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

source stringlengths 1 2.05k ⌀	target stringlengths 1 11.7k
At 6 cm, the peak polarization fraction is in the eastern half of the survey and in the western half of the survey.	At 6 cm, the peak polarization fraction is in the eastern half of the survey and in the western half of the survey.
These values are consistent with other single-dish surveys (Tsuboietal.1986;Haynesetal. 1992),, which confirms the validity of techniques and maps of the VLA survey.	These values are consistent with other single-dish surveys \citep{t86,h92}, which confirms the validity of techniques and maps of the VLA survey.
At 20 cm, the upper limit on the polarization fraction is roughly of the total intensity measured by the GBT.	At 20 cm, the upper limit on the polarization fraction is roughly of the total intensity measured by the GBT.
Figure 6 shows two maps of RM smoothed over 125-arcsec tiles with the histogram-fitting method.	Figure \ref{padilg} shows two maps of RM smoothed over 125-arcsec tiles with the histogram-fitting method.
The images show there is coherent structure on degree size scales.	The images show there is coherent structure on degree size scales.
The east side of the survey tends to have RM greater than zero and the west side less than zero.	The east side of the survey tends to have RM greater than zero and the west side less than zero.
'The east-west structure is seen more clearly in averages calculated over all latitudes, as shown in Figure 7..	The east-west structure is seen more clearly in averages calculated over all latitudes, as shown in Figure \ref{rmlong}.
In the east, for 0°2<\|—0°3, RM z4-330 rad τη”. then the RM changes rapidly for —0?3«\| —0?55, and in the west, for —0°95«\| —0?55, RM—880+50 rrad m~?.	In the east, for $0\ddeg2<l<-0\ddeg3$, RM $\approx+330$ rad $^{-2}$, then the RM changes rapidly for $-0\ddeg3<l<-0\ddeg55$ , and in the west, for $-0\ddeg95<l<-0\ddeg55$ , $\approx-880\pm50$ rad $^{-2}$ .
Averaging RM over the top half ofthe survey (0245«b 0?7) shows a similar structure as the average over all latitudes, but with a larger range.	Averaging RM over the top half ofthe survey $0\ddeg45<b<0\ddeg7$ ) shows a similar structure as the average over all latitudes, but with a larger range.
The maximum RM is+660+75 rrad m~? nnear \|=—0°25 oon the east side, while the minimum RM is —1320+τὸ rrad m7? nnear \|——0?65 oon the west side.	The maximum RM is$+660\pm75$ rad $^{-2}$ near $l=-0\ddeg25$ on the east side, while the minimum RM is $-1320\pm75$ rad $^{-2}$ near $l=-0\ddeg65$ on the west side.
imply a cutolf in the spectrum of accelerated: protons at ~100 TeV. roughly a factor of 30 short of the knee.	imply a cutoff in the spectrum of accelerated protons at $\sim 100$ TeV, roughly a factor of 30 short of the knee.
[t is worth keeping in mind that in an expanding SNR. the highest cosmic rav energy is expected to be reached around the beginning of the Sedoy. phase.	It is worth keeping in mind that in an expanding SNR the highest cosmic ray energy is expected to be reached around the beginning of the Sedov phase.
Before and after that time the maximum energy of accelerated particles does not need to be as high as the knee energy.	Before and after that time the maximum energy of accelerated particles does not need to be as high as the knee energy.
Moreover. cilferent SNRs nueht accelerate to clilferent maximum energies because of the different environment in which they explode.	Moreover, different SNRs might accelerate to different maximum energies because of the different environment in which they explode.
In this sense it is only natural that most SNRs do not show proton acceleration up to the energy of the knee.	In this sense it is only natural that most SNRs do not show proton acceleration up to the energy of the knee.
The strength. and. topology of the magnetic field. in the acceleration/radiation region regulate the clliciency of particle acceleration (nuclei and electrons) and the radiation losses of electrons.	The strength and topology of the magnetic field in the acceleration/radiation region regulate the efficiency of particle acceleration (nuclei and electrons) and the radiation losses of electrons.
The recent detection of marrow X-ray bright rims in several SNRs (Bambaetal.2003.2005:Lazen-dicetal.2003.2004:Vink&Laming2003) has allowed to infer the strength of the field. if the thickness of the rims is interpreted. as the svnehrotron loss length of the radiating electrons. (Ballet 2006)...	The recent detection of narrow X-ray bright rims in several SNRs \cite[]{bamba03, bamba05, laz03, laz04, vink03} has allowed to infer the strength of the field, if the thickness of the rims is interpreted as the synchrotron loss length of the radiating electrons \cite[]{ballet}. .
Typical values of. 501000507 have been inferred. which suggest. efficient. magnetic field amplification in the shock region.	Typical values of $50-1000\mu G$ have been inferred, which suggest efficient magnetic field amplification in the shock region.
One more argument in favor of strong magnetic fields was made by Uchivamaetal.(2007) who interpreted the rapid time variability (of the orders of [ew vears) observed in some X-ray emitting regions Of RN J1713.7-3946 as due to rapid synchrotron cooling.	One more argument in favor of strong magnetic fields was made by \cite{uch07} who interpreted the rapid time variability (of the orders of few years) observed in some X-ray emitting regions of RX J1713.7-3946 as due to rapid synchrotron cooling.
The field strength inferred based on this interpretation is as high as ] mCG. The same ellect was also observed in some knots of Cas A (Uchivama&Aharonian2008).	The field strength inferred based on this interpretation is as high as $\sim 1$ mG. The same effect was also observed in some knots of Cas A \cite[]{uch08}.
. There is however a large source of ambiguity in that the narrow thickness of the X-ray rims might be due to damping of the magnetic field (for instance due to waveswave non-linear coupling) (Pohletal.2005).	There is however a large source of ambiguity in that the narrow thickness of the X-ray rims might be due to damping of the magnetic field (for instance due to wave-wave non-linear coupling) \cite[]{pohl05}.
. In this case the magnetic lield inferred. by assuming that the rims are due to severe svnchrotron losses might be overestimated.	In this case the magnetic field inferred by assuming that the rims are due to severe synchrotron losses might be overestimated.
We discuss this issue at several points throughout the paper.	We discuss this issue at several points throughout the paper.
Alagnetic field amplification could result from turbulent amplification (Ciacalone&Jokipii2007) or from cosmic rav induced streaming instability.	Magnetic field amplification could result from turbulent amplification \cite[]{joki} or from cosmic ray induced streaming instability.
An open question is whether the large magnetic fields present in the X-rav rims are widespread: throughout the remnant or are rather confined in thin filaments with a relatively small filling factor (this would be the case if damping plavs a role downstream of the shock).	An open question is whether the large magnetic fields present in the X-ray rims are widespread throughout the remnant or are rather confined in thin filaments with a relatively small filling factor (this would be the case if damping plays a role downstream of the shock).
This dillerence might have important consequences on the interpretation of the observed. non-thermal emission [rom SNRs. as we discuss below.	This difference might have important consequences on the interpretation of the observed non-thermal emission from SNRs, as we discuss below.
Interestingly enough. the magnetic field strength inforrec from N-rav. observations is of the same order of magnitude as that required. by the theory of shock acceleration in order to account for particle acceleration up to the knee region. provided the diffusion coellicient is ohm-like.	Interestingly enough, the magnetic field strength inferred from X-ray observations is of the same order of magnitude as that required by the theory of shock acceleration in order to account for particle acceleration up to the knee region, provided the diffusion coefficient is Bohm-like.
From the theoretical point of view. a major improvement has been achieved in the last few vears in that the calculations are carried out in the context. of the so-called non-linear theory of particle acceleration.	From the theoretical point of view, a major improvement has been achieved in the last few years in that the calculations are carried out in the context of the so-called non-linear theory of particle acceleration.
This theory allows us to calculate the spectrum ancl spatial distribution of accelerated: particles around the shock. their dynamical reaction on the shock and the magnetic field amplification that cosmic rays induce due to streaming instability.	This theory allows us to calculate the spectrum and spatial distribution of accelerated particles around the shock, their dynamical reaction on the shock and the magnetic field amplification that cosmic rays induce due to streaming instability.
Although the non-linear theory has been previously applied to SNRs. this paper improves on previous attempts in two major aspects: 1) the magnetic field in the shock region is caleulated from. streaming instability ancl from conservation equations instead. of being inserted. in such a wav to fit the X-ray observations: 2) we include the dynamical reaction of the turbulent magnetic field on the shock. which is a very important elfect in shaping the shock precursor (C'apriolietal.(2008a.b))).	Although the non-linear theory has been previously applied to SNRs, this paper improves on previous attempts in two major aspects: 1) the magnetic field in the shock region is calculated from streaming instability and from conservation equations instead of being inserted in such a way to fit the X-ray observations; 2) we include the dynamical reaction of the turbulent magnetic field on the shock, which is a very important effect in shaping the shock precursor \cite{cap08,long}) ).
The first point is of crucial importance in that it allows us to achieve a unified. picture of the spectra of X-ray and ganuna ray emission. together with the morphology of the X-ray emission. the strength of the magnetic field and finally the dilfusion properties of the accelerated particles.	The first point is of crucial importance in that it allows us to achieve a unified picture of the spectra of X-ray and gamma ray emission, together with the morphology of the X-ray emission, the strength of the magnetic field and finally the diffusion properties of the accelerated particles.
Inclusion of the dynamical reaction of the field. then. as showed by Capriolietal.(2008a).. leads to à substantial reduction of the compression in the precursor. thereby also reducing the concavitv of the spectrum of accelerated. particles (C'apriolietal.(2008b))).	Inclusion of the dynamical reaction of the field, then, as showed by \cite{cap08}, leads to a substantial reduction of the compression in the precursor, thereby also reducing the concavity of the spectrum of accelerated particles \cite{long}) ).
A reduced concavity of the spectrum should also be expected as a result of the enhanced. velocity of the scattering centers when the magnetic field is amplified (see for instance Zirakashvili&Ptuskin (2000))).	A reduced concavity of the spectrum should also be expected as a result of the enhanced velocity of the scattering centers when the magnetic field is amplified (see for instance \cite{zir08}) ).
The large values of the magnetic field strength inferred from X-ray observations ancl confirmed by our calculations clearly favor a hacronie interpretation of the observed. ganima ray emission. because a subdominant population of electrons is sullicient to explain the spectrum and intensity of the observed X-ray. emission. but is insullicient to produce the observed. gamma ray emission through inverse Compton scattering (LCS) on the CMD and infrared/optical photons (IR\|Opt).	The large values of the magnetic field strength inferred from X-ray observations and confirmed by our calculations clearly favor a hadronic interpretation of the observed gamma ray emission, because a subdominant population of electrons is sufficient to explain the spectrum and intensity of the observed X-ray emission, but is insufficient to produce the observed gamma ray emission through inverse Compton scattering (ICS) on the CMB and infrared/optical photons (IR+Opt).
The issue of whether the large fields are present in large fractions of the remnant volume or are rather confined in narrow filaments. remains however an open Issue.	The issue of whether the large fields are present in large fractions of the remnant volume or are rather confined in narrow filaments, remains however an open issue.
For this reason we also investigate the possibility that he filaments have some alternative explanation. so that here is no constraint on the streneth of the magnetic ield clownstream.	For this reason we also investigate the possibility that the filaments have some alternative explanation, so that there is no constraint on the strength of the magnetic field downstream.
We still use our non-linear calculations o derive the spectra of accelerated: protons and. electrons. oit. force. the injection to be low enough to avoid. large magnetic fields produced by streaming instability.	We still use our non-linear calculations to derive the spectra of accelerated protons and electrons, but force the injection to be low enough to avoid large magnetic fields produced by streaming instability.
We find hat a marginal fit to the gamma ray and. X-ray data is »xossible. although a large density of Ht photons needs to be assumed. inside the remnant.	We find that a marginal fit to the gamma ray and X-ray data is possible, although a large density of IR photons needs to be assumed inside the remnant.
The fit to the highest energy xwt of the gamma ray spectrum is not às good. as for the mielronic interpretation.	The fit to the highest energy part of the gamma ray spectrum is not as good as for the hadronic interpretation.
The general conclusion we draw is that although there are numerous indications that the observed. gamma. ravs may be of hadronic origin. a clear answer on this point may only come from: a) the extension of the gamma rav observationsto lower energies. and b) the detection of high energv neutrinos. which would be produced in the same haclronic interactions (Morlinoetal.2008).	The general conclusion we draw is that although there are numerous indications that the observed gamma rays may be of hadronic origin, a clear answer on this point may only come from: a) the extension of the gamma ray observationsto lower energies, and b) the detection of high energy neutrinos, which would be produced in the same hadronic interactions \cite[]{neutrinos}.
. The paper is organized as follows: in 82. we discuss in some detail the general lines of the calculations we carry out. including the non-linear theory of particle acceleration. the magnetic field amplification and the dillerent. channels of non-thermal emissions.	The paper is organized as follows: in \ref{sec:model} we discuss in some detail the general lines of the calculations we carry out, including the non-linear theory of particle acceleration, the magnetic field amplification and the different channels of non-thermal emissions.
ln 83. we discuss the results we obtain by specializing the caleulations tothe case of the SN RN J1713.7-3946.	In \ref{sec:results} we discuss the results we obtain by specializing the calculations tothe case of the SNR RX J1713.7-3946.
We conclude in ΚΕ.	We conclude in \ref{sec:conc}. .
In this section. we discuss the technical aspects of the	In this section we discuss the technical aspects of the
The primary purpose of our archival search was to find. simultaneous observations of Ser A* at	The primary purpose of our archival search was to find simultaneous observations of Sgr A* at
communication)	communication).
In BATSE. the burst was observed. 64 above the horizon. implving that the source remained visible for at least ~15 min after the trigger: thus. E900 s is a conservative lower limit for the interval between two resolved bursts. (	In BATSE, the burst was observed $64^\circ$ above the horizon, implying that the source remained visible for at least $\sim 15$ min after the trigger; thus, $\pm900$ s is a conservative lower limit for the interval between two resolved bursts. (
Also relevant are the data from. Ulysses which saw no burst consistent with the location of GRB 990123 [or a period of at least three days. before and. after the event (Ix. Hurley. private communication). although coverage was only about complete and we cannot completely exclude a second burst.)	Also relevant are the data from Ulysses which saw no burst consistent with the location of GRB 990123 for a period of at least three days before and after the event (K. Hurley, private communication), although coverage was only about complete and we cannot completely exclude a second burst.)
1L as we argue. Ls“fyfox900s is excluded. then so are magnilications 40<µου400.	If, as we argue, $1~s\leq t_3-t_2 \leq 900~s$ is excluded, then so are magnifications $40\leq \mu_{2,3} \leq 400$.
Furthermore. we can use limits on additional point sources in the HSTT image within 2" ⋠⋠⋅∕∕⋅of the afterglow⋅ to place constraints⋠ on. lensed images.	Furthermore, we can use limits on additional point sources in the HST image within $2^{\prime\prime}$ of the afterglow to place constraints on lensed images.
Hf µου<40. then using yy=4 (from eq.	If $\mu_{2,3}<40$, then using $\mu_1=4$ (from eq.
11). we find that burst Lo would have had a [luence »3510.7 ere on or around Jan. 15.	11), we find that burst 1 would have had a fluence $>3\times10^{-5}$ erg $^{-2}$ on or around Jan. 15.
It is unlikely. though not completely exeluded. that this Failed to trigger any detector.	It is unlikely, though not completely excluded, that this failed to trigger any detector.
However. the afterglow associated with burst 1 would have en brighter than V728.8 at the time ofthe LIST image even allowing for its additional [acing with time.	However, the afterglow associated with burst 1 would have been brighter than $V\sim28.8$ at the time of the HST image even allowing for its additional fading with time.
We have »erformoed two-dimensional Gaussian fits (including sloping. Xanar baselines) to all local maxima within 2" of the OT in the LIST image.	We have performed two-dimensional Gaussian fits (including sloping, planar baselines) to all local maxima within $2^{\prime\prime}$ of the OT in the HST image.
The only feature consistent with the psf (derived from a similar fit to the OT as EWIIM = 3.240. Pixels) is the faint object located 14 north of the OT.	The only feature consistent with the psf (derived from a similar fit to the OT as FWHM = $3.2 \pm 0.1$ pixels) is the faint object located $1.4^{\prime\prime}$ north of the OT.
This ~le excess has a magnitude of approximately V~28.4 (scaled to the value of V—25.2 for the OT reported. by Bloom et al. (	This $\sim 4 \sigma$ excess has a magnitude of approximately $V \sim 28.4$ (scaled to the value of $V=25.2$ for the OT reported by Bloom et al. (
1999)).	1999)).
We take this as an upper limit to the magnitude of the first afterglow.	We take this as an upper limit to the magnitude of the first afterglow.
We can therefore almos exclude µου<40.	We can therefore almost exclude $\mu_{2,3} \leq 40$.
The remaining parameter space is described bv fols and pro&400.	The remaining parameter space is described by $t_{2,3} \leq 1~s$ and $\mu_{2,3} \geq 400$.
In this case. the first afterglow will be uncdetectable.	In this case, the first afterglow will be undetectable.
However. the finite size of the source becomes a factor at these high magnifications.	However, the finite size of the source becomes a factor at these high magnifications.
For a source angular size Bit). the magnification is limited to This limit should not allect. the burst itself. although it will eventually influence the afterglow.	For a source angular size B(t), the magnification is limited to This limit should not affect the burst itself, although it will eventually influence the afterglow.
Unfortunately. our lack of understanding of the ambient environment ancl the nature of the explosion precludes a confident expression for Bit).	Unfortunately, our lack of understanding of the ambient environment and the nature of the explosion precludes a confident expression for B(t).
However. a naive estimate for a spherical. relativistic blastwave with £~107 erg and m~1 cm? (eg. DBlandford and. Melxee 1977) gives D—20/1d)*"pas.	However, a naive estimate for a spherical, relativistic blastwave with $E\sim10^{52}$ erg and $n\sim 1$ ${\rm cm}^{-3}$ (e.g., Blandford and McKee 1977) gives $B\sim2(t/1{\rm d})^{5/8} \mu {\rm as}$.
This limits the magnificationὃν to foaX6000/17d)"7.	This limits the magnification to $\mu_{2,3}\leq 600(t/17{\rm d})^{-0.3}$.
After this inequality is violated. the afterglow emission. will decline correspondingly more steeply with time.	After this inequality is violated, the afterglow emission will decline correspondingly more steeply with time.
In fact. just such an increase in the rate of decline has been reported. at \|—ll d (Yadigaroglu Halpern 1999).	In fact, just such an increase in the rate of decline has been reported at $t=11$ d (Yadigaroglu Halpern 1999).
We therefore cannot confidently. exclude lensing with µου400 at this stage.	We therefore cannot confidently exclude lensing with $\mu_{2,3}\sim400$ at this stage.
However. if it is possible to examine the subsecond time variations in the BATSE lishteurve of GRBOSOL23 and thereby limit f;9£5 to z10 ms. then fro, would have to exceed z1000. and all multiple imaging by a z;=1.6 dellector would ellectively be ruled out.	However, if it is possible to examine the subsecond time variations in the BATSE lightcurve of GRB980123 and thereby limit $t_3-t_2$ to $\approx10$ ms, then $\mu_{2,3}$ would have to exceed $\approx1000$, and all multiple imaging by a $z_d=1.6$ deflector would effectively be ruled out.
In summary. three arguments (the high Αη of the galaxy. the implausibilitv of missing the first burst and of failing to detect. its afterglow) can already be marshalled against the lensing hypothesis.	In summary, three arguments (the high $M/L$ of the galaxy, the implausibility of missing the first burst and of failing to detect its afterglow) can already be marshalled against the lensing hypothesis.
Vhree additional steps might ellectivelv eliminate it - searching for double structure on subsecond. timescales in the BATSE data. setting a better limit on the presence of additional afterglow images at the predicted locations and obtaining a reliable photometric or spectroscopic redshift for the galaxy.	Three additional steps might effectively eliminate it - searching for double structure on subsecond timescales in the BATSE data, setting a better limit on the presence of additional afterglow images at the predicted locations and obtaining a reliable photometric or spectroscopic redshift for the galaxy.
C'ontrariwise. iit turns out that the burst was highly magnilied by lensing. then the burst energv would be reduced to ~9LOBpa1000)+ erg.	Contrariwise, if it turns out that the burst was highly magnified by lensing, then the burst energy would be reduced to $\sim9\times10^{51}{\cal B}(2\mu_{2,3}/1000)^{-1}$ erg.
GRB 990123 serves as a reminder that multiple imaging of a gamma-ray burst is to be expected eventually in a large enough sample and the analysis of §22 should be generally applicable.	GRB 990123 serves as a reminder that multiple imaging of a gamma-ray burst is to be expected eventually in a large enough sample and the analysis of 2 should be generally applicable.
While we cannot completely rule out the possibility that it has been multiply imaged and strongly magnified. it should be possible to do so soon.	While we cannot completely rule out the possibility that it has been multiply imaged and strongly magnified, it should be possible to do so soon.
In this case. if we have not observed (or do not observe) an echo of GRB 990123. then the magnification is limited to fr2. except under quite contrived models. leaving CRB 990123 as the most intrinsically luminous cosmic event vet observed in its entirety.	In this case, if we have not observed (or do not observe) an echo of GRB 990123, then the magnification is limited to $\mu\sim2$, except under quite contrived models, leaving GRB 990123 as the most intrinsically luminous cosmic event yet observed in its entirety.
We thank Martin. Rees for encouragement. the Institute of Astronomy. University of Cambridge for hospitality. and the Beverly and. Raymond Sackler Foundation for support during the preparation of this paper.	We thank Martin Rees for encouragement, the Institute of Astronomy, University of Cambridge for hospitality, and the Beverly and Raymond Sackler Foundation for support during the preparation of this paper.
Support under NSE evant AST 95-290170 and NASA erant. 5-2837 is also gratefully acknowledgect.	Support under NSF grant AST 95-29170 and NASA grant 5-2837 is also gratefully acknowledged.
null	.
and	and.
where /: aud /. are the radial ancl vertical wavenumbers. respectively. J,,(ha) are Bessel functions of the first kind and ay. ao. 54. bs and ¢ ave functions determined by the initial field distribution and the conditions of continuity on 2=zz.	where $k$ and $k_z$ are the radial and vertical wavenumbers, respectively, $J_m(k\varpi)$ are Bessel functions of the first kind and $a_1$ , $a_2$, $b_1$, $b_2$ and $c$ are functions determined by the initial field distribution and the conditions of continuity on $z=\pm z_0$.
The decay rate is (he+hr), proporlional to the inverse of the modulus of the vector wavenumber k=fe+/.e.	The decay rate is (k_z^2+k^2), proportional to the inverse of the modulus of the vector wavenumber ${\bf k}=k\hat{\bf e}_\varpi+k_z\hat{\bf e}$.
The condition of continuity of QP/0z at 2τμ leads to the relation (2h. τι)= Ohh, The limit of an infinitesimally thin disk is recovered under the following ordering: (the disk thickness is much smaller than the vertical wavelength. that in {urnis much smaller than the radial wavelength).	The condition of continuity of $\partial P/\partial z$ at $z=\pm z_0$ leads to the relation (2k_z z_0)=2 k_z k. The limit of an infinitesimally thin disk is recovered under the following ordering: $z_0 \ll k_z^{-1} \ll k^{-1} \ll \varpi$ (the disk thickness is much smaller than the vertical wavelength, that in turnis much smaller than the radial wavelength).
With these approximations. eeuation (5) then gives he/2z, and equation (AT)) becomes 52yh?&ΜΕ τμ. as found in our case.	With these approximations, equation \ref{cont_cond}) ) then gives $k\approx k_z^2 z_0$ and equation\ref{rate}) ) becomes $\gamma\approx \eta k_z^2\approx k/z_0$ , as found in our case.
aud ©.	and $\Omega$.
These measurements were eeucrated assuming that here is a planetary companion with orbital parameters iu Table 1.. and (7.9)(0.0.1.0 rad).	These measurements were generated assuming that there is a planetary companion with orbital parameters in Table \ref{HD 154345 orbit}, , and $(I, \Omega) = (0.0, 1.0$ rad).
This simulated data was used together with the real RV measurements oiblished iu Ws to find the Πιο T4 or which the rue nass of the planet could still be measured with the SIM telescope.	This simulated data was used together with the real RV measurements published in W08 to find the limiting $T_{A}$ for which the true mass of the planet could still be measured with the SIM telescope.
The selection £=Oo was made because changing this value would resul in a higher planetary nass and hence ina stronger astrometric VAsignal. making he detection of orbital plane parameters even casicr.	The selection $I=0$ was made because changing this value would result in a higher planetary mass and hence in a stronger astrometric signal, making the detection of orbital plane parameters even easier.
Reeardless of large error bars. we found that it is possible o detect the orbital plane parameters with 7T,=1.0 vears.	Regardless of large error bars, we found that it is possible to detect the orbital plane parameters with $T_{A} = 1.0$ years.
With this short timeline. the error bars of the yaralucters were [020, 0.22] aud [0.39. 1.5L) for 7 and ©. respectively, demoustrating that it was indeed possible to determine their values.	With this short timeline, the error bars of the parameters were [-0.30, 0.22] and [0.39, 1.54] for $I$ and $\Omega$, respectively, demonstrating that it was indeed possible to determine their values.
The time needed to make ai positive detection of an extrasolar planetary companion candidate depends essentially on its orbital period.	The time needed to make a positive detection of an extrasolar planetary conpanion candidate depends essentially on its orbital period.
It is comunonly assumed that. to be able to detect the signature of such companion. an observational timeline longer than the orbital period is required.	It is commonly assumed that, to be able to detect the signature of such companion, an observational timeline longer than the orbital period is required.
Also. since most of the cxoplanet candidates have been detected using the RV method. only the lower lit of their mass is available.	Also, since most of the exoplanet candidates have been detected using the RV method, only the lower limit of their mass is available.
With the iid of future space telescopes aud accurate astrometric mcasiurciuicuts. it will be possible to detect the inclination aud thus the true mass of plauctary candidates.	With the aid of future space telescopes and accurate astrometric measurements, it will be possible to detect the inclination and thus the true mass of planetary candidates.
We have shown that when high-precision RV and accurate astrometric measurements are both available. it is possible to detect the true mass of stellar companions with observational timelines cousiderably shorter than 1ο] orbital periods.	We have shown that when high-precision RV and accurate astrometric measurements are both available, it is possible to detect the true mass of stellar companions with observational timelines considerably shorter than their orbital periods.
Also. when the RV measurements wve a long time span. astrometric measurements can reveal the true mass of a stellar companion in less time iu one tenth of the orbital period of the syste.	Also, when the RV measurements have a long time span, astrometric measurements can reveal the true mass of a stellar companion in less time than one tenth of the orbital period of the system.
This bility is also clemonstrated using the BV. measurements f HIID151315 as an example.	This ability is also demonstrated using the RV measurements of HD154345 as an example.
We find that. having jose lüueasuremuients with Fay=10.1 vears idu haud. astrometric observatious with SIM telescope are sufficieu or obtaiuiug the true mass. within a single vear.	We find that, having these measurements with $T_{RV} = 10.4$ years in hand, astrometric observations with SIM telescope are sufficient for obtaining the true mass, within a single year.
Davesiu iufereunco plavs an portant τοις when extracting information from several sources of neasurelents.	Bayesian inference plays an important role when extracting information from several sources of measurements.

At 6 cm, the peak polarization fraction is in the eastern half of the survey and in the western half of the survey.

These values are consistent with other single-dish surveys (Tsuboietal.1986;Haynesetal. 1992),, which confirms the validity of techniques and maps of the VLA survey.

These values are consistent with other single-dish surveys \citep{t86,h92}, which confirms the validity of techniques and maps of the VLA survey.

At 20 cm, the upper limit on the polarization fraction is roughly of the total intensity measured by the GBT.

Figure 6 shows two maps of RM smoothed over 125-arcsec tiles with the histogram-fitting method.

Figure \ref{padilg} shows two maps of RM smoothed over 125-arcsec tiles with the histogram-fitting method.

The images show there is coherent structure on degree size scales.

The east side of the survey tends to have RM greater than zero and the west side less than zero.

'The east-west structure is seen more clearly in averages calculated over all latitudes, as shown in Figure 7..

The east-west structure is seen more clearly in averages calculated over all latitudes, as shown in Figure \ref{rmlong}.

In the east, for 0°2<|—0°3, RM z4-330 rad τη”. then the RM changes rapidly for —0?3«| —0?55, and in the west, for —0°95«| —0?55, RM—880+50 rrad m~?.

In the east, for $0\ddeg2<l<-0\ddeg3$, RM $\approx+330$ rad $^{-2}$, then the RM changes rapidly for $-0\ddeg3<l<-0\ddeg55$ , and in the west, for $-0\ddeg95<l<-0\ddeg55$ , $\approx-880\pm50$ rad $^{-2}$ .

Averaging RM over the top half ofthe survey (0245«b 0?7) shows a similar structure as the average over all latitudes, but with a larger range.

Averaging RM over the top half ofthe survey $0\ddeg45<b<0\ddeg7$ ) shows a similar structure as the average over all latitudes, but with a larger range.

The maximum RM is+660+75 rrad m~? nnear |=—0°25 oon the east side, while the minimum RM is —1320+τὸ rrad m7? nnear |——0?65 oon the west side.

The maximum RM is$+660\pm75$ rad $^{-2}$ near $l=-0\ddeg25$ on the east side, while the minimum RM is $-1320\pm75$ rad $^{-2}$ near $l=-0\ddeg65$ on the west side.

imply a cutolf in the spectrum of accelerated: protons at ~100 TeV. roughly a factor of 30 short of the knee.

imply a cutoff in the spectrum of accelerated protons at $\sim 100$ TeV, roughly a factor of 30 short of the knee.

[t is worth keeping in mind that in an expanding SNR. the highest cosmic rav energy is expected to be reached around the beginning of the Sedoy. phase.

It is worth keeping in mind that in an expanding SNR the highest cosmic ray energy is expected to be reached around the beginning of the Sedov phase.

Before and after that time the maximum energy of accelerated particles does not need to be as high as the knee energy.

Moreover. cilferent SNRs nueht accelerate to clilferent maximum energies because of the different environment in which they explode.

Moreover, different SNRs might accelerate to different maximum energies because of the different environment in which they explode.

In this sense it is only natural that most SNRs do not show proton acceleration up to the energy of the knee.

The strength. and. topology of the magnetic field. in the acceleration/radiation region regulate the clliciency of particle acceleration (nuclei and electrons) and the radiation losses of electrons.

The strength and topology of the magnetic field in the acceleration/radiation region regulate the efficiency of particle acceleration (nuclei and electrons) and the radiation losses of electrons.

The recent detection of marrow X-ray bright rims in several SNRs (Bambaetal.2003.2005:Lazen-dicetal.2003.2004:Vink&Laming2003) has allowed to infer the strength of the field. if the thickness of the rims is interpreted. as the svnehrotron loss length of the radiating electrons. (Ballet 2006)...

The recent detection of narrow X-ray bright rims in several SNRs \cite[]{bamba03, bamba05, laz03, laz04, vink03} has allowed to infer the strength of the field, if the thickness of the rims is interpreted as the synchrotron loss length of the radiating electrons \cite[]{ballet}. .

Typical values of. 501000507 have been inferred. which suggest. efficient. magnetic field amplification in the shock region.

Typical values of $50-1000\mu G$ have been inferred, which suggest efficient magnetic field amplification in the shock region.

One more argument in favor of strong magnetic fields was made by Uchivamaetal.(2007) who interpreted the rapid time variability (of the orders of [ew vears) observed in some X-ray emitting regions Of RN J1713.7-3946 as due to rapid synchrotron cooling.

One more argument in favor of strong magnetic fields was made by \cite{uch07} who interpreted the rapid time variability (of the orders of few years) observed in some X-ray emitting regions of RX J1713.7-3946 as due to rapid synchrotron cooling.

The field strength inferred based on this interpretation is as high as ] mCG. The same ellect was also observed in some knots of Cas A (Uchivama&Aharonian2008).

The field strength inferred based on this interpretation is as high as $\sim 1$ mG. The same effect was also observed in some knots of Cas A \cite[]{uch08}.

. There is however a large source of ambiguity in that the narrow thickness of the X-ray rims might be due to damping of the magnetic field (for instance due to waveswave non-linear coupling) (Pohletal.2005).

There is however a large source of ambiguity in that the narrow thickness of the X-ray rims might be due to damping of the magnetic field (for instance due to wave-wave non-linear coupling) \cite[]{pohl05}.

. In this case the magnetic lield inferred. by assuming that the rims are due to severe svnchrotron losses might be overestimated.

In this case the magnetic field inferred by assuming that the rims are due to severe synchrotron losses might be overestimated.

We discuss this issue at several points throughout the paper.

Alagnetic field amplification could result from turbulent amplification (Ciacalone&Jokipii2007) or from cosmic rav induced streaming instability.

Magnetic field amplification could result from turbulent amplification \cite[]{joki} or from cosmic ray induced streaming instability.

An open question is whether the large magnetic fields present in the X-rav rims are widespread: throughout the remnant or are rather confined in thin filaments with a relatively small filling factor (this would be the case if damping plavs a role downstream of the shock).

An open question is whether the large magnetic fields present in the X-ray rims are widespread throughout the remnant or are rather confined in thin filaments with a relatively small filling factor (this would be the case if damping plays a role downstream of the shock).

This dillerence might have important consequences on the interpretation of the observed. non-thermal emission [rom SNRs. as we discuss below.

This difference might have important consequences on the interpretation of the observed non-thermal emission from SNRs, as we discuss below.

Interestingly enough. the magnetic field strength inforrec from N-rav. observations is of the same order of magnitude as that required. by the theory of shock acceleration in order to account for particle acceleration up to the knee region. provided the diffusion coellicient is ohm-like.

Interestingly enough, the magnetic field strength inferred from X-ray observations is of the same order of magnitude as that required by the theory of shock acceleration in order to account for particle acceleration up to the knee region, provided the diffusion coefficient is Bohm-like.

From the theoretical point of view. a major improvement has been achieved in the last few vears in that the calculations are carried out in the context. of the so-called non-linear theory of particle acceleration.

From the theoretical point of view, a major improvement has been achieved in the last few years in that the calculations are carried out in the context of the so-called non-linear theory of particle acceleration.

This theory allows us to calculate the spectrum ancl spatial distribution of accelerated: particles around the shock. their dynamical reaction on the shock and the magnetic field amplification that cosmic rays induce due to streaming instability.

This theory allows us to calculate the spectrum and spatial distribution of accelerated particles around the shock, their dynamical reaction on the shock and the magnetic field amplification that cosmic rays induce due to streaming instability.

Although the non-linear theory has been previously applied to SNRs. this paper improves on previous attempts in two major aspects: 1) the magnetic field in the shock region is caleulated from. streaming instability ancl from conservation equations instead. of being inserted. in such a wav to fit the X-ray observations: 2) we include the dynamical reaction of the turbulent magnetic field on the shock. which is a very important elfect in shaping the shock precursor (C'apriolietal.(2008a.b))).

Although the non-linear theory has been previously applied to SNRs, this paper improves on previous attempts in two major aspects: 1) the magnetic field in the shock region is calculated from streaming instability and from conservation equations instead of being inserted in such a way to fit the X-ray observations; 2) we include the dynamical reaction of the turbulent magnetic field on the shock, which is a very important effect in shaping the shock precursor \cite{cap08,long}) ).

The first point is of crucial importance in that it allows us to achieve a unified. picture of the spectra of X-ray and ganuna ray emission. together with the morphology of the X-ray emission. the strength of the magnetic field and finally the dilfusion properties of the accelerated particles.

The first point is of crucial importance in that it allows us to achieve a unified picture of the spectra of X-ray and gamma ray emission, together with the morphology of the X-ray emission, the strength of the magnetic field and finally the diffusion properties of the accelerated particles.

Inclusion of the dynamical reaction of the field. then. as showed by Capriolietal.(2008a).. leads to à substantial reduction of the compression in the precursor. thereby also reducing the concavitv of the spectrum of accelerated. particles (C'apriolietal.(2008b))).

Inclusion of the dynamical reaction of the field, then, as showed by \cite{cap08}, leads to a substantial reduction of the compression in the precursor, thereby also reducing the concavity of the spectrum of accelerated particles \cite{long}) ).

A reduced concavity of the spectrum should also be expected as a result of the enhanced. velocity of the scattering centers when the magnetic field is amplified (see for instance Zirakashvili&Ptuskin (2000))).

A reduced concavity of the spectrum should also be expected as a result of the enhanced velocity of the scattering centers when the magnetic field is amplified (see for instance \cite{zir08}) ).

The large values of the magnetic field strength inferred from X-ray observations ancl confirmed by our calculations clearly favor a hacronie interpretation of the observed. ganima ray emission. because a subdominant population of electrons is sullicient to explain the spectrum and intensity of the observed X-ray. emission. but is insullicient to produce the observed. gamma ray emission through inverse Compton scattering (LCS) on the CMD and infrared/optical photons (IR|Opt).

The large values of the magnetic field strength inferred from X-ray observations and confirmed by our calculations clearly favor a hadronic interpretation of the observed gamma ray emission, because a subdominant population of electrons is sufficient to explain the spectrum and intensity of the observed X-ray emission, but is insufficient to produce the observed gamma ray emission through inverse Compton scattering (ICS) on the CMB and infrared/optical photons (IR+Opt).

The issue of whether the large fields are present in large fractions of the remnant volume or are rather confined in narrow filaments. remains however an open Issue.

The issue of whether the large fields are present in large fractions of the remnant volume or are rather confined in narrow filaments, remains however an open issue.

For this reason we also investigate the possibility that he filaments have some alternative explanation. so that here is no constraint on the streneth of the magnetic ield clownstream.

For this reason we also investigate the possibility that the filaments have some alternative explanation, so that there is no constraint on the strength of the magnetic field downstream.

We still use our non-linear calculations o derive the spectra of accelerated: protons and. electrons. oit. force. the injection to be low enough to avoid. large magnetic fields produced by streaming instability.

We still use our non-linear calculations to derive the spectra of accelerated protons and electrons, but force the injection to be low enough to avoid large magnetic fields produced by streaming instability.

We find hat a marginal fit to the gamma ray and. X-ray data is »xossible. although a large density of Ht photons needs to be assumed. inside the remnant.

We find that a marginal fit to the gamma ray and X-ray data is possible, although a large density of IR photons needs to be assumed inside the remnant.

The fit to the highest energy xwt of the gamma ray spectrum is not às good. as for the mielronic interpretation.

The fit to the highest energy part of the gamma ray spectrum is not as good as for the hadronic interpretation.

The general conclusion we draw is that although there are numerous indications that the observed. gamma. ravs may be of hadronic origin. a clear answer on this point may only come from: a) the extension of the gamma rav observationsto lower energies. and b) the detection of high energv neutrinos. which would be produced in the same haclronic interactions (Morlinoetal.2008).

The general conclusion we draw is that although there are numerous indications that the observed gamma rays may be of hadronic origin, a clear answer on this point may only come from: a) the extension of the gamma ray observationsto lower energies, and b) the detection of high energy neutrinos, which would be produced in the same hadronic interactions \cite[]{neutrinos}.

. The paper is organized as follows: in 82. we discuss in some detail the general lines of the calculations we carry out. including the non-linear theory of particle acceleration. the magnetic field amplification and the dillerent. channels of non-thermal emissions.

The paper is organized as follows: in \ref{sec:model} we discuss in some detail the general lines of the calculations we carry out, including the non-linear theory of particle acceleration, the magnetic field amplification and the different channels of non-thermal emissions.

ln 83. we discuss the results we obtain by specializing the caleulations tothe case of the SN RN J1713.7-3946.

In \ref{sec:results} we discuss the results we obtain by specializing the calculations tothe case of the SNR RX J1713.7-3946.

We conclude in ΚΕ.

We conclude in \ref{sec:conc}. .

In this section. we discuss the technical aspects of the

In this section we discuss the technical aspects of the

The primary purpose of our archival search was to find. simultaneous observations of Ser A* at

The primary purpose of our archival search was to find simultaneous observations of Sgr A* at

communication)

communication).

In BATSE. the burst was observed. 64 above the horizon. implving that the source remained visible for at least ~15 min after the trigger: thus. E900 s is a conservative lower limit for the interval between two resolved bursts. (

In BATSE, the burst was observed $64^\circ$ above the horizon, implying that the source remained visible for at least $\sim 15$ min after the trigger; thus, $\pm900$ s is a conservative lower limit for the interval between two resolved bursts. (

Also relevant are the data from. Ulysses which saw no burst consistent with the location of GRB 990123 [or a period of at least three days. before and. after the event (Ix. Hurley. private communication). although coverage was only about complete and we cannot completely exclude a second burst.)

Also relevant are the data from Ulysses which saw no burst consistent with the location of GRB 990123 for a period of at least three days before and after the event (K. Hurley, private communication), although coverage was only about complete and we cannot completely exclude a second burst.)

1L as we argue. Ls“fyfox900s is excluded. then so are magnilications 40<µου400.

If, as we argue, $1~s\leq t_3-t_2 \leq 900~s$ is excluded, then so are magnifications $40\leq \mu_{2,3} \leq 400$.

Furthermore. we can use limits on additional point sources in the HSTT image within 2" ⋠⋠⋅∕∕⋅of the afterglow⋅ to place constraints⋠ on. lensed images.

Furthermore, we can use limits on additional point sources in the HST image within $2^{\prime\prime}$ of the afterglow to place constraints on lensed images.

Hf µου<40. then using yy=4 (from eq.

If $\mu_{2,3}<40$, then using $\mu_1=4$ (from eq.

11). we find that burst Lo would have had a [luence »3510.7 ere on or around Jan. 15.

11), we find that burst 1 would have had a fluence $>3\times10^{-5}$ erg $^{-2}$ on or around Jan. 15.

It is unlikely. though not completely exeluded. that this Failed to trigger any detector.

It is unlikely, though not completely excluded, that this failed to trigger any detector.

However. the afterglow associated with burst 1 would have en brighter than V728.8 at the time ofthe LIST image even allowing for its additional [acing with time.

However, the afterglow associated with burst 1 would have been brighter than $V\sim28.8$ at the time of the HST image even allowing for its additional fading with time.

We have »erformoed two-dimensional Gaussian fits (including sloping. Xanar baselines) to all local maxima within 2" of the OT in the LIST image.

We have performed two-dimensional Gaussian fits (including sloping, planar baselines) to all local maxima within $2^{\prime\prime}$ of the OT in the HST image.

The only feature consistent with the psf (derived from a similar fit to the OT as EWIIM = 3.240. Pixels) is the faint object located 14 north of the OT.

The only feature consistent with the psf (derived from a similar fit to the OT as FWHM = $3.2 \pm 0.1$ pixels) is the faint object located $1.4^{\prime\prime}$ north of the OT.

This ~le excess has a magnitude of approximately V~28.4 (scaled to the value of V—25.2 for the OT reported. by Bloom et al. (

This $\sim 4 \sigma$ excess has a magnitude of approximately $V \sim 28.4$ (scaled to the value of $V=25.2$ for the OT reported by Bloom et al. (

1999)).

We take this as an upper limit to the magnitude of the first afterglow.

We can therefore almos exclude µου<40.

We can therefore almost exclude $\mu_{2,3} \leq 40$.

The remaining parameter space is described bv fols and pro&400.

The remaining parameter space is described by $t_{2,3} \leq 1~s$ and $\mu_{2,3} \geq 400$.

In this case. the first afterglow will be uncdetectable.

In this case, the first afterglow will be undetectable.

However. the finite size of the source becomes a factor at these high magnifications.

However, the finite size of the source becomes a factor at these high magnifications.

For a source angular size Bit). the magnification is limited to This limit should not allect. the burst itself. although it will eventually influence the afterglow.

For a source angular size B(t), the magnification is limited to This limit should not affect the burst itself, although it will eventually influence the afterglow.

Unfortunately. our lack of understanding of the ambient environment ancl the nature of the explosion precludes a confident expression for Bit).

Unfortunately, our lack of understanding of the ambient environment and the nature of the explosion precludes a confident expression for B(t).

However. a naive estimate for a spherical. relativistic blastwave with £~107 erg and m~1 cm? (eg. DBlandford and. Melxee 1977) gives D—20/1d)*"pas.

However, a naive estimate for a spherical, relativistic blastwave with $E\sim10^{52}$ erg and $n\sim 1$ ${\rm cm}^{-3}$ (e.g., Blandford and McKee 1977) gives $B\sim2(t/1{\rm d})^{5/8} \mu {\rm as}$.

This limits the magnificationὃν to foaX6000/17d)"7.

This limits the magnification to $\mu_{2,3}\leq 600(t/17{\rm d})^{-0.3}$.

After this inequality is violated. the afterglow emission. will decline correspondingly more steeply with time.

After this inequality is violated, the afterglow emission will decline correspondingly more steeply with time.

In fact. just such an increase in the rate of decline has been reported. at |—ll d (Yadigaroglu Halpern 1999).

In fact, just such an increase in the rate of decline has been reported at $t=11$ d (Yadigaroglu Halpern 1999).

We therefore cannot confidently. exclude lensing with µου400 at this stage.

We therefore cannot confidently exclude lensing with $\mu_{2,3}\sim400$ at this stage.

However. if it is possible to examine the subsecond time variations in the BATSE lishteurve of GRBOSOL23 and thereby limit f;9£5 to z10 ms. then fro, would have to exceed z1000. and all multiple imaging by a z;=1.6 dellector would ellectively be ruled out.

However, if it is possible to examine the subsecond time variations in the BATSE lightcurve of GRB980123 and thereby limit $t_3-t_2$ to $\approx10$ ms, then $\mu_{2,3}$ would have to exceed $\approx1000$, and all multiple imaging by a $z_d=1.6$ deflector would effectively be ruled out.

In summary. three arguments (the high Αη of the galaxy. the implausibilitv of missing the first burst and of failing to detect. its afterglow) can already be marshalled against the lensing hypothesis.

In summary, three arguments (the high $M/L$ of the galaxy, the implausibility of missing the first burst and of failing to detect its afterglow) can already be marshalled against the lensing hypothesis.

Vhree additional steps might ellectivelv eliminate it - searching for double structure on subsecond. timescales in the BATSE data. setting a better limit on the presence of additional afterglow images at the predicted locations and obtaining a reliable photometric or spectroscopic redshift for the galaxy.

Three additional steps might effectively eliminate it - searching for double structure on subsecond timescales in the BATSE data, setting a better limit on the presence of additional afterglow images at the predicted locations and obtaining a reliable photometric or spectroscopic redshift for the galaxy.

C'ontrariwise. iit turns out that the burst was highly magnilied by lensing. then the burst energv would be reduced to ~9LOBpa1000)+ erg.

Contrariwise, if it turns out that the burst was highly magnified by lensing, then the burst energy would be reduced to $\sim9\times10^{51}{\cal B}(2\mu_{2,3}/1000)^{-1}$ erg.

GRB 990123 serves as a reminder that multiple imaging of a gamma-ray burst is to be expected eventually in a large enough sample and the analysis of §22 should be generally applicable.

GRB 990123 serves as a reminder that multiple imaging of a gamma-ray burst is to be expected eventually in a large enough sample and the analysis of 2 should be generally applicable.

While we cannot completely rule out the possibility that it has been multiply imaged and strongly magnified. it should be possible to do so soon.

While we cannot completely rule out the possibility that it has been multiply imaged and strongly magnified, it should be possible to do so soon.

In this case. if we have not observed (or do not observe) an echo of GRB 990123. then the magnification is limited to fr2. except under quite contrived models. leaving CRB 990123 as the most intrinsically luminous cosmic event vet observed in its entirety.

In this case, if we have not observed (or do not observe) an echo of GRB 990123, then the magnification is limited to $\mu\sim2$, except under quite contrived models, leaving GRB 990123 as the most intrinsically luminous cosmic event yet observed in its entirety.

We thank Martin. Rees for encouragement. the Institute of Astronomy. University of Cambridge for hospitality. and the Beverly and. Raymond Sackler Foundation for support during the preparation of this paper.

We thank Martin Rees for encouragement, the Institute of Astronomy, University of Cambridge for hospitality, and the Beverly and Raymond Sackler Foundation for support during the preparation of this paper.

Support under NSE evant AST 95-290170 and NASA erant. 5-2837 is also gratefully acknowledgect.

Support under NSF grant AST 95-29170 and NASA grant 5-2837 is also gratefully acknowledged.

null

.

and

and.

where /: aud /. are the radial ancl vertical wavenumbers. respectively. J,,(ha) are Bessel functions of the first kind and ay. ao. 54. bs and ¢ ave functions determined by the initial field distribution and the conditions of continuity on 2=zz.

where $k$ and $k_z$ are the radial and vertical wavenumbers, respectively, $J_m(k\varpi)$ are Bessel functions of the first kind and $a_1$ , $a_2$, $b_1$, $b_2$ and $c$ are functions determined by the initial field distribution and the conditions of continuity on $z=\pm z_0$.

The decay rate is (he+hr), proporlional to the inverse of the modulus of the vector wavenumber k=fe+/.e.

The decay rate is (k_z^2+k^2), proportional to the inverse of the modulus of the vector wavenumber ${\bf k}=k\hat{\bf e}_\varpi+k_z\hat{\bf e}$.

The condition of continuity of QP/0z at 2τμ leads to the relation (2h. τι)= Ohh, The limit of an infinitesimally thin disk is recovered under the following ordering: (the disk thickness is much smaller than the vertical wavelength. that in {urnis much smaller than the radial wavelength).

The condition of continuity of $\partial P/\partial z$ at $z=\pm z_0$ leads to the relation (2k_z z_0)=2 k_z k. The limit of an infinitesimally thin disk is recovered under the following ordering: $z_0 \ll k_z^{-1} \ll k^{-1} \ll \varpi$ (the disk thickness is much smaller than the vertical wavelength, that in turnis much smaller than the radial wavelength).

With these approximations. eeuation (5) then gives he/2z, and equation (AT)) becomes 52yh?&ΜΕ τμ. as found in our case.

With these approximations, equation \ref{cont_cond}) ) then gives $k\approx k_z^2 z_0$ and equation\ref{rate}) ) becomes $\gamma\approx \eta k_z^2\approx k/z_0$ , as found in our case.

aud ©.

and $\Omega$.

These measurements were eeucrated assuming that here is a planetary companion with orbital parameters iu Table 1.. and (7.9)(0.0.1.0 rad).

These measurements were generated assuming that there is a planetary companion with orbital parameters in Table \ref{HD 154345 orbit}, , and $(I, \Omega) = (0.0, 1.0$ rad).

This simulated data was used together with the real RV measurements oiblished iu Ws to find the Πιο T4 or which the rue nass of the planet could still be measured with the SIM telescope.

This simulated data was used together with the real RV measurements published in W08 to find the limiting $T_{A}$ for which the true mass of the planet could still be measured with the SIM telescope.

The selection £=Oo was made because changing this value would resul in a higher planetary nass and hence ina stronger astrometric VAsignal. making he detection of orbital plane parameters even casicr.

The selection $I=0$ was made because changing this value would result in a higher planetary mass and hence in a stronger astrometric signal, making the detection of orbital plane parameters even easier.

Reeardless of large error bars. we found that it is possible o detect the orbital plane parameters with 7T,=1.0 vears.

Regardless of large error bars, we found that it is possible to detect the orbital plane parameters with $T_{A} = 1.0$ years.

With this short timeline. the error bars of the yaralucters were [020, 0.22] aud [0.39. 1.5L) for 7 and ©. respectively, demoustrating that it was indeed possible to determine their values.

With this short timeline, the error bars of the parameters were [-0.30, 0.22] and [0.39, 1.54] for $I$ and $\Omega$, respectively, demonstrating that it was indeed possible to determine their values.

The time needed to make ai positive detection of an extrasolar planetary companion candidate depends essentially on its orbital period.

The time needed to make a positive detection of an extrasolar planetary conpanion candidate depends essentially on its orbital period.

It is comunonly assumed that. to be able to detect the signature of such companion. an observational timeline longer than the orbital period is required.

It is commonly assumed that, to be able to detect the signature of such companion, an observational timeline longer than the orbital period is required.

Also. since most of the cxoplanet candidates have been detected using the RV method. only the lower lit of their mass is available.

Also, since most of the exoplanet candidates have been detected using the RV method, only the lower limit of their mass is available.

With the iid of future space telescopes aud accurate astrometric mcasiurciuicuts. it will be possible to detect the inclination aud thus the true mass of plauctary candidates.

With the aid of future space telescopes and accurate astrometric measurements, it will be possible to detect the inclination and thus the true mass of planetary candidates.

We have shown that when high-precision RV and accurate astrometric measurements are both available. it is possible to detect the true mass of stellar companions with observational timelines cousiderably shorter than 1ο] orbital periods.

We have shown that when high-precision RV and accurate astrometric measurements are both available, it is possible to detect the true mass of stellar companions with observational timelines considerably shorter than their orbital periods.

Also. when the RV measurements wve a long time span. astrometric measurements can reveal the true mass of a stellar companion in less time iu one tenth of the orbital period of the syste.

Also, when the RV measurements have a long time span, astrometric measurements can reveal the true mass of a stellar companion in less time than one tenth of the orbital period of the system.

This bility is also clemonstrated using the BV. measurements f HIID151315 as an example.

This ability is also demonstrated using the RV measurements of HD154345 as an example.

We find that. having jose lüueasuremuients with Fay=10.1 vears idu haud. astrometric observatious with SIM telescope are sufficieu or obtaiuiug the true mass. within a single vear.

We find that, having these measurements with $T_{RV} = 10.4$ years in hand, astrometric observations with SIM telescope are sufficient for obtaining the true mass, within a single year.

Davesiu iufereunco plavs an portant τοις when extracting information from several sources of neasurelents.

Bayesian inference plays an important role when extracting information from several sources of measurements.