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Consequently. we shall ucelect the disk geometrical height in iu our analyze here and assume that the disk wiud originates from the equatorial plane. | Consequently, we shall neglect the disk geometrical height in in our analyze here and assume that the disk wind originates from the equatorial plane. |
The outflow from the optically thick. disk iradiated by the central star can be understood within the framework of the wind driven by external irraciation (Cavleyetal. 1999). | The outflow from the optically thick disk irradiated by the central star can be understood within the framework of the wind driven by external irradiation \citep{abla}. |
. We study the disk outflow iu nonimertial frame corotating with the disk. | We study the disk outflow in noninertial frame corotating with the disk. |
We use the Cartesian coordinates with : axis perpendicular to the disk (see Fig. A1)). | We use the Cartesian coordinates with $z$ axis perpendicular to the disk (see Fig. \ref{coord}) ). |
The disk wind originates iu the disk plane 2=0. | The disk wind originates in the disk plane $z=0$. |
We assume purely vertical flow with velocity e.tτ} and we ucelect a potentially inportaut part of the radiative force due to the Ieplerian velocity eracicnt (Gavleyetal.2001). | We assume purely vertical flow with velocity $v_z(z)$ and we neglect a potentially important part of the radiative force due to the Keplerian velocity gradient \citep{diskra}. |
. The stationary contiuuitv equation takes within our assuniptious the form of where fis the disk wind mass-loss rate per unit of disk surface. | The stationary continuity equation takes within our assumptions the form of where $\dot m$ is the disk wind mass-loss rate per unit of disk surface. |
The radiative. force of the ensemble of lines in the Sobolev approximation is then (Rybicki&που1975.Crammer&Owocki1995.Carley1995) where (Q and a are line force parameters. | The radiative force of the ensemble of lines in the Sobolev approximation is then \citep{rybashumrem,nerad,gayley}
where $\bar Q$ and $\alpha$ are line force parameters. |
οποιο the incomine beam. and simply assumingall the locally normal incident raciation from oue hemisphere is directly reflected upward in vertical beam normal to the disk. the | Ignoring the incoming beam, and simply assumingall the locally normal incident radiation from one hemisphere is directly reflected upward in vertical beam normal to the disk, the |
Prior to the eclipse. there is a marked decrease in soft X-rav photons over the phase range ó~0.7 1.0. compared to those at higher energies. | Prior to the eclipse, there is a marked decrease in soft X-ray photons over the phase range $\phi\sim$ 0.7–1.0, compared to those at higher energies. |
This phenomenon has been seen in other polars (eg Watson ct al 1989). ancl occurs when the aceretion stream obscures our view of the hot accretion region located in the upper hemisphere on the white dwarf. | This phenomenon has been seen in other polars (eg Watson et al 1989) and occurs when the accretion stream obscures our view of the hot accretion region located in the upper hemisphere on the white dwarf. |
Compared to V2301 Oph (for instance. Ramsay Cropper 2007). the ‘pre-eclipse’ dip seen in is more extended. suggesting that material gets lifted out. of the orbital plane over a wider range in azimuth. | Compared to V2301 Oph (for instance, Ramsay Cropper 2007), the `pre-eclipse' dip seen in is more extended suggesting that material gets lifted out of the orbital plane over a wider range in azimuth. |
At softer energies (κ κο) there is also a clip in the light curve centered at ó 70.4 and with a duration of ~0.1 eveles. | At softer energies $<$ 1keV) there is also a dip in the light curve centered at $\phi\sim$ 0.4 and with a duration of $\sim$ 0.1--0.2 cycles. |
At higher energies. there is no obvious broad. dip at these orbital phases although there are a couple of bins between O=0.40.5 which are consistent with zero counts. | At higher energies, there is no obvious broad dip at these orbital phases although there are a couple of bins between $\phi$ =0.4–0.5 which are consistent with zero counts. |
However. since other bins with negligible flux are also seen at dillerent. phases this may just. be due to low counting statistics. | However, since other bins with negligible flux are also seen at different phases this may just be due to low counting statistics. |
This dip could either be due to a second dip caused by an accretion stream or it could be due to the rotation of the accretion regions rotating into ancl out of view as the white dwarl rotates. | This dip could either be due to a second dip caused by an accretion stream or it could be due to the rotation of the accretion regions rotating into and out of view as the white dwarf rotates. |
We will ciscuss this further in | We will discuss this further in \ref{discussion}. |
We extracted: spectra from cach EPIC detector in. the manner described in §2.. | We extracted spectra from each EPIC detector in the manner described in \ref{obs}. |
Initially we extracted spectra using all the available data. | Initially we extracted spectra using all the available data. |
However. since the light curves (c£ ligure 1)) imply the presence of a pre-eclipse dip. we then extracted spectra from the phase interval which was not strongly allected by absorption. ie ὁ ~0.050.7. | However, since the light curves (cf Figure \ref{light}) ) imply the presence of a pre-eclipse dip, we then extracted spectra from the phase interval which was not strongly affected by absorption, ie $\phi\sim$ 0.05–0.7. |
We also exclude the phase interval ó-0.380.5 which could. also be alfected by absorption (83). | We also exclude the phase interval $\phi$ =0.38–0.5 which could also be affected by absorption 3). |
In polars. X-rays are generated in a post-shock region at some height above the photosphere of the white dwarf. | In polars, X-rays are generated in a post-shock region at some height above the photosphere of the white dwarf. |
Since the X-ray. spectrum of has a relatively low signal to noise compared to many polars previously studied using (eg Ramsay Cropper 2004). we used a simple single temperature thermal bremsstrahlung emission model rather than a more complex. (and. more ohvsical) stratified cooling Low model. (eg Cropper ct al 1998. 1999). | Since the X-ray spectrum of has a relatively low signal to noise compared to many polars previously studied using (eg Ramsay Cropper 2004), we used a simple single temperature thermal bremsstrahlung emission model rather than a more complex (and more physical) stratified cooling flow model (eg Cropper et al 1998, 1999). |
We used the package (Arnaud 1996) to fi he XNX-rav spectra. | We used the package (Arnaud 1996) to fit the X-ray spectra. |
We fitted all three EPIC spectra simultaneously and tied. the spectral parameters apar rom the normalisation parameters. | We fitted all three EPIC spectra simultaneously and tied the spectral parameters apart from the normalisation parameters. |
We used the absorption model (the TübbingenBoulder absorption LSA model. Wilms. Allen AleCray 2000). a single temperature hermal bremsstrahlung component with temperature fixed at AT= 20keV. We added a Ciaussian component to accoun or any emission. between GA6.8keV. The spectra along with the best fit 12) are shown in Figure 3.. | We used the absorption model (the Tübbingen–Boulder absorption ISM model, Wilms, Allen McCray 2000), a single temperature thermal bremsstrahlung component with temperature fixed at $kT=20$ keV. We added a Gaussian component to account for any emission between 6.4–6.8keV. The spectra along with the best fit 1.12) are shown in Figure \ref{xray-spec}. . |
We show the spectral parameters. the observed and unabsorbed xometric fluxes in Table 1.. | We show the spectral parameters, the observed and unabsorbed bolometric fluxes in Table \ref{fits}. |
Due to the low signal to noise of the spectra. the equivalent. width of the Fe Ike emission ine features was poorly constrained. | Due to the low signal to noise of the spectra, the equivalent width of the Fe $\alpha$ emission line features was poorly constrained. |
In many polars. a strong soft’ N-ray component (Alin ~400V) is seen in their N-rav. spectra. (ce Ramsay et al 1994. Deuermann Jurwitz 1995). | In many polars, a strong soft X-ray component $kT_{bb}\sim$ 40eV) is seen in their X-ray spectra (eg Ramsay et al 1994, Beuermann Burwitz 1995). |
his is due to the hard. X-rays irradiating the photosphere of the white cwarl which are then re-emittec as soft. N-ravs. | This is due to the hard X-rays irradiating the photosphere of the white dwarf which are then re-emitted as soft X-rays. |
The standard: accretion model predicts that Loopflare00.5. where Loop) and Lys are the luminosities of the soft. and. hard X-ray components respectively (Lamb Masters. 1979. Wing Lasota 1979). | The standard accretion model predicts that $L_{soft}/L_{hard}\sim$ 0.5, where $L_{soft}$ and $L_{hard}$ are the luminosities of the soft and hard X-ray components respectively (Lamb Masters 1979, King Lasota 1979). |
Although the energy balance in polars was a source of great debate for many vears. Ramsay Cropper (200.) showed that the majority of polars in a high accretion state have X-ray spectra which are in good agreement with the standard. model. | Although the energy balance in polars was a source of great debate for many years, Ramsay Cropper (2004) showed that the majority of polars in a high accretion state have X-ray spectra which are in good agreement with the standard model. |
‘To see if such a soft X-ray component could be hidden bv the moderate. level of absorption (c£. Table 1)) we added a blackbody with a range of dillerent. temperatures. | To see if such a soft X-ray component could be `hidden' by the moderate level of absorption (cf Table \ref{fits}) ) we added a blackbody with a range of different temperatures. |
We fixed its normalisation so that the implied. ratio. LoiLoa~O0.5. | We fixed its normalisation so that the implied ratio, $L_{soft}/L_{hard}\sim$ 0.5. |
Since the soft. N-ravs are optically thick. and hence the intrinsic soft X-ray luminosity is viewing angle dependant. we assumed a viewing anele of 45° for argument. | Since the soft X-rays are optically thick, and hence the intrinsic soft X-ray luminosity is viewing angle dependant, we assumed a viewing angle of $^{\circ}$ for argument. |
Η we just consider the X-ray data. we find a blackbods with temperature less than &720eV can easily be hidden. | If we just consider the X-ray data, we find a blackbody with temperature less than $kT$ 20eV can easily be hidden. |
We were fortunate in. being able to obtain a short observation of the field of using on the 3rd and 4th Dee 2008. | We were fortunate in being able to obtain a short observation of the field of using on the 3rd and 4th Dec 2008. |
Observations using the UV Optical Telescope (Roming et al 2005) were made using the UVW?2 filter (peak ellective wavelength 2120)). | Observations using the UV Optical Telescope (Roming et al 2005) were made using the UVW2 filter (peak effective wavelength ). |
was not detected. anc we estimated. a 30 upper limit of ~24105! FA4. | was not detected, and we estimated a $\sigma$ upper limit of $\sim2.4\times10^{-17}$ $^{-1}$. |
ME we assume a blackbocly of dillerent. temperatures and with a normalisation such that Loopflares ~O-5. we Lined that a rlackbody of kL ~520cV can be present anc not detected in the near UV. or soft. X-ray energy. ranges. ( | If we assume a blackbody of different temperatures and with a normalisation such that $L_{soft}/L_{hard}\sim$ 0.5, we find that a blackbody of $kT\sim$ 5–20eV can be present and not detected in the near UV or soft X-ray energy ranges. ( |
Although a handful of X-ray events were detected near the source yosition Of5731. they were too low to derive any meaningful information). | Although a handful of X-ray events were detected near the source position of, they were too low to derive any meaningful information). |
The unabsorbed bolometric Dux implies an X-ray uminosity. ofB ~δι10720diay» erg/s. where d,» is. the distance. in units of LOO pe. | The unabsorbed bolometric flux implies an X-ray luminosity of $\sim8\times10^{29} d_{100}^{2}$ erg/s, where $d_{100}^{2}$ is the distance in units of 100 pc. |
Ramsay Cropper (2004) found. that he mean bolometric luminosity in their sample of polars observed in a high state using was ~2.107 orefs. In the next section we find that shows a range in optical brightness over the longer term and of polars). | Ramsay Cropper (2004) found that the mean bolometric luminosity in their sample of polars observed in a high state using was $\sim2\times10^{32}$ erg/s. In the next section we find that shows a range in optical brightness over the longer term and therefore a range of accretion states (a general characteristic of polars). |
Assuming that in à high accretion state at the epoch of the observations we find that in order that has an X-rav luminosity consistent with other polars in a high state it must [ie at a distance of ~1.52.0 kpc. | Assuming that was observed in a high accretion state at the epoch of the observations we find that in order that has an X-ray luminosity consistent with other polars in a high state it must lie at a distance of $\sim$ 1.5–2.0 kpc. |
With Galactic co-ordinates of/=107.2" and b=—L6. this places close to the Perseus spiral arm (Xu et al 2005). | With Galactic co-ordinates of $l=107.2^{\circ}$ and $b=-1.6^{\circ}$, this places close to the Perseus spiral arm (Xu et al 2005). |
'To locate the optical counterpart of we obtained optical photometry using ALEOSC on the Nordic Optical Telescope (NOT) located on La Palma during 28th Sept 2008. | To locate the optical counterpart of we obtained optical photometry using ALFOSC on the Nordic Optical Telescope (NOT) located on La Palma during 28th Sept 2008. |
Each exposure was in white light, and 15 sec in length. with another 5 sec of readout time.resulting in 2.9 h of data in total. | Each exposure was in `white light' and 15 sec in length, with another 5 sec of readout time,resulting in 2.9 h of data in total. |
Each source in the field (Figure 4)) was searched. for variability. | Each source in the field (Figure \ref{finding}) ) was searched for variability. |
One source showed a clear eclipse lasting for 12 mins and a depth 3.5 mag (Figure 1)). | One source showed a clear eclipse lasting for $\sim$ 12 mins and a depth 3.5 mag (Figure \ref{light}) ). |
This is the opticalcounterpart to and. its | This is the opticalcounterpart to and its |
steepened at brighter magnitudes: Ale16.5 comparec with Ag13.5 (Mp 15) for the Phillipps e al. ( | steepened at brighter magnitudes: $M_B = -16.5$ compared with $M_B = -13.5$ $M_R = -15$ ) for the Phillipps et al. ( |
19982) inner area LE. | 1998a) inner area LF. |
This discrepancy can be explainec if the Phillipps ct al. ( | This discrepancy can be explained if the Phillipps et al. ( |
1998a). sample sullers from. severe background.> contamination at the faint end. | 1998a) sample suffers from severe background contamination at the faint end. |
Alternaively it could. means that our samp cis incomplete (it. woul need to be incomplete at. about the level) a the faint end relative to the Phillipps et al. ( | Alternatively it could means that our sample is incomplete (it would need to be incomplete at about the level) at the faint end relative to the Phillipps et al. ( |
998a) sample. | 1998a) sample. |
Such incompleteness could follow from us (and Sandage e al. | Such incompleteness could follow from us (and Sandage et al. |
1985) erroneously rejecting the higher surace-brightness cluster members from. our sample because we think tha hey are background galaxies. | 1985) erroneously rejecting the higher surface-brightness cluster members from our sample because we think that they are background galaxies. |
We will return o this point in Section 7. | We will return to this point in Section 7. |
Finally. we note that the final twe» points in Phillipps et al. ( | Finally, we note that the final two points in the Phillipps et al. ( |
1998a) LE may have been OVerestLALec ov a [actor of two. meaning that a [aii11οhie 4ope of a1.0 may be appropriate for that dataset. not à022 (S. Phillipps. private communication). | 1998a) LF may have been overestimated by a factor of two, meaning that a faint-end slope of $\alpha \sim -1.9$ may be appropriate for that dataset, not $\alpha \sim -2.2$ (S. Phillipps, private communication). |
Tus would make inconsistency with the current dataset smaleL. | This would make the inconsistency with the current dataset smaller. |
‘Table 3 also gives à. the logariinc slope of the uninosity function. at. each absolu =naenitucle. | Table 3 also gives $\alpha$, the logarithmic slope of the luminosity function, at each absolute magnitude. |
The curvature in the LF is real ancl statisicalv significant: a single vaue of a. independent: of abscLute| magnitude. is uehly inconsistent with the data. Neiher a power-law or a Schecher (1976) function. provides : LSetislactory [it to he data over any appreciable magnittide range. | The curvature in the LF is real and statistically significant: a single value of $\alpha$, independent of absolute magnitude, is highly inconsistent with the data, Neither a power-law or a Schechter (1976) function provides a satisfactory fit to the data over any appreciable magnitude range. |
That we are able to make such a statement folOWS rom the small (Poisson) error bars in Table 3. which in turn follows [rom he large number of galaxies in our sanxe. | That we are able to make such a statement follows from the small (Poisson) error bars in Table 3, which in turn follows from the large number of galaxies in our sample. |
1 (is interesting. lOWOCVOLD. hat the average value of à fainter twan Alp=15 is α—35. close to the Eünt-end. slope 1wt Sandage et al. ( | It is interesting, however, that the average value of $\alpha$ fainter than $M_B = -18$ is $\alpha = -1.35$, close to the faint-end slope that Sandage et al. ( |
1985) [oun for the VCC. | 1985) found for the VCC. |
Over the magnitude range lv<Alp14 the average slope is more like a=L7. similar to the slope in the Phillipps οἱ al. ( | Over the magnitude range $-17 < M_B < -14$ the average slope is more like $\alpha = -1.7$, similar to the slope in the Phillipps et al. ( |
1998a) sample over this magniude range. allowing for a 4I? colour of 1.5. | 1998a) sample over this magnitude range, allowing for a $B-R$ colour of 1.5. |
Over the hall-magnitude interval 1l«Alpc 10.5. only have 29 galaxies classified 01112. implving that the logarithm of the LE at Mg10.75 is 0.37£0.08 mag 7. | Over the half-magnitude interval $-11 < M_B < -10.5$ , only have 29 galaxies classified 0+1+2, implying that the logarithm of the LF at $M_B = -10.75$ is $0.37 \pm 0.08$ $^{-1}$ $^{-2}$. |
This could be a sign of a weak turnover in the LE. but there are other ways to explain the paucity of galaxies in us interval. | This could be a sign of a weak turnover in the LF, but there are other ways to explain the paucity of galaxies in this interval. |
For example. the sample could be incomplete at rese faint levels (only: a modest amount of incompleteness would be required to generate this kind of feature in the LE. | For example, the sample could be incomplete at these faint levels (only a modest amount of incompleteness would be required to generate this kind of feature in the LF. |
This kind of incompleteness could. follow from the reduced vnamic range in surface brightness over which we classify 5lealaxies 1 or 2 at these [faint levels (Lrentham Tully 001). | This kind of incompleteness could follow from the reduced dynamic range in surface brightness over which we classify galaxies 1 or 2 at these faint levels (Trentham Tully 2001). |
Galaxies with surface-brignesses a little. brighter iui about 27 D mag 7 will be missing from the sample because they are indistinguishable from field galaxies of the tvpe seen in large number in our blank fields. | Galaxies with surface-brightnesses a little brighter than about 27 $B$ mag $^{-2}$ will be missing from the sample because they are indistinguishable from field galaxies of the type seen in large number in our blank fields. |
Cialaxies with surface-brightnesses a little fainter than about 27 Db mag aresec7 will also be missing from the sample because they are not detected above the sky. | Galaxies with surface-brightnesses a little fainter than about 27 $B$ mag $^{-2}$ will also be missing from the sample because they are not detected above the sky. |
Consequently at these very faint levels our sample may be incomplete. | Consequently at these very faint levels our sample may be incomplete. |
The contribution to the total galaxy LE. from galaxies. of different morphological tvpes is presented in Figure 6. | The contribution to the total galaxy LF from galaxies of different morphological types is presented in Figure 6. |
At the faint end. the vast majority of galaxies in he sample are dl galaxies. as identified on morphological erounds. | At the faint end, the vast majority of galaxies in the sample are dE galaxies, as identified on morphological grounds. |
The structural parameters (see. Figure 7) and colours (see Figure SN) of the galaxies are consistent with his interpretation. | The structural parameters (see Figure 7) and colours (see Figure 8) of the galaxies are consistent with this interpretation. |
Many of these dl galaxies are nucleated. rut few: ofthe dlrr galaxies in the cluster are. | Many of these dE galaxies are nucleated, but few of the dIrr galaxies in the cluster are. |
This suggests either that the two kinds of galaxies orm in dillerent ways (despite the similarity in their scaling laws) or that cIs are des in ormation ancl that the nucleus is the last part o form. | This suggests either that the two kinds of galaxies form in different ways (despite the similarity in their scaling laws) or that dIs are dEs in formation and that the nucleus is the last part to form. |
In the faintest three bins about one-third. of t galaxies are rated 2. | In the faintest three bins about one-third of the galaxies are rated 2. |
‘These tended. το be high. surface-»rightnesses cles that could conceivalv be background late-vpe galaxies. | These tended to be high surface-brightnesses dEs that could conceivably be background late-type galaxies. |
Even excluding these galaxies. eds are still t dominant types at the faintest magnitudes. | Even excluding these galaxies, dEs are still the dominant types at the faintest magnitudes. |
The VLSD ogalaxiesnever contribute significantly> to t otal luminosity function. | The VLSB galaxiesnever contribute significantly to the total luminosity function. |
This result. cannot be clirectly | This result cannot be directly |
in such a wav that thev are scalable with each other. | in such a way that they are scalable with each other. |
However there is one more additional parameter M.. which is used to fix these units. | However there is one more additional parameter $M_s$, which is used to fix these units. |
I. Larsou’s relation between the sizes ancl velocily dispersions of clouds (Larson 1981) holds for our model cloud. then the Mach nunmber. which is (he velocity dispersion of our model cloud. can determine its corresponding size. | If Larson's relation between the sizes and velocity dispersions of clouds (Larson 1981) holds for our model cloud, then the Mach number, which is the velocity dispersion of our model cloud, can determine its corresponding size. |
In fact. a Larson-tvpe relation of the form M,=5(L/Ipc)2. if we take 0.5 as the power index (lor example. Myers 1983). is used. | In fact, a Larson-type relation of the form $M_s=5(L/1 {\rm pc})^{1/2}$, if we take 0.5 as the power index (for example, Myers 1983), is used. |
Then density. and magnetic field strength could be determined from relations. n=500(J/(L/1pc))? . and B=0.205(0/3)? µ (see also equation (7) aud equation (8) in Vázzquez-Semadeni οἱ al. | Then density and magnetic field strength could be determined from relations, $n = 500(J/(L/1 {\rm pc}))^2$ $^{-3}$, and $B=0.205(n/\beta)^{1/2}$ $\mu$ G (see also equation (7) and equation (8) in Vázzquez-Semadeni et al. |
2005). | 2005). |
So if we choose 9=0.1. J—4. and Af,=10. the size of our computational box. the initial number density. and the initial magnetic field strength. become 4 pe. 500 oE. and 14.5 μα, respectively. | So if we choose $\beta=0.1$, $J=4$, and $M_s=10$, the size of our computational box, the initial number density, and the initial magnetic field strength become 4 pc, 500 $^{-3}$, and 14.5 $\mu$ G, respectively. |
Our dvnamical model has a few limitations such as turning on sel[-gravitv alter generating a [ully saturated turbulent flow. driving turbulent flows by adding velocity fields generated in the Fourier space. not taking into account ambipolar diffusion. ancl assuming the isothermal condition. | Our dynamical model has a few limitations such as turning on self-gravity after generating a fully saturated turbulent flow, driving turbulent flows by adding velocity fields generated in the Fourier space, not taking into account ambipolar diffusion, and assuming the isothermal condition. |
However. they are common in numerical models of a turbulent molecular cloud (see. [ον example. lessen et al. | However, they are common in numerical models of a turbulent molecular cloud (see, for example, Klessen et al. |
2000: Ostriker et al. | 2000; Ostriker et al. |
2001: Li et al. | 2001; Li et al. |
2004: Vazequez-Senmadeni et al. | 2004; Vazquez-Semadeni et al. |
2005). | 2005). |
Due to the limited space. we only mention (he effects of the latter (wo limitations on our results. | Due to the limited space, we only mention the effects of the latter two limitations on our results. |
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