The stellar disk thickness of LSB galaxies

a r X i v :a s t r o -p h /0406498v 1 23 J u n 2004

The stellar disk thickness of LSB galaxies

https://www.sodocs.net/doc/6a13123252.html,yaev 1,2,3dmbiz@sai.msu.ru

and

S.Kajsin 4skai@sao.ru ABSTRACT

We present surface photometry results for a sample of eleven edge-on galaxies observed with the 6m telescope at the Special Astrophysical Observatory (Rus-sia).The photometric scale length,scale height,and central surface brightness of the stellar disks of our sample galaxies are estimated.We show that four galax-ies in our sample,which are visually referred as objects of the lowest surface brightness class in the Revised Flat Galaxies Catalog,have bona ?de low surface brightness (LSB)disks.We ?nd from the comparison of photometric scales that the stellar disks of LSB galaxies are thinner than those of high surface brightness (HSB)ones.There is a clear correlation between the central surface brightness of the stellar disk and its vertical to radial scale ratio.The masses of spherical subsystems (dark halo +bulge)and the dark halo masses are obtained for the sample galaxies based on the thickness of their stellar disks.The LSB galaxies tend to harbor more massive spherical subsystems than the HSB objects,whereas no systematic di?erence in the dark halo masses between LSB and HSB galaxies is found.At the same time,the inferred mass-to-luminosity ratio for the LSB disks appears to be systematically higher than for HSB disks.

Subject headings:galaxies:spiral —galaxies:structure —dark matter

1.Introduction

Low surface brightness spiral galaxies(hereafter,LSB galaxies)have been studied exten-sively in recent years.Their main distinctive feature from”regular”,high surface brightness (HSB)galaxies,is roughly a two magnitude lower central surface brightness of their stellar disks.They are thought to harbor massive dark halos(de Blok et al.2003).The LSB rota-tion curves are shallower in their central parts(McGaugh et al.2001),which points toward a large dark matter fraction.

By observing the thickness of the stellar disk in a galaxy,one can constrain the relative mass of the dark halo(Zasov et al.1991).Until recently,only few edge-on LSB galaxies have been explored in detail(e.g.UGC7321Matthews(2000)and IC5249van der Kruit et al. (2001)).

We conducted a study of a small uniform sample of LSB and HSB galaxies observed with the same instrument to compare their structural parameters.Here we present the results of photometric observations in the V and R bands of a sample of eleven edge-on galaxies.The paper is structured as follows:in section2we describe the sample of galaxies and observations.In section3we discuss the data reduction and present the structural parameters of our galaxies.In section4we use the inferred disk thickness to estimate the dark halo mass.Section5contains a discussion of selection e?ects and relations between the inferred parameters.The main results are summarized in section6.

2.Sample of galaxies and observations

Our sample is based on the Revised Catalog of Flat Galaxies(Karachentsev et al. (1999),RFGC hereafter).All galaxies included in this catalog are highly inclined objects. We select object from the faintest surface brightness(SB)class(IV according to RFGC)as candidates to LSB galaxies,and objects from intermediate or high surface brightness classes as reference HSB objects.We narrowed the sample of objects to galaxies large enough for srtuctural studies(major axis size>2′in RFGC)which?t inside the3.5′?eld-of-view of our CCD imager.In three observing nights of our program we obtained data for11galaxies.

Photometric observations were performed with the prime focus camera on the6-m telescope at the Special Astrophysical Observatory of the Russian Academy of Sciences. This setup provides a plate scale of0.2arcsec/pixel and good sensitivity for faint regions of galaxies.The data were taken on April27,28,and30,2000in the Johnson-Cousins V and R photometric bands.The V-band images were utilized mostly for calibration purposes, while the R images were used for the measurements of structural parameters.For most of the galaxies in our sample we made two to four images shifted by a few pixels in both photometric bands.

The Landolt photometric standards(Landolt1992)were observed every night.Table1 summarizes our observations listing object names,surface brightness class(according to RFGC),date of the observation,total integration time in every photometric band,number of exposures,and average seeing when the target was observed.

3.Data reduction and results

The data were reduced using standard tools in the MIDAS package.The images of galaxies and photometric standards were corrected for the bias and dark current,and?at ?elded.The images were then sky subtracted,aligned,and combined.We checked the quality of?at?elding and sky subtraction by comparing the background level in those parts of the image that are free of foreground stars and are located close to a sample galaxy.The large-scale pattern of the background does not introduce uncertainties above0.1%.Three galaxies have very bright stars in their?elds,which raises the large-scale background?uctuations up to0.2%.

Eight and twelve Landolt’s stars from three selected areas were available on April27 and30,respectively.The residuals for photometric solutions were0.m02for April27(in both V and R bands),and0.m04(in both V and R bands)for the night on April30.The sky brightness level is tabulated in Table1.The surface brightness corresponding to a3σlevel of the background noise in the?nal combined images is shown in Table1as well.

The observing conditions were non-photometric during part of the night on April28. However,most of our galaxies have the major axes photometric pro?les in the R band published by Karachentsev et al.(1992).It enables us to verify the calibration and to adjust it for the non-photometric night.The mean di?erence between the surface brightnesses we derived and those published by Karachentsev et al.(1992)is of the order of0.m3.The largest source of the discrepance comes from the use of di?erent procedures of the major axis pro?les extraction.

Comparison of the sky brightness in R images can be used to estimate roughly the zero point of calibration for the objects taken on April28.If we use this way of calibration,the R-band surface brightnesses of UGC9138and UGC9556would be0m.4lower than those used in the present paper.

The combined and calibrated images were utilized to obtain the radial scale length h, vertical scale height z0,and”face-on”central surface brightness of the stellar disk,as well as bulge-to-disk luminosity ratio L b/L d.

The images were rotated to align the galactic plane parallel to the horizontal axis. Choosing the rotation angle,we point our attention at the intermediate regions of galactic disks where a possible bulge does not reveal itself and the signal-to-noise ratio(S/N hereafter) is high enough.

We applied a standard method(van der Kruit&Searle1981)to derive the structural parameters extracting photometric pro?les parallel to the major and minor galactic axes. The radial scale length was obtained from two photometric pro?les extracted parallel to the major axis and displaced with respect to the galactic midplane.This allows us to minimize the e?ects of dust absorption,because we avoid the galactic midplane.An average displacement is of the order0.7z0(see below).If the bulge was present,the central part of radial photometric pro?les(typically,1h from the center)is excluded from further analysis. We?t the function f(r)=2I0sech2(z/z0) R max0exp(?l/h)r dl to the radial pro?les and ?nd mean values of I0and h.Here,r is the distance to the center,and R max is the distance to the edge of disk.One can assume that R max=4h according to Pohlen et al.(2002); Holley-Bockelmann&Mihos(2001).The integration was made along the line of sight l. Two radial pro?les utilized for the?tting are shown in the middle panels of Fig.1–14by the solid lines.Note that each a pro?le was manually cleaned from foreground stars before the

?tting.The radial pro?le drawn through the galactic plane is shown in the middle panels of Fig.1–14by the dashed line.

As a next step,we draw10to14cuts made parallel to the minor axis of a galaxy and?t each photometric pro?le with the function f(z)=I sech2(|z+dz|/z0).Here|z| designates the distance to the galactic plane.The”displacement term”dz enables us to correct the values of the disk scale height for a possible disorientation of major axis or disk warp.The resulting value of the scale height z0and its error were found by averaging the values throughout the disk.Our galaxies show no signi?cant variations of the scale height with radius.Hence,we de?ned the mean scale height with no weights.

Fitting the pro?les,we convolved the functions f(z)with the gaussian smearing function assuming its FWHM from Table1.The corresponding vertical pro?les are shown in the upper frames of Fig.1–11.They were manually cleaned of the foreground stars and artifacts before the?tting.

The value of the disk central surface brightnessμ0corrected to the face-on inclina-tion was calculated with the parameters I0and z0inferred above taking into account the photometric calibration equations.The extinction of our Galaxy(according to the LEDA database)is also included into the analysis and listed in Table2.

In order to check how examining only a limited number of brightness pro?les(two radial and10-14vertical)a?ects the inferred values,we derive the same values for each a galaxy by extracting the radial pro?les(drawn along the major axis)with the increment of one pixel from0.2z max to0.8z max in the vertical direction,where z max is the minor axis of an ellipse encompassing the galaxy by the level of S/N=3.The vertical pro?les in this analysis were drawn with one-pixel increment taking a step o?the disk edge and its center.The resulting structural parameters are similar to those obtained above using only a few photometric pro?les.All conclusions of the paper remain unchanged in this case.

As was shown by de Grijs et al.(1997),we can neglect inclination corrections for in-clinations larger than86-87degrees.Our V images are deep enough to see obscuration by dust in most of our galaxies.Although dust is not seen in the galaxy FGC1273,its bulge has a high degree of symmetry.Because its edge-on disk is very thin,we assume that its inclination angle is90?.For all other galaxies we can estimate the inclination angle of the galactic plane from the shape and positions of their dust layers and asymmetric position of center of brightness respective to external isophotes.The value of the inclination is shown in Table3,its typical error is0.7?.Based on those values,we applied no additional correction for non edge-on inclination to the photometric parameters derived above.

Assuming the inferred disk parameters,we subtracted the disk and extracted the bulge images from the central parts of our galaxies.Then,the central parts of two radial pro-?les mentioned above,as well as the vertical pro?les extracted along the minor axis,were utilized to estimate the bulge parameters.The King’s pro?leρ0L(1+(r/a k b)2)?3/2,as well as the exponential oneρ0L exp(?r/a e b),were used to?t the bulge volume luminosity density distribution.Here,ρ0L denotes the central volume luminosity density.The bulge scales a k b and a e b could be di?erent in the vertical and radial directions(i.e.for oblate bulges).The inner part of the vertical pro?les were excluded from the analysis.

Bulges of most galaxies in our sample are best?tted by the King’s pro?le.The only exception is UGC9556,the bulge of which is best?tted by the exponential pro?le.Because the central part of the latter galaxy is oblate,we suggest that that it probably has two

disks:an HSB disk is encompassed by more extended LSB one.We consider its LSB disk throughout the paper.According to RFGC,UGC9556may have a lens in its central part. On the other hand,its type was de?ned as a galaxy with a bar(SB?c)in the UGC catalog (Nilson1973).More over,UGC9556has an asymmetry of bright isophotes close to the galactic plane,which points toward a possible bar shielded by dust whose nerby side is seen. Indeed,photometric identi?cation of bars in edge-on galaxies can rarely be conclusive.

With the help of the obtained parameters we infer the bulge-to-disk luminosity ratio L b/L d.The main results of the?tting are shown in Table3.The values of h and z0 are converted to the spatial units according to the adopted distances to the galaxies D. Table3also shows R-magnitudes and colors(V-R)derived for our objects.The magnitudes were obtained by integrating background-subtracted images of the galaxies within elliptical diaphragms.Major and minor axes of the diaphragms correspond to the sizes from the RFGC cataloge,which are quite similar to the galaxies’dimensions at S/N=3level.

The distribution ofμ0(see Table3)indicates the presence of two subsamples:that with μ0greater than23.5mag/arcsec2,which we de?ne as LSB galaxies,and that with a higher surface brightness,which is designated as HSB galaxies in this paper.Hence,our sample consists of four LSB and seven HSB galaxies.Note that all galaxies in the faintest RFGC surface brightness class were classi?ed here as LSB objects.

Although our sample of objects enables to compare the structural parameters of LSB and HSB disks,the sample is very limited.We incorporated one more sample of edge-on galaxies whose photometric parameters have been published by Barteldrees&Dettmar (1994).They made use of similar red photometric band and technique to extract the pho-tometric parameters.We will utilize their data together with ours throughout the paper in order to increase the available sample of HSB galaxies.As it will be seen,the sample of Barteldrees&Dettmar includes also one object,which can be classi?ed as a LSB galaxy.

4.LSB versus HSB:the vertical scale height of galactic disk as a new feature

to compare

As was shown in Bizyaev(2000);Bizyaev&Mitronova(2002);Reshetnikov et al.(2003), the galaxies of lower surface brightness tend to have smaller z0/h ratios.However,this conclusion was based on studies of mostly HSB galaxies.Now,we can incorporate our LSB subsample and consider the relation between z0/h and the central surface brightnessμ0. The objects from our sample are denoted by squares in Fig.12.The open squares show the HSB subsample,whereas the?lled ones designate LSB galaxies.The galaxies taken from Barteldrees&Dettmar(1994)are shown in Fig.12with the crosses.

Furthermore,the near-infrared K s-band sample of edge-on galaxies from Bizyaev& Mitronova(2002)is available for comparison(the2MASS sample hereafter).Here we have to take into account the systematic di?erence in the brightness and z0/h between the R and K photometric bands.As was noticed by Zasov et al.(2002),the ratio of scales z0/h is1.4 times less for the stellar disk in K against R.It can be explained by stronger dust extinction in the R band,and was well illustrated by Xilouris et al.(1998).We corrected z0/h for the2MASS galaxies taken from Bizyaev&Mitronova(2002)according to this value.The typical color(R-K)=2m.1inferred for late-type face-on spirals by de Jong(1996)was added to the central surface brightnesses of the2MASS galaxies as well.The?nal correction that

we applied was addition of the internal extinction to the2MASS central surface brightness, because it is low in the infrared band and non-negligible in the R band.The value of this correction,1m.2,is chosen so that the2MASS sample coincides with our HSB objects in Fig.12.

Fig.12shows all three samples together,where the2MASS objects are denoted by the small?lled triangles.A trend in Fig.12is seen,an average di?erence of2m inμ0leads to

1.5change in the ratio of scales.At the same time,there is no clear correlation found when

h and z0were plotted againstμ0separately.The correlation ofμ0versus h was shown by Graham(2001),but that conclusion was based on mostly early-type spiral galaxies.

We also incorporate general galactic properties taken from the LEDA database into the analysis:absolute B magnitude B abs,maximum of the rotation curve V m,and HI index.The latter index denotes the di?erence between the B magnitude and the”HI magnitude”.We found that LSB and HSB subsamples do not di?er systematically in B abs,V m,and HI index. There is no correlation found between the values ofμ0and z0/h on the one hand,and B abs, V m,or HI index on the other hand.

In Fig.13one can see a relation of Tully-Fisher type,where the values of the radial scale length are well correlated with the maximum of rotational velocity V m.According to Zwaan et al.(1995);Sprayberry et al.(1995);Chung et al.(2002),LSB and HSB spiral galaxies follow the same Tully-Fisher relation,and our Fig.13is in a good agreement with this.It argues that we did not made a mistake deriving the spatial values.Thus,the galaxy UGC 7808was investigated by de Grijs&van der Kruit(1996)where the shorter scale height value (in kpc)was inferred because of the lower adopted distance to the galaxy.Fig.13shows that our value of the scale length for the galaxy,13.55kpc,places the galaxy very close to the general dependence in Fig.13,whereas the scale length of1.9-2.7kpc taken from de Grijs &van der Kruit(1996)would place this object far o?.At the same time,the angular values of the scale length found in the present work and in the latter cited one,are very similar.

Following Zasov et al.(2002),we calculated the ratio of the total mass M t inside the optical radius to the luminosity of the galactic disk in the B band,L B.We suppose that M t=G?14hV2m,where G is the gravitational constant and4h radius encompasses the whole galaxy.The value of L B is obtained from the absolute B-magnitude,which was taken from the LEDA and corrected for the internal galactic absorption.The values of M t/L B are plotted against the ratio z0/h in Fig.14.

The notation in Fig.14is the same as in Fig.12.As was noticed by Zasov et al.(1991), the ratio of scales z0/h indicates the total mass of the spherical component of a galaxy expressed in its disk mass M s/M d.The relation between z0/h and M s/M d obtained from numerical modeling(N body simulations)was published by Mikhailova et al.(2001)and shown in Fig.15.We made use of that dependence to evaluate the model values of M s/M d for our galaxies.

Here,we have to clarify that we distinguish between a spherical and disk subsystem throughout the paper.By the”spherical subsystem”we refer to both a stellar bulge and dark halo,even if their shapes are not spherical but rather oblate(see discussion in section 5.5).In a general case,the spherical subsystem means a non-disk component,either stellar or not.The disk in our understanding is the galactic stellar disk.It consists mostly of stars for our https://www.sodocs.net/doc/6a13123252.html,ter in the paper we also evaluate the ratio of dark-to-luminous masses. The dark mass belongs to the dark halo,whereas the luminous matter means the stellar bulge and disk.

Then,we take into account that M t=M s+M d and L B=M d/(M/L),where(M/L) denotes the B-band stellar mass-to-light ratio in the disk.Hence M t/L B=(M s/M d+1)·(M/L).It is seen that the model value of M t/L B depends on the adopted B-band stellar mass-to-light ratio.The three curves in Fig.14present the model values of M t/L B which were calculated based on Fig.15with the mass to light ratio(M/L)of1,5,and15.As is seen in Fig.14,most of the galaxies have values of(M/L)between3and10.The B-band stellar mass-to-light ratio(M/L)in Fig.14corresponds to the distance taken along the horizontal axis toward the curve of(M/L)=1.The value of the stellar mass-to-light ratio is systematically higher for our LSB galaxies as compared to that of HSB galaxies.

This conclusion contradicts the bluer color of LSB galaxies found by(de Blok et al. 1995)who give lower values for their(M/L),but the bulge-dominated LSB galaxies have colors comparable with HSB ones(Beijersbergen et al.1999).The dereddened colors from our both LSB and HSB subsamples are almost the same(Table3).On the other hand,LSB spirals have low metallicity as a rule.It might give the comparable colors,whereas stellar disk’s(M/L)takes larger values in LSB spirals.Another reasonable explanation might be an excess of the dark matter in the disks of bulge dominated LSB spirals.

Large LSB galaxies have,on average,two times more mass in their gaseous component (Romanishin et al.1982)in comparison with HSB.Our LSB subsample has almost twice larger value of”HI index”against the HSB one.But this di?erence is not enough to explain the systematic di?erence in(M/L)in Fig.14since the gas component does not dominate by mass in our galaxies.

The mass of the dark halo M h can be estimated from the relation shown in Fig.4.The dark-to-luminous ratio is(M d+M b)/M h=(1+M b/M d)·(M d/M h),where M b and M d denote masses of bulge and dark halo,respectively.On the other hand,M s/M d=(M h+M b)/M d and hence,M h/M d=M s/M d?M b/M https://www.sodocs.net/doc/6a13123252.html,bining previous equations,one can obtain:

M h

(1)

1+M b/M d

The values of M b/M d can be estimated from observations making a rough assumption that the bulge-to-disk luminosity ratio follows the bulge-to-disk mass ratio M b/M d=L b/L d(we consider how our conclusions might change for real galaxies where(M/L)is di?erent for bulges and disks in section5).At the same time,M s/M d can be estimated from Fig.15. The ratio of dark-to-luminous mass M h/(M d+M b)for our galaxies is shown in Fig.16. Surprisingly,there is no systematic di?erence between the values of dark-to-luminous mass ratio for the galaxies with di?erent central surface brightnesses,see Fig.14.It is generally assumed that the LSB galaxies are dark-matter dominated,but all those conclusions were based on studies of bulgeless galaxies.Our sample,on the contrary,comprises mostly of the galaxies possessing non-negligible bulges.

We can also compare masses of the spherical subsystem M s(i.e.the sum of the bulge and halo)in our galaxies.In Fig.17we present how the spherical to disk mass ratio M s/M d depends on the disk central surface brightness.We kept the same notation as in Fig.12and Fig.14.Fig.17indicates that the LSB galaxies do not have more massive dark matter halos. Instead,they have more massive spherical subsystems.This supports a result by Graham (2002)that not all LSB galaxies are dark matter dominated objects.Nevertheless,our result does not contradict previously made conclusions since the dark matter halo and the spherical subsystem become identical for bulgeless galaxies.

Di?erentiation between the bulge and halo allows us to demonstrate that there are dark-matter halo dominated large LSB galaxies as well LSB galaxies,the halos of which are less massive than their disks.

5.Discussion

5.1.The sample selection

There is no systematic di?erence in the obtained values ofμ0among our sample galaxies of I–III surface brightness class(it was noticed by Bizyaev(2000)as well).On the other hand,most galaxies of IV SB class are apparently bona?de LSB galaxies.They constitute a small part of all RFGC objects(3%).As was noticed by McGaugh et al.(1995),there is a signi?cant fraction of LSB galaxies with a large bulge to disk ratio.Bulges of LSB and HSB systems are indistinguishable(Beijersbergen et al.1999),yet their disks are di?erent. Hence,one have to distinguish between LSB galaxies with and without bulges and take these possible bulges into account while undertaking a study of properties of dark halos in LSB galaxies,

Our paper does not attempt to present a statistically completed study of LSB spiral galaxies with large bulges.Instead,we compare two samples of objects of opposite properties. To make statistically reliable conclusions the sample has to be extended.

5.2.Selection e?ects

Fig.12presents a correlation betweenμ0and z0/h.Indeed,the values ofμ0and z0/h have not been obtained independently from each other,as it follows from the formulae in section3.Let us consider how the non-90?inclination of the disk plane a?ectsμ0and z0/h. If the inclination angle is less than90?,the scale height z0calculated in section3becomes overestimated.At the same time,the scale length h is much less a?ected by the value of inclination angle.On the other hand,the value of z0was taken into account when the central surface brightness was calculated.While overestimating the ratio z0/h,we underestimate the disk central surface brightness(hence,its numerical value will be larger).It means that a non-90?inclination of disks shifts data points in Fig.12toward the right upper corner.Hence, the systematic errors due to inclination may only scatter the dependence shown in Fig.12 (say,for the2MASS galaxies)and do not explain a good correlation.

The second e?ect that has to be considered is the internal dust absorption in galaxies. According to Xilouris et al.(1999),the scale length in dusty disks appears higher because of the scattering and absorption e?ects.On the other hand,the dust absorption decreases the derived central surface brightness.In our case it would shift data points in Fig.12from the upper left to the lower right corner and would form a dependence similar to that seen in Fig.12.Nevertheless,we decreased the in?uence of dust by avoiding the dust layer when extracting the radial pro?les.This allowed us to minimize the dust absorption.Furthermore, one can see that the infrared and optical subsamples follow the similar dependence in Fig.12. This argues that the internal absorption has little e?ect on the di?erence between LSB and HSB photometric parameters and Fig.12has a physical meaning.

5.3.Internal absorption in galactic disks and the ratios M s/M d and

M h/(M b+M d)

As was noted in section4,the disk thickness is di?erent when it is estimated in di?erent photometric bands.All the considered relations between the mass of a dark halo,stellar disk, and spherical component are made using the data taken in the R band.On the other hand, the infrared ratios of photometric scales z0/h are less than the optical ones.The infrared values are more preferable because of the lower dust absorption,so we could decrease all our ratios z0/h by a factor of1.4.As is seen in Figs.14and15,a proportional decrease of the scale ratio a?ects Figs.16and17only quantitatively.Hence,all previous conclusions remain unchanged.

The values ofμ0inferred for our HSB galaxies are less than the Freeman’s value(taking into account a di?erence between the R and B bands).It implies that the internal extinction may be important in the disks of our galaxies.Since all the galaxies are spiral and are relatively nearby,one can assume roughly the same dust-to-stars ratio in them.Then,the internal extinction proportionally increases the values ofμ0.At the same time,it does not change the main trends in Fig.12,14,16,and17.

In a more complicated case,the internal dust extinction may be systematically di?erent in the galaxies of our sample.Thus,according to(McGaugh1994;Matthews&Wood 2001)LSB spirals are likely to be less dusty than HSB ones.One can see that it strengthens the relation shown in Fig.12:extinction correction ofμ0for HSB spirals moves data points further to the left than it does for LSB spirals.As a result,we can always distinguish between these two subsamples.It corresponds to the conclusion made by Beijersbergen et al.(1999) that the dust extinction alone can not explain the di?erence in surface brightness between LSB and HSB spirals.

Another way to take the extinction into account is to connect it with the global galactic parameters such as the absolute magnitude or rotational velocity,see(Tully et al1998)and references therein.Correction ofμ0for the extinction with the help of absolute R-magnitudes or V m moves data points to the left in Fig.12and does not change its general trend.

The bulge-to-disk luminosity ratio has been utilized to draw Fig.12and16.Since part of our galaxies has bulges,attention should be paid to how the extinction may change the derived values of L b/L d.In addition to the pro?le?tting,we conducted a direct integration of bulges.At?rst,the model disk(constructed according to the parameters de?ned during the disk?tting)was subtracted from the images of galaxies.Then,we integrated all the central part which was above the zero level.The ratio of the integrated luminosity of the bulge to the model disk luminosity L I b/L d gives us a lower bound of L b/L d ratio(because the model disk is”dust-free”,and the bulge is dimmed by the extinction).The value of L I b/L d is2-6times lower than the value of L b/L d given in Table3.If we use L I b/L d instead of L b/L d,Fig.12does not change qualitatively.On the other hand,in Fig.16all our LSB galaxies move to the right,since a larger fraction of mass of their spherical component is assigned to the dark halo.Then,if we apply L I b/L d as a bulge-to-disk luminosity ratio,one cannot conclude that the ratio”(dark halo+bulge)/disk”in the bulge-dominated galaxies is systematically higher whereas dark-to-luminous ratio not.In this case dark-to-luminous mass ratio would be higher in our LSB systems too.

Alternatively,one can obtain the ratio L b/L d from direct integration of the bulge and disk from our images.In contrast to the previous case that gives the lower limit on L b/L d,

this integration yields values of L b/L d that are systematically higher than it can be seen in Table3.This method of evaluation of bulge-to-disk luminosity ratio does not change our conclusions as well.

5.4.M/L may be di?erent for bulge and disk

Assuming that M b/M d=L b/L d,one can notice that indeed,bulges and disks have di?erent colors and,hence,their stellar population has to show di?erent mass-to-light ratios. It does not a?ect all our results except for Eq.(1)and Fig.16.Bulges are redder than disks as a rule(Peletier&Balcells1996)and have larger M/L.Then,M h/(M d+M b)is overestimated for galaxies with signi?cant bulges(LSB galaxies in our sample).Hence, it supports our conclusion that dark halo does not dominate in LSB galaxies which have big bulges.It should be noticed that the di?erence between colors of bulges and disks is very small(Peletier&Balcells1996;Gadotti&dos Anjos2001),which makes the e?ect mentioned above insigni?cant.

5.5.Oblate bulges,non-spherical halos

Dark matter halos and bulges of galaxies may not be exactly spherical,but rather oblate. Our de?nition of M t=G?14hV2m works well for the case of spherical symmetry.In a general case M t=ηG?14hV2m,whereηis a dimensionless parameter,the value of which is determined by the mass distribution,andη<1for the case of galaxies.If the whole mass of a galaxy was enclosed in a thin exponential disk,the parameterηtaken at4h distance from the center is approximately equal to0.5(Freeman1970).All other reasonable geometric cases represent a mixture of disk and spherical components and giveηbetween0.5and1.For the case of non-spherical dark halo,the di?erence between LSB and HSB galaxies in Fig.14(and,hence, in M/L for the stellar disk)would be even more prominent,because M t calculated usingηis systematically lower for disk-dominated HSB spirals than for bulge-dominated LSB galaxies in our sample.Note that once a non-disk component is presented in all our galaxies,the di?erence inηbe signi?cantly less than a factor of2.At the same time,it does not change other conclusions of this paper.

A possible existence of a non-spherical,oblate component was not taken into account by Mikhailova et al.(2001).If one takes it into account,the general trend shown in Fig.14 remains unchanged.However,a systematic di?erence between the ellipticity of dark halos in LS

B and HSB galaxies can signi?cantly a?ect Fig.14.For instance,an assumption of oblate halo in LSB spirals and spherical halo in HSB ones decreases the di?erence between the B-band mass-to-luminosity ratio in stellar disks mentioned above,since it shifts data points to the left(though,by less than a factor of2).On the other hand,we show that the dark halos are likely to be not too massive and,hence,not dominant by mass in our bulge-dominated LSB spirals.Therefore,the role of their non-spherical shapes is insigni?cant.It is doubtful that the systematic di?erence between the ellipticity of dark halos in LSB and HSB galaxies can a?ect our conclusions.Furthermore,if a signi?cant fraction of dark matter in the bulge-dominated LSB galaxies is located in their disks,it helps to rise their(M/L) as it can be seen from Fig.14.Note that one of candidates to the dark matter,namely cold molecular clouds,could form a disk-like subsystem(Pfenniger et al.1994).

6.Conclusion

1)We present results of photometric observations of a sample of edge-on galaxies.Our sample includes four LSB and seven HSB galaxies.The photometric disk scales(both vertical and radial),disk central surface brightness,and bulge-to-disk luminosity ratios were derived.

2)Stellar disks of LSB galaxies are thinner(when parameterized by the ratio z0/h)than HSB ones.There is a clear correlation between their central surface brightnesses and the vertical to radial scale ratios.

3)While having di?erent central surface brightnesses and bulge-to-disk ratios,the LSB and HSB galaxies in our sample follow the same dependence”disk scale length versus the maximum rotational velocity”.

4)Our LSB galaxies tend to harbor massive spherical subsystems(bulge+halo)as well as to have higher values of the mass-to-luminosity ratio in their disks when compared to the HSB objects.Nevertheless,the dark halo is not strictly the most massive subsystem in our bulge-dominated LSB galaxies.The LSB spirals appear to be the”spherical subsystem dominated”galaxies but not always the”dark matter dominated”.

D.B.is supported by NASA/JPL through the grant99-04-OSS-058.The project was partially supported by Russian Foundation for Basic research via the grant04-02-16518.We have made use of the LEDA database.We thank Verne Smith and Michael Endl for their comments on the manuscript and the anonymous referee whose commentaries and corrections essentially improved the paper.D.B.is grateful to A.Khoperskov and Eduard Vorobyov for fruitful discussions and help.

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Table1:Summary of the observing run

Name SB class Band Date Int.time Nexp Seeing Sky S/N=3level

1999sec.arcsec mag/arcsec2mag/arcsec2 UGC10111IV V27Apr6001 1.921.3726.58

R27Apr12004 2.020.7226.77 UGC11301III V27Apr7003 1.620.7625.17

R27Apr10004 1.620.3825.81 UGC5662III V30Apr6001 3.021.3926.64

R30Apr12002 2.420.5926.63 UGC6080II V30Apr6001 1.921.4926.46

R30Apr12002 1.720.6826.60 UGC6686III V27Apr12002 1.821.3526.85

R27Apr9003 1.720.4826.45 UGC7808IV V27Apr6001 2.221.3526.40

R27Apr12002 2.020.5626.66 UGC9138I V28Apr9002 1.121.3726.48

R28Apr9002 1.020.6326.90 UGC9422I R30Apr12002 1.720.5726.91 UGC9556IV V28Apr18004 1.021.4626.51

R28Apr29006 1.020.6827.26 FGC1273IV V27Apr6002 1.821.4326.54

R27Apr9002 1.720.5026.59 NGC4738I R30Apr12002 1.520.4526.56

Table2:General galactic parameters utilized in the paper

Name D,Mpc Type logD25b t A B logV m B abs

UGC10111139.6Sc 1.22116.0.178 2.370-21.3

UGC1130162.3Sc 1.29515.5 1.273 2.379-21.2

UGC566217.1SBb 1.49515.40.115 1.899-17.6

UGC608030.3Scd 1.315.80.036 1.877-18.6

UGC668686.4Sb 1.41815.00.135 2.283-21.2

UGC780896.3Sb 1.49214.60.098 2.403-21.8

UGC913861.9Sc 1.28414.80.108 2.161-20.9

UGC942245.6Sc 1.27914.70.1 2.140-20.5

UGC955632.5SBc 1.09916.00.043 1.974-18.1

FGC127349.4Sc0.80116.50.103 2.166-18.0

NGC473863.6Sc 1.29714.30.076 2.335-21.4

Table3:The derived structural parameters of the galaxies

Name i PA h z0z0/hμ0L b/L d m R V-R deg deg kpc kpc mag/arcsec2mag mag UGC1011188.237.515.84±0.14 2.60±0.420.16824.63±0.110.5815.080.63 UGC1130188.2110.8.24±0.84 1.30±0.080.16022.12±0.130.2513.010.81 UGC566289.3147.5 2.16±0.510.50±0.060.23722.70±0.370.2113.620.61 UGC608086(?)125. 2.93±0.180.70±0.050.23622.69±0.160.0014.450.50 UGC668688.050.9.82±1.27 1.89±0.210.19622.51±0.130.1013.440.71 UGC780888.793.513.55±2.63 1.44±0.180.15823.97±0.180.8613.600.69 UGC913887.0168.5 4.71±0.12 1.05±0.060.21422.42±0.380.0714.790.76 UGC942288.3159. 3.54±0.130.80±0.050.22522.64±0.350.0014.96—UGC955687.0133. 3.63±0.490.54±0.090.14124.77±0.60 1.0015.390.39 FGC127389.7170. 5.17±0.980.63±0.100.11824.33±0.18 1.3714.700.68 NGC473885.732.5 4.68±0.21 1.23±0.080.27021.11±0.160.0113.39—

Fig.1.—Upper:Examples of the vertical pro?les of UGC10111extracted parallel to its minor axis.Both lines show pro?les taken along two vertical cuts closest to the galactic center,see isophotal map in the lower panel.The10arcseconds bar indicates the level of S/N=3.Middle:The radial pro?les extracted along the major axis(dashed curve)and parallel to it(solid curves).The latter were used to derive the structural parameters of the galaxy.Upper and lower curves are shifted by+2and-2mag/arcsec2respectively from their real position.They are extracted along the upper and lower radial cuts shown on the isophotal map. The10arcseconds bar indicates the level of S/N=3.Lower:the isophotal map of UGC10111.The isophotes correspond to20.5,21,21.5,22,22.5,23,23.5,24,24.5,25,and25.5mag/arcsec2in the R band.The places where the pro?les were extracted are shown by lines.All artifacts and stars which can be seen in the picture

were cleaned out manually before the structural parameters were found.

Fig. 2.—The same for UGC11301.The isophotes correspond to19.5,20.5,21,21.5,22,

Fig.3.—The same for UGC5662.The isophotes correspond to20.5,21,21.5,22,22.5,23,

Fig.4.—The same for UGC6080.The isophotes correspond to20.5,21,21.5,22,22.5,23,

硬盘产品编码分析

硬盘产品编码分析 希捷硬盘 产品编码 希捷硬盘的产品编号,例如:ST31500341AS含义如下： 其中并没有磁盘速度信息，不能直接分析产品编号获取硬盘转速。 现在已经得到了希捷硬盘的产品帮助文档，根据文档可以由产品编号，查出该型号硬盘的转速。 编程实现 可以考虑建立产品型号的库文件，然后根据产品编号，查询库文件，得到该硬盘的转速。 日立硬盘 产品编码 日立硬盘的产品编码，总体上可以分为两个总类：一是沿用IBM编码的，以IC开头表示的产品编码方式。第二种是以H（Hitachi，日立）开头的产品编码方式。具体含义如下：

编程实现 日立的硬盘编码比较标准，可以直接分析产品型号的字符串，得到硬盘的转速。

西部数据 西部数据的产品号中包含了硬盘的转速信息，可以直接使用，但是官网提供的最新代码型号说明与之前文档中的说明不一致。 产品编码 1，厂商代号 用WD两个字母表面是西部数据的产品 2，硬盘容量 2,3或者4位数字来表示容量，最大支持999.9。例如7500表示750G，在1TB和更大的硬盘表示上（根据第三部分来判断），容量数字的小数点将移到第一位数字后面，比如”WD1000E。。”表示的是1T。企业版的硬盘通常也会使用容量的最后一位数字作为产品代码，比如WD5001ABYS，最后一个数字不表示额外的容量。 3，容量的单位/系数 A GB/3.5英寸 B GB/2.5英寸 C GB/1.5英寸 E TB/3.5英寸 F TB/3.5英寸 G GB/3.5英寸 H GB/3.5英寸 J TB/3.5英寸 4，商务标识 A Desktop/WD Caviar(R) B Enterprise/WD RE4; WD RE3; WD RE2 (3-platter) 。。。 。。。 5，转速和缓存大小 A5400RPM 2MB缓存 B 7200RPM 2MB缓存 C 5400RPM 16MB缓存 D 5400RPM 32MB缓存 E 7200RPM 64MB缓存 F 10000RPM 16MB缓存

蚁群算法简述及实现

蚁群算法简述及实现 1 蚁群算法的原理分析 蚁群算法是受自然界中真实蚁群算法的集体觅食行为的启发而发展起来的一种基于群体的模拟进化算法,属于随机搜索算法,所以它更恰当的名字应该叫“人工蚁群算法”,我们一般简称为蚁群算法。M.Dorigo等人充分的利用了蚁群搜索食物的过程与著名的TSP问题的相似性,通过人工模拟蚁群搜索食物的行为来求解TSP问题。 蚂蚁这种社会性动物,虽然个体行为及其简单,但是由这些简单个体所组成的群体却表现出及其复杂的行为特征。这是因为蚂蚁在寻找食物时,能在其经过的路径上释放一种叫做信息素的物质,使得一定范围内的其他蚂蚁能够感觉到这种物质,且倾向于朝着该物质强度高的方向移动。蚁群的集体行为表现为一种正反馈现象,蚁群这种选择路径的行为过程称之为自催化行为。由于其原理是一种正反馈机制,因此也可以把蚁群的行为理解成所谓的增强型学习系统(Reinforcement Learning System)。 引用M.Dorigo所举的例子来说明蚁群发现最短路径的原理和机制,见图1所示。假设D 和H之间、B和H之间以及B和D之间(通过C)的距离为1,C位于D和B的中央(见图1(a))。现在我们考虑在等间隔等离散世界时间点(t=0,1,2……)的蚁群系统情况。假设每单位时间有30只蚂蚁从A到B,另三十只蚂蚁从E到D,其行走速度都为1(一个单位时间所走距离为1),在行走时,一只蚂蚁可在时刻t留下浓度为1的信息素。为简单起见,设信息素在时间区间(t+1，t+2)的中点(t+1.5)时刻瞬时完全挥发。在t=0时刻无任何信息素,但分别有30只蚂蚁在B、30只蚂蚁在D等待出发。它们选择走哪一条路径是完全随机的,因此在两个节点上蚁群可各自一分为二,走两个方向。但在t=1时刻,从A到B的30只蚂蚁在通向H的路径上(见图1(b))发现一条浓度为15的信息素,这是由15只从B走向H的先行蚂蚁留下来的;而在通向C的路径上它们可以发现一条浓度为30的信息素路径,这是由15只走向BC的路径的蚂蚁所留下的气息与15只从D经C到达B留下的气息之和(图1(c))。这时,选择路径的概率就有了偏差,向C走的蚂蚁数将是向H走的蚂蚁数的2倍。对于从E到D来的蚂蚁也是如此。 （a）（b）（c） 图1 蚁群路径搜索实例 这个过程一直会持续到所有的蚂蚁最终都选择了最短的路径为止。 这样,我们就可以理解蚁群算法的基本思想:如果在给定点,一只蚂蚁要在不同的路径中选择,那么,那些被先行蚂蚁大量选择的路径(也就是信息素留存较浓的路径)被选中的概率就更大,较多的信息素意味着较短的路径,也就意味着较好的问题回答。

(完整版)西数硬盘维修WDR5.3教程

WD硬盘维修教程 WDR5.3使用教程： 第一步：注册完打开软件 第二步：设置维修盘端口：点击设置______端口_____会出现主要端口，次要端口，定制端口USB。一般如果不是USB移动硬盘都选择“定制端口” 如果选择了定制端口会出现：

注意这个框里有6行参数其中有一行是我们刚好待修盘端口，如果不知道那个才是。我们要逐一试点击界面来与获取到的参数核对，找出要修的盘为止。 第三步进入维修程序：如图下： 可以清楚的看到硬盘的型号FW S/N LBA 容量请大家仔细查看是不是自己要修的那个硬盘。 下面讲解一下软件的全部功能如图下： 我们在这里讲修盘的功能： 第一个：识别硬盘是在软件空白的时候你点击一下就会出现硬盘的容量和型号 第二个查看SMART：主要是看SMART的好坏不在去用HDD检测SMART好坏 第三个：清SMART：有的硬盘查看SMART，或者用HDD检测有红黄块，点击一下这个清 SMART的即可完成，也可以清除硬盘的使用时间和次数。 第四个起转电机：这个功能为辅助功能，主要是让硬盘转起来，一般硬盘通上电就会转，所

以这个功能一般不会用。 第五个直接复位：主要是让硬盘重启的功能不用你手动把电在插上，只要你点击了这个按钮 就好比电脑重启一样。在维修时候会用到（报错的时候也会用到）。 第六个加载永久覆盖：这个是用于写01好模块的，是用于写通刷用的。 第七个加载瞬时覆盖：这个是用于加载完01模块在加载它。也是用于写通刷用的 第八个Flash操作：也就是ROM操作。主要用于读取ROM和备份ROM（在维修前备份 ROM是维修人员的良好习惯） 第九个模块操作：也就是固件操作主要用于备份固件和读取固件以及检测固件的好坏（在维 修前备份固件是维修人员的良好习惯） 第十九配置信息主要用于修改硬盘的型号个LBA的（比如刷完通刷固件发现容量和型号不 对用这个修改一下） 第三十一个清G表：比如说G表满了清一下G表就可以继续加G表坏到了。这个也是辅助功能。 第三十二个清P表：这个一般不要动，因为清了P表可能造成你全盘坏道 第三十六个格式化：这个格式化是超级格式化，主要用于坏道及色块少的硬盘来进行维修。 第三十九个磁头检测：有的硬盘接上去敲盘，但是在这个软件里面能识别到硬盘。点击这个 看下那个磁头是坏的那个是好的好的就（GOOD）坏的（BAD） 第四十五个逻辑扫描：是检测硬盘是否有坏道的，但是本人不建议你使用这个逻辑扫描检测 坏道。建议用VCR或者MHDD检测。 第四十七个快速启动自小准：是修坏道使用的一个功能，自小准=SF=工厂模式维修，自小 准需要一个完美的固件才可以自小准。不然在自小准的过程中会报错。 第五十个编辑脚本：是编辑自小准的脚本，这个脚本可以让你清楚的看到自小准的过程中有那些流程，走到那一步了。

西数硬盘的命名规则培训课件

西数硬盘的命名规则

西数硬盘的命名规则（举例和解释）： WD10EARS主编好，00Y5B1副编号。主板编号中，WD是公司前缀，1代表1TB，0为产品编码，E代表GB/3.5英寸，A代表桌面级/WD Caviar，R代表5400转64MB缓存，S代表SATA 3GB/s 22针SATA接口。副编号只能识别到5是第五代的意思，B1是固件版本。 具体的西数硬盘官方定义的命名规则（中文翻译如下）。英文原本PDF在附件中。 主编号命名规则 基本型号编码由六个字段组成： 1．公司前缀（WD） 2．容量（GB/TB） 3．容量等级/外形规格 4．市场等级/品牌 5．转速/缓存大小或属性 6．接口 产品型号编码 1. 公司前缀 WD 2. 容量 两位、三位或者四位数字，最大为999.9。

在2007年9月之后生产的1TB或更大容量的企业版硬盘（参看字段3）的产品编号中，第一个数字代表TB。（例如，WD1000FYPS是一个1TB容量的硬盘）。企业版产品也用最后一位数字来表示产品编码（例如WD5001ABYS），这种情况，最后一位不在表示为容量。 3．容量等级/外形规格 A GB/3.5英寸 B GB/2.5英寸 C GB/1.0英寸 E TB/3.5英寸 F TB/3.5英寸（新规格） G GB/2.5英寸转3.5英寸适配器 H GB/2.5英寸转3.5 英寸背板适配器 J TB/2.5英寸 4．市场等级/品牌 A 桌面级/WD Caviar B 企业级/WD RE4；WD RE3；WD RE2（3盘片） C 桌面级/W D Protégé? D 企业级/WD Raptor E 笔记本/WD Scorpio H 发烧级/WD Raptor X J 笔记本/WD Scorpio 带有自由下落传感器 K 企业级/WD S25

基本蚁群算法

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各品牌硬盘型号标识

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教你看型号买硬盘

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硬盘MDL解析

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蚁群算法

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西数硬盘的命名规则（举例和解释）： WD10EARS主编好，00Y5B1副编号。主板编号中，WD是公司前缀，1代表1TB，0为产品编码，E代表GB/3.5英寸，A代表桌面级/WD Caviar，R代表5400转64MB缓存，S代表SATA 3GB/s 22针SATA接口。副编号只能识别到5是第五代的意思，B1是固件版本。 具体的西数硬盘官方定义的命名规则（中文翻译如下）。英文原本PDF在附件中。 主编号命名规则 基本型号编码由六个字段组成： 1．公司前缀（WD） 2．容量（GB/TB） 3．容量等级/外形规格 4．市场等级/品牌 5．转速/缓存大小或属性 6．接口 产品型号编码 1. 公司前缀 WD 2. 容量 两位、三位或者四位数字，最大为999.9。 在2007年9月之后生产的1TB或更大容量的企业版硬盘（参看字段3）的产品编号中，第一个数字代表TB。（例如，WD1000FYPS是一个1TB容量的硬盘）。企业版产品也用最后一位数字来表示产品编码（例如WD5001ABYS），这种情况，最后一位不在表示为容量。3．容量等级/外形规格 A GB/3.5英寸 B GB/2.5英寸 C GB/1.0英寸 E TB/3.5英寸 F TB/3.5英寸（新规格） G GB/2.5英寸转3.5英寸适配器 H GB/2.5英寸转3.5 英寸背板适配器 J TB/2.5英寸 4．市场等级/品牌 A 桌面级/WD Caviar B 企业级/WD RE4；WD RE3；WD RE2（3盘片） C 桌面级/W D Protégé? D 企业级/WD Raptor E 笔记本/WD Scorpio H 发烧级/WD Raptor X J 笔记本/WD Scorpio 带有自由下落传感器 K 企业级/WD S25

识别西部数据硬盘型号

[硬盘]怎样识别西部数据硬盘型号 识别西部数据硬盘型号有哪些步骤： 首先，“WD”是“Western Digital”的简称，表示其为西部数据公司的产品。 前6位主编号： 第一部分的四个“X”表示为硬盘容量，通常由3到4位数字组成，单位为GB。其标识和希捷是一样的，如4位的“1200”代表120GB，3位的“800”则代表80GB。 第二部分的“X”表示为硬盘转速及缓存容量。 “A”表示转速为5400 RPM/分的鱼子酱硬盘 “B”表示转速是7200 RPM/分的鱼子酱硬盘 “E”表示转速是5400 RPM/分的Protege系列硬盘 “J”表示转速为7200 RPM/分，数据缓存为8MB的高端鱼子酱硬盘 “G”表示为转速拥有10000 RPM/分，数据缓存为8MB的最高端桌面硬盘Raptor系列 第三部分的“X”表示接口的类型。 “A”表示为Ultra ATA/66或者更早期的接口类型 “B”表示为Ultra ATA/100 “W”表示应用于A/V(数码影音)领域的硬盘 “D”表示为Serial ATA150接口 后六位附加编号： 对于后面的六位附加编号，笔者很抱歉，找不到相关于Serial ATA150接口规范的硬盘附加编号资料，这不能不说是一个遗憾。 第四部分的两个“X”表示为OEM客户标志。如今西数面向零售市场的产品，其两个编号都是为数字“00”。如果作为其它字符的话，则为OEM客户的代码，不同的编号对应不同OEM客户，而这种编号的硬盘通常是不面向零售市场的。 第五部分的“X”代表硬盘单碟容量，单位是GB。“C”代表硬盘单碟容量为40GB，“D”代表66GB，“E”代表83GB。 第六部分的“X”表示同系列硬盘的版本代码，该代码随着不同系列而变。 “A”表示7200转/分，Ultra ATA100接口的BB系列； “B”表示5400转/分，Ultra ATA66接口的AB系列； “P”表示5400转/分，Ultra ATA100接口的EB系列； “R”表示7200转/分，Ultra ATA100接口，具有8MB缓存的JB系列。 而在单碟66GB和83GB的产品中，还出现了“U”，“V”等其他字母，分别对应JB系列和BB系列产品。 最后部分的两个“X”表示为硬盘的Firmware版本。我们目前常见的一般都是“A0”。 我们以“WD2500JB-00EVA0”的硬盘编号作例子，我们从主编号可以知道这是一块西部数据公司出品的容量为250GB、7200转/分并且具有8MB缓存的硬盘。从后面的附加编号我们还可以看出这是西部数据面向零售市场，单碟容量为83GB的产品。其实，我认为对一般消费者来说，买西数硬盘看前面的6位主编号就可以得知性能了，加上了后面的6位附加编号反而还会增加了难度。 对于现在西数公司新出的Serial ATA150接口的硬盘，如主6位编号为“WD2500JD”，我们就可以知道他是转速为7200 RPM/分，数据缓存为8MB，采用接口为Serial ATA150接口的硬盘。还有对于西数公司最高端桌面硬盘Raptor(猛禽)系列，其主编号“WD740GD”亦代表了大部分的信息，其“容量为74GB，转速拥有10000 RPM/分，数据缓存为8MB，采用Serial ATA150接口。

基本蚁群算法

摘要 许多实际工程问题可以抽象为相应的组合优化问题，TSP问题是作为所有组合优化问题的范例而存在的，它已成为并将继续成为测试组合优化新算法的标准问题。从理论上讲，使用穷举法可以求解出TSP问题的最优解；但是对现有的计算机来说，让它在如此庞大的搜索空间中寻求最优解，几乎是不可能的。所以，各种求TSP问题近似解的算法应运而生了，本文所描述的蚁群算法（AC）也在其中。 目前已出现了很多的启发式算法，而蚁群算法作为一种新型的启发式算法，已成功地应用于求解TSP问题。蚂蚁通过分泌信息素来加强较好路径上信息素的浓度，同时按照路径上的信息素浓度来选择下一步的路径：好的路径将会被越来越多的蚂蚁选择，因此更多的信息素将会覆盖较好的路径；最终所有的蚂蚁都集中到了好的路径上。蚂蚁的这种基于信息素的正反馈原理正是整个算法的关键所在。 本文介绍了基本蚁群算法概念、原理及蚁群算法的特点，再根据蚁群算法的缺点做出了优化。采用轮盘赌选择代替了基本框架中通过启发式函数和信息素选择路径，改进蚁群算法的信息素传递参数，让整个算法更快速的找到最优解。其次，采用最大最小优化系统限制最大值和最小值，让整个系统更快收敛，得到最优解。 关键字：蚁群算法，TSP问题，启发式函数，轮盘算法，最大最小优化

ABSTRACT Many practical engineering problems can be abstracted as corresponding combinatorial optimization problem, TSP problem is an example of all as a combinatorial optimization problem, it has become and will continue to be a new combinatorial optimization algorithm of standard test problems. In theory, using the exhaustion method can solve the TSP problem optimal solution; But for the existing computer, let it in such a large search space to seek the optimal solution, it is almost impossible. So, all kinds of algorithm arises at the historic moment, the approximate solution of the TSP problem described in this paper, ant colony algorithm (AC) is among them. Has appeared a lot of heuristic algorithm and ant colony algorithm as a kind of new heuristic algorithm, has been successfully used in solving TSP problems. Ant secretion by pheromones to strengthen the good path pheromone concentration, at the same time according to the path to choose the next path pheromone concentration: good paths will be more and more ants to choose, so that more information will cover good path; Eventually all the ants on a good path. This positive feedback based on the pheromone of ant principle is the key to the whole algorithm. This paper introduces the basic concept of ant colony algorithm, principle and characteristics of ant colony algorithm, according to the disadvantages of ant colony algorithm optimization. Adopting roulette selection instead of the basic framework by heuristic function and choose path pheromone, pheromone passing parameters of improved ant colony algorithm, make the whole algorithm find the optimal solution more quickly. Second, limiting the maximum and the minimum maximum minimum optimization system, make the whole system faster convergence and the optimal solution is obtained. Keywords: ant colony algorithm, the TSP problem, a heuristic function, roulette algorithm, maximum_minimum optimization