Some statistical properties of spiral galaxies along the Hubble sequence

CHINESE ASTRONOMY AND ASTROPHYSICS PERGAMON

Chinese Astronomy

and Astrophysics

Some statistical

24 (2000)

properties

along the Hubble MA Jun1y2T3 ZHAO Jun-liang4F2 ‘Beijing

‘National 3Joint

Astronomical

Observatory,

Astronomical

Observatories,

Laboratory 4Shanghai

5Department

Chinese

of Astronomy,

of spiral galaxies sequence

*

t

ZHANG Fei-peng412

Chinese

Academy

Chinese

for Optical Astronomy, Observatory,

435-443

Chinese

Academy Academy

Academy Nanjing

PENG Qiu-he5

of Sciences, of Sciences,

100012

Shanghai

Shanghai Nanjing

100012

Beijing

of Sciences,

of Sciences, University,

Beijing

200030

200030

210008

Abstract A statistical study has been made for the variations along the Hubble sequence, of such parameters as the degree of tightness of winding of spiral arm A, the pitch angle ,u, the flatness of the disk H/Da5 and the thickness H along the

Hubble

sequence

for 365 spiral

The mean values of these obtained for the first time. Hubble

classification

statistical theory satisfy Key

of spiral

significance,

galaxies

published

in A&Ap

galaxies

and 2) that

spiral galaxy-spiral

1.

Spiral galaxies

Series.

is one which has only a qualitative

the dispersion

relation

is valid for most spiral galaxies, i.e., the arms the requirements of being tightly wound. words:

Supplement

quantities for the various Hubble types have been The results of the statistics show clearly 1) that the

arm-pitch

angle-

in the density

of most

spiral

the Hubble

and wave

galaxies

sequence

INTRODUCTION

are also called disk-like galaxies.

Their obvious characteristic

is their beautiful

spiral structure. As shown by many photographs, galaxies of this kind are rather flat, with spiral arms located in a very thin plane. In the improved Hubble classification system, spiral galaxies are classified according to the following three parameter&l: (1) the size of the bulge in galactic centre relative to the t Supported by Wang Kuan-cheng Postdoctoral Award Foundation Science Foundation Received 1999-04-19; revised version 1999-08-20

and National

* A translation of Acta

2000

0275-1062/00/$

Astron.

Sin.

Vol. 41, No. 2, pp.

172-180,

Natural

- see front matter @ 2000 Elsevier Science B. V. All rights reserved.

PII: SO275-1062(00)00073-4

436

MA Jun et al. / Chinese Astronomy

disk; (2) the degree of tightness

of winding

24 (2000)

and Astrophysics

4.95-443

of the spiral arm; (3) the degree of disintegration

of the arm into stars. A spiral galaxy of type Sa (SBa) possesses a tightly wound spiral arm and a protruding central bulge. The brightness distribution of the arm is comparatively smooth

and

uniform,

(SBc), the spiral

patterns of clustering. quantities lie between put forward,

and there

arm is wound

people

is no clustering

of stars.

loosely, and the central

For a spiral

galaxy

bulge and arm display

of type

rather

SC

strong

The clusters are composed of stars. For type Sb (SBb), all the three those of the above two types. Since the Hubble classification was have tried

to find out relations

between

this classification

and other

characteristic quantities. With about 1500 galaxies in Ref. [3] as sample, Sersi# discovered that the colours of galaxies exhibit a good correspondence with Hubble’s sequence. For instance, galaxies of the late type are somewhat blue. However, the intrinsic dispersion of this correlation is too large for it to be used as basis for a quantitative classification. Broschef4] carried out a statistical study of 53 galaxies possessing very large velocities of rotation, and obtained the following linear formula connecting the largest rotational velocity and the Hubble

type t: w, =(290 -24t) km/s.

(1)

Elmegreen et a1.15] made photometric studies of surface brightness sources in blue and infrared wavelength regions for 15 barred spiral galaxies. They concluded that the bars of early-type galaxies can extend to the vicinity of the corotation radius, but the bars of late-type galaxies, only to the neighbourhood of the inner Lindblad corotation radius. The distribution of intensity along the bars of early-type galaxies is uniform, while that of latetype galaxies diminishes exponentially. Morphological study of the arms of spiral galaxies was started earlier than the Hubquestions regarding the arms. ble classification. Von der Pahlen isI attacked mathematical Groot[7y8] investigated the spiral arms of 15 galaxies and thought rather well with logarithmic helices. DanverLg] and Kennicutt[l”]

that the arms may be fitted systematically researched

the morphology of the arms of 203 Sa-Sc galaxies, and identified the pitch angle as an important measure for the tightness of winding of arms. Kennicutt[l’] carried out a statistical study of the pitch angle and came to the conclusion: The pitch angle monotonicaRy increases from the early type to the late type along the Hubble sequence, but the range of variation of the pitch angle within

each type is quite large, so he thought

is not such an ideal one-dimensional performed De Vaucouleurs[“] determined

the thickness

that

the Hubble

classification

classification system as was generally believed it to be. a detailed photoelectric photometric study of M31 and

of its disk. Van der Kruit et a1.[12-15] investigated the luminosity Under the hypothesis that galactic disks are lospiral galaxies.

distribution of edge-on cally adiabatic, self-gravitating

and exponentially cut-off, they obtained a three-dimensional With this model, they carried out surface model of the edge-on luminosity distribution. photometry for ‘? edge-on spiral galaxies, whose bulges are not too evident, and obtained the thickness of their disks. Peng Qiu-he[16] proposed a method of deducing the thickness by observation of the spiral pattern and obtained the thickness of the disk for 4 spiral galaxies. Using the DSS digital optical disks of Xinglong Observing Station of Beijing Astronomical Observatory and the PDS scanning photometer of Purple Mountain Observatory, study of 500 spiral patterns. Applying the Ma Jun et a~[“-~~] carried out a morphological the disk thicknesses of these galaxformula proposed by Peng Qiu-he [16], they determined

MA Jun et al. / Chinese

ies.

In this article,

Astronomy

the 416 galaxies

listed

and Astrophysics

24 (2000)

in the appendix

435-443

437

of Ref. [17] are used as sample

(among these 51 galaxies with errors larger than 100% are omitted) and for the first time the statistical mean values of some parameters for the various Hubble types have been obtained.

2. STATISTICAL 2.1

Varition

of the Winding

Parameter

RESULTS (A) along the Hubble

Sequence

Fig. 1 presents the relation between the winding parameter and the Hubble sequence. As may be seen from the figure, generally speaking, as we move from the early to the late types the spiral arms becomes more and more loosely wound, but within each type there is a large dispersion in the winding parameter. The main cause of the dispersion is as follows: The degree of tightness of winding of spiral arm in the Hubble classification is merely a qualitative measure, and it is affected also by the inclination of the galaxy. In a galaxy with large inclination, the spiral arm which is actually loosely wound may appear to be tightly wound in the image. The Hubble classification was conceived only with photographs of galaxies, and no correction for inclination was made. For this reason, galaxies which should belong to a later type were classified as belonging to an earlier type. The winding parameters that we use in this paper have already been corrected for the effect of inclination.

ot.~‘.‘..‘.‘.‘..‘...““..‘...c Sbc Sb Sab

SC

Scd

Hubble type

Fig. 1 Distribution

of winding parameter for different Hubble type spirals

In Table 1 and Fig. 2 we present for each type the mean value of the winding parameter and its error. Among these values the smallest mean winding parameter is 6 & 0.24. As we know, in the derivation of the dispersion relation in density wave theory the WKB approximation must be adopted. From this it can be inferred that only in the case of tightly wound helicons, the dispersion relation may be valid. This requires that A >> 1. As may be seen from our statistical

results,

on the average,

A 2 6. This

implies

that

the requirement

438

MA Jun et al. / Chinese

of tightly

wound

helicons

is valid for most spiral Table 1

Astronomy

is approximately

and Astrophysics

satisfied.

24

(.%OOO) 435-443

In other words, the dispersion

relation

galaxies. Mean

HUBBLETYPE Sample size Mean value Dispersion

Winding

Parameter

for Different Hubble Type Galaxies

Sab

Sb

Sbe

10 7.77 f 0.62

49 7.39 z!z0.32

65 6.64 f 0.29

212 6.31 k 0.13

29 6.0 f 0.24

1.96

2.24

2.34

1.89

1.29

5,5t”““““.“““.““..‘..,. SSb

Sb

Sbc

SC

SC

Scd

Scd

Hubble type

Fig. 2 Mean winding parameter

2.1

Varition

of the Pitch

Fig.3 illustrates formation

of winding

Angle

the variation parameter

and error bar for different Hubble type spirals (A) along the Hubble

Sequence

of pitch angle along the Hubble

sequence.

For the trans-

(A) into pitch angle (p), we used the formula: p = arctan(

where m is the number of spiral arms. In fact, in the fitting of spiral arms what is got is the pitch angle;-the concept of winding parameter only arises in the density wave theory. Table 2 HUBBLETYPE Sample size Mean value Dispersion

Mean

Pitch

Angle for Different

Hubble

Type

Galaxies

Sab 10

Sb 49

Sbe

SC

65

212

Scd 29

15.5 f 0.84 2.66

16.6 f 0.68 4.76

18.9 zt 0.83 6.69

19.8 f 0.46 6.70

19.8 f 0.78 4.20

As shown in Fig. 3, the pitch angle of spiral arms gets larger and larger as we move from the early to the late types, that is, the arms become more and more loosely wound. However, within each Hubble type the dispersion in the value of pitch angle is quite large, and the chief cause has been stated above.

MA Jun et al. / Chinese

Astronomy

and Astrophysics

ot...“...“....‘....‘....‘.” Sb Sab

Sbc

24 (2000)

439

435-443

Scd

SC

Hubble type

Fig. 3 Distribution

of pitch angle for different Hubble type spirals

20 E

i

3

19-

5 : 0 $ ISB : 5 . .6 175 : z 16r

l~t...“..‘.‘....‘.‘..“.“‘..‘.J

SbC

Sb

Sab

Scd

SC

Hubble type

Fig. 4 Mean pitch angle and error bar for different Hubble type spirals The Table

mean

value of pitch

2. It can be seen that,

angle for each type of spiral on the average,

galaxies

is given in Fig. 4 and

the pitch angle becomes

larger and larger as

we move from the early to the late types. 2.3

Variation

of Flatness

Fig. 5 displays

distribution

As shown by the figure, and flatter

of Galactic

Disk (H/I&,)

of the flatness

generally

speaking,

as we go from the early

of galactic

along the Hubble disks along the Hubble

the disks have a tendency

to the late types.

However,

sequence sequence.

of becoming

for each type

flatter

there

is a

440

MA Jun et al. / Chinese

large dispersion

Astronomy

in the degree of flatness.

and Astrophysics

This implies

that

be a characteristic quantity in the Hubble classification. values for each type and the error bars. On the average, early-type ones. seems reasonable.

24 (2000)

435-443

the flatness

cannot

be taken

to

Table 3 and Fig. 6 give the mean late-type galaxies are flatter than

However, SC galaxies are flatter than Scd ones, and this local fluctuation It follows from Table 3 that the values of flatness of SC galaxies are almost

half those of Sab galaxies. 10

x

8x

i x x

0

.,..‘....‘.,..‘....I,...I,...’ Sbc Sb Sab

*

x

SC

WI

Hubble type

Fig. 5

Distribution

t . . . .

I

.

Sab

of flatness

.

.

.

for different

Hubble

type spirals

9..,“‘.‘.‘,..‘#“‘-

Sb

SIX

SC

SCd

Hubble type

Fig. 6 Mean flatness

and error

bar for different

Hubble

type spirals

MA Jun et al. / ChineseAstronomyand Astrophysics24 (.2000) 435-443

Table 3

HUBBLETYPE Sample size Mean value Dispersion

2.4

Variation

441

Mean Flatness for Different Hubble Type Galaxies Sab

Sbe Sb SC Scd 65 212 29 10 49 0.059f 0.006 0.046f 0.002 0.044f 0.003 0.030rt0.001 0.034* 0.003 0.024 0.015 0.016 0.019 0.014

of the Thickness

of Galactic

Disk (H)

along the Hubble

Sequence

Fig. 7 presents the variation of the thickness of galactic disk along the Hubble sequence. As may be seen in the figure, the disks become thinner and thinner as we go from the early to the late types. Especially for SC galaxies, the values of disk thickness are concentrated in a small range;-and centered around a small value. Table 4 and Fig. 8 give the average thickness of spiral galaxies of various Hubble types together with the errors bars. 5

-*t....l....l....‘..,.‘... Sab

Sb

Hubble

Fig. 7 Distribution 2.5

SC

Sbc

I..., Scd

type

of thickness for different Hubble type spirals

,

t

I

Sab

Sb

Fig. 8 Mean

thickness

SC

Sbc Hubble

Scd

type

and error bar for different

Hubble

type spirals

442

MA Jun et al. / Chinese

Table 4 HUBBLE TYPE Sample size

Mean value Dispersion

Mean

Thickness

Sab 9 2.04f 0.31 0.93

and Astrophysics

for Different

Sb 42 1.46 f 0.12 0.78

3.

As seen from our statistical

Astronomy

Hubble

Sbe 54 1.41 f 0.12 0.88

24 (2000) 435-443

Type

Galaxies

SC 157 0.86 f 0.05 0.63

Scd 23 0.95 fO.13 0.62

DISCUSSIONS

results, the degree of tightness of winding of spiral arms is not

evidently embodied in the Hubble classification. That is, as we go from the early to late types, the degree of tightness does not change monotonically. Certain Scd galaxies even have the same degree of tightness of winding as some Sab galaxies. This leads us to doubt the usefulness of this parameter in the Hubble classification;-and the accuracy of a classification so involved. Actually, opinions on this issue are widely divided. Some authors put forward rather sharp criticisms to the Hubble classificationI20l and thought it to be merely a qualitative classification that does not have quantitative significance and to be too stochastic. When one and the same galaxy is classified by different authors, the results sometimes differ very much from one another. This implies that there exists an inherent uncertainty.

Keeping in mind these criticisms,

6 groups of authors, who are engaged in the

classification of galaxies, carried out independent classifications for 831 galaxies that have isophotovisual diameters (down to 24.5 stellar magnitudes /square arc-second) larger than 1.2 arc-minutes12’~221 Their results led to the following: the dispersion of errors of classification among various groups in the de Vaucouleurs et al. ’s [231digital Hubble classification ranges between 1.3 and 2.3, with typical value 1.8. For large galaxies, the errors of classification are relatively smaller. For galaxies with small inclinations (inclination is defined as the angle between the normal to the galaxy ‘s surface and the observer’s line of sight), the errors are also relatively smaller.

At the same time, the results show that among the 831

galaxies only 8, that is, only l%, got exactly the same type assignation from all the 6 teams. In the digital Hubble classification, the numbers -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 90 and 99 correspond, respectively, to cE, EO, Et, SO-, SO’, SO/a, Sa, Sab, Sb, Sbc, SC, Scd, Sd, Sdm, Sm,Im, c1, IO and Pet. Still, some statistical results do indicate systematic differences among different Hubble types in respect of certain properties. For instance, Roberts et a1.[24l using the galaxies in RC3 as sample[231, carried out a statistical study of the average luminosity (in B band), mass-luminosity ratio, surface brightness, surface density, mass of neutral hydrogen and B - V colour index, and found some systematic variations. Kennicutt1251 made a statistical investigation of the relation between the rate of star formation and Hubble types, and also got some systematic variations. However, the dispersions in the statistics are very large, and the question whether part of the dispersion comes from the Hubble classification itself is worth addressing. This is because remarkable statistical results may emerge if the Hubble types of some galaxies are altered. The Hubble classification suffers many unfavourable conditions, especially the quality of galaxy images on photographs. Let us take spiral galaxies as an example. If the photographs are insufficiently exposed, the arms are invisible. On the other hand, if overexposed, the proportion occupied by the bulge may increase. Moreover, both the size of the bulge and the degree of

MA Jun et al. / Chinese

disintegration

Astronomy

443

24 (tOO0) 435-443

and Astrophysics

of spiral arms into stars depend on the distance.

Now we like to emphasize

that if the spiral arm is clearly seen in a picture, we can determine the pitch angle which expresses the degree of tightness of winding of the arm. This is a characteristic quantity which has nothing to do with distance, and the effect of the inclination of the galaxy can be corrected for. If we use the pitch angle as the criterion of classification of spiral galaxies, then in the classification on distance.

there is only one characteristic

quantity and it does not depend

Of course, the arms of some spiral galaxies are not very clear, and some are

mere “feathery structures”. Nevertheless, as long as the arm possesses some “macroscopic structure”, its pitch angle may be found by fitting. References 1

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