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If we consider a simplified picture of the magnetosphere in which there is no parallel electric field in the closed field line region, the potential drop across open field lines is given roughly by the longitudinal potential drop along field lines.
If we consider a simplified picture of the magnetosphere in which there is no parallel electric field in the closed field line region, the potential drop across open field lines is given roughly by the longitudinal potential drop along field lines.
The differential rotation can then be roughly related to the longitudinal potential drop by In the laboratory frame, the field lines are undergoing rotation about the pulsar spin axis (with the angular frequency (©), and in addition they are rotating differentially around the maximum potential axis in a retrograde sense.
The differential rotation can then be roughly related to the longitudinal potential drop by In the laboratory frame, the field lines are undergoing rotation about the pulsar spin axis (with the angular frequency $\Omega$ ), and in addition they are rotating differentially around the maximum potential axis in a retrograde sense.
The differential rotation of plasma can explain sub-pulse emission features that drift with respect to the otherwise periodic light curve of the pulsar.
The differential rotation of plasma can explain sub-pulse emission features that drift with respect to the otherwise periodic light curve of the pulsar.
Our result is in contrast to the standard picture in which the plasma precesses about the magnetic axis (Ruderman&Sutherland 1975).
Our result is in contrast to the standard picture in which the plasma precesses about the magnetic axis \citep{rudermansutherland75}.
. The magnetic colatitude parameter in the cartographic transformation of, e.g. DeshpandeRankin must then be modified accordingly.
The magnetic colatitude parameter in the cartographic transformation of, e.g. \cite{DeshpandeRankin}, must then be modified accordingly.
To better (2001),,visualize the differential rotation in the context of our resistive magnetospheres, consider the full drift velocity again in the corotating frame.
To better visualize the differential rotation in the context of our resistive magnetospheres, consider the full drift velocity again in the corotating frame.
Fig.
Fig.
5 shows magnetic field lines in the ji—Q plane for a 60° inclined dipole at conductivity (c/Q)?=4.
\ref{velocity} shows magnetic field lines in the $\vec{\mu}-\vec{\Omega}$ plane for a $60^{\circ}$ inclined dipole at conductivity $(\sigma/\Omega)^2=4$.
Color indicates out-of-plane drift velocity, with red (blue) representing velocity into the page.
Color indicates out-of-plane drift velocity, with red (blue) representing velocity into (out of) the page.
The velocity has been rescaled by raising(out of)its magnitude to the 1/2 power.
The velocity has been rescaled by raising its magnitude to the $1/2$ power.
The axis of maximum potential extends from the star roughly halfway between the rotation and magnetic axes.
The axis of maximum potential extends from the star roughly halfway between the rotation and magnetic axes.
The differential rotation of plasma about this axis is denoted by the transition from red to blue across the axis, indicating a reversal in the sign of the out-of-plane drift velocity.
The differential rotation of plasma about this axis is denoted by the transition from red to blue across the axis, indicating a reversal in the sign of the out-of-plane drift velocity.
Note that the axis bends off in the direction of open field lines beyond the light cylinder.
Note that the axis bends off in the direction of open field lines beyond the light cylinder.
These corotating frame drift velocities can be quite substantial.
These corotating frame drift velocities can be quite substantial.
The maximum illustrated drift velocity occurs near the current sheets and corresponds to a velocity of 0.8c.
The maximum illustrated drift velocity occurs near the current sheets and corresponds to a velocity of $0.8c$.
The differential rotation is much stronger than that implied by sub-pulse drift, but we expect the qualitative features of differential rotation to persist in solutions with more realistic open field line potential drops.
The differential rotation is much stronger than that implied by sub-pulse drift, but we expect the qualitative features of differential rotation to persist in solutions with more realistic open field line potential drops.
At lower conductivities the magnitude of differential rotation about the axis of maximum potential drop increases, and the conductivity is a parameter that can be tuned to attempt to match observed sub-pulse emission features.
At lower conductivities the magnitude of differential rotation about the axis of maximum potential drop increases, and the conductivity is a parameter that can be tuned to attempt to match observed sub-pulse emission features.
Incidentally, the bundle of field lines surrounding the axis of the maximum potential corresponds to the field lines that carry the largest distributed current density on the polar cap (see Fig.
Incidentally, the bundle of field lines surrounding the axis of the maximum potential corresponds to the field lines that carry the largest distributed current density on the polar cap (see Fig.
4 in Bai&Spitkovsky 2010)).
4 in \citealt{BS10}) ).
If the strength of the current is associated with radio emission, then the core emission would have a centroid that is offset from the magnetic pole.
If the strength of the current is associated with radio emission, then the core emission would have a centroid that is offset from the magnetic pole.
The offset could be as large as half of the polar cap radius.
The offset could be as large as half of the polar cap radius.
This would introduce potentially significant modifications to the polarization sweep of the core radio emission and cause deviations from the expected S-curve of Radhakrishnan&Cooke (1969).
This would introduce potentially significant modifications to the polarization sweep of the core radio emission and cause deviations from the expected S-curve of \cite{RadCooke69}.
. For a number of pulsars, it would imply differences in the inclination and viewing angles inferred from the shape of the polarization sweep.
For a number of pulsars, it would imply differences in the inclination and viewing angles inferred from the shape of the polarization sweep.
We conclude with prospects for future research.
We conclude with prospects for future research.
We will generalize our assumption that c/€) is constant in the magnetosphere.
We will generalize our assumption that $\sigma/\Omega$ is constant in the magnetosphere.
In addition to having higher conductivity in the closed zone, we will experiment with prescriptions for anomalous resistivity in the current sheet.
In addition to having higher conductivity in the closed zone, we will experiment with prescriptions for anomalous resistivity in the current sheet.
These improvements will yield a more realistic magnetospheric structure, that can be accurate enough for geometrical modeling of gamma-ray light curves from pulsars.
These improvements will yield a more realistic magnetospheric structure, that can be accurate enough for geometrical modeling of gamma-ray light curves from pulsars.
The gamma-ray pulse formation is sensitive to the geometry of the magnetosphere, and, in particular, to the field lines near the current sheet (Bai&Spitkovsky 2010)..
The gamma-ray pulse formation is sensitive to the geometry of the magnetosphere, and, in particular, to the field lines near the current sheet \citep{BS10}. .
Deviations from the force-free geometry may be important for modeling the light curves of older pulsars which require wider gaps in the outer-gap models (Wattersetal.
Deviations from the force-free geometry may be important for modeling the light curves of older pulsars which require wider gaps in the outer-gap models \citep{Watters09}. .
AT acknowledges 2009)..supportby the Princeton Center for Theoretical Science fellowship and by the National
AT acknowledges supportby the Princeton Center for Theoretical Science fellowship and by the National
For each merger tree, we set Mie;=Mox10~°.
For each merger tree, we set $\mres \,=\, M_2\times10^{-5}$.
For 10!!Mo haloes, this value of M;e; is comparable to the mass of an individual dark matter particle in our numerical simulations (SH09).
For $10^{11}\,\Msun$ haloes, this value of $\mres$ is comparable to the mass of an individual dark matter particle in our numerical simulations (SH09).
We tested the effect of changing Mies, 21 and the number of redshift levels and found that our choices produce convergent results for the estimation of the unbound gas.
We tested the effect of changing $\mres$, $z_1$ and the number of redshift levels and found that our choices produce convergent results for the estimation of the unbound gas.
With these merger histories, we follow all mergers from z—10 to z=0 that lead to a halo of mass M», and eject a fraction of gas from the mergers with mass ratios greater than 7min.
With these merger histories, we follow all mergers from $z=10$ to $z=0$ that lead to a halo of mass $M_2$, and eject a fraction of gas from the mergers with mass ratios greater than $\etam$.
The cumulative sum of the unbound gas produces the total gas released in assembling a particular halo.
The cumulative sum of the unbound gas produces the total gas released in assembling a particular halo.
This yields the fractional gas lost by z—0 on a basis.
This yields the fractional gas lost by $z=0$ on a basis.
We repeat this process for realisations, which provides the variance in the gas lost.
We repeat this process for realisations, which provides the variance in the gas lost.
We can find the total gas released in generating all haloes in the Universe by convolving with the co-moving number density of those haloes at z= 0(?)..
We can find the total gas released in generating all haloes in the Universe by convolving with the co-moving number density of those haloes at $z=0$ \citep{WAHT06}.
Summing over the final halo masses yields the effect of halo assembly on populating the
Summing over the final halo masses yields the effect of halo assembly on populating the.
WHIM.. Figure 1 shows the redshift evolution of the cumulative gas mass lost from all haloes in a co-moving Mpc? volume for the run Majorl.
Figure \ref{figure:gasmasslostwhalo} shows the redshift evolution of the cumulative gas mass lost from all haloes in a co-moving $^3$ volume for the run Major1.
To generate Figure 1,, we first take the mean of realisations for the unbound gas mass in each redshift step for each halo.
To generate Figure \ref{figure:gasmasslostwhalo}, we first take the mean of realisations for the unbound gas mass in each redshift step for each halo.
This unbound gas mass is added up along the redshift track to yield the cumulative mass at each redshift step and then multiplied by the co-moving number density of that particular halo at z=0.
This unbound gas mass is added up along the redshift track to yield the cumulative mass at each redshift step and then multiplied by the co-moving number density of that particular halo at $z=0$.
This is the cumulative co-moving density of the unbound gas for one halo mass.
This is the cumulative co-moving density of the unbound gas for one halo mass.
Repeating this process for the 100 final halo masses yields the individual tracks spanning the x-axis.
Repeating this process for the 100 final halo masses yields the individual tracks spanning the x-axis.
Figure 1 shows that the most massive haloes unbind the most gas at all redshifts, in spite of their lower number densities.
Figure \ref{figure:gasmasslostwhalo} shows that the most massive haloes unbind the most gas at all redshifts, in spite of their lower number densities.
For example, the current number density in a co-moving Mpc? of a 1015Mo halo is ~10 times smaller than for a 105Mo halo; so the mass-density of the 105M halo is an order of magnitude larger than the 1012Mo halo.
For example, the current number density in a co-moving $^3$ of a $10^{13}\, \Msun$ halo is $\sim 10^6$ times smaller than for a $10^8\,\Msun$ halo; so the mass-density of the $10^8 \,\Msun$ halo is an order of magnitude larger than the $10^{13}\,\Msun$ halo.
This biasing towards higher mass is explained by the hierarchical assembly of haloes — more massive objects today undergo many more mergers in the
This biasing towards higher mass is explained by the hierarchical assembly of haloes – more massive objects today undergo many more mergers in the.
past?.. Figure 2. shows the redshift evolution of the unbound gas mass over the total baryon mass in all the haloes considered in the merger tree.
Figure \ref{figure:gasmasslostwz} shows the redshift evolution of the unbound gas mass over the total baryon mass in all the haloes considered in the merger tree.
We find that and of the baryons can be ejected by mergers for the Majorl and Minor1 runs respectively.
We find that and of the baryons can be ejected by mergers for the Major1 and Minor1 runs respectively.
The mass range of 10?—Mo and 105—10'°Mo contain and of the total collapsed mass in the Universe respectively.
The mass range of $10^{10}-10^{13}\,\Msun$ and $10^{8}-10^{13}\,\Msun$ contain and of the total collapsed mass in the Universe respectively.
Thus, the IGM pollution caused by the mergers presented in this paper can only reflect the history of at most half the total matter.
Thus, the IGM pollution caused by the mergers presented in this paper can only reflect the history of at most half the total matter.
If we assume that the same pattern holds true globally, then the fractions presented here (Figure 2)) can be interpreted as normalised by the total baryonic matter density of the Universe.
If we assume that the same pattern holds true globally, then the fractions presented here (Figure \ref{figure:gasmasslostwz}) ) can be interpreted as normalised by the total baryonic matter density of the Universe.
Notice that the fraction of gas lost increases more rapidly with redshift for ri,=0.1 — this is because 10:1 mergers occur more frequently than 3:1 (e.g.,??)..
Notice that the fraction of gas lost increases more rapidly with redshift for $\etam=0.1$ – this is because 10:1 mergers occur more frequently than 3:1 \citep[e.g.,][]{FM08, GGBN09}.
We can interpret Figure 2 in the following way: in the Major1 run, the convergence to of the universal gas mass is tantamount to saying that the average halo undergoes one major merger in a Hubble time, since we set major mergers to release of the gas mass.
We can interpret Figure \ref{figure:gasmasslostwz} in the following way: in the Major1 run, the convergence to of the universal gas mass is tantamount to saying that the average halo undergoes one major merger in a Hubble time, since we set major mergers to release of the gas mass.
Likewise, the convergence of the Minorl run can be understood by noting that minor mergers (η>0.1) are 2—3 times more frequent than major mergers (7>0.3, ?)).
Likewise, the convergence of the Minor1 run can be understood by noting that minor mergers $\eta > 0.1$ ) are $2-3$ times more frequent than major mergers $\eta > 0.3$, \citet[see bottom panel of Fig. 8 in][]{FM08}) ).
Thus, the overall unbound density converges to ~20—3096 for the Minor1 run.
Thus, the overall unbound density converges to $\sim 20-30\%$ for the Minor1 run.
In run Major-Keres with multiphase accretion, we find that only ~ of the gas can be released due to mergers.
In run Major-Keres with multiphase accretion, we find that only $\sim$ of the gas can be released due to mergers.
Since the simulations of SH09 only included hot gas, we chose to unbind only from that phase.
Since the simulations of SH09 only included hot gas, we chose to unbind only from that phase.
In the multiphase scenario, too much gas is in the cold phase and hence, can not be released during mergers.
In the multiphase scenario, too much gas is in the cold phase and hence, can not be released during mergers.
Even adding a mechanism to heat cold gas by major mergers (Eqn.4?) does not convert enough cold gas into a hot phase to be unbound later.
Even adding a mechanism to heat cold gas by major mergers \citep[Eqn. 4][]{CPJS04} does not convert enough cold gas into a hot phase to be unbound later.
If the haloes are only accreting cold gas and this gas can not be unbound from the haloes before heating it first, then the gas currently populating the may not have ever fallen into virialised haloes.
If the haloes are only accreting cold gas and this gas can not be unbound from the haloes before heating it first, then the gas currently populating the may not have ever fallen into virialised haloes.
In a given merger tree, a fraction of unbound gas is released by mergers between small haloes.
In a given merger tree, a fraction of unbound gas is released by mergers between small haloes.
To isolate the fraction (Table 2,, Column 5)created during the assembly of the massive galaxies, we run two sets of merger trees with a lower mass limit of 101°Mo.
To isolate the fraction (Table \ref{table:results}, Column 5)created during the assembly of the massive galaxies, we run two sets of merger trees with a lower mass limit of $10^{10}\,\Msun$.
Table 2 shows that most of the unbound gas that is released comes during the formation of the massive galaxies.
Table \ref{table:results} shows that most of the unbound gas that is released comes during the formation of the massive galaxies.
In particular, Major4, with only the massive haloes, produces nearly all of the unbound gas produced in the Major1 run.
In particular, Major4, with only the massive haloes, produces nearly all of the unbound gas produced in the Major1 run.
Although small haloes merging with massive haloes do not eject any gas, these minor accretion events increase the gas content of the remnant.
Although small haloes merging with massive haloes do not eject any gas, these minor accretion events increase the gas content of the remnant.
This could potentially increase
This could potentially increase
The reason why we did not simply use uniform distributions in all parameters and thus cover (he whole parameter space is to avoid unphysical light curves.
The reason why we did not simply use uniform distributions in all parameters and thus cover the whole parameter space is to avoid unphysical light curves.
Such lieht curves. when ον comprise a significant [raction of the whole sample. have a notable adverse impact on the networks recognition ability. especially lor second-order parameters such as esino and ecose (?)..
Such light curves, when they comprise a significant fraction of the whole sample, have a notable adverse impact on the network's recognition ability, especially for second-order parameters such as $e \sin \omega$ and $e \cos \omega$ \citep{prsa2008}.
LSST will survey. the sky according to the so-called cadence.
LSST will survey the sky according to the so-called cadence.
This scanning model is optimized Lor the uniform observed depth of Á24.5 and a uniform number of visits across 20.000 square degrees of the southern skv (7.82.1)...
This scanning model is optimized for the uniform observed depth of $r \sim 24.5$ and a uniform number of visits across 20,000 square degrees of the southern sky \citepalias[\S 2.1]{LSSTbook}.
A is delined as a pair of 5s exposures. performed back-to-back. wilh a 4ss readout separation. to aid in cosmic rav rejection.
A is defined as a pair of s exposures, performed back-to-back, with a s readout separation, to aid in cosmic ray rejection.
Most fields will be observed twice during the nightly run. wilh visits separated
Most fields will be observed twice during the nightly run, with visits separated
Ry.
.
.. The projected radius and its uncertainties cam be obtained from a tabulated version of thensa spectral model (2)..
The projected radius and its uncertainties can be obtained from a tabulated version of the spectral model \citep{zavlin96}.
However. this model (or nsa) is less adapted than the or models (7). because it was calculated for a single value of the surface eravity g=2.3«103enis.7? while the other two models consider a range of values.
However, this model (or ) is less adapted than the or models \citep{webb07} because it was calculated for a single value of the surface gravity $g = 2.43\tee{14}\cgsaccel$ while the other two models consider a range of values.
Nevertheless. the best-fit vvalue with this model is: A4.=12.1!"lau (consisteut with the value calculated in the previous paragraph). for a temperature Tig=76'SeV (0.02)).
Nevertheless, the best-fit value with this model is: $\rinfty= 12.1 \ud{1.5}{0.9}\km$ (consistent with the value calculated in the previous paragraph), for a temperature $\kteff=76\ud{2}{3}\eV$ ).
A second method to estimate the uncertainties involves ecolctric construction. by reading graphically the eror region of oon the ALR contours (Fieure tj).
A second method to estimate the uncertainties involves geometric construction, by reading graphically the error region of on the M-R contours (Figure \ref{fig:contours}) ).
For that. we choose to use the line of constant surface gravity (ic. coustant ΟΠ) that goes through the poiut CR.M)=(Okun.03...) and the poiut of best fit in AL space.
For that, we choose to use the line of constant surface gravity (i.e., constant $M\left(R\right)$ ) that goes through the point $\left(R,M\right) = \left(0\km,0\msun\right)$ and the point of best fit in M-R space.
This line intersects the contour at the points (R.M)=(9.018kan.1.015AL.) and (RM)=(10.39kin.1.215 A7...
This line intersects the contour at the points $\left(R,M\right) = \left(9.048\km,1.045\msun\right)$ and $\left(R,M\right) = \left(10.39\km,1.245\msun\right)$ .
These two points correspond to the values RY=11.15lan aud RY=12.92kii. which are. respectively. estimates of the lower aud upper confidence uncertaiuties on A4. assmnuins a coustaut value of the surface gravity.
These two points correspond to the values $\rinfty=11.15\km$ and $\rinfty=12.92\km$ which are, respectively, estimates of the lower and upper confidence uncertainties on $\rinfty$, assuming a constant value of the surface gravity.
Therefore. the projected radius aud its estimated confidence uncertainties ave: RL=11.9!)kn.
Therefore, the projected radius and its estimated confidence uncertainties are: $\rinfty=11.9\ud{1.0}{0.8}\km$.
With the achieved unucertiüntv. U21 becomes the third best radius measurement of a NS among the population of GC qLAINBs. after the ones in citepgendred3a and in MIS (7)..
With the achieved uncertainty, U24 becomes the third best radius measurement of a NS among the population of GC qLMXBs, after the ones in \\citep{gendre03a} and in M13 \citep{gendre03b}.
The high S/N spectra aud the precise radius nieasurenmients obtained m the work preseuted here cau be used to constrain the EoS of dense matter.
The high S/N spectra and the precise radius measurements obtained in the work presented here can be used to constrain the EoS of dense matter.
A hieh precision on the NS radius is maudatory to exclude some of the existing nuclear deuse matter EoSs aud provide the necessary constraints to understiuud the behavior of such matter.
A high precision on the NS radius is mandatory to exclude some of the existing nuclear dense matter EoSs and provide the necessary constraints to understand the behavior of such matter.
However. other sources of error come iuto plav in this type of measurements.
However, other sources of error come into play in this type of measurements.
To quantify the total uncertainty on the radius measurement prescuted here. we estimate the contribution of cach source of error iuto an error budget. icliding the distance to the GC NGC 6397. uncertainties iutrinsic to the mocel used. systematic and statistical uncertainties.
To quantify the total uncertainty on the radius measurement presented here, we estimate the contribution of each source of error into an error budget, including the distance to the GC NGC 6397, uncertainties intrinsic to the model used, systematic and statistical uncertainties.
In those references where these uncertiünties are discussed (for exanuple. 73). only two of the three unucertaiufies we discuss here (distance aud detector systematics) are addressed.
In those references where these uncertainties are discussed (for example, \citealt{heinke06}) ), only two of the three uncertainties we discuss here (distance and detector systematics) are addressed.
No work that we cau find in the literature discusses the impact of the uncertainty in the spectral model on derived model parameters: therefore. we do so here.
No work that we can find in the literature discusses the impact of the uncertainty in the spectral model on derived model parameters; therefore, we do so here.
Consequently. the distance uncertainty. (2.1%}) is the ouly quantifiable error not taken iuto account in the radius nieasureineut obtained from spectral fitting.
Consequently, the distance uncertainty ) is the only quantifiable error not taken into account in the radius measurement obtained from spectral fitting.
It is therefore added in quadrature to the svstematic aud statistical uncertainties to obtain the total quantifiable uucertaintv in the radius measurement.
It is therefore added in quadrature to the systematic and statistical uncertainties to obtain the total quantifiable uncertainty in the radius measurement.
For example. the upper bound uncertainty linüt of wwas and is when accounting for the distance uncertainty.
For example, the upper bound uncertainty limit of was and is when accounting for the distance uncertainty.
The lower bound ΠΕ ΠΜ. was and becomes.
The lower bound uncertainty limit was and becomes.
. Consequently. the physical radius is Ryy=89Me (for Mxa4= LLM.) while the estimated radiation radius is RY=11.9!)8). when considering the sources of uncertainty listed above.
Consequently, the physical radius is $\rns = 8.9\ud{0.9}{0.6}$ (for $\mns = 1.4 \msun$ ) while the estimated radiation radius is $\rinfty = 11.9\ud{1.0}{0.8}\km$, when considering the sources of uncertainty listed above.
Iu conclusion. in NGC 6397. the distance uucertaiutv of NGC 6397 alone minimally affects the current unucertaintv ou the radius measurement.
In conclusion, in NGC 6397, the distance uncertainty of NGC 6397 alone minimally affects the current uncertainty on the radius measurement.
may not be as significant as previously thought, at least for late-type giant galaxies.
may not be as significant as previously thought, at least for late-type giant galaxies.
À detailed comparison of the observed scatter with the predictions from population synthesis models (eg, is beyond the scope of this paper because of the wide ????)range of stellar compositions and star formation histories represented by our galaxy sample.
A detailed comparison of the observed scatter with the predictions from population synthesis models \citep[eg,][]{bruzual93, bruzual03, maraston98, li08} is beyond the scope of this paper because of the wide range of stellar compositions and star formation histories represented by our galaxy sample.
The B—H colour for each galaxy can be compared with the morphological type (Figure [16] ).
The $B - H$ colour for each galaxy can be compared with the morphological type (Figure \ref{fig:BmHvstype}) ).
'There we include the combined samples of ? and the Virgo cluster data in the white boxes and the new LSI data is shown by the black boxes.
There we include the combined samples of \cite{kassin06} and the Virgo cluster data in the white boxes and the new LSI data is shown by the black boxes.
The combined Virgo cluster and ? sample is ten times the size of our sample but is dominated by giant, luminous galaxies.
The combined Virgo cluster and \cite{kassin06} sample is ten times the size of our sample but is dominated by giant, luminous galaxies.