliding cell algorithm has problems in the case of crowded fields, extended sources, etc.; (
2) the count rates are obtained musing a constant value of the exposure time (nominal time) across the field. tlis the source count rate can be unuderestimated if the source lies close to tlιο detector ribs or the border: (3) the band. used to obtain the count rates corresponds to clainels 24200 or 0.2]2.0 keV. lis excludes the baud 0.10.21 keV. whiclis extremely Huportaut for stellar XTAY SOUICOSN.
2) the count rates are obtained using a constant value of the exposure time (nominal time) across the field, thus the source count rate can be underestimated if the source lies close to the detector ribs or the border; (3) the band used to obtain the count rates corresponds to channels 24–200 or 0.24–2.0 keV, this excludes the band 0.1–0.24 keV, which is extremely important for stellar X–ray sources.
Thus the WOA catalogue was used only tfo identity the xnrces detected x the PSPC from our opical sample.
Thus the WGA catalogue was used only to identify the sources detected by the PSPC from our optical sample.
Each observatious then reanalyzed interactively using the NIMACE )ackagoe.
Each observations was then re–analyzed interactively using the XIMAGE package.
Count rates were measured in the enerev baud M122.1 keV (PSPC channels 11.235) hy Xocessine the eveut files retrieved from the ROSAT public archive.
Count rates were measured in the energy band $0.1 - 2.4$ keV (PSPC channels 11–235) by processing the event files retrieved from the ROSAT public archive.
The effective exposure times were measured frou the exposure uaps provider by the ROSAT Standard Aalysis Software Svseni (SASS).
The effective exposure times were measured from the exposure maps provided by the ROSAT Standard Analysis Software System (SASS).
These exposure maps account for the clescope vignetting. the occultation effects due to the support ribs in the detector window aud he “wobble” of he spacecraft.
These exposure maps account for the telescope vignetting, the occultation effects due to the support ribs in the detector window and the “wobble" of the spacecraft.
These corrections are often important for our XPav οος because amost all of them have been cleected sercudipitously. i.ο, they were in he field of view of other targets (15'A of οιw sources were located near the detector ribs or borderj.
These corrections are often important for our X–ray sources because almost all of them have been detected serendipitously, i.e. they were in the field of view of other targets $\sim 45\%$ of our sources were located near the detector ribs or border).
We also compπο our results with those obtained rou the ROSAT AllSky Survev (RASSBSC. Voses et al.
We also compared our results with those obtained from the ROSAT All–Sky Survey (RASS–BSC, Voges et al.
1996: RASS. IIüuusch. et. al.
1996; RASS, Hünnsch et al.
1998).
1998).
Of our supposedly single stars. 8 A and 26 Ftype stars are detecte also iithe RASS.
Of our supposedly single stars, 8 A– and 26 F--type stars are detected also in the RASS.
We found good aereemient in the count rate νιdues inplviug that no strong variability is present.
We found good agreement in the count rate values implying that no strong variability is present.
Iu order to obtain he usual hareHOSS 1atio IIR-(/IS)/GI|S) (seo e.g. Schuütt e al.
In order to obtain the usual hardness ratio $(H - S)/(H + S)$ (see e.g. Schmitt et al.
1995). we! ealeulated the count rates in the "soft"$: channels 11.ll 50.1Q.28 keV) and "αναGE channels 52201 zx0.52.0 keV) PSPC Xrav bands. respectively.
1995), we calculated the count rates in the “soft": channels 11–41 $\approx 0.1 - 0.28$ keV) and “hard": channels 52–201 $\approx 0.5 - 2.0$ keV) PSPC X–ray bands, respectively.
A value of UR —1 mdieates an extremely soft spectruu. TR 20 indicates an equal uunnber of soft aud jud photons aud IIR —|1 an extremely hard one.
A value of HR $\simeq -1$ indicates an extremely soft spectrum, HR $\simeq 0$ indicates an equal number of soft and hard photons and HR $\simeq +1$ an extremely hard one.
The results of our data analysis ire also tabulaed in Table column 9 lists the PSPC count rate aud cola 10 lists the larcucss ratio.
The results of our data analysis are also tabulated in Table 1, column 9 lists the PSPC count rate and column 10 lists the hardness ratio.
The PSPC has a moderate spectral capability. with an energy resolution AE/Ezz0.12 at LkeVaxd. in principle. it allows to study the temperaure of the plasina in the 0.12.1 keV energy band.
The PSPC has a moderate spectral capability, with an energy resolution $\Delta E / E \approx 0.42$ at 1 keV and, in principle, it allows to study the temperature of the plasma in the 0.1–2.4 keV energy band.
However. as 1 is typical for serendipitous ¢etectious. the majority of our sources lacks the required signaltonoise ralo fo nuoccl the spectral cherey distribution.
However, as it is typical for serendipitous detections, the majority of our sources lacks the required signal–to–noise ratio to model the spectral energy distribution.
Ouly for few of thoi. 9 Α and 11 carly Ἐtype sars. there :Ue oeneh COULs to perform a detailed spectral analysis.
Only for few of them, 3 A– and 11 early F–type stars, there are enough counts to perform a detailed spectral analysis.
For this analysis we considered ouly the sources with more than δ00 οςouts.
For this analysis we considered only the sources with more than 800 counts.
The Xrav pulse height spectra were extracted rou the event files using the NSELECT/FTOOLS pacsage and were rebinned to give at least 25 counts per bin.
The X--ray pulse height spectra were extracted from the event files using the XSELECT/FTOOLS package and were rebinned to give at least 25 counts per bin.
Staudard
Standard
be properly modeled.
be properly modeled.
Acceleration of the star and subsequent feedback into the spiral structure is explicitly suppressed.
Acceleration of the star and subsequent feedback into the spiral structure is explicitly suppressed.
In a sense, the star has infinite inertia and becomes a sink for momentum.
In a sense, the star has infinite inertia and becomes a sink for momentum.
Under these conditions, SLING amplification (??) of spiral structure cannot be properly computed.
Under these conditions, SLING amplification \citep{adams1989,shu1990} of spiral structure cannot be properly computed.
The concern about our earlier calculations is then two-fold: 1) The physics in our simulations of Gl-active disks may be inaccurate, e.g., leading to erroneous estimates of the effective os for mass transport, and may lack important features, e.g., stronger and more coherent one-armed spirals.
The concern about our earlier calculations is then two-fold: 1) The physics in our simulations of GI-active disks may be inaccurate, e.g., leading to erroneous estimates of the effective $\alpha$ s for mass transport, and may lack important features, e.g., stronger and more coherent one-armed spirals.
2.)
2.)
The stellar motions that we suppress could be a significant and observable signature of GI activity in disks (?)..
The stellar motions that we suppress could be a significant and observable signature of GI activity in disks \citep{rice2003a}.
Authors have approached the problem of stellar motion for disk simulations in different ways.
Authors have approached the problem of stellar motion for disk simulations in different ways.
In Smoothed Particle Hydrodynamics (SPH) simulations of GIs (?????),, the stellar motion is included automatically by treating the star as a central sink particle that is smoothed differently from the rest of the SPH particles.
In Smoothed Particle Hydrodynamics (SPH) simulations of GIs \citep{rice2003b,mayer2004,lodato2004,stamatellos2008,forgan2009}, the stellar motion is included automatically by treating the star as a central sink particle that is smoothed differently from the rest of the SPH particles.
However, these simulations, as in ?,, can exhibit a large initial accretion rate onto the central object.
However, these simulations, as in \citet{rice2003a}, can exhibit a large initial accretion rate onto the central object.
How the transfer of angular momentum from the disk material to the central object is handled could be quite important to the star's motion.
How the transfer of angular momentum from the disk material to the central object is handled could be quite important to the star's motion.
The only global 3D grid-based hydrodynamics scheme other than the IUHG code so far used for published simulations of GIs in protoplanetary disks around solar-type stars is the Eulerian spherical-grid code of Alan Boss.
The only global 3D grid-based hydrodynamics scheme other than the IUHG code so far used for published simulations of GIs in protoplanetary disks around solar-type stars is the Eulerian spherical-grid code of Alan Boss.
Although he does not explicitly integrate the stellar equation of motion, ? allows the central protostar to wobble in response to the growth of nonaxisymmetry in the disk by repositioning the star to keep the system COM at the grid center.
Although he does not explicitly integrate the stellar equation of motion, \citet{boss2000} allows the central protostar to wobble in response to the growth of nonaxisymmetry in the disk by repositioning the star to keep the system COM at the grid center.
There is no guarantee with this scheme that the star’s displacement is a true response to Newtonian reaction forces applied by the disk.
There is no guarantee with this scheme that the star's displacement is a true response to Newtonian reaction forces applied by the disk.
The star’s motion could simply represent an accumulation of numerical error in the location of the COM.
The star's motion could simply represent an accumulation of numerical error in the location of the COM.
In principle, then, this treatment is no better than what was done in the IUHG simulations.
In principle, then, this treatment is no better than what was done in the IUHG simulations.
In order to explore the effect of the star/disk interaction, we have now implemented the indirect potential method (e.g.,?)..
In order to explore the effect of the star/disk interaction, we have now implemented the indirect potential method \citep[e.g.,][]{nelson2000b}.
This effectively puts our simulations into the accelerated reference frame of the star and therefore properly accounts for stellar motion while keeping the star at the center of our computational grid.
This effectively puts our simulations into the accelerated reference frame of the star and therefore properly accounts for stellar motion while keeping the star at the center of our computational grid.
In this article, we present the results of a simulation for a nonfragmenting disk using the indirect potential to treat stellar motion and compare it to results of an identical simulation with an artificially fixed central star from Mejíaa et al. (
In this article, we present the results of a simulation for a nonfragmenting disk using the indirect potential to treat stellar motion and compare it to results of an identical simulation with an artificially fixed central star from Mejíaa et al. (
2005).
2005).
In refsec:results,, we first present an overall qualitative comparison, followed by a detailed analysis of the stellar motion and of differences in the disk behaviors.
In \\ref{sec:results}, we first present an overall qualitative comparison, followed by a detailed analysis of the stellar motion and of differences in the disk behaviors.
We compare our results to those obtained via other numerical methods and briefly discuss possible observational consequences in refsec:compare..
We compare our results to those obtained via other numerical methods and briefly discuss possible observational consequences in \\ref{sec:compare}.
Finally, refsec:conclude presents our main conclusions.
Finally, \\ref{sec:conclude} presents our main conclusions.
The two disk simulations in this paper are evolved using the standard IUHG 3D hydrodynamics code (??)..
The two disk simulations in this paper are evolved using the standard IUHG 3D hydrodynamics code \citep{pickett2003,mejia2005}.
This code solves the equations of hydrodynamics in conservative form on an evenly spaced Eulerian cylindrical grid (cc, ϕ. 2) to second order in space and time.
This code solves the equations of hydrodynamics in conservative form on an evenly spaced Eulerian cylindrical grid $\varpi$, $\phi$, $z$ ) to second order in space and time.
For these calculations, the equation of stateis that of an ideal gas with a ratio of specific heats =5/3.
For these calculations, the equation of stateis that of an ideal gas with a ratio of specific heats $\gamma = 5/ 3$.
The rotation axis is in the z-direction, reflection symmetry is assumed about the equatorial plane, and the cell widths in the cc and z-directions are the same.
The rotation axis is in the $z$ -direction, reflection symmetry is assumed about the equatorial plane, and the cell widths in the $\varpi$ and $z$ -directions are the same.
Shocks are mediated through the inclusion of von Neumann-Winkler artificial bulk viscosity terms in the momentum and energy equations (?),, and free outflow boundary conditions are assumed along the top, outer, and inner (central hole) edges of the grid.
Shocks are mediated through the inclusion of von Neumann-Winkler artificial bulk viscosity terms in the momentum and energy equations \citep{pickettphd1995}, and free outflow boundary conditions are assumed along the top, outer, and inner (central hole) edges of the grid.
The (w,¢,z)-directions will hereafter be referred to as the cylindrically radial, azimuthal, and vertical directions, respectively.
The $\varpi$ $\phi$ $z$ )-directions will hereafter be referred to as the cylindrically radial, azimuthal, and vertical directions, respectively.
When needed, the spherical radius from grid center is represented by r.
When needed, the spherical radius from grid center is represented by $r$.
Cooling is introduced into the energy equation as a local volumetric cooling rate A=€/tcoo1, where e is the internal energy density and £coo1 is a constant time scale on which the disk is assumed to be losing thermal energy due to radiation.
Cooling is introduced into the energy equation as a local volumetric cooling rate $\Lambda = \epsilon/t_{\mathrm{cool}}$, where $\epsilon$ is the internal energy density and $t_{\mathrm{cool}}$ is a constant time scale on which the disk is assumed to be losing thermal energy due to radiation.
The potential whose gradient yields the gravitational source terms in the momentum equation of the disk is made up of several components, namely, the disk component, the stellar component, and the indirect component.
The potential whose gradient yields the gravitational source terms in the momentum equation of the disk is made up of several components, namely, the disk component, the stellar component, and the indirect component.
So Saia is calculated by first determining the disk boundary potential by multipole expansion of spherical harmonics up to |=|m|10.
So $\Phi_{\mathrm{disk}}$ is calculated by first determining the disk boundary potential by multipole expansion of spherical harmonics up to $l=|m|=10$ .
Once the boundary conditions have been obtained, the density data is Fourier transformed in the ¢-direction.
Once the boundary conditions have been obtained, the density data is Fourier transformed in the $\phi$ -direction.
Each of the Fourier components yields a 2D boundary value problem which can be cast into a block-tridiagonal matrix and solved using cyclic reduction (?)..
Each of the Fourier components yields a 2D boundary value problem which can be cast into a block-tridiagonal matrix and solved using cyclic reduction \citep{tohline1980}.
The solution in Fourier space is then transformed back into real space.
The solution in Fourier space is then transformed back into real space.
Pstar is GM./r, and Φιμα is described in the next section.
$\Phi_{\mathrm{star}}$ is $-GM_{\ast}/r$, and $\Phi_{\mathrm{ind}}$ is described in the next section.
For the comparison calculation in ?,, Bing is zero.
For the comparison calculation in \citet{mejia2005}, $\Phi_{\mathrm{ind}}$ is zero.
Although the star remains at the grid center in both simulations that we discuss, we refer to the ? simulation without the indirect potential as the "fixed star" case and the simulation with the indirect potential as the "indirect case".
Although the star remains at the grid center in both simulations that we discuss, we refer to the \citet{mejia2005} simulation without the indirect potential as the “fixed star” case and the simulation with the indirect potential as the “indirect case”.
In our earlier constant ἔςοοι simulations with 256 or 512 radial grid cells that have a fixed central stellar potential, the disk’s COM moved at most only a few radial cells away from the grid center over many disk rotations due to numerical errors.
In our earlier constant $t_{\mathrm{cool}}$ simulations with 256 or 512 radial grid cells that have a fixed central stellar potential, the disk's COM moved at most only a few radial cells away from the grid center over many disk rotations due to numerical errors.
Nevertheless, even if fixing the star at the center of the inertial frame does not lead to pathological behavior, it also does not capture the full interaction between the star and disk, including possible feedback between stellar motion and growth of spiral modes (e.g.,??)..
Nevertheless, even if fixing the star at the center of the inertial frame does not lead to pathological behavior, it also does not capture the full interaction between the star and disk, including possible feedback between stellar motion and growth of spiral modes \citep[e.g.,][]{adams1989,shu1990}.
To model the stellar motion explicitly, we use the indirect potential method (e.g.,?)..
To model the stellar motion explicitly, we use the indirect potential method \citep[e.g.,][]{nelson2000b}.
The grid is now considered to be the accelerated reference frame of the star, with the practical benefit that the star remains fixed at the grid center.
The grid is now considered to be the accelerated reference frame of the star, with the practical benefit that the star remains fixed at the grid center.
The acceleration of the star-centered reference frame due to gravitational forces can be included into the fluid equation of motion as an additional gradient of a potential, termed the
The acceleration of the star-centered reference frame due to gravitational forces can be included into the fluid equation of motion as an additional gradient of a potential, termed the .
potential. As in ?,, the indirect potential at some point in the disk is given by where the integration over the primed coordinates extends over the whole computational grid.
As in \citeauthor{nelson2000b}, , the indirect potential at some point in the disk is given by where the integration over the primed coordinates extends over the whole computational grid.
In practice, we compute and then for each cell.
In practice, we compute and then for each cell.
Of course, this turns out to have much
Of course, this turns out to have much
stars in the field. with the package.
stars in the field, with the package.
Using 33 stars in the feld. for the final R-band image we obtained an rus error of 07,11 in right asceusion (R.A.) aud 0”..20 iu declination. adding up to a radial error of 001.
Using 33 stars in the field, for the final $R$ -band image we obtained an rms error of .14 in right ascension (R.A.) and .20 in declination, adding up to a radial error of .24.
For the final g-baud image. the residuals were Q07..13 and 07.18 for R. and declination. respectively. eiving a total error of 0"..22,A.
For the final $g$ -band image, the residuals were .13 and .18 for R.A. and declination, respectively, giving a total error of .22.
We measured fluxes with aperture photometry usimg the package.
We measured fluxes with aperture photometry using the package.
For each might. we measured the seeing (FWIAL) and set the aperture to one seenmg radius (Alighell1999)..
For each night, we measured the seeing (FWHM) and set the aperture to one seeing radius \citep{aperturephot}.
We extracted the skv from au anuulus 510 secing radii wide.
We extracted the sky from an annulus 5–10 seeing radii wide.
We had observed nearby a Sloan Digital Sky Survey (SDSS:Yorketal.2000) with the same settings as the science field.
We had observed nearby a Sloan Digital Sky Survey \citep[SDSS;][]{thesdss} with the same settings as the science field.
The calibration field was observed inuneciately after the science exposures. aud had airmass L.l as compared to L.6 for the tarect.
The calibration field was observed immediately after the science exposures, and had airmass 1.4 as compared to 1.6 for the target.
We used the magnitudes of six stars from that field to calculate the photometric zero point and calibrated six reference stars in the science fieldL.. 13).
We used the magnitudes of six stars from that field to calculate the photometric zero point and calibrated six reference stars in the science field, ).
δ baud magnitudes were calculated using plotometric prescribed ly Jesteretal.(2005). forstars with &,I.<1.15.
$R$ band magnitudes were calculated using photometric prescribed by \citet{sdssequations} forstars with $R_c - I_c < 1.15$.
The typical tucertaimty in g-band iiaguitudes for stars with i,720 is 0.03 μας,
The typical uncertainty in $g$ -band magnitudes for stars with $m_g \sim 20$ is $0.03$ mag.
In R baud we have Aimy=0.07 for ing 20. including the uncertainty in the trausformationus.
In $R$ band we have $\Delta m_R = 0.07$ for $m_R \sim 20$ , including the uncertainty in the transformations.
Tu the vicinity of the nominal pulsar position. we find a faint source (labeled "P) in the R baud 1)).
In the vicinity of the nominal pulsar position, we find a faint source (labeled “P”) in the $R$ band ).
We do uot detect anything within oof the tarect in the g baud.
We do not detect anything within of the target in the $g$ band.
The optical coordinates of this source. the timing position of the pulsar aud a proposed X-rav counterpart are sumnnmarzed in2.
The optical coordinates of this source, the timing position of the pulsar and a proposed X-ray counterpart are summarized in.
. To compare this with the source location. we first have to correct for the > proper motion of the source.
To compare this with the source location, we first have to correct for the $^{-1}$ proper motion of the source.
The LRIS source P is about 070.50 South of the pulsar position (extrapolated for the epoch of LRIS obscrvatious).
The LRIS source P is about .50 South of the pulsar position (extrapolated for the epoch of LRIS observations).
Caven the 0”..21 0) astrometric uncertainty of the optical nuages. this position is consistent with the location of the pulsar.
Given the .24 $\sigma$ ) astrometric uncertainty of the optical images, this position is consistent with the location of the pulsar.
The density of objects brighter than star P iu this ficld is aaveseconud7.
The density of objects brighter than star P in this field is $^{-2}$.
Using the 07.85 seeing FWIINM as the mean diameter of stars. we calculate a false ideutification probability of 1%.
Using the .85 seeing FWHM as the mean diameter of stars, we calculate a false identification probability of $1\%$.
The excellent astrometric comceideuce aud the low probability of chance coincidence emiboldeu us to sugeest that star P is the optical counterpart of2230.
The excellent astrometric coincidence and the low probability of chance coincidence embolden us to suggest that star P is the optical counterpart of.
. Counterpart P is located oulv 17.2 from the 16.3 mag starO129635.. aud is coutaminated by the fiux in the winesL- of its poiut-spread fiction.
Counterpart P is located only .2 from the 16.3 mag star, and is contaminated by the flux in the wings of its point-spread function.
The proximity to this bright source will bias both the photometry aud the astrometry of the counterpart.
The proximity to this bright source will bias both the photometry and the astrometry of the counterpart.
To calculate the bias. we injected fake Gaussian sources with PWHAL matched to the seeimg and brightuess comparable to the faint object.
To calculate the bias, we injected fake Gaussian sources with FWHM matched to the seeing and brightness comparable to the faint object.
We then measured the coordinates aud maguitude of the injected source using the same procedure as for the faint object.
We then measured the coordinates and magnitude of the injected source using the same procedure as for the faint object.