A Method for Estimating the Distances of Extragalactic Radio Sources with Jets Using VLBI B

Astronomy Reports, Vol. 48, No. 9, 2004, pp. 699–704. Translated from Astronomicheski˘ı Zhurnal, Vol. 81, No. 9, 2004, pp. 771–776. Original Russian Text Copyright c 2004 by Komberg. A Method for Estimating the Distances of Extragalactic Radio Sources with Jets Using VLBI B. V. Komberg Astro Space Center, Lebedev Physical Institute, Moscow, Russia Received July 25, 2003; in final form, March 15, 2004 Abstract—A method is proposed for estimating the distances to extragalactic radio sources using spec- troscopic data on the sizes of the broad-line regions of quasars and radio galaxies (RBL)andVLBIdata j on the transverse angular sizes of the radio jets emerging from their nuclei (θ⊥). This approach is based j on the fact that observational data on the transverse linear sizes of radio jets (l⊥) associated with the nearest radio sources and theoretical concepts about the formation of radio jets in the central regions of a j magnetized accretion disk suggest that l⊥ and RBL should be approximately equal. c 2004 MAIK “Nau- ka/Interperiodica”. 1. INTRODUCTION lines [5]: ∼ 0 2 (1) Several methods have been proposed for the LHβ (∆VHβ) . estimation of the distances to extragalactic objects whose spectra do not display strong lines that can be (2) The quadratic dependence of the line luminosi- used to derive their redshifts, or for the estimation of ties on the line widths (i.e., the velocity dispersions) the Hubble expansion of the Metagalaxy. These are provides evidence that the broad lines are formed in all based on the assumed existence of some stan- disklike circumnuclear structures.2 This conclusion dard quantities (luminosity, surface brightness, ve- has recently been supported by data on the masses locity, dimensions, etc.)1 or on the time evolution of of the black holes in the nuclei of nearby galaxies and these quantities. For example, Faber and Jackson [2] quasars (M•). A number of studies (see, for example, constructed a relationship between the luminosities [7–10]) have demonstrated the relations for super- of elliptical galaxies and the velocity dispersions for massive black holes σ 8 bul 4 the stars in them, v, which were estimated from the M• =10 M(σ∗ /200 km/s) , (1) widths of absorption lines arising in the stellar at- ∼ 4 bul mospheres: LEG σv. Tully and Fisher [3] obtained where σ∗ is the velocity dispersion for stars in the an analogous relationship for spiral galaxies based bulge of the host galaxy and M is the mass of the on the width of the 21-cm neutral-hydrogen line, Sun, and which characterizes the rotational speed of the gas 8 2 M• =10 M(∆V1/2(Hβ)/3000 km/s) (2) in the galaxy and the galaxy’s inclination: LSG ∼ 2 × 44 0.5 (vmax sin i) . Relationships between the luminosities (L5100 A˚ /10 erg/s) , of Seyfert-galaxy nuclei in the X-ray (L0.5–4.5 keV) where ∆V1/2(Hβ) is the half-width of the Hβ line and and radio (L400 MHz) and the widths of the Balmer lines in their spectra were obtained in [4]: L5100 A˚ is the optical luminosity. Relations (1) and (2) for galaxies with various luminosities (masses) yield ∼ 0 2 ∼ 0 2 5 9 LXR (∆VH(β,α)) and L400 MHz (∆VH(β,α)) . values for M• from 10 to 3 × 10 M. Sincewehavefromthedefinition of the Keplerian It was elucidated that there exists a similar depen- 2 2 velocity V = GM•/R, it follows that M• ∼ V R; dence between the luminosities and widths of these comparing this relation with (2), it is easy to see that ∼ 0.5 1In [1], it is proposed to estimate the distances to ultralumi- R L . That is, the size of the broad-line region nous IR galaxies based on observations at 450 and 850 µm, (BLR) in the circumnuclear disk, RBL, is proportional since the spectra of these galaxies are “standard,” having 2 their maxima at λ0 ≈ 100 µm. The accuracy of this method Although there are also other points of view; see, for example, is ∼30%. [6]. 1063-7729/04/4809-0699$26.00 c 2004 MAIK “Nauka/Interperiodica” 700 KOMBERG to the square of the luminosity of the ionizing radia- be comparable to RBL = tens of light days [22–25]. tion from the nucleus. These small radio sizes provide hope that evolution (3) Various dependences that can, in principle, be will not play an appreciable role in the cosmological j used to estimate RBL can be found in the literature. dependence θ⊥(z), in contrast to the situation with For example, according to [11–13], the angular sizes of the extended radio structures, RBL(light days) (3a) which are subject to strong evolutionary effects over the course of their long lifetime (∼108–109 yrs). This =(26.1 ± 3.6)(λL /1037 W)0.5 3000 A˚ fact has already been considered in a number of stud- or ies, such as [26, 27], where the dependence θ(z) is RBL(light days) (3b) constructed using the smallest components of the radio jets resolved with VLBI. =(35.5 ± 4.9)(λL /1037 W)0.5. 5100 A˚ In addition, the transverse size of the radio jet j near its base (l⊥) should not depend strongly on the The relation angle between the line of sight and the direction of the M• (4) jet. This is not true of the sizes of radio components 5 3 2 along the jet, which must be corrected for the effect of =10 R (light days)(∆V (Hβ)/10 km/s) M BL 1/2 projection. is given in [14], which, together with (1), can be used to obtain the approximate expression 2. RELATIONSHIP RBL(light days) (5) BETWEEN THE CORE RADIO 3 bul 4 3 2 PROPERTIES AND THE SPECTRAL =10 (σ∗ /200 km/s) /(∆V1/2(Hβ)/10 km/s) . CHARACTERISTICS OF AGN 4 bul Assuming ∆V1/2(Hβ)=10 km/s [15] and σ∗ = (1) The existence of certain relationships between 200 km/s, we obtain the radio properties of the VLBI core components and the spectral characteristics of AGN has already R ≈ . BL tens of light days been noted in the literature. In particular, there have This is in good agreement with estimates of RBL been attempts to identify various types of AGN on derived from the time delays (∆t) between variations diagrams analogous to the Hertzsprung–Russell di- in the ionizing fluxand the onset of variations in the agram for stars (see, for example, [28–30]). Indeed, line profiles: RBL ≈ ∆tc (see, for example, [16–18]). certain trends are visible when AGN of various types For nearby galaxies or quasars, the size RBL ≈ are plotted in a “Principal Component 2 (PC2)– 10 light days ≈0.01 pc can already be resolved by Principal Component 1 (PC1)” plane, where PC1 current optical interferometers, such as the VLTI. reflects the width of the Hβ line (which, according to For example, it should be possible to resolve RBL (2), is related to the mass of the central black hole) for active galactic nuclei (AGN) with z<0.4 when and PC2 reflects the ratio of the equivalent widths ∆θ =0.1 milliarcsecond (mas) and for AGN with (W ) of the Fe 4570 Aand˚ Hβ lines (which is related z =2when ∆θ =0.01 mas [19, 20]. This raises the to the accretion rate m˙ ). The nonthermal radio emis- possibility of estimating the distances to AGN using sion of the core grows relative to the quasi-thermal thevaluesofRBL derived from observations [formula optical emission of the disk as M• increases and as 18 (5)] and data on ∆θBL obtained using optical interfer- m/˙ m˙ Edd decreases (m˙ Edd =1.38 × 10 M•/M g/s ometers. and corresponds for an accretion efficiency η =0.1 38 (4) Even more promising possibilities of this sort to the luminosity LEdd =1.38 × 10 M•/M erg/s). are opened if we consider radio observations, since Thus, AGN that are stronger in the radio (for a given ground-based VLBI, and all the moreso space VLBI, Lopt) should have broader optical lines. This, in turn, −4 −5 can attain angular resolutions of 10 –10 arcsec leads to smaller values of RBL, in accordance with (5). at centimeter wavelengths (for example, in the Rus- This raises the question of whether the sizes of sian project “RadioAstron” [21]). With such angular the BLRs in AGN are related to the transverse di- resolutions, it becomes possible to obtain information mensions of the bases of their radio jets. If these two about the angular diameters of the bases of the radio quantities are related, we can estimate the distances jets ejected by AGN. Indeed, the transverse angular to strong radio sources by estimating RBL from spec- j sizes of the radio jets (θ⊥) of the most nearby ra- troscopic data and deriving the transverse angular dio galaxies (Cygnus A, Perseus A, and Virgo A) size of the radio jet from VLBI data. and some Seyfert galaxies (NGC 4151, for example) What do we find in the literature in connection have been measured using VLBI and have proven to with this question? ASTRONOMY REPORTS Vol. 48 No. 9 2004 DISTANCES OF EXTRAGALACTIC RADIO SOURCES 701 1030 3 l ~ 1029 L 1028 1027 26 2 (W/Hz) 10 l ~ core L L 1025 1024 1023 1022 10–4 10–3 10–2 10–1 lcore(pc) Dependence of the core radio luminosity at 15 GHz (Lcore in W/Hz) on the size of the radio core (lcore in pc), constructed using VLBA data for 160 extragalactic radio sources [33].

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