MODELO 1 SISTEMA DE POTENCIA CLÁSICO DE 3 NODOS

2.4 ULIRG stellar velocities and black hole masses

The stellar dispersions extracted (according to the prescriptions of § 2.2) by the Fourier quotient technique from the central-aperture spectrum of each source are listed in Table 2.3. In the fainter sources, σ may be somewhat overestimated (at most by 20%) due to low signal-to-noise ratio, which can mimic broader dispersions. The stellar velocity dispersion may vary when measured from different bandheads (typically by 15%). This is both due to a possible template mismatch and to the sky-line contamination of our spectra. The velocity error bars are equal to the standard deviation of the measurements performed at the individual bandheads.

The mean observed dispersion of our binary ULIRG sample, combined with the sources in Genzel et al. (2001), is 142 km s−1 _{(with a standard deviation} of 21 km s−1 ). Sources of intrinsic nuclear separation close to or less than 1 kpc (Arp 220 and NGC 6240, see Genzel et al. 2001, Tecza et al. 2000 ) were removed from the above statistics. By the time the nuclei of two merging galaxies are separated by .1 kpc, the stellar velocities have almost reached their final relaxation values (Genzel et al. 2001, Mihos 2000, Bendo & Barnes 2000). As a consequence, these systems have dispersions very close to their (common) equilibrium value and resemble more the coalesced ULIRGs, despite the fact that their nuclei can still be resolved.

We measure the rotational velocity along each slit and we correct it for the angular deviation φα from the major axis of rotation as discussed in § 2.2. After averaging the results over the slits, we obtain the observed rotational velocity, Vrot(obs), which we display in Table 2.3 together with its error bar (calculated similarly to that ofσ). In the same Table we also present the final, inclination corrected rotational velocity Vrot.

The ratio of the observed rotational velocity to the dispersion, Vrot(obs)/σ, is given in Table 2.3 for each source. The meanVrot(obs)/σratio for the sam- ple presented in this study is 0.42, while when using the inclination corrected velocity, the ratio Vrot/σincreases to 0.77. Both values are low compared to those of spiral galaxies. We now investigate whether this result is due to the violent relaxation process or due to systematics, such as beam-smearing ef- fects. To check for beam smearing we calculate theVrot/σratio for the sources for which we have been able to derive rotation curves (due to their large ra- dial extent). These are the sources with z<0.07 as well as IRAS 20046-0623. We find that theVrot/σratio for these sources is similar to that of our entire sample: 0.58 and 1.16 when using the inclined-disk and inclination-corrected velocities, respectively. We conclude that the low rotational velocitites ob- served in the binary ULIRGs is due to the actual dynamical heating of the merging systems. Similar conclusions are drawn from the work of Mihos

(2000), who presents simulations of the velocity moments during the merger process. The Vrot(obs)/σ ratio implied from Mihos (2000) for our median nuclear separation (5 kpc) and for the radius containing 50% of the stellar mass (or the Reff for constant M/L within the galaxy) is also∼0.4.

Using the stellar dispersions listed in Table 2.3, we estimate a BH mass,

MBH, with the aid of the MBH−σ relation (e.g. Gebhardt et al. 2001; Fer- rarese & Merritt 2001). The published estimates for the slope of the MBH−σ relation span a significant range (see Tremaine et al. 2002; Gebhardt et al. 2001; Merritt & Ferrarese 2001). We use the Tremaine et al. (2002) expres- sion MBH = 1.35×108(σ/200)4.02M which lies between those of Gebhardt

et al. (2001) and Merritt & Ferrarese (2001). We present the BH mass cal- culated for each source in Table 2.3. The mean black hole mass of the binary ULIRG sample is an order of magnitude greater than that of the Milky Way and equals 3.9×107 _M

(for each nucleus). Converting the stellar dispersions

into black hole masses carries the uncertainty of applying the MBH−σ rela- tion to systems that are not in dynamical equilibrium. The errors introduced by this conversion and the conditions under which the MBH−σ relation may provide an accurate estimate of MBH during a merger will be presented in a forthcoming paper (Dasyra et al. 2006, in preparation).

In Table 2.3 we present the (minimum) black hole mass that each source would have, if it were accreting at the Eddington rate (LEddington/L =

3.8 ×104MBH(Eddington)/M). We assign to the Eddington luminosity LEddington half of that emitted in the IR (Genzel et al. 1998; Sanders & Mirabel 1996). This is a statistically plausible assumption based on the fact that some ULIRGs are largely AGN- while others are starburst- powered (see Genzel et al. 1998; Duc et al. 1997; Lutz et al. 1999). However, for individual sources, the numbers given in Table 2.3 may be higher up to a factor 2 or much lower. We assign the luminosity to each nucleus according to the K-band luminosity ratios (Kim et al. 2002; Duc et al. 1997), under the assumption that both progenitors have a BH. To distribute the luminosity between the two nuclei of IRAS 12071-0444 and IRAS 21329-2346 we used the

H-band count ratios (1.23 and 2.17 respectively; also see the Appendix) since no photometric information on individual nuclei was available in the literature. For the sources of apparent nuclear separation < 0.700 we distributed 50% of the luminosity to each nucleus, since we used pixel masking (that affects the number counts) to deblend the progenitors. The ratio of the Eddington to the dynamical BH mass, the Eddington efficiency ηEdd, is given in the last column of Table 2.3. On average, it is 0.34 for the individual nuclei, which implies that at the pre-merger phase the accretion onto the BH is lower than the Eddington limit.

2.4 ULIRG stellar velocities and black hole masses

Table 2.3: Stellar velocities and resulting black hole masses.

IRAS source σ Vrot(obs)a Vrotb Vrot(obs)/σ MBH MBH(Edd.) ηEdd

(km s−1) (km s−1) (km s−1) (M) (M) 00199-7426 137 (±55) 30 (±13) 76 0.22 2.95×107 2.23×107 0.76 01166-0844(s) 156 (±61) . . . 4.97×107 7.31×106 0.48 01166-0844(n) 116 (±58) . . . 1.51×107 6.79×106 0.14 02364-4751(s) 151 (±32) . . . 4.36×107 _8.28×106 _0.19 02364-4751(n) 100 (±32) . . . 8.32×106 8.28×106 0.96 06035-7102(sw) 136 (±24) 41 (±13) 52 0.30 2.86×107 5.61×106 0.20 06035-7102(ne) 125 (±16) 14 (±15) 17 0.11 2.04×107 1.17×107 0.57 10190+1322(ne) 169 (±35) 107 (±17) 143 0.63 6.86×107 _7.69×106 _0.11 10190+1322(sw) 127 (±12) 105 (±42) 159 0.83 2.18×107 5.47×106 0.25 10565+2448(s) 125 (±31) 134 (±23) 446 1.07 2.04×107 1.38×107 0.68 10565+2448(n) . . . . 11095-0238(ne) 147 (±32) . . . 3.92×107 1.04×107 0.27 11095-0238(sw) 137 (±38) . . . 2.95×107 1.04×107 0.35 12071-0444(s) 143 (±36) . . . 3.50×107 _1.32×107 _0.38 12071-0444(n) 130 (±29) . . . 2.39×107 1.62×107 0.68 12112+0305(sw) 133 (±10) 34 (±19) 107 0.26 2.62×107 1.53×107 0.58 12112+0305(ne) 124 (±23) 5 (±18) 6 0.04 1.98×107 _9.81×106 _0.50 13335-2612(s) 175 (±43) . . . 7.89×107 8.25×106 0.10 13335-2612(n) 140 (±27) . . . 3.22×107 6.86×106 0.21 13451+1232(w) 167 (±48) . . . 6.54×107 1.75×107 0.27 13451+1232(e) 146 (±28) . . . 3.81×107 _7.57×106 _0.20 16156+0146(n) 189 (±27) . . . 1.08×108 9.22×106 0.09 16156+0146(s) . . . 5.21×106 . . . 16300+1558(s) 141 (±47) . . . 3.31×107 _2.81×107 _0.85 16300+1558(n) . . . . 19254-7245(s) 175 (±24) 99 (±22) 135 0.57 7.89×107 9.16×106 0.12 19254-7245(n) 120 (±19) 47 (±34) 113 0.39 1.73×107 _4.00×106 _0.23 20046-0623(w) 145 (±14) 103 (±13) 104 0.71 3.71×107 1.23×107 0.33 20046-0623(e) . . . . 21130-4446(ne) 165 (±37) . . . 6.23×107 _8.48×106 _0.14 21130-4446(sw) 152 (±28) . . . 4.48×107 5.33×106 0.12 21208-0519(s) 171 (±22) . . . 7.19×107 4.28×106 0.06 21208-0519(n) 126 (±21) . . . 2.12×107 _9.19×106 _0.44 21329-2346(n) 115 (±21) . . . 1.46×107 1.13×107 0.78 21329-2346(s) 113 (±22) . . . 1.36×107 4.86×106 0.36 22491-1808(e) 146 (±20) 16 (±31) 20 0.11 3.81×107 7.02×106 0.18 22491-1808(w) 121 (±34) 27 (±50) 64 0.23 1.79×107 _9.17×106 _0.51 23128-5919(n) 151 (±21) 29 (±16) 43 0.20 4.36×107 4.13×106 0.09 23128-5919(s) 148 (±18) 82 (±12) 110 0.56 4.02×107 7.87×106 0.20 23234+0946(n) 152 (±23) . . . 4.48×107 _1.16×107 _0.26 23234+0946(s) 113 (±40) . . . 1.36×107 3.14×106 0.23

The stellar dispersion and rotational velocities, and theVrot/σratio are derived from

the spectra of Fig. 2.2 with the aid of the parameters of Table 2.2. The dynamical and Eddington black hole mass of each nucleus and the ratio of the two are also presented here.

a _{Velocity corrected for deviations from the major axis of rotation.} b _{Observed velocity corrected for inclination effects.}