3 Results

In the monitoring period of 5.5 years, the flux densities of the primary calibrators, 3C 48, 3C 138, 3C 147, 3C 286, 3C 295, and NGC 7027 (and also few other sources, as reported in Sect. 3.2), remained constant as expected at a level of about 2% at wavelength $\lambda \geq 2.8$ cm, and about 3% at $\lambda=1.3$ cm.

3.1 Light curves and source spectra

Light curves for each source are plotted in Figs. 1-20 at the four best observed wavelengths 11, 6, 2.8 and 1.3 cm. In case there are less than 3 data points at a given wavelength, the plot has been omitted. We make brief comments on individual sources in Sect. 4.

Spectra of all sources are presented in Figs. 21-25, by taking all fluxes measured at each wavelength over the 5.5 year monitoring period. Obviously, the flux variations of a source are reflected in its spectrum. Although the reliability of the spectra suffer from flux density variations, it is interesting to note that,

• the spectra of the flat spectrum sources 0153+744 and 1253-055 steepen for $\lambda \leq 11$ cm, and 0735+178 probably steepens for $\lambda \leq 6$ cm;

• the spectra of sources 0316+413 and 0615+820 are inverted at $\lambda \leq 11$ cm, 0212+735, 0454+844, 1641+399, 1928+738, 2007+777 and 2251+158 inverted at $\lambda \leq$ 6 cm, 0917+624 at $\lambda \leq 3.6$ cm, 1803+784 at $\lambda \leq 2$ cm;

• sources 0420-014, 0528+134, 0836+710, 0851+202, 1226+023 and 2105+420 (NGC 7027) have flat spectra at $\lambda \leq 6$ cm, and 0923+392 has a flat spectrum at $\lambda \leq 2.8$ cm;

• through the whole range of observing wavelengths, sources 0016+731, 0235+164, 0716+714, 0804+499, 0954+658, 1039+811,1150+812, 1652+398, 1739+522, 1749+701, 1823+568 and 2200+420 have flat spectra. It is further noticeable that most of the steep spectrum sources are not variable with an exceptionally weak variability for 3C 309.1. In other words, variability is a common phenomenon in the flat spectrum sources. This is consistent with previous evidence that most variable sources have flat spectra (Kellermann 1974; Fanti et al. 1981).

We also investigate variations of the spectral indices, by calculating a two-point power law spectrum (6 cm and 2.8 cm, simply derived from $\alpha_{2.8}^{6} = \frac{\ln(S_{6}/S_{2.8})}{\ln(\lambda_{6}/\lambda_{2.8})}$), for those sources showing correspondingly at least one pronounced outburst at both wavelengths with enough simultaneous measurements (with more than 8 data points) during the monitoring period. As seen from Figs. 26 and 27, the spectral indices ( $\alpha _{2.8}^{6}$) follow the expectations of shock models (Marscher & Gear 1985; Valtaoja et al. 1992; Qian 1996) that shocks propagate from an optically thick to an optically thin regime in each outburst, most evidently seen in sources 0235+164, 0528+165, 0716+714, 0804+499, 0836+710, 1641+399 and 2007+777, so that the variations in these sources were probably intrinsic.

 

  Table 2: Summary of source variabilities at 21 cm. N denotes number of observations during this 5.5 years period, <S> the mean flux in Jy, m the modulation index in % and $\chi ^{2}_{\rm red}$ the reduced $\chi ^{2}$ value (we denote > when the $\chi ^{2}_{\rm red} \ge 100.0$). For the statistical analysis (m and $\chi ^{2}_{\rm red}$), only data sets with N $\ge$ 8 are taken into consideration

Source	N	<S> [Jy]	m [%]	$\chi ^{2}_{\rm red}$
0134+329	6	$16.14\pm 0.21$
0153+744	5	$1.95\pm 0.05$
0212+735	5	$2.38\pm 0.03$
0316+413	4	$27.28\pm 0.27$
0420-014	2	$2.08\pm 0.10$
0454+844	6	$0.28\pm 0.05$
0518+165	6	$8.65\pm 0.09$
0528+134	4	$2.46\pm 0.34$
0538+498	4	$21.76\pm 0.14$
0615+820	5	$0.69\pm 0.02$
0716+714	7	$0.78\pm 0.07$
0804+499	4	$0.97\pm 0.08$
0835+580	5	$2.26\pm 0.02$
0836+710	7	$3.47\pm 0.18$
0851+202	2	$1.14\pm 0.07$
0917+624	5	$1.24\pm 0.06$
0954+658	5	$0.48\pm 0.04$
1039+811	5	$0.76\pm 0.02$
1150+812	5	$1.64\pm 0.07$
1226+023	1	$51.88\pm 0.52$
1253-055	1	$9.32\pm 0.09$
1328+307	6	$14.65\pm 0.05$
1409+524	6	$22.14\pm 0.11$
1641+399	4	$7.54\pm 0.15$
1652+398	3	$1.82\pm 0.04$
1739+522	3	$1.43\pm 0.42$
1749+701	5	$0.79\pm 0.02$
1803+784	7	$2.07\pm 0.17$
1823+568	3	$1.56\pm 0.04$
1928+738	5	$3.95\pm 0.05$
2007+777	6	$0.95\pm 0.16$
2105+420	4	$1.39\pm 0.03$
2200+420	3	$4.39\pm 0.34$
2251+158	2	$14.35\pm 0.74$

 

  Table 3: Summary of source variability at 18 cm

Source	N	<S> [Jy]	m [%]	$\chi ^{2}_{\rm red}$
0134+329	6	$14.00\pm 0.19$
0153+744	2	$2.02\pm 0.01$
0212+735	3	$2.33\pm 0.06$
0316+413	7	$28.79\pm 0.68$
0420-014	2	$2.22\pm 0.30$
0454+844	2	$0.25\pm 0.03$
0518+165	6	$7.76\pm 0.14$
0528+134	3	$2.21\pm 0.05$
0538+498	4	$19.79\pm 0.19$
0615+820	2	$0.75\pm 0.02$
0716+714	5	$0.78\pm 0.11$
0804+499	3	$0.92\pm 0.05$
0835+580	2	$1.93\pm 0.03$
0836+710	7	$3.35\pm 0.15$
0851+202	3	$1.41\pm 0.26$
0917+624	8	$1.27\pm 0.06$	4.6	5.0
0954+658	4	$0.48\pm 0.13$
1039+811	2	$0.73\pm 0.04$
1150+812	2	$1.61\pm 0.13$
1226+023	7	$49.30\pm 1.77$
1253-055	5	$10.01\pm 0.31$
1328+307	10	$13.53\pm 0.11$	0.9	0.2
1409+524	9	$19.27\pm 0.18$	1.0	0.3
1641+399	5	$7.46\pm 0.38$
1652+398	1	$1.80\pm 0.02$
1749+701	2	$0.76\pm 0.02$
1803+784	5	$2.25\pm 0.03$
1928+738	8	$3.92\pm 0.15$	4.0	6.2
2007+777	4	$1.01\pm 0.19$
2105+420	7	$1.87\pm 0.03$
2200+420	2	$3.18\pm 1.10$
2251+158	4	$14.27\pm 0.36$

 

  Table 4: Summary of source variabilities at 11 cm. In the last column we denote > when the $\chi ^{2}_{\rm red} \ge 100.0$

Source	N	<S> [Jy]	m [%]	$\chi ^{2}_{\rm red}$
0016+731	3	$1.35\pm 0.58$
0134+329	24	$9.44\pm 0.09$	0.9	0.5
0153+744	2	$1.86\pm 0.02$
0212+735	3	$2.64\pm 0.24$
0235+164	8	$1.31\pm 0.56$	45.7	>
0316+413	7	$30.37\pm 2.46$
0420-014	7	$2.35\pm 0.08$
0454+844	15	$0.31\pm 0.06$	19.4	>
0518+165	12	$5.71\pm 0.03$	0.5	0.3
0528+134	15	$2.76\pm 0.23$	8.5	26.8
0538+498	4	$13.34\pm 0.04$
0615+820	2	$0.87\pm 0.03$
0716+714	43	$0.64\pm 0.16$	25.1	>
0735+178	2	$2.28\pm 0.01$
0804+499	15	$1.02\pm 0.11$	10.6	47.1
0835+580	8	$1.15\pm 0.01$	0.4	0.2
0836+710	39	$2.60\pm 0.16$	6.2	22.3
0851+202	17	$1.38\pm 0.18$	13.2	94.0
0917+624	15	$1.40\pm 0.12$	8.5	17.7
0923+392	15	$6.01\pm 0.20$	3.5	5.2
0951+699	13	$5.03\pm 0.01$	0.3	0.1
0954+658	20	$0.48\pm 0.11$	23.6	>
1039+811	3	$0.79\pm 0.07$
1150+812	6	$1.56\pm 0.16$
1226+023	4	$45.20\pm 1.79$
1328+307	31	$10.62\pm 0.07$	0.7	0.3
1409+524	20	$12.28\pm 0.11$	0.9	0.2
1458+718	6	$4.71\pm 0.09$
1641+399	7	$8.34\pm 0.22$
1652+398	8	$1.72\pm 0.05$	3.1	3.8
1739+522	9	$1.37\pm 0.51$	39.3	>
1749+701	4	$0.71\pm 0.04$
1803+784	15	$2.34\pm 0.26$	11.5	66.6
1823+568	1	$1.43\pm 0.01$
1928+738	14	$3.91\pm 0.14$	3.6	6.9
2007+777	13	$1.36\pm 0.15$	11.1	79.6
2105+420	30	$3.69\pm 0.04$	1.0	0.7
2200+420	14	$3.71\pm 0.63$	17.6	>
2251+158	5	$13.77\pm 0.46$

 

  Table 5: Summary of source variabilities at 6 cm. In the last column we denote > when the $\chi ^{2}_{\rm red} \ge 100.0$

Source	N	<S> [Jy]	m [%]	$\chi ^{2}_{\rm red}$
0016+731	15	$1.30\pm 0.47$	37.5	>
0134+329	68	$5.53\pm 0.07$	1.2	0.6
0153+744	12	$1.21\pm 0.04$	3.8	6.0
0212+735	14	$3.08\pm 0.19$	6.5	19.3
0235+164	19	$1.19\pm 0.84$	72.3	>
0316+413	29	$25.71\pm 3.19$	12.6	88.3
0420-014	14	$2.75\pm 0.30$	11.5	51.9
0454+844	31	$0.32\pm 0.05$	17.4	>
0518+165	35	$3.79\pm 0.04$	1.2	0.6
0528+134	37	$4.29\pm 1.31$	30.9	>
0538+498	13	$7.92\pm 0.08$	1.0	0.5
0615+820	10	$0.77\pm 0.03$	4.2	6.0
0716+714	74	$0.66\pm 0.25$	37.7	>
0735+178	8	$1.91\pm 0.33$	18.3	>
0804+499	35	$1.00\pm 0.28$	28.4	>
0835+580	30	$0.60\pm 0.01$	1.0	0.4
0836+710	75	$2.12\pm 0.21$	10.2	45.2
0851+202	33	$1.62\pm 0.24$	15.0	78.0
0917+624	45	$1.53\pm 0.09$	5.8	10.1
0923+392	29	$10.98\pm 0.35$	3.3	4.2
0951+699	32	$3.33\pm 0.03$	0.8	0.3
0954+658	39	$0.50\pm 0.13$	26.8	>
1039+811	12	$0.81\pm 0.06$	7.9	22.6
1150+812	14	$1.50\pm 0.11$	7.9	20.3
1226+023	20	$39.48\pm 2.32$	6.0	11.8
1253-055	11	$14.40\pm 2.82$	20.5	>
1328+307	74	$7.49\pm 0.07$	0.9	0.7
1409+524	39	$6.58\pm 0.08$	1.1	0.7
1458+718	10	$3.36\pm 0.16$	5.1	9.6
1641+399	27	$8.47\pm 0.29$	3.4	3.8
1652+398	13	$1.59\pm 0.04$	2.4	2.2
1739+522	21	$1.48\pm 0.48$	33.1	>
1749+701	14	$0.69\pm 0.06$	8.6	22.2
1803+784	40	$2.60\pm 0.23$	9.1	31.8
1823+568	6	$1.64\pm 0.20$
1928+738	36	$3.92\pm 0.16$	4.2	6.8
2007+777	34	$1.39\pm 0.22$	16.4	96.1
2105+420	66	$5.48\pm 0.06$	1.0	0.5
2200+420	23	$3.90\pm 0.89$	23.3	>
2251+158	26	$14.97\pm 1.65$	11.3	49.4

 

  Table 6: Summary of source variability at 3.6 cm. In the last column we denote > when the $\chi ^{2}_{\rm red} \ge 100.0$

Source	N	<S> [Jy]	m [%]	$\chi ^{2}_{\rm red}$
0016+731	6	$1.39\pm 0.40$
0134+329	9	$3.22\pm 0.04$	1.2	0.4
0153+744	1	$0.64\pm 0.01$
0212+735	1	$3.08\pm 0.04$
0235+164	2	$2.48\pm 1.67$
0316+413	21	$24.53\pm 2.39$	10.0	14.0
0420-014	1	$3.00\pm 0.15$
0454+844	5	$0.29\pm 0.06$
0518+165	6	$2.37\pm 0.07$
0528+134	7	$3.49\pm 0.70$
0538+498	5	$4.67\pm 0.19$
0615+820	1	$0.64\pm 0.01$
0716+714	16	$0.82\pm 0.35$	44.4	>
0735+178	1	$2.15\pm 0.03$
0804+499	6	$1.36\pm 0.46$
0835+580	5	$0.31\pm 0.01$
0836+710	19	$1.84\pm 0.41$	22.9	77.5
0851+202	8	$2.01\pm 0.26$	13.9	30.0
0917+624	14	$1.71\pm 0.21$	12.7	29.5
0923+392	11	$13.29\pm 0.41$	3.2	1.1
0951+699	4	$2.12\pm 0.03$
0954+658	8	$0.45\pm 0.16$	38.5	>
1039+811	2	$0.95\pm 0.24$
1226+023	5	$38.79\pm 3.14$
1253-055	6	$14.66\pm 0.57$
1328+307	20	$5.11\pm 0.07$	1.5	0.4
1409+524	11	$3.38\pm 0.04$	1.2	0.2
1458+718	2	$2.55\pm 0.04$
1641+399	11	$8.45\pm 0.44$	5.4	4.3
1652+398	3	$1.53\pm 0.04$
1739+522	4	$1.20\pm 0.62$
1749+701	3	$0.59\pm 0.05$
1803+784	11	$2.51\pm 0.23$	9.5	12.8
1928+738	5	$3.71\pm 0.22$
2007+777	4	$1.31\pm 0.13$
2105+420	12	$6.02\pm 0.12$	2.0	0.3
2200+420	7	$3.17\pm 0.64$
2251+158	3	$13.91\pm 1.05$

   
3.2 Statistical analysis

We measure the degree of variability by deriving the modulation index $m[\%] =100\times \frac{\sigma_{S}}{<S>}$, where < > denotes the mean. To see whether a source is variable, we performed a $\chi ^{2}$ test, $\chi^{2} \equiv \sum (\frac{S_{i}-<S>}{\sigma_{i}^{2}})^{2}$, (similarly to, e.g. Fanti et al. 1981 and Bondi et al. 1996), where the uncertainties $\sigma_{i}$ are a combination of the experimental uncertainties $\sigma_{{\rm e}i}$ and the statistical uncertainties $\sigma_{{\rm s}i}$ at the i-th epoch, i.e., $\sigma_{i}^{2}=\sigma_{{\rm e}i}^{2}+\sigma_{{\rm s}i}^{2}$ (Eqs. (6-1) in Bevington 1969).

Our data were not obtained under identical conditions but rather comprised various observations during such a long-term monitoring period. For each calibrator source, $\sigma_{{\rm s}i}$ is taken to be the standard deviation of the data set during the monitoring period, and for each target source, $\sigma_{{\rm s}i}$ is approximated by taking the value of the $m_{0, \rm max}\ \times <S>$, where $m_{0, \rm max}$ is the maximum of the m₀ (the modulation index of a non-variable source) from calibrators at each wavelength. We take $m_{0, \rm max}$ as 1.0% at $\lambda \geq$ 11 cm, as 1.2, 2.0, 2.3 and 3.1% at $\lambda =6$, 3.6, 2.8 and 1.3 cm, and as 4.6% at $\lambda \leq 9$ mm respectively.

The statistical results (only for data sets with $N \geq 8$ at each wavelength) are presented in Tables 2-11 for all sources at wavelengths of 21, 18, 11, 6, 3.6, 2.8, 2 and 1.3 cm, 9 and 7 mm respectively, with the source name, number of observations, the mean flux density with estimated error, the modulation index, and the reduced $\chi ^{2}_{\rm red}$. Obviously, the statistical results confirm that nearly all sources, with the exception of 0835+580 and 0951+699 and the six primary flux calibrators, are variable at a confidence level of more than 99.95% at most of the radio wavelengths over this 5.5 years period.

  

  Table 7: Summary of source variabilities at 2.8 cm. In the last column we denote > when the $\chi ^{2}_{\rm red} \ge 100.0$

Source	N	<S> [Jy]	m [%]	$\chi ^{2}_{\rm red}$
0016+731	5	$1.37\pm 0.41$
0134+329	37	$2.58\pm 0.05$	2.1	0.6
0153+744	7	$0.58\pm 0.01$
0212+735	13	$3.18\pm 0.28$	9.1	10.1
0235+164	15	$1.83\pm 1.29$	73.0	>
0316+413	13	$22.23\pm 1.13$	5.3	3.3
0420-014	14	$3.31\pm 0.30$	9.3	12.7
0454+844	22	$0.28\pm 0.06$	21.1	49.1
0518+165	28	$2.08\pm 0.05$	2.3	0.5
0528+134	29	$4.84\pm 1.96$	41.3	>
0538+498	6	$3.95\pm 0.08$
0615+820	5	$0.58\pm 0.04$
0716+714	59	$0.73\pm 0.39$	54.0	>
0735+178	3	$1.23\pm 0.30$
0804+499	23	$1.10\pm 0.50$	46.4	>
0835+580	13	$0.24\pm 0.01$	2.0	0.5
0836+710	58	$1.91\pm 0.52$	27.3	>
0851+202	21	$1.82\pm 0.35$	19.9	45.9
0917+624	29	$1.51\pm 0.16$	10.8	9.4
0923+392	20	$13.11\pm 0.42$	3.3	1.5
0951+699	12	$1.87\pm 0.03$	1.8	0.4
0954+658	22	$0.52\pm 0.14$	28.4	90.6
1039+811	11	$1.11\pm 0.08$	7.4	7.8
1150+812	4	$1.51\pm 0.06$
1226+023	6	$34.09\pm 4.03$
1253-055	3	$23.14\pm 6.02$
1328+307	44	$4.45\pm 0.06$	1.3	0.3
1409+524	31	$2.60\pm 0.03$	1.1	0.6
1458+718	12	$2.34\pm 0.17$	7.6	8.4
1641+399	15	$7.96\pm 0.60$	7.8	5.4
1652+398	13	$1.40\pm 0.04$	2.7	0.9
1739+522	14	$1.52\pm 0.63$	43.1	>
1749+701	4	$0.66\pm 0.10$
1803+784	25	$2.70\pm 0.20$	7.4	7.1
1823+568	8	$1.67\pm 0.33$	21.0	62.4
1928+738	17	$3.76\pm 0.25$	6.7	4.1
2007+777	23	$1.34\pm 0.17$	13.2	22.0
2105+420	44	$6.05\pm 0.10$	1.7	0.5
2200+420	20	$4.02\pm 0.63$	16.1	28.8
2251+158	15	$12.03\pm 2.04$	17.6	48.1

  Table 8: Summary of source variability at 2 cm

Source	N	<S> [Jy]	m [%]	$\chi ^{2}_{\rm red}$
0538+498	4	$2.88\pm 0.14$
1409+524	7	$1.69\pm 0.05$
1641+399	6	$7.73\pm 0.52$
2105+420	6	$5.82\pm 0.13$

  

  Table 9: Summary of source variabilities at 1.3 cm

Source	N	<S> [Jy]	m [%]	$\chi ^{2}_{\rm red}$
0016+731	2	$0.66\pm 0.19$
0134+329	10	$1.11\pm 0.03$	2.8	0.4
0153+744	2	$0.42\pm 0.02$
0212+735	3	$2.25\pm 0.28$
0235+164	4	$2.04\pm 1.78$
0316+413	12	$17.23\pm 1.89$	11.4	5.8
0420-014	9	$3.57\pm 0.44$	12.9	3.4
0454+844	6	$0.33\pm 0.13$
0518+165	10	$1.10\pm 0.03$	3.1	0.3
0528+134	14	$4.17\pm 1.58$	39.3	49.5
0538+498	5	$1.91\pm 0.11$
0615+820	1	$0.40\pm 0.02$
0716+714	19	$0.92\pm 0.55$	60.9	92.3
0804+499	8	$1.10\pm 0.33$	32.5	30.1
0836+710	49	$1.74\pm 0.38$	22.2	23.9
0851+202	10	$1.92\pm 0.30$	16.3	9.8
0917+624	10	$1.19\pm 0.09$	7.5	3.2
0923+392	5	$11.13\pm 0.62$
0951+699	2	$1.00\pm 0.06$
0954+658	7	$0.55\pm 0.19$
1150+812	1	$1.06\pm 0.06$
1226+023	3	$34.27\pm 9.55$
1328+307	16	$2.46\pm 0.05$	1.9	0.2
1409+524	12	$0.92\pm 0.02$	2.8	0.3
1458+718	2	$1.42\pm 0.22$
1641+399	10	$7.45\pm 0.75$	10.7	5.4
1652+398	8	$1.13\pm 0.07$	6.5	1.6
1739+522	6	$1.64\pm 0.64$
1749+701	1	$0.62\pm 0.05$
1803+784	12	$2.27\pm 0.12$	5.6	1.5
1928+738	9	$3.27\pm 0.27$	8.8	3.0
2007+777	12	$1.16\pm 0.10$	9.0	3.0
2105+420	22	$5.58\pm 0.10$	1.8	0.2
2200+420	8	$4.00\pm 0.62$	16.5	10.6
2251+158	6	$10.26\pm 3.44$

  Table 10: Summary of source variability at 9 mm

Source	N	<S> [Jy]	m [%]	$\chi ^{2}_{\rm red}$
0134+329	10	$0.81\pm 0.02$	2.2	0.3
0518+165	6	$0.76\pm 0.07$
0716+714	21	$0.88\pm 0.53$	60.9	54.5
0851+202	4	$2.03\pm 0.37$
0917+624	10	$1.01\pm 0.07$	6.9	0.6
0954+658	5	$0.45\pm 0.19$
1328+307	15	$1.92\pm 0.03$	1.7	0.1
1409+524	10	$0.56\pm 0.02$	4.6	0.3
1652+398	4	$1.00\pm 0.03$
1739+522	4	$1.57\pm 0.51$
1928+738	4	$2.73\pm 0.29$
2007+777	8	$1.05\pm 0.16$	16.0	3.5
2105+420	15	$5.25\pm 0.14$	2.7	0.3
2200+420	11	$3.61\pm 0.58$	16.8	7.0
2251+158	3	$8.01\pm 1.14$

 

  Table 11:Summary of source variability at 7 mm

Source	N	<S> [Jy]	m [%]	$\chi ^{2}_{\rm red}$
0134+329	7	$0.55\pm 0.07$
0316+413	4	$11.87\pm 2.51$
0518+165	5	$0.63\pm 0.05$
0528+134	7	$4.39\pm 1.76$
0716+714	6	$0.92\pm 0.53$
0804+499	5	$1.08\pm 0.30$
0836+710	25	$1.63\pm 0.32$	20.2	7.7
0851+202	5	$1.52\pm 0.35$
1328+307	7	$1.49\pm 0.03$
1409+524	5	$0.44\pm 0.08$
1641+399	6	$6.79\pm 0.74$
1803+784	5	$1.89\pm 0.27$
1928+738	4	$2.86\pm 0.32$
2105+420	10	$5.01\pm 0.22$	4.6	0.3

3.3 Variability dependence

We investigate whether there is any dependence of the degree of variability on either source galactic latitude ( $b^{\rm II}$), redshift (z), spectral indices ( $\alpha _{6}^{11}$ and $\alpha _{2.8}^{6}$ only), or superluminal motions by taking the modulation index of each source at 6 cm, where the sources have been observed most frequently.

As shown in Fig. 28, there is no obvious dependence of the degree of variability on most of the above mentioned quantities. This is confirmed by the formal estimates of the correlation probabilities (coefficients are less than 0.26) of these relationships with an exception, that is a weak correlation (coefficient is 0.48) between the degree of variability and the 6 to 2.8 cm spectral index. Both the degree of variability and its rate of occurrence appear to be higher when the source spectra are flatter. This is consistent with previous findings: sources with flat spectra are small, and are variable, while sources with steep spectra are less variable (Heeschen et al. 1987). Furthermore, there is a trend showing that the degree of variability decreases with increasing wavelength, as seen in Fig. 29 by taking only the derived m of the common 16 sources at the four wavelengths of 11, 6, 2.8 and 1.3 cm, which has been shown in other variability studies (e.g. Peng et al. 2000). The maximum values for m are derived to be 25.1, 37.7, 54.0 and 60.9% respectively at the four wavelengths sequenced above. This is contrary to the expectations of the interstellar scintillation (ISS, e.g. Rickett 1990), but in favor of shock models (e.g. Marscher & Gear 1985).