Global Hot Gas Excess in (U)LIRGs: Replicating Galactic Nuclei Scaling Relations between Diffuse X-ray Emission and Star Formation on Galaxy-Wide Scales

TL;DR

This study analyzes X-ray data from 78 luminous infrared galaxies, revealing a super-linear relation between hot gas X-ray luminosity and star formation rate, and exploring how galactic mergers and gas absorption influence hot gas emission.

Contribution

It replicates and extends galactic nuclei scaling relations to galaxy-wide scales in (U)LIRGs, highlighting the impact of mergers and gas absorption on hot gas X-ray emission.

Findings

Hot gas X-ray luminosity exceeds standard SFR predictions in high-SFR galaxies.

Super-linear L_X-SFR relation with slope 1.34 for SFR > 50 M_sun/yr.

Negative correlation between apparent and intrinsic X-ray luminosity ratios and gas absorption.

Abstract

Hot ionized interstellar medium interlinks star formation and stellar feedback processes, redistributing energy, momentum, and material throughout galaxies. We use X-ray data from $Chandra$ to extract the hot gas emission from 78 of the most luminous infrared-selected galaxies in the local Universe. In the extreme star-forming environments, the intrinsic thermal X-ray luminosity of hot gas ($L_{\rm 0.5 - 2\,keV}^{\rm gas}$) shows a significant excess over the predictions of the standard linear $L_{\rm X}$$-$SFR relation for most objects with very high star formation rates (SFRs). The contribution of active galactic nuclei (AGNs) appears to have little impact on the global hot gas luminosity. For galaxies with SFR $\gt$ 50 ${M_{\rm \odot}}\,\,{\rm yr^{-1}}$, the Bayesian analysis gives a super-linear relation of ${\rm log}(L_{\rm 0.5-2\,keV}^{\rm gas} /{\rm erg\,s^{-1}})=1.34\,{\rm log}({\rm SFR}/{M_{\rm \odot}}\,{\rm yr^{-1}})+39.82$, similar to that found in the central regions of normal spiral galaxies. These results suggest a scenario in which the merger of galaxies delivers substantial amounts of gas, triggering intense star formation in both the nuclear region and the galactic disk, and ultimately enhancing the global thermal X-ray emission. The ratio of the apparent thermal luminosity in the 0.5$-$2 keV band ($L_{\rm 0.5 - 2\,keV}^{\rm appar}$) to $L_{\rm 0.5 - 2\,keV}^{\rm gas}$ shows statistically significant negative correlations with the intrinsic column density ($N_{\rm H}$) and SFR. Moreover, in contrast to the luminosity ratio, SFR shows a moderate positive correlation with intrinsic $N_{\rm H}$. This suggests that the correlation between $L_{\rm 0.5 - 2\,keV}^{\rm appar}$/$L_{\rm 0.5 - 2\,keV}^{\rm gas}$ and SFR may be driven by the underlying $L_{\rm 0.5 - 2\,keV}^{\rm appar}$/$L_{\rm 0.5 - 2\,keV}^{\rm gas}$$-$$N_{\rm H}$ and SFR$-$$N_{\rm H}$ relations.

Tables

Table 1. Table 1: Galaxy Sample

Galaxy	R.A. (J2000)	Decl. (J2000)	$z$	$D_L$	IRX	SFR	Stage	$N_{H,\mathrm{Gal}}$	AGN
(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)
IRAS F01364–1042	01h38m52.92s	–10d27m11.4s	0.0483	210.0	3.136	122.61	d	2.0	…
ESO 255-IG7	06h27m22.45s	–47d10m48.7s	0.0388	173.0	2.048	140.00	b	3.8	…
ESO 60-IG16	08h52m31.29s	–69d01m57.0s	0.0463	210.0	2.495	115.40	b	5.2	Y
IRAS 09022–3615	09h04m12.70s	–36d27m01.1s	0.0596	271.0	3.451	359.05	d	26.6	Y
IRAS F09111–1007	09h13m37.61s	–10d19m24.8s	0.0541	246.0	2.619	198.46	b	4.6	…
ESO 374-IG32	10h06m04.80s	–33d53m15.0s	0.0341	156.0	2.394	106.13	d	8.8	…
VV 340 N	14h57m00.70s	+24d37m05.8s	0.0337	157.0	2.610	79.04	b	3.3	Y
IRAS F17132+5313	17h14m20.00s	+53d10m30.0s	0.0509	232.0	2.435	159.67	b	1.9	…
ESO 593-IG8	19h14m30.90s	–21d19m07.0s	0.0487	222.0	2.209	150.38	d	8.1	…
IRAS F19297–0406	19h32m21.25s	–03d59m56.3s	0.0857	395.0	4.401	494.79	d	15.1	…
CGCG 448-020	20h57m23.90s	+17d07m39.0s	0.0361	161.0	1.662	156.77	c	6.9	…
IRAS F22491–1808	22h51m49.26s	–17d52m23.5s	0.0778	351.0	2.198	279.16	d	2.3	…
ESO 77-IG14	23h21m04.53s	–69d12m54.2s	0.0416	186.0	2.856	100.48	b	3.3	…
IRAS F05189-2524	05h21m01.47s	–25d21m45.4s	0.0425	187.0	2.783	253.48	d	1.7	Y
UGC 4881	09h15m55.11s	+44d19m54.1s	0.0393	178.0	2.197	97.13	c	1.4	…
UGC 5101	09h35m51.65s	+61d21m11.3s	0.0394	177.0	2.925	180.18	d	3.0	Y
IRAS F10565+2448	10h59m18.14s	+24d32m34.3s	0.0431	197.0	3.247	209.13	d	1.1	…
NGC 3690	11h28m32.25s	+58d33m44.0s	0.0104	50.7	1.771	150.55	c	0.9	Y
IRAS F12112+0305	12h13m46.00s	+02d48m38.0s	0.0733	340.0	2.510	402.89	d	1.8	…
IRAS F14348-1447	14h37m38.37s	–15d00m22.8s	0.0827	387.0	2.466	428.54	d	7.5	Y
VV 705	15h18m06.28s	+42d44m41.2s	0.0402	183.0	2.061	147.81	b	1.8	…
IRAS F15250+3608	15h26m59.40s	+35d58m37.5s	0.0552	254.0	2.264	211.11	d	1.5	…
UGC 9913	15h34m57.12s	+23d30m11.5s	0.0182	87.9	3.423	327.74	d	3.9	…
NGC 6240	16h52m58.89s	+02d24m03.4s	0.0245	116.0	2.336	148.44	d	4.9	Y
IRAS F17207-0014	17h23m21.96s	–00d17m00.9s	0.0428	198.0	5.154	501.22	d	9.7	…
ESO 286-IG19	20h58m26.79s	–42d39m00.3s	0.0430	193.0	2.108	203.56	d	3.3	…
ESO 148-IG2	23h15m46.78s	–59d03m15.6s	0.0446	199.0	2.054	204.60	c	1.6	Y
UGC 08387	13h20m35.34s	+34d08m22.2s	0.0233	110.0	2.379	94.18	d	1.0	Y
CGCG 436–030	01h20m02.72s	+14d21m42.9s	0.0312	134.0	1.974	85.87	b	3.4	…
NGC 0695	01h51m14.24s	+22d34m56.5s	0.0325	139.0	2.053	84.64	N	6.9	…
CGCG 043–099	13h01m50.80s	+04d20m00.0s	0.0375	175.0	2.330	84.73	d	1.9	…
MCG+07–23–019	11h03m53.20s	+40d50m57.0s	0.0345	158.0	1.761	75.13	d	1.0	…
NGC 6670 (E)	18h33m37.67s	+59d53m21.3s	0.0289	129.5	2.229	41.39	b	3.9	…
NGC 6670 (W)	18h33m32.78s	+59d53m11.7s	0.0289	129.5	2.558	36.78	b	3.9	…
NGC 5331 (N)	13h52m16.43s	+02d06m30.9s	0.033	155.0	1.398	18.10	c	2.0	…
NGC 5331 (S)	13h52m16.21s	+02d06m05.1s	0.033	155.0	2.393	60.78	c	2.0	…
IC 2810 (NW)	11h25m45.07s	+14d40m36.0s	0.0342	157.0	2.266	49.68	a	2.5	…
NGC 3256	10h27m51.27s	–43d54m13.8s	0.0094	38.9	2.299	76.46	d	9.1	…
IRAS F16164–0746	16h19m11.79s	–07d54m02.8s	0.0272	128.0	2.573	72.75	d	11.3	Y
IC 4687	18h13m39.80s	–57d43m30.7s	0.0173	81.9	2.241	38.51	b	11.5	…
IC 4689	18h13m40.38s	–57d44m54.3s	0.0173	81.9	2.176	15.49	b	11.5	…
IC 5298	23h16m00.70s	+25d33m24.1s	0.0274	119.0	2.451	69.67	N	5.7	Y
NGC 6090	16h11m40.70s	+52d27m24.0s	0.0293	137.0	1.325	71.10	c	1.6	…
NGC 5256	13h38m17.52s	+48d16m36.7s	0.0279	129.0	1.679	65.00	b	1.7	Y
IRAS F03359+1523	03h38m46.70s	+15d32m55.0s	0.0354	152.0	2.562	61.22	d	13.8	…
ESO 550–IG025	04h21m20.02s	–18d48m47.6s	0.0322	135.8	2.142	56.46	b	3.2	…
NGC 0034	00h11m06.55s	+12d06m26.3s	0.0196	84.1	1.799	55.25	d	2.1	Y
MCG+12–02–001	00h54m03.61s	+73d05m11.8s	0.0157	69.8	3.593	54.49	c	22.0	…
ESO 440–IG058 (S)	12h06m51.87s	–31d56m59.2s	0.0232	112.0	2.819	41.15	b	5.6	…
NGC 7130	21h48m19.50s	–34d57m04.7s	0.0162	72.7	1.712	46.88	N	1.9	Y
NGC 7771	23h51m24.80s	+20d06m42.2s	0.0143	61.2	2.214	25.79	a	4.0	…
NGC 7770	23h51m22.55s	+20d05m49.2s	0.0143	61.2	1.396	8.16	a	4.0	…
NGC 7592 (E)	23h18m22.60s	–04d24m58.0s	0.0244	106.0	0.991	17.96	b	3.8	…
NGC 7592 (W)	23h18m21.78s	–04d24m57.0s	0.0244	106.0	2.097	25.85	b	3.8	Y
NGC 6285	16h58m23.99s	+58d57m21.7s	0.0183	85.7	1.532	7.58	b	1.8	…
NGC 6286	16h58m31.63s	+58d56m13.3s	0.0183	85.7	2.204	33.01	b	1.8	Y
NGC 4922 (N)	13h01m25.27s	+29d18m49.5s	0.0236	111.0	2.615	41.61	c	0.9	Y
NGC 3110	10h04m02.11s	–06d28m29.2s	0.0169	79.5	1.646	41.72	a	3.5	…
NGC 0232	00h42m45.82s	–23d33m40.9s	0.0227	95.2	2.404	48.65	b	1.4	Y
MCG+08–18–013 (E)	09h36m37.19s	+48d28m27.7s	0.0259	117.0	2.066	36.24	a	1.7	…
CGCG 049–057	15h13m13.09s	+07d13m31.8s	0.013	65.4	4.156	39.16	N	2.6	Y
NGC 1068	02h42m40.71s	–00d00m47.8s	0.0038	15.9	1.865	44.29	N	2.9	Y
UGC 02238	02h46m17.49s	+13d05m44.4s	0.0219	92.4	2.591	37.70	d	8.9	…
MCG–03–34–064	13h22m24.46s	–16d43m42.9s	0.0165	82.2	2.204	27.08	d	5.0	Y
ESO 350–IG038	00h36m52.25s	–33d33m18.1s	0.0206	89.0	1.128	37.02	N	2.4	…
MCG–01–60–022	23h42m00.85s	–03d36m54.6s	0.0232	100.0	1.654	28.44	N	3.6	Y
NGC 5135	13h25m44.06s	–29d50m01.2s	0.0137	60.9	1.804	35.41	N	4.9	Y
IC 5179	22h16m09.10s	–36d50m37.4s	0.0114	51.4	1.619	31.01	N	1.4	…
CGCG 465–012	03h54m16.08s	+15d55m43.4s	0.0222	94.3	2.920	20.18	d	14.8	…
MCG–02–33–098–9	13h02m19.70s	–15d46m03.0s	0.0159	78.7	1.973	25.87	c	3.7	…
ESO 343–IG013	21h36m10.83s	–38d32m37.9s	0.0191	85.8	2.014	24.22	d	2.8	…
NGC 2146	06h18m37.71s	+78d21m25.3s	0.003	17.5	2.820	22.87	N	7.1	…
NGC 5653	14h30m10.42s	+31d12m55.8s	0.0119	60.2	1.640	24.24	a	1.3	…
NGC 0023	00h09m53.41s	+25d55m25.6s	0.0152	65.2	1.724	23.34	N	3.4	…
NGC 7552	23h16m10.77s	–42d35m05.4s	0.0054	23.5	1.793	22.98	N	1.2	…
NGC 1961	05h42m04.65s	+69d22m42.4s	0.0131	59.0	1.403	21.38	b	8.1	…
NGC 1365	03h33m36.37s	–36d08m25.4s	0.0055	17.9	1.760	17.83	N	1.3	Y
NGC 3221	10h22m19.98s	+21d34m10.5s	0.0137	65.7	1.896	21.75	N	1.9	…

Table 2. Table 2: C ​ h ​ a ​ n ​ d ​ r ​ a Chandra Data

Galaxy	Exp. Time	Obs. ID	Galaxy	Exp. Times	Obs. ID
	(ks)			(ks)
IRAS F01364–1042	14.57	7801	IC 4687	14.48	15056
ESO 255-IG7	14.57	7803	IC 4689	14.48	15056
ESO 60-IG16	14.57	7888	IC 5298	14.78	15059
IRAS 09022–3615	14.85	7805	NGC 6090	14.79	6859
IRAS F09111–1007	14.63	7806	NGC 5256	19.69	2044
ESO 374-IG32	14.36	7807	IRAS F03359+1523	14.76	6856
VV 340 N	14.57	7812	ESO 550–IG025	14.78	15060
IRAS F17132+5313	14.85	7814	NGC 0034	14.78	15061
ESO 593-IG8	14.97	7816	MCG+12–02–001	14.31	15062
IRAS F19297–0406	16.42	7890	ESO 440–IG058 (S)	14.78	15064
CGCG 448-020	14.57	7818	NGC 7130	38.64	2188
IRAS F22491–1808	14.97	7821	NGC 7771	16.71	10397
ESO 77-IG14	14.98	7822	NGC 7770	16.71	10397
IRAS F05189-2524	34.55	2034, 3432	NGC 7592 (E)	14.99	6860
UGC 4881	14.77	6857	NGC 7592 (W)	14.99	6860
UGC 5101	49.32	2033	NGC 6285	14.00	10566
IRAS F10565+2448	28.87	3952	NGC 6286	14.00	10566
NGC 3690	124.86	1641, 6227,	NGC 4922 (N)	24.42	4775, 15065,
		15077, 15619			18201
IRAS F12112+0305	28.96	4110, 4934	NGC 3110	14.87	15069
IRAS F14348–1447	14.72	6861	NGC 0232	21.65	12872, 15066
VV 705	14.47	6858	MCG+08–18–013 (E)	13.79	15067
IRAS F15250+3608	9.84	4112	CGCG 049–057	19.06	10399
UGC 9913	292.42	869, 1609(2-3)	NGC 1068	47.44	344
NGC 6240	182.05	1590, 12713	UGC 02238	14.87	15068
IRAS F17207–0014	57.72	2035, 4114	MCG–03–34–064	71.49	7373, 23690, 25253,
					27267, 2780(2–3)
ESO 286-IG19	44.87	2036	ESO 350–IG038	127.23	8175, 1669(5–7)
ESO 148-IG2	49.31	2037	MCG–01–60–022	18.90	10570
UGC 08387	14.07	7811	NGC 5135	29.30	2187
CGCG 436–030	13.82	15047	IC 5179	11.96	10392
NGC 0695	14.78	15046	CGCG 465–012	14.87	15071
CGCG 043–099	14.78	15048	MCG–02–33–098–9	14.87	15072
MCG+07–23–019	52.34	12977	ESO 343–IG013	14.78	15073
NGC 6670 (E)	14.77	15049	NGC 2146	63.08	313(1–6), 24706
NGC 6670 (W)	14.77	15049	NGC 5653	16.52	10396
NGC 5331 (N)	14.78	15051	NGC 0023	19.45	10401
NGC 5331 (S)	14.78	15051	NGC 7552	200.94	7848, 2026(7–8),
					2167(5–6)
IC 2810 (NW)	14.78	15053	NGC 1961	32.83	10531
NGC 3256	70.37	835, 3569, 16026	NGC 1365	101.93	3554, 68(68–73)
IRAS F16164–0746	14.78	15057	NGC 3221	28.98	10398, 19334

Table 3. Table 3: Hot Gas X-ray Spectral Properties

Galaxy	$N_H$	Model	$L_{0.5-2\mathrm{keV}}^{\mathrm{appar}}$	$L_{0.5-2\mathrm{keV}}^{\mathrm{gas}}$	$kT$	C-stat/d.o.f
	(1022cm-2)		(erg s-1)	(erg s-1)	(keV)
(1)	(2)	(3)	(4)	(5)	(6)	(7)
IRAS F01364–1042	1.28	1	40.20 $\pm$ 0.65	42.47 $\pm$ 0.39	0.22 $\pm$ 0.50	46.65/46
ESO 255-IG7	0.82	1	41.13 $\pm$ 0.05	43.42 $\pm$ 0.10	0.11 $\pm$ 0.02	62.26/51
ESO 60-IG16	1.01	2	40.79 $\pm$ 0.15	42.47 $\pm$ 0.35	0.24	51.77/41
IRAS 09022–3615	1.42	4	41.44 $\pm$ 0.08	43.69 $\pm$ 0.41	0.17 $\pm$ 0.06	34.25/23
IRAS F09111–1007	1.06	5	41.03 $\pm$ 0.18	42.42 $\pm$ 0.36	0.24	54.83/57
ESO 374-IG32	0.97	2	40.54 $\pm$ 0.65	41.81 $\pm$ 0.37	0.24	26.14/32
VV 340 N	1.06	3	41.24 $\pm$ 0.03	42.16 $\pm$ 0.09	0.71	88.73/42
IRAS F17132+5313	0.98	1	41.39 $\pm$ 0.05	43.31 $\pm$ 0.14	0.18 $\pm$ 0.02	37.74/31
ESO 593-IG8	0.89	1	41.47 $\pm$ 0.06	43.26 $\pm$ 0.15	0.17 $\pm$ 0.03	34.47/37
IRAS F19297–0406	1.83	2	41.45 $\pm$ 0.14	43.48 $\pm$ 0.15	0.24	25.71/11
CGCG 448-020	0.66	2	41.21 $\pm$ 0.06	42.25 $\pm$ 0.14	0.24	49.11/55
IRAS F22491–1808	0.88	1	40.87 $\pm$ 0.28	42.71 $\pm$ 0.54	0.19 $\pm$ 0.17	11.79/7
ESO 77-IG14	1.16	2	40.87 $\pm$ 0.07	42.50 $\pm$ 0.26	0.24	62.44/50
IRAS F05189-2524	1.13	5	41.17 $\pm$ 0.06	42.75 $\pm$ 0.17	0.24	411.34/378
UGC 4881	0.88	4	40.90 $\pm$ 0.06	43.18 $\pm$ 0.10	0.14 $\pm$ 0.02	56.1/48
UGC 5101	1.19	1	40.95 $\pm$ 0.05	43.53 $\pm$ 0.11	0.10 $\pm$ 0.02	169.97/146
IRAS F10565+2448	1.33	2	41.09 $\pm$ 0.05	42.82 $\pm$ 0.32	0.24	104.17/64
NGC 3690	0.70	1	41.32 $\pm$ 0.01	42.60 $\pm$ 0.17	0.21 $\pm$ 0.01	818.19/510
IRAS F12112+0305	1.02	1	40.81 $\pm$ 0.26	42.95 $\pm$ 0.63	0.17 $\pm$ 0.08	10.85/8
IRAS F14348-1447	1.00	4	41.62 $\pm$ 0.07	43.20 $\pm$ 0.16	0.22 $\pm$ 0.07	26.75/18
VV 705	0.82	4	40.97 $\pm$ 0.07	42.72 $\pm$ 0.22	0.20 $\pm$ 0.04	58.5/47
IRAS F15250+3608	0.91	1	41.26 $\pm$ 0.10	43.48 $\pm$ 0.11	0.13 $\pm$ 0.08	51.65/36
UGC 9913	1.41	2	40.91 $\pm$ 0.01	42.83 $\pm$ 0.08	0.24	1190.94/519
NGC 6240	0.94	2	41.86 $\pm$ 0.01	43.32 $\pm$ 0.13	0.24	1397.98/522
IRAS F17207-0014	2.15	2	41.29 $\pm$ 0.04	43.36 $\pm$ 0.33	0.24	240.44/188
ESO 286-IG19	0.84	4	41.14 $\pm$ 0.04	42.78 $\pm$ 0.21	0.19	183.51/168
ESO 148-IG2	0.82	1	41.28 $\pm$ 0.06	42.83 $\pm$ 0.23	0.18 $\pm$ 0.04	549.96/518
UGC 08387	0.90	1	40.43 $\pm$ 0.08	42.47 $\pm$ 0.20	0.16 $\pm$ 0.08	49.65/33
CGCG 436–030	0.74	1	40.76 $\pm$ 0.10	42.95 $\pm$ 0.23	0.13 $\pm$ 0.04	77.04/73
NGC 0695	0.77	6	41.32 $\pm$ 0.04	42.00 $\pm$ 0.06	0.71	114.24/87
CGCG 043–099	0.88	2	40.63 $\pm$ 0.15	42.10 $\pm$ 0.35	0.24	41.36/27
MCG+07–23–019	0.65	1	41.04 $\pm$ 0.03	42.53 $\pm$ 0.12	0.18 $\pm$ 0.03	227.46/191
NGC 6670 (E)	0.84	2	40.38 $\pm$ 0.09	41.64 $\pm$ 0.63	0.09 $\pm$ 0.13	4.9/3
NGC 6670 (W)	0.97	2	40.74 $\pm$ 0.06	42.18 $\pm$ 0.43	0.24	21.61/16
NGC 5331 (N)	0.51	2	40.57 $\pm$ 0.21	41.32 $\pm$ 0.74	0.24	14.03/4
NGC 5331 (S)	0.90	2	41.36 $\pm$ 0.59	41.96 $\pm$ 0.49	0.24	15.72/6
IC 2810 (NW)	0.85	5	40.59 $\pm$ 0.14	41.80 $\pm$ 0.35	0.24	24.87/19
NGC 3256	0.86	1	41.10 $\pm$ 0.01	42.62 $\pm$ 0.04	0.20 $\pm$ 0.01	604.17/520
IRAS F16164–0746	0.97	1	40.06 $\pm$ 0.68	42.04 $\pm$ 0.46	0.11 $\pm$ 0.62	93.94/74
IC 4687	0.84	7	40.72 $\pm$ 0.04	42.53 $\pm$ 0.15	1.15/0.13	28.25/28
IC 4689	0.81	5	40.61 $\pm$ 0.06	41.67 $\pm$ 0.25	0.24	25.53/21
IC 5298	0.92	2	40.57 $\pm$ 0.11	41.88 $\pm$ 0.21	0.24	99.43/68
NGC 6090	0.48	4	40.99 $\pm$ 0.06	42.29 $\pm$ 0.31	0.12 $\pm$ 0.02	114.17/104
NGC 5256	0.62	2	41.52 $\pm$ 0.02	42.64 $\pm$ 0.16	0.24	289.68/170
IRAS F03359+1523	0.97	5	40.85 $\pm$ 0.16	41.79 $\pm$ 0.44	0.24	58.42/56
ESO 550–IG025	0.80	1	40.57 $\pm$ 0.61	42.27 $\pm$ 0.12	0.18 $\pm$ 0.14	49.51/45
NGC 0034	0.67	1	40.59 $\pm$ 0.07	41.80 $\pm$ 0.28	0.22 $\pm$ 0.05	67.16/57
MCG+12–02–001	1.38	1	40.59 $\pm$ 0.08	42.26 $\pm$ 0.16	0.23 $\pm$ 0.12	92.7/79
ESO 440–IG058 (S)	1.07	2	40.54 $\pm$ 0.06	42.17 $\pm$ 0.29	0.24	16.37/10
NGC 7130	0.63	1	40.79 $\pm$ 0.02	42.18 $\pm$ 0.29	0.18 $\pm$ 0.01	241.83/206
NGC 7771	0.83	2	40.79 $\pm$ 0.02	42.11 $\pm$ 0.34	0.24	138.88/109
NGC 7770	0.51	1	40.25 $\pm$ 0.07	41.23 $\pm$ 0.43	0.20 $\pm$ 0.05	50.43/42
NGC 7592 (E)	0.36	2	40.56 $\pm$ 0.05	41.11 $\pm$ 0.21	0.24	18.64/12
NGC 7592 (W)	0.78	5	40.28 $\pm$ 0.07	41.60 $\pm$ 0.18	0.24	11.3/7
NGC 6285	0.56	1	40.19 $\pm$ 0.10	41.34 $\pm$ 0.21	0.18 $\pm$ 0.07	40.31/31
NGC 6286	0.83	3	40.99 $\pm$ 0.03	41.78 $\pm$ 0.04	0.71	170.16/104
NGC 4922 (N)	0.99	1	40.14 $\pm$ 0.12	42.09 $\pm$ 0.62	0.15 $\pm$ 0.10	3.39/3
NGC 3110	0.61	1	40.84 $\pm$ 0.05	41.91 $\pm$ 0.42	0.22 $\pm$ 0.04	143.11/114
NGC 0232	0.91	5	40.51 $\pm$ 0.05	42.01 $\pm$ 0.28	0.24	70.54/52
MCG+08–18–013 (E)	0.77	5	40.51 $\pm$ 0.09	41.80 $\pm$ 0.46	0.24	17.7/16
CGCG 049–057	1.61	4	39.61 $\pm$ 0.31	41.07 $\pm$ 0.52	0.26 $\pm$ 1.06	44.51/41
NGC 1068	0.69	1	41.10 $\pm$ 0.01	42.55 $\pm$ 0.11	0.12 $\pm$ 0.01	4796.17/499
UGC 02238	0.98	6	40.66 $\pm$ 0.08	41.47 $\pm$ 0.30	0.71	62.08/54
MCG–03–34–064	0.83	2	40.57 $\pm$ 0.06	41.76 $\pm$ 0.20	0.24	274.51/191
ESO 350–IG038	0.41	1	40.58 $\pm$ 0.04	41.35 $\pm$ 0.18	0.21 $\pm$ 0.02	423.51/415
MCG–01–60–022	0.61	1	40.61 $\pm$ 0.09	42.21 $\pm$ 0.12	0.14 $\pm$ 0.05	220.8/160
NGC 5135	0.67	4	41.03 $\pm$ 0.01	42.23 $\pm$ 0.04	0.23 $\pm$ 0.01	304.56/255
IC 5179	0.60	4	40.58 $\pm$ 0.04	41.78 $\pm$ 0.06	0.20 $\pm$ 0.03	200.72/168
CGCG 465–012	1.11	3	40.65 $\pm$ 0.09	41.49 $\pm$ 0.13	0.71	56.78/59
MCG-02-33-098-9	0.73	2	39.96 $\pm$ 0.14	41.02 $\pm$ 0.50	0.71	39.76/27
ESO 343–IG013	0.75	4	40.44 $\pm$ 0.07	41.92 $\pm$ 0.50	0.21 $\pm$ 0.05	37.06/35
NGC 2146	1.07	1	40.18 $\pm$ 0.01	42.01 $\pm$ 0.09	0.19 $\pm$ 0.01	918.33/520
NGC 5653	0.60	1	40.37 $\pm$ 0.06	42.02 $\pm$ 0.09	0.13 $\pm$ 0.03	170.28/169
NGC 0023	0.64	4	40.71 $\pm$ 0.06	41.60 $\pm$ 0.20	0.32 $\pm$ 0.07	227.87/205
NGC 7552	0.66	1	40.43 $\pm$ 0.01	41.58 $\pm$ 0.23	0.23 $\pm$ 0.01	589.54/519
NGC 1961	0.51	1	40.75 $\pm$ 0.03	41.41 $\pm$ 0.16	0.29 $\pm$ 0.05	220.48/177
NGC 1365	0.65	1	40.62 $\pm$ 0.01	41.93 $\pm$ 0.01	0.20 $\pm$ 0.01	1371.01/417
NGC 3221	0.70	4	40.36 $\pm$ 0.63	41.46 $\pm$ 0.24	0.24 $\pm$ 0.07	269.53/235

Equations

$$\log (\frac{L_{0.5-2\mathrm{keV}}^{\mathrm{gas}}}{\mathrm{erg}{\mathrm{s}}^{-1}})=1.08(\pm 0.17)\log \frac{\mathrm{SFR}}{M_{\odot }{\mathrm{yr}}^{-1}}+40.08(\pm 0.08).$$

$$\log (\frac{L_{0.5-2\mathrm{keV}}^{\mathrm{gas}}}{\mathrm{erg}{\mathrm{s}}^{-1}})=1.34(\pm 0.23)\log \frac{\mathrm{SFR}}{M_{\odot }{\mathrm{yr}}^{-1}}+39.82(\pm 0.50).$$

$$L_{\mathrm{X}}(\mathrm{unresolved}\mathrm{HMXBs})=3.725\mathrm{SFR}[L_{\mathrm{upper}}^{0.4}-0.025].$$

$$L_{\mathrm{X}}(\mathrm{unresolved}\mathrm{LMXBs})=(8\pm 0.5)\times 10^{39}\mathrm{erg}{\mathrm{s}}^{-1}\mathrm{per}10^{11}{\mathrm{M}}_{\odot }.$$

$$L_{\mathrm{X}}(\mathrm{young})/\mathrm{SFR}=(1.7\pm 0.9)\times 10^{38}(\mathrm{erg}{\mathrm{s}}^{-1})/({\mathrm{M}}_{\odot }\mathrm{y}{\mathrm{r}}^{-1}).$$

Full text

galaxies: hot ISM — galaxies: structure — galaxies: molecules — galaxies: star formation

1 Introduction

Luminous infrared galaxies (LIRGs) are systems with infrared luminosities exceeding $10^{11}\,L_{\rm\odot}$, encompassing a diverse population that ranges from isolated galaxies to interacting pairs and late-stage mergers. LIRGs are typically gas-rich, which fuels intense star formation and enhanced AGN activity (Hernquist, 1989; Di Matteo et al., 2005). Moreover, in the most luminous regime, ultraluminous infrared galaxies (ULIRGs; $L_{\rm IR}$ $\geqslant$ $10^{12}\,L_{\rm\odot}$) are considered an important evolutionary stage toward the formation of quasars (QSOs) (Sanders et al., 1988a, b; Hopkins et al., 2005) and massive elliptical galaxies (Toomre & Toomre, 1972; Tacconi et al., 2002; Cox et al., 2006; Sparre & Springel, 2017).

These objects contribute significantly to the cosmic infrared background and are common at redshifts 1$-$3, where the peak of star formation occurs in the Universe (Casey et al., 2014). Accordingly, they certainly play a key role in deepening our understanding of the general evolution of galaxies and black holes.

In the scenario proposed by Sanders et al. (1988a) and Hopkins et al. (2005), ULIRGs at a late stage of merger are expected to consume or expel their gas and subsequently evolve into an obscured Type II QSO, and eventually become an exposed (Type I) QSO. This process ultimately leads to the formation of an elliptical galaxy and contributes significantly to the growth of the central supermassive black hole. However, more recent simulations indicate that when mergers preserve substantial reservoirs of cold interstellar gas, this material can subsequently settle into a rotationally supported plane and form a new disk (e.g., Barnes, 2002; Springel & Hernquist, 2005; Robertson et al., 2006). This means that the final galactic morphology (elliptical or spiral) following a merger event critically depends on the evolution of the interstellar gas.

The amount of the interstellar gas is regulated by the star formation processes and AGN, both of which inject energy into the surrounding medium. In particular, stellar winds and supernova feedback from massive stars heat the gas intensely and can even drive it into the galactic halo (Grimes et al., 2005; Mineo et al., 2012a; Li & Wang, 2013; Hopkins et al., 2013). AGN feedback also heats the interstellar gas and has the potential to quench star formation by preventing gas cooling and collapse (Di Matteo et al., 2005; Springel & Hernquist, 2005; Choi et al., 2015).

X-ray observations are a powerful tool for studying these high-energy feedback phenomena. In spiral galaxies, the thermal diffuse X-ray emission from hot gas shows a strong linear correlation with the star formation rate (Mineo et al., 2012a). The ratio $L_{\mathrm{X}}(\mathrm{gas})/{\rm SFR}\thickapprox 5.5\times 10^{39}(\mathrm{erg\,s^{-1}})/({\rm M_{\odot}\ yr^{-1}})$ from Smith et al. (2018) indicates that the feedback in star-forming galaxies reaches a quasi-steady state, where about 2% of the mechanical energy from supernovae and stellar winds is converted into X-ray emission. However, unlike the linear L_{\rm X}$$-SFR scaling relation, a recent study based on the first eROSITA all-sky survey found a significant excess in the integrated X-ray luminosity at low SFRs ($\textless$ 1 ${M_{\rm\odot}}\,\,{\rm yr^{-1}}$) compared to the expectations from the linear scaling relation (e.g., Kyritsis et al., 2025). This integrated result implies that in galaxies with low-level star formation, many of which are very faint or distant, the properties of the hot ionized interstellar gas emission may differ from our anticipations. Nevertheless, for extremely high SFR galaxies, it remains unclear whether the hot gas emission follows the standard linear L_{\rm X}$$-SFR scaling relation.

In this paper, we aim to investigate the hot gas L_{\rm X}$$-SFR relation in nearby LIRGs and ULIRGs, and to examine whether the X-ray excess exists in these extreme star-forming galaxies. We apply a dust extinction method to estimate the intrinsic hydrogen column density ($N_{\rm H}$) for 78 (U)LIRGs selected from the C-GOALS (the X-ray component of the GOALS multi-wavelength survey; Iwasawa et al., 2011; Torres-Albà et al., 2018) program, and then correct the observed diffuse X-ray emission for intrinsic absorption.

This paper is organized as follows: In Section 2 we describe the sample of galaxies, the data, and the methods used in our data reduction and analysis. In Section 3 we present our main results on the properties of hot gas in (U)LIRGs. Conclusions are summarized in Section 4.

2 data and reduction

2.1 Sample

Based on the Great Observatories All-sky LIRG Survey (GOALS111http://goals.ipac.caltech.edu/; Armus et al., 2009), we selected 78 (ultra)luminous infrared galaxies with $Chandra$ X-ray data of adequate quality to study the diffuse X-ray-emitting gas from C-GOALS ($Chandra$-GOALS; Iwasawa et al., 2011; Torres-Albà et al., 2018). GOALS is a comprehensive, multi-wavelength study of the brightest infrared galaxies in the local Universe, with targets selected from the IRAS Revised Bright Galaxy Sample (RBGS; Sanders et al., 2003). The RBGS comprises 629 extragalactic objects detected by IRAS, all with 60 $\mu$m flux density greater than 5.24 Jy, and provides full-sky coverage above Galactic latitude $|b|$ $\textgreater$ $5^{\circ}$. As the brightest infrared galaxies in the sky, these objects are unparalleled laboratories for studying hot gas in extreme star-forming environments.

The sample in this work consists of 14 isolated galaxies and 58 systems in different merger stages. A total of 12 galaxies in the 6 systems (NGC 6670, NGC 5331, KTS 57, KTG 82, NGC 7592, and Arp 293) were resolved in both GALEX FUV and point source-excluded X-ray images. Table 1 presents the basic parameters for all 78 galaxies in the C-GOALS sample. The redshift range of the sample galaxies is $z$ = 0.003$-$0.0857, with total SFR spanning $\thicksim$2 dex (e.g., $\thicksim$6$-$501 ${M_{\rm\odot}}\,\,{\rm yr^{-1}}$) at the extreme high-SFR end. The distributions of distance, SFR, and merger stage are shown in Figure 1.

2.2 Extraction of X-Ray Spectra

All of the $Chandra$ data used in this study were downloaded from the $Chandra$ Data Archive. The detailed observation ID (obsid) and exposure time for each galaxy are listed in Table 2. We reprocessed these data using the $Chandra$ Interactive Analysis of Observations (CIAO) software version 4.17 with CALDB version 4.11.6. When multiple observations were available for an object, we combined them to enhance the sensitivity.

The point spread function (PSF) of $Chandra$ at each sky location was determined using the CIAO routine $mkpsfmap$. With the PSF map and the wavelet-based source detection algorithm $wavdetect$ (Freeman et al., 2002), the point source detections were performed on the scales of 1, $\sqrt{2}$, 2, 2$\sqrt{2}$, 4, and 8 pixels ($0^{\prime\prime}.492$/pixel) and in the soft (0.5 ${-}$ 2.0 keV), hard (2.0 ${-}$ 8.0 keV), and total (0.5 ${-}$ 8.0 keV) energy bands. The radius of the point source was set to enclose 90% of the source counts based on the PSF shape. For brighter sources, we manually increased the size of the radius to remove visible ring-like features due to spillage from the PSF wings (Gaetz et al., 2004; Allen et al., 2004). The point source removal was performed individually for each observation as the PSF of an object could vary significantly for multiple observations.

The CIAO routine $specextract$ was used to extract the point source-excluded spectra to obtain the diffuse X-ray emission in the 0.5$-$2 keV band. The background regions were selected from source-free areas on the same CCD chip. For the majority of the sample galaxies, which have few counts, we grouped the spectra to achieve a signal-to-noise ratio (S/N) $\textgreater$ 2 per bin. Thus, we used the C statistic (Cash, 1979) as the fit statistic instead of chi-squared.

2.3 Correction for Intrinsic Absorption

To determine the intrinsic X-ray luminosity of the hot gas, it is necessary to take into account the absorption of the foreground gas in the Milky Way and the gas within the host galaxy. For Galactic absorption, we used the Galactic hydrogen column densities $N_{\rm H}$ from the LAB HI map drawn by Kalberla et al. (2005). The values of Galactic $N_{\rm H}$ are shown in Table 1. For intrinsic absorption of galaxies, the high S/N X-ray data of luminous targets could constrain the intrinsic hydrogen column density through the X-ray spectra.

However, the intrinsic $N_{\rm H}$ cannot be reliably constrained by the X-ray spectra for most targets due to large uncertainties. Thus, we use dust extinction to estimate the intrinsic $N_{\rm H}$ (e.g., the dust-to-gas ratio) in this work. Following Hao et al. (2011), we utilized the total infrared to FUV luminosity ratio (IRX) to determine the FUV extinction $A_{\rm FUV}$. We then converted $A_{\rm FUV}$ to optical extinction $A_{\rm V}$ using Calzetti (2001) dust attenuation law. Combining the extinction curve of $A_{\rm V}$/$E$(B$$-$$V) = 3.1 (Savage & Mathis, 1979) and $N_{\rm H}$/$E$(B$$-$$V) = 8.8 $\times$ $10^{21}$ cm*-2* mag*-1* (Lenz et al., 2017), we inferred the color excess $E$(B$$-$$V) and calculated the intrinsic $N_{\rm H}$ for each sample galaxy. The derived values of the intrinsic $N_{\rm H}$ are listed in Table 3.

Although the method of dust-to-gas ratio can estimate the hydrogen column density, we note that it may not always be reliable since this method depends on the assumed geometry of the hot gas relative to the young massive stars. Therefore, in order to check on the intrinsic $N_{\rm H}$ derived from $A_{\rm V}$, we modeled 11 X-ray bright objects, whose spectra contain at least 20 bins with the S/N $\textgreater$ 5$\sigma$ per bin, using the model described in Section 2.4.

Figure 2 shows the intrinsic $N_{\rm H}$ given by the best-fitting model compared to the $A_{\rm V}$-derived $N_{\rm H}$. For 9 out of 11 objects, the two methods yield consistent $N_{\rm H}$ with differences of less than 0.2 $\times$ 1022 cm*-2*, and the remaining two (NGC 5256 and UGC 9913) are slightly above this range. We have calculated the X-ray luminosities corrected using both methods and found no statistically significant differences. Thus, the $A_{\rm V}$-derived $N_{\rm H}$ can serve as the absorbing column density of the host galaxy when more direct X-ray spectral measurements are unavailable.

2.4 Spectral Fitting

We used the thermal plasma emission model APEC (Smith et al., 2001) and the power-law model to fit the point source-excluded X-ray spectra in the xspec222https://heasarc.gsfc.nasa.gov/xanadu/xspec/ software version 12.14.1. In star-forming galaxies, the hot gas is primarily generated and heated through supernova shocks and stellar winds from massive stars (Grimes et al., 2005; Fabbiano, 2019; Nardini et al., 2022; Zhang et al., 2025). Given that the APEC component is generally considered to be dominated by the emission from hot gas, throughout this work, we assume this plasma component originates from hot gas and refer to the absorption-corrected luminosity of the APEC component in the 0.5$-$2 keV band as $L_{\rm 0.5-2\,keV}^{\rm gas}$. The power-law component is the light from faint unresolved compact sources, which are below the point source detection threshold and typically have a non-thermal spectrum.

For our initial fits, we varied the plasma temperature T and the power-law photon index $\Gamma$ of the spectral model consisting of an absorbed APEC component plus an absorbed power-law, which we refer to hereafter as model (1). This fit is generally good for the sample galaxies. However, to obtain the best-fitting model for the X-ray spectra, we ran another six spectral models, including (2) fixing $\Gamma$ = 1.8 and T = 0.24 keV for the absorbed power-law and APEC components, (3) fixing $\Gamma$ = 1.8 and T = 0.71 keV, (4) fixing $\Gamma$ = 1.8, (5) fixing T = 0.24 keV, (6) fixing T = 0.71 keV, (7) two absorbed APEC components plus the power-law with both T and $\Gamma$ free. For these models, $\Gamma$ = 1.8 is typically expected for X-ray binaries and AGNs in nearby galaxies (Nandra & Pounds, 1994; Kong et al., 2002; Swartz et al., 2004). T = 0.24 keV and 0.71 keV are the characteristic temperatures of hot gas in spiral galaxies (Grimes et al., 2005; Mineo et al., 2012a).

We compared the degrees of freedom and the C-statistics of these models to identify the good-fitting models. We rejected models that yielded non-physical results, such as very high/low temperatures or extreme photon indices. When multiple good models with different parameters were available, we preferred the one with a higher plasma temperature and fewer degrees of freedom.

Table 3 presents the best-fitting models for all objects, along with the thermal X-ray luminosities corrected for the intrinsic absorption by the $A_{\rm V}$-derived $N_{\rm H}$. We note that more than one third of the X-ray spectra (31/78) in our sample are best fitted by model (1), while only one galaxy IC 4687 is better described by the two-component APEC model. Ideally, the data should be fitted with multiple APEC components characterized by discrete temperatures and differing absorption column densities. However, due to the poor quality of the X-ray data for most objects in the sample, this would lead to severe over-fitting.

3 Results

In the following sections, we primarily focus on the diffuse thermal X-ray luminosity ($L_{\rm 0.5-2\,keV}^{\rm gas}$) of the hot gas in the 0.5$-$2 keV band. We assume that $L_{\rm 0.5-2\,keV}^{\rm gas}$ is equal to the APEC component in our best-fitting models of the point source-excluded X-ray spectra. The corrected X-ray luminosities, SFRs, and merger stages for our targets are presented in Table 1 and 3.

3.1 Correlation between Hot Gas and SFR in LIRGs and ULIRGs

The apparent luminosity of the diffuse emission from hot gas linearly correlates with SFR in both star-forming galaxies (Ranalli et al., 2003; Mineo et al., 2012a; Li & Wang, 2013) and (ultra)luminous infrared galaxies (Grimes et al., 2005; Iwasawa et al., 2011). However, most LIRGs and nearly all ULIRGs are merger remnants with intense, compact dust obscuration, resulting in strong absorption of the soft X-ray emission. In star-forming galaxies, only $\thicksim$10% of the soft X-ray light is able to pass through the intrinsic column density (Mineo et al., 2012a; Zhang et al., 2024). Given the stronger intrinsic absorption in LIRGs and ULIRGs, it is essential to study the correlation between SFR and intrinsic thermal X-ray emission from these systems, as it helps in understanding star formation feedback in the intense star-forming environments.

Figure 3 shows the L_{\rm 0.5-2\,keV}^{\rm gas}$$-SFR correlation with all X-ray luminosities corrected for the intrinsic absorption. We used 23 star-forming galaxies from Zhang & Wang (2025) as a comparison sample. These galaxies are all nearby ($\textless$ 24 Mpc) and have no companions according to the NASA Extragalactic Database (NED)333http://ned.ipac.caltech.edu. With the comparison sample, our measurements span $\thicksim$5 dex in X-ray luminosity (1039$-$1044 erg s*-1*) and $\thicksim$4 dex in SFR (10*-1*$-$103 ${M_{\rm\odot}}\,\,{\rm yr^{-1}}$). The SFR of our (U)LIRG sample is estimated using a combination of GALEX FUV and total infrared luminosity (8-1000 $\mu$m; Howell et al., 2010), with an uncertainty of typically less than ten percent.

The dashed line in Figure 3 is the linear L_{\rm 0.5-2\,keV}^{\rm gas}$$-SFR relation of the comparison sample fitted by Zhang & Wang (2025) at the low star formation end (e.g., SFR $\textless$ 10 ${M_{\rm\odot}}\,\,{\rm yr^{-1}}$):

[TABLE]

This relation is consistent with the results of Mineo et al. (2012a) and Smith et al. (2018) after correction for the intrinsic absorption in their samples.

For SFR $\textless$ 50 ${M_{\rm\odot}}\,\,{\rm yr^{-1}}$ (the left of the dotted line in Figure 3), the intrinsic $L_{\rm 0.5-2\,keV}^{\rm gas}$ and SFR follow the linear relation well. However, at high SFRs, the thermal X-ray luminosity shows a steeper trend, with significant excess over the linear relation in the majority of our targets. Therefore, we re-quantified the L_{\rm 0.5-2\,keV}^{\rm gas}$$-SFR relation for objects with SFR greater than 50 ${M_{\rm\odot}}\,\,{\rm yr^{-1}}$ (high SFR, hereafter), using the Bayesian linear regression method as implemented in the LINMIX package (Kelly, 2007). The best-fit relation is

[TABLE]

The $rms$ scatter of this relation is $\sigma$ = 0.38 dex, with a Spearman rank correlation coefficient of $r_{\rm s}$ = 0.72. The right panel of Figure 3 shows the same figure but with the targets color-coded by their merger stages. Information on the merger stage was obtained from Stierwalt et al. (2013), based on visual inspection of IRAC 3.6 $\mu$m images. The stage classifications are: (1) non-merger, (2) pre-merger (galaxy pairs before first encounter), (3) early-merger (after first encounter, with symmetric and intact disks but visible tidal tails), (4) mid-merger (featuring disrupted or amorphous disks, tidal tails, and other signs of interaction), and (5) late-merger (two nuclei embedded in a common envelope). More than half of the objects with high SFR are in late-merger, followed by early- and mid-merger. This suggests that the large scatter of the L_{\rm 0.5-2\,keV}^{\rm gas}$$-SFR relation in the (U)LIRGs can be attributed to the merger activities, which typically involve long timescales (greater than 1 Gyr) and strongly affect the evolution of hot gas (Smith et al., 2018).

In Figure 3, we use purple circles to highlight the objects hosting AGN (see Table 1, and also see Iwasawa et al. 2011 and Torres-Albà et al. 2018 for the detailed source classification) and find no significant excess in thermal X-ray luminosity compared to the non-AGN galaxies. Moreover, we note that AGN exist throughout all stages of the merger process within the sample. This indicates that the heating from AGN does not govern the evolution of the hot gas on a galactic scale, which is instead dominated by star formation processes (e.g., supernovae and stellar winds). Similar results have been reported in a systematic study of 49 major mergers (Smith et al., 2018), as well as in the Seyfert 2 galaxy M51 (Zhang et al., 2025). In their work, the influence of AGN on the intrinsic X-ray luminosity of hot gas is not significant on either resolved or global scales.

The slope of the L_{\rm 0.5-2\,keV}^{\rm gas}$$-SFR relation for the high SFR targets is consistent with the super-linear relation observed in the central regions ($\thicksim$0.3$-$2 kpc) of the comparison sample, as reported by Zhang & Wang (2025). This suggests that the global environments of objects with high SFR have similar characteristics to the central regions of normal spiral galaxies. It can be inferred that the merger of galaxies provides substantial amounts of gas, triggering bursts of star formation not only in the nuclear region of the system but also throughout the galactic disk. Subsequently, as the system reaches a high level of star formation (e.g., global SFR $\textgreater$ 50 ${M_{\rm\odot}}\,\,{\rm yr^{-1}}$), large amounts of gas distributed across the galactic disk are intensely heated, and this eventually leads to the excess of the intrinsic X-ray luminosity. To further understand the origin and heating mechanisms of hot gas, observations with higher sensitivity and spatial resolution are essential, but such observations are beyond the scope of this work.

3.2 Hot Gas Luminosities for Galactic and Intrinsic Absorption

In this section, we first examine the correlation between SFR and the thermal X-ray luminosity corrected only for Galactic absorption. Figure 4(a) shows that, compared to the slightly higher relation for galactic coronae reported by Li & Wang (2013), the objects are consistent with the scaling relation of $L_{\rm X}$/SFR $\thicksim$ 8.3 $\cdot$ 1038 (erg s*-1*)/(${M_{\rm\odot}}\,\,{\rm yr^{-1}}$) established by Mineo et al. (2012a). This could be attributed to the fact that the diffuse emission of our sample galaxies is mainly from the galactic disk. However, the significant dispersion in these data points suggests that both the origin and absorption of hot gas emission in (U)LIRGs involve complex and diverse physical processes. In addition, the inclination of galaxies is likely to play a role in this dispersion, but a detailed investigation lies beyond the scope of this study because most of the galaxies in our sample are mergers and are located at relatively large distances.

We subsequently analyzed the ratio between the apparent luminosity ($L_{\rm 0.5-2\,keV}^{\rm appar}$) and the intrinsic luminosity ($L_{\rm 0.5-2\,keV}^{\rm gas}$). Figures 4(b) and (c) show this ratio as a function of intrinsic $N_{\rm H}$ and SFR, respectively. As expected, the $L_{\rm 0.5-2\,keV}^{\rm appar}$/$L_{\rm 0.5-2\,keV}^{\rm gas}$ ratio declines with increasing $N_{\rm H}$, reflecting stronger absorption at higher column densities. Notably, a similar decreasing trend is observed with SFR, although the $L_{\rm 0.5-2\,keV}^{\rm appar}$/L_{\rm 0.5-2\,keV}^{\rm gas}$$-SFR relation shows considerable dispersion. A Spearman rank test analysis yields a correlation coefficient of $r_{\rm s}$ = $-$0.53 ($p$-value = 5.2$\times$10*-7*) for $N_{\rm H}$, and $r_{\rm s}$ = $-$0.61 ($p$-value = 3.5$\times$10*-9*) for SFR, indicating statistically significant negative correlations in both cases.

We next explored the correlation between the intrinsic $N_{\rm H}$ and SFR. The column density includes both atomic and molecular hydrogen (e.g., $N_{\rm H}$ = $N_{\rm H_{I}}$ + 2$N_{\rm H_{2}}$), where the molecular hydrogen is the most abundant molecule in the Universe and the primary raw material for star formation (Bigiel et al., 2008; Schruba, 2013). Figure 4(d) indeed shows a moderate positive correlation between $N_{\rm H}$ and SFR, with $r_{\rm s}$ = 0.57 and $p$-value = 6.4$\times$10*-8*. The large dispersion in the SFR-$$N_{\rm H} correlation could be attributed to variations in the fraction of atomic gas within the total column density.

Comparing the $L_{\rm 0.5-2\,keV}^{\rm appar}$/L_{\rm 0.5-2\,keV}^{\rm gas}$$-$$N_{\rm H} relation, we infer that the correlation between $L_{\rm 0.5-2\,keV}^{\rm appar}$/$L_{\rm 0.5-2\,keV}^{\rm gas}$ and SFR is primarily driven by or related to the correlation of $N_{\rm H}$ with SFR, since the soft X-ray absorption is directly affected by the column density.

3.3 Contribution of Unresolved Compact Sources

For the observed diffuse X-ray spectra, several intrinsically faint compact sources below the point source detection threshold could contribute a non-thermal component. The unresolved sources include high-mass X-ray binaries (HMXBs), low-mass X-ray binaries (LMXBs), cataclysmic variables (CVs), coronally active binaries (ABs), and young faint objects, including protostars and young stars. For unresolved young supernova remnants, they are expected to have a thermal X-ray spectrum (Long et al., 2010) and thus are incorporated within the hot gas component of our analysis.

The contribution from unresolved HMXBs is scaled with SFR (Grimm et al., 2003; Mineo et al., 2012b). Thus, we estimated the total luminosities of these sources following the method of Smith et al. (2018):

[TABLE]

where a power-law X-ray spectrum is assumed and $L_{\rm upper}$ is the luminosity of HMXBs in units of 1038 erg s*-1*. To obtain the upper limit of the unresolved luminosities, we set $L_{\rm upper}$ equal to 10 $\times$ 1038 erg s*-1*, with assuming a photon index of $\Gamma$ = 1.8, which is typical for point sources in nearby galaxies (Kong et al., 2002; Swartz et al., 2004).

The emission from unresolved LMXBs is expected to scale with the stellar mass (Gilfanov, 2004; Boroson et al., 2011). We calculated the X-ray luminosity from unresolved LMXBs using the prescription of Gilfanov (2004):

[TABLE]

For young faint objects, Bogdán & Gilfanov (2011) found that the hard X-ray luminosity in the 2$-$10 keV band of these objects shows a tight correlation with SFR:

[TABLE]

Following Kyritsis et al. (2025), we adopted a conversion factor of 0.64 to estimate the emission in the 0.5$-$2 keV band from the hard X-ray luminosities.

Revnivtsev et al. (2008) found that the total X-ray luminosity of ABs and CVs follows a constant ratio of log($L_{\rm X}/L_{\rm K}$) $\thicksim$ $-$5.8 relative to the $K$-band emission of galaxies, indicating a minor contribution to the global X-ray emission. Boroson et al. (2011) also reported that, on average, the X-ray luminosity of LMXBs is approximately ten times greater than that of ABs and CVs. Therefore, we conclude that the contribution of ABs and CVs to the observed diffuse X-ray emission in the sample galaxies is negligible.

In Figure 5, we plot the SFR against the luminosities of these unresolved sources, individually and in total, normalized by the intrinsic thermal X-ray luminosity $L_{\rm 0.5-2\,keV}^{\rm gas}$. We find that the normalized luminosities of each type of source show a decreasing trend with SFR. Compared to the diffuse luminosity in the 0.5$-$2 keV band, the total contribution of unresolved sources exceeds 10% in only 3 out of 78 objects, with the highest reaching 19%. These small contributions have little impact on our results and thus can be safely ignored. In conclusion, the luminosity derived from the point source-excluded X-ray spectra is a reasonable estimate of the hot gas emission.

4 Summary

In this paper, we study the properties of hot ionized interstellar gas in 78 nearby (U)LIRGs selected from the C-GOALS program. Nearly all galaxies in the sample (64/78) are undergoing mergers at various stages of interaction. For the extreme star-forming environments, surrounded by a substantial amount of gaseous material, we use a dust extinction method to estimate the intrinsic $N_{\rm H}$ for these systems. After correcting for the intrinsic absorption, the diffuse hot gas luminosities of most objects with high SFRs ($\textgreater$ 50 ${M_{\rm\odot}}\,\,{\rm yr^{-1}}$) show a significant excess over the predictions of the standard linear L_{\rm X}$$-SFR relation. The Bayesian method gives a super-linear relation between $L_{\rm 0.5-2\,keV}^{\rm gas}$ and SFR for the high-SFR objects with a slope of 1.34. However, the scatter of this relation is relatively large ($\thicksim$ 0.38 dex) compared to that observed in normal star-forming galaxies, possibly due to the strong influence of mergers. The heating from AGN appears to have little effect on the global hot gas luminosities throughout all five merger stages. Thus, this super-linear relation suggests a scenario in which the merger of galaxies delivers substantial gas, triggering widespread star formation in both the nuclear region and the galactic disk, ultimately enhancing the global hot gas emission and leading to the excess of X-ray luminosity.

The ratio of $L_{\rm 0.5-2\,keV}^{\rm appar}$ to $L_{\rm 0.5-2\,keV}^{\rm gas}$ shows statistically significant negative correlations with intrinsic $N_{\rm H}$ and SFR. However, in contrast to the luminosity ratio, the SFR shows a moderate positive correlation with the $N_{\rm H}$ ($r_{\rm s}$ = 0.57). Thus, compared to the $L_{\rm 0.5-2\,keV}^{\rm appar}$/L_{\rm 0.5-2\,keV}^{\rm gas}$$-$$N_{\rm H} relation, the correlation between $L_{\rm 0.5-2\,keV}^{\rm appar}$/$L_{\rm 0.5-2\,keV}^{\rm gas}$ and SFR may be driven by the underlying SFR-$$N_{\rm H} relation, since the observed X-ray luminosity depends strongly on the absorbing column density.

We thank the anonymous referee for providing helpful comments that improved our work. We acknowledge support from the National Key R$\&$D Program of China (grant No. 2023YFA1607904) and the National Natural Science Foundation of China (NSFC) grants 12033004, 12221003, and 12333002 and the science research grant from CMS-CSST-2025-A10 and CMS-CSST-2025-A07. This paper employs a list of Chandra datasets, obtained by the Chandra X-ray Observatory, contained in the Chandra Data Collection (CDC) 439https://doi.org/10.25574/cdc.439 (catalog doi:10.25574/cdc.439). This research has also made use of the NASA/IPAC Extragalactic Database (NED), which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration. The Chandra data archive is maintained by the Chandra X-ray Center at the Smithsonian Astrophysical Observatory. CARTA is the Cube Analysis and Rendering Tool for Astronomy, a new image visualization and analysis tool designed for the ALMA, the VLA, and the SKA pathfinders. This work makes use of data from GOALS team. GOALS is combining imaging and spectroscopic data from NASA’s Spitzer, Hubble, Chandra and GALEX space-borne observatories in a comprehensive study of over 200 of the most luminous infrared-selected galaxies in the local Universe.