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Exploring the influence of mixing lenetl. Cassisi&Saaris find a dependence ο©—0.27 mag with unl in units of A, aud with the metalliciy unspecified. a result that is in rough agreement witl
Exploring the influence of mixing length, \citeauthor{cas3} find a dependence $\Delta V_\mathrm{bump}/\Delta \mathrm{ml} \approx -0.27$ mag with $\Delta$ ml in units of $H_p$ and with the metallicity unspecified, a result that is in rough agreement with
Exploring the influence of mixing lenetl. Cassisi&Saaris find a dependence ο©—0.27 mag with unl in units of A, aud with the metalliciy unspecified. a result that is in rough agreement witli
Exploring the influence of mixing length, \citeauthor{cas3} find a dependence $\Delta V_\mathrm{bump}/\Delta \mathrm{ml} \approx -0.27$ mag with $\Delta$ ml in units of $H_p$ and with the metallicity unspecified, a result that is in rough agreement with
For a neutron star of around (wo solar masses. AMzz2A. and bv assuming Czz20 MeVT and bzz. 6. we obtainoN atas1.85.
For a neutron star of around two solar masses, $M\approx 2M_{\odot }$ and by assuming $C\approx 20$ MeV and $b\approx 6$ , we obtain $\frac{\Delta \rho }{% \rho }\approx 1.8 5.
Ol course this result is strongly dependent on (he precise numerical values of C aud 5. which are generally poorly known.
Of course this result is strongly dependent on the precise numerical values of $C$ and $b$ , which are generally poorly known.
C is also a neutron matter equation of state dependent parameter.
$C$ is also a neutron matter equation of state dependent parameter.
For example. assuming for Co à value of 10 MeV. will lead to =x0.92.
For example, assuming for $C$ a value of $10$ MeV will lead to $\frac{\Delta \rho }{\rho }\approx 0.92$.
An increase in the mass M. of the star will also decrease the value of the relative change in the density of the star necessary to convert the neutron star.
An increase in the mass $M$ of the star will also decrease the value of the relative change in the density of the star necessary to convert the neutron star.
At present. we have very little observational knowledge about how fast newborn neutron star can rotate.
At present, we have very little observational knowledge about how fast newborn neutron star can rotate.
The most well-known voung pulsar is that the Crab pulsar was born with a rotational period of about 20 ms1971).
The most well-known young pulsar is that the Crab pulsar was born with a rotational period of about $20$ ms.
. 1 κο, during its lifetime the pulsar its central density only increases about Ap,/p,20.0011996).
If so, during its lifetime the pulsar its central density only increases about $\Delta \rho _{c}/\rho _{c}\approx 0.001$.
. Currently thefastest rotating pulsar known is PSR19374-214. which has a period of 1.551ms or !.
Currently thefastest rotating pulsar known is PSR1937+214, which has a period of 1.55ms or $\Omega \approx 4,000 s^{-1}$ .
But it has weak magnetic field and is suggested to be spun-up by accretion1982).
But it has weak magnetic field and is suggested to be spun-up by accretion.
. ILowever. some rapidly spinning millisecond pulsars are suggested to be born bv accretion induced collapse from white cdwarls1933).
However, some rapidly spinning millisecond pulsars are suggested to be born by accretion induced collapse from white dwarfs.
. Therefore it can not ruled out (hat some pulsars can be born with milliseconds and strong magnetic field.
Therefore it can not ruled out that some pulsars can be born with milliseconds and strong magnetic field.
The theoretical investigation of rotating general relativistic objects performed by shows that for some realistic equations of state of neutron malter (his variation of the central density can be achieved during the complete spin-cown ol the star (see Table I).
The theoretical investigation of rotating general relativistic objects performed by shows that for some realistic equations of state of neutron matter this variation of the central density can be achieved during the complete spin-down of the star (see Table I).
The central densitv increase due to the spin-«down can be easily realized in a short lime interval for a special class of stellar type objects. called magnetars.
The central density increase due to the spin-down can be easily realized in a short time interval for a special class of stellar type objects, called magnetars.
Magnetars are compact objects with super strongmagnetic fields ofthe order Dzs104? Gauss or even hieher 1996).
Magnetars are compact objects with super strongmagnetic fields ofthe order $B\approx 10^{15}$ Gauss or even higher .
..
It
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suggests that our uncertainty estimates are reasonable. and the result is robust.
suggests that our uncertainty estimates are reasonable, and the result is robust.
This experiment. also shows what the cllect might be of a non-member being included in the fit.
This experiment also shows what the effect might be of a non-member being included in the fit.
Were a non-member very far from the fitted: sequence it would have been clipped out by the procedure described at the end of Section 5.4..
Were a non-member very far from the fitted sequence it would have been clipped out by the procedure described at the end of Section \ref{the_fit}.
r Were it close to the sequence. then it could deviate the fit sullicientlv to have a reasonable 77. but then would only change the best fit by a small amount. similar o the elfect of removing a data point.
Were it close to the sequence, then it could deviate the fit sufficiently to have a reasonable $\tau^2$, but then would only change the best fit by a small amount, similar to the effect of removing a data point.
As a final check of the uncertainties. in Figures 4. to we o the data over the best fitting models if the age is κο] at the PAIS age (left) or left as à [ree parameter (right).
As a final check of the uncertainties, in Figures \ref{ngc6530} to \ref{onc} we plot the data over the best fitting models if the age is fixed at the PMS age (left) or left as a free parameter (right).
The first two examples (NGC6530 and A Ori) are ones where he PADS age lies far outside the 68 percent confidence region or the upper-main-sequence age.
The first two examples (NGC6530 and $\lambda$ Ori) are ones where the PMS age lies far outside the 68 percent confidence region for the upper-main-sequence age.
As one expects. we see that he brightest stars lie to the right of the mocdel when the age is fixed at the PAIS age.
As one expects, we see that the brightest stars lie to the right of the model when the age is fixed at the PMS age.
Our final example. the ONC. is one where the PAIS age lies almost exactly on the edge of the 68 »ercent confidence limit.
Our final example, the ONC, is one where the PMS age lies almost exactly on the edge of the 68 percent confidence limit.
Here the improvement in the fit is. as it should be. marginal.
Here the improvement in the fit is, as it should be, marginal.
Although such comparisons with our expectations are at. best subjective. that they fit with our expectations adds to our confidence in the result.
Although such comparisons with our expectations are at best subjective, that they fit with our expectations adds to our confidence in the result.
When combined with the experiment of missing out the brightest datapoint. we have a strong case that our uncertainties are correct. and the result is robust.
When combined with the experiment of missing out the brightest datapoint, we have a strong case that our uncertainties are correct, and the result is robust.
The obvious problems with the mocdels are the absence of rotation. uncertainties as to the mass-Ioss rates. and the treatment of convective core overshoot.
The obvious problems with the models are the absence of rotation, uncertainties as to the mass-loss rates, and the treatment of convective core overshoot.
Figure 9 of 7. shows that if the stars were rotating. and we fitted. then with isochrones for stationary stars. the resulting ages would be too voung by about LO percent.
Figure 9 of \cite{2000A&A...361..101M} shows that if the stars were rotating, and we fitted them with isochrones for stationary stars, the resulting ages would be too young by about 10 percent.
This therefore exacerbates the discrepaney tween the PAIS and AIS ages.
This therefore exacerbates the discrepancy between the PMS and MS ages.
All modern models include a degree of core overshoot. which has the ellect of mixing more hydrogen into the core. and hence lengthening the MS lifetime.
All modern models include a degree of core overshoot, which has the effect of mixing more hydrogen into the core, and hence lengthening the MS lifetime.
Naively. models with no overshoot will have shorter AIS Lifetimes than those used here. bv roughly the decrease in available hydrogen (»erhaps 20-40 percent). which is of the right order to bring the MS and PAIS ages mack into agreement.
Naively, models with no overshoot will have shorter MS lifetimes than those used here, by roughly the decrease in available hydrogen (perhaps 20-40 percent), which is of the right order to bring the MS and PMS ages back into agreement.
However. our CMD fitting does not measure lifetime on the MS. but how far from the ZAAIS a star at à given luminosity (no mass) has moved.
However, our CMD fitting does not measure lifetime on the MS, but how far from the ZAMS a star at a given luminosity (not mass) has moved.
X cose comparison of Figures 4 and 5 of ? shows that for the voungest ages they calculate (254 vr)the dilference in the position of the isochrone corresponds to an age dillerence of around 5 percent.
A close comparison of Figures 4 and 5 of \cite{1981A&A....93..136M} shows that for the youngest ages they calculate (25Myr) the difference in the position of the isochrone corresponds to an age difference of around 5 percent.
1o. 3 as the local angle of tilt of the disk relative to the z-axis aud > marks the position of the deceudiug node of the disk.
i.e., $\beta$ is the local angle of tilt of the disk relative to the $z$ -axis and $\gamma$ marks the position of the decending node of the disk.
We shall also establish a polar coordinate svstem (CR.60) on the surface of the warped disk.
We shall also establish a polar coordinate system $(R,\phi)$ on the surface of the warped disk.
We shall denote as x the position vector of the point ou the disk with coordinates (2.0): the corresponding uuit vector shall be denoted x.
We shall denote as ${\bf x}$ the position vector of the point on the disk with coordinates $(R,\phi)$; the corresponding unit vector shall be denoted $\hat{\bf x}$.
Pringle (1996) eives From equ. (
Pringle (1996) gives From eqn. (
2.13) of Pringle (1996). the rate at which a patch dS of the disk surface intercepts photous from the central primary source (ucelecting possible shadowing) is where 2/2dfdR aud J—db/dR.
2.13) of Pringle (1996), the rate at which a patch ${\bf dS}$ of the disk surface intercepts photons from the central primary source (neglecting possible shadowing) is where $\gamma~^\prime\equiv d\gamma/dR$ and $\beta^\prime\equiv d\beta/dR$.
The augle 05 between the wracdiating flux aud local dixk normal is eiven by Given the irradiating continua photon flux aud the incident angle. we use equs.
The angle $\theta_0$ between the irradiating flux and local disk normal is given by Given the irradiating continuum photon flux and the incident angle, we use eqns.
1-7 of George Fabian (1991) to compute the uuuber of Auorescent wou line photons generated by the patch. NR(FRdo.
4-7 of George Fabian (1991) to compute the number of fluorescent iron line photons generated by the patch, $N_lR\,dR\,d\phi$.
We then apply a scaling factor of 1.3 (Matt et al.
We then apply a scaling factor of 1.3 (Matt et al.
1997) to correct the results of George Fabian (1991) to those expected for Aucders Crevesse (1989) soli abuucauces.
1997) to correct the results of George Fabian (1991) to those expected for Anders Grevesse (1989) solar abundances.
Assuming that these photons are cmitting isotropically fom the optically-thick surface of the disk. the iron line photon emission rate from the patch per unit solid angle towards the observer is cos0NpRdRdofz. where 0 is the anele between the local disk normal and the observers line of sight given by.
Assuming that these photons are emitting isotropically from the optically-thick surface of the disk, the iron line photon emission rate from the patch per unit solid angle towards the observer is $\cos\theta\,N_lR\,dR\,d\phi/\pi$, where $\theta$ is the angle between the local disk normal and the observer's line of sight given by.
The contribution of a given radial yauge e.»&|dr to the observed line cussion is given by aud the total umber of] observed iron. line. pliotous isη -44=UNACCRO)HR
The contribution of a given radial range $r\rightarrow r+dr$ to the observed line emission is given by and the total number of observed iron line photons is ${\cal N}~_{\rm tot}=\int_0^{\infty}{\cal N}(R)\,dR$.
The: observed equivaleut. width. is. derived. by ratioig this against the πινο of contimmun photons emittedli per unit solid anele at the line energy. Finally. to compute a line profile. we need to know the liuc-o£-siglt velocity of a eiven patch of the disk.
The observed equivalent width is derived by ratioing this against the number of continuum photons emitted per unit solid angle at the line energy, Finally, to compute a line profile, we need to know the line-of-sight velocity of a given patch of the disk.
Assuming Iseplerian flow. the velocity of the disk is eiven by
Assuming Keplerian flow, the velocity of the disk is given by
The best choice for an exact measurement of the power spectral slope are wavelets with a high ratio between the diameter of the annulus and the core of the filter.
The best choice for an exact measurement of the power spectral slope are wavelets with a high ratio between the diameter of the annulus and the core of the filter.
Here. the French-hat and the Mexican-hat filter are equally well suited.
Here, the French-hat and the Mexican-hat filter are equally well suited.
For the detection of pronounced size scales the Mexican-hat filter and low diameter ratios are preferred.
For the detection of pronounced size scales the Mexican-hat filter and low diameter ratios are preferred.
A good compromise between the different requirements is the Mexican-hat filter with a diameter ratio of 1.5 always providing a A-variance spectrum with approximately the correct slope and without missing any special spectral feature.
A good compromise between the different requirements is the Mexican-hat filter with a diameter ratio of 1.5 always providing a $\Delta$ -variance spectrum with approximately the correct slope and without missing any special spectral feature.
We provide àn easy-to-use IDL widget program implementing the A-variance analysis as described here implementing the different filters and edge-treatment methods for the analysis of arbitrary maps in FITSformat’.
We provide an easy-to-use IDL widget program implementing the $\Delta$ -variance analysis as described here implementing the different filters and edge-treatment methods for the analysis of arbitrary maps in FITS.
on the optimum filter shape with the weighting function and return to the analysis of data with a varying reliability within the map.
on the optimum filter shape with the weighting function and return to the analysis of data with a varying reliability within the map.
To test how the improved A-variance analysis recovers the properties of an original structure from measurements influenced by a varying noise level. we create maps where white noise with a spatial pattern of different noise amplitudes was added.
To test how the improved $\Delta$ -variance analysis recovers the properties of an original structure from measurements influenced by a varying noise level, we create maps where white noise with a spatial pattern of different noise amplitudes was added.
We use combinations of the different spatial structures discussed in Sect.
We use combinations of the different spatial structures discussed in Sect.
2.2. for the structure to be measured and for the spatial distribution of a noise level superimposed to the data.
\ref{sect_testdata} for the structure to be measured and for the spatial distribution of a noise level superimposed to the data.
Fig.
Fig.
Al shows one example of a resulting A-variance spectrum for an fBm structure with a spectral index Z=3.1 where a noise pattern given by the filled circle deseribed in Sect.
\ref{fig_circlenoise} shows one example of a resulting $\Delta$ -variance spectrum for an fBm structure with a spectral index $\zeta=3.1$ where a noise pattern given by the filled circle described in Sect.
2.2.2 and d=2/3 was added.
\ref{sect_nonperdata} and $d=2/3$ was added.
The average signal-to-noise ratio. defined as the ratio betweer the maximum in the fBm structure and the noise RMS. is | and the variation between the noise levels inside and outside of the circle is a factor 9.
The average signal-to-noise ratio, defined as the ratio between the maximum in the fBm structure and the noise RMS, is 1 and the variation between the noise levels inside and outside of the circle is a factor 9.
This example may represent the situation of an observed map where the inner part is covered by many integrations. so that it shows a high signal-to-noise ratio. whereas the outer part is observed with few integrations leading to a higher noise level.
This example may represent the situation of an observed map where the inner part is covered by many integrations, so that it shows a high signal-to-noise ratio, whereas the outer part is observed with few integrations leading to a higher noise level.
The solid line represents the A-variance spectrum of the original fBm structure.
The solid line represents the $\Delta$ -variance spectrum of the original fBm structure.
The dotted line 1s the spectrum that is obtained by the direct analysis of the noisy map without any reliability weighting.
The dotted line is the spectrum that is obtained by the direct analysis of the noisy map without any reliability weighting.
Because there is no correlation in the noise between neighbouring data points. the added noise contributes to the A-variance spectrum only on small scales with a decay proportional to “7 towards larger lags.
Because there is no correlation in the noise between neighbouring data points, the added noise contributes to the $\Delta$ -variance spectrum only on small scales with a decay proportional to $l^{-2}$ towards larger lags.
Due to the relatively high average noise level. the A-variance spectrum is dominated by the noise contribution up to lags of about 0.2.
Due to the relatively high average noise level, the $\Delta$ -variance spectrum is dominated by the noise contribution up to lags of about 0.2.
The original fBm spectrum is only matched within a very narrow scale range at the largest lags.
The original fBm spectrum is only matched within a very narrow scale range at the largest lags.
The dashed line shows the improvement that is obtained by using the knowledge on the noise level in terms of a weighting function w(r) inversely proportional to the local noise RMS.
The dashed line shows the improvement that is obtained by using the knowledge on the noise level in terms of a weighting function $w(\vec{r})$ inversely proportional to the local noise RMS.
Due to the relative suppression of contributions from the outer noisy parts of the map the original fBm spectrum is recovered over a nuch broader range of scales.
Due to the relative suppression of contributions from the outer noisy parts of the map the original fBm spectrum is recovered over a much broader range of scales.
We find. however. a small distortion at the data point for the largest lag.
We find, however, a small distortion at the data point for the largest lag.
This can be interpreted as the effect of a slight “cross talk” from the weighting function to the measured structure.
This can be interpreted as the effect of a slight “cross talk” from the weighting function to the measured structure.
The obvious strong improvement of the recovery of the original A-variance spectrum from the noisy data is thus achieved at the cost of a slightly reduced data reliability on the characteristic scales of the weighting function.
The obvious strong improvement of the recovery of the original $\Delta$ -variance spectrum from the noisy data is thus achieved at the cost of a slightly reduced data reliability on the characteristic scales of the weighting function.
To study this effect more systematically we perform a number of parameter studies combining the different structures with varying noise patterns. varying noise levels and varying noise dynamic ranges.
To study this effect more systematically we perform a number of parameter studies combining the different structures with varying noise patterns, varying noise levels and varying noise dynamic ranges.
In the resulting A-variance spectra we computed the scale range over which the spectrum agrees with the spectrum of the original structure within range. which allows a reliable derivation of the true scaling behaviour. is a measure for the quality of the structure recovery.
In the resulting $\Delta$ -variance spectra we computed the scale range over which the spectrum agrees with the spectrum of the original structure within range, which allows a reliable derivation of the true scaling behaviour, is a measure for the quality of the structure recovery.
To test the influence of selection effects we repeat each computation for a number of different initialisers for fBm structures and for the noise fields. so that we arrive at 30-80 computations for each parameter set providing a statistically significant sample.
To test the influence of selection effects we repeat each computation for a number of different initialisers for fBm structures and for the noise fields, so that we arrive at 30–80 computations for each parameter set providing a statistically significant sample.
The result of such a parameter scan is demonstrated in Fig. A2..
The result of such a parameter scan is demonstrated in Fig. \ref{fig_chessnoisescan}.
In this example. the original structure is an fBmstructure with €=3.0 and the superimposed noise amplitude follows http://www.phl.uni-koeln.de/”ossk/ftpspace/deltavar/a chess board structure (see Sect. 2.2.1))
In this example, the original structure is an fBmstructure with $\zeta=3.0$ and the superimposed noise amplitude follows a chess board structure (see Sect. \ref{sect_pertestdata}) )
with four fields. i.e.
with four fields, i.e.
portion of the light curve (4,4,~3days) to the Einsteintimescale (£r160days) Ist —αμτι~0.02.
portion of the light curve $t_{\rm anom}\sim 3\ \mbox{days}$ ) to the Einsteintimescale $t_{\rm E}\sim 160\ \mbox{days}$ is $r=t_{\rm anom}/t_{\rm E} \sim 0.02$.
For light curves perturbed by planetary caustics. one typically finds gy~»D1992).
For light curves perturbed by planetary caustics, one typically finds $q\sim r^2$.
. This relation clearly does not apply to the caustics of extreme-separation binaries.
This relation clearly does not apply to the caustics of extreme-separation binaries.
Models with ¢<0.01 (and y:100) are formally rejected at Ay?~32. which is significant but not in itself an overwhelming rejection of the planetary hypothesis.
Models with $q\le 0.01$ (and $q\ge 100$ ) are formally rejected at $\Delta\chi^2\simeq 32$, which is significant but not in itself an overwhelming rejection of the planetary hypothesis.
Hence. we examine the least V model for ¢=0.01 (A4?=:2.3) for its plausibility and the origin of statistical discriminating power.
Hence, we examine the least $\chi^2$ model for $q=0.01$ $\Delta\chi^2=32.3$ ) for its plausibility and the origin of statistical discriminating power.
We discover that the difference of 4? is mostly from the MACHO data between HJD 2151310 and 2151360. approximately 2 months prior to the photometric peak.
We discover that the difference of $\chi^2$ is mostly from the MACHO data between HJD $2451310$ and $2451360$, approximately 2 months prior to the photometric peak.
However. we also find that the "planetary" model exhibits an extremely high peak magnification (las~15000). and consequently. requires the event to be much longer (tg&LO vr) and more extremely blended (7,225.7. ΕνΕμzz024 ) than the already unusually long and highly blended best-fit models.
However, we also find that the “planetary” model exhibits an extremely high peak magnification $A_{\rm max}\sim 15000$ ), and consequently, requires the event to be much longer $t_{\rm E}\simeq 40\ \mbox{yr}$ ) and more extremely blended $I_{\rm s}\simeq 25.7$, $F_{\rm s}/F_{\rm base}\simeq 0.2\%$ ) than the already unusually long and highly blended best-fit models.
In addition. there is a clear trend of increasing peak magnification (and thus timescale and blend as well) as ¢ is lowered beyond 0.01.
In addition, there is a clear trend of increasing peak magnification (and thus timescale and blend as well) as $q$ is lowered beyond $0.01$.
This follows from the fact that the observed timescale of the anomaly in the light curve essentially fixes the source movement relative to the caustic.
This follows from the fact that the observed timescale of the anomaly in the light curve essentially fixes the source movement relative to the caustic.
However. as y becomes smaller. the size of the caustic relative to the Einstein ring shrinks. and therefore. the timescale of the event. that is the time required for the source to cross the Einstein ring. increases. (
However, as $q$ becomes smaller, the size of the caustic relative to the Einstein ring shrinks, and therefore, the timescale of the event, that is the time required for the source to cross the Einstein ring, increases. (
Note that this behavior causes a mild continuous degeneracy between y and the blending.)
Note that this behavior causes a mild continuous degeneracy between $q$ and the blending.)
These parameters determined for the “planetary” model are extremely contrived and highly improbable a priori.
These parameters determined for the “planetary” model are extremely contrived and highly improbable a priori.
Furthermore. the timescale associated with the “planet” component. ,=τς~ Lyris much longer than that of typical stellar lenses. which further reduces the plausibility of the planetary interpretation.
Furthermore, the timescale associated with the “planet” component, $t_{\rm p}=q^{1/2}t_{\rm E}\sim 4\ \mbox{yr}$ is much longer than that of typical stellar lenses, which further reduces the plausibility of the planetary interpretation.
In summary. while in simple statistical terms. the star/planet scenario 1s not overwhelmingly disfavored relative to extreme-separation binaries. we nevertheless can conclude that it is highly unlikely that this event is due to a star/planet system.
In summary, while in simple statistical terms, the star/planet scenario is not overwhelmingly disfavored relative to extreme-separation binaries, we nevertheless can conclude that it is highly unlikely that this event is due to a star/planet system.
From the standpoint of refining microlensing planet detection strategies. it is important to ask how one could have discriminated between the planetary and extreme-separation binary solutions with greater statistical significance.
From the standpoint of refining microlensing planet detection strategies, it is important to ask how one could have discriminated between the planetary and extreme-separation binary solutions with greater statistical significance.
As noted above. most of the discriminating power came from the MACHO data points on the rising wing of the light curve. even though (or in asense. because) these had the largest errors and the lowest density of the non-baseline coverage.
As noted above, most of the discriminating power came from the MACHO data points on the rising wing of the light curve, even though (or in a sense, because) these had the largest errors and the lowest density of the non-baseline coverage.
That is. the precision PLANET photometry over the peak and falling wing "predicts" the rising wing for each of the models. but the noisier MACHO data can only roughly discriminate between these predictions.
That is, the precision PLANET photometry over the peak and falling wing “predicts” the rising wing for each of the models, but the noisier MACHO data can only roughly discriminate between these predictions.
Hence. the key would have been to get better data on the rising part of the light curve.
Hence, the key would have been to get better data on the rising part of the light curve.
In practice this is difficult: the MACHO data are noisier exactly because they are survey data. and one does not know to monitor an event intensively until the light curve has actually started to rise.
In practice this is difficult: the MACHO data are noisier exactly because they are survey data, and one does not know to monitor an event intensively until the light curve has actually started to rise.
The long duration of the event. £r.=160days (close binary) or fez220days (wide binary). may lead one to expect that the event would show some sign of parallax effects).
The long duration of the event, $t_{\rm E}\simeq 160\ \mbox{days}$ (close binary) or $t_{\rm E}\simeq 220\ \mbox{days}$ (wide binary), may lead one to expect that the event would show some sign of parallax effects.