Luminosity evolution of quasars

KIf."URA and LIU / GONG and XIA

18

at least two different types, silicates and iron compounds. The above results are preliminary, and further studies are required to ascertain the true dust model of the solar system. The function f(v) discussed in the paper, should be useful particularly in clarifying the above two-componentmodel.

drawn according to the two-component model proposed by Oishi et al. [lo] on the basis of near-infrared polarization and photometric observations of C/West. Although that model was simplified, it qualitatively agrees with our findings. Recent studies of other dust particles in the solar system, for example, the zodiacal light observation [ll] also showed the necessity for a bimodal distribution, andBrownlee [12] pointed out that dust particles directly sampled from space contain

ACKNOWLEDGEMENT We thank our colleagues in the Computing Division of the Purple Mountain Observatory for assistance.

REFERENCES

t11 KIMURA Hiroshi and LIU Cai-pin, Chin.Astron.I (1977) 235-264. Original in Act.Astron.Sin. 16 (1975) 138-166. [21

Finaon, M. L. and Probate&

131

Hagam,

r41

Ceplecbs, Z., PubI. Czech. Astr. Inst., 84(1958),

W.

R. F.. Ap.

Richter. N.,

and

E. p. and Merrill.

I31

Ney,

[31

&?kauin% Z. and Miller,

F.

I71

Lillie. C. F. end Keller,

H. U., in “The

[31

Meisel.

D.

D.

r91

Jscchia, L. Q., Skg

and

[lOI

Oili.

Y.,

R.

1111

G&e,

R. II.

Okuda,

Brownlee.

D.

1976,

E.,

D..

Tel.,

in

47Q974).

327,

Atlas

Springer-Verlag,

1960.

1061.

179(1973), Study

“The

363.

OP Corn&“,

36.

194(1976),

B&we,

C. a.,

and

and Griin. E.,

Pbyaics. No. 46. 1121

F., D.. ~&OS,

and Morris,

J>54(1963),

‘ ‘Isopbotometric

665.

of

Stati

Comets”, of Comets’:

NASA

SP-393,

NASA

1976,

f@393,1%‘6,

323. 410.

216.

Wickrarnssingbe,

N. C., Ptlbl.

in “Interplanetary

Dust

A.&.

Sot.

and %&seal

Japor, light“,

39(1978).

161.

Lecture Notes

in

135.

in “Comnic

Dust”

ed. bs J. A.

M. McDonnell.

John Wiley

b- f3oone.1978,

295.

Pergamon Press. Printedin Great Britain 0275-1062/83/010018-07$07.50/O

Chin.Astron.Astrophys.7 (1983) 18-24 Act.Astron.Sin.23 119821 243-254

LUMINOSITY

EVOLUTION

GONG Shu-mu,

OF QUASARS

XIA Chang-li*

Purple Mountain Observatory

Received 1981 November 30

ABSTRACT Based on four previous studies with standard-candlequasars and using the correct formula for the luminosity distance, we obtain an improved determination of the deceleration parameter, o - +2.07. From the new catalog of quasars, we find the statistical Bila s--.a relation and hence the mean quasar luminosity ??(a)or z(t) and its rates of change &Uz)/ds and cB(tJ/dt. Finally, we discuss the question whether there is a Malmquist effect in our sample and the question of the dichotomy of published qg-values.

1. INTRODUCTION The theory of universal expansion began with Hubble's proposal that the spectral redshift, interpreted as a doppler recession, increased linearly with distance [l]. At present, the most widely accepted model of expanding universe is the Friedmann model. This contains

two parameters, the Hubble constant Ho and the deceleration parameter, q . Observations over many decades have reduce3 the value of Ho by about a factor of 10, but because of differences in the data and reduction methods used, some authors have given

*Colleague LI Jie participated incomputingand graphics.

Luminosity Evolution

X,=55 km/(sec.Mpc), [2], some, 95-100, [3], and some, 75 [4]. We shall adopt the last in the present paper. A change of +25(-25) in Ho will alter the absolute magnitudes of quasars by +0!%5 (-Om88); but, as will be shown below, this will have no effect on the rate of evolution. There is a wide divergence in the value of 90 by previous authors [S]. The early determinations generally came from the apparent magnitude - redshift diagram (or Hubble diagram) of galaxies. Since the magnitude-redshift curves for different q. become distinguishable only at large z, recent determinations have mostly used quasars ever since these were found in the 60’s to possess large reshifts. But this brought in a serious difficulty, namely, the dispersion in the quasar luminosity is so large that their Hubble diagram scarely shows any obvious Apart from the large dispersion, relation [6]. the quasar luminosity may also undergo evolution [7] in the sense of a decrease with decreasing z or increasing time. The featurelersness of the Hugble diagram of quasars is therefore not surprising. Our observational data consists of only the apparent magnitudes and redshifts of quasars, and to determine the unknown qo and quasar evolution from these, an iterative method with successive approximation has to be used. To simplify the problem, many authors used some feature or other to pick out subsets of quasars possessing a standard candle so as to get a more satisfactory diagram. The criteria used include strong radio emission [8], greatest optical brightness [9] and the optical soectral index (101. A In China, authors have used subsets consisting of double radio sources [Ill, strong-scintillation radio sources [12], compact radio sources, [I33 and quasars with small amplitudes of light variation to In these works construct the Hubble diagram. a second-degree approximation to the rigourous formula for the luminosity distance has been used, hence the value of qo they found should only be used as the basis for an optimal This will be fully explained determination. by the actual example in Section 2. In Section 3, we shall take the 1500 or so quasars in the catalog of Hewitt and Burbidge, [15], apply the various magnitude corrections, and sort them into 36 z-bins of size Az=O.l. We shall find the mean apparent magnitude R(z) in each bin and then fit the mean values with a quadratic curve by least squares. In Section 4, using the adopted value of Ho and the qo value obtained, we shall then obtain the quasar luminosity evolution ?ZfzJ and 19(t), and their gradient. In Section 5, we shall compare our qo and &Ifs) with results obtained by other authors and discuss the question of Malmquist bias [16].

of Quasars

19

2. DETERMINATION OF IMPROVED q ON THE BASIS OF PREVIOUSRESULTSUSINGSTANDIRDCANDLES a)

The Hubble Relation for Quasars with Luminosity Evolution In the general case we have. Z(a) - a(r) - 5 +

51qdL,

where fAfzJ and Z(z) are the mean apparent and absolute magnitudes of quasars at redshift z, d, is the luminosity distance in units of parsecs. In the Friedmann model, after the universe became matter-dominated, the deceleration parameter q. must necessarily be greater than zero. The correct expression for the luminosity distance is then, [17], 6. -

-&{zqo + (so- 1)(-l

where c is the velocity b)

+

A-=zL

(21

of light.

The Hubble Relation for Quasars with a Standard Candle This is

Z(z) - M - 5 + 51og iof

- a + Slo!gf(E), (3)

in which M is the constant absolute magnitude representing the standard candle, and a is hence also a constant. When the standard candle method is used in forcing a fit of the Hubble relation, the luminosity distance in the expression cannot in general be put in the correct form (2), rather, it is often written in the approximate form of a quadratic in z, &H_”‘v z + 1~1 _ qo)ea - f(s). c 2

(4)

This form was usedinthe four papers [ll-141. It is suitable only for small z, e.g. 2~0.3 The observed values of z may be as large as 2~3, hence the magnitude-redshift relation of quasars formed through (3) and (4) cannot give a reliable determination of qo. But we can use the results obtained to find an improved value. The reason is as follows: there is an intrinsic dispersion in the quasars luminosities, i.e., the absolute magnitude M of quasars at the same z has a certain distribution, &CM), and there is also an evolutionary effect, M(z), for the quasar luminosity at different z. That standard-candle quasars show an approximate Hubble relation, is because, on one hand, their $zfM) at different z have more or less the same form, such as found in Ref. [7(3)], although possessing a finite spread, and on the other hand, the evolution M(z) is unidirectional along z and is comparatively Under these circumstances, smooth and slow. we can regard the constant M in (3) as an average value, B&1, at the average redshift of the quasars of the subset.

20

GONG and XIA

Substituting R&J into (1) and (3), and using (2), we can obtain’ an improved determination of qO, for the quantity Wr(Z) -a *equal to -

lq$d~ c

logQqo+(qa4:

magnitude at the appropriate Z of each subset, calculated from the value of a, and using Ho= 75 km/sec.Mpc. In column qo, values obtained with the approximate formula (4) are shown in brackets, to distinguish them from the values obtained here. If we now plot the Bi’Z,J against Z for the four as in Fig. 2, then the four points subsets, show rather well the decrease in the mean luminosity with decreasing redshift. This suggests that the subsets constitute a

1) (51 C-1

+ 4Gz.F))

-

log j(Z),

The left side of (5) uniquely determines qo. represents a series of curves for different q -values, and the right side is the logarithm OF the f(Z1found for the given standard-candle subset of quasars, the latter should fall on the curve of the sought-for q. at Z. In Fig.1,

.

1.0 3!

i

/qo=o.s

.

0.9 0.8 0.7

;I

_j/,

0.6

-242

-24.4

-24.6

-24.8

M(i)

Fig.

2

Average 2 and 8&J from four quasar subsets.

unified whole. We can thus regard the members of each subset to be members of one whole set, and we get a final improved qovalue by taking a weighted average of the four values, with weights equal to the sample size n: we obtain q0=+2.07f0.12.

3. THE %&-RELATION FROM THE HEWITTBLJRBIDGEQUASAR CATALOG First we converted the equatorial coordinates in the catalog [15] into galactic coordinates and applied the correction for interstellar absorption according to the formula given in

a

Fig.

1

The log (Hod,/cl-curves various q. values

for

[181, A. - 0.165(1.192 - tan].9’]+]9’],

a series of loglHOdL/c)-curves for q0=1/2,1,2, ...10 are drawn, also the three f(z)-curves of Refs. [ll-141 - Refs [ll] and [12] give the same curve, but have different z values, hence give two points of intersection. The values of q. at the observed Z-values, found in general by interpolation, are shown in TABLE 1. In this TABLE, n is the number of objects in the subset, M(Z) is the average absolute TABLE 1

Imoroved

Value

(6)

This formula applied only for I$] 550’; for 141 > 5o”, A,= 0. We then made the K-corrections. In [191, the authors have given a rather complete set of K-corrections depending on spectral type, but as no spectral types are given in of

on from various

Subsets

Luminosity Evolution of Quasars

21

20 t

16

0.95

1.45

1.95

z

Fig. 3 TABLE 2

,.,,I,,,,),,, 2.45

2.95

3.25

Average apparent magnitude if;) of quasars

Average Apparent Magnitude m of Quasars in Each AZ= 0.

-

-

-

-

n

Iii

(1)

(3)

(4)

(1)

0.05

20

16.58

1.82

1.15

39

la.55

0.15

36

17.45

1.57

1.25

42

la.54

0.25

36

17.54

1.32

1.35

44

la.43

0.35

67

17.82

1.13

1.45

53

18.44

0.45

38

la.25

1.13

1.55

42

la.84

0.55

39

18.12

1.13

1.65

30

18.69

0.65

45

la.17

1.09

1.75

39

la.99

0.75

30

18.14

1.08

1.85

53

18.78

0.85

42

la.20

0.79

1.95

81

18.71

0.95

40

la.42

0.90

2.05

78

la.94

46

la.47

0.81 -

2.15

-

-3

n

I

-

-

0

-

69

--

Fii -

0

z

(4)

(1)

1.03

2.25

57

0.92

2.35

1.10

2.45

0.89

-

(3)

i-

Interval

-

(2)

z

1.05

_1 t

1!111,1!1/11!11,,!,, 0.45

19.24 -

n

0

5

_-

-is-

(4)

19.27

1.01

40

19.14

0.86

18

19.28

1.06

2.55

10

19.05

0.61

0.88

2.65

15

la.99

1.20

1.12

2.75

11

la.19

1.09

1.12

2.85

12

18.98

0.76

1.02

2.95

4

19.26

0.87

0.99

3.05

4

la.39

0.38

1.14

3.15

a

19.41

0.99

0.96 -

3.25

5

la.95

0.88

our source data [15] we had to use the of 1193 quasars in 33 bins between a=O.OSaverage values over the spectral types. We 3.25 were used in this plot, (the last three then put the 1500-odd quasars into 36 z-bins bins had either one or none each). TABLE 2 each of width Az=O.l, centered at the gives, for each of the 33 bins, its central values 0.05, 0.15,...3.55, and found the a-values, the sample size n, m(z) and the average value BilZlin each bin. standard deviation u. K(z) is the average Ref. [15] contains various notes relating value of m=mV-AV- K,, mv being the magnitude to the catalog quasars, in particular, a) given in the catalog f151, and A,, Kv the asterisks mark those with variable optical absorption and K-corrections. components, b) where no (U-B) or LB- VI was The points in Fig. 3 appear to lie about a given, the V magnitude, given to 0.5, was quadratic curve. A least-square fit to a estimated from Sky Survey prints, and may have second-degreepolynomial gave, errors up to O'?S- lm0, c) redshift values shown nt -(I) - 17.32 + 1.350~ - 0.271z', (7) in brackets represent uncertain emission line Applying transformed linear regression values. To avoid too large a scatter in our m(z) -z analysis gave for (7), a correlation diagram, we first discarded all quasars with coefficient r= -0.549, a mean residual s =Om29. The correlation is significant since, for ($1< 20°, to avoid the effect of large interstellar absorption correction on iii(z). n= 33, the threshold value for significance at 1% is 0.499. We then discarded, one at a time, quasars under the headings a), b), c) above, and plotted three iii(z) - .adiagrams. We foundtheone 4. THE MEAN ABSOLUTE MAGNITUDE OF QUASARS AND after discarding c) to be the best, showing ITS RATES OF CHANGE WITH RESPECT TO a AND t the smallest dispersion. This one is shown in Fig. 3. The number of objects in each Having determined the value of 4 and the z-bin are beside the points plotted. A total second-degreeexpression for m(z9 at (7), we

GONG and XIA

22

can use (1) and (2) to give j&r)- 17.32 + 1.3502-0.271s'-25 - 5log-IHO (8)

5.

and hence &lzl/dz. Using the relation between z and t for the case qo>1/2,

Hd - &qo - 1)-M(e- sin&,

we find fi;l(tl dii(r) -I--.

dt

(9)

and

dii(r)

(11)

da

With q= +2.07, H =75 km/sec.Mpc inserted into (8) - fll), the calculated

TABLE 3

values of B(z), t(z),dHl(zl/dz, and are tabulated in TABLE 3 with z as argument. &'(z)is also shown in Fig. 4, where both z and t are marked on the abscissa. The values of dWzl/dt and &(tl/dt are plotted in Fig. 5. c&(z)/dt

DISCUSSIONS

1. To check whether our sample has the Malmquist-effect (the tendancy of including more luminous members at larger distances or z), we repeated our calculations of &fzl using the brighter half in each z-bin, and the ten brightest members in each bin, respectively. These two curves are also shown in Fig. 4. Compared to the whole-sample curve, the brighter-half-samplecurve is brighter by about I?0 in the range ~~0.4, and the difference decreases with increasing z, until at z=3.2, it is Om6. This shows that the Malmquist effect exists, but it is not too serious. As to the "top ten" curve, it is about 0?5 brighter than

_1

The Mean Absolute Magnitude of Quasars and its Evolution d+

z

-(1)

(2)

0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8

ma* -21.76 -22.91 -23.50 -23.86 -24.12 -24.32 -24.49 -24.64 -24.78

-

(3) (4) (5) mag (’l0.Y) mgpo y -8.94 4.23 1.34 -3.83 3.19 0.94 -2.24 2.52 0.82 -1.51 2.06 0.78 -1.21 1.72 0.78 1.48 -0.91 0.82 -0.78 1.28 0.90 1.12 -0.72 1.03 1.00 -0.69 1.21 -

(1)

‘wz) (2)

ma*

2.0 2.2 2.4 2.6 2.8 3.0 3.2 3.4

-24.92

-25.06 -25.21 -25.36 -25.52 -25.70 -25.89 -26.09

1

_-

(3) m=g -0.69 -0.72 -0.75 -0.80 -0.85 -0.92 -0.99 -1.06

(4) (5) 'IO'Y) mag/lO Y 0.89 1.46 0.81 1.79 0.73 2.20 0.67 2.72 0.62 3.36 4.13 0.57 0.53 5.04 0.49 6.11 I

:

-26

4.2 0

Fig. 4

t (X10’ Y) 2.6 1.7 1.3 1.0 0.81 0.67 0.57 0.4Y 0.4 0.8 1.2 1.6 2.0 2.4 2.8 3.2

Mean Absolute Magnitude of quasar! as a function of either z or t. 1. The whole sample, 2. the brighter-half sample. 3. the ten brightest members in each z-bin).

Luminosity Evolution

. _ dzf? -27

0

d&t

dl

0

0

0

Fig. 5

Rate of change of quasar. with respect to z (filled or t (unfilled circles).

luminosity

circles)

the “brighter-half” curve in the region ~51.5, but as z increases, the sample size in each bin decreases and the difference rapidly diminishes, until at z=2.6 and beyond, the sample size in each bin becomes less than 20, and the “top ten” curve falls below the “brighthalf” curve. 2. The value of 40 is very uncertain, as already stated in [S]. Recent determinations also show a scatter because of differences in the method used. Using Ho=50 and the age of the universe as inferred from globular clusters gives q0=0.03-0.2, [21]. From the Hubble diagram of galaxies, not considering evolution, one gets 40=1.6- 2.1, [22]. Turner [23] applied a method of ordered statistics to 119 3CR and 4C sources, not assuming any standard candles but assuming the form of the luminosity function to be the same at all z, found that either 90 is between 2 and 32 with a most probable value at 5 or there is a strong luminosity evolution. In this paper we considered the quasar luminosity evolution and found an improved on = 2.07. The determined values of 90 fall roughly into two classes: the age of the universe or the mean cosmic density give small values ~0 =0.03%0.2, while the Hubble diagrams of galaxies and quasars give large values, 40 >l. How are we to explain this discrepancy? To explain away the small value inferred from the mean density, we can invoke “missing mass” in the form of galactic halos,

of Quasars

23

intergalactic matter, or the rest-mass of neutrinos. But the age of globular clusters is based on a vast quantity observational data and the theory of stellar evolution, so it cannot be too far out. Hence, we must wonder whether the Friedmann model gives a true representation of the actual universe. From the statistics on the X-ray luminosity and redshift of quasars, Segal [24] believes that the chronometric model fits the observations better than the Friedmann model. However, the data used was not large, containing only 49 quasars, the method of treatment was fairly rough and evolutionary effect was not considered. It seems that further analysis of more and better data is required to decide on the correct model of the universe.* *Translater’s Note: The rest of the paper is concerned with a detailed comparison with some reults obtained in Refs [25-291. Becauses it makes heavy references to papers of which English translations are not generally available, it seems better to omit the translation at present. REFERENCES VI

PI r31

[41

[81 PI

1101 t113 WI

Hubble, E. Proc. Nat. Acad. Sci., -15 (1929)) 168. Sandage, A. “Galaxies and Universe”, 1975, 783. 1) Bergh, S. Van den, “Galaxies and Universe”, 1975, 534. 2) Vaucouleurs, G. de, Bull. Amer. Ast. 12(1980), No.4. Sm., 3) AarGson, M. et al., Ap. J., 229(1979) 1. 1)

Obs. Hanes, D. A., Anglo-Australian Preprint, No.40 1980. 2) Stenning, M., Hartwick, F., A. J., -85 (1980)) 101. and Cosmology”, Weinberg, S. “Gravitation 1972, 449. Sandage, A., Ap. J. 178(1972), 25. 1) Gott III, J et al., Ap. J., 194(1974), 543. 2) ZHOUYou-yuan, et al., chin. Astmn. 2 (1978) 147. Original in Acta astron. %&a, 18(1977) 113. 3) ZHlJBao-yu and LI Ze-qing, A&z Astrophys. Sinica, l(1981) 106. Setti, G., Woltjer,~L., AP. J. Lett., 181(1973), L 63. FBahcall, J. N. et al., Ap. J. 179 11973). 699. 2) B&ridge, G., O’Dell, S., Ap. J., -183 (1973), 759. Netzer H. et al., M.N. 184 (1978) 219. L(1977) FANGLi-Zhi et al., Chin?iAstron.. Original in Actu astron. sm., 278. -17 (1976) . . 134. QU Qin-yue et al., chin. A&r. 4(1980)97. Oriainal in Actu. Astr. Sin.. 2b(1979)98.

24

P31 u41 V51

[201

GONG and XIA / DING et al

Sandage, A., Tamman, G., Ap. J., 197 (1975) 265. 1) Kristian, J., Sandage, A., Westpahl, L .> APP. J.. 221(1978). 383. 2) Meinel, k., A.‘N.,'302(1981) 170. zwitt. A., Burbridge, G., "A Revised Turner, E., App. J., 230(1979) 291. Optical Catalogue of Quasi-Stellar f2243iSegal, I., Segal, W., Proc. Nat. Acad. Objects", 1980 Publ. Kitt Peak Nat. Obs. Sei. U.S.A., 77(1980), 3080. Malmquist, K. Arkiv., Mat. Ast. 24(1979) 1123. [251 SUN Kai, KemeTongbao Fysik, 16(1921) No, 23. SUN Kai, Actu Astrophys,Siniea L(1981) Mattig,x., A. N., 284(1958), 109; _285 [261 97. (1959) 1. CA0 Sheng-lin et al., KelcueZ'ongbao20 [271 Sandage, A., Ap. J. 178(1972) 1. (1980) 937. XIAO Xing-hua et al.Ckin. Astron. BIAN Yu-lin et al., Keme Tongbao 21 [281 Astrophys. S(1981) 174. Original in (1981) 159. Acta Astron, Sin., 21(1980) 368. HU Fu-xing Chin. !lstron.Astrophys., 6 Weinberg, S., "Gravitation andCosmology" [291 (1982) 93. Original in Aeta Astron. ?%z. 1972, 482. L(1981) 1. [211 ZHANG Fu-jun, Acata Astr. Sin., -21 (1980) 7. YANG Lan-tian et al., Acta astron. Sin., [221 21(1980) 208.

Chin.Astron.Astrophys.7 (1983) 24-30 Aet.Astron.Sin. -23 (198Zl 287-298

PEAK YEARS

OF VARIOUS

Ding You-ji,

SOLAR

Luo Bao-rong,

Pergamon Press. Printed in Great Britain 0275-1062/83/010024-07$07.50/O

CYCLES Feng Yong-ming,

Yunnan

Observatory

Received 1978 June 5

ABSTRACT Using more extensive data than before, we have verified the ll-year, 60-year and c250-year periods in solar activity and identified the peak years of these cycles.

1.

INTRODUCTION

China is the country with the longest history of solar observations and recordings. There were already sunspot records as early as 700 years B.C., anticipating other countries by some one thousand years. Since 1975, the Ancient Sunspot Team of this Observatory, based on the previous labours of ZHU Wen-xian [l] and CHENG Ting-fang [2], have collected and tidied up 112 sunspot records from our dynastic annals, inquired into solar cycles in the past [3] and found possible periods of 10.60+0.43 y, 62.2k2.8 y and -250 y. The first agreed with the llyear cycle established by modern observations. Later, DING You-ji and ZHANG Zhu-wen also discussed in depth the question of stability of the ll-year cycle, [4]. Recently, the Chinese History of Astronomy Group have collected and put to order a total of nearly 300 old records of sunspots from both dynastic annals and local gazetteers, thus

greatly enriching this treasure-house of historical data. We have now used this extended material in an auto-correlation analysis and further confirmed our previous conclusions reached in [3]. We have also used the records of large naked-eye sunspot groups to fix the possible peak years of the various periods in the past. 2.

VARIOUS POSSIBLE PERIODS OF SOLAR ACTIVITY

A total of nearly 300 records of naked-eye sunspots between 781 B.C. and 1918 A.D. has been collected and tidied up by the Chinese History of Astronomy Group. A few of these lacked the year of observation and these we did not use. All the others belonged to 171 different years within a span of one thousand nine hundred and sixty-one years (43 B.C. - 1918 A.D.). We take the time distribution X(t) of the large susnspots to be a discrete time series of a random process. Its autocorrelation function is then